Finite Group Databasebeta

← #7674859

Subgroups — #7674859

Order 512.

7632 conjugacy classes of subgroups.

The subgroup lattice has 1819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic, complemented
2C2×#3501C211yesmaximal, characteristic, complemented
3#59111C212yesmaximal, complemented
4#59094C212yesmaximal, complemented
5#59076C212yesmaximal, complemented
6#59075C212yesmaximal, complemented
7#59024C212yesmaximal, complemented
8#59014C212yesmaximal, complemented
9#59005C212yesmaximal, complemented
10#58996C212yesmaximal, complemented
11#43912C214yesmaximal, complemented
12#43908C214yesmaximal, complemented
13#43028C214yesmaximal, complemented
14#43024C214yesmaximal, complemented
15#39166C212yesmaximal, complemented
16#39165C214yesmaximal, complemented
17#39165C212yesmaximal, complemented
18#39160C214yesmaximal, complemented
19#36518C212yesmaximal, complemented
20#36434C212yesmaximal, complemented
21#35359C212yesmaximal, complemented
22#35358C212yesmaximal, complemented
23#35019C211yesmaximal, characteristic, complemented
24#34993C212yesmaximal, complemented
25C2×#2417C211yesmaximal, characteristic, complemented
26C2×#2416C211yesmaximal, characteristic, complemented
27#34205C212yesmaximal, complemented
28C2×#2360C211yesmaximal, characteristic, complemented
29C4×#534C211yesmaximal, characteristic, complemented
30#3505—216no—
31#3501—216no—
32C2×#554C2214yescomplemented
33C2×#554C2212yescomplemented
34C2×#554C2212yescomplemented
35C2×#554C2214yescomplemented
36C2×#553C2212yescomplemented
37C2×#553C2214yescomplemented
38C2×#552C2212yes—
39C2×#551C2214yes—
40C2×D4×Q8C2212yescomplemented
41C2×D4×Q8C2212yescomplemented
42C2×#548C2212yescomplemented
43C2×#548C2212yescomplemented
44C2×#546C2212yes—
45C2×#544C2212yescomplemented
46C2×#543C2212yes—
47C2×#543C2212yescomplemented
48C2×#539C2212yescomplemented
49C2×#538C2212yescomplemented
50C2×#534C2211yescharacteristic
51C2×#534C2212yes—
52C2×#533C2212yescomplemented
53C2×#529C2212yescomplemented
54C2×#525C2212yescomplemented
55C22×C22⋊Q8C2211yescharacteristic
56C22×C22⋊Q8C2211yescharacteristic
57C22×C22⋊Q8C2212yescomplemented
58C22×C22⋊Q8C2211yescharacteristic, complemented
59C22×#121C2212yes—
60C22×#121C2211yescharacteristic
61C22×#121C2211yescharacteristic, complemented
62C2×#518C2212yes—
63C2×#518C2212yes—
64C22×C4×Q8C2211yescharacteristic, complemented
65C22×C4×D4C2211yescharacteristic
66C22×C4×D4C2211yescharacteristic
67C23×C4⋊C4C2211yescharacteristic
68#2850C2214yescomplemented
69#2850C2212yescomplemented
70#2850C2214yescomplemented
71#2850C2212yescomplemented
72#2731C2214yescomplemented
73#2730C2214yescomplemented
74#2729C2214yescomplemented
75#2728C2214yescomplemented
76#2725C2214yescomplemented
77#2725C2214yescomplemented
78#2725C2214yescomplemented
79#2723C2214yescomplemented
80#2719C2214yescomplemented
81#2716C2214yescomplemented
82#2711C2214yescomplemented
83#2707C2214yescomplemented
84#2707C2214yescomplemented
85#2707C2214yescomplemented
86#2702C2214yescomplemented
87#2702C2214yescomplemented
88#2702C2214yescomplemented
89#2696C2214yescomplemented
90#2690C2214yescomplemented
91#2681C2214yescomplemented
92#2681C2214yescomplemented
93#2681C2214yescomplemented
94#2676C2214yescomplemented
95#2674C2214yescomplemented
96#2639C2214yescomplemented
97#2639C2214yescomplemented
98#2639C2212yescomplemented
99#2639C2212yescomplemented
100#2591C2214yescomplemented
101#2564C2214yescomplemented
102#2564C2214yescomplemented
103#2561C2214yescomplemented
104#2560C2214yescomplemented
105#2558C2214yescomplemented
106#2550C2212yescomplemented
107#2545C2214yescomplemented
108#2545C2212yescomplemented
109#2543C2214yescomplemented
110#2543C2214yescomplemented
111#2540C2212yescomplemented
112#2536C2214yescomplemented
113#2536C2212yescomplemented
114#2519C2214yescomplemented
115#2504C2212yescomplemented
116#2503C2212yescomplemented
117#2491C2212yescomplemented
118#2489C2212yescomplemented
119#2488C2214yes—
120#2488C2214yes—
121#2488C2214yescomplemented
122#2488C2214yescomplemented
123#2481C2214yescomplemented
124#2477C2214yescomplemented
125#2475C2214yescomplemented
126#2472C2214yes—
127#2472C2214yes—
128#2472C2214yescomplemented
129#2472C2214yescomplemented
130#2469C2214yescomplemented
131#2463C2214yescomplemented
132#2461C2214yescomplemented
133#2460C2214yescomplemented
134#2458C2214yescomplemented
135#2453C2214yescomplemented
136#2453C2212yescomplemented
137#2452C2214yescomplemented
138#2452C2212yescomplemented
139#2450C2214yescomplemented
140#2450C2214yescomplemented
141#2449C2214yescomplemented
142#2449C2214yescomplemented
143#2448C2212yescomplemented
144#2446C2212yescomplemented
145#2443C2214yescomplemented
146#2442C2214yescomplemented
147#2442C2212yescomplemented
148#2439C2214yescomplemented
149#2439C2212yescomplemented
150#2438C2214yescomplemented
151#2438C2214yescomplemented
152#2437C2214yescomplemented
153#2437C2214yescomplemented
154#2436C2212yescomplemented
155#2436C2212yescomplemented
156#2435C2212yescomplemented
157#2432C2212yescomplemented
158#2429C2214yescomplemented
159#2429C2212yescomplemented
160#2427C2214yescomplemented
161#2427C2212yescomplemented
162#2426C2214yescomplemented
163#2426C2212yescomplemented
164#2426C2212yescomplemented
165#2426C2214yescomplemented
166#2425C2214yescomplemented
167#2425C2214yescomplemented
168#2424C2214yescomplemented
169#2424C2214yescomplemented
170#2421C2212yescomplemented
171#2421C2212yescomplemented
172#2417C2214yes—
173#2417C2212yes—
174#2417C2212yes—
175#2417C2214yescomplemented
176#2417C2214yescomplemented
177#2417C2212yescomplemented
178#2417C2214yescomplemented
179#2417C2212yescomplemented
180#2416C2214yes—
181#2416C2212yes—
182#2416C2212yes—
183#2416C2214yescomplemented
184#2416C2214yescomplemented
185#2416C2212yescomplemented
186#2416C2214yescomplemented
187#2416C2212yescomplemented
188#2416C2214yescomplemented
189#2416C2212yescomplemented
190#2415C2214yescomplemented
191#2415C2212yescomplemented
192#2413C2214yes—
193#2412C2214yes—
194#2411C2214yes—
195#2410C2214yes—
196#2409C2212yescomplemented
197#2407C2212yescomplemented
198C2×#398C2212yescomplemented
199C2×#396C2212yescomplemented
200C2×#396C2212yescomplemented
201C2×#394C2212yescomplemented
202#2367C2212yescomplemented
203#2364C2214yescomplemented
204#2364C2214yescomplemented
205#2362C2212yescomplemented
206#2361C2214yescomplemented
207#2361C2212yescomplemented
208#2361C2214yescomplemented
209#2360C2214yescomplemented
210#2360C2214yescomplemented
211#2360C2212yescomplemented
212#2360C2212yescomplemented
213#2360C2212yescomplemented
214#2360C2212yescomplemented
215#2352C2212yescomplemented
216#2351C2212yescomplemented
217#2344C2214yescomplemented
218#2342C2214yescomplemented
219#2342C2214yescomplemented
220#2341C2212yescomplemented
221Q8×C22⋊C4C2212yescomplemented
222D4×C22⋊C4C2214yescomplemented
223#2325C2212yescomplemented
224#2325C2212yescomplemented
225#2325C2214yescomplemented
226#2325C2214yescomplemented
227#2322C2212yes—
228#2322C2212yescomplemented
229#2321C2212yes—
230#2321C2212yescomplemented
231#2315C2211yescharacteristic
232#2308C2212yes—
233#2308C2211yescharacteristic
234#2308C2211yescharacteristic
235#2308C2212yes—
236C4×#123C2212yes—
237C4×#123C2212yescomplemented
238C4×#121C2212yescomplemented
239C4×#121C2212yescomplemented
240C4×#121C2214yescomplemented
241C4×#121C2214yescomplemented
242C4×#120C2212yes—
243C4×#120C2212yescomplemented
244C2×#391C2211yescharacteristic, complemented
245C2×#391C2211yescharacteristic, complemented
246C2×#390C2211yescharacteristic, complemented
247C2×#389C2212yescomplemented
248C2×#389C2211yescharacteristic, complemented
249C2×#389C2211yescharacteristic, complemented
250C2×#389C2211yescharacteristic, complemented
251C2×#387C2212yescomplemented
252C2×#386C2212yes—
253C2×#386C2212yes—
254C2×#385C2212yes—
255C2×#380C2212yes—
256C2×#380C2211yescharacteristic, complemented
257C2×#380C2211yescharacteristic, complemented
258C2×C4×C4⋊C4C2211yescharacteristic, complemented
259C2×C4×C22⋊C4C2211yescharacteristic
260C2×C4×C22⋊C4C2212yes—
261C22×#41C2312yes—
262C23×Q8C2312yes—
263C23×Q8C2311yescharacteristic
264C23×Q8C2311yescharacteristic
265C23×D4C2312yes—
266C23×D4C2311yescharacteristic
267C23×D4C2311yescharacteristic
268C23×D4C2311yescharacteristic
269C23×D4C2312yes—
270C24×C4C2311yescharacteristic
271C24×C4C2311yescharacteristic
272C24×C4C2312yes—
273C24×C4C2311yescharacteristic
274#554—216no—
275#554—232no—
276#554—216no—
277#554—232no—
278#553—216no—
279#553—232no—
280#552—216no—
281#551—232no—
282D4×Q8—216no—
283D4×Q8—216no—
284#548—216no—
285#548—48no—
286#546—216no—
287#544—216no—
288#543—216no—
289#543—216no—
290#539—216no—
291#538—216no—
292#534—28no—
293#534—216no—
294#533—216no—
295C2×C4⋊Q8C2314yes—
296C2×C4⋊Q8C2312yes—
297C2×C4⋊Q8C2312yes—
298C2×C4⋊Q8C2314yes—
299#529—216no—
300C2×#126C2314yes—
301C2×#126C2314yes—
302C2×#126C2314yes—
303C2×#125C2312yes—
304C2×#125C2314yes—
305C2×#125C2314yes—
306C2×#125C2314yes—
307C2×#125C2314yes—
308C2×#124C2312yes—
309C2×#124C2314yes—
310C2×#124C2312yes—
311C2×#124C2314yes—
312C2×#124C2312yes—
313C2×#124C2314yes—
314#525—216no—
315C2×#123C2312yes—
316C2×#123C2312yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×C22⋊Q8—28no—
323C2×C22⋊Q8—216no—
324C2×C22⋊Q8—44no—
325C2×C22⋊Q8D4116yescomplemented
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×#121—216no—
355C2×#121—28no—
356C2×#121—44no—
357C2×#121C2314yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2314yes—
363C2×#121C2314yes—
364C2×#121C2314yes—
365C2×#121C2312yes—
366C2×#121C2314yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#121C2312yes—
371C2×#121C2314yes—
372C2×#121C2312yes—
373C2×#121C2314yes—
374C2×#121C2314yes—
375C2×#121C2314yes—
376C2×#120C2312yes—
377C2×#120C2312yes—
378C2×#120C2314yes—
379C2×#120C2314yes—
380#518—216no—
381#518—216no—
382C2×C4×Q8—44no—
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2314yes—
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2314yes—
390C2×C4×D4—28no—
391C2×C4×D4—28no—
392C2×C4×D4C2314yes—
393C2×C4×D4C2314yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2314yes—
399C2×C4×D4C2314yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2314yes—
402C2×C4×D4C2314yes—
403C2×C4×D4C2314yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2314yes—
410C2×C4×D4C2314yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2314yes—
414C2×#117C2314yes—
415C2×#117C2314yes—
416C2×#117C2312yes—
417C2×#117C2314yes—
418C22×C4⋊C4—44no—
419C22×C4⋊C4C2311yescharacteristic
420C22×C4⋊C4C2311yescharacteristic
421C22×C4⋊C4C2312yes—
422C22×C4⋊C4C2312yes—
423C22×C4⋊C4C2312yes—
424C22×C4⋊C4C2311yescharacteristic
425C22×C4⋊C4C2311yescharacteristic
426C22×C4⋊C4C2311yescharacteristic
427C22×C4⋊C4C2311yescharacteristic
428C22×C4⋊C4C2311yescharacteristic
429C22×C4⋊C4C2314yes—
430C22×C4⋊C4C2312yes—
431C22×C4⋊C4C2312yes—
432C22×C4⋊C4C2311yescharacteristic
433C22×C4⋊C4C2311yescharacteristic
434C22×C4⋊C4C2312yes—
435C22×C4⋊C4C2312yes—
436C22×C4⋊C4C2311yescharacteristic
437C22×C4⋊C4C2312yes—
438C22×C4⋊C4C2312yes—
439C22×C4⋊C4C2312yes—
440C22×C4⋊C4C2311yescharacteristic
441C22×C4⋊C4C2312yes—
442C22×C22⋊C4C2312yes—
443C22×C22⋊C4C2311yescharacteristic
444C22×C22⋊C4C2311yescharacteristic
445C22×C22⋊C4C2312yes—
446C22×C22⋊C4C2311yescharacteristic
447C22×C22⋊C4C2311yescharacteristic
448C22×C22⋊C4C2311yescharacteristic
449C22×C22⋊C4C2311yescharacteristic
450C22×C22⋊C4C2314yes—
451C22×C22⋊C4C2314yes—
452C22×C22⋊C4C2312yes—
453C22×C22⋊C4C2312yes—
454C22×C22⋊C4C2312yes—
455C22×C22⋊C4C2312yes—
456C22×C22⋊C4C2312yes—
457C22×C22⋊C4C2312yes—
458C22×C22⋊C4C2312yes—
459C22×C42C2311yescharacteristic
460C22×C42C2311yescharacteristic
461C22×C42C2312yes—
462C22×C42C2311yescharacteristic
463C22×C42C2311yescharacteristic
464C22×C42C2312yes—
465#400C2314yes—
466#400C2314yes—
467#400C2314yes—
468#400C2314yes—
469#400C2314yes—
470#400C2314yes—
471#400C2314yes—
472#400C2314yes—
473#399C2314yes—
474#399C2314yes—
475#398C2314yes—
476#398C2314yes—
477#398C2314yes—
478#398C2314yes—
479#398C2314yes—
480#398C2314yes—
481#398C2314yes—
482#398C2314yes—
483#398C2314yes—
484#398C2314yes—
485#397C2314yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#397C2314yes—
490#397C2314yes—
491#397C2314yes—
492#397C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2314yes—
504#396C2314yes—
505#396C2314yes—
506#396C2314yes—
507#396C2314yes—
508#396C2314yes—
509#395C2314yes—
510#395C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#393C2314yes—
528#393C2314yes—
529#393C2314yes—
530#393C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#392C2314yes—
536#392C2314yes—
537#391C2314yes—
538#391C2312yes—
539#391C2314yes—
540#391C2312yes—
541#391C2312yes—
542#391C2314yes—
543#391C2312yes—
544#391C2312yes—
545#391C2314yes—
546#391C2312yes—
547#391C2314yes—
548#391C2314yes—
549#390C2314yes—
550#390C2312yes—
551#390C2312yes—
552#390C2314yes—
553#390C2312yes—
554#390C2314yes—
555#390C2312yes—
556#390C2314yes—
557#390C2312yes—
558#390C2314yes—
559#390C2314yes—
560#390C2312yes—
561#390C2314yes—
562#389C2312yes—
563#389C2312yes—
564#389C2314yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2314yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2314yes—
580#389C2312yes—
581#389C2314yes—
582#389C2312yes—
583#388C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2312yes—
634#386C2312yes—
635#386C2312yes—
636#386C2312yes—
637#386C2312yes—
638#386C2312yes—
639#386C2312yes—
640#386C2314yes—
641#386C2312yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2312yes—
651#386C2312yes—
652#386C2312yes—
653#386C2312yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2312yes—
672#385C2312yes—
673#385C2312yes—
674#385C2312yes—
675#385C2312yes—
676#385C2312yes—
677#385C2312yes—
678#385C2312yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#382C2312yes—
688#382C2314yes—
689#382C2312yes—
690#382C2314yes—
691#381C2314yes—
692#381C2314yes—
693#381C2312yes—
694#381C2312yes—
695#380C2312yes—
696#380C2314yes—
697#380C2314yes—
698#380C2312yes—
699#380C2314yes—
700#380C2312yes—
701#380C2314yes—
702#380C2312yes—
703#380C2314yes—
704#380C2314yes—
705#380C2312yes—
706#380C2312yes—
707#380C2314yes—
708#380C2314yes—
709#380C2314yes—
710#380C2314yes—
711#379C2314yes—
712#379C2314yes—
713#379C2312yes—
714#379C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2314yes—
731C4×C22⋊C4C2314yes—
732C4×C22⋊C4C2314yes—
733C4×C22⋊C4C2314yes—
734C4×C22⋊C4C2312yes—
735C4×C22⋊C4C2312yes—
736C4×C22⋊C4C2312yes—
737C4×C22⋊C4C2312yes—
738C2×#95C2312yes—
739C2×#95C2312yes—
740C2×#95C2311yescharacteristic
741C2×#95C2312yes—
742C2×#95C2311yescharacteristic
743C2×#95C2312yes—
744C2×#95C2312yes—
745C2×#95C2312yes—
746C2×#95C2312yes—
747C2×#95C2312yes—
748C2×#95C2312yes—
749C2×#95C2312yes—
750C25C2412yes—
751C25C2411yescharacteristic
752C25C2411yescharacteristic
753C25C2411yescharacteristic
754C2×#41—28no—
755C2×#41—44no—
756C2×#41—44no—
757C22×Q8—28no—
758C22×Q8—24no—
759C22×Q8—42no—
760C22×Q8—42no—
761C22×Q8—42no—
762C22×Q8—44no—
763C22×Q8—42no—
764C22×Q8—44no—
765C22×Q8C2×D418yescomplemented
766C22×Q8C2412yes—
767C22×Q8C2412yes—
768C22×Q8C2414yes—
769C22×Q8C2412yes—
770C22×Q8C2414yes—
771C22×Q8C2412yes—
772C22×D4—24no—
773C22×D4—24no—
774C22×D4—24no—
775C22×D4—28no—
776C22×D4—28no—
777C22×D4—24no—
778C22×D4—24no—
779C22×D4—28no—
780C22×D4—28no—
781C22×D4—24no—
782C22×D4—42no—
783C22×D4—44no—
784C22×D4—42no—
785C22×D4—82no—
786C22×D4#4118yescomplemented
787C22×D4C2412yes—
788C22×D4C2414yes—
789C22×D4C2414yes—
790C22×D4C2412yes—
791C22×D4C2412yes—
792C22×D4C2414yes—
793C22×D4C2412yes—
794C22×D4C2412yes—
795C22×D4C2412yes—
796C22×D4C2414yes—
797C22×D4C2412yes—
798C22×D4C2414yes—
799C22×D4C2412yes—
800C22×D4C2414yes—
801C23×C4—28no—
802C23×C4—24no—
803C23×C4—24no—
804C23×C4—42no—
805C23×C4—42no—
806C23×C4—44no—
807C23×C4—42no—
808C23×C4—42no—
809C23×C4—42no—
810C23×C4—42no—
811C23×C4—82no—
812C23×C4C2×D418yes—
813C23×C4C2412yes—
814C23×C4C2412yes—
815C23×C4C2411yescharacteristic
816C23×C4C2412yes—
817C23×C4C2412yes—
818C23×C4C2412yes—
819C23×C4C2412yes—
820C23×C4C2411yescharacteristic
821C23×C4C2411yescharacteristic
822C23×C4C2411yescharacteristic
823C23×C4C2411yescharacteristic
824C23×C4C2411yescharacteristic
825C23×C4C2412yes—
826C23×C4C2411yescharacteristic
827C23×C4C2412yes—
828C23×C4C2411yescharacteristic
829C23×C4C2412yes—
830C23×C4C2411yescharacteristic
831C23×C4C2411yescharacteristic
832C23×C4C2414yes—
833C23×C4C2412yes—
834C23×C4C2414yes—
835C23×C4C2414yes—
836C23×C4C2414yes—
837C23×C4C2411yescharacteristic
838C23×C4C2411yescharacteristic
839C23×C4C2411yescharacteristic
840C23×C4C2412yes—
841C23×C4C2412yes—
842C23×C4C2412yes—
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C4⋊Q8—28no—
849C4⋊Q8—216no—
850C4⋊Q8—28no—
851C4⋊Q8—216no—
852#126—216no—
853#126—216no—
854#126—216no—
855#125—28no—
856#125—216no—
857#125—216no—
858#125—216no—
859#125—216no—
860#124—28no—
861#124—216no—
862#124—48no—
863#124—44no—
864#124—44no—
865#124—84no—
866#123—28no—
867#123—28no—
868#123—216no—
869#123—216no—
870#123—216no—
871#123—216no—
872#123—216no—
873C22⋊Q8—28no—
874C22⋊Q8—28no—
875C22⋊Q8—216no—
876C22⋊Q8—216no—
877C22⋊Q8—28no—
878C22⋊Q8—28no—
879C22⋊Q8—28no—
880C22⋊Q8—28no—
881C22⋊Q8—216no—
882C22⋊Q8—216no—
883C22⋊Q8—28no—
884C22⋊Q8—216no—
885C22⋊Q8—216no—
886C22⋊Q8—216no—
887C22⋊Q8—216no—
888C22⋊Q8—28no—
889C22⋊Q8—216no—
890C22⋊Q8—216no—
891C22⋊Q8—216no—
892C22⋊Q8—216no—
893C22⋊Q8—48no—
894C22⋊Q8—48no—
895C22⋊Q8—44no—
896C22⋊Q8—84no—
897C22⋊Q8C2×D4116yes—
898C22⋊Q8C2×D4116yes—
899C22⋊Q8C2×D4116yescomplemented
900C22⋊Q8C2×D4116yescomplemented
901#121—216no—
902#121—216no—
903#121—216no—
904#121—216no—
905#121—28no—
906#121—28no—
907#121—28no—
908#121—28no—
909#121—28no—
910#121—28no—
911#121—216no—
912#121—216no—
913#121—28no—
914#121—216no—
915#121—28no—
916#121—48no—
917#121—48no—
918#121—44no—
919#121—84no—
920#120—28no—
921#120—28no—
922#120—216no—
923#120—216no—
924C4×Q8—28no—
925C4×Q8—28no—
926C4×Q8—28no—
927C4×Q8—216no—
928C4×Q8—28no—
929C4×Q8—48no—
930C4×Q8—44no—
931C4×D4—28no—
932C4×D4—28no—
933C4×D4—28no—
934C4×D4—28no—
935C4×D4—28no—
936C4×D4—28no—
937C4×D4—28no—
938C4×D4—28no—
939C4×D4—216no—
940C4×D4—216no—
941C4×D4—216no—
942C4×D4—216no—
943C4×D4—216no—
944C4×D4—28no—
945C4×D4—216no—
946C4×D4—216no—
947C4×D4—216no—
948C4×D4—216no—
949C4×D4—48no—
950C4×D4—44no—
951C4×D4—44no—
952C4×D4—84no—
953#117—28no—
954#117—216no—
955#117—216no—
956#117—216no—
957C2×C4⋊C4—24no—
958C2×C4⋊C4—24no—
959C2×C4⋊C4—24no—
960C2×C4⋊C4—28no—
961C2×C4⋊C4—24no—
962C2×C4⋊C4—28no—
963C2×C4⋊C4—216no—
964C2×C4⋊C4—28no—
965C2×C4⋊C4—24no—
966C2×C4⋊C4—24no—
967C2×C4⋊C4—24no—
968C2×C4⋊C4—42no—
969C2×C4⋊C4—44no—
970C2×C4⋊C4—42no—
971C2×C4⋊C4—44no—
972C2×C4⋊C4—42no—
973C2×C4⋊C4—44no—
974C2×C4⋊C4—44no—
975C2×C4⋊C4—44no—
976C2×C4⋊C4—82no—
977C2×C4⋊C4—82no—
978C2×C4⋊C4C2×D418yescomplemented
979C2×C4⋊C4C2×D4116yescomplemented
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2411yescharacteristic
1032C2×C22⋊C4—24no—
1033C2×C22⋊C4—24no—
1034C2×C22⋊C4—28no—
1035C2×C22⋊C4—28no—
1036C2×C22⋊C4—24no—
1037C2×C22⋊C4—24no—
1038C2×C22⋊C4—24no—
1039C2×C22⋊C4—24no—
1040C2×C22⋊C4—28no—
1041C2×C22⋊C4—28no—
1042C2×C22⋊C4—216no—
1043C2×C22⋊C4—216no—
1044C2×C22⋊C4—44no—
1045C2×C22⋊C4—44no—
1046C2×C22⋊C4—82no—
1047C2×C22⋊C4—82no—
1048C2×C22⋊C4C2×D4116yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C42—24no—
1108C2×C42—24no—
1109C2×C42—42no—
1110C2×C42—44no—
1111C2×C42—42no—
1112C2×C42—82no—
1113C2×C42C2414yes—
1114C2×C42C2414yes—
1115C2×C42C2412yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2412yes—
1122C2×C42C2414yes—
1123C2×C42C2412yes—
1124C2×C42C2414yes—
1125C2×C42C2414yes—
1126C2×C42C2412yes—
1127C2×C42C2414yes—
1128C2×C42C2412yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173C24—22no—
1174C24—22no—
1175C24—22no—
1176C24—24no—
1177C24—22no—
1178C24—24no—
1179C24—22no—
1180C24—24no—
1181C24—41no—
1182C24—41no—
1183C24—41no—
1184C24—41no—
1185C24—41no—
1186C24—41no—
1187C24—41no—
1188C24—41no—
1189C24—41no—
1190C24—41no—
1191C24—41no—
1192C24—41no—
1193C24—42no—
1194C24—42no—
1195C24—42no—
1196C24—42no—
1197C24C22×D414yes—
1198C24C2×#4114yes—
1199C24C2×#4114yes—
1200C242−1+414yes—
1201C24C2512yes—
1202C24C2514yes—
1203C24C2512yes—
1204C24C2511yescharacteristic
1205C24C2511yescharacteristic
1206C24C2511yescharacteristic
1207#41—816no—
1208C2×Q8—24no—
1209C2×Q8—28no—
1210C2×Q8—24no—
1211C2×Q8—28no—
1212C2×Q8—24no—
1213C2×Q8—24no—
1214C2×Q8—24no—
1215C2×Q8—24no—
1216C2×Q8—42no—
1217C2×Q8—42no—
1218C2×Q8—42no—
1219C2×Q8—44no—
1220C2×Q8—44no—
1221C2×Q8—42no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×Q8—416no—
1225C2×Q8—88no—
1226C2×Q8—816no—
1227C2×Q8C22×D418yes—
1228C2×Q8C22×D418yes—
1229C2×D4—232no—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—28no—
1236C2×D4—24no—
1237C2×D4—28no—
1238C2×D4—24no—
1239C2×D4—28no—
1240C2×D4—28no—
1241C2×D4—28no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—28no—
1245C2×D4—24no—
1246C2×D4—28no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—28no—
1250C2×D4—24no—
1251C2×D4—28no—
1252C2×D4—28no—
1253C2×D4—24no—
1254C2×D4—28no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—44no—
1258C2×D4—42no—
1259C2×D4—42no—
1260C2×D4—42no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4—42no—
1264C2×D4—44no—
1265C2×D4—44no—
1266C2×D4—42no—
1267C2×D4—44no—
1268C2×D4—42no—
1269C2×D4—44no—
1270C2×D4—416no—
1271C2×D4—432no—
1272C2×D4—88no—
1273C2×D4—816no—
1274C2×D4C2×#4118yes—
1275C2×D4C2×#4118yes—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—24no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—24no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—24no—
1298C22×C4—22no—
1299C22×C4—24no—
1300C22×C4—22no—
1301C22×C4—24no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—24no—
1305C22×C4—24no—
1306C22×C4—24no—
1307C22×C4—24no—
1308C22×C4—24no—
1309C22×C4—24no—
1310C22×C4—24no—
1311C22×C4—24no—
1312C22×C4—24no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—28no—
1316C22×C4—28no—
1317C22×C4—28no—
1318C22×C4—28no—
1319C22×C4—24no—
1320C22×C4—24no—
1321C22×C4—416no—
1322C22×C4—41no—
1323C22×C4—42no—
1324C22×C4—41no—
1325C22×C4—41no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—41no—
1329C22×C4—41no—
1330C22×C4—41no—
1331C22×C4—42no—
1332C22×C4—41no—
1333C22×C4—41no—
1334C22×C4—41no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—41no—
1338C22×C4—42no—
1339C22×C4—41no—
1340C22×C4—41no—
1341C22×C4—41no—
1342C22×C4—42no—
1343C22×C4—41no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—42no—
1347C22×C4—42no—
1348C22×C4—42no—
1349C22×C4—42no—
1350C22×C4—41no—
1351C22×C4—41no—
1352C22×C4—41no—
1353C22×C4—42no—
1354C22×C4—44no—
1355C22×C4—44no—
1356C22×C4—44no—
1357C22×C4—44no—
1358C22×C4—42no—
1359C22×C4—42no—
1360C22×C4—42no—
1361C22×C4—42no—
1362C22×C4—41no—
1363C22×C4—41no—
1364C22×C4—44no—
1365C22×C4—44no—
1366C22×C4—41no—
1367C22×C4—42no—
1368C22×C4—41no—
1369C22×C4—41no—
1370C22×C4—44no—
1371C22×C4—42no—
1372C22×C4—44no—
1373C22×C4—88no—
1374C22×C4—88no—
1375C22×C4—816no—
1376C22×C4C22×D414yes—
1377C22×C4C22×D414yes—
1378C22×C4C22×D414yes—
1379C22×C4C22×D414yes—
1380C22×C4C22×D414yes—
1381C22×C4C22×D418yes—
1382C22×C4C22×D418yes—
1383C22×C4C22×D414yes—
1384C22×C4C2×#4114yes—
1385C22×C4C2512yes—
1386C22×C4C2512yes—
1387C22×C4C2512yes—
1388C22×C4C2512yes—
1389C22×C4C2514yes—
1390C22×C4C2512yes—
1391C22×C4C2512yes—
1392C22×C4C2512yes—
1393C22×C4C2512yes—
1394C22×C4C2512yes—
1395C22×C4C2512yes—
1396C22×C4C2512yes—
1397C22×C4C2514yes—
1398C22×C4C2514yes—
1399C22×C4C2512yes—
1400C22×C4C2514yes—
1401C22×C4C2514yes—
1402C22×C4C2511yescharacteristic
1403C22×C4C2511yescharacteristic
1404C22×C4C2511yescharacteristic
1405C22×C4C2512yes—
1406C22×C4C2512yes—
1407C22×C4C2511yescharacteristic
1408C4⋊C4—28no—
1409C4⋊C4—24no—
1410C4⋊C4—24no—
1411C4⋊C4—24no—
1412C4⋊C4—24no—
1413C4⋊C4—24no—
1414C4⋊C4—24no—
1415C4⋊C4—24no—
1416C4⋊C4—24no—
1417C4⋊C4—28no—
1418C4⋊C4—28no—
1419C4⋊C4—28no—
1420C4⋊C4—28no—
1421C4⋊C4—28no—
1422C4⋊C4—28no—
1423C4⋊C4—28no—
1424C4⋊C4—28no—
1425C4⋊C4—28no—
1426C4⋊C4—28no—
1427C4⋊C4—28no—
1428C4⋊C4—28no—
1429C4⋊C4—28no—
1430C4⋊C4—28no—
1431C4⋊C4—28no—
1432C4⋊C4—24no—
1433C4⋊C4—24no—
1434C4⋊C4—24no—
1435C4⋊C4—22no—
1436C4⋊C4—24no—
1437C4⋊C4—22no—
1438C4⋊C4—24no—
1439C4⋊C4—22no—
1440C4⋊C4—28no—
1441C4⋊C4—28no—
1442C4⋊C4—42no—
1443C4⋊C4—42no—
1444C4⋊C4—42no—
1445C4⋊C4—44no—
1446C4⋊C4—44no—
1447C4⋊C4—44no—
1448C4⋊C4—44no—
1449C4⋊C4—44no—
1450C4⋊C4—44no—
1451C4⋊C4—42no—
1452C4⋊C4—42no—
1453C4⋊C4—42no—
1454C4⋊C4—42no—
1455C4⋊C4C22×D418yes—
1456C4⋊C4C22×D4116yes—
1457C4⋊C4C22×D4116yes—
1458C4⋊C4C22×D418yes—
1459C4⋊C4H(5,𝔽2)14yes—
1460C22⋊C4—24no—
1461C22⋊C4—28no—
1462C22⋊C4—24no—
1463C22⋊C4—24no—
1464C22⋊C4—24no—
1465C22⋊C4—28no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—28no—
1469C22⋊C4—28no—
1470C22⋊C4—24no—
1471C22⋊C4—24no—
1472C22⋊C4—24no—
1473C22⋊C4—24no—
1474C22⋊C4—28no—
1475C22⋊C4—24no—
1476C22⋊C4—28no—
1477C22⋊C4—28no—
1478C22⋊C4—24no—
1479C22⋊C4—24no—
1480C22⋊C4—28no—
1481C22⋊C4—28no—
1482C22⋊C4—24no—
1483C22⋊C4—28no—
1484C22⋊C4—28no—
1485C22⋊C4—28no—
1486C22⋊C4—28no—
1487C22⋊C4—28no—
1488C22⋊C4—28no—
1489C22⋊C4—28no—
1490C22⋊C4—24no—
1491C22⋊C4—24no—
1492C22⋊C4—28no—
1493C22⋊C4—28no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—42no—
1502C22⋊C4—42no—
1503C22⋊C4—44no—
1504C22⋊C4—42no—
1505C22⋊C4—42no—
1506C22⋊C4—42no—
1507C22⋊C4—42no—
1508C22⋊C4—44no—
1509C22⋊C4—42no—
1510C22⋊C4—44no—
1511C22⋊C4—44no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—44no—
1515C22⋊C4—42no—
1516C22⋊C4C22×D4116yes—
1517C22⋊C4C22×D4116yes—
1518C42—24no—
1519C42—24no—
1520C42—24no—
1521C42—24no—
1522C42—28no—
1523C42—28no—
1524C42—28no—
1525C42—28no—
1526C42—28no—
1527C42—24no—
1528C42—24no—
1529C42—42no—
1530C42—44no—
1531C42—42no—
1532C42—44no—
1533C42—44no—
1534C23—21no—
1535C23—21no—
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—22no—
1547C23—22no—
1548C23—22no—
1549C23—22no—
1550C23—22no—
1551C23—22no—
1552C23—28no—
1553C23—22no—
1554C23—24no—
1555C23—24no—
1556C23—22no—
1557C23—22no—
1558C23—24no—
1559C23—22no—
1560C23—24no—
1561C23—24no—
1562C23—22no—
1563C23—22no—
1564C23—24no—
1565C23—24no—
1566C23—22no—
1567C23—44no—
1568C23—44no—
1569C23—44no—
1570C23—44no—
1571C23—44no—
1572C23—44no—
1573C23—44no—
1574C23—44no—
1575C23—44no—
1576C23—44no—
1577C23—44no—
1578C23—48no—
1579C23—82no—
1580C23—82no—
1581C23—82no—
1582C23—82no—
1583C23—82no—
1584C23—82no—
1585C23—82no—
1586C23—82no—
1587C23—84no—
1588C23—84no—
1589C23—84no—
1590C23—84no—
1591C23—84no—
1592C23—84no—
1593C23#548116yescomplemented
1594C23C23×D412yes—
1595C23C23×D412yes—
1596C23C23×D412yes—
1597C23C22×#4114yes—
1598C23C22×#4112yes—
1599C23C22×#4112yes—
1600C23C22×#4112yes—
1601C23C2×2−1+412yes—
1602C23C2×2−1+412yes—
1603C23C2×2−1+412yes—
1604C23C2611yescharacteristic
1605Q8—216no—
1606Q8—48no—
1607Q8—48no—
1608Q8—88no—
1609Q8—84no—
1610Q8—88no—
1611D4—216no—
1612D4—216no—
1613D4—416no—
1614D4—48no—
1615D4—416no—
1616D4—48no—
1617D4—416no—
1618D4—48no—
1619D4—88no—
1620D4—84no—
1621D4—88no—
1622D4—84no—
1623D4—84no—
1624D4—88no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—24no—
1636C2×C4—22no—
1637C2×C4—24no—
1638C2×C4—24no—
1639C2×C4—28no—
1640C2×C4—28no—
1641C2×C4—28no—
1642C2×C4—28no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—24no—
1649C2×C4—24no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—24no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—24no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—22no—
1668C2×C4—24no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—24no—
1673C2×C4—22no—
1674C2×C4—22no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—22no—
1678C2×C4—24no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—22no—
1682C2×C4—22no—
1683C2×C4—22no—
1684C2×C4—22no—
1685C2×C4—24no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—44no—
1689C2×C4—44no—
1690C2×C4—44no—
1691C2×C4—48no—
1692C2×C4—48no—
1693C2×C4—48no—
1694C2×C4—48no—
1695C2×C4—48no—
1696C2×C4—44no—
1697C2×C4—44no—
1698C2×C4—48no—
1699C2×C4—44no—
1700C2×C4—48no—
1701C2×C4—48no—
1702C2×C4—88no—
1703C2×C4—88no—
1704C2×C4—84no—
1705C2×C4—84no—
1706C2×C4—88no—
1707C2×C4—88no—
1708C2×C4—82no—
1709C2×C4—82no—
1710C2×C4—82no—
1711C2×C4—84no—
1712C2×C4—82no—
1713C2×C4—84no—
1714C2×C4—84no—
1715C2×C4—84no—
1716C2×C4—82no—
1717C2×C4—82no—
1718C2×C4—84no—
1719C2×C4C23×D412yes—
1720C2×C4C23×D418yes—
1721C2×C4C23×D418yes—
1722C2×C4C23×D412yes—
1723C2×C4C23×D412yes—
1724C2×C4C23×D412yes—
1725C2×C4C22×#4114yes—
1726C2×C4C2×H(5,𝔽2)14yes—
1727C2×C4C2×H(5,𝔽2)12yes—
1728C2×C4#58512yes—
1729C22—22no—
1730C22—22no—
1731C22—22no—
1732C22—22no—
1733C22—22no—
1734C22—22no—
1735C22—22no—
1736C22—22no—
1737C22—22no—
1738C22—22no—
1739C22—22no—
1740C22—22no—
1741C22—22no—
1742C22—22no—
1743C22—22no—
1744C22—22no—
1745C22—22no—
1746C22—22no—
1747C22—24no—
1748C22—24no—
1749C22—24no—
1750C22—416no—
1751C22—42no—
1752C22—42no—
1753C22—42no—
1754C22—42no—
1755C22—44no—
1756C22—42no—
1757C22—42no—
1758C22—44no—
1759C22—42no—
1760C22—44no—
1761C22—44no—
1762C22—42no—
1763C22—42no—
1764C22—44no—
1765C22—42no—
1766C22—44no—
1767C22—42no—
1768C22—44no—
1769C22—88no—
1770C22—88no—
1771C22—168no—
1772C22C2×#54814yes—
1773C22C2×#54814yes—
1774C22C2×#54814yes—
1775C22C24×D411yescharacteristic
1776C22C23×#4111yescharacteristic
1777C22C22×H(5,𝔽2)11yescharacteristic
1778C22C22×2−1+411yescharacteristic
1779C22C2×#58511yescharacteristic
1780C22H(7,𝔽2)11yescharacteristic
1781C222−1+611yescharacteristic
1782C4—24no—
1783C4—22no—
1784C4—22no—
1785C4—22no—
1786C4—28no—
1787C4—28no—
1788C4—24no—
1789C4—42no—
1790C4—42no—
1791C4—42no—
1792C4—42no—
1793C4—42no—
1794C4—42no—
1795C4—42no—
1796C4—44no—
1797C4—42no—
1798C4—44no—
1799C4—42no—
1800C4—42no—
1801C4—42no—
1802C4—42no—
1803C4—44no—
1804C4#349614yes—
1805C2—24no—
1806C2—24no—
1807C2—24no—
1808C2—44no—
1809C2—82no—
1810C2—84no—
1811C2C22×#54811yescharacteristic
1812C2C2×#349611yescharacteristic
1813C2#6285311yescharacteristic
1814C2#6289311yescharacteristic
1815C2#6290211yescharacteristic
1816C2#6298311yescharacteristic
1817C2#6299111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3505C2semidirect
2. C2×#3501C2semidirect
3. #59111C2semidirect
4. #59094C2semidirect
5. #59076C2semidirect
6. #59075C2semidirect
7. #59024C2semidirect
8. #59014C2semidirect
9. #59005C2semidirect
10. #58996C2semidirect
11. #43912C2semidirect
12. #43908C2semidirect
13. #43028C2semidirect
14. #43024C2semidirect
15. #39166C2semidirect
16. #39165C2semidirect
17. #39165C2semidirect
18. #39160C2semidirect
19. #36518C2semidirect
20. #36434C2semidirect
21. #35359C2semidirect
22. #35358C2semidirect
23. #35019C2semidirect
24. #34993C2semidirect
25. C2×#2417C2semidirect
26. C2×#2416C2semidirect
27. #34205C2semidirect
28. C2×#2360C2semidirect
29. C4×#534C2semidirect
32. C2×#554C22semidirect
33. C2×#554C22semidirect
34. C2×#554C22semidirect
35. C2×#554C22semidirect
36. C2×#553C22semidirect
37. C2×#553C22semidirect
40. C2×D4×Q8C22semidirect
41. C2×D4×Q8C22semidirect
42. C2×#548C22semidirect
43. C2×#548C22semidirect
45. C2×#544C22semidirect
47. C2×#543C22semidirect
48. C2×#539C22semidirect
49. C2×#538C22semidirect
52. C2×#533C22semidirect
53. C2×#529C22semidirect
54. C2×#525C22semidirect
57. C22×C22⋊Q8C22semidirect
58. C22×C22⋊Q8C22semidirect
61. C22×#121C22semidirect
64. C22×C4×Q8C22semidirect
68. #2850C22semidirect
69. #2850C22semidirect
70. #2850C22semidirect
71. #2850C22semidirect
72. #2731C22semidirect
73. #2730C22semidirect
74. #2729C22semidirect
75. #2728C22semidirect
76. #2725C22semidirect
77. #2725C22semidirect
78. #2725C22semidirect
79. #2723C22semidirect
80. #2719C22semidirect
81. #2716C22semidirect
82. #2711C22semidirect
83. #2707C22semidirect
84. #2707C22semidirect
85. #2707C22semidirect
86. #2702C22semidirect
87. #2702C22semidirect
88. #2702C22semidirect
89. #2696C22semidirect
90. #2690C22semidirect
91. #2681C22semidirect
92. #2681C22semidirect
93. #2681C22semidirect
94. #2676C22semidirect
95. #2674C22semidirect
96. #2639C22semidirect
97. #2639C22semidirect
98. #2639C22semidirect
99. #2639C22semidirect
100. #2591C22semidirect
101. #2564C22semidirect
102. #2564C22semidirect
103. #2561C22semidirect
104. #2560C22semidirect
105. #2558C22semidirect
106. #2550C22semidirect
107. #2545C22semidirect
108. #2545C22semidirect
109. #2543C22semidirect
110. #2543C22semidirect
111. #2540C22semidirect
112. #2536C22semidirect
113. #2536C22semidirect
114. #2519C22semidirect
115. #2504C22semidirect
116. #2503C22semidirect
117. #2491C22semidirect
118. #2489C22semidirect
121. #2488C22semidirect
122. #2488C22semidirect
123. #2481C22semidirect
124. #2477C22semidirect
125. #2475C22semidirect
128. #2472C22semidirect
129. #2472C22semidirect
130. #2469C22semidirect
131. #2463C22semidirect
132. #2461C22semidirect
133. #2460C22semidirect
134. #2458C22semidirect
135. #2453C22semidirect
136. #2453C22semidirect
137. #2452C22semidirect
138. #2452C22semidirect
139. #2450C22semidirect
140. #2450C22semidirect
141. #2449C22semidirect
142. #2449C22semidirect
143. #2448C22semidirect
144. #2446C22semidirect
145. #2443C22semidirect
146. #2442C22semidirect
147. #2442C22semidirect
148. #2439C22semidirect
149. #2439C22semidirect
150. #2438C22semidirect
151. #2438C22semidirect
152. #2437C22semidirect
153. #2437C22semidirect
154. #2436C22semidirect
155. #2436C22semidirect
156. #2435C22semidirect
157. #2432C22semidirect
158. #2429C22semidirect
159. #2429C22semidirect
160. #2427C22semidirect
161. #2427C22semidirect
162. #2426C22semidirect
163. #2426C22semidirect
164. #2426C22semidirect
165. #2426C22semidirect
166. #2425C22semidirect
167. #2425C22semidirect
168. #2424C22semidirect
169. #2424C22semidirect
170. #2421C22semidirect
171. #2421C22semidirect
175. #2417C22semidirect
176. #2417C22semidirect
177. #2417C22semidirect
178. #2417C22semidirect
179. #2417C22semidirect
183. #2416C22semidirect
184. #2416C22semidirect
185. #2416C22semidirect
186. #2416C22semidirect
187. #2416C22semidirect
188. #2416C22semidirect
189. #2416C22semidirect
190. #2415C22semidirect
191. #2415C22semidirect
196. #2409C22semidirect
197. #2407C22semidirect
198. C2×#398C22semidirect
199. C2×#396C22semidirect
200. C2×#396C22semidirect
201. C2×#394C22semidirect
202. #2367C22semidirect
203. #2364C22semidirect
204. #2364C22semidirect
205. #2362C22semidirect
206. #2361C22semidirect
207. #2361C22semidirect
208. #2361C22semidirect
209. #2360C22semidirect
210. #2360C22semidirect
211. #2360C22semidirect
212. #2360C22semidirect
213. #2360C22semidirect
214. #2360C22semidirect
215. #2352C22semidirect
216. #2351C22semidirect
217. #2344C22semidirect
218. #2342C22semidirect
219. #2342C22semidirect
220. #2341C22semidirect
221. Q8×C22⋊C4C22semidirect
222. D4×C22⋊C4C22semidirect
223. #2325C22semidirect
224. #2325C22semidirect
225. #2325C22semidirect
226. #2325C22semidirect
228. #2322C22semidirect
230. #2321C22semidirect
237. C4×#123C22semidirect
238. C4×#121C22semidirect
239. C4×#121C22semidirect
240. C4×#121C22semidirect
241. C4×#121C22semidirect
243. C4×#120C22semidirect
244. C2×#391C22semidirect
245. C2×#391C22semidirect
246. C2×#390C22semidirect
247. C2×#389C22semidirect
248. C2×#389C22semidirect
249. C2×#389C22semidirect
250. C2×#389C22semidirect
251. C2×#387C22semidirect
256. C2×#380C22semidirect
257. C2×#380C22semidirect
258. C2×C4×C4⋊C4C22semidirect
325. C2×C22⋊Q8D4semidirect
765. C22×Q8C2×D4semidirect
786. C22×D4#41semidirect
899. C22⋊Q8C2×D4semidirect
900. C22⋊Q8C2×D4semidirect
978. C2×C4⋊C4C2×D4semidirect
979. C2×C4⋊C4C2×D4semidirect
1593. C23#548semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35052
C2×#35012
#591112
#590942
#590762
#590752
#590242
#590142
#590052
#589962
#439122
#439082
#430282
#430242
#391662
#391652
#391602
#365182
#364342
#353592
#353582
#350192
#349932
C2×#24172
C2×#24162
#342052
C2×#23602
C4×#5342