Finite Group Databasebeta

← #7672872

Subgroups — #7672872

Order 512.

8582 conjugacy classes of subgroups.

The subgroup lattice has 1791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic, complemented
2C2×#3496C211yesmaximal, characteristic, complemented
3#43531C214yesmaximal, complemented
4#43530C214yesmaximal, complemented
5#43102C214yesmaximal, complemented
6#43101C214yesmaximal, complemented
7#38087C214yesmaximal, complemented
8#38086C214yesmaximal, complemented
9#38077C214yesmaximal, complemented
10#38076C214yesmaximal, complemented
11#37747C212yesmaximal, complemented
12#37746C212yesmaximal, complemented
13#37745C212yesmaximal, complemented
14#37744C212yesmaximal, complemented
15#37698C212yesmaximal, complemented
16#37697C212yesmaximal, complemented
17#37693C212yesmaximal, complemented
18#37692C212yesmaximal, complemented
19#35360C212yesmaximal, complemented
20#35347C212yesmaximal, complemented
21#35010C211yesmaximal, characteristic, complemented
22#35000C211yesmaximal, characteristic, complemented
23#34984C212yesmaximal, complemented
24C2×#2639C211yesmaximal, characteristic, complemented
25#34256C212yesmaximal, complemented
26C2×#2325C211yesmaximal, characteristic, complemented
27C2×#2325C211yesmaximal, characteristic, complemented
28C22×H(5,𝔽2)C2212yes—
29#3505—216no—
30#3496—216no—
31C2×#553C2212yescomplemented
32C2×#553C2214yescomplemented
33C2×#552C2212yescomplemented
34C2×#551C2214yescomplemented
35C2×#548C2212yescomplemented
36C2×#547C2212yescomplemented
37C2×#547C2212yescomplemented
38C2×#546C2214yescomplemented
39C2×#546C2214yescomplemented
40C2×#546C2212yescomplemented
41C2×D42C2212yescomplemented
42C2×D42C2212yescomplemented
43C2×#539C2212yescomplemented
44C2×#538C2212yescomplemented
45C2×#537C2212yes—
46C2×#534C2212yes—
47C2×#534C2212yes—
48C2×#534C2212yescomplemented
49C2×#534C2212yescomplemented
50C2×#532C2212yes—
51C2×#529C2212yescomplemented
52C2×#525C2212yescomplemented
53C22×C22⋊Q8C2211yescharacteristic, complemented
54C22×#121C2211yescharacteristic
55C22×#121C2211yescharacteristic
56C22×#121C2212yes—
57C22×#121C2211yescharacteristic
58C2×#518C2212yescomplemented
59C22×C4×D4C2211yescharacteristic
60C22×C4×D4C2211yescharacteristic, complemented
61C22×C4×D4C2212yescomplemented
62#2855C2212yescomplemented
63#2854C2212yescomplemented
64#2854C2214yescomplemented
65#2848C2212yescomplemented
66#2847C2212yescomplemented
67#2847C2214yescomplemented
68#2716C2214yescomplemented
69#2715C2214yescomplemented
70#2714C2214yescomplemented
71#2713C2214yescomplemented
72#2712C2214yescomplemented
73#2711C2214yescomplemented
74#2710C2214yescomplemented
75#2709C2214yescomplemented
76#2708C2214yescomplemented
77#2703C2214yescomplemented
78#2700C2214yescomplemented
79#2696C2214yescomplemented
80#2695C2214yescomplemented
81#2694C2214yescomplemented
82#2693C2214yescomplemented
83#2692C2214yescomplemented
84#2691C2214yescomplemented
85#2691C2214yescomplemented
86#2690C2214yescomplemented
87#2689C2214yescomplemented
88#2688C2214yescomplemented
89#2688C2214yescomplemented
90#2687C2214yescomplemented
91#2686C2214yescomplemented
92#2685C2214yescomplemented
93#2684C2214yescomplemented
94#2681C2214yescomplemented
95#2678C2214yescomplemented
96#2676C2214yescomplemented
97#2673C2214yescomplemented
98#2671C2214yescomplemented
99#2668C2214yescomplemented
100#2639C2212yescomplemented
101#2639C2212yescomplemented
102#2639C2212yescomplemented
103#2639C2212yescomplemented
104#2639C2214yescomplemented
105#2639C2214yescomplemented
106#2627C2212yescomplemented
107#2626C2212yescomplemented
108#2618C2212yescomplemented
109#2618C2214yescomplemented
110#2617C2212yescomplemented
111#2617C2214yescomplemented
112#2579C2214yescomplemented
113#2564C2214yescomplemented
114#2543C2214yescomplemented
115#2534C2214yescomplemented
116#2498C2214yescomplemented
117#2498C2214yescomplemented
118#2487C2212yescomplemented
119#2486C2212yescomplemented
120#2481C2214yescomplemented
121#2480C2214yescomplemented
122#2477C2214yescomplemented
123#2476C2214yescomplemented
124#2473C2214yescomplemented
125#2472C2214yescomplemented
126#2471C2214yescomplemented
127#2470C2214yescomplemented
128#2467C2214yescomplemented
129#2466C2214yescomplemented
130#2465C2214yescomplemented
131#2464C2214yescomplemented
132#2460C2214yescomplemented
133#2459C2214yescomplemented
134#2458C2214yescomplemented
135#2457C2214yescomplemented
136#2450C2214yescomplemented
137#2450C2214yescomplemented
138#2444C2214yescomplemented
139#2444C2214yescomplemented
140#2444C2214yescomplemented
141#2444C2214yescomplemented
142#2443C2214yescomplemented
143#2443C2214yescomplemented
144#2438C2214yescomplemented
145#2437C2214yescomplemented
146#2430C2214yescomplemented
147#2430C2214yescomplemented
148#2430C2214yescomplemented
149#2430C2214yescomplemented
150#2430C2214yescomplemented
151#2425C2214yescomplemented
152#2425C2214yescomplemented
153#2425C2214yescomplemented
154#2425C2214yescomplemented
155#2425C2214yescomplemented
156#2424C2214yescomplemented
157#2424C2214yescomplemented
158#2424C2214yescomplemented
159#2424C2214yescomplemented
160#2424C2214yescomplemented
161#2419C2214yescomplemented
162#2419C2214yescomplemented
163#2419C2214yescomplemented
164#2418C2214yescomplemented
165#2418C2214yescomplemented
166#2418C2214yescomplemented
167#2417C2212yescomplemented
168#2417C2212yescomplemented
169#2416C2212yescomplemented
170#2416C2212yescomplemented
171#2412C2214yescomplemented
172#2412C2214yescomplemented
173#2412C2214yescomplemented
174#2411C2214yescomplemented
175#2410C2214yescomplemented
176#2410C2214yescomplemented
177#2410C2214yescomplemented
178#2410C2214yescomplemented
179#2410C2214yescomplemented
180#2409C2212yescomplemented
181#2408C2212yescomplemented
182#2406C2214yescomplemented
183#2405C2214yescomplemented
184#2405C2214yescomplemented
185#2404C2214yescomplemented
186#2404C2214yescomplemented
187#2403C2214yescomplemented
188C2×#400C2212yescomplemented
189C2×#397C2212yescomplemented
190C2×#394C2212yescomplemented
191C2×#393C2212yescomplemented
192#2339C2214yescomplemented
193#2339C2214yescomplemented
194#2339C2214yescomplemented
195#2339C2214yescomplemented
196D4×C22⋊C4C2214yescomplemented
197D4×C22⋊C4C2214yescomplemented
198D4×C22⋊C4C2214yescomplemented
199D4×C22⋊C4C2214yescomplemented
200#2325C2214yescomplemented
201#2325C2214yescomplemented
202#2325C2214yescomplemented
203#2325C2214yescomplemented
204#2325C2212yescomplemented
205#2325C2212yescomplemented
206#2325C2212yescomplemented
207#2325C2212yescomplemented
208#2325C2214yescomplemented
209#2325C2214yescomplemented
210#2315C2212yescomplemented
211#2311C2214yescomplemented
212#2308C2212yes—
213#2308C2212yescomplemented
214#2308C2214yescomplemented
215#2297C2214yescomplemented
216C2×#388C2211yescharacteristic, complemented
217C2×#388C2211yescharacteristic, complemented
218C2×#388C2212yescomplemented
219C2×#387C2211yescharacteristic, complemented
220C2×#387C2211yescharacteristic, complemented
221C2×#387C2212yescomplemented
222C2×#386C2211yescharacteristic
223C2×#386C2212yescomplemented
224C2×#386C2212yescomplemented
225C2×#386C2212yescomplemented
226C2×#386C2211yescharacteristic, complemented
227C2×#386C2211yescharacteristic, complemented
228C2×#386C2211yescharacteristic, complemented
229C2×#386C2212yescomplemented
230C2×#386C2214yescomplemented
231C2×#385C2211yescharacteristic, complemented
232C2×#385C2211yescharacteristic, complemented
233C2×#385C2212yescomplemented
234C2×#380C2211yescharacteristic, complemented
235C2×#380C2211yescharacteristic, complemented
236C22×#95C2211yescharacteristic, complemented
237C2×H(5,𝔽2)—216no—
238C2×H(5,𝔽2)—216no—
239C2×H(5,𝔽2)—48no—
240C22×#41C2314yes—
241C22×#41C2314yes—
242C22×#41C2314yes—
243C22×#41C2312yes—
244C23×Q8C2311yescharacteristic
245C23×D4C2312yes—
246C23×D4C2311yescharacteristic
247C23×D4C2314yes—
248C23×D4C2314yes—
249C23×D4C2314yes—
250C23×D4C2312yes—
251C23×D4C2311yescharacteristic
252C23×D4C2311yescharacteristic
253C23×D4C2311yescharacteristic
254C23×D4C2312yes—
255C23×D4C2311yescharacteristic
256C24×C4C2311yescharacteristic
257C24×C4C2311yescharacteristic
258C24×C4C2311yescharacteristic
259C24×C4C2311yescharacteristic
260C24×C4C2312yes—
261C24×C4C2311yescharacteristic
262#553—216no—
263#553—232no—
264#552—216no—
265#551—232no—
266#548—216no—
267#547—216no—
268#547—216no—
269#546—216no—
270#546—232no—
271#546—232no—
272D42—216no—
273D42—216no—
274#539—216no—
275#538—216no—
276#537—216no—
277#534—216no—
278#534—216no—
279#534—216no—
280#534—48no—
281#532—216no—
282C2×C4⋊Q8C2312yes—
283C2×#127C2312yes—
284#529—216no—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2314yes—
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2314yes—
293#525—216no—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×C22⋊Q8—28no—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×#121—28no—
319C2×#121—28no—
320C2×#121—216no—
321C2×#121D4116yescomplemented
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2312yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2314yes—
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#120C2314yes—
350C2×#120C2314yes—
351C2×#120C2314yes—
352C2×#120C2314yes—
353C2×#120C2314yes—
354C2×#120C2314yes—
355C2×#120C2314yes—
356C2×#120C2314yes—
357C2×#120C2314yes—
358C2×#120C2314yes—
359#518—216no—
360C2×C4×Q8C2312yes—
361C2×C4×D4—28no—
362C2×C4×D4—28no—
363C2×C4×D4—48no—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2314yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2314yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2314yes—
385C2×#117C2314yes—
386C2×#117C2314yes—
387C2×#117C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2311yescharacteristic
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2311yescharacteristic
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2312yes—
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2311yescharacteristic
398C22×C4⋊C4C2311yescharacteristic
399C22×C4⋊C4C2311yescharacteristic
400C22×C4⋊C4C2311yescharacteristic
401C22×C22⋊C4C2312yes—
402C22×C22⋊C4C2312yes—
403C22×C22⋊C4C2311yescharacteristic
404C22×C22⋊C4C2314yes—
405C22×C22⋊C4C2311yescharacteristic
406C22×C22⋊C4C2311yescharacteristic
407C22×C22⋊C4C2311yescharacteristic
408C22×C22⋊C4C2312yes—
409C22×C22⋊C4C2311yescharacteristic
410C22×C22⋊C4C2311yescharacteristic
411C22×C22⋊C4C2314yes—
412C22×C22⋊C4C2312yes—
413C22×C22⋊C4C2311yescharacteristic
414C22×C22⋊C4C2311yescharacteristic
415C22×C22⋊C4C2312yes—
416C22×C22⋊C4C2312yes—
417C22×C22⋊C4C2314yes—
418C22×C22⋊C4C2314yes—
419C22×C22⋊C4C2312yes—
420C22×C22⋊C4C2312yes—
421C22×C22⋊C4C2312yes—
422C22×C22⋊C4C2312yes—
423C22×C22⋊C4C2311yescharacteristic
424C22×C22⋊C4C2311yescharacteristic
425C22×C22⋊C4C2312yes—
426C22×C42C2311yescharacteristic
427C22×C42C2311yescharacteristic
428C22×C42C2312yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#399C2314yes—
437#399C2314yes—
438#399C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#393C2314yes—
494#393C2314yes—
495#393C2314yes—
496#393C2314yes—
497#393C2314yes—
498#393C2314yes—
499#393C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2312yes—
514#391C2312yes—
515#390C2314yes—
516#390C2314yes—
517#390C2314yes—
518#390C2314yes—
519#390C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2314yes—
654#380C2314yes—
655#380C2312yes—
656#380C2312yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#379C2314yes—
662#379C2314yes—
663#379C2314yes—
664#379C2314yes—
665#379C2314yes—
666#379C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C2×#95C2312yes—
672C2×#95C2312yes—
673C2×#95C2312yes—
674C2×#95C2311yescharacteristic
675C2×#95C2312yes—
676C2×#95C2311yescharacteristic
677C2×#95C2311yescharacteristic
678C2×#95C2312yes—
679C2×#95C2311yescharacteristic
680C2×#95C2311yescharacteristic
681C2×#95C2311yescharacteristic
682C2×#95C2312yes—
683C2×#95C2312yes—
684C2×#95C2314yes—
685C2×#95C2314yes—
686C2×#95C2312yes—
687C2×#95C2312yes—
688C2×#95C2311yescharacteristic
689C2×#95C2311yescharacteristic
690C2×#95C2312yes—
691C2×#95C2312yes—
692C2×#95C2311yescharacteristic
693C2×#95C2311yescharacteristic
694C25C2412yes—
695C25C2411yescharacteristic
696C25C2414yes—
697C25C2412yes—
698C25C2411yescharacteristic
699C25C2411yescharacteristic
700H(5,𝔽2)—4128no—
701C2×#41—216no—
702C2×#41—216no—
703C2×#41—28no—
704C2×#41—216no—
705C2×#41—216no—
706C2×#41—216no—
707C2×#41—216no—
708C2×#41—48no—
709C2×#41—48no—
710C2×#41—48no—
711C2×#41—82no—
712C2×#41—82no—
713C22×Q8—24no—
714C22×Q8—81no—
715C22×Q8—81no—
716C22×Q8C2414yes—
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×D4—24no—
720C22×D4—28no—
721C22×D4—28no—
722C22×D4—24no—
723C22×D4—24no—
724C22×D4—28no—
725C22×D4—216no—
726C22×D4—24no—
727C22×D4—216no—
728C22×D4—28no—
729C22×D4—24no—
730C22×D4—28no—
731C22×D4—24no—
732C22×D4—216no—
733C22×D4—216no—
734C22×D4—216no—
735C22×D4—216no—
736C22×D4—28no—
737C22×D4—24no—
738C22×D4—48no—
739C22×D4—48no—
740C22×D4—48no—
741C22×D4—81no—
742C22×D4—81no—
743C22×D4—81no—
744C22×D4—81no—
745C22×D4—82no—
746C22×D4—82no—
747C22×D4—81no—
748C22×D4—81no—
749C22×D4C2×D4116yes—
750C22×D4C2×D418yescomplemented
751C22×D4#4118yescomplemented
752C22×D4C2412yes—
753C22×D4C2412yes—
754C22×D4C2414yes—
755C22×D4C2414yes—
756C22×D4C2414yes—
757C22×D4C2414yes—
758C22×D4C2414yes—
759C22×D4C2414yes—
760C22×D4C2414yes—
761C22×D4C2412yes—
762C22×D4C2412yes—
763C22×D4C2414yes—
764C22×D4C2414yes—
765C22×D4C2412yes—
766C22×D4C2414yes—
767C22×D4C2412yes—
768C22×D4C2414yes—
769C22×D4C2414yes—
770C22×D4C2414yes—
771C22×D4C2414yes—
772C22×D4C2412yes—
773C22×D4C2412yes—
774C23×C4—24no—
775C23×C4—24no—
776C23×C4—24no—
777C23×C4—24no—
778C23×C4—44no—
779C23×C4—81no—
780C23×C4—81no—
781C23×C4—81no—
782C23×C4—81no—
783C23×C4—81no—
784C23×C4—81no—
785C23×C4—81no—
786C23×C4—81no—
787C23×C4—81no—
788C23×C4—81no—
789C23×C4—82no—
790C23×C4—82no—
791C23×C4C2×D418yes—
792C23×C4C2411yescharacteristic
793C23×C4C2412yes—
794C23×C4C2414yes—
795C23×C4C2414yes—
796C23×C4C2414yes—
797C23×C4C2412yes—
798C23×C4C2411yescharacteristic
799C23×C4C2412yes—
800C23×C4C2411yescharacteristic
801C23×C4C2412yes—
802C23×C4C2411yescharacteristic
803C23×C4C2412yes—
804C23×C4C2411yescharacteristic
805C23×C4C2411yescharacteristic
806C23×C4C2412yes—
807C23×C4C2411yescharacteristic
808C23×C4C2414yes—
809C23×C4C2411yescharacteristic
810C23×C4C2411yescharacteristic
811C23×C4C2412yes—
812C23×C4C2414yes—
813C23×C4C2412yes—
814C23×C4C2412yes—
815C23×C4C2412yes—
816C23×C4C2412yes—
817C23×C4C2412yes—
818C23×C4C2411yescharacteristic
819C23×C4C2412yes—
820C23×C4C2412yes—
821C23×C4C2414yes—
822C23×C4C2414yes—
823C23×C4C2411yescharacteristic
824C23×C4C2411yescharacteristic
825C23×C4C2411yescharacteristic
826C23×C4C2411yescharacteristic
827C23×C4C2411yescharacteristic
828C23×C4C2411yescharacteristic
829C4⋊Q8—28no—
830#127—28no—
831#126—216no—
832#126—216no—
833#126—216no—
834#125—28no—
835#125—216no—
836#124—28no—
837#124—216no—
838#124—216no—
839#123—216no—
840#123—216no—
841#123—216no—
842#123—216no—
843#123—216no—
844#123—216no—
845#123—216no—
846#123—216no—
847#123—216no—
848#123—48no—
849#123—48no—
850#123—84no—
851#123—84no—
852C22⋊Q8—28no—
853C22⋊Q8—28no—
854C22⋊Q8—28no—
855C22⋊Q8—28no—
856C22⋊Q8—28no—
857C22⋊Q8—216no—
858C22⋊Q8—216no—
859C22⋊Q8—216no—
860C22⋊Q8—82no—
861C22⋊Q8—82no—
862#121—216no—
863#121—28no—
864#121—28no—
865#121—216no—
866#121—216no—
867#121—216no—
868#121—216no—
869#121—216no—
870#121—216no—
871#121—216no—
872#121—28no—
873#121—28no—
874#121—28no—
875#121—28no—
876#121—28no—
877#121—216no—
878#121—216no—
879#121—48no—
880#121—48no—
881#121—82no—
882#121—84no—
883#121—84no—
884#121—82no—
885#121C2×D4116yes—
886#121C2×D4116yes—
887#121C2×D4116yescomplemented
888#121C2×D4116yescomplemented
889#120—216no—
890#120—216no—
891#120—216no—
892#120—216no—
893#120—216no—
894#120—216no—
895#120—48no—
896#120—48no—
897#120—84no—
898#120—84no—
899C4×Q8—28no—
900C4×D4—216no—
901C4×D4—216no—
902C4×D4—216no—
903C4×D4—216no—
904C4×D4—28no—
905C4×D4—28no—
906C4×D4—28no—
907C4×D4—28no—
908C4×D4—28no—
909C4×D4—28no—
910C4×D4—28no—
911C4×D4—28no—
912C4×D4—28no—
913C4×D4—28no—
914C4×D4—28no—
915C4×D4—216no—
916C4×D4—216no—
917C4×D4—48no—
918C4×D4—48no—
919C4×D4—48no—
920C4×D4—48no—
921#117—216no—
922#117—28no—
923#117—216no—
924C2×C4⋊C4—24no—
925C2×C4⋊C4—24no—
926C2×C4⋊C4—24no—
927C2×C4⋊C4—24no—
928C2×C4⋊C4—28no—
929C2×C4⋊C4—24no—
930C2×C4⋊C4—28no—
931C2×C4⋊C4—44no—
932C2×C4⋊C4—81no—
933C2×C4⋊C4—81no—
934C2×C4⋊C4—81no—
935C2×C4⋊C4—81no—
936C2×C4⋊C4C2×D418yescomplemented
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C22⋊C4—24no—
971C2×C22⋊C4—24no—
972C2×C22⋊C4—28no—
973C2×C22⋊C4—216no—
974C2×C22⋊C4—24no—
975C2×C22⋊C4—28no—
976C2×C22⋊C4—24no—
977C2×C22⋊C4—24no—
978C2×C22⋊C4—28no—
979C2×C22⋊C4—24no—
980C2×C22⋊C4—216no—
981C2×C22⋊C4—44no—
982C2×C22⋊C4—81no—
983C2×C22⋊C4—81no—
984C2×C22⋊C4—84no—
985C2×C22⋊C4—82no—
986C2×C22⋊C4—82no—
987C2×C22⋊C4—84no—
988C2×C22⋊C4—82no—
989C2×C22⋊C4—82no—
990C2×C22⋊C4—82no—
991C2×C22⋊C4—82no—
992C2×C22⋊C4—81no—
993C2×C22⋊C4—81no—
994C2×C22⋊C4C2×D4116yescomplemented
995C2×C22⋊C4C2412yes—
996C2×C22⋊C4C2414yes—
997C2×C22⋊C4C2414yes—
998C2×C22⋊C4C2412yes—
999C2×C22⋊C4C2412yes—
1000C2×C22⋊C4C2412yes—
1001C2×C22⋊C4C2412yes—
1002C2×C22⋊C4C2412yes—
1003C2×C22⋊C4C2414yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2414yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2414yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C42—24no—
1054C2×C42—24no—
1055C2×C42—44no—
1056C2×C42C2414yes—
1057C2×C42C2414yes—
1058C2×C42C2412yes—
1059C2×C42C2412yes—
1060C2×C42C2412yes—
1061C2×C42C2412yes—
1062C2×C42C2414yes—
1063C2×C42C2414yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2412yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104C24—22no—
1105C24—24no—
1106C24—24no—
1107C24—22no—
1108C24—22no—
1109C24—22no—
1110C24—28no—
1111C24—24no—
1112C24—28no—
1113C24—24no—
1114C24—22no—
1115C24—24no—
1116C24—41no—
1117C24—41no—
1118C24—41no—
1119C24—41no—
1120C24—41no—
1121C24—42no—
1122C24—41no—
1123C24—41no—
1124C24—42no—
1125C24—41no—
1126C24—41no—
1127C24—42no—
1128C24—41no—
1129C24—41no—
1130C24—42no—
1131C24—41no—
1132C24—44no—
1133C24—42no—
1134C24—42no—
1135C24—42no—
1136C24—42no—
1137C24—44no—
1138C24—44no—
1139C24—44no—
1140C24—44no—
1141C24C22×D418yes—
1142C24C22×D414yes—
1143C24C2×#4114yes—
1144C24C2×#4114yes—
1145C24H(5,𝔽2)14yes—
1146C24C2514yes—
1147C24C2512yes—
1148C24C2514yes—
1149C24C2512yes—
1150C24C2511yescharacteristic
1151C24C2511yescharacteristic
1152C24C2511yescharacteristic
1153#41—464no—
1154#41—464no—
1155#41—464no—
1156#41—816no—
1157C2×Q8—24no—
1158C2×Q8—28no—
1159C2×Q8—24no—
1160C2×Q8—28no—
1161C2×Q8—42no—
1162C2×Q8—42no—
1163C2×Q8—44no—
1164C2×Q8—42no—
1165C2×Q8—42no—
1166C2×Q8—88no—
1167C2×D4—264no—
1168C2×D4—232no—
1169C2×D4—24no—
1170C2×D4—24no—
1171C2×D4—28no—
1172C2×D4—28no—
1173C2×D4—28no—
1174C2×D4—28no—
1175C2×D4—24no—
1176C2×D4—24no—
1177C2×D4—24no—
1178C2×D4—24no—
1179C2×D4—28no—
1180C2×D4—28no—
1181C2×D4—28no—
1182C2×D4—28no—
1183C2×D4—24no—
1184C2×D4—24no—
1185C2×D4—28no—
1186C2×D4—28no—
1187C2×D4—28no—
1188C2×D4—28no—
1189C2×D4—24no—
1190C2×D4—28no—
1191C2×D4—24no—
1192C2×D4—28no—
1193C2×D4—28no—
1194C2×D4—28no—
1195C2×D4—28no—
1196C2×D4—28no—
1197C2×D4—28no—
1198C2×D4—24no—
1199C2×D4—28no—
1200C2×D4—24no—
1201C2×D4—28no—
1202C2×D4—44no—
1203C2×D4—44no—
1204C2×D4—44no—
1205C2×D4—42no—
1206C2×D4—42no—
1207C2×D4—42no—
1208C2×D4—42no—
1209C2×D4—42no—
1210C2×D4—42no—
1211C2×D4—44no—
1212C2×D4—44no—
1213C2×D4—44no—
1214C2×D4—44no—
1215C2×D4—44no—
1216C2×D4—42no—
1217C2×D4—42no—
1218C2×D4—44no—
1219C2×D4—44no—
1220C2×D4—44no—
1221C2×D4—44no—
1222C2×D4—44no—
1223C2×D4—44no—
1224C2×D4—44no—
1225C2×D4—44no—
1226C2×D4—44no—
1227C2×D4—44no—
1228C2×D4—44no—
1229C2×D4—464no—
1230C2×D4—464no—
1231C2×D4—464no—
1232C2×D4—416no—
1233C2×D4—432no—
1234C2×D4—88no—
1235C2×D4—88no—
1236C2×D4—816no—
1237C2×D4—88no—
1238C2×D4C22×D4116yes—
1239C2×D4C22×D4116yes—
1240C2×D4C22×D418yes—
1241C2×D4C22×D418yes—
1242C2×D4C2×#4118yes—
1243C2×D4C2×#4118yes—
1244C22×C4—22no—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—24no—
1250C22×C4—28no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—28no—
1255C22×C4—24no—
1256C22×C4—24no—
1257C22×C4—22no—
1258C22×C4—24no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—22no—
1265C22×C4—28no—
1266C22×C4—28no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—24no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—24no—
1274C22×C4—28no—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—28no—
1278C22×C4—28no—
1279C22×C4—28no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—41no—
1283C22×C4—41no—
1284C22×C4—41no—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—41no—
1301C22×C4—41no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—44no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—42no—
1308C22×C4—42no—
1309C22×C4—41no—
1310C22×C4—41no—
1311C22×C4—44no—
1312C22×C4—42no—
1313C22×C4—42no—
1314C22×C4—42no—
1315C22×C4—42no—
1316C22×C4—42no—
1317C22×C4—44no—
1318C22×C4—41no—
1319C22×C4—41no—
1320C22×C4—42no—
1321C22×C4—41no—
1322C22×C4—41no—
1323C22×C4—42no—
1324C22×C4—41no—
1325C22×C4—44no—
1326C22×C4—41no—
1327C22×C4—42no—
1328C22×C4—42no—
1329C22×C4—44no—
1330C22×C4—42no—
1331C22×C4—41no—
1332C22×C4—41no—
1333C22×C4—44no—
1334C22×C4—44no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—44no—
1338C22×C4—44no—
1339C22×C4—42no—
1340C22×C4—42no—
1341C22×C4—44no—
1342C22×C4—42no—
1343C22×C4—41no—
1344C22×C4—44no—
1345C22×C4—42no—
1346C22×C4—41no—
1347C22×C4—88no—
1348C22×C4—88no—
1349C22×C4—88no—
1350C22×C4—88no—
1351C22×C4—88no—
1352C22×C4—816no—
1353C22×C4C22×D418yes—
1354C22×C4C22×D414yes—
1355C22×C4C22×D414yes—
1356C22×C4C22×D414yes—
1357C22×C4C22×D414yes—
1358C22×C4C22×D414yes—
1359C22×C4C22×D414yes—
1360C22×C4C2×#4114yes—
1361C22×C4C2512yes—
1362C22×C4C2512yes—
1363C22×C4C2512yes—
1364C22×C4C2512yes—
1365C22×C4C2514yes—
1366C22×C4C2514yes—
1367C22×C4C2514yes—
1368C22×C4C2512yes—
1369C22×C4C2512yes—
1370C22×C4C2512yes—
1371C22×C4C2514yes—
1372C22×C4C2514yes—
1373C22×C4C2512yes—
1374C22×C4C2512yes—
1375C22×C4C2511yescharacteristic
1376C22×C4C2511yescharacteristic
1377C22×C4C2514yes—
1378C22×C4C2511yescharacteristic
1379C22×C4C2511yescharacteristic
1380C22×C4C2512yes—
1381C4⋊C4—24no—
1382C4⋊C4—24no—
1383C4⋊C4—28no—
1384C4⋊C4—24no—
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—28no—
1389C4⋊C4—24no—
1390C4⋊C4—28no—
1391C4⋊C4—24no—
1392C4⋊C4—28no—
1393C4⋊C4—28no—
1394C4⋊C4—28no—
1395C4⋊C4—28no—
1396C4⋊C4—28no—
1397C4⋊C4—28no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—44no—
1408C4⋊C4—44no—
1409C4⋊C4—44no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4C22×D418yes—
1413C4⋊C4C22×D418yes—
1414C22⋊C4—24no—
1415C22⋊C4—28no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—28no—
1420C22⋊C4—28no—
1421C22⋊C4—28no—
1422C22⋊C4—28no—
1423C22⋊C4—28no—
1424C22⋊C4—28no—
1425C22⋊C4—28no—
1426C22⋊C4—28no—
1427C22⋊C4—28no—
1428C22⋊C4—28no—
1429C22⋊C4—28no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—28no—
1435C22⋊C4—28no—
1436C22⋊C4—28no—
1437C22⋊C4—28no—
1438C22⋊C4—28no—
1439C22⋊C4—28no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—44no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4C22×D4116yes—
1471C22⋊C4C22×D4116yes—
1472C42—24no—
1473C42—24no—
1474C42—24no—
1475C42—24no—
1476C42—28no—
1477C42—28no—
1478C42—44no—
1479C42—44no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—22no—
1493C23—24no—
1494C23—24no—
1495C23—22no—
1496C23—22no—
1497C23—22no—
1498C23—24no—
1499C23—22no—
1500C23—24no—
1501C23—24no—
1502C23—22no—
1503C23—24no—
1504C23—28no—
1505C23—216no—
1506C23—22no—
1507C23—24no—
1508C23—22no—
1509C23—24no—
1510C23—22no—
1511C23—24no—
1512C23—24no—
1513C23—24no—
1514C23—24no—
1515C23—22no—
1516C23—22no—
1517C23—22no—
1518C23—24no—
1519C23—22no—
1520C23—44no—
1521C23—44no—
1522C23—44no—
1523C23—44no—
1524C23—44no—
1525C23—44no—
1526C23—48no—
1527C23—44no—
1528C23—48no—
1529C23—44no—
1530C23—416no—
1531C23—44no—
1532C23—44no—
1533C23—44no—
1534C23—48no—
1535C23—82no—
1536C23—82no—
1537C23—84no—
1538C23—84no—
1539C23—84no—
1540C23—82no—
1541C23—82no—
1542C23—82no—
1543C23—82no—
1544C23—84no—
1545C23—82no—
1546C23—82no—
1547C23—84no—
1548C23—88no—
1549C23—84no—
1550C23—84no—
1551C23—84no—
1552C23—84no—
1553C23—84no—
1554C23—88no—
1555C23—88no—
1556C23—88no—
1557C23—164no—
1558C23—164no—
1559C23#546116yes—
1560C23C23×D418yes—
1561C23C23×D412yes—
1562C23C23×D412yes—
1563C23C23×D412yes—
1564C23C22×#4114yes—
1565C23C22×#4112yes—
1566C23C22×#4112yes—
1567C23C22×#4112yes—
1568C23C2×H(5,𝔽2)12yes—
1569C23C2×H(5,𝔽2)12yes—
1570C23C2×H(5,𝔽2)12yes—
1571C23C2611yescharacteristic
1572Q8—416no—
1573Q8—48no—
1574Q8—84no—
1575D4—216no—
1576D4—216no—
1577D4—232no—
1578D4—232no—
1579D4—48no—
1580D4—48no—
1581D4—416no—
1582D4—416no—
1583D4—48no—
1584D4—416no—
1585D4—48no—
1586D4—48no—
1587D4—416no—
1588D4—416no—
1589D4—84no—
1590D4—88no—
1591D4—88no—
1592D4—88no—
1593D4—88no—
1594D4—88no—
1595D4—164no—
1596D4—164no—
1597C2×C4—22no—
1598C2×C4—24no—
1599C2×C4—24no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—216no—
1610C2×C4—28no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—24no—
1616C2×C4—24no—
1617C2×C4—22no—
1618C2×C4—24no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—24no—
1623C2×C4—24no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—22no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—24no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—24no—
1643C2×C4—24no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—24no—
1650C2×C4—22no—
1651C2×C4—24no—
1652C2×C4—22no—
1653C2×C4—44no—
1654C2×C4—44no—
1655C2×C4—44no—
1656C2×C4—44no—
1657C2×C4—44no—
1658C2×C4—44no—
1659C2×C4—416no—
1660C2×C4—416no—
1661C2×C4—416no—
1662C2×C4—48no—
1663C2×C4—48no—
1664C2×C4—44no—
1665C2×C4—48no—
1666C2×C4—44no—
1667C2×C4—44no—
1668C2×C4—48no—
1669C2×C4—84no—
1670C2×C4—84no—
1671C2×C4—82no—
1672C2×C4—88no—
1673C2×C4—84no—
1674C2×C4—82no—
1675C2×C4—84no—
1676C2×C4—82no—
1677C2×C4—82no—
1678C2×C4—84no—
1679C2×C4—84no—
1680C2×C4—82no—
1681C2×C4—82no—
1682C2×C4—84no—
1683C2×C4—84no—
1684C2×C4—84no—
1685C2×C4—88no—
1686C2×C4—88no—
1687C2×C4—88no—
1688C2×C4C23×D412yes—
1689C2×C4C23×D412yes—
1690C2×C4C23×D418yes—
1691C2×C4C23×D412yes—
1692C2×C4C23×D412yes—
1693C2×C4C22×#4114yes—
1694C22—22no—
1695C22—22no—
1696C22—22no—
1697C22—22no—
1698C22—22no—
1699C22—22no—
1700C22—22no—
1701C22—22no—
1702C22—22no—
1703C22—22no—
1704C22—22no—
1705C22—22no—
1706C22—22no—
1707C22—22no—
1708C22—22no—
1709C22—22no—
1710C22—22no—
1711C22—22no—
1712C22—28no—
1713C22—24no—
1714C22—24no—
1715C22—28no—
1716C22—24no—
1717C22—28no—
1718C22—416no—
1719C22—42no—
1720C22—44no—
1721C22—44no—
1722C22—42no—
1723C22—44no—
1724C22—42no—
1725C22—44no—
1726C22—42no—
1727C22—42no—
1728C22—44no—
1729C22—42no—
1730C22—44no—
1731C22—42no—
1732C22—44no—
1733C22—42no—
1734C22—44no—
1735C22—42no—
1736C22—44no—
1737C22—42no—
1738C22—44no—
1739C22—44no—
1740C22—42no—
1741C22—816no—
1742C22—88no—
1743C22—88no—
1744C22—168no—
1745C22—1616no—
1746C22C2×#54614yes—
1747C22C2×#54614yes—
1748C22C2×#54614yes—
1749C22C24×D411yescharacteristic
1750C22C23×#4111yescharacteristic
1751C22C22×H(5,𝔽2)11yescharacteristic
1752C22H(7,𝔽2)11yescharacteristic
1753C22H(7,𝔽2)11yescharacteristic
1754C22H(7,𝔽2)11yescharacteristic
1755C222−1+611yescharacteristic
1756C4—22no—
1757C4—22no—
1758C4—22no—
1759C4—22no—
1760C4—24no—
1761C4—28no—
1762C4—42no—
1763C4—42no—
1764C4—44no—
1765C4—42no—
1766C4—42no—
1767C4—42no—
1768C4—44no—
1769C4—42no—
1770C4—42no—
1771C4—42no—
1772C4—44no—
1773C4—44no—
1774C4—44no—
1775C4—42no—
1776C2—24no—
1777C2—24no—
1778C2—24no—
1779C2—48no—
1780C2—44no—
1781C2—82no—
1782C2—84no—
1783C2C22×#54611yescharacteristic
1784C2#6284211yescharacteristic
1785C2#6284611yescharacteristic
1786C2#6284711yescharacteristic
1787C2#6285311yescharacteristic
1788C2#6286311yescharacteristic
1789C2#6286611yescharacteristic
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×#3496C2semidirect
3. #43531C2semidirect
4. #43530C2semidirect
5. #43102C2semidirect
6. #43101C2semidirect
7. #38087C2semidirect
8. #38086C2semidirect
9. #38077C2semidirect
10. #38076C2semidirect
11. #37747C2semidirect
12. #37746C2semidirect
13. #37745C2semidirect
14. #37744C2semidirect
15. #37698C2semidirect
16. #37697C2semidirect
17. #37693C2semidirect
18. #37692C2semidirect
19. #35360C2semidirect
20. #35347C2semidirect
21. #35010C2semidirect
22. #35000C2semidirect
23. #34984C2semidirect
24. C2×#2639C2semidirect
25. #34256C2semidirect
26. C2×#2325C2semidirect
27. C2×#2325C2semidirect
31. C2×#553C22semidirect
32. C2×#553C22semidirect
33. C2×#552C22semidirect
34. C2×#551C22semidirect
35. C2×#548C22semidirect
36. C2×#547C22semidirect
37. C2×#547C22semidirect
38. C2×#546C22semidirect
39. C2×#546C22semidirect
40. C2×#546C22semidirect
41. C2×D42C22semidirect
42. C2×D42C22semidirect
43. C2×#539C22semidirect
44. C2×#538C22semidirect
48. C2×#534C22semidirect
49. C2×#534C22semidirect
51. C2×#529C22semidirect
52. C2×#525C22semidirect
53. C22×C22⋊Q8C22semidirect
58. C2×#518C22semidirect
60. C22×C4×D4C22semidirect
61. C22×C4×D4C22semidirect
62. #2855C22semidirect
63. #2854C22semidirect
64. #2854C22semidirect
65. #2848C22semidirect
66. #2847C22semidirect
67. #2847C22semidirect
68. #2716C22semidirect
69. #2715C22semidirect
70. #2714C22semidirect
71. #2713C22semidirect
72. #2712C22semidirect
73. #2711C22semidirect
74. #2710C22semidirect
75. #2709C22semidirect
76. #2708C22semidirect
77. #2703C22semidirect
78. #2700C22semidirect
79. #2696C22semidirect
80. #2695C22semidirect
81. #2694C22semidirect
82. #2693C22semidirect
83. #2692C22semidirect
84. #2691C22semidirect
85. #2691C22semidirect
86. #2690C22semidirect
87. #2689C22semidirect
88. #2688C22semidirect
89. #2688C22semidirect
90. #2687C22semidirect
91. #2686C22semidirect
92. #2685C22semidirect
93. #2684C22semidirect
94. #2681C22semidirect
95. #2678C22semidirect
96. #2676C22semidirect
97. #2673C22semidirect
98. #2671C22semidirect
99. #2668C22semidirect
100. #2639C22semidirect
101. #2639C22semidirect
102. #2639C22semidirect
103. #2639C22semidirect
104. #2639C22semidirect
105. #2639C22semidirect
106. #2627C22semidirect
107. #2626C22semidirect
108. #2618C22semidirect
109. #2618C22semidirect
110. #2617C22semidirect
111. #2617C22semidirect
112. #2579C22semidirect
113. #2564C22semidirect
114. #2543C22semidirect
115. #2534C22semidirect
116. #2498C22semidirect
117. #2498C22semidirect
118. #2487C22semidirect
119. #2486C22semidirect
120. #2481C22semidirect
121. #2480C22semidirect
122. #2477C22semidirect
123. #2476C22semidirect
124. #2473C22semidirect
125. #2472C22semidirect
126. #2471C22semidirect
127. #2470C22semidirect
128. #2467C22semidirect
129. #2466C22semidirect
130. #2465C22semidirect
131. #2464C22semidirect
132. #2460C22semidirect
133. #2459C22semidirect
134. #2458C22semidirect
135. #2457C22semidirect
136. #2450C22semidirect
137. #2450C22semidirect
138. #2444C22semidirect
139. #2444C22semidirect
140. #2444C22semidirect
141. #2444C22semidirect
142. #2443C22semidirect
143. #2443C22semidirect
144. #2438C22semidirect
145. #2437C22semidirect
146. #2430C22semidirect
147. #2430C22semidirect
148. #2430C22semidirect
149. #2430C22semidirect
150. #2430C22semidirect
151. #2425C22semidirect
152. #2425C22semidirect
153. #2425C22semidirect
154. #2425C22semidirect
155. #2425C22semidirect
156. #2424C22semidirect
157. #2424C22semidirect
158. #2424C22semidirect
159. #2424C22semidirect
160. #2424C22semidirect
161. #2419C22semidirect
162. #2419C22semidirect
163. #2419C22semidirect
164. #2418C22semidirect
165. #2418C22semidirect
166. #2418C22semidirect
167. #2417C22semidirect
168. #2417C22semidirect
169. #2416C22semidirect
170. #2416C22semidirect
171. #2412C22semidirect
172. #2412C22semidirect
173. #2412C22semidirect
174. #2411C22semidirect
175. #2410C22semidirect
176. #2410C22semidirect
177. #2410C22semidirect
178. #2410C22semidirect
179. #2410C22semidirect
180. #2409C22semidirect
181. #2408C22semidirect
182. #2406C22semidirect
183. #2405C22semidirect
184. #2405C22semidirect
185. #2404C22semidirect
186. #2404C22semidirect
187. #2403C22semidirect
188. C2×#400C22semidirect
189. C2×#397C22semidirect
190. C2×#394C22semidirect
191. C2×#393C22semidirect
192. #2339C22semidirect
193. #2339C22semidirect
194. #2339C22semidirect
195. #2339C22semidirect
196. D4×C22⋊C4C22semidirect
197. D4×C22⋊C4C22semidirect
198. D4×C22⋊C4C22semidirect
199. D4×C22⋊C4C22semidirect
200. #2325C22semidirect
201. #2325C22semidirect
202. #2325C22semidirect
203. #2325C22semidirect
204. #2325C22semidirect
205. #2325C22semidirect
206. #2325C22semidirect
207. #2325C22semidirect
208. #2325C22semidirect
209. #2325C22semidirect
210. #2315C22semidirect
211. #2311C22semidirect
213. #2308C22semidirect
214. #2308C22semidirect
215. #2297C22semidirect
216. C2×#388C22semidirect
217. C2×#388C22semidirect
218. C2×#388C22semidirect
219. C2×#387C22semidirect
220. C2×#387C22semidirect
221. C2×#387C22semidirect
223. C2×#386C22semidirect
224. C2×#386C22semidirect
225. C2×#386C22semidirect
226. C2×#386C22semidirect
227. C2×#386C22semidirect
228. C2×#386C22semidirect
229. C2×#386C22semidirect
230. C2×#386C22semidirect
231. C2×#385C22semidirect
232. C2×#385C22semidirect
233. C2×#385C22semidirect
234. C2×#380C22semidirect
235. C2×#380C22semidirect
236. C22×#95C22semidirect
321. C2×#121D4semidirect
750. C22×D4C2×D4semidirect
751. C22×D4#41semidirect
887. #121C2×D4semidirect
888. #121C2×D4semidirect
936. C2×C4⋊C4C2×D4semidirect
994. C2×C22⋊C4C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#34962
#435312
#435302
#431022
#431012
#380872
#380862
#380772
#380762
#377472
#377462
#377452
#377442
#376982
#376972
#376932
#376922
#353602
#353472
#350102
#350002
#349842
C2×#26392
#342562
C2×#23252