Finite Group Databasebeta

← #7732019

Subgroups — #7732019

Order 512.

6984 conjugacy classes of subgroups.

The subgroup lattice has 1786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3538C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic
3#49586C214yesmaximal, complemented
4#49581C214yesmaximal, complemented
5#47454C214yesmaximal, complemented
6#46374C214yesmaximal, complemented
7#43905C214yesmaximal, complemented
8#43490C214yesmaximal, complemented
9#39463C212yesmaximal, complemented
10#39423C212yesmaximal, complemented
11#39413C212yesmaximal, complemented
12#39371C212yesmaximal, complemented
13#39368C212yesmaximal, complemented
14#39343C212yesmaximal, complemented
15#38048C212yesmaximal, complemented
16#38027C212yesmaximal, complemented
17#37837C212yesmaximal, complemented
18#37651C212yesmaximal, complemented
19#37442C211yesmaximal, characteristic, complemented
20#37378C212yesmaximal, complemented
21#37376C212yesmaximal, complemented
22#36375C212yesmaximal, complemented
23#36274C212yesmaximal, complemented
24#35635C212yesmaximal, complemented
25#35621C212yesmaximal, complemented
26#35306C211yesmaximal, characteristic, complemented
27#35010C211yesmaximal, characteristic, complemented
28C2×#2415C211yesmaximal, characteristic, complemented
29#34202C211yesmaximal, characteristic, complemented
30#3538—216no—
31C2×#563C2214yescomplemented
32C2×#552C2212yes—
33C2×#552C2212yescomplemented
34C2×#551C2214yes—
35C2×D4×Q8C2212yes—
36C2×D4×Q8C2212yescomplemented
37#3460—216no—
38C2×#544C2212yes—
39C2×#544C2211yescharacteristic
40C2×#544C2212yescomplemented
41C2×#542C2212yes—
42C2×#542C2212yes—
43C2×#541C2212yescomplemented
44C2×#540C2212yes—
45C2×#540C2212yes—
46C2×#539C2212yes—
47C2×#539C2212yescomplemented
48C2×#538C2211yescharacteristic
49C2×#538C2212yes—
50C2×#538C2211yescharacteristic
51C2×#537C2211yescharacteristic
52C2×#536C2212yescomplemented
53C2×#536C2212yescomplemented
54C2×#536C2211yescharacteristic, complemented
55C2×#535C2212yes—
56C2×#532C2212yes—
57C2×#532C2212yes—
58C2×#529C2212yes—
59C2×#529C2212yes—
60C2×#525C2212yes—
61C2×#525C2211yescharacteristic
62C2×#525C2211yescharacteristic
63C22×C22⋊Q8C2211yescharacteristic
64C22×C22⋊Q8C2211yescharacteristic
65C22×C22⋊Q8C2211yescharacteristic
66C2×#520C2211yescharacteristic, complemented
67C2×C4×#41C2212yes—
68C22×C4×D4C2211yescharacteristic
69C22×#117C2211yescharacteristic
70#2857C2212yes—
71#2857C2212yescomplemented
72#2855C2212yes—
73#2855C2212yescomplemented
74#2855C2212yescomplemented
75#2851C2212yescomplemented
76#2850C2212yes—
77#2848C2212yes—
78#2814C2214yescomplemented
79#2734C2214yescomplemented
80#2731C2214yescomplemented
81#2726C2214yescomplemented
82#2725C2214yescomplemented
83#2724C2214yescomplemented
84#2722C2214yescomplemented
85#2718C2214yescomplemented
86#2717C2214yescomplemented
87#2716C2214yescomplemented
88#2715C2214yes—
89#2713C2214yescomplemented
90#2713C2214yescomplemented
91#2711C2214yescomplemented
92#2709C2214yes—
93#2709C2214yes—
94#2708C2214yescomplemented
95#2707C2214yescomplemented
96#2707C2214yescomplemented
97#2704C2214yescomplemented
98#2704C2214yescomplemented
99#2701C2214yes—
100#2701C2214yescomplemented
101#2701C2214yescomplemented
102#2700C2214yes—
103#2698C2214yescomplemented
104#2698C2214yescomplemented
105#2695C2214yescomplemented
106#2695C2214yescomplemented
107#2691C2214yes—
108#2691C2214yescomplemented
109#2686C2214yes—
110#2686C2214yescomplemented
111#2681C2214yescomplemented
112#2680C2214yescomplemented
113#2677C2214yescomplemented
114#2674C2214yescomplemented
115#2674C2214yescomplemented
116#2674C2214yescomplemented
117#2672C2214yes—
118#2672C2214yescomplemented
119#2659C2212yescomplemented
120#2639C2212yescomplemented
121#2629C2212yescomplemented
122#2627C2212yes—
123#2627C2212yes—
124#2626C2212yes—
125#2625C2212yescomplemented
126#2621C2212yescomplemented
127#2621C2212yescomplemented
128#2620C2212yescomplemented
129#2618C2212yes—
130#2616C2212yescomplemented
131#2616C2212yescomplemented
132#2616C2212yescomplemented
133#2584C2212yescomplemented
134#2582C2212yescomplemented
135#2581C2212yescomplemented
136#2579C2214yes—
137#2568C2212yescomplemented
138#2564C2214yes—
139#2562C2212yescomplemented
140#2559C2214yes—
141#2559C2214yescomplemented
142#2558C2214yescomplemented
143#2556C2214yescomplemented
144#2553C2214yescomplemented
145#2551C2214yescomplemented
146#2549C2214yescomplemented
147#2547C2214yescomplemented
148#2546C2214yescomplemented
149#2545C2214yescomplemented
150#2544C2214yes—
151#2542C2212yescomplemented
152#2538C2212yescomplemented
153#2536C2212yescomplemented
154#2534C2214yes—
155#2521C2214yes—
156#2521C2214yescomplemented
157#2519C2214yescomplemented
158#2519C2214yescomplemented
159#2506C2214yescomplemented
160#2506C2214yescomplemented
161#2496C2214yescomplemented
162#2491C2214yescomplemented
163#2488C2214yescomplemented
164#2487C2212yes—
165#2486C2212yes—
166#2485C2212yescomplemented
167#2485C2212yescomplemented
168#2478C2214yescomplemented
169#2478C2214yescomplemented
170#2476C2214yes—
171#2475C2214yescomplemented
172#2474C2214yes—
173#2474C2214yescomplemented
174#2472C2214yes—
175#2466C2214yescomplemented
176#2462C2214yescomplemented
177#2451C2214yescomplemented
178#2450C2214yes—
179#2450C2214yescomplemented
180#2445C2214yes—
181#2444C2214yes—
182#2443C2214yes—
183#2440C2214yes—
184#2439C2214yescomplemented
185#2438C2214yes—
186#2438C2214yes—
187#2438C2214yescomplemented
188#2425C2214yes—
189#2425C2214yes—
190#2425C2214yescomplemented
191#2425C2214yescomplemented
192#2425C2214yescomplemented
193#2422C2214yescomplemented
194#2419C2214yes—
195#2419C2214yescomplemented
196#2418C2214yes—
197#2417C2212yes—
198#2417C2212yes—
199#2417C2212yes—
200#2417C2212yes—
201#2417C2212yescomplemented
202#2417C2212yescomplemented
203#2417C2212yescomplemented
204#2417C2212yescomplemented
205#2415C2212yes—
206#2415C2212yes—
207#2415C2214yes—
208#2415C2212yes—
209#2415C2212yes—
210#2415C2214yes—
211#2415C2212yescomplemented
212#2415C2212yescomplemented
213#2415C2212yescomplemented
214#2415C2212yescomplemented
215#2413C2214yescomplemented
216#2412C2214yes—
217#2412C2214yes—
218#2411C2214yes—
219#2409C2212yes—
220#2409C2212yes—
221#2409C2212yescomplemented
222#2409C2212yescomplemented
223#2406C2214yes—
224C2×#397C2212yes—
225C2×#394C2212yes—
226#2359C2214yes—
227#2359C2214yescomplemented
228#2358C2214yes—
229#2354C2212yescomplemented
230#2352C2212yes—
231#2352C2212yescomplemented
232#2349C2214yes—
233D4×C4⋊C4C2212yes—
234#2344C2214yes—
235#2339C2214yes—
236#2324C2212yescomplemented
237#2323C2212yescomplemented
238#2323C2212yescomplemented
239#2323C2212yescomplemented
240#2317C2211yescharacteristic, complemented
241#2317C2211yescharacteristic, complemented
242#2315C2212yes—
243#2311C2211yescharacteristic, complemented
244#2311C2212yescomplemented
245#2311C2211yescharacteristic, complemented
246#2310C2211yescharacteristic, complemented
247#2308C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2212yescomplemented
250C4×C22⋊Q8C2212yescomplemented
251C4×#121C2212yes—
252#2296C2212yescomplemented
253C2×#391C2211yescharacteristic
254C2×#391C2212yescomplemented
255C2×#389C2211yescharacteristic
256C2×#389C2212yes—
257C2×#388C2212yes—
258C2×#380C2211yescharacteristic
259C2×#380C2211yescharacteristic
260#2274C2211yescharacteristic, complemented
261C22×#41C2312yes—
262C22×#41C2312yes—
263C22×#41C2311yescharacteristic
264C22×#41C2311yescharacteristic
265C23×Q8C2311yescharacteristic
266C23×Q8C2311yescharacteristic
267C23×Q8C2312yes—
268C23×D4C2311yescharacteristic
269C24×C4C2311yescharacteristic
270C24×C4C2311yescharacteristic
271#563—232no—
272#552—216no—
273#552—216no—
274#551—232no—
275D4×Q8—216no—
276D4×Q8—216no—
277#544—28no—
278#544—216no—
279#544—216no—
280#542—216no—
281#542—216no—
282#541—216no—
283#540—216no—
284#540—216no—
285#539—216no—
286#539—216no—
287#538—28no—
288#538—28no—
289#538—216no—
290#537—28no—
291#536—216no—
292#536—44no—
293#536—48no—
294#535—216no—
295#532—216no—
296#532—216no—
297C2×C4⋊Q8C2312yes—
298C2×C4⋊Q8C2314yes—
299C2×C4⋊Q8C2312yes—
300C2×C4⋊Q8C2312yes—
301C2×C4⋊Q8C2314yes—
302C2×C4⋊Q8C2314yes—
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2314yes—
305C2×#127C2312yes—
306C2×#127C2312yes—
307#529—216no—
308#529—216no—
309C2×#126C2312yes—
310C2×#126C2312yes—
311C2×#126C2312yes—
312C2×#126C2312yes—
313C2×#126C2314yes—
314C2×#126C2314yes—
315C2×#126C2314yes—
316C2×#126C2314yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×#125C2314yes—
321C2×#125C2314yes—
322C2×#125C2314yes—
323C2×#125C2314yes—
324C2×#124C2312yes—
325C2×#124C2312yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2314yes—
331C2×#124C2312yes—
332C2×#124C2314yes—
333#525—28no—
334#525—216no—
335#525D4116yes—
336C2×#123C2314yes—
337C2×#123C2312yes—
338C2×#123C2312yes—
339C2×#123C2312yes—
340C2×#123C2312yes—
341C2×#123C2312yes—
342C2×#123C2312yes—
343C2×#123C2312yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×#123C2314yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×#123C2312yes—
352C2×C22⋊Q8—28no—
353C2×C22⋊Q8—28no—
354C2×C22⋊Q8—44no—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2311yescharacteristic
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2311yescharacteristic
364C2×C22⋊Q8C2312yes—
365C2×C22⋊Q8C2312yes—
366C2×C22⋊Q8C2312yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2312yes—
369C2×C22⋊Q8C2312yes—
370C2×C22⋊Q8C2312yes—
371C2×C22⋊Q8C2312yes—
372C2×C22⋊Q8C2312yes—
373C2×C22⋊Q8C2314yes—
374C2×C22⋊Q8C2314yes—
375C2×C22⋊Q8C2314yes—
376C2×C22⋊Q8C2314yes—
377C2×C22⋊Q8C2312yes—
378C2×C22⋊Q8C2312yes—
379C2×C22⋊Q8C2312yes—
380C2×C22⋊Q8C2312yes—
381C2×C22⋊Q8C2312yes—
382C2×C22⋊Q8C2312yes—
383C2×C22⋊Q8C2314yes—
384C2×C22⋊Q8C2311yescharacteristic
385C2×C22⋊Q8C2311yescharacteristic
386C2×#121C2311yescharacteristic
387C2×#121C2311yescharacteristic
388C2×#121C2312yes—
389C2×#121C2312yes—
390C2×#121C2312yes—
391C2×#121C2312yes—
392C2×#121C2312yes—
393C2×#121C2312yes—
394C2×#121C2312yes—
395C2×#121C2312yes—
396C2×#121C2312yes—
397C2×#121C2312yes—
398C2×#121C2312yes—
399C2×#121C2312yes—
400C2×#121C2311yescharacteristic
401C2×#121C2311yescharacteristic
402C2×#120C2312yes—
403C2×#120C2312yes—
404C2×#120C2312yes—
405C2×#120C2312yes—
406#520—44no—
407C4×#41—216no—
408C2×C4×Q8C2312yes—
409C2×C4×Q8C2312yes—
410C2×C4×Q8C2312yes—
411C2×C4×Q8C2312yes—
412C2×C4×Q8C2312yes—
413C2×C4×D4—28no—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2314yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2312yes—
421C2×C4×D4C2312yes—
422C2×C4×D4C2312yes—
423C2×C4×D4C2312yes—
424C2×C4×D4C2312yes—
425C2×C4×D4C2312yes—
426C2×C4×D4C2312yes—
427C2×C4×D4C2314yes—
428C2×C4×D4C2312yes—
429C2×C4×D4C2314yes—
430C2×C4×D4C2314yes—
431C2×C4×D4C2312yes—
432C2×C4×D4C2312yes—
433C2×#117—44no—
434C2×#117C2311yescharacteristic
435C2×#117C2312yes—
436C2×#117C2311yescharacteristic
437C2×#117C2312yes—
438C2×#117C2312yes—
439C2×#117C2314yes—
440C2×#117C2312yes—
441C2×#117C2311yescharacteristic
442C2×#117C2312yes—
443C2×#117C2312yes—
444C2×#117C2314yes—
445C2×#117C2311yescharacteristic
446C2×#117C2311yescharacteristic
447C2×#117C2312yes—
448C2×#117C2312yes—
449C2×#117C2311yescharacteristic
450C22×C4⋊C4C2311yescharacteristic
451C22×C4⋊C4C2312yes—
452C22×C4⋊C4C2312yes—
453C22×C4⋊C4C2311yescharacteristic
454C22×C4⋊C4C2312yes—
455C22×C4⋊C4C2311yescharacteristic
456C22×C4⋊C4C2311yescharacteristic
457C22×C4⋊C4C2312yes—
458C22×C4⋊C4C2311yescharacteristic
459C22×C4⋊C4C2311yescharacteristic
460C22×C4⋊C4C2311yescharacteristic
461C22×C4⋊C4C2312yes—
462C22×C22⋊C4C2312yes—
463C22×C22⋊C4C2311yescharacteristic
464C22×C22⋊C4C2311yescharacteristic
465C22×C22⋊C4C2312yes—
466C22×C22⋊C4C2312yes—
467C22×C22⋊C4C2312yes—
468C22×C22⋊C4C2312yes—
469C22×C22⋊C4C2312yes—
470C22×C42C2312yes—
471C22×C42C2311yescharacteristic
472C22×C42C2312yes—
473C22×C42C2312yes—
474#400C2314yes—
475#400C2314yes—
476#400C2314yes—
477#400C2314yes—
478#400C2314yes—
479#400C2314yes—
480#399C2314yes—
481#399C2314yes—
482#399C2314yes—
483#398C2314yes—
484#398C2314yes—
485#398C2314yes—
486#398C2314yes—
487#398C2314yes—
488#398C2314yes—
489#398C2314yes—
490#398C2314yes—
491#398C2314yes—
492#398C2314yes—
493#398C2314yes—
494#398C2314yes—
495#398C2314yes—
496#398C2314yes—
497#398C2314yes—
498#398C2314yes—
499#398C2314yes—
500#398C2314yes—
501#397C2314yes—
502#397C2314yes—
503#397C2314yes—
504#397C2314yes—
505#397C2314yes—
506#397C2314yes—
507#397C2314yes—
508#397C2314yes—
509#397C2314yes—
510#397C2314yes—
511#397C2314yes—
512#397C2314yes—
513#397C2314yes—
514#397C2314yes—
515#397C2314yes—
516#396C2314yes—
517#396C2314yes—
518#396C2314yes—
519#396C2314yes—
520#396C2314yes—
521#396C2314yes—
522#396C2314yes—
523#396C2314yes—
524#396C2314yes—
525#396C2314yes—
526#396C2314yes—
527#396C2314yes—
528#395C2314yes—
529#395C2314yes—
530#395C2314yes—
531#395C2314yes—
532#395C2314yes—
533#395C2314yes—
534#395C2314yes—
535#395C2314yes—
536#395C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2314yes—
540#394C2314yes—
541#394C2314yes—
542#394C2314yes—
543#394C2314yes—
544#394C2314yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2314yes—
549#394C2314yes—
550#394C2314yes—
551#394C2314yes—
552#394C2314yes—
553#394C2314yes—
554#394C2314yes—
555#394C2314yes—
556#394C2314yes—
557#394C2314yes—
558#393C2314yes—
559#393C2314yes—
560#393C2314yes—
561#393C2314yes—
562#391C2312yes—
563#391C2312yes—
564#391C2312yes—
565#391C2312yes—
566#391C2312yes—
567#391C2312yes—
568#391C2314yes—
569#391C2312yes—
570#391C2314yes—
571#391C2312yes—
572#391C2312yes—
573#391C2312yes—
574#391C2314yes—
575#391C2312yes—
576#391C2312yes—
577#391C2314yes—
578#391C2314yes—
579#391C2314yes—
580#390C2312yes—
581#390C2312yes—
582#390C2314yes—
583#390C2314yes—
584#390C2314yes—
585#390C2314yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2314yes—
592#389C2314yes—
593#389C2314yes—
594#389C2312yes—
595#389C2312yes—
596#389C2312yes—
597#389C2314yes—
598#389C2312yes—
599#389C2314yes—
600#389C2314yes—
601#389C2312yes—
602#389C2314yes—
603#389C2314yes—
604#389C2314yes—
605#389C2314yes—
606#389C2314yes—
607#389C2314yes—
608#389C2314yes—
609#389C2314yes—
610#389C2314yes—
611#389C2314yes—
612#389C2314yes—
613#389C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
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#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#384C2312yes—
695#384C2312yes—
696#384C2314yes—
697#382C2314yes—
698#382C2312yes—
699#382C2312yes—
700#381C2314yes—
701#381C2314yes—
702#381C2314yes—
703#381C2314yes—
704#381C2314yes—
705#380C2312yes—
706#380C2312yes—
707#380C2312yes—
708#380C2312yes—
709#380C2314yes—
710#380C2314yes—
711#380C2312yes—
712#380C2312yes—
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2314yes—
719#380C2314yes—
720#380C2314yes—
721#380C2314yes—
722#380C2314yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2314yes—
727#380C2314yes—
728#380C2314yes—
729#380C2314yes—
730#379C2314yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2314yes—
736C4×C4⋊C4C2314yes—
737C4×C4⋊C4C2314yes—
738C4×C4⋊C4C2314yes—
739C4×C4⋊C4C2314yes—
740C4×C22⋊C4C2314yes—
741C4×C22⋊C4C2314yes—
742C4×C22⋊C4C2314yes—
743C4×C22⋊C4C2314yes—
744C4×C22⋊C4C2314yes—
745C2×#95C2312yes—
746C2×#95C2312yes—
747C2×#95C2314yes—
748C2×#95C2312yes—
749C2×#95C2314yes—
750C2×#95C2312yes—
751C2×#95C2312yes—
752C25C2411yescharacteristic
753C25C2411yescharacteristic
754C2×#41—28no—
755C2×#41—24no—
756C2×#41—28no—
757C2×#41—28no—
758C2×#41—42no—
759C2×#41—42no—
760C2×#41—44no—
761C2×#41—42no—
762C2×#41—42no—
763C2×#41—44no—
764C2×#41—44no—
765C2×#41C2×D418yes—
766C22×Q8—24no—
767C22×Q8—24no—
768C22×Q8—28no—
769C22×Q8—42no—
770C22×Q8—44no—
771C22×Q8—42no—
772C22×Q8—42no—
773C22×Q8—42no—
774C22×Q8—44no—
775C22×Q8C2412yes—
776C22×Q8C2412yes—
777C22×Q8C2412yes—
778C22×Q8C2412yes—
779C22×Q8C2412yes—
780C22×Q8C2414yes—
781C22×Q8C2411yescharacteristic
782C22×Q8C2412yes—
783C22×Q8C2411yescharacteristic
784C22×D4—24no—
785C22×D4—24no—
786C22×D4—42no—
787C22×D4C2412yes—
788C22×D4C2412yes—
789C22×D4C2412yes—
790C22×D4C2412yes—
791C22×D4C2412yes—
792C22×D4C2412yes—
793C22×D4C2412yes—
794C22×D4C2412yes—
795C22×D4C2412yes—
796C22×D4C2412yes—
797C22×D4C2412yes—
798C22×D4C2412yes—
799C22×D4C2411yescharacteristic
800C22×D4C2412yes—
801C22×D4C2412yes—
802C22×D4C2411yescharacteristic
803C23×C4—24no—
804C23×C4—42no—
805C23×C4—42no—
806C23×C4—42no—
807C23×C4—42no—
808C23×C4C2×D418yes—
809C23×C4C2412yes—
810C23×C4C2412yes—
811C23×C4C2412yes—
812C23×C4C2412yes—
813C23×C4C2412yes—
814C23×C4C2412yes—
815C23×C4C2411yescharacteristic
816C23×C4C2411yescharacteristic
817C23×C4C2411yescharacteristic
818C23×C4C2412yes—
819C23×C4C2411yescharacteristic
820C23×C4C2412yes—
821C23×C4C2412yes—
822C23×C4C2411yescharacteristic
823C23×C4C2411yescharacteristic
824C23×C4C2412yes—
825C23×C4C2412yes—
826C23×C4C2412yes—
827C23×C4C2412yes—
828C23×C4C2412yes—
829C23×C4C2414yes—
830C23×C4C2412yes—
831C23×C4C2412yes—
832C23×C4C2414yes—
833C23×C4C2411yescharacteristic
834C23×C4C2411yescharacteristic
835C23×C4C2411yescharacteristic
836C4⋊Q8—28no—
837C4⋊Q8—216no—
838C4⋊Q8—28no—
839C4⋊Q8—216no—
840C4⋊Q8—216no—
841C4⋊Q8—28no—
842C4⋊Q8—44no—
843C4⋊Q8—48no—
844#127—28no—
845#127—28no—
846#126—28no—
847#126—28no—
848#126—28no—
849#126—28no—
850#126—216no—
851#126—216no—
852#126—216no—
853#126—216no—
854#125—28no—
855#125—28no—
856#125—216no—
857#125—216no—
858#125—216no—
859#125—216no—
860#125—28no—
861#124—28no—
862#124—28no—
863#124—216no—
864#124—28no—
865#124—28no—
866#124—28no—
867#124—28no—
868#124—44no—
869#124—48no—
870#123—28no—
871#123—216no—
872#123—216no—
873#123—216no—
874#123—216no—
875#123—28no—
876#123—28no—
877#123—28no—
878#123—28no—
879#123—28no—
880#123—28no—
881#123—48no—
882#123—48no—
883#123—48no—
884#123—48no—
885#123C2×D4116yes—
886C22⋊Q8—28no—
887C22⋊Q8—28no—
888C22⋊Q8—28no—
889C22⋊Q8—28no—
890C22⋊Q8—28no—
891C22⋊Q8—28no—
892C22⋊Q8—28no—
893C22⋊Q8—28no—
894C22⋊Q8—24no—
895C22⋊Q8—24no—
896C22⋊Q8—28no—
897C22⋊Q8—28no—
898C22⋊Q8—28no—
899C22⋊Q8—28no—
900C22⋊Q8—28no—
901C22⋊Q8—28no—
902C22⋊Q8—28no—
903C22⋊Q8—28no—
904C22⋊Q8—216no—
905C22⋊Q8—216no—
906C22⋊Q8—216no—
907C22⋊Q8—216no—
908C22⋊Q8—48no—
909C22⋊Q8—44no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—44no—
915C22⋊Q8C2×D418yes—
916C22⋊Q8C2×D418yes—
917#121—28no—
918#121—28no—
919#121—28no—
920#121—28no—
921#121—28no—
922#121—28no—
923#121—28no—
924#121—24no—
925#121—24no—
926#121—28no—
927#121—28no—
928#121—28no—
929#121—28no—
930#121—28no—
931#121C2×D418yes—
932#121C2×D418yes—
933#120—28no—
934#120—28no—
935#120—28no—
936#120C2×D4116yes—
937C4×Q8—28no—
938C4×Q8—28no—
939C4×Q8—28no—
940C4×Q8—28no—
941C4×Q8—44no—
942C4×D4—28no—
943C4×D4—216no—
944C4×D4—216no—
945C4×D4—28no—
946C4×D4—28no—
947C4×D4—28no—
948C4×D4—28no—
949C4×D4—28no—
950C4×D4—28no—
951C4×D4—28no—
952C4×D4—28no—
953C4×D4—28no—
954C4×D4—28no—
955C4×D4—28no—
956C4×D4—44no—
957C4×D4—48no—
958C4×D4—48no—
959C4×D4C2×D4116yes—
960C4×D4C2×D4116yes—
961#117—24no—
962#117—28no—
963#117—28no—
964#117—24no—
965#117—24no—
966#117—28no—
967#117—28no—
968#117—28no—
969#117—216no—
970#117—216no—
971#117—28no—
972#117—44no—
973#117—44no—
974#117—42no—
975#117—42no—
976#117C2×D418yes—
977C2×C4⋊C4—24no—
978C2×C4⋊C4—28no—
979C2×C4⋊C4—28no—
980C2×C4⋊C4—24no—
981C2×C4⋊C4—24no—
982C2×C4⋊C4—28no—
983C2×C4⋊C4—24no—
984C2×C4⋊C4—42no—
985C2×C4⋊C4—42no—
986C2×C4⋊C4—44no—
987C2×C4⋊C4—42no—
988C2×C4⋊C4—44no—
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2411yescharacteristic
1049C2×C4⋊C4C2411yescharacteristic
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2411yescharacteristic
1052C2×C22⋊C4—24no—
1053C2×C22⋊C4—28no—
1054C2×C22⋊C4—28no—
1055C2×C22⋊C4—24no—
1056C2×C22⋊C4—44no—
1057C2×C22⋊C4—44no—
1058C2×C22⋊C4—44no—
1059C2×C22⋊C4—44no—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C42—24no—
1115C2×C42—28no—
1116C2×C42—28no—
1117C2×C42—44no—
1118C2×C42C2414yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2414yes—
1126C2×C42C2414yes—
1127C2×C42C2414yes—
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130C2×C42C2412yes—
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2414yes—
1134C2×C42C2414yes—
1135C2×C42C2412yes—
1136#95C2414yes—
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#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176C24—22no—
1177C24—22no—
1178C24—22no—
1179C24—22no—
1180C24—22no—
1181C24—41no—
1182C24—41no—
1183C24—41no—
1184C24—41no—
1185C24—41no—
1186C24—41no—
1187C24—41no—
1188C24—41no—
1189C24C22×D414yes—
1190C24C2512yes—
1191C24C2512yes—
1192C24C2511yescharacteristic
1193C24C2511yescharacteristic
1194C24C2512yes—
1195C24C2511yescharacteristic
1196#41—416no—
1197#41—432no—
1198#41—88no—
1199#41—816no—
1200C2×Q8—24no—
1201C2×Q8—24no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—24no—
1205C2×Q8—22no—
1206C2×Q8—24no—
1207C2×Q8—28no—
1208C2×Q8—24no—
1209C2×Q8—24no—
1210C2×Q8—24no—
1211C2×Q8—24no—
1212C2×Q8—24no—
1213C2×Q8—41no—
1214C2×Q8—42no—
1215C2×Q8—41no—
1216C2×Q8—42no—
1217C2×Q8—42no—
1218C2×Q8—44no—
1219C2×Q8—41no—
1220C2×Q8—42no—
1221C2×Q8—42no—
1222C2×Q8—42no—
1223C2×Q8—44no—
1224C2×Q8—41no—
1225C2×Q8—42no—
1226C2×Q8—88no—
1227C2×Q8—88no—
1228C2×Q8—816no—
1229C2×Q8C22×D414yes—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—24no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—24no—
1245C2×D4—22no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—41no—
1250C2×D4—42no—
1251C2×D4—42no—
1252C2×D4—42no—
1253C2×D4—42no—
1254C2×D4—42no—
1255C2×D4—41no—
1256C2×D4—42no—
1257C2×D4—42no—
1258C2×D4—416no—
1259C2×D4—42no—
1260C2×D4—42no—
1261C2×D4—42no—
1262C2×D4—41no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—41no—
1271C2×D4—42no—
1272C2×D4—42no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4C22×D418yes—
1276C2×D4C22×D418yes—
1277C2×D4C22×D418yes—
1278C2×D4C22×D414yes—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—24no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—24no—
1291C22×C4—24no—
1292C22×C4—24no—
1293C22×C4—24no—
1294C22×C4—24no—
1295C22×C4—22no—
1296C22×C4—24no—
1297C22×C4—24no—
1298C22×C4—24no—
1299C22×C4—22no—
1300C22×C4—28no—
1301C22×C4—24no—
1302C22×C4—24no—
1303C22×C4—24no—
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—416no—
1315C22×C4—41no—
1316C22×C4—41no—
1317C22×C4—41no—
1318C22×C4—41no—
1319C22×C4—41no—
1320C22×C4—41no—
1321C22×C4—42no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—41no—
1329C22×C4—42no—
1330C22×C4—42no—
1331C22×C4—44no—
1332C22×C4—42no—
1333C22×C4—41no—
1334C22×C4—42no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—41no—
1338C22×C4—41no—
1339C22×C4—42no—
1340C22×C4—42no—
1341C22×C4—42no—
1342C22×C4—42no—
1343C22×C4—44no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—44no—
1347C22×C4—42no—
1348C22×C4—42no—
1349C22×C4—44no—
1350C22×C4—42no—
1351C22×C4—44no—
1352C22×C4—42no—
1353C22×C4—88no—
1354C22×C4C22×D414yes—
1355C22×C4C22×D418yes—
1356C22×C4C22×D414yes—
1357C22×C4C22×D414yes—
1358C22×C4C22×D414yes—
1359C22×C4C22×D414yes—
1360C22×C4C22×D414yes—
1361C22×C42−1+414yes—
1362C22×C4C2512yes—
1363C22×C4C2512yes—
1364C22×C4C2514yes—
1365C22×C4C2512yes—
1366C22×C4C2512yes—
1367C22×C4C2512yes—
1368C22×C4C2514yes—
1369C22×C4C2512yes—
1370C22×C4C2514yes—
1371C22×C4C2514yes—
1372C22×C4C2512yes—
1373C22×C4C2514yes—
1374C22×C4C2514yes—
1375C22×C4C2512yes—
1376C22×C4C2512yes—
1377C22×C4C2512yes—
1378C22×C4C2512yes—
1379C22×C4C2511yescharacteristic
1380C22×C4C2511yescharacteristic
1381C22×C4C2511yescharacteristic
1382C22×C4C2512yes—
1383C22×C4C2512yes—
1384C22×C4C2511yescharacteristic
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—28no—
1390C4⋊C4—28no—
1391C4⋊C4—28no—
1392C4⋊C4—28no—
1393C4⋊C4—24no—
1394C4⋊C4—24no—
1395C4⋊C4—24no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—24no—
1399C4⋊C4—24no—
1400C4⋊C4—22no—
1401C4⋊C4—24no—
1402C4⋊C4—22no—
1403C4⋊C4—24no—
1404C4⋊C4—28no—
1405C4⋊C4—28no—
1406C4⋊C4—28no—
1407C4⋊C4—28no—
1408C4⋊C4—24no—
1409C4⋊C4—24no—
1410C4⋊C4—24no—
1411C4⋊C4—28no—
1412C4⋊C4—28no—
1413C4⋊C4—28no—
1414C4⋊C4—28no—
1415C4⋊C4—24no—
1416C4⋊C4—22no—
1417C4⋊C4—22no—
1418C4⋊C4—24no—
1419C4⋊C4—22no—
1420C4⋊C4—28no—
1421C4⋊C4—28no—
1422C4⋊C4—28no—
1423C4⋊C4—28no—
1424C4⋊C4—24no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—44no—
1436C4⋊C4—44no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4—44no—
1443C4⋊C4C22×D418yes—
1444C4⋊C4C22×D414yes—
1445C4⋊C4C22×D414yes—
1446C4⋊C4C22×D418yes—
1447C4⋊C4H(5,𝔽2)14yes—
1448C22⋊C4—28no—
1449C22⋊C4—28no—
1450C22⋊C4—24no—
1451C22⋊C4—24no—
1452C22⋊C4—28no—
1453C22⋊C4—28no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—28no—
1458C22⋊C4—24no—
1459C22⋊C4—24no—
1460C22⋊C4—28no—
1461C22⋊C4—28no—
1462C22⋊C4—28no—
1463C22⋊C4—24no—
1464C22⋊C4—24no—
1465C22⋊C4—24no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—24no—
1469C22⋊C4—24no—
1470C22⋊C4—24no—
1471C22⋊C4—24no—
1472C22⋊C4—24no—
1473C22⋊C4—24no—
1474C22⋊C4—24no—
1475C22⋊C4—28no—
1476C22⋊C4—28no—
1477C22⋊C4—28no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—42no—
1482C22⋊C4—42no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—44no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4C22×D418yes—
1498C22⋊C4C22×D418yes—
1499C22⋊C4C22×D418yes—
1500C22⋊C4C22×D418yes—
1501C22⋊C4C22×D418yes—
1502C42—24no—
1503C42—24no—
1504C42—24no—
1505C42—24no—
1506C42—24no—
1507C42—24no—
1508C42—24no—
1509C42—28no—
1510C42—28no—
1511C42—28no—
1512C42—24no—
1513C42—24no—
1514C42—28no—
1515C42—42no—
1516C42—42no—
1517C42—44no—
1518C42—44no—
1519C42C22×D418yes—
1520C23—21no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—21no—
1525C23—21no—
1526C23—22no—
1527C23—22no—
1528C23—21no—
1529C23—21no—
1530C23—21no—
1531C23—22no—
1532C23—21no—
1533C23—21no—
1534C23—22no—
1535C23—21no—
1536C23—22no—
1537C23—22no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—28no—
1543C23—22no—
1544C23—22no—
1545C23—22no—
1546C23—22no—
1547C23—22no—
1548C23—22no—
1549C23—22no—
1550C23—22no—
1551C23—22no—
1552C23—22no—
1553C23—22no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—44no—
1558C23—44no—
1559C23—44no—
1560C23—44no—
1561C23—44no—
1562C23—82no—
1563C23—82no—
1564C23—82no—
1565C23—82no—
1566C23—82no—
1567C23—82no—
1568C23—82no—
1569C23—82no—
1570C23C23×D412yes—
1571C23C23×D412yes—
1572C23C23×D414yes—
1573C23C23×D412yes—
1574C23C2×2−1+412yes—
1575C23#58512yes—
1576C23C2611yescharacteristic
1577Q8—44no—
1578Q8—48no—
1579Q8—48no—
1580Q8—48no—
1581Q8—84no—
1582Q8—84no—
1583Q8—88no—
1584Q8—82no—
1585Q8—84no—
1586D4—216no—
1587D4—48no—
1588D4—44no—
1589D4—48no—
1590D4—48no—
1591D4—48no—
1592D4—48no—
1593D4—48no—
1594D4—84no—
1595D4—82no—
1596D4—84no—
1597D4—84no—
1598D4—84no—
1599D4—84no—
1600D4—84no—
1601D4—84no—
1602C2×C4—22no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—28no—
1619C2×C4—28no—
1620C2×C4—28no—
1621C2×C4—28no—
1622C2×C4—216no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—24no—
1626C2×C4—24no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—24no—
1635C2×C4—22no—
1636C2×C4—24no—
1637C2×C4—24no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—24no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—24no—
1645C2×C4—24no—
1646C2×C4—24no—
1647C2×C4—22no—
1648C2×C4—24no—
1649C2×C4—24no—
1650C2×C4—24no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—24no—
1655C2×C4—22no—
1656C2×C4—24no—
1657C2×C4—24no—
1658C2×C4—22no—
1659C2×C4—24no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—44no—
1666C2×C4—44no—
1667C2×C4—44no—
1668C2×C4—48no—
1669C2×C4—48no—
1670C2×C4—48no—
1671C2×C4—48no—
1672C2×C4—48no—
1673C2×C4—48no—
1674C2×C4—48no—
1675C2×C4—84no—
1676C2×C4—84no—
1677C2×C4—82no—
1678C2×C4—84no—
1679C2×C4—84no—
1680C2×C4—82no—
1681C2×C4—84no—
1682C2×C4—84no—
1683C2×C4—88no—
1684C2×C4—164no—
1685C2×C4—162no—
1686C2×C4—162no—
1687C2×C4C23×D414yes—
1688C2×C4C23×D414yes—
1689C2×C4C23×D414yes—
1690C2×C4C23×D412yes—
1691C2×C4C23×D412yes—
1692C2×C4C23×D412yes—
1693C2×C4C23×D412yes—
1694C2×C4C2×H(5,𝔽2)14yes—
1695C2×C4C2×H(5,𝔽2)12yes—
1696C2×C4C2×2−1+414yes—
1697C2×C4#58512yes—
1698C22—22no—
1699C22—22no—
1700C22—22no—
1701C22—22no—
1702C22—22no—
1703C22—22no—
1704C22—22no—
1705C22—22no—
1706C22—24no—
1707C22—24no—
1708C22—22no—
1709C22—22no—
1710C22—22no—
1711C22—24no—
1712C22—22no—
1713C22—42no—
1714C22—41no—
1715C22—41no—
1716C22—42no—
1717C22—41no—
1718C22—41no—
1719C22—42no—
1720C22—41no—
1721C22—41no—
1722C22—41no—
1723C22—42no—
1724C22—41no—
1725C22—42no—
1726C22—42no—
1727C22—42no—
1728C22—42no—
1729C22—42no—
1730C22—42no—
1731C22—42no—
1732C22—42no—
1733C22—42no—
1734C22—42no—
1735C22—42no—
1736C22—42no—
1737C22—42no—
1738C22—42no—
1739C22—88no—
1740C22—88no—
1741C22#348914yes—
1742C22C24×D411yescharacteristic
1743C22C22×H(5,𝔽2)11yescharacteristic
1744C22C22×2−1+411yescharacteristic
1745C22C2×#58511yescharacteristic
1746C22C2×#58511yescharacteristic
1747C222−1+611yescharacteristic
1748C222−1+611yescharacteristic
1749C4—22no—
1750C4—22no—
1751C4—22no—
1752C4—24no—
1753C4—24no—
1754C4—24no—
1755C4—24no—
1756C4—24no—
1757C4—42no—
1758C4—42no—
1759C4—44no—
1760C4—44no—
1761C4—44no—
1762C4—42no—
1763C4—44no—
1764C4—42no—
1765C4—42no—
1766C4—42no—
1767C4—42no—
1768C4—42no—
1769C4—44no—
1770C4—44no—
1771C4#349614yes—
1772C2—24no—
1773C2—44no—
1774C2—42no—
1775C2—42no—
1776C2—82no—
1777C2—82no—
1778C2C2×#349611yescharacteristic
1779C2C2×#348911yescharacteristic
1780C2#6285911yescharacteristic
1781C2#6291511yescharacteristic
1782C2#6291911yescharacteristic
1783C2#6293211yescharacteristic
1784C2#6293411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3460C2
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×#3538C2semidirect
3. #49586C2semidirect
4. #49581C2semidirect
5. #47454C2semidirect
6. #46374C2semidirect
7. #43905C2semidirect
8. #43490C2semidirect
9. #39463C2semidirect
10. #39423C2semidirect
11. #39413C2semidirect
12. #39371C2semidirect
13. #39368C2semidirect
14. #39343C2semidirect
15. #38048C2semidirect
16. #38027C2semidirect
17. #37837C2semidirect
18. #37651C2semidirect
19. #37442C2semidirect
20. #37378C2semidirect
21. #37376C2semidirect
22. #36375C2semidirect
23. #36274C2semidirect
24. #35635C2semidirect
25. #35621C2semidirect
26. #35306C2semidirect
27. #35010C2semidirect
28. C2×#2415C2semidirect
29. #34202C2semidirect
31. C2×#563C22semidirect
33. C2×#552C22semidirect
36. C2×D4×Q8C22semidirect
40. C2×#544C22semidirect
43. C2×#541C22semidirect
47. C2×#539C22semidirect
52. C2×#536C22semidirect
53. C2×#536C22semidirect
54. C2×#536C22semidirect
66. C2×#520C22semidirect
71. #2857C22semidirect
73. #2855C22semidirect
74. #2855C22semidirect
75. #2851C22semidirect
78. #2814C22semidirect
79. #2734C22semidirect
80. #2731C22semidirect
81. #2726C22semidirect
82. #2725C22semidirect
83. #2724C22semidirect
84. #2722C22semidirect
85. #2718C22semidirect
86. #2717C22semidirect
87. #2716C22semidirect
89. #2713C22semidirect
90. #2713C22semidirect
91. #2711C22semidirect
94. #2708C22semidirect
95. #2707C22semidirect
96. #2707C22semidirect
97. #2704C22semidirect
98. #2704C22semidirect
100. #2701C22semidirect
101. #2701C22semidirect
103. #2698C22semidirect
104. #2698C22semidirect
105. #2695C22semidirect
106. #2695C22semidirect
108. #2691C22semidirect
110. #2686C22semidirect
111. #2681C22semidirect
112. #2680C22semidirect
113. #2677C22semidirect
114. #2674C22semidirect
115. #2674C22semidirect
116. #2674C22semidirect
118. #2672C22semidirect
119. #2659C22semidirect
120. #2639C22semidirect
121. #2629C22semidirect
125. #2625C22semidirect
126. #2621C22semidirect
127. #2621C22semidirect
128. #2620C22semidirect
130. #2616C22semidirect
131. #2616C22semidirect
132. #2616C22semidirect
133. #2584C22semidirect
134. #2582C22semidirect
135. #2581C22semidirect
137. #2568C22semidirect
139. #2562C22semidirect
141. #2559C22semidirect
142. #2558C22semidirect
143. #2556C22semidirect
144. #2553C22semidirect
145. #2551C22semidirect
146. #2549C22semidirect
147. #2547C22semidirect
148. #2546C22semidirect
149. #2545C22semidirect
151. #2542C22semidirect
152. #2538C22semidirect
153. #2536C22semidirect
156. #2521C22semidirect
157. #2519C22semidirect
158. #2519C22semidirect
159. #2506C22semidirect
160. #2506C22semidirect
161. #2496C22semidirect
162. #2491C22semidirect
163. #2488C22semidirect
166. #2485C22semidirect
167. #2485C22semidirect
168. #2478C22semidirect
169. #2478C22semidirect
171. #2475C22semidirect
173. #2474C22semidirect
175. #2466C22semidirect
176. #2462C22semidirect
177. #2451C22semidirect
179. #2450C22semidirect
184. #2439C22semidirect
187. #2438C22semidirect
190. #2425C22semidirect
191. #2425C22semidirect
192. #2425C22semidirect
193. #2422C22semidirect
195. #2419C22semidirect
201. #2417C22semidirect
202. #2417C22semidirect
203. #2417C22semidirect
204. #2417C22semidirect
211. #2415C22semidirect
212. #2415C22semidirect
213. #2415C22semidirect
214. #2415C22semidirect
215. #2413C22semidirect
221. #2409C22semidirect
222. #2409C22semidirect
227. #2359C22semidirect
229. #2354C22semidirect
231. #2352C22semidirect
236. #2324C22semidirect
237. #2323C22semidirect
238. #2323C22semidirect
239. #2323C22semidirect
240. #2317C22semidirect
241. #2317C22semidirect
243. #2311C22semidirect
244. #2311C22semidirect
245. #2311C22semidirect
246. #2310C22semidirect
249. C4×C22⋊Q8C22semidirect
250. C4×C22⋊Q8C22semidirect
252. #2296C22semidirect
254. C2×#391C22semidirect
260. #2274C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35382
C2×#34602
#495862
#495812
#474542
#463742
#439052
#434902
#394632
#394232
#394132
#393712
#393682
#393432
#380482
#380272
#378372
#376512
#374422
#373782
#373762
#363752
#362742
#356352
#356212
#353062
#350102
C2×#24152
#342022