Finite Group Databasebeta

← #7683711

Subgroups — #7683711

Order 512.

8048 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×#3485C211yesmaximal, characteristic
3#59418C214yesmaximal, complemented
4#59416C214yesmaximal, complemented
5#59098C214yesmaximal, complemented
6#59094C214yesmaximal, complemented
7#59012C218yesmaximal, complemented
8#45335C214yesmaximal, complemented
9#45187C214yesmaximal, complemented
10#45175C214yesmaximal, complemented
11#45084C214yesmaximal, complemented
12#43930C218yesmaximal, complemented
13#35673C211yesmaximal, characteristic, complemented
14#35667C211yesmaximal, characteristic, complemented
15#35661C211yesmaximal, characteristic, complemented
16#35633C211yesmaximal, characteristic, complemented
17#35616C211yesmaximal, characteristic, complemented
18#35515C211yesmaximal, characteristic, complemented
19#34813C211yesmaximal, characteristic, complemented
20#34742C211yesmaximal, characteristic, complemented
21C2×#2432C211yesmaximal, characteristic, complemented
22#34276C211yesmaximal, characteristic, complemented
23#34258C211yesmaximal, characteristic, complemented
24#34211C211yesmaximal, characteristic, complemented
25#34174C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C23×#41C2211yescharacteristic
28#3509—216no—
29#3485—216no—
30C2×#557C2214yescomplemented
31C2×#556C2214yescomplemented
32C2×#552C2218yescomplemented
33C2×#547C2214yes—
34C2×#547C2214yes—
35C2×#546C2214yes—
36C2×#546C2214yes—
37C2×#541C2214yescomplemented
38C2×#536C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#536C2211yescharacteristic
41C2×#536C2211yescharacteristic
42C2×#534C2214yes—
43C2×#533C2211yescharacteristic, complemented
44C2×#533C2214yescomplemented
45C22×C4⋊Q8C2211yescharacteristic, complemented
46C22×#124C2211yescharacteristic
47C2×#525C2211yescharacteristic
48C2×#525C2211yescharacteristic
49C22×#123C2214yes—
50C22×C22⋊Q8C2211yescharacteristic, complemented
51C2×#520C2211yescharacteristic
52C2×#519C2211yescharacteristic, complemented
53C2×#519C2211yescharacteristic, complemented
54C2×#519C2211yescharacteristic, complemented
55C2×#518C2211yescharacteristic
56C2×C4×#41C2211yescharacteristic
57#2711C2218yescomplemented
58#2711C2218yescomplemented
59#2707C2218yescomplemented
60#2707C2218yescomplemented
61#2695C2218yescomplemented
62#2694C2218yescomplemented
63#2694C2218yescomplemented
64#2691C2218yescomplemented
65#2687C2218yescomplemented
66#2685C2218yescomplemented
67#2685C2218yescomplemented
68#2681C2218yescomplemented
69#2580C2214yescomplemented
70#2559C2218yescomplemented
71#2558C2218yescomplemented
72#2558C2218yescomplemented
73#2553C2218yescomplemented
74#2546C2212yescomplemented
75#2546C2212yescomplemented
76#2545C2212yescomplemented
77#2545C2212yescomplemented
78#2538C2214yescomplemented
79#2538C2214yescomplemented
80#2536C2214yescomplemented
81#2534C2214yescomplemented
82#2498C2218yescomplemented
83#2492C2212yescomplemented
84#2491C2212yescomplemented
85#2490C2218yescomplemented
86#2490C2212yescomplemented
87#2489C2212yescomplemented
88#2488C2214yescomplemented
89#2486C2214yescomplemented
90#2480C2218yescomplemented
91#2480C2218yescomplemented
92#2476C2218yescomplemented
93#2473C2218yescomplemented
94#2473C2218yescomplemented
95#2472C2218yescomplemented
96#2472C2214yescomplemented
97#2470C2218yescomplemented
98#2458C2218yescomplemented
99#2458C2218yescomplemented
100#2454C2214yescomplemented
101#2452C2214yescomplemented
102#2448C2214yescomplemented
103#2446C2214yescomplemented
104#2442C2218yescomplemented
105#2437C2218yescomplemented
106#2437C2218yescomplemented
107#2435C2212yescomplemented
108#2435C2212yescomplemented
109#2435C2214yescomplemented
110#2432C2212yescomplemented
111#2432C2214yescomplemented
112#2432C2214yescomplemented
113#2432C2212yescomplemented
114#2432C2214yescomplemented
115#2432C2214yescomplemented
116#2432C2214yescomplemented
117#2429C2214yescomplemented
118#2429C2214yescomplemented
119#2429C2214yescomplemented
120#2429C2214yescomplemented
121#2427C2214yescomplemented
122#2426C2218yescomplemented
123#2426C2214yescomplemented
124#2423C2212yescomplemented
125#2423C2214yescomplemented
126#2422C2212yescomplemented
127#2421C2214yescomplemented
128#2421C2212yescomplemented
129#2420C2212yescomplemented
130#2419C2214yescomplemented
131#2418C2214yescomplemented
132#2417C2214yescomplemented
133#2415C2214yescomplemented
134#2413C2214yescomplemented
135#2413C2218yescomplemented
136#2411C2218yescomplemented
137#2411C2214yescomplemented
138#2405C2218yes—
139#2398C2214yescomplemented
140#2395C2214yescomplemented
141C2×#394C2214yescomplemented
142#2367C2214yescomplemented
143#2367C2214yescomplemented
144#2362C2214yescomplemented
145#2360C2218yescomplemented
146#2360C2214yescomplemented
147#2359C2218yescomplemented
148#2342C2218yescomplemented
149#2342C2218yescomplemented
150#2341C2214yescomplemented
151#2341C2214yescomplemented
152#2341C2214yescomplemented
153#2341C2214yescomplemented
154#2341C2214yescomplemented
155D4×C22⋊C4C2218yes—
156D4×C22⋊C4C2214yescomplemented
157#2327C2212yescomplemented
158#2326C2214yescomplemented
159#2326C2212yescomplemented
160#2317C2211yescharacteristic, complemented
161#2316C2211yescharacteristic, complemented
162#2311C2211yescharacteristic
163#2311C2212yescomplemented
164#2310C2211yescharacteristic, complemented
165#2309C2211yescharacteristic
166#2309C2211yescharacteristic
167#2309C2214yescomplemented
168#2309C2212yescomplemented
169C4×C4⋊Q8C2212yescomplemented
170C4×#124C2212yescomplemented
171C4×#124C2214yescomplemented
172C4×#124C2214yescomplemented
173C4×#123C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2212yescomplemented
178#2296C2211yescharacteristic, complemented
179C2×#391C2211yescharacteristic, complemented
180C2×#390C2211yescharacteristic
181C2×#390C2212yescomplemented
182C2×#385C2214yescomplemented
183#2285C2211yescharacteristic, complemented
184#2280C2211yescharacteristic, complemented
185#2280C2211yescharacteristic, complemented
186#2280C2214yescomplemented
187C4×#117C2211yescharacteristic, complemented
188C2×C4×C22⋊C4C2211yescharacteristic, complemented
189C2×H(5,𝔽2)—28no—
190C2×H(5,𝔽2)—28no—
191C2×H(5,𝔽2)—44no—
192C22×#41—28no—
193C22×#41—28no—
194C22×#41—44no—
195C22×#41C2311yescharacteristic
196C22×#41C2314yes—
197C22×#41C2314yes—
198C22×#41C2312yes—
199C22×#41C2312yes—
200C22×#41C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×D4C2312yes—
204C23×D4C2312yes—
205C23×D4C2314yes—
206C23×D4C2312yes—
207C23×D4C2311yescharacteristic
208C24×C4C2311yescharacteristic
209C24×C4C2312yes—
210#557—232no—
211#556—232no—
212#552—264no—
213#547—232no—
214#547—232no—
215#546—232no—
216#546—232no—
217#541—232no—
218#536—28no—
219#536—28no—
220#536—44no—
221#536D4116yes—
222#534—232no—
223#533—232no—
224#533—28no—
225C2×C4⋊Q8—28no—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×#126C2318yes—
235C2×#126C2318yes—
236C2×#125C2312yes—
237C2×#125C2318yes—
238C2×#125C2318yes—
239C2×#125C2318yes—
240C2×#124—28no—
241C2×#124C2312yes—
242C2×#124C2314yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2314yes—
248C2×#124C2312yes—
249#525—28no—
250#525—28no—
251C2×#123—232no—
252C2×#123C2314yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2318yes—
257C2×#123C2318yes—
258C2×#123C2318yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×C22⋊Q8—44no—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2318yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2318yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2318yes—
278C2×#121C2318yes—
279C2×#120C2312yes—
280C2×#120C2318yes—
281C2×#120C2312yes—
282#520—44no—
283#519—28no—
284#519—28no—
285#519—44no—
286#518—28no—
287C4×#41—28no—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2314yes—
293C2×C4×Q8C2318yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2312yes—
313C2×#117C2314yes—
314C2×#117C2311yescharacteristic
315C2×#117C2314yes—
316C2×#117C2318yes—
317C2×#117C2314yes—
318C2×#117C2312yes—
319C2×#117C2311yescharacteristic
320C22×C4⋊C4C2311yescharacteristic
321C22×C4⋊C4C2318yes—
322C22×C4⋊C4C2314yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C22⋊C4C2314yes—
326C22×C22⋊C4C2314yes—
327C22×C22⋊C4C2318yes—
328C22×C22⋊C4C2314yes—
329C22×C22⋊C4C2318yes—
330C22×C22⋊C4C2312yes—
331C22×C22⋊C4C2312yes—
332C22×C42C2311yescharacteristic
333C22×C42C2312yes—
334C22×C42C2311yescharacteristic
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2318yes—
339#399C2318yes—
340#399C2314yes—
341#399C2318yes—
342#398C2314yes—
343#398C2318yes—
344#398C2318yes—
345#398C2318yes—
346#398C2318yes—
347#398C2318yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2318yes—
354#397C2318yes—
355#396C2318yes—
356#396C2318yes—
357#396C2318yes—
358#396C2318yes—
359#396C2318yes—
360#396C2318yes—
361#396C2318yes—
362#394C2318yes—
363#394C2318yes—
364#394C2318yes—
365#394C2318yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2318yes—
371#394C2318yes—
372#394C2318yes—
373#394C2318yes—
374#394C2318yes—
375#394C2318yes—
376#393C2318yes—
377#393C2314yes—
378#393C2314yes—
379#391C2311yescharacteristic
380#391C2312yes—
381#391C2314yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2311yescharacteristic
386#391C2312yes—
387#391C2311yescharacteristic
388#391C2314yes—
389#391C2314yes—
390#391C2312yes—
391#391C2311yescharacteristic
392#390C2312yes—
393#390C2312yes—
394#390C2312yes—
395#390C2314yes—
396#390C2314yes—
397#390C2312yes—
398#390C2311yescharacteristic
399#390C2312yes—
400#390C2312yes—
401#390C2318yes—
402#390C2318yes—
403#390C2318yes—
404#390C2318yes—
405#390C2318yes—
406#390C2314yes—
407#390C2311yescharacteristic
408#390C2318yes—
409#390C2318yes—
410#390C2311yescharacteristic
411#390C2314yes—
412#390C2312yes—
413#390C2312yes—
414#390C2311yescharacteristic
415#389C2318yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2312yes—
420#389C2318yes—
421#389C2318yes—
422#389C2318yes—
423#389C2318yes—
424#389C2312yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2314yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#387C2318yes—
445#387C2318yes—
446#387C2314yes—
447#387C2318yes—
448#387C2314yes—
449#387C2318yes—
450#386C2314yes—
451#386C2318yes—
452#386C2314yes—
453#386C2318yes—
454#386C2314yes—
455#386C2314yes—
456#386C2318yes—
457#386C2314yes—
458#385C2314yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2314yes—
468#385C2314yes—
469#385C2318yes—
470#385C2318yes—
471#385C2318yes—
472#384C2312yes—
473#384C2312yes—
474#382C2312yes—
475#382C2312yes—
476#382C2314yes—
477#381C2314yes—
478#381C2314yes—
479#381C2312yes—
480#381C2312yes—
481#380C2314yes—
482#380C2318yes—
483#380C2314yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2318yes—
489#380C2318yes—
490#380C2314yes—
491#380C2318yes—
492#380C2318yes—
493#379C2314yes—
494#379C2314yes—
495#379C2312yes—
496#379C2312yes—
497#379C2318yes—
498#379C2318yes—
499#379C2318yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523#376C2312yes—
524C2×#95C2314yes—
525C2×#95C2312yes—
526C43C2312yes—
527C25C2411yescharacteristic
528C25C2414yes—
529C25C2412yes—
530H(5,𝔽2)—464no—
531C2×#41—216no—
532C2×#41—216no—
533C2×#41—28no—
534C2×#41—216no—
535C2×#41—216no—
536C2×#41—28no—
537C2×#41—28no—
538C2×#41—24no—
539C2×#41—28no—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—24no—
544C2×#41—48no—
545C2×#41—48no—
546C2×#41—44no—
547C2×#41—44no—
548C2×#41—464no—
549C2×#41C2×D418yes—
550C22×Q8—24no—
551C22×Q8—24no—
552C22×Q8—24no—
553C22×Q8—24no—
554C22×Q8—24no—
555C22×Q8C2×D418yes—
556C22×Q8C2412yes—
557C22×Q8C2412yes—
558C22×Q8C2411yescharacteristic
559C22×Q8C2414yes—
560C22×Q8C2412yes—
561C22×Q8C2412yes—
562C22×Q8C2411yescharacteristic
563C22×D4—28no—
564C22×D4—216no—
565C22×D4—216no—
566C22×D4—28no—
567C22×D4—28no—
568C22×D4—28no—
569C22×D4—24no—
570C22×D4—28no—
571C22×D4—28no—
572C22×D4—24no—
573C22×D4—44no—
574C22×D4—44no—
575C22×D4—44no—
576C22×D4—48no—
577C22×D4#4118yes—
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2418yes—
581C22×D4C2414yes—
582C22×D4C2414yes—
583C22×D4C2412yes—
584C22×D4C2411yescharacteristic
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2414yes—
588C22×D4C2414yes—
589C23×C4—28no—
590C23×C4—28no—
591C23×C4—24no—
592C23×C4—24no—
593C23×C4—24no—
594C23×C4—44no—
595C23×C4C2412yes—
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2414yes—
602C23×C4C2418yes—
603C23×C4C2414yes—
604C23×C4C2412yes—
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2418yes—
609C23×C4C2414yes—
610C23×C4C2411yescharacteristic
611C4⋊Q8—28no—
612C4⋊Q8—28no—
613C4⋊Q8—216no—
614C4⋊Q8—28no—
615C4⋊Q8—28no—
616C4⋊Q8—28no—
617C4⋊Q8—44no—
618C4⋊Q8C2×D4116yes—
619#126—232no—
620#126—232no—
621#125—28no—
622#125—232no—
623#125—232no—
624#125—232no—
625#124—28no—
626#124—28no—
627#124—28no—
628#124—216no—
629#124—28no—
630#124—44no—
631#124—48no—
632#124C2×D4116yes—
633#123—28no—
634#123—216no—
635#123—216no—
636#123—232no—
637#123—232no—
638#123—28no—
639#123—232no—
640#123—48no—
641#123—48no—
642#123C2×D4132yes—
643C22⋊Q8—28no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—28no—
647C22⋊Q8—216no—
648C22⋊Q8—232no—
649C22⋊Q8—416no—
650C22⋊Q8—48no—
651C22⋊Q8—48no—
652C22⋊Q8—44no—
653C22⋊Q8—44no—
654C22⋊Q8C2×D4132yes—
655#121—28no—
656#121—28no—
657#121—232no—
658#121—232no—
659#120—28no—
660#120—28no—
661#120—232no—
662C4×Q8—28no—
663C4×Q8—216no—
664C4×Q8—216no—
665C4×Q8—216no—
666C4×Q8—232no—
667C4×Q8—216no—
668C4×Q8—216no—
669C4×Q8—44no—
670C4×Q8—44no—
671C4×Q8—44no—
672C4×Q8—44no—
673C4×Q8—44no—
674C4×D4—216no—
675C4×D4—28no—
676C4×D4—216no—
677C4×D4—216no—
678C4×D4—216no—
679C4×D4—216no—
680C4×D4—44no—
681C4×D4—48no—
682#117—24no—
683#117—28no—
684#117—24no—
685#117—24no—
686#117—216no—
687#117—24no—
688#117—24no—
689#117—216no—
690#117—232no—
691#117—48no—
692#117—44no—
693#117C2×D418yes—
694C2×C4⋊C4—216no—
695C2×C4⋊C4—24no—
696C2×C4⋊C4—232no—
697C2×C4⋊C4—44no—
698C2×C4⋊C4—44no—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2418yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2418yes—
716C2×C4⋊C4C2418yes—
717C2×C4⋊C4C2418yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2418yes—
728C2×C4⋊C4C2418yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2412yes—
734C2×C22⋊C4—216no—
735C2×C22⋊C4—216no—
736C2×C22⋊C4—232no—
737C2×C22⋊C4—48no—
738C2×C22⋊C4—416no—
739C2×C22⋊C4—44no—
740C2×C22⋊C4—44no—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2418yes—
761C2×C22⋊C4C2418yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2418yes—
765C2×C22⋊C4C2418yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2418yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2418yes—
783C2×C42—24no—
784C2×C42—28no—
785C2×C42—24no—
786C2×C42C2412yes—
787C2×C42C2418yes—
788C2×C42C2418yes—
789C2×C42C2411yescharacteristic
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2414yes—
795C2×C42C2412yes—
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2412yes—
799C2×C42C2411yescharacteristic
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2412yes—
806#95C2412yes—
807#95C2412yes—
808#95C2412yes—
809#95C2412yes—
810#95C2418yes—
811#95C2418yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2418yes—
824#95C2418yes—
825#95C2418yes—
826#95C2418yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2418yes—
833C24—24no—
834C24—24no—
835C24—22no—
836C24—28no—
837C24—22no—
838C24—22no—
839C24—28no—
840C24—44no—
841C24—42no—
842C24—44no—
843C24—42no—
844C24—44no—
845C24—48no—
846C24—48no—
847C24C2×#4118yes—
848C24C2512yes—
849C24C2512yes—
850C24C2512yes—
851C24C2514yes—
852C24C2511yescharacteristic
853#41—232no—
854#41—432no—
855#41—464no—
856#41—464no—
857#41—432no—
858#41—416no—
859C2×Q8—232no—
860C2×Q8—28no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—22no—
864C2×Q8—24no—
865C2×Q8—24no—
866C2×Q8—22no—
867C2×Q8—24no—
868C2×Q8—24no—
869C2×Q8—22no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—22no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—22no—
876C2×Q8—28no—
877C2×Q8—44no—
878C2×Q8—416no—
879C2×Q8C22×D418yes—
880C2×Q8C22×D414yes—
881C2×Q8C22×D418yes—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—24no—
889C2×D4—216no—
890C2×D4—24no—
891C2×D4—28no—
892C2×D4—232no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—216no—
896C2×D4—28no—
897C2×D4—22no—
898C2×D4—28no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—22no—
905C2×D4—432no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—48no—
909C2×D4—432no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—432no—
915C2×D4—464no—
916C2×D4C22×D418yes—
917C2×D4C22×D414yes—
918C2×D4C2×#4118yes—
919C2×D4C2×#4118yes—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—24no—
927C22×C4—22no—
928C22×C4—24no—
929C22×C4—22no—
930C22×C4—216no—
931C22×C4—28no—
932C22×C4—24no—
933C22×C4—22no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—216no—
937C22×C4—28no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—216no—
950C22×C4—48no—
951C22×C4—44no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—42no—
955C22×C4—44no—
956C22×C4—48no—
957C22×C4—48no—
958C22×C4—42no—
959C22×C4—48no—
960C22×C4—44no—
961C22×C4—432no—
962C22×C4—416no—
963C22×C4C22×D418yes—
964C22×C4C22×D418yes—
965C22×C4C22×D414yes—
966C22×C4C2×#4114yes—
967C22×C4H(5,𝔽2)14yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2512yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—216no—
991C4⋊C4—216no—
992C4⋊C4—216no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—216no—
999C4⋊C4—216no—
1000C4⋊C4—216no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—28no—
1010C4⋊C4—44no—
1011C4⋊C4—48no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4C22×D4132yes—
1022C4⋊C4C22×D418yes—
1023C22⋊C4—24no—
1024C22⋊C4—28no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—28no—
1028C22⋊C4—216no—
1029C22⋊C4—216no—
1030C22⋊C4—216no—
1031C22⋊C4—24no—
1032C22⋊C4—24no—
1033C22⋊C4—28no—
1034C22⋊C4—216no—
1035C22⋊C4—216no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—216no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—42no—
1043C22⋊C4—48no—
1044C22⋊C4—42no—
1045C22⋊C4—48no—
1046C22⋊C4—48no—
1047C22⋊C4—48no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—48no—
1051C22⋊C4—44no—
1052C22⋊C4—48no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—48no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4C22×D418yes—
1064C22⋊C4C22×D4132yes—
1065C42—22no—
1066C42—24no—
1067C42—22no—
1068C42—28no—
1069C42—24no—
1070C42—216no—
1071C42—216no—
1072C42—24no—
1073C42—24no—
1074C42—22no—
1075C42—22no—
1076C42—24no—
1077C42—24no—
1078C42—24no—
1079C42—44no—
1080C42—44no—
1081C42—44no—
1082C42—44no—
1083C42—44no—
1084C42C22×D418yes—
1085C23—22no—
1086C23—22no—
1087C23—24no—
1088C23—22no—
1089C23—22no—
1090C23—24no—
1091C23—28no—
1092C23—24no—
1093C23—28no—
1094C23—24no—
1095C23—216no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—24no—
1105C23—22no—
1106C23—22no—
1107C23—24no—
1108C23—416no—
1109C23—416no—
1110C23—44no—
1111C23—44no—
1112C23—44no—
1113C23—84no—
1114C23—88no—
1115C23—84no—
1116C23—84no—
1117C23—84no—
1118C23—816no—
1119C23—816no—
1120C23—164no—
1121C23—164no—
1122C23C23×D414yes—
1123C23C23×D412yes—
1124C23C22×#4118yes—
1125C23C22×#4112yes—
1126C23C2×H(5,𝔽2)12yes—
1127C23C2611yescharacteristic
1128Q8—216no—
1129Q8—216no—
1130Q8—28no—
1131Q8—416no—
1132Q8—48no—
1133Q8—48no—
1134Q8—44no—
1135D4—216no—
1136D4—216no—
1137D4—216no—
1138D4—28no—
1139D4—416no—
1140D4—432no—
1141D4—416no—
1142D4—48no—
1143D4—44no—
1144D4—88no—
1145D4—88no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—216no—
1155C2×C4—216no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—28no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—48no—
1194C2×C4—416no—
1195C2×C4—432no—
1196C2×C4—416no—
1197C2×C4—44no—
1198C2×C4—48no—
1199C2×C4—48no—
1200C2×C4—48no—
1201C2×C4—48no—
1202C2×C4—816no—
1203C2×C4—84no—
1204C2×C4—84no—
1205C2×C4—164no—
1206C2×C4#546116yes—
1207C2×C4C23×D418yes—
1208C2×C4C23×D418yes—
1209C2×C4C23×D414yes—
1210C2×C4C23×D412yes—
1211C2×C4C23×D412yes—
1212C2×C4C22×#4112yes—
1213C2×C4C22×#4112yes—
1214C2×C4C2×H(5,𝔽2)12yes—
1215C2×C4C2×H(5,𝔽2)12yes—
1216C2×C4#58514yes—
1217C22—24no—
1218C22—24no—
1219C22—22no—
1220C22—22no—
1221C22—216no—
1222C22—28no—
1223C22—24no—
1224C22—28no—
1225C22—44no—
1226C22—48no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—44no—
1234C22—42no—
1235C22—42no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—816no—
1244C22—88no—
1245C22—1616no—
1246C22C2×#54614yes—
1247C22C24×D411yescharacteristic
1248C22C23×#4111yescharacteristic
1249C22C22×H(5,𝔽2)11yescharacteristic
1250C22C2×#58512yes—
1251C222−1+612yes—
1252C4—24no—
1253C4—28no—
1254C4—24no—
1255C4—28no—
1256C4—42no—
1257C4—42no—
1258C4—44no—
1259C4—42no—
1260C4—44no—
1261C4—44no—
1262C4—42no—
1263C4—44no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—44no—
1270C4C2×#54614yes—
1271C4C2×#54614yes—
1272C2—24no—
1273C2—48no—
1274C2—44no—
1275C2—82no—
1276C2—82no—
1277C2C22×#54611yescharacteristic
1278C2#6283611yescharacteristic
1279C2#6288711yescharacteristic
1280C2#6299112yes—
1281C2#6300212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3485C2
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×#3509C2semidirect
3. #59418C2semidirect
4. #59416C2semidirect
5. #59098C2semidirect
6. #59094C2semidirect
7. #59012C2semidirect
8. #45335C2semidirect
9. #45187C2semidirect
10. #45175C2semidirect
11. #45084C2semidirect
12. #43930C2semidirect
13. #35673C2semidirect
14. #35667C2semidirect
15. #35661C2semidirect
16. #35633C2semidirect
17. #35616C2semidirect
18. #35515C2semidirect
19. #34813C2semidirect
20. #34742C2semidirect
21. C2×#2432C2semidirect
22. #34276C2semidirect
23. #34258C2semidirect
24. #34211C2semidirect
25. #34174C2semidirect
30. C2×#557C22semidirect
31. C2×#556C22semidirect
32. C2×#552C22semidirect
37. C2×#541C22semidirect
43. C2×#533C22semidirect
44. C2×#533C22semidirect
45. C22×C4⋊Q8C22semidirect
50. C22×C22⋊Q8C22semidirect
52. C2×#519C22semidirect
53. C2×#519C22semidirect
54. C2×#519C22semidirect
57. #2711C22semidirect
58. #2711C22semidirect
59. #2707C22semidirect
60. #2707C22semidirect
61. #2695C22semidirect
62. #2694C22semidirect
63. #2694C22semidirect
64. #2691C22semidirect
65. #2687C22semidirect
66. #2685C22semidirect
67. #2685C22semidirect
68. #2681C22semidirect
69. #2580C22semidirect
70. #2559C22semidirect
71. #2558C22semidirect
72. #2558C22semidirect
73. #2553C22semidirect
74. #2546C22semidirect
75. #2546C22semidirect
76. #2545C22semidirect
77. #2545C22semidirect
78. #2538C22semidirect
79. #2538C22semidirect
80. #2536C22semidirect
81. #2534C22semidirect
82. #2498C22semidirect
83. #2492C22semidirect
84. #2491C22semidirect
85. #2490C22semidirect
86. #2490C22semidirect
87. #2489C22semidirect
88. #2488C22semidirect
89. #2486C22semidirect
90. #2480C22semidirect
91. #2480C22semidirect
92. #2476C22semidirect
93. #2473C22semidirect
94. #2473C22semidirect
95. #2472C22semidirect
96. #2472C22semidirect
97. #2470C22semidirect
98. #2458C22semidirect
99. #2458C22semidirect
100. #2454C22semidirect
101. #2452C22semidirect
102. #2448C22semidirect
103. #2446C22semidirect
104. #2442C22semidirect
105. #2437C22semidirect
106. #2437C22semidirect
107. #2435C22semidirect
108. #2435C22semidirect
109. #2435C22semidirect
110. #2432C22semidirect
111. #2432C22semidirect
112. #2432C22semidirect
113. #2432C22semidirect
114. #2432C22semidirect
115. #2432C22semidirect
116. #2432C22semidirect
117. #2429C22semidirect
118. #2429C22semidirect
119. #2429C22semidirect
120. #2429C22semidirect
121. #2427C22semidirect
122. #2426C22semidirect
123. #2426C22semidirect
124. #2423C22semidirect
125. #2423C22semidirect
126. #2422C22semidirect
127. #2421C22semidirect
128. #2421C22semidirect
129. #2420C22semidirect
130. #2419C22semidirect
131. #2418C22semidirect
132. #2417C22semidirect
133. #2415C22semidirect
134. #2413C22semidirect
135. #2413C22semidirect
136. #2411C22semidirect
137. #2411C22semidirect
139. #2398C22semidirect
140. #2395C22semidirect
141. C2×#394C22semidirect
142. #2367C22semidirect
143. #2367C22semidirect
144. #2362C22semidirect
145. #2360C22semidirect
146. #2360C22semidirect
147. #2359C22semidirect
148. #2342C22semidirect
149. #2342C22semidirect
150. #2341C22semidirect
151. #2341C22semidirect
152. #2341C22semidirect
153. #2341C22semidirect
154. #2341C22semidirect
156. D4×C22⋊C4C22semidirect
157. #2327C22semidirect
158. #2326C22semidirect
159. #2326C22semidirect
160. #2317C22semidirect
161. #2316C22semidirect
163. #2311C22semidirect
164. #2310C22semidirect
167. #2309C22semidirect
168. #2309C22semidirect
169. C4×C4⋊Q8C22semidirect
170. C4×#124C22semidirect
171. C4×#124C22semidirect
172. C4×#124C22semidirect
173. C4×#123C22semidirect
177. #2297C22semidirect
178. #2296C22semidirect
179. C2×#391C22semidirect
181. C2×#390C22semidirect
182. C2×#385C22semidirect
183. #2285C22semidirect
184. #2280C22semidirect
185. #2280C22semidirect
186. #2280C22semidirect
187. C4×#117C22semidirect
188. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#34852
#594182
#594162
#590982
#590942
#590122
#453352
#451872
#451752
#450842
#439302
#356732
#356672
#356612
#356332
#356162
#355152
#348132
#347422
C2×#24322
#342762
#342582
#342112
#341742