Finite Group Databasebeta

← #7626717

Subgroups — #7626717

Order 512.

8278 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3485C211yesmaximal, characteristic
2#34495C214yesmaximal, complemented
3#34480C214yesmaximal, complemented
4#34478C214yesmaximal, complemented
5#34476C214yesmaximal, complemented
6#34473C214yesmaximal, complemented
7#34473C214yesmaximal, complemented
8#34408C218yesmaximal, complemented
9#34376C214yesmaximal, complemented
10#34320C214yesmaximal, complemented
11#34316C214yesmaximal, complemented
12#34266C212yesmaximal, complemented
13#34258C212yesmaximal, complemented
14#34255C212yesmaximal, complemented
15#34238C214yesmaximal, complemented
16#34202C212yesmaximal, complemented
17#34136C212yesmaximal, complemented
18C2×#2341C211yesmaximal, characteristic, complemented
19C4×#536C212yesmaximal, complemented
20#34044C211yesmaximal, characteristic, complemented
21C22×H(5,𝔽2)C2211yescharacteristic
22C23×#41C2211yescharacteristic
23#3485C4132yescomplemented
24C2×#547C2214yes—
25C2×#547C2214yes—
26C2×#546C2214yes—
27C2×#546C2214yes—
28C2×#536C2212yes—
29C2×#534C2214yes—
30C2×#525C2212yes—
31C22×#123C2214yes—
32C2×#520C2212yes—
33C2×#518C2211yescharacteristic
34C2×C4×#41C2212yes—
35C22×C4×Q8C2212yescomplemented
36C22×#117C2212yescomplemented
37#2377C2218yescomplemented
38#2377C2218yescomplemented
39#2376C2218yescomplemented
40#2376C2218yescomplemented
41#2376C2218yescomplemented
42#2375C2218yescomplemented
43#2374C2218yescomplemented
44#2374C2218yescomplemented
45#2374C2218yescomplemented
46#2367C2214yescomplemented
47#2367C2214yescomplemented
48#2365C2214yescomplemented
49#2365C2214yescomplemented
50#2363C2218yescomplemented
51#2363C2212yescomplemented
52#2363C2218yescomplemented
53#2363C2212yescomplemented
54#2362C2212yescomplemented
55#2362C2214yescomplemented
56#2362C2212yescomplemented
57#2362C2214yescomplemented
58#2361C2212yescomplemented
59#2361C2212yescomplemented
60#2360C2214yescomplemented
61#2360C2212yescomplemented
62#2360C2212yescomplemented
63#2360C2214yescomplemented
64#2359C2214yescomplemented
65#2359C2218yescomplemented
66#2359C2214yescomplemented
67#2358C2218yescomplemented
68#2358C2214yescomplemented
69#2358C2214yescomplemented
70#2358C2218yescomplemented
71#2357C2214yescomplemented
72#2357C2214yescomplemented
73#2354C2214yescomplemented
74#2354C2214yescomplemented
75#2354C2214yescomplemented
76#2352C2214yescomplemented
77#2352C2214yescomplemented
78D4×C4⋊C4C2214yescomplemented
79#2345C2218yescomplemented
80#2345C2218yescomplemented
81#2342C2218yescomplemented
82#2342C2218yescomplemented
83#2342C2218yescomplemented
84#2342C2218yescomplemented
85#2341C2214yescomplemented
86#2341C2214yescomplemented
87#2341C2214yescomplemented
88#2341C2214yescomplemented
89#2341C2214yescomplemented
90#2341C2214yescomplemented
91D4×C22⋊C4C2218yes—
92D4×C22⋊C4C2218yes—
93D4×C22⋊C4C2214yescomplemented
94D4×C22⋊C4C2214yescomplemented
95#2335C2218yescomplemented
96#2335C2218yescomplemented
97#2335C2218yescomplemented
98#2335C2218yescomplemented
99#2335C2218yescomplemented
100#2335C2218yescomplemented
101#2333C2218yescomplemented
102#2333C2218yescomplemented
103#2327C2214yescomplemented
104#2326C2214yescomplemented
105#2324C2218yescomplemented
106#2324C2218yescomplemented
107#2324C2214yescomplemented
108#2323C2214yescomplemented
109#2323C2214yescomplemented
110#2323C2214yescomplemented
111#2322C2218yescomplemented
112#2322C2218yescomplemented
113#2321C2218yescomplemented
114#2321C2218yescomplemented
115#2319C2214yescomplemented
116#2319C2214yescomplemented
117#2317C2212yescomplemented
118#2316C2214yescomplemented
119#2315C2214yescomplemented
120#2313C2214yescomplemented
121#2313C2214yescomplemented
122#2312C2214yescomplemented
123#2312C2214yescomplemented
124#2311C2212yes—
125#2311C2214yescomplemented
126#2311C2214yescomplemented
127#2311C2214yescomplemented
128#2310C2211yescharacteristic, complemented
129#2310C2211yescharacteristic, complemented
130#2309C2212yes—
131#2309C2214yescomplemented
132#2308C2214yescomplemented
133C4×C4⋊Q8C2214yescomplemented
134C4×#124C2214yescomplemented
135C4×C22⋊Q8C2214yescomplemented
136C4×C22⋊Q8C2214yescomplemented
137C4×C22⋊Q8C2214yescomplemented
138C4×#123C2218yescomplemented
139C4×#123C2218yescomplemented
140C4×#121C2214yescomplemented
141#2297C2212yes—
142#2297C2214yescomplemented
143#2297C2214yescomplemented
144#2297C2214yescomplemented
145#2296C2212yescomplemented
146#2293C2214yescomplemented
147#2293C2214yescomplemented
148#2293C2214yescomplemented
149C2×#390C2212yes—
150C2×#390C2214yescomplemented
151C2×#390C2214yescomplemented
152#2290C2214yescomplemented
153#2290C2214yescomplemented
154#2280C2214yescomplemented
155C2×#380C2212yescomplemented
156C2×#380C2211yescharacteristic, complemented
157#2274C2214yescomplemented
158#2274C2212yescomplemented
159#2273C2214yescomplemented
160C42×D4C2214yescomplemented
161C4×#117C2212yescomplemented
162C2×C4×C22⋊C4C2211yescharacteristic, complemented
163C2×C4×C22⋊C4C2212yescomplemented
164C2×H(5,𝔽2)—48no—
165C2×H(5,𝔽2)C2×C4116yescomplemented
166C22×#41—48no—
167C22×#41C2×C4116yescomplemented
168C22×#41C2312yes—
169C22×#41C2314yes—
170C22×#41C2314yes—
171C22×#41C2314yes—
172C23×Q8C2311yescharacteristic
173C23×D4C2311yescharacteristic
174C23×D4C2312yes—
175C23×D4C2314yes—
176C23×D4C2314yes—
177C24×C4C2311yescharacteristic
178C24×C4C2312yes—
179#547C2×C4164yescomplemented
180#547C2×C4164yescomplemented
181#546C2×C4164yescomplemented
182#546C2×C4164yescomplemented
183#536C2×C4132yescomplemented
184#534C2×C4164yescomplemented
185C2×C4⋊Q8C2314yes—
186C2×#124C2314yes—
187#525C2×C4132yescomplemented
188C2×#123C2×C4164yescomplemented
189C2×#123C2318yes—
190C2×#123C2318yes—
191C2×#123C2318yes—
192C2×#123C2318yes—
193C2×#123C2314yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2312yes—
198C2×#121C2312yes—
199C2×#121C2318yes—
200C2×#121C2318yes—
201C2×#121C2312yes—
202C2×#120C2318yes—
203C2×#120C2314yes—
204#520—48no—
205#518C2×C4116yescomplemented
206C4×#41—48no—
207C2×C4×Q8—48no—
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2312yes—
214C2×C4×Q8C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2318yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×#117—48no—
229C2×#117C2312yes—
230C2×#117C2312yes—
231C2×#117C2314yes—
232C2×#117C2314yes—
233C2×#117C2314yes—
234C2×#117C2318yes—
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2314yes—
238C2×#117C2318yes—
239C2×#117C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2314yes—
244C22×C4⋊C4C2314yes—
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2314yes—
247C22×C22⋊C4C2314yes—
248C22×C22⋊C4C2318yes—
249C22×C22⋊C4C2314yes—
250C22×C22⋊C4C2312yes—
251C22×C22⋊C4C2318yes—
252C22×C22⋊C4C2314yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2314yes—
255C22×C22⋊C4C2314yes—
256C22×C22⋊C4C2314yes—
257C22×C42C2312yes—
258C22×C42C2314yes—
259C22×C42C2314yes—
260C22×C42C2314yes—
261#391C2314yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#391C2312yes—
267#391C2312yes—
268#390C2314yes—
269#390C2314yes—
270#390C2314yes—
271#390C2314yes—
272#390C2312yes—
273#390C2314yes—
274#390C2314yes—
275#390C2318yes—
276#390C2318yes—
277#390C2314yes—
278#390C2314yes—
279#390C2318yes—
280#390C2318yes—
281#390C2318yes—
282#390C2314yes—
283#390C2318yes—
284#390C2318yes—
285#390C2318yes—
286#390C2318yes—
287#390C2314yes—
288#390C2314yes—
289#390C2312yes—
290#389C2318yes—
291#389C2318yes—
292#389C2314yes—
293#389C2318yes—
294#389C2318yes—
295#389C2314yes—
296#389C2314yes—
297#389C2312yes—
298#389C2312yes—
299#389C2318yes—
300#389C2314yes—
301#389C2312yes—
302#389C2312yes—
303#388C2314yes—
304#388C2314yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2318yes—
328#388C2318yes—
329#388C2314yes—
330#388C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2314yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2314yes—
353#386C2314yes—
354#386C2318yes—
355#386C2318yes—
356#386C2314yes—
357#386C2318yes—
358#386C2314yes—
359#386C2314yes—
360#386C2318yes—
361#386C2314yes—
362#385C2314yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2318yes—
370#385C2314yes—
371#385C2318yes—
372#385C2314yes—
373#385C2314yes—
374#385C2314yes—
375#384C2314yes—
376#382C2314yes—
377#381C2314yes—
378#381C2314yes—
379#381C2318yes—
380#381C2318yes—
381#380C2314yes—
382#380C2314yes—
383#380C2314yes—
384#380C2314yes—
385#380C2318yes—
386#380C2318yes—
387#380C2318yes—
388#380C2314yes—
389#380C2318yes—
390#380C2314yes—
391#380C2318yes—
392#380C2314yes—
393#380C2318yes—
394#380C2314yes—
395#379C2318yes—
396#379C2318yes—
397#379C2318yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2318yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2318yes—
443C4×C22⋊C4C2314yes—
444#376C2314yes—
445C2×#95C2311yescharacteristic
446C2×#95C2311yescharacteristic
447C2×#95C2312yes—
448C43C2314yes—
449C25C2411yescharacteristic
450C25C2412yes—
451C25C2414yes—
452H(5,𝔽2)—464no—
453C2×#41—28no—
454C2×#41—28no—
455C2×#41—464no—
456C2×#41—48no—
457C2×#41—48no—
458C2×#41—48no—
459C2×#41—48no—
460C2×#41—48no—
461C2×#41—48no—
462C2×#41C22×C4116yes—
463C2×#41C22×C4132yes—
464C2×#41C22×C4132yes—
465C2×#41C22×C4132yes—
466C22×Q8—28no—
467C22×Q8C22×C418yes—
468C22×Q8C2414yes—
469C22×Q8C2412yes—
470C22×D4—28no—
471C22×D4—48no—
472C22×D4—48no—
473C22×D4—48no—
474C22×D4—416no—
475C22×D4C22×C418yes—
476C22×D4C22×C4132yes—
477C22×D4C22×C4116yes—
478C22×D4C22×C4132yes—
479C22×D4C2414yes—
480C22×D4C2412yes—
481C22×D4C2414yes—
482C22×D4C2414yes—
483C22×D4C2414yes—
484C22×D4C2418yes—
485C22×D4C2418yes—
486C23×C4—28no—
487C23×C4—48no—
488C23×C4C22×C418yes—
489C23×C4C22×C4116yes—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2414yes—
494C23×C4C2411yescharacteristic
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2418yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2414yes—
506C23×C4C2414yes—
507C23×C4C2414yes—
508C23×C4C2411yescharacteristic
509C4⋊Q8C22×C4132yes—
510#124C22×C4132yes—
511#123C22×C4132yes—
512#123C22×C4164yes—
513#123C22×C4164yes—
514#123C22×C4164yes—
515#123C22×C4164yes—
516C22⋊Q8C22×C4116yes—
517C22⋊Q8C22×C4116yes—
518C22⋊Q8C22×C4132yes—
519C22⋊Q8C22×C4132yes—
520#121C22×C4116yes—
521#121C22×C4116yes—
522#121C22×C4164yes—
523#121C22×C4164yes—
524#120C22×C4132yes—
525#120C22×C4164yes—
526C4×Q8—48no—
527C4×Q8—48no—
528C4×Q8—48no—
529C4×Q8—48no—
530C4×Q8—44no—
531C4×Q8—44no—
532C4×Q8—48no—
533C4×D4—48no—
534C4×D4—44no—
535C4×D4—44no—
536C4×D4—48no—
537C4×D4—48no—
538C4×D4—48no—
539C4×D4—48no—
540C4×D4—416no—
541C4×D4—88no—
542C4×D4C22×C4132yes—
543C4×D4C22×C4132yes—
544C4×D4C22×C4132yes—
545C4×D4C22×C4132yes—
546#117—28no—
547#117—28no—
548#117—48no—
549#117—48no—
550#117—416no—
551#117—48no—
552#117—44no—
553#117—44no—
554#117—48no—
555#117—88no—
556#117C22×C4116yes—
557C2×C4⋊C4—28no—
558C2×C4⋊C4—44no—
559C2×C4⋊C4—44no—
560C2×C4⋊C4—48no—
561C2×C4⋊C4—48no—
562C2×C4⋊C4C22×C4132yes—
563C2×C4⋊C4C22×C4132yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C22⋊C4—48no—
590C2×C22⋊C4—416no—
591C2×C22⋊C4—44no—
592C2×C22⋊C4—48no—
593C2×C22⋊C4—84no—
594C2×C22⋊C4—88no—
595C2×C22⋊C4—82no—
596C2×C22⋊C4C22×C4132yes—
597C2×C22⋊C4C22×C4132yes—
598C2×C22⋊C4C22×C4132yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C42—28no—
634C2×C42—48no—
635C2×C42—48no—
636C2×C42—48no—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2418yes—
648C2×C42C2418yes—
649C2×C42C2418yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2414yes—
653C2×C42C2418yes—
654C2×C42C2418yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657#95C2411yescharacteristic
658#95C2412yes—
659#95C2411yescharacteristic
660#95C2412yes—
661#95C2414yes—
662#95C2411yescharacteristic
663#95C2414yes—
664#95C2411yescharacteristic
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2414yes—
676#95C2418yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2418yes—
685#95C2418yes—
686#95C2414yes—
687#95C2418yes—
688#95C2414yes—
689C24—24no—
690C24—28no—
691C24—44no—
692C24—42no—
693C24—42no—
694C24—41no—
695C24—42no—
696C24—41no—
697C24—48no—
698C24—44no—
699C24—48no—
700C24—44no—
701C24C23×C418yes—
702C24C23×C414yes—
703C24C23×C4116yes—
704C24C2514yes—
705C24C2514yes—
706C24C2512yes—
707C24C2511yescharacteristic
708#41—264no—
709#41—464no—
710#41—464no—
711#41—464no—
712C2×Q8—232no—
713C2×Q8—28no—
714C2×Q8—28no—
715C2×Q8—24no—
716C2×Q8—24no—
717C2×Q8C23×C4116yes—
718C2×Q8C23×C418yes—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—232no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—464no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—432no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—44no—
736C2×D4—464no—
737C2×D4C23×C4116yes—
738C2×D4C23×C4116yes—
739C2×D4C23×C418yes—
740C2×D4C23×C4116yes—
741C2×D4C23×C4116yes—
742C2×D4C23×C4132yes—
743C2×D4C23×C4132yes—
744C22×C4—28no—
745C22×C4—24no—
746C22×C4—232no—
747C22×C4—24no—
748C22×C4—28no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—28no—
758C22×C4—48no—
759C22×C4—44no—
760C22×C4—432no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—42no—
764C22×C4—44no—
765C22×C4—48no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—42no—
771C22×C4—44no—
772C22×C4—42no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—48no—
782C22×C4—48no—
783C22×C4—48no—
784C22×C4C23×C418yes—
785C22×C4C23×C418yes—
786C22×C4C23×C4116yes—
787C22×C4C23×C414yes—
788C22×C4C23×C418yes—
789C22×C4C23×C4116yes—
790C22×C4C23×C4116yes—
791C22×C4C23×C4116yes—
792C22×C4C23×C4116yes—
793C22×C4C23×C4116yes—
794C22×C4C23×C414yes—
795C22×C4H(5,𝔽2)18yes—
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2518yes—
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2511yescharacteristic
810C22×C4C2512yes—
811C22×C4C2512yes—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—44no—
825C4⋊C4—48no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4C23×C4116yes—
832C4⋊C4C23×C4116yes—
833C4⋊C4C23×C4132yes—
834C4⋊C4C23×C4132yes—
835C4⋊C4C23×C418yes—
836C4⋊C4C23×C418yes—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—216no—
840C22⋊C4—28no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—42no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—42no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—44no—
858C22⋊C4—48no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—48no—
862C22⋊C4—44no—
863C22⋊C4C23×C4116yes—
864C22⋊C4C23×C4116yes—
865C22⋊C4C23×C4116yes—
866C22⋊C4C23×C4132yes—
867C22⋊C4C23×C4132yes—
868C22⋊C4C23×C4132yes—
869C22⋊C4C23×C4116yes—
870C22⋊C4C23×C4116yes—
871C42—24no—
872C42—24no—
873C42—24no—
874C42—24no—
875C42—28no—
876C42—28no—
877C42—28no—
878C42—44no—
879C42—44no—
880C42—44no—
881C42—44no—
882C42—48no—
883C42—48no—
884C42—44no—
885C42—48no—
886C42—48no—
887C42—44no—
888C42—48no—
889C42—44no—
890C42C23×C4116yes—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—24no—
896C23—24no—
897C23—22no—
898C23—28no—
899C23—28no—
900C23—24no—
901C23—22no—
902C23—22no—
903C23—24no—
904C23—24no—
905C23—22no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—22no—
910C23—28no—
911C23—216no—
912C23—48no—
913C23—44no—
914C23—48no—
915C23—44no—
916C23—416no—
917C23—416no—
918C23—416no—
919C23—84no—
920C23—88no—
921C23—84no—
922C23—88no—
923C23—168no—
924C23—168no—
925C23C24×C418yes—
926C23C24×C414yes—
927C23C24×C418yes—
928C23C24×C412yes—
929C23C2×H(5,𝔽2)14yes—
930C23C2611yescharacteristic
931Q8—232no—
932Q8—216no—
933D4—232no—
934D4—232no—
935D4—216no—
936D4—432no—
937D4—432no—
938D4—416no—
939D4—416no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—216no—
953C2×C4—216no—
954C2×C4—216no—
955C2×C4—232no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—416no—
981C2×C4—416no—
982C2×C4—416no—
983C2×C4—416no—
984C2×C4—416no—
985C2×C4—48no—
986C2×C4—88no—
987C2×C4—84no—
988C2×C4—88no—
989C2×C4—88no—
990C2×C4—88no—
991C2×C4—88no—
992C2×C4—168no—
993C2×C4#518116yes—
994C2×C4C24×C418yes—
995C2×C4C24×C418yes—
996C2×C4C24×C412yes—
997C2×C4C24×C412yes—
998C2×C4C24×C418yes—
999C2×C4C24×C418yes—
1000C2×C4C24×C414yes—
1001C2×C4C2×H(5,𝔽2)14yes—
1002C2×C4C2×H(5,𝔽2)14yes—
1003C2×C4#58514yes—
1004C22—22no—
1005C22—22no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—28no—
1010C22—28no—
1011C22—28no—
1012C22—24no—
1013C22—28no—
1014C22—28no—
1015C22—24no—
1016C22—28no—
1017C22—42no—
1018C22—44no—
1019C22—42no—
1020C22—48no—
1021C22—44no—
1022C22—42no—
1023C22—44no—
1024C22—44no—
1025C22—42no—
1026C22—48no—
1027C22—88no—
1028C22—816no—
1029C22—1616no—
1030C22C2×#51814yes—
1031C22C25×C411yescharacteristic
1032C22C22×H(5,𝔽2)12yes—
1033C22C2×#58512yes—
1034C22H(7,𝔽2)11yescharacteristic
1035C222−1+611yescharacteristic
1036C4—22no—
1037C4—22no—
1038C4—28no—
1039C4—28no—
1040C4—28no—
1041C4—28no—
1042C4—24no—
1043C4—42no—
1044C4—44no—
1045C4—44no—
1046C4—42no—
1047C4—44no—
1048C4—42no—
1049C4—48no—
1050C4—44no—
1051C4C2×#51818yes—
1052C2—24no—
1053C2—44no—
1054C2—48no—
1055C2—48no—
1056C2C22×#51811yescharacteristic
1057C2C4×#58511yescharacteristic
1058C2#6265411yescharacteristic
1059C2#6295412yes—
1060C2#6295512yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3485C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34495C2semidirect
3. #34480C2semidirect
4. #34478C2semidirect
5. #34476C2semidirect
6. #34473C2semidirect
7. #34473C2semidirect
8. #34408C2semidirect
9. #34376C2semidirect
10. #34320C2semidirect
11. #34316C2semidirect
12. #34266C2semidirect
13. #34258C2semidirect
14. #34255C2semidirect
15. #34238C2semidirect
16. #34202C2semidirect
17. #34136C2semidirect
18. C2×#2341C2semidirect
19. C4×#536C2semidirect
20. #34044C2semidirect
23. #3485C4semidirect
35. C22×C4×Q8C22semidirect
36. C22×#117C22semidirect
37. #2377C22semidirect
38. #2377C22semidirect
39. #2376C22semidirect
40. #2376C22semidirect
41. #2376C22semidirect
42. #2375C22semidirect
43. #2374C22semidirect
44. #2374C22semidirect
45. #2374C22semidirect
46. #2367C22semidirect
47. #2367C22semidirect
48. #2365C22semidirect
49. #2365C22semidirect
50. #2363C22semidirect
51. #2363C22semidirect
52. #2363C22semidirect
53. #2363C22semidirect
54. #2362C22semidirect
55. #2362C22semidirect
56. #2362C22semidirect
57. #2362C22semidirect
58. #2361C22semidirect
59. #2361C22semidirect
60. #2360C22semidirect
61. #2360C22semidirect
62. #2360C22semidirect
63. #2360C22semidirect
64. #2359C22semidirect
65. #2359C22semidirect
66. #2359C22semidirect
67. #2358C22semidirect
68. #2358C22semidirect
69. #2358C22semidirect
70. #2358C22semidirect
71. #2357C22semidirect
72. #2357C22semidirect
73. #2354C22semidirect
74. #2354C22semidirect
75. #2354C22semidirect
76. #2352C22semidirect
77. #2352C22semidirect
78. D4×C4⋊C4C22semidirect
79. #2345C22semidirect
80. #2345C22semidirect
81. #2342C22semidirect
82. #2342C22semidirect
83. #2342C22semidirect
84. #2342C22semidirect
85. #2341C22semidirect
86. #2341C22semidirect
87. #2341C22semidirect
88. #2341C22semidirect
89. #2341C22semidirect
90. #2341C22semidirect
93. D4×C22⋊C4C22semidirect
94. D4×C22⋊C4C22semidirect
95. #2335C22semidirect
96. #2335C22semidirect
97. #2335C22semidirect
98. #2335C22semidirect
99. #2335C22semidirect
100. #2335C22semidirect
101. #2333C22semidirect
102. #2333C22semidirect
103. #2327C22semidirect
104. #2326C22semidirect
105. #2324C22semidirect
106. #2324C22semidirect
107. #2324C22semidirect
108. #2323C22semidirect
109. #2323C22semidirect
110. #2323C22semidirect
111. #2322C22semidirect
112. #2322C22semidirect
113. #2321C22semidirect
114. #2321C22semidirect
115. #2319C22semidirect
116. #2319C22semidirect
117. #2317C22semidirect
118. #2316C22semidirect
119. #2315C22semidirect
120. #2313C22semidirect
121. #2313C22semidirect
122. #2312C22semidirect
123. #2312C22semidirect
125. #2311C22semidirect
126. #2311C22semidirect
127. #2311C22semidirect
128. #2310C22semidirect
129. #2310C22semidirect
131. #2309C22semidirect
132. #2308C22semidirect
133. C4×C4⋊Q8C22semidirect
134. C4×#124C22semidirect
135. C4×C22⋊Q8C22semidirect
136. C4×C22⋊Q8C22semidirect
137. C4×C22⋊Q8C22semidirect
138. C4×#123C22semidirect
139. C4×#123C22semidirect
140. C4×#121C22semidirect
142. #2297C22semidirect
143. #2297C22semidirect
144. #2297C22semidirect
145. #2296C22semidirect
146. #2293C22semidirect
147. #2293C22semidirect
148. #2293C22semidirect
150. C2×#390C22semidirect
151. C2×#390C22semidirect
152. #2290C22semidirect
153. #2290C22semidirect
154. #2280C22semidirect
155. C2×#380C22semidirect
156. C2×#380C22semidirect
157. #2274C22semidirect
158. #2274C22semidirect
159. #2273C22semidirect
160. C42×D4C22semidirect
161. C4×#117C22semidirect
162. C2×C4×C22⋊C4C22semidirect
163. C2×C4×C22⋊C4C22semidirect
165. C2×H(5,𝔽2)C2×C4semidirect
167. C22×#41C2×C4semidirect
179. #547C2×C4semidirect
180. #547C2×C4semidirect
181. #546C2×C4semidirect
182. #546C2×C4semidirect
183. #536C2×C4semidirect
184. #534C2×C4semidirect
187. #525C2×C4semidirect
188. C2×#123C2×C4semidirect
205. #518C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#34852
#344952
#344802
#344782
#344762
#344732
#344082
#343762
#343202
#343162
#342662
#342582
#342552
#342382
#342022
#341362
C2×#23412
C4×#5362
#340442