Finite Group Databasebeta

← #7685402

Subgroups — #7685402

Order 512.

7983 conjugacy classes of subgroups.

The subgroup lattice has 1039 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C22×D4×Q8C211yesmaximal, characteristic, complemented
3#59413C213yesmaximal, complemented
4#59144C213yesmaximal, complemented
5#59042C213yesmaximal, complemented
6#59027C216yesmaximal, complemented
7#45416C216yesmaximal, complemented
8#45322C216yesmaximal, complemented
9#38954C213yesmaximal, complemented
10#38911C213yesmaximal, complemented
11#37663C216yesmaximal, complemented
12#36577C211yesmaximal, characteristic, complemented
13Q8×#121C211yesmaximal, characteristic, complemented
14Q8×#120C212yesmaximal, complemented
15#36446C211yesmaximal, characteristic, complemented
16#36161C213yesmaximal, complemented
17#36129C213yesmaximal, complemented
18#35723C212yesmaximal, complemented
19#35700C212yesmaximal, complemented
20#34700C213yesmaximal
21#34311C211yesmaximal, characteristic, complemented
22#34173C212yesmaximal, complemented
23C4×D4×Q8C211yesmaximal, characteristic, complemented
24C24×Q8C2212yes—
25#3523—216no—
26C2×#557C2213yescomplemented
27C2×#557C2211yescharacteristic, complemented
28C2×#556C2213yes—
29C2×#552C2216yescomplemented
30C2×D4×Q8—216no—
31C2×D4×Q8C2216yes—
32C2×D4×Q8C2213yes—
33C2×D4×Q8C2213yes—
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2212yes—
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2212yescomplemented
39C2×D4×Q8C2212yescomplemented
40C2×#541C2216yescomplemented
41C2×#533C2213yescomplemented
42C22×C4⋊Q8C2213yes—
43C2×#529C2213yes—
44C22×C22⋊Q8C2216yes—
45C2×#519C2212yescomplemented
46C2×#519C2212yescomplemented
47C22×C4×Q8C2211yescharacteristic
48C22×C4×Q8C2211yescharacteristic, complemented
49C22×C4×D4C2213yes—
50#2862C2213yescomplemented
51#2857C2213yes—
52#2857C2213yescomplemented
53#2848C2216yes—
54#2713C22112yescomplemented
55#2704C22112yescomplemented
56#2698C22112yescomplemented
57#2698C22112yescomplemented
58#2690C22112yescomplemented
59#2689C22112yescomplemented
60#2687C22112yescomplemented
61#2625C2216yescomplemented
62#2621C2216yescomplemented
63#2582C2213yescomplemented
64#2568C2213yescomplemented
65#2568C2213yescomplemented
66#2556C22112yescomplemented
67#2550C2216yescomplemented
68#2550C2216yescomplemented
69#2547C2213yes—
70#2546C2216yescomplemented
71#2546C2213yescomplemented
72#2538C2213yes—
73#2536C2216yescomplemented
74#2499C2216yescomplemented
75#2492C2216yescomplemented
76#2489C2216yescomplemented
77#2489C2216yescomplemented
78#2485C2216yes—
79#2480C2216yes—
80#2480C22112yes—
81#2477C22112yescomplemented
82#2473C22112yes—
83#2468C2216yes—
84#2466C22112yes—
85#2457C2216yes—
86#2454C2213yes—
87#2453C2216yescomplemented
88#2451C2216yescomplemented
89#2451C2216yescomplemented
90#2447C2213yes—
91#2447C2216yes—
92#2446C2216yescomplemented
93#2446C2216yescomplemented
94#2442C2213yes—
95#2442C2216yes—
96#2442C2216yes—
97#2439C2216yescomplemented
98#2435C2213yes—
99#2434C2216yes—
100#2434C2216yescomplemented
101#2434C2216yescomplemented
102#2429C2216yescomplemented
103#2429C2216yescomplemented
104#2429C2216yescomplemented
105#2427C2213yes—
106#2423C2216yescomplemented
107#2421C2216yescomplemented
108#2420C2213yes—
109#2418C2216yes—
110#2417C2213yes—
111#2417C2216yescomplemented
112#2415C2216yes—
113#2415C2216yescomplemented
114#2409C2216yes—
115#2409C2216yescomplemented
116#2409C2216yescomplemented
117#2408C2211yescharacteristic
118#2395C2216yes—
119#2392C2216yes—
120#2367C2216yes—
121#2365C2213yescomplemented
122#2365C2213yescomplemented
123#2362C2216yescomplemented
124#2360C2216yes—
125#2360C2213yes—
126#2360C2213yescomplemented
127#2354C2213yes—
128#2352C2216yes—
129#2351C2212yescomplemented
130Q8×C4⋊C4C2211yescharacteristic, complemented
131Q8×C4⋊C4C2211yescharacteristic, complemented
132D4×C4⋊C4C2213yes—
133Q8×C22⋊C4C2216yes—
134Q8×C22⋊C4C2216yes—
135Q8×C22⋊C4C2211yescharacteristic
136Q8×C22⋊C4C2212yes—
137Q8×C22⋊C4C2212yescomplemented
138Q8×C22⋊C4C2216yescomplemented
139Q8×C22⋊C4C2216yescomplemented
140Q8×C22⋊C4C2212yescomplemented
141Q8×C22⋊C4C2212yescomplemented
142Q8×C22⋊C4C2211yescharacteristic, complemented
143Q8×C22⋊C4C2212yescomplemented
144#2323C2216yescomplemented
145#2310C2216yescomplemented
146#2310C2216yescomplemented
147C4×C4⋊Q8C2213yescomplemented
148C4×C4⋊Q8C2213yescomplemented
149C4×#124C2213yes—
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2213yes—
152C4×C22⋊Q8C2213yescomplemented
153C4×#121C2213yes—
154C4×#120C2216yes—
155#2293C2213yes—
156#2280C2216yes—
157#2280C2216yes—
158C42×Q8C2211yescharacteristic, complemented
159C42×D4C2213yes—
160C23×Q8—216no—
161C23×Q8—216no—
162C23×Q8—48no—
163C23×Q8C2312yes—
164C23×Q8C2311yescharacteristic
165C23×Q8C2316yes—
166C23×Q8C2316yes—
167C23×Q8C2316yes—
168C23×Q8C2312yes—
169C23×Q8C2311yescharacteristic
170C23×D4C2311yescharacteristic
171C24×C4C2316yes—
172#557—224no—
173#557—28no—
174#556—224no—
175#552—248no—
176D4×Q8—216no—
177D4×Q8—216no—
178D4×Q8—28no—
179D4×Q8—224no—
180D4×Q8—248no—
181D4×Q8—28no—
182D4×Q8—224no—
183D4×Q8—48no—
184D4×Q8D4116yescomplemented
185#541—248no—
186#533—224no—
187C2×C4⋊Q8—224no—
188C2×C4⋊Q8C2313yes—
189C2×C4⋊Q8C2313yes—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2316yes—
192C2×C4⋊Q8C2316yes—
193C2×C4⋊Q8C2316yes—
194C2×C4⋊Q8C2316yes—
195C2×C4⋊Q8C2316yes—
196C2×C4⋊Q8C2313yes—
197#529—224no—
198C2×#126C2316yes—
199C2×#126C23112yes—
200C2×#125C2313yes—
201C2×#125C2316yes—
202C2×#125C2316yes—
203C2×#125C23112yes—
204C2×#124C2313yes—
205C2×#124C2313yes—
206C2×#123C2316yes—
207C2×C22⋊Q8—248no—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2313yes—
211C2×C22⋊Q8C2313yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2316yes—
216C2×C22⋊Q8C23112yes—
217C2×C22⋊Q8C23112yes—
218C2×C22⋊Q8C2313yes—
219C2×C22⋊Q8C2316yes—
220C2×C22⋊Q8C2316yes—
221C2×C22⋊Q8C2316yes—
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#120C2312yes—
225#519—216no—
226#519—48no—
227C2×C4×Q8—28no—
228C2×C4×Q8—28no—
229C2×C4×Q8C2313yes—
230C2×C4×Q8C2313yes—
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2316yes—
237C2×C4×Q8C2316yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2313yes—
241C2×C4×Q8C2316yes—
242C2×C4×Q8C2313yes—
243C2×C4×Q8C2316yes—
244C2×C4×Q8C2316yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—224no—
247C2×C4×D4C2313yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2313yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2316yes—
257C2×C4×D4C2313yes—
258C2×#117C2316yes—
259C2×#117C2316yes—
260C2×#117C2316yes—
261C2×#117C2316yes—
262C2×#117C2316yes—
263C22×C4⋊C4C2313yes—
264C22×C4⋊C4C2313yes—
265C22×C4⋊C4C2316yes—
266C22×C4⋊C4C2313yes—
267C22×C22⋊C4C2316yes—
268C22×C42C2313yes—
269C22×C42C2313yes—
270#400C23112yes—
271#400C23112yes—
272#400C23112yes—
273#400C2316yes—
274#399C2316yes—
275#398C23112yes—
276#398C23112yes—
277#398C23112yes—
278#398C23112yes—
279#398C2316yes—
280#398C2316yes—
281#398C23112yes—
282#397C2316yes—
283#397C23112yes—
284#397C2316yes—
285#397C23112yes—
286#397C2316yes—
287#397C2316yes—
288#397C23112yes—
289#396C2316yes—
290#396C2316yes—
291#396C23112yes—
292#395C23112yes—
293#395C23112yes—
294#395C23112yes—
295#394C2316yes—
296#394C2316yes—
297#394C2316yes—
298#394C2312yes—
299#394C2316yes—
300#393C23112yes—
301#392C2312yes—
302#391C2313yes—
303#391C2313yes—
304#391C2316yes—
305#391C2313yes—
306#391C2316yes—
307#391C2316yes—
308#391C2316yes—
309#391C2316yes—
310#391C2316yes—
311#391C2316yes—
312#391C23112yes—
313#391C23112yes—
314#391C23112yes—
315#391C23112yes—
316#391C2313yes—
317#391C2316yes—
318#391C2316yes—
319#391C2316yes—
320#391C2316yes—
321#391C2316yes—
322#391C2313yes—
323#391C2313yes—
324#390C2313yes—
325#390C2313yes—
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#389C2313yes—
329#389C2316yes—
330#389C2316yes—
331#389C2316yes—
332#389C2316yes—
333#389C2313yes—
334#389C2316yes—
335#389C2316yes—
336#389C2316yes—
337#389C2316yes—
338#389C2316yes—
339#389C2313yes—
340#389C2313yes—
341#389C23112yes—
342#389C2313yes—
343#389C23112yes—
344#389C2313yes—
345#388C2316yes—
346#388C23112yes—
347#388C23112yes—
348#388C2316yes—
349#388C23112yes—
350#388C23112yes—
351#388C2316yes—
352#388C2316yes—
353#388C2316yes—
354#387C23112yes—
355#387C23112yes—
356#387C2316yes—
357#387C23112yes—
358#387C2316yes—
359#387C23112yes—
360#387C2316yes—
361#386C2316yes—
362#386C2316yes—
363#386C2316yes—
364#386C2316yes—
365#385C23112yes—
366#385C23112yes—
367#385C23112yes—
368#385C2316yes—
369#385C2316yes—
370#385C2316yes—
371#385C2316yes—
372#385C2316yes—
373#385C2316yes—
374#384C2313yes—
375#384C2313yes—
376#382C2313yes—
377#382C2316yes—
378#382C2316yes—
379#382C2316yes—
380#381C2316yes—
381#381C23112yes—
382#381C2316yes—
383#380C2316yes—
384#380C2316yes—
385#380C2316yes—
386#380C2313yes—
387#380C2316yes—
388#380C2316yes—
389#380C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2313yes—
394#380C2316yes—
395#380C2313yes—
396#380C2316yes—
397#380C2311yescharacteristic
398#379C2316yes—
399#379C2312yes—
400#379C2316yes—
401C4×C4⋊C4C2313yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2316yes—
411C4×C4⋊C4C2313yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C23112yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C23112yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2313yes—
424C4×C22⋊C4C2313yes—
425C43C2313yes—
426C25C2412yes—
427C22×Q8—24no—
428C22×Q8—28no—
429C22×Q8—28no—
430C22×Q8—24no—
431C22×Q8—24no—
432C22×Q8—224no—
433C22×Q8—224no—
434C22×Q8—28no—
435C22×Q8—24no—
436C22×Q8—224no—
437C22×Q8—224no—
438C22×Q8—28no—
439C22×Q8—24no—
440C22×Q8—28no—
441C22×Q8—224no—
442C22×Q8—224no—
443C22×Q8—412no—
444C22×Q8—412no—
445C22×Q8—412no—
446C22×Q8—4128no—
447C22×Q8C2×D4116yes—
448C22×Q8#4118yes—
449C22×Q8C2413yes—
450C22×Q8C2413yes—
451C22×Q8C2416yes—
452C22×Q8C24112yes—
453C22×Q8C2416yes—
454C22×Q8C2413yes—
455C22×Q8C2411yescharacteristic
456C22×D4—24no—
457C22×D4—24no—
458C22×D4—24no—
459C22×D4C2412yes—
460C22×D4C2412yes—
461C22×D4C2412yes—
462C22×D4C2411yescharacteristic
463C22×D4C2411yescharacteristic
464C22×D4C2411yescharacteristic
465C23×C4—224no—
466C23×C4—224no—
467C23×C4—412no—
468C23×C4C2413yes—
469C23×C4C2416yes—
470C23×C4C2411yescharacteristic
471C23×C4C2413yes—
472C23×C4C2416yes—
473C23×C4C2413yes—
474C23×C4C2416yes—
475C23×C4C2416yes—
476C23×C4C2416yes—
477C23×C4C2413yes—
478C23×C4C2411yescharacteristic
479C4⋊Q8—224no—
480C4⋊Q8—224no—
481C4⋊Q8—212no—
482C4⋊Q8—224no—
483C4⋊Q8—224no—
484C4⋊Q8—212no—
485C4⋊Q8—212no—
486C4⋊Q8—412no—
487C4⋊Q8C2×D4124yes—
488#126—224no—
489#126—248no—
490#125—212no—
491#125—224no—
492#125—248no—
493#125—224no—
494#124—212no—
495#124—212no—
496#123—224no—
497C22⋊Q8—224no—
498C22⋊Q8—224no—
499C22⋊Q8—212no—
500C22⋊Q8—224no—
501C22⋊Q8—224no—
502C22⋊Q8—212no—
503C22⋊Q8—212no—
504C22⋊Q8—248no—
505C22⋊Q8—224no—
506C22⋊Q8—212no—
507C22⋊Q8—248no—
508C22⋊Q8—412no—
509C22⋊Q8—412no—
510C22⋊Q8C2×D4148yes—
511#121—24no—
512#121—24no—
513#120—28no—
514C4×Q8—24no—
515C4×Q8—24no—
516C4×Q8—224no—
517C4×Q8—28no—
518C4×Q8—224no—
519C4×Q8—24no—
520C4×Q8—24no—
521C4×Q8—28no—
522C4×Q8—212no—
523C4×Q8—212no—
524C4×Q8—224no—
525C4×Q8—212no—
526C4×Q8—212no—
527C4×Q8—212no—
528C4×Q8—412no—
529C4×Q8—412no—
530C4×Q8C2×D418yes—
531C4×D4—212no—
532C4×D4—212no—
533C4×D4—224no—
534C4×D4—224no—
535C4×D4—212no—
536C4×D4—24no—
537C4×D4—212no—
538C4×D4—224no—
539C4×D4—212no—
540C4×D4—412no—
541C4×D4C2×D4124yes—
542#117—224no—
543#117—224no—
544#117—224no—
545#117—412no—
546#117—412no—
547C2×C4⋊C4—212no—
548C2×C4⋊C4—212no—
549C2×C4⋊C4—212no—
550C2×C4⋊C4—224no—
551C2×C4⋊C4C2413yes—
552C2×C4⋊C4C2413yes—
553C2×C4⋊C4C2416yes—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2416yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2416yes—
558C2×C4⋊C4C24112yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C24112yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C24112yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2413yes—
587C2×C22⋊C4—224no—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2413yes—
596C2×C22⋊C4C2413yes—
597C2×C22⋊C4C2411yescharacteristic
598C2×C22⋊C4C2413yes—
599C2×C22⋊C4C2411yescharacteristic
600C2×C22⋊C4C2413yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2412yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C42—212no—
617C2×C42—212no—
618C2×C42C2413yes—
619C2×C42C24112yes—
620C2×C42C2413yes—
621C2×C42C2416yes—
622C2×C42C2416yes—
623C2×C42C2413yes—
624C2×C42C2413yes—
625C2×C42C2413yes—
626C2×C42C2413yes—
627C2×C42C2411yescharacteristic
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2413yes—
632C2×C42C24112yes—
633C2×C42C2413yes—
634C2×C42C2413yes—
635#95C2413yes—
636#95C2413yes—
637#95C2416yes—
638#95C2413yes—
639#95C2413yes—
640#95C2413yes—
641#95C2413yes—
642#95C2416yes—
643#95C24112yes—
644#95C2416yes—
645#95C2416yes—
646#95C2416yes—
647#95C24112yes—
648#95C24112yes—
649#95C2416yes—
650#95C2416yes—
651#95C2416yes—
652#95C2416yes—
653#95C2416yes—
654#95C2416yes—
655#95C2412yes—
656#95C2416yes—
657#95C24112yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C24112yes—
662#95C24112yes—
663C24—24no—
664C24—24no—
665C24—24no—
666C24—24no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24C2512yes—
671C24C2512yes—
672C24C2511yescharacteristic
673C24C2511yescharacteristic
674C2×Q8—232no—
675C2×Q8—264no—
676C2×Q8—26no—
677C2×Q8—26no—
678C2×Q8—26no—
679C2×Q8—224no—
680C2×Q8—212no—
681C2×Q8—212no—
682C2×Q8—26no—
683C2×Q8—224no—
684C2×Q8—212no—
685C2×Q8—212no—
686C2×Q8—26no—
687C2×Q8—26no—
688C2×Q8—212no—
689C2×Q8—26no—
690C2×Q8—26no—
691C2×Q8—412no—
692C2×Q8—496no—
693C2×Q8—496no—
694C2×Q8—496no—
695C2×Q8—416no—
696C2×Q8—432no—
697C2×Q8C22×D4124yes—
698C2×Q8C22×D414yes—
699C2×Q8C2×#41112yes—
700C2×Q8C2×#4114yes—
701C2×Q8H(5,𝔽2)14yes—
702C2×D4—232no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—24no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C22×D414yes—
719C2×D42−1+414yes—
720C2×D42−1+414yes—
721C22×C4—22no—
722C22×C4—26no—
723C22×C4—212no—
724C22×C4—212no—
725C22×C4—26no—
726C22×C4—22no—
727C22×C4—212no—
728C22×C4—212no—
729C22×C4—26no—
730C22×C4—26no—
731C22×C4—22no—
732C22×C4—26no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—212no—
736C22×C4—212no—
737C22×C4—212no—
738C22×C4—26no—
739C22×C4—212no—
740C22×C4—212no—
741C22×C4—212no—
742C22×C4—26no—
743C22×C4—212no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—46no—
747C22×C4—46no—
748C22×C4—46no—
749C22×C4—43no—
750C22×C4—43no—
751C22×C4—496no—
752C22×C4C22×D4124yes—
753C22×C4C2×#41112yes—
754C22×C42−1+414yes—
755C22×C4C2513yes—
756C22×C4C2512yes—
757C22×C4C2513yes—
758C22×C4C2511yescharacteristic
759C22×C4C2511yescharacteristic
760C22×C4C2516yes—
761C22×C4C2516yes—
762C22×C4C2516yes—
763C22×C4C2513yes—
764C22×C4C2512yes—
765C22×C4C2513yes—
766C22×C4C2513yes—
767C22×C4C2513yes—
768C22×C4C2516yes—
769C22×C4C2513yes—
770C22×C4C2511yescharacteristic
771C22×C4C2511yescharacteristic
772C22×C4C2513yes—
773C22×C4C2511yescharacteristic
774C4⋊C4—26no—
775C4⋊C4—212no—
776C4⋊C4—26no—
777C4⋊C4—212no—
778C4⋊C4—26no—
779C4⋊C4—212no—
780C4⋊C4—224no—
781C4⋊C4—212no—
782C4⋊C4—212no—
783C4⋊C4—212no—
784C4⋊C4—212no—
785C4⋊C4—212no—
786C4⋊C4—212no—
787C4⋊C4—22no—
788C4⋊C4—224no—
789C4⋊C4—212no—
790C4⋊C4—26no—
791C4⋊C4—26no—
792C4⋊C4—212no—
793C4⋊C4—26no—
794C4⋊C4—212no—
795C4⋊C4—22no—
796C4⋊C4—26no—
797C4⋊C4—22no—
798C4⋊C4—26no—
799C4⋊C4—212no—
800C4⋊C4—46no—
801C4⋊C4—46no—
802C4⋊C4—46no—
803C4⋊C4—46no—
804C4⋊C4—46no—
805C4⋊C4—46no—
806C4⋊C4—412no—
807C4⋊C4C22×D4112yes—
808C4⋊C4C22×D4124yes—
809C4⋊C4C22×D4112yes—
810C22⋊C4—212no—
811C22⋊C4—24no—
812C22⋊C4—212no—
813C22⋊C4—212no—
814C22⋊C4—26no—
815C22⋊C4—26no—
816C22⋊C4—22no—
817C22⋊C4—26no—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—212no—
821C22⋊C4—212no—
822C22⋊C4—212no—
823C22⋊C4—212no—
824C22⋊C4—212no—
825C22⋊C4—212no—
826C22⋊C4—26no—
827C22⋊C4—22no—
828C22⋊C4—24no—
829C22⋊C4—24no—
830C22⋊C4—42no—
831C22⋊C4—46no—
832C22⋊C4—46no—
833C22⋊C4—42no—
834C22⋊C4—46no—
835C22⋊C4—46no—
836C22⋊C4—46no—
837C22⋊C4C22×D4124yes—
838C42—26no—
839C42—26no—
840C42—26no—
841C42—26no—
842C42—26no—
843C42—26no—
844C42—224no—
845C42—212no—
846C42—26no—
847C42—26no—
848C42—212no—
849C42—22no—
850C42—26no—
851C42—26no—
852C42—43no—
853C42—412no—
854C42C22×D4112yes—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—216no—
860C23—21no—
861C23—22no—
862C23—21no—
863C23—22no—
864C23—22no—
865C23—21no—
866C23—22no—
867C23—22no—
868C23—21no—
869C23—22no—
870C23—22no—
871C23—21no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—21no—
878C23—48no—
879C23—48no—
880C23—48no—
881C23—48no—
882C23—48no—
883C23—48no—
884C23C23×D414yes—
885C23C22×#4112yes—
886C23C2×2−1+414yes—
887C23C2×2−1+412yes—
888C23C2×2−1+412yes—
889C23C2×2−1+412yes—
890C23C2611yescharacteristic
891Q8—224no—
892Q8—248no—
893Q8—448no—
894Q8—412no—
895Q8—424no—
896Q8—412no—
897Q8#546116yes—
898D4—216no—
899D4—28no—
900D4—28no—
901D4—28no—
902D4—48no—
903D4—48no—
904C2×C4—21no—
905C2×C4—23no—
906C2×C4—21no—
907C2×C4—26no—
908C2×C4—26no—
909C2×C4—23no—
910C2×C4—21no—
911C2×C4—23no—
912C2×C4—21no—
913C2×C4—23no—
914C2×C4—224no—
915C2×C4—248no—
916C2×C4—28no—
917C2×C4—23no—
918C2×C4—21no—
919C2×C4—26no—
920C2×C4—22no—
921C2×C4—23no—
922C2×C4—23no—
923C2×C4—26no—
924C2×C4—23no—
925C2×C4—23no—
926C2×C4—26no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—23no—
930C2×C4—26no—
931C2×C4—23no—
932C2×C4—26no—
933C2×C4—23no—
934C2×C4—23no—
935C2×C4—23no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—26no—
941C2×C4—26no—
942C2×C4—23no—
943C2×C4—23no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—26no—
947C2×C4—21no—
948C2×C4—23no—
949C2×C4—26no—
950C2×C4—23no—
951C2×C4—22no—
952C2×C4—23no—
953C2×C4—424no—
954C2×C4—412no—
955C2×C4—412no—
956C2×C4—424no—
957C2×C4—424no—
958C2×C4—424no—
959C2×C4—412no—
960C2×C4—44no—
961C2×C4C23×D416yes—
962C2×C4C23×D4112yes—
963C2×C4C23×D416yes—
964C2×C4C23×D412yes—
965C2×C4C22×#4116yes—
966C2×C4C22×#4116yes—
967C2×C4C2×H(5,𝔽2)16yes—
968C2×C4C2×2−1+412yes—
969C2×C4C2×2−1+412yes—
970C2×C4C2×2−1+412yes—
971C2×C4C2×2−1+412yes—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—24no—
980C22—24no—
981C22—22no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—22no—
986C22—24no—
987C22—432no—
988C22—42no—
989C22—41no—
990C22—42no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—41no—
1000C22#352314yescomplemented
1001C22C24×D411yescharacteristic
1002C22C23×#4111yescharacteristic
1003C22C22×H(5,𝔽2)11yescharacteristic
1004C22C22×2−1+411yescharacteristic
1005C22C22×2−1+411yescharacteristic
1006C22C22×2−1+411yescharacteristic
1007C222−1+611yescharacteristic
1008C4—26no—
1009C4—22no—
1010C4—22no—
1011C4—26no—
1012C4—212no—
1013C4—43no—
1014C4—43no—
1015C4—42no—
1016C4—43no—
1017C4—43no—
1018C4—42no—
1019C4—41no—
1020C4—46no—
1021C4—41no—
1022C4—46no—
1023C4—46no—
1024C4—43no—
1025C4C2×#546112yes—
1026C4#348614yes—
1027C2—24no—
1028C2—42no—
1029C2—44no—
1030C2—44no—
1031C2C22×#54611yescharacteristic
1032C2C2×#348611yescharacteristic
1033C2C2×#352311yescharacteristic
1034C2#6291311yescharacteristic
1035C2D4×2−1+411yescharacteristic
1036C2#6299811yescharacteristic
1037C2#6301611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2408C22
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×#3523C2semidirect
2. C22×D4×Q8C2semidirect
3. #59413C2semidirect
4. #59144C2semidirect
5. #59042C2semidirect
6. #59027C2semidirect
7. #45416C2semidirect
8. #45322C2semidirect
9. #38954C2semidirect
10. #38911C2semidirect
11. #37663C2semidirect
12. #36577C2semidirect
13. Q8×#121C2semidirect
14. Q8×#120C2semidirect
15. #36446C2semidirect
16. #36161C2semidirect
17. #36129C2semidirect
18. #35723C2semidirect
19. #35700C2semidirect
21. #34311C2semidirect
22. #34173C2semidirect
23. C4×D4×Q8C2semidirect
26. C2×#557C22semidirect
27. C2×#557C22semidirect
29. C2×#552C22semidirect
38. C2×D4×Q8C22semidirect
39. C2×D4×Q8C22semidirect
40. C2×#541C22semidirect
41. C2×#533C22semidirect
45. C2×#519C22semidirect
46. C2×#519C22semidirect
48. C22×C4×Q8C22semidirect
50. #2862C22semidirect
52. #2857C22semidirect
54. #2713C22semidirect
55. #2704C22semidirect
56. #2698C22semidirect
57. #2698C22semidirect
58. #2690C22semidirect
59. #2689C22semidirect
60. #2687C22semidirect
61. #2625C22semidirect
62. #2621C22semidirect
63. #2582C22semidirect
64. #2568C22semidirect
65. #2568C22semidirect
66. #2556C22semidirect
67. #2550C22semidirect
68. #2550C22semidirect
70. #2546C22semidirect
71. #2546C22semidirect
73. #2536C22semidirect
74. #2499C22semidirect
75. #2492C22semidirect
76. #2489C22semidirect
77. #2489C22semidirect
81. #2477C22semidirect
87. #2453C22semidirect
88. #2451C22semidirect
89. #2451C22semidirect
92. #2446C22semidirect
93. #2446C22semidirect
97. #2439C22semidirect
100. #2434C22semidirect
101. #2434C22semidirect
102. #2429C22semidirect
103. #2429C22semidirect
104. #2429C22semidirect
106. #2423C22semidirect
107. #2421C22semidirect
111. #2417C22semidirect
113. #2415C22semidirect
115. #2409C22semidirect
116. #2409C22semidirect
121. #2365C22semidirect
122. #2365C22semidirect
123. #2362C22semidirect
126. #2360C22semidirect
129. #2351C22semidirect
130. Q8×C4⋊C4C22semidirect
131. Q8×C4⋊C4C22semidirect
137. Q8×C22⋊C4C22semidirect
138. Q8×C22⋊C4C22semidirect
139. Q8×C22⋊C4C22semidirect
140. Q8×C22⋊C4C22semidirect
141. Q8×C22⋊C4C22semidirect
142. Q8×C22⋊C4C22semidirect
143. Q8×C22⋊C4C22semidirect
144. #2323C22semidirect
145. #2310C22semidirect
146. #2310C22semidirect
147. C4×C4⋊Q8C22semidirect
148. C4×C4⋊Q8C22semidirect
152. C4×C22⋊Q8C22semidirect
158. C42×Q8C22semidirect
184. D4×Q8D4semidirect
1000. C22#3523semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C22×D4×Q82
#594132
#591442
#590422
#590272
#454162
#453222
#389542
#389112
#376632
#365772
Q8×#1212
Q8×#1202
#364462
#361612
#361292
#357232
#357002
#347002
#343112
#341732
C4×D4×Q82