Finite Group Databasebeta

← #7632724

Subgroups — #7632724

Order 512.

8429 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C211yesmaximal, characteristic
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3Q8×#123C212yesmaximal, complemented
4#36483C212yesmaximal, complemented
5#36217C216yesmaximal, complemented
6#36216C216yesmaximal, complemented
7#35998C216yesmaximal, complemented
8#35987C216yesmaximal, complemented
9#35801C212yesmaximal, complemented
10#35723C212yesmaximal, complemented
11#35673C213yesmaximal, complemented
12#35672C213yesmaximal, complemented
13#35530C213yesmaximal, complemented
14#35516C213yesmaximal, complemented
15#35255C213yesmaximal, complemented
16#35182C213yesmaximal, complemented
17#34742C213yesmaximal, complemented
18C2×#2423C213yesmaximal, complemented
19#34259C211yesmaximal, characteristic, complemented
20#34250C211yesmaximal, characteristic, complemented
21#34183C211yesmaximal, characteristic, complemented
22#34175C211yesmaximal, characteristic, complemented
23C22⋊C4×#41C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C23×#41C2211yescharacteristic
26#3489—216no—
27C2×D4×Q8C2212yes—
28C2×#548C2212yes—
29C2×#547C2216yes—
30C2×#546C2216yes—
31C2×#537C2213yes—
32C2×#536C2213yes—
33C2×#525C2213yes—
34C22×C22⋊Q8C2213yes—
35C4×2−1+4—216no—
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2216yescomplemented
40C2×#520C2213yescomplemented
41C2×#519C2213yescomplemented
42C2×#519C2212yescomplemented
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2216yescomplemented
46C2×C4×#41C2213yescomplemented
47C22×C4×Q8C2213yescomplemented
48C22×C4×Q8C2212yescomplemented
49#2855C2216yescomplemented
50#2854C2216yescomplemented
51#2853C22112yescomplemented
52#2625C2216yescomplemented
53#2624C2216yescomplemented
54#2623C22112yescomplemented
55#2502C2216yescomplemented
56#2501C2216yescomplemented
57#2500C2216yescomplemented
58#2499C2216yescomplemented
59#2498C22112yescomplemented
60#2498C22112yescomplemented
61#2487C2216yes—
62#2486C2216yescomplemented
63#2485C2216yes—
64#2485C2216yescomplemented
65#2484C22112yescomplemented
66#2482C22112yes—
67#2448C2216yescomplemented
68#2448C2216yescomplemented
69#2448C2216yescomplemented
70#2448C2216yescomplemented
71#2446C2216yescomplemented
72#2446C2216yescomplemented
73#2446C2216yescomplemented
74#2446C2216yescomplemented
75#2444C22112yescomplemented
76#2443C22112yescomplemented
77#2443C22112yescomplemented
78#2443C22112yescomplemented
79#2423C2216yes—
80#2423C2216yes—
81#2423C2216yes—
82#2423C2213yes—
83#2423C2216yes—
84#2423C2216yescomplemented
85#2423C2216yescomplemented
86#2423C2213yescomplemented
87#2423C2216yescomplemented
88#2423C2216yescomplemented
89#2423C2216yescomplemented
90#2423C2216yescomplemented
91#2422C2211yescharacteristic
92#2422C2213yescomplemented
93#2422C2216yescomplemented
94#2421C2213yes—
95#2421C2216yes—
96#2421C2216yescomplemented
97#2421C2216yescomplemented
98#2421C2216yescomplemented
99#2421C2213yescomplemented
100#2420C2213yes—
101#2420C2213yescomplemented
102#2419C2216yescomplemented
103#2419C22112yescomplemented
104#2419C2216yescomplemented
105#2418C2216yes—
106#2418C22112yes—
107#2418C2216yes—
108#2395C2216yes—
109#2395C2216yescomplemented
110C2×#399C2216yes—
111C2×#398C2216yescomplemented
112#2351C2212yescomplemented
113Q8×C4⋊C4C2212yescomplemented
114Q8×C4⋊C4C2212yescomplemented
115Q8×C4⋊C4C2212yescomplemented
116#2349C2216yescomplemented
117D4×C4⋊C4C2216yescomplemented
118D4×C4⋊C4C2216yescomplemented
119D4×C4⋊C4C2216yescomplemented
120#2341C2211yescharacteristic
121#2341C2211yescharacteristic
122#2341C2212yes—
123Q8×C22⋊C4C2211yescharacteristic
124Q8×C22⋊C4C2211yescharacteristic
125Q8×C22⋊C4C2212yes—
126Q8×C22⋊C4C2212yescomplemented
127Q8×C22⋊C4C2212yescomplemented
128#2339C2213yes—
129#2339C2213yes—
130#2339C2216yes—
131#2339C2216yescomplemented
132#2339C2216yescomplemented
133D4×C22⋊C4C2213yes—
134D4×C22⋊C4C2213yes—
135D4×C22⋊C4C2216yes—
136#2317C2213yescomplemented
137#2317C2213yescomplemented
138#2317C2213yescomplemented
139#2316C2213yescomplemented
140#2311C2213yes—
141#2311C2213yes—
142#2311C2213yescomplemented
143#2310C2213yescomplemented
144C4×#123C2216yes—
145C4×#123C2216yescomplemented
146#2297C2213yes—
147#2297C2213yes—
148#2297C2213yescomplemented
149#2296C2213yescomplemented
150C2×#391C2213yescomplemented
151C2×#389C2213yescomplemented
152C2×#388C2216yes—
153C2×#387C2216yescomplemented
154#2285C2213yescomplemented
155C2×#384C2213yescomplemented
156#2280C2213yes—
157#2280C2213yes—
158C2×#380C2213yes—
159C2×C4×C22⋊C4C2213yes—
160C2×2−1+4—28no—
161C2×2−1+4—28no—
162C2×2−1+4D4116yes—
163C22×#41—28no—
164C22×#41—28no—
165C22×#41—28no—
166C22×#41C2313yes—
167C22×#41C2313yes—
168C22×#41C2311yescharacteristic
169C22×#41C2313yes—
170C22×#41C2316yes—
171C22×#41C2311yescharacteristic
172C23×Q8C2311yescharacteristic
173C23×Q8C2313yes—
174C23×Q8C2312yes—
175C23×D4C2313yes—
176C24×C4C2313yes—
177D4×Q8—216no—
178#548—216no—
179#547—248no—
180#546—248no—
181#537—224no—
182#536—224no—
183C2×C4⋊Q8C2316yes—
184C2×#124C2316yes—
185#525—224no—
186C2×#123C23112yes—
187C2×#123C2316yes—
188C2×#123C2312yes—
189C2×#123C2316yes—
190C2×#123C23112yes—
191C2×C22⋊Q8—224no—
192C2×C22⋊Q8C2316yes—
193C2×C22⋊Q8C2313yes—
194C2×C22⋊Q8C2316yes—
195C2×C22⋊Q8C2316yes—
196C2×C22⋊Q8C2316yes—
197C2×C22⋊Q8C2313yes—
198C2×#121C2316yes—
199C2×#121C2311yescharacteristic
200C2×#121C2313yes—
201C2×#121C23112yes—
202C2×#120C2316yes—
203#520—28no—
204#520—28no—
205#520—224no—
206#520—248no—
207#520—28no—
208#519—224no—
209#519—216no—
210C4×#41—28no—
211C4×#41—224no—
212C4×#41—248no—
213C4×#41—28no—
214C2×C4×Q8—224no—
215C2×C4×Q8—216no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2313yes—
224C2×C4×Q8C2316yes—
225C2×C4×Q8C2316yes—
226C2×C4×Q8C2316yes—
227C2×C4×Q8C2316yes—
228C2×C4×Q8C2313yes—
229C2×C4×Q8C2316yes—
230C2×C4×D4C2313yes—
231C2×C4×D4C2313yes—
232C2×C4×D4C2316yes—
233C2×C4×D4C2313yes—
234C2×C4×D4C2316yes—
235C2×C4×D4C2313yes—
236C2×C4×D4C2316yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2316yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C23112yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2313yes—
244C2×#117C2313yes—
245C2×#117C2313yes—
246C2×#117C2313yes—
247C2×#117C2313yes—
248C2×#117C2313yes—
249C2×#117C2316yes—
250C2×#117C23112yes—
251C2×#117C2316yes—
252C22×C4⋊C4C2313yes—
253C22×C4⋊C4C2313yes—
254C22×C4⋊C4C2313yes—
255C22×C4⋊C4C2316yes—
256C22×C4⋊C4C2316yes—
257C22×C4⋊C4C2316yes—
258C22×C4⋊C4C2316yes—
259C22×C4⋊C4C2316yes—
260C22×C4⋊C4C2316yes—
261C22×C22⋊C4C2313yes—
262C22×C22⋊C4C2316yes—
263C22×C22⋊C4C2313yes—
264C22×C22⋊C4C2316yes—
265C22×C42C2316yes—
266C22×C42C2316yes—
267C22×C42C2313yes—
268C22×C42C2313yes—
269#400C2316yes—
270#400C23112yes—
271#400C23112yes—
272#400C2316yes—
273#399C23112yes—
274#399C23112yes—
275#399C2316yes—
276#399C23112yes—
277#399C23112yes—
278#399C2316yes—
279#398C23112yes—
280#398C23112yes—
281#398C2316yes—
282#398C23112yes—
283#398C23112yes—
284#398C2316yes—
285#397C2316yes—
286#397C23112yes—
287#397C23112yes—
288#397C2316yes—
289#397C23112yes—
290#397C2316yes—
291#397C2316yes—
292#397C2312yes—
293#397C2316yes—
294#394C2316yes—
295#394C23112yes—
296#394C2312yes—
297#394C2316yes—
298#394C2316yes—
299#391C2313yes—
300#391C2316yes—
301#391C2316yes—
302#391C2316yes—
303#391C2316yes—
304#391C2316yes—
305#391C2313yes—
306#391C2313yes—
307#391C2313yes—
308#391C2313yes—
309#391C2316yes—
310#391C2316yes—
311#391C2313yes—
312#390C2316yes—
313#390C2316yes—
314#390C2313yes—
315#390C2313yes—
316#390C2313yes—
317#390C2313yes—
318#390C2313yes—
319#390C2311yescharacteristic
320#389C2313yes—
321#389C2316yes—
322#389C2316yes—
323#389C2316yes—
324#389C2313yes—
325#389C2316yes—
326#389C2316yes—
327#389C2316yes—
328#389C2316yes—
329#389C2316yes—
330#389C2316yes—
331#389C2313yes—
332#389C2311yescharacteristic
333#388C2316yes—
334#388C23112yes—
335#388C23112yes—
336#388C23112yes—
337#388C23112yes—
338#388C2316yes—
339#388C23112yes—
340#388C2316yes—
341#388C2316yes—
342#388C23112yes—
343#387C2316yes—
344#387C23112yes—
345#387C23112yes—
346#387C23112yes—
347#387C23112yes—
348#387C2316yes—
349#387C23112yes—
350#387C2316yes—
351#387C2316yes—
352#387C23112yes—
353#386C23112yes—
354#386C23112yes—
355#386C23112yes—
356#386C2316yes—
357#386C2316yes—
358#386C2316yes—
359#386C2316yes—
360#386C2316yes—
361#386C2316yes—
362#386C2316yes—
363#386C2316yes—
364#385C23112yes—
365#385C23112yes—
366#385C23112yes—
367#385C2316yes—
368#385C23112yes—
369#385C2316yes—
370#385C2312yes—
371#385C2316yes—
372#384C2316yes—
373#384C2316yes—
374#384C2316yes—
375#384C2316yes—
376#384C2311yescharacteristic
377#384C2313yes—
378#382C2313yes—
379#382C2313yes—
380#382C2316yes—
381#381C23112yes—
382#381C2316yes—
383#381C2316yes—
384#381C2316yes—
385#381C2316yes—
386#380C2313yes—
387#380C2316yes—
388#380C2313yes—
389#380C2316yes—
390#380C2316yes—
391#380C23112yes—
392#380C2313yes—
393#380C2316yes—
394#380C2313yes—
395#380C2313yes—
396#380C2316yes—
397#380C2313yes—
398#380C2316yes—
399#380C2316yes—
400#380C2313yes—
401#380C2311yescharacteristic
402#379C2316yes—
403#379C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2316yes—
408C4×C22⋊C4C2313yes—
409C4×C22⋊C4C2316yes—
410C4×C22⋊C4C2313yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2313yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2311yescharacteristic
420C4×C22⋊C4C2313yes—
421C2×#95C2313yes—
422C2×#95C2316yes—
423C2×#95C2313yes—
424C2×#95C2316yes—
425C2×#95C2316yes—
426C2×#95C2316yes—
427C25C2413yes—
4282−1+4—2128no—
429C2×#41—24no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—212no—
433C2×#41—224no—
434C2×#41—224no—
435C2×#41—212no—
436C2×#41—212no—
437C2×#41—212no—
438C2×#41—212no—
439C2×#41—212no—
440C2×#41—212no—
441C2×#41—212no—
442C2×#41—464no—
443C2×#41C2×D4124yes—
444C2×#41C2×D4148yes—
445C2×#41C2×D418yes—
446C2×#41#4118yes—
447C2×#41#4118yes—
448C22×Q8—28no—
449C22×Q8—28no—
450C22×Q8—24no—
451C22×Q8—24no—
452C22×Q8—24no—
453C22×Q8—212no—
454C22×Q8—212no—
455C22×Q8C2×D4124yes—
456C22×Q8C2×D4116yes—
457C22×Q8C2413yes—
458C22×Q8C2413yes—
459C22×Q8C2416yes—
460C22×Q8C2411yescharacteristic
461C22×D4—212no—
462C22×D4—212no—
463C22×D4—212no—
464C22×D4C2416yes—
465C22×D4C2413yes—
466C22×D4C2412yes—
467C22×D4C2416yes—
468C22×D4C2411yescharacteristic
469C22×D4C2416yes—
470C22×D4C2413yes—
471C23×C4—212no—
472C23×C4—212no—
473C23×C4—212no—
474C23×C4C2413yes—
475C23×C4C2413yes—
476C23×C4C2413yes—
477C23×C4C2411yescharacteristic
478C23×C4C2413yes—
479C23×C4C2413yes—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C2412yes—
483C23×C4C2416yes—
484C23×C4C2416yes—
485C23×C4C2416yes—
486C23×C4C2413yes—
487C23×C4C2416yes—
488C23×C4C2416yes—
489C23×C4C2416yes—
490C23×C4C2413yes—
491C4⋊Q8—224no—
492#124—224no—
493#123—224no—
494#123—248no—
495#123—28no—
496#123—412no—
497#123—812no—
498C22⋊Q8—212no—
499C22⋊Q8—224no—
500C22⋊Q8—224no—
501C22⋊Q8—224no—
502C22⋊Q8—212no—
503C22⋊Q8—224no—
504#121—24no—
505#121—212no—
506#121—248no—
507#121—224no—
508#120—224no—
509C4×Q8—212no—
510C4×Q8—224no—
511C4×Q8—24no—
512C4×Q8—224no—
513C4×Q8—224no—
514C4×Q8—224no—
515C4×Q8—28no—
516C4×Q8—212no—
517C4×Q8—224no—
518C4×Q8—24no—
519C4×Q8—28no—
520C4×Q8—24no—
521C4×Q8—24no—
522C4×Q8—28no—
523C4×D4—224no—
524C4×D4—24no—
525C4×D4—212no—
526C4×D4—248no—
527C4×D4—224no—
528C4×D4—212no—
529C4×D4—212no—
530C4×D4—224no—
531C4×D4—224no—
532C4×D4—212no—
533C4×D4—212no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—224no—
537#117—248no—
538#117—224no—
539#117—224no—
540#117—212no—
541#117—212no—
542#117—212no—
543#117—212no—
544#117—212no—
545C2×C4⋊C4—224no—
546C2×C4⋊C4—224no—
547C2×C4⋊C4—212no—
548C2×C4⋊C4—212no—
549C2×C4⋊C4—224no—
550C2×C4⋊C4—212no—
551C2×C4⋊C4—412no—
552C2×C4⋊C4—86no—
553C2×C4⋊C4—86no—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2416yes—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2416yes—
558C2×C4⋊C4C24112yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C24112yes—
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2416yes—
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C24112yes—
579C2×C4⋊C4C24112yes—
580C2×C4⋊C4C24112yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2416yes—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—212no—
586C2×C22⋊C4—46no—
587C2×C22⋊C4—86no—
588C2×C22⋊C4C2411yescharacteristic
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C24112yes—
591C2×C22⋊C4C2413yes—
592C2×C22⋊C4C2413yes—
593C2×C22⋊C4C2413yes—
594C2×C22⋊C4C2413yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C24112yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2413yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2411yescharacteristic
619C2×C42—224no—
620C2×C42—224no—
621C2×C42—212no—
622C2×C42—212no—
623C2×C42C2413yes—
624C2×C42C2416yes—
625C2×C42C2413yes—
626C2×C42C2416yes—
627C2×C42C24112yes—
628C2×C42C2413yes—
629C2×C42C2416yes—
630C2×C42C2416yes—
631C2×C42C2411yescharacteristic
632C2×C42C2413yes—
633C2×C42C2416yes—
634C2×C42C2413yes—
635C2×C42C2413yes—
636C2×C42C2411yescharacteristic
637#95C2411yescharacteristic
638#95C2411yescharacteristic
639#95C2416yes—
640#95C2416yes—
641#95C2416yes—
642#95C2416yes—
643#95C2413yes—
644#95C2413yes—
645#95C2413yes—
646#95C2413yes—
647#95C2413yes—
648#95C2413yes—
649#95C24112yes—
650#95C24112yes—
651#95C24112yes—
652#95C24112yes—
653#95C2412yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2412yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667C24—26no—
668C24—26no—
669C24—26no—
670C24—26no—
671C24—43no—
672C24—43no—
673C24—43no—
674C24C2513yes—
675C24C2512yes—
676C24C2511yescharacteristic
677C24C2513yes—
678#41—2192no—
679#41—296no—
680#41—416no—
681#41—448no—
682#41—448no—
683#41#123164yescomplemented
684C2×Q8—264no—
685C2×Q8—296no—
686C2×Q8—26no—
687C2×Q8—26no—
688C2×Q8—212no—
689C2×Q8—212no—
690C2×Q8—26no—
691C2×Q8—26no—
692C2×Q8—26no—
693C2×Q8—416no—
694C2×Q8C22×D4112yes—
695C2×Q8C22×D4124yes—
696C2×Q8C22×D414yes—
697C2×Q8C2×#4114yes—
698C2×Q8C2×#4114yes—
699C2×D4—212no—
700C2×D4—212no—
701C2×D4—24no—
702C2×D4—212no—
703C2×D4—212no—
704C2×D4—212no—
705C2×D4—24no—
706C2×D4—212no—
707C2×D4—26no—
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—26no—
711C2×D4—26no—
712C2×D4—42no—
713C2×D4—46no—
714C2×D4—46no—
715C2×D4—448no—
716C2×D4C22×D4124yes—
717C2×D4C22×D414yes—
718C2×D4C22×D4112yes—
719C2×D4C2×#41112yes—
720C2×D4C2×#41112yes—
721C22×C4—212no—
722C22×C4—212no—
723C22×C4—212no—
724C22×C4—212no—
725C22×C4—24no—
726C22×C4—26no—
727C22×C4—26no—
728C22×C4—26no—
729C22×C4—26no—
730C22×C4—26no—
731C22×C4—26no—
732C22×C4—212no—
733C22×C4—26no—
734C22×C4—212no—
735C22×C4—212no—
736C22×C4—212no—
737C22×C4—26no—
738C22×C4—26no—
739C22×C4—22no—
740C22×C4—26no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—26no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—26no—
747C22×C4—26no—
748C22×C4—26no—
749C22×C4—26no—
750C22×C4—26no—
751C22×C4—24no—
752C22×C4—26no—
753C22×C4—43no—
754C22×C4—43no—
755C22×C4—42no—
756C22×C4—43no—
757C22×C4—43no—
758C22×C4—46no—
759C22×C4—46no—
760C22×C4—46no—
761C22×C4—46no—
762C22×C4—43no—
763C22×C4—46no—
764C22×C4—46no—
765C22×C4—46no—
766C22×C4—46no—
767C22×C4—448no—
768C22×C4C22×D4124yes—
769C22×C4C22×D4124yes—
770C22×C4C22×D4112yes—
771C22×C4C2×#41112yes—
772C22×C4C2×#41112yes—
773C22×C4C2511yescharacteristic
774C22×C4C2513yes—
775C22×C4C2512yes—
776C22×C4C2513yes—
777C22×C4C2513yes—
778C22×C4C2516yes—
779C22×C4C2513yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2511yescharacteristic
783C22×C4C2513yes—
784C22×C4C2516yes—
785C22×C4C2516yes—
786C22×C4C2516yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2513yes—
791C22×C4C2511yescharacteristic
792C4⋊C4—212no—
793C4⋊C4—224no—
794C4⋊C4—26no—
795C4⋊C4—212no—
796C4⋊C4—26no—
797C4⋊C4—26no—
798C4⋊C4—212no—
799C4⋊C4—212no—
800C4⋊C4—224no—
801C4⋊C4—212no—
802C4⋊C4—26no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—212no—
806C4⋊C4—26no—
807C4⋊C4—212no—
808C4⋊C4—22no—
809C4⋊C4—26no—
810C4⋊C4—26no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—212no—
814C4⋊C4—412no—
815C4⋊C4—46no—
816C4⋊C4—46no—
817C4⋊C4—412no—
818C4⋊C4—412no—
819C4⋊C4—42no—
820C4⋊C4—46no—
821C4⋊C4—46no—
822C22⋊C4—24no—
823C22⋊C4—212no—
824C22⋊C4—212no—
825C22⋊C4—212no—
826C22⋊C4—212no—
827C22⋊C4—24no—
828C22⋊C4—212no—
829C22⋊C4—212no—
830C22⋊C4—212no—
831C22⋊C4—26no—
832C22⋊C4—24no—
833C22⋊C4—212no—
834C22⋊C4—224no—
835C22⋊C4—212no—
836C22⋊C4—26no—
837C22⋊C4—26no—
838C22⋊C4—24no—
839C22⋊C4—22no—
840C22⋊C4—26no—
841C22⋊C4—24no—
842C22⋊C4—43no—
843C22⋊C4—43no—
844C22⋊C4—46no—
845C22⋊C4—412no—
846C22⋊C4—46no—
847C22⋊C4—46no—
848C22⋊C4—46no—
849C22⋊C4—46no—
850C22⋊C4—46no—
851C22⋊C4—46no—
852C22⋊C42−1+414yescomplemented
853C42—212no—
854C42—26no—
855C42—22no—
856C42—224no—
857C42—212no—
858C42—212no—
859C42—26no—
860C42—26no—
861C42—212no—
862C42—22no—
863C42—26no—
864C42—26no—
865C42—26no—
866C42—212no—
867C23—23no—
868C23—23no—
869C23—23no—
870C23—23no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—21no—
878C23—22no—
879C23—21no—
880C23—22no—
881C23—22no—
882C23—21no—
883C23—23no—
884C23—23no—
885C23—23no—
886C23—23no—
887C23—23no—
888C23—23no—
889C23—23no—
890C23—412no—
891C23—412no—
892C23—412no—
893C23—412no—
894C23—86no—
895C23—86no—
896C23—86no—
897C23C23×D414yes—
898C23C23×D416yes—
899C23C22×#4116yes—
900C23C22×#4116yes—
901C23C2×2−1+412yes—
902C23C2611yescharacteristic
903Q8—248no—
904Q8—224no—
905Q8—412no—
906Q8C2×#123116yes—
907D4—248no—
908D4—28no—
909D4—48no—
910D4—424no—
911D4—412no—
912D4—812no—
913D4C2×#123148yes—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—26no—
918C2×C4—26no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—248no—
923C2×C4—248no—
924C2×C4—23no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—23no—
928C2×C4—26no—
929C2×C4—22no—
930C2×C4—26no—
931C2×C4—21no—
932C2×C4—23no—
933C2×C4—22no—
934C2×C4—23no—
935C2×C4—23no—
936C2×C4—26no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—23no—
940C2×C4—23no—
941C2×C4—22no—
942C2×C4—23no—
943C2×C4—23no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—23no—
949C2×C4—23no—
950C2×C4—26no—
951C2×C4—26no—
952C2×C4—23no—
953C2×C4—26no—
954C2×C4—26no—
955C2×C4—23no—
956C2×C4—21no—
957C2×C4—26no—
958C2×C4—23no—
959C2×C4—22no—
960C2×C4—23no—
961C2×C4—26no—
962C2×C4—22no—
963C2×C4—412no—
964C2×C4—412no—
965C2×C4—48no—
966C2×C4—412no—
967C2×C4—412no—
968C2×C4—44no—
969C2×C4—412no—
970C2×C4—412no—
971C2×C4—412no—
972C2×C4—86no—
973C2×C4—812no—
974C2×C4—812no—
975C2×C4—812no—
976C2×C4—812no—
977C2×C4C2×#123148yes—
978C2×C4C23×D4112yes—
979C2×C4C23×D416yes—
980C2×C4C23×D412yes—
981C2×C4C22×#4112yes—
982C2×C4C22×#4116yes—
983C2×C4C22×#4116yes—
984C2×C4C22×#4112yes—
985C2×C4C2×2−1+412yes—
986C2×C4C2×2−1+412yes—
987C2×C4#58512yes—
988C22—26no—
989C22—26no—
990C22—26no—
991C22—26no—
992C22—26no—
993C22—26no—
994C22—24no—
995C22—22no—
996C22—22no—
997C22—24no—
998C22—22no—
999C22—24no—
1000C22—42no—
1001C22—41no—
1002C22—42no—
1003C22—41no—
1004C22—42no—
1005C22—42no—
1006C22—41no—
1007C22—41no—
1008C22—43no—
1009C22—43no—
1010C22—43no—
1011C22—43no—
1012C22—43no—
1013C22—43no—
1014C22—43no—
1015C22—824no—
1016C22C22×#123112yes—
1017C22C24×D411yescharacteristic
1018C22C23×#4111yescharacteristic
1019C22C23×#4111yescharacteristic
1020C22C22×2−1+411yescharacteristic
1021C22C2×#58511yescharacteristic
1022C22H(7,𝔽2)11yescharacteristic
1023C222−1+611yescharacteristic
1024C4—22no—
1025C4—22no—
1026C4—22no—
1027C4—212no—
1028C4—43no—
1029C4—43no—
1030C4—42no—
1031C4—42no—
1032C4—43no—
1033C4—41no—
1034C4—43no—
1035C4—46no—
1036C4—46no—
1037C4—42no—
1038C4—46no—
1039C4—41no—
1040C4—43no—
1041C4C22×#123112yes—
1042C4C22×#12314yes—
1043C2—212no—
1044C2—44no—
1045C2—42no—
1046C2—83no—
1047C2C23×#12311yescharacteristic
1048C2#6280511yescharacteristic
1049C2#6285711yescharacteristic
1050C2#6299311yescharacteristic
1051C2D4×2−1+411yescharacteristic
1052C2#6300011yescharacteristic
1053C2#6300311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3489C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×2−1+4C2semidirect
3. Q8×#123C2semidirect
4. #36483C2semidirect
5. #36217C2semidirect
6. #36216C2semidirect
7. #35998C2semidirect
8. #35987C2semidirect
9. #35801C2semidirect
10. #35723C2semidirect
11. #35673C2semidirect
12. #35672C2semidirect
13. #35530C2semidirect
14. #35516C2semidirect
15. #35255C2semidirect
16. #35182C2semidirect
17. #34742C2semidirect
18. C2×#2423C2semidirect
19. #34259C2semidirect
20. #34250C2semidirect
21. #34183C2semidirect
22. #34175C2semidirect
23. C22⋊C4×#41C2semidirect
39. C2×#520C22semidirect
40. C2×#520C22semidirect
41. C2×#519C22semidirect
42. C2×#519C22semidirect
45. C2×C4×#41C22semidirect
46. C2×C4×#41C22semidirect
47. C22×C4×Q8C22semidirect
48. C22×C4×Q8C22semidirect
49. #2855C22semidirect
50. #2854C22semidirect
51. #2853C22semidirect
52. #2625C22semidirect
53. #2624C22semidirect
54. #2623C22semidirect
55. #2502C22semidirect
56. #2501C22semidirect
57. #2500C22semidirect
58. #2499C22semidirect
59. #2498C22semidirect
60. #2498C22semidirect
62. #2486C22semidirect
64. #2485C22semidirect
65. #2484C22semidirect
67. #2448C22semidirect
68. #2448C22semidirect
69. #2448C22semidirect
70. #2448C22semidirect
71. #2446C22semidirect
72. #2446C22semidirect
73. #2446C22semidirect
74. #2446C22semidirect
75. #2444C22semidirect
76. #2443C22semidirect
77. #2443C22semidirect
78. #2443C22semidirect
84. #2423C22semidirect
85. #2423C22semidirect
86. #2423C22semidirect
87. #2423C22semidirect
88. #2423C22semidirect
89. #2423C22semidirect
90. #2423C22semidirect
92. #2422C22semidirect
93. #2422C22semidirect
96. #2421C22semidirect
97. #2421C22semidirect
98. #2421C22semidirect
99. #2421C22semidirect
101. #2420C22semidirect
102. #2419C22semidirect
103. #2419C22semidirect
104. #2419C22semidirect
109. #2395C22semidirect
111. C2×#398C22semidirect
112. #2351C22semidirect
113. Q8×C4⋊C4C22semidirect
114. Q8×C4⋊C4C22semidirect
115. Q8×C4⋊C4C22semidirect
116. #2349C22semidirect
117. D4×C4⋊C4C22semidirect
118. D4×C4⋊C4C22semidirect
119. D4×C4⋊C4C22semidirect
126. Q8×C22⋊C4C22semidirect
127. Q8×C22⋊C4C22semidirect
131. #2339C22semidirect
132. #2339C22semidirect
136. #2317C22semidirect
137. #2317C22semidirect
138. #2317C22semidirect
139. #2316C22semidirect
142. #2311C22semidirect
143. #2310C22semidirect
145. C4×#123C22semidirect
148. #2297C22semidirect
149. #2296C22semidirect
150. C2×#391C22semidirect
151. C2×#389C22semidirect
153. C2×#387C22semidirect
154. #2285C22semidirect
155. C2×#384C22semidirect
683. #41#123semidirect
852. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×C4×2−1+42
Q8×#1232
#364832
#362172
#362162
#359982
#359872
#358012
#357232
#356732
#356722
#355302
#355162
#352552
#351822
#347422
C2×#24232
#342592
#342502
#341832
#341752
C22⋊C4×#412