Finite Group Databasebeta

← #7632060

Subgroups — #7632060

Order 512.

8080 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic, complemented
2C2×#3428C211yesmaximal, characteristic, complemented
3#36234C218yesmaximal, complemented
4#36230C218yesmaximal, complemented
5#36080C214yesmaximal, complemented
6#35997C214yesmaximal, complemented
7#35982C214yesmaximal, complemented
8#35686C214yesmaximal, complemented
9#35639C212yesmaximal, complemented
10#35633C212yesmaximal, complemented
11#35452C214yesmaximal, complemented
12#35354C214yesmaximal, complemented
13#35311C211yesmaximal, characteristic, complemented
14#35305C211yesmaximal, characteristic, complemented
15#35138C214yesmaximal, complemented
16#34875C214yesmaximal, complemented
17#34809C211yesmaximal, characteristic, complemented
18#34736C211yesmaximal, characteristic
19#34266C212yesmaximal, complemented
20#34200C212yesmaximal, complemented
21#34179C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C2×#552—216no—
24C2×#552C2214yes—
25C2×#552C2214yes—
26C2×#552C2214yescomplemented
27C2×#552C2214yescomplemented
28C2×#536C2212yes—
29C22×#126C2212yes—
30C22×#125C2211yescharacteristic, complemented
31C22×#125C2212yescomplemented
32C2×#525C2212yes—
33C22×#123C2212yes—
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic, complemented
36#3428—216no—
37C2×#520C2212yes—
38C2×#520C2212yes—
39C2×#520C2212yescomplemented
40C2×#520C2212yescomplemented
41C2×#519C2212yescomplemented
42C2×#518C2214yes—
43C2×#518C2212yescomplemented
44C2×C4×#41C2214yes—
45C2×C4×#41C2214yescomplemented
46C22×C4×Q8C2211yescharacteristic, complemented
47C22×C4×D4C2211yescharacteristic
48C22×#117C2211yescharacteristic
49C22×#117C2211yescharacteristic
50C22×#117C2212yescomplemented
51C22×#117C2214yescomplemented
52C23×C4⋊C4C2211yescharacteristic, complemented
53#2855C2214yescomplemented
54#2851C22116yescomplemented
55#2848C2214yescomplemented
56#2634C2218yescomplemented
57#2633C2218yescomplemented
58#2625C2214yescomplemented
59#2616C2214yescomplemented
60#2611C22116yescomplemented
61#2609C22116yescomplemented
62#2599C2218yescomplemented
63#2598C2218yescomplemented
64#2584C2218yescomplemented
65#2579C2218yescomplemented
66#2562C2218yescomplemented
67#2534C2218yescomplemented
68#2503C2212yescomplemented
69#2502C2212yescomplemented
70#2499C2214yescomplemented
71#2487C2218yescomplemented
72#2487C2212yescomplemented
73#2486C2218yescomplemented
74#2486C2212yescomplemented
75#2485C2214yes—
76#2484C2214yescomplemented
77#2484C2212yescomplemented
78#2483C2214yes—
79#2483C2212yes—
80#2482C2212yescomplemented
81#2480C22116yescomplemented
82#2478C22116yescomplemented
83#2470C22116yes—
84#2468C22116yescomplemented
85#2466C22116yescomplemented
86#2457C22116yescomplemented
87#2455C22116yescomplemented
88#2454C2218yescomplemented
89#2453C2218yescomplemented
90#2442C2218yescomplemented
91#2441C2218yescomplemented
92#2435C2212yescomplemented
93#2434C2212yescomplemented
94#2432C2214yescomplemented
95#2429C2218yescomplemented
96#2427C2218yescomplemented
97#2418C22116yes—
98#2417C2218yescomplemented
99#2415C2218yescomplemented
100#2409C2212yes—
101#2408C2212yes—
102#2407C2214yes—
103#2406C2214yes—
104#2406C2212yes—
105#2405C2212yes—
106#2405C2214yes—
107#2405C2212yes—
108#2404C2212yes—
109#2403C2212yes—
110#2396C2218yescomplemented
111#2395C2214yes—
112#2392C2218yescomplemented
113#2388C2214yes—
114#2367C2218yescomplemented
115#2365C2218yescomplemented
116#2362C2218yescomplemented
117#2361C2218yescomplemented
118#2360C2218yescomplemented
119#2360C2218yescomplemented
120#2352C2218yescomplemented
121D4×C4⋊C4C2218yescomplemented
122#2347C2214yescomplemented
123#2347C2214yescomplemented
124#2346C2214yescomplemented
125#2346C2214yescomplemented
126#2322C2218yescomplemented
127#2322C2218yescomplemented
128#2317C2212yescomplemented
129#2316C2212yescomplemented
130#2312C2214yes—
131#2311C2212yes—
132#2310C2212yescomplemented
133C4×#123C2218yescomplemented
134C4×#123C2214yescomplemented
135C4×#120C2214yes—
136C4×#120C2218yescomplemented
137#2297C2212yes—
138#2296C2212yescomplemented
139#2290C22116yescomplemented
140#2283C2214yescomplemented
141#2280C2211yescharacteristic
142#2280C2211yescharacteristic
143#2280C2212yescomplemented
144#2274C2212yescomplemented
145C22×#41—216no—
146C22×#41—28no—
147C22×#41C2312yes—
148C22×#41C2312yes—
149C22×#41C2312yes—
150C22×#41C2312yes—
151C23×Q8C2311yescharacteristic
152C23×Q8C2311yescharacteristic
153C23×D4C2312yes—
154C23×D4C2311yescharacteristic
155C23×D4C2311yescharacteristic
156C24×C4C2312yes—
157C24×C4C2311yescharacteristic
158C24×C4C2311yescharacteristic
159C24×C4C2312yes—
160#552—232no—
161#552—232no—
162#552—232no—
163#552—232no—
164#536—216no—
165C2×C4⋊Q8C2314yes—
166C2×#126—216no—
167C2×#126C2318yes—
168C2×#126C2318yes—
169C2×#125—28no—
170C2×#125—216no—
171C2×#125C2318yes—
172C2×#125C2318yes—
173C2×#125C2314yes—
174C2×#125C2314yes—
175C2×#124C2314yes—
176#525—216no—
177C2×#123—216no—
178C2×#123C2314yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×#123C2318yes—
182C2×#123C2314yes—
183C2×C22⋊Q8—28no—
184C2×C22⋊Q8—28no—
185C2×C22⋊Q8C2312yes—
186C2×C22⋊Q8C2318yes—
187C2×C22⋊Q8C2312yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×#121C2314yes—
194C2×#120C2314yes—
195C2×#120C2314yes—
196#520—216no—
197#520—216no—
198#520—216no—
199#520—216no—
200#519—216no—
201#518—216no—
202#518—232no—
203C4×#41—232no—
204C4×#41—232no—
205C2×C4×Q8—28no—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2314yes—
208C2×C4×Q8C2314yes—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×C4×D4—28no—
213C2×C4×D4C2314yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2318yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C23116yes—
227C2×#117—28no—
228C2×#117—232no—
229C2×#117—216no—
230C2×#117D4116yescomplemented
231C2×#117C2312yes—
232C2×#117C2312yes—
233C2×#117C2312yes—
234C2×#117C2318yes—
235C2×#117C2314yes—
236C2×#117C2318yes—
237C2×#117C2318yes—
238C2×#117C2312yes—
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2318yes—
242C2×#117C2314yes—
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C22×C4⋊C4—28no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2311yescharacteristic
266C22×C22⋊C4C2318yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C42C2318yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276#400C2314yes—
277#400C2318yes—
278#400C23116yes—
279#399C2314yes—
280#399C23116yes—
281#398C23116yes—
282#398C2314yes—
283#398C2318yes—
284#398C23116yes—
285#397C2314yes—
286#397C23116yes—
287#397C23116yes—
288#397C2318yes—
289#396C23116yes—
290#396C23116yes—
291#395C2314yes—
292#395C2318yes—
293#394C2314yes—
294#394C2318yes—
295#394C23116yes—
296#394C23116yes—
297#394C2318yes—
298#394C2318yes—
299#393C2314yes—
300#392C2314yes—
301#392C2318yes—
302#391C2318yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#390C2314yes—
308#390C2314yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C23116yes—
313#389C23116yes—
314#389C23116yes—
315#389C23116yes—
316#389C2314yes—
317#389C2314yes—
318#388C23116yes—
319#388C23116yes—
320#388C23116yes—
321#388C23116yes—
322#388C23116yes—
323#388C23116yes—
324#388C2318yes—
325#387C23116yes—
326#387C23116yes—
327#387C23116yes—
328#387C2318yes—
329#387C23116yes—
330#387C23116yes—
331#386C2318yes—
332#386C2314yes—
333#386C2314yes—
334#386C23116yes—
335#386C23116yes—
336#386C2318yes—
337#386C2314yes—
338#386C2314yes—
339#385C2318yes—
340#385C2314yes—
341#385C23116yes—
342#385C23116yes—
343#385C2314yes—
344#385C23116yes—
345#385C23116yes—
346#385C2318yes—
347#385C2318yes—
348#385C23116yes—
349#385C2318yes—
350#385C2314yes—
351#385C2314yes—
352#384C2314yes—
353#383C2318yes—
354#382C2314yes—
355#382C2318yes—
356#381C2318yes—
357#381C2314yes—
358#381C2318yes—
359#381C2312yes—
360#381C2312yes—
361#381C2314yes—
362#380C23116yes—
363#380C23116yes—
364#380C2318yes—
365#380C2318yes—
366#380C2312yes—
367#380C2312yes—
368#380C2312yes—
369#380C2312yes—
370#380C2314yes—
371#380C2314yes—
372#379C2312yes—
373#379C2312yes—
374#379C2318yes—
375#379C2314yes—
376#379C2314yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C2318yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C23116yes—
381C4×C4⋊C4C2318yes—
382C4×C22⋊C4C2318yes—
383C4×C22⋊C4C2312yes—
384C4×C22⋊C4C2312yes—
385C4×C22⋊C4C2312yes—
386C4×C22⋊C4C2312yes—
387C4×C22⋊C4C23116yes—
388C4×C22⋊C4C2318yes—
389C4×C22⋊C4C2318yes—
390C4×C22⋊C4C23116yes—
391#376C2318yes—
392C25C2411yescharacteristic
393C25C2412yes—
394C25C2411yescharacteristic
395C2×#41—2128no—
396C2×#41—28no—
397C2×#41—216no—
398C2×#41—28no—
399C2×#41—28no—
400C2×#41—28no—
401C2×#41—28no—
402C2×#41—28no—
403C2×#41—216no—
404C2×#41—28no—
405C2×#41#41116yes—
406C22×Q8—28no—
407C22×Q8—24no—
408C22×Q8—24no—
409C22×Q8—28no—
410C22×Q8C2412yes—
411C22×Q8C2412yes—
412C22×Q8C2412yes—
413C22×Q8C2412yes—
414C22×D4—28no—
415C22×D4—216no—
416C22×D4—28no—
417C22×D4—24no—
418C22×D4—24no—
419C22×D4—44no—
420C22×D4C2412yes—
421C22×D4C2414yes—
422C22×D4C2418yes—
423C22×D4C2412yes—
424C22×D4C2412yes—
425C22×D4C2414yes—
426C22×D4C2412yes—
427C23×C4—28no—
428C23×C4—216no—
429C23×C4—28no—
430C23×C4—28no—
431C23×C4—24no—
432C23×C4—28no—
433C23×C4—48no—
434C23×C4C2×D418yes—
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2414yes—
441C23×C4C2418yes—
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2414yes—
448C23×C4C2411yescharacteristic
449C23×C4C2412yes—
450C23×C4C2418yes—
451C23×C4C2412yes—
452C23×C4C2418yes—
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C4⋊Q8—216no—
459#126—232no—
460#126—232no—
461#125—216no—
462#125—216no—
463#125—232no—
464#125—232no—
465#124—216no—
466#123—216no—
467#123—232no—
468#123—232no—
469#123—232no—
470#123—48no—
471C22⋊Q8—216no—
472C22⋊Q8—28no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—28no—
476C22⋊Q8—232no—
477C22⋊Q8—216no—
478C22⋊Q8—216no—
479#121—216no—
480#120—216no—
481#120—48no—
482C4×Q8—216no—
483C4×Q8—216no—
484C4×Q8—216no—
485C4×Q8—216no—
486C4×Q8—216no—
487C4×Q8—216no—
488C4×D4—28no—
489C4×D4—28no—
490C4×D4—28no—
491C4×D4—28no—
492C4×D4—232no—
493C4×D4—232no—
494C4×D4—232no—
495C4×D4—216no—
496C4×D4—216no—
497C4×D4—232no—
498C4×D4—232no—
499C4×D4—216no—
500C4×D4—216no—
501C4×D4—432no—
502#117—28no—
503#117—28no—
504#117—28no—
505#117—28no—
506#117—28no—
507#117—28no—
508#117—216no—
509#117—216no—
510#117—232no—
511#117—232no—
512#117—232no—
513#117—232no—
514#117C2×D4116yes—
515#117C2×D4116yes—
516#117C2×D4116yes—
517#117C2×D4116yes—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—28no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—28no—
523C2×C4⋊C4—28no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—28no—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—216no—
529C2×C4⋊C4—216no—
530C2×C4⋊C4—216no—
531C2×C4⋊C4—216no—
532C2×C4⋊C4C2×D418yes—
533C2×C4⋊C4C2×D418yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C24116yes—
555C2×C4⋊C4C24116yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C24116yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C22⋊C4—28no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—28no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—28no—
568C2×C22⋊C4—232no—
569C2×C22⋊C4C2×D4116yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C24116yes—
587C2×C22⋊C4C24116yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C42—28no—
598C2×C42—28no—
599C2×C42—24no—
600C2×C42—232no—
601C2×C42C2×D4116yes—
602C2×C42C2414yes—
603C2×C42C2418yes—
604C2×C42C2414yes—
605C2×C42C2418yes—
606C2×C42C2418yes—
607C2×C42C2414yes—
608C2×C42C2414yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C24116yes—
612C2×C42C2414yes—
613C2×C42C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C24116yes—
617#95C2418yes—
618#95C2414yes—
619#95C2414yes—
620#95C24116yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C24116yes—
625#95C24116yes—
626#95C24116yes—
627#95C2418yes—
628#95C2418yes—
629#95C24116yes—
630C24—22no—
631C24—24no—
632C24—24no—
633C24—28no—
634C24—24no—
635C24—24no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—44no—
640C24—44no—
641C24C22×D414yes—
642C24C2511yescharacteristic
643C24C2511yescharacteristic
644C24C2514yes—
645C24C2512yes—
646C24C2511yescharacteristic
647#41—264no—
648#41—264no—
649#41—264no—
650#41—264no—
651C2×Q8—232no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—24no—
656C2×Q8—28no—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—28no—
660C2×Q8—416no—
661C2×Q8C2×#4118yes—
662C2×D4—264no—
663C2×D4—232no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—216no—
672C2×D4—216no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—28no—
678C2×D4—24no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—48no—
682C2×D4—416no—
683C2×D4C2×#41116yes—
684C2×D4C2×#4118yes—
685C22×C4—264no—
686C22×C4—24no—
687C22×C4—28no—
688C22×C4—24no—
689C22×C4—232no—
690C22×C4—28no—
691C22×C4—28no—
692C22×C4—24no—
693C22×C4—28no—
694C22×C4—24no—
695C22×C4—28no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—28no—
699C22×C4—22no—
700C22×C4—24no—
701C22×C4—22no—
702C22×C4—24no—
703C22×C4—22no—
704C22×C4—24no—
705C22×C4—28no—
706C22×C4—216no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—216no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—216no—
715C22×C4—216no—
716C22×C4—44no—
717C22×C4—48no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—416no—
723C22×C4—44no—
724C22×C4—416no—
725C22×C4—44no—
726C22×C4—432no—
727C22×C4—416no—
728C22×C4C22×D414yes—
729C22×C4C22×D414yes—
730C22×C4C22×D414yes—
731C22×C4C22×D414yes—
732C22×C4C22×D414yes—
733C22×C4C22×D418yes—
734C22×C4C22×D418yes—
735C22×C4C22×D414yes—
736C22×C4C2×#41116yes—
737C22×C4C2×#4118yes—
738C22×C4C2518yes—
739C22×C4C2514yes—
740C22×C4C2518yes—
741C22×C4C2512yes—
742C22×C4C2514yes—
743C22×C4C2514yes—
744C22×C4C2512yes—
745C22×C4C2512yes—
746C22×C4C2514yes—
747C22×C4C2511yescharacteristic
748C22×C4C2511yescharacteristic
749C22×C4C2514yes—
750C22×C4C2514yes—
751C22×C4C2514yes—
752C22×C4C2511yescharacteristic
753C22×C4C2511yescharacteristic
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—24no—
758C4⋊C4—216no—
759C4⋊C4—216no—
760C4⋊C4—216no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—216no—
766C4⋊C4—24no—
767C4⋊C4—24no—
768C4⋊C4—216no—
769C4⋊C4—216no—
770C4⋊C4—216no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—216no—
774C4⋊C4—232no—
775C4⋊C4—416no—
776C4⋊C4—48no—
777C4⋊C4—416no—
778C4⋊C4—48no—
779C4⋊C4C22×D418yes—
780C4⋊C4C22×D418yes—
781C4⋊C4C22×D418yes—
782C4⋊C4C22×D418yes—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—216no—
792C22⋊C4—232no—
793C22⋊C4—216no—
794C22⋊C4—24no—
795C22⋊C4—24no—
796C22⋊C4—216no—
797C22⋊C4—216no—
798C22⋊C4—216no—
799C22⋊C4—216no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—416no—
805C22⋊C4—44no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C22⋊C4C22×D4116yes—
809C22⋊C4C22×D4116yes—
810C42—28no—
811C42—216no—
812C42—216no—
813C42—28no—
814C42—216no—
815C42—24no—
816C42—24no—
817C42—28no—
818C42—28no—
819C42—416no—
820C42C22×D4116yes—
821C42C22×D4116yes—
822C23—22no—
823C23—22no—
824C23—28no—
825C23—216no—
826C23—22no—
827C23—24no—
828C23—24no—
829C23—22no—
830C23—22no—
831C23—24no—
832C23—28no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—24no—
838C23—22no—
839C23—28no—
840C23—28no—
841C23—44no—
842C23—44no—
843C23—416no—
844C23—44no—
845C23—44no—
846C23—88no—
847C23—816no—
848C23—84no—
849C23—84no—
850C23C23×D412yes—
851C23C23×D412yes—
852C23C23×D412yes—
853C23C22×#4118yes—
854C23C22×#4114yes—
855C23#58514yes—
856C23C2611yescharacteristic
857Q8—216no—
858Q8—216no—
859Q8—48no—
860Q8—48no—
861D4—216no—
862D4—232no—
863D4—232no—
864D4—216no—
865D4—432no—
866D4—48no—
867D4—48no—
868C2×C4—216no—
869C2×C4—232no—
870C2×C4—24no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—28no—
880C2×C4—28no—
881C2×C4—232no—
882C2×C4—22no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—22no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—24no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—22no—
897C2×C4—28no—
898C2×C4—22no—
899C2×C4—28no—
900C2×C4—24no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—48no—
904C2×C4—48no—
905C2×C4—432no—
906C2×C4—44no—
907C2×C4—48no—
908C2×C4—44no—
909C2×C4—44no—
910C2×C4—48no—
911C2×C4—48no—
912C2×C4—48no—
913C2×C4—816no—
914C2×C4—816no—
915C2×C4—84no—
916C2×C4—84no—
917C2×C4#525116yes—
918C2×C4C23×D412yes—
919C2×C4C23×D418yes—
920C2×C4C23×D418yes—
921C2×C4C23×D412yes—
922C2×C4C23×D412yes—
923C2×C4C23×D412yes—
924C2×C4C22×#4118yes—
925C2×C4C22×#4114yes—
926C2×C4C22×#4114yes—
927C22—28no—
928C22—22no—
929C22—22no—
930C22—28no—
931C22—216no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—28no—
940C22—416no—
941C22—44no—
942C22—48no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—42no—
948C22—42no—
949C22—88no—
950C22—816no—
951C22C2×#52514yes—
952C22C24×D411yescharacteristic
953C22C23×#4112yes—
954C22C2×#58512yes—
955C222−1+612yes—
956C4—28no—
957C4—28no—
958C4—22no—
959C4—22no—
960C4—28no—
961C4—48no—
962C4—48no—
963C4—44no—
964C4—42no—
965C4—44no—
966C4—42no—
967C4—44no—
968C4—42no—
969C4—44no—
970C4C2×#52514yes—
971C4C2×#52514yes—
972C2—24no—
973C2—44no—
974C2—48no—
975C2—42no—
976C2—42no—
977C2C22×#52511yescharacteristic
978C2#6281111yescharacteristic
979C2#6285911yescharacteristic
980C2#6299314yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34736C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#552C2semidirect
2. C2×#3428C2semidirect
3. #36234C2semidirect
4. #36230C2semidirect
5. #36080C2semidirect
6. #35997C2semidirect
7. #35982C2semidirect
8. #35686C2semidirect
9. #35639C2semidirect
10. #35633C2semidirect
11. #35452C2semidirect
12. #35354C2semidirect
13. #35311C2semidirect
14. #35305C2semidirect
15. #35138C2semidirect
16. #34875C2semidirect
17. #34809C2semidirect
19. #34266C2semidirect
20. #34200C2semidirect
21. #34179C2semidirect
26. C2×#552C22semidirect
27. C2×#552C22semidirect
30. C22×#125C22semidirect
31. C22×#125C22semidirect
35. C22×C22⋊Q8C22semidirect
39. C2×#520C22semidirect
40. C2×#520C22semidirect
41. C2×#519C22semidirect
43. C2×#518C22semidirect
45. C2×C4×#41C22semidirect
46. C22×C4×Q8C22semidirect
50. C22×#117C22semidirect
51. C22×#117C22semidirect
52. C23×C4⋊C4C22semidirect
53. #2855C22semidirect
54. #2851C22semidirect
55. #2848C22semidirect
56. #2634C22semidirect
57. #2633C22semidirect
58. #2625C22semidirect
59. #2616C22semidirect
60. #2611C22semidirect
61. #2609C22semidirect
62. #2599C22semidirect
63. #2598C22semidirect
64. #2584C22semidirect
65. #2579C22semidirect
66. #2562C22semidirect
67. #2534C22semidirect
68. #2503C22semidirect
69. #2502C22semidirect
70. #2499C22semidirect
71. #2487C22semidirect
72. #2487C22semidirect
73. #2486C22semidirect
74. #2486C22semidirect
76. #2484C22semidirect
77. #2484C22semidirect
80. #2482C22semidirect
81. #2480C22semidirect
82. #2478C22semidirect
84. #2468C22semidirect
85. #2466C22semidirect
86. #2457C22semidirect
87. #2455C22semidirect
88. #2454C22semidirect
89. #2453C22semidirect
90. #2442C22semidirect
91. #2441C22semidirect
92. #2435C22semidirect
93. #2434C22semidirect
94. #2432C22semidirect
95. #2429C22semidirect
96. #2427C22semidirect
98. #2417C22semidirect
99. #2415C22semidirect
110. #2396C22semidirect
112. #2392C22semidirect
114. #2367C22semidirect
115. #2365C22semidirect
116. #2362C22semidirect
117. #2361C22semidirect
118. #2360C22semidirect
119. #2360C22semidirect
120. #2352C22semidirect
121. D4×C4⋊C4C22semidirect
122. #2347C22semidirect
123. #2347C22semidirect
124. #2346C22semidirect
125. #2346C22semidirect
126. #2322C22semidirect
127. #2322C22semidirect
128. #2317C22semidirect
129. #2316C22semidirect
132. #2310C22semidirect
133. C4×#123C22semidirect
134. C4×#123C22semidirect
136. C4×#120C22semidirect
138. #2296C22semidirect
139. #2290C22semidirect
140. #2283C22semidirect
143. #2280C22semidirect
144. #2274C22semidirect
230. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#34282
#362342
#362302
#360802
#359972
#359822
#356862
#356392
#356332
#354522
#353542
#353112
#353052
#351382
#348752
#348092
#347362
#342662
#342002
#341792