Finite Group Databasebeta

← #7629119

Subgroups — #7629119

Order 512.

7634 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3461C211yesmaximal, characteristic, complemented
2C22×#529C211yesmaximal, characteristic, complemented
3#35677C212yesmaximal, complemented
4#35661C212yesmaximal, complemented
5#35649C211yesmaximal, characteristic, complemented
6#35640C211yesmaximal, characteristic, complemented
7#35638C218yesmaximal, complemented
8#35584C211yesmaximal, characteristic, complemented
9#35572C218yesmaximal, complemented
10#35565C211yesmaximal, characteristic
11#35469C214yesmaximal, complemented
12#35396C214yesmaximal, complemented
13#34965C214yesmaximal, complemented
14#34934C218yesmaximal, complemented
15#34919C218yesmaximal, complemented
16#34877C214yesmaximal, complemented
17C4×#535C212yesmaximal, complemented
18C4×#525C212yesmaximal, complemented
19C4×#519C211yesmaximal, characteristic, complemented
20#3461—216no—
21C2×#544C2211yescharacteristic
22C2×#542C2214yescomplemented
23C2×#541C2214yescomplemented
24C2×#539C2214yes—
25C2×#537C2211yescharacteristic
26C2×#536C2212yes—
27C2×#535C2212yes—
28C2×#533C2214yescomplemented
29C2×#529—216no—
30C2×#529C2218yes—
31C2×#529C2214yes—
32C2×#529C2218yes—
33C2×#529C2214yescomplemented
34C22×#126C2212yes—
35C22×#125C2211yescharacteristic
36C22×#124C2211yescharacteristic
37C2×#525C2212yes—
38C22×#123C2212yes—
39C22×C22⋊Q8C2211yescharacteristic
40C22×#121C2211yescharacteristic
41C2×#519C2212yes—
42C2×C4×#41C2212yes—
43C22×C4×Q8C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45C22×C4×D4C2212yes—
46C22×#117C2212yes—
47C23×C42C2211yescharacteristic
48#2611C2218yescomplemented
49#2610C2218yescomplemented
50#2603C22116yescomplemented
51#2601C22116yescomplemented
52#2591C2214yes—
53#2583C2214yes—
54#2566C2218yescomplemented
55#2561C2214yes—
56#2560C22116yescomplemented
57#2558C22116yescomplemented
58#2554C22116yescomplemented
59#2554C22116yescomplemented
60#2552C2218yescomplemented
61#2550C2218yescomplemented
62#2548C2218yescomplemented
63#2545C2218yescomplemented
64#2544C2218yescomplemented
65#2541C2218yes—
66#2540C2218yes—
67#2539C2214yes—
68#2538C2218yescomplemented
69#2536C2218yescomplemented
70#2519C22116yescomplemented
71#2512C22116yescomplemented
72#2504C2214yes—
73#2502C2214yes—
74#2491C2218yes—
75#2490C2218yes—
76#2490C2218yescomplemented
77#2489C2218yescomplemented
78#2461C22116yescomplemented
79#2445C22116yescomplemented
80#2435C2214yes—
81#2433C2214yes—
82#2429C2218yescomplemented
83#2426C2218yescomplemented
84#2426C2218yescomplemented
85#2426C2218yescomplemented
86#2413C2218yes—
87#2411C2218yes—
88#2411C2218yes—
89#2411C2218yes—
90#2396C2218yescomplemented
91#2392C2218yescomplemented
92#2392C22116yescomplemented
93#2328C2214yescomplemented
94#2326C2214yescomplemented
95#2324C2218yescomplemented
96#2321C2218yes—
97#2317C2212yes—
98#2311C2212yes—
99#2309C2212yes—
100C4×#127C2214yescomplemented
101C4×#127C2218yescomplemented
102C4×#124C2214yescomplemented
103C4×#124C2218yescomplemented
104C4×C22⋊Q8C2214yescomplemented
105C4×C22⋊Q8C2214yescomplemented
106C4×#123C2214yes—
107C4×#123C2214yes—
108C4×#121C2218yescomplemented
109C4×#121C2214yescomplemented
110C4×#121C2214yescomplemented
111C4×#120C2218yes—
112C4×#120C2214yes—
113C4×#120C2214yes—
114#2297C2212yes—
115#2296C2212yes—
116#2293C22116yescomplemented
117#2290C2218yescomplemented
118#2280C2212yes—
119#2276C2218yescomplemented
120#2274C2211yescharacteristic
121#2274C2211yescharacteristic
122#2274C2214yes—
123C42×Q8C2218yescomplemented
124C42×D4C2218yescomplemented
125C4×#117C2212yes—
126C4×#117C2214yes—
127C22×#41C2312yes—
128C23×Q8C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2312yes—
131C24×C4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135#544—28no—
136#542—232no—
137#541—232no—
138#539—232no—
139#537—28no—
140#536—216no—
141#535—216no—
142#533—232no—
143C2×C4⋊Q8C2314yes—
144C2×C4⋊Q8C2314yes—
145C2×#127C2314yes—
146C2×#127C2318yes—
147#529—264no—
148#529—264no—
149#529—232no—
150#529—232no—
151C2×#126—216no—
152C2×#126C23116yes—
153C2×#126C2318yes—
154C2×#126C2318yes—
155C2×#125—28no—
156C2×#125C2314yes—
157C2×#125C2318yes—
158C2×#125C2314yes—
159C2×#125C2318yes—
160C2×#124—28no—
161C2×#124C2314yes—
162C2×#124C2314yes—
163C2×#124C2318yes—
164C2×#124C2314yes—
165C2×#124C2318yes—
166#525—216no—
167C2×#123—216no—
168C2×#123C23116yes—
169C2×#123C2318yes—
170C2×#123C2314yes—
171C2×#123C2318yes—
172C2×C22⋊Q8—28no—
173C2×C22⋊Q8C2318yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2318yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×#121—28no—
181C2×#121C2318yes—
182C2×#121C2314yes—
183C2×#121C2318yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#120C2318yes—
187C2×#120C2314yes—
188#519—216no—
189C4×#41—216no—
190C2×C4×Q8D4116yescomplemented
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2314yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2318yes—
195C2×C4×Q8C2318yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×D4—216no—
199C2×C4×D4—28no—
200C2×C4×D4C2314yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C23116yes—
212C2×C4×D4C2318yes—
213C2×#117—216no—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2314yes—
217C2×#117C2318yes—
218C2×#117C2318yes—
219C2×#117C2318yes—
220C2×#117C2318yes—
221C2×#117C2312yes—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C42—28no—
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2314yes—
238C22×C42C2314yes—
239C22×C42C2314yes—
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242#400C2318yes—
243#399C2318yes—
244#398C23116yes—
245#398C2318yes—
246#398C23116yes—
247#397C23116yes—
248#397C2318yes—
249#396C23116yes—
250#396C23116yes—
251#396C23116yes—
252#396C23116yes—
253#395C2318yes—
254#394C23116yes—
255#394C2318yes—
256#394C23116yes—
257#394C23116yes—
258#394C23116yes—
259#393C2318yes—
260#392C23116yes—
261#392C2318yes—
262#391C2318yes—
263#391C2314yes—
264#391C2314yes—
265#390C23116yes—
266#390C2314yes—
267#390C2318yes—
268#390C2314yes—
269#390C23116yes—
270#390C23116yes—
271#390C23116yes—
272#390C2318yes—
273#390C2318yes—
274#390C2314yes—
275#390C2318yes—
276#390C23116yes—
277#390C2314yes—
278#389C2318yes—
279#389C23116yes—
280#389C23116yes—
281#389C2314yes—
282#389C2314yes—
283#388C23116yes—
284#388C23116yes—
285#388C23116yes—
286#388C23116yes—
287#388C23116yes—
288#388C23116yes—
289#388C2318yes—
290#388C23116yes—
291#388C23116yes—
292#388C2318yes—
293#387C2318yes—
294#387C2318yes—
295#386C23116yes—
296#386C2318yes—
297#386C23116yes—
298#386C2314yes—
299#386C2318yes—
300#386C2314yes—
301#386C2318yes—
302#385C2318yes—
303#385C23116yes—
304#385C2318yes—
305#385C2314yes—
306#385C2314yes—
307#385C2318yes—
308#384C2318yes—
309#384C2314yes—
310#382C2318yes—
311#382C2314yes—
312#381C2314yes—
313#380C2318yes—
314#380C2314yes—
315#380C2314yes—
316#379C2318yes—
317#379C2314yes—
318C4×C4⋊C4C23116yes—
319C4×C4⋊C4C2318yes—
320C4×C4⋊C4C2314yes—
321C4×C4⋊C4C2318yes—
322C4×C4⋊C4C2318yes—
323C4×C4⋊C4C23116yes—
324C4×C4⋊C4C2318yes—
325C4×C4⋊C4C2318yes—
326C4×C4⋊C4C2314yes—
327C4×C4⋊C4C2318yes—
328C4×C4⋊C4C2318yes—
329C4×C22⋊C4C2318yes—
330C4×C22⋊C4C2314yes—
331C4×C22⋊C4C2314yes—
332C4×C22⋊C4C2314yes—
333C4×C22⋊C4C2318yes—
334C4×C22⋊C4C2318yes—
335C4×C22⋊C4C23116yes—
336C4×C22⋊C4C2318yes—
337C4×C22⋊C4C2318yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2318yes—
340#376C2314yes—
341#376C2318yes—
342C43C2314yes—
343C43C2318yes—
344C25C2411yescharacteristic
345C25C2412yes—
346C2×#41—28no—
347C2×#41—28no—
348C2×#41—28no—
349C22×Q8—28no—
350C22×Q8C2×D418yes—
351C22×Q8C2412yes—
352C22×Q8C2414yes—
353C22×Q8C2414yes—
354C22×D4—28no—
355C22×D4—24no—
356C22×D4—28no—
357C22×D4—48no—
358C22×D4C2414yes—
359C22×D4C2414yes—
360C22×D4C2412yes—
361C22×D4C2418yes—
362C22×D4C2418yes—
363C22×D4C24116yes—
364C22×D4C2414yes—
365C23×C4—28no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—28no—
370C23×C4—44no—
371C23×C4—48no—
372C23×C4—44no—
373C23×C4C2411yescharacteristic
374C23×C4C2414yes—
375C23×C4C2414yes—
376C23×C4C2414yes—
377C23×C4C2414yes—
378C23×C4C2412yes—
379C23×C4C2414yes—
380C23×C4C2412yes—
381C23×C4C2411yescharacteristic
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2414yes—
386C23×C4C2414yes—
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C4⋊Q8—216no—
392C4⋊Q8—216no—
393#127—216no—
394#127—416no—
395#126—264no—
396#126—232no—
397#126—232no—
398#125—232no—
399#125—216no—
400#125—232no—
401#125—216no—
402#124—232no—
403#124—216no—
404#124—216no—
405#124—216no—
406#124—416no—
407#123—232no—
408#123—264no—
409#123—232no—
410#123—216no—
411C22⋊Q8—232no—
412C22⋊Q8—216no—
413C22⋊Q8—216no—
414C22⋊Q8—216no—
415C22⋊Q8—216no—
416C22⋊Q8—232no—
417C22⋊Q8—216no—
418#121—216no—
419#121—232no—
420#121—216no—
421#121—216no—
422#121—232no—
423#120—216no—
424#120—232no—
425C4×Q8—232no—
426C4×Q8—28no—
427C4×Q8—28no—
428C4×Q8—216no—
429C4×Q8—232no—
430C4×Q8C2×D4132yes—
431C4×Q8C2×D4132yes—
432C4×D4—216no—
433C4×D4—216no—
434C4×D4—216no—
435C4×D4—216no—
436C4×D4—232no—
437C4×D4—232no—
438C4×D4—28no—
439C4×D4—28no—
440C4×D4—216no—
441C4×D4—232no—
442C4×D4—416no—
443C4×D4—432no—
444C4×D4—416no—
445#117—28no—
446#117—28no—
447#117—232no—
448#117—232no—
449#117—232no—
450#117—216no—
451#117—232no—
452#117#41116yes—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—28no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—28no—
457C2×C4⋊C4C2×D418yes—
458C2×C4⋊C4C2×D4116yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C24116yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C24116yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2414yes—
481C2×C22⋊C4—28no—
482C2×C22⋊C4—28no—
483C2×C22⋊C4—28no—
484C2×C22⋊C4—28no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C2418yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2418yes—
498C2×C22⋊C4C2418yes—
499C2×C22⋊C4C2418yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C24116yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C24116yes—
506C2×C22⋊C4C24116yes—
507C2×C22⋊C4C24116yes—
508C2×C22⋊C4C2414yes—
509C2×C42—24no—
510C2×C42—24no—
511C2×C42—24no—
512C2×C42—216no—
513C2×C42—216no—
514C2×C42—216no—
515C2×C42C2×D4116yes—
516C2×C42C2×D418yes—
517C2×C42C2412yes—
518C2×C42C2414yes—
519C2×C42C2414yes—
520C2×C42C24116yes—
521C2×C42C2414yes—
522C2×C42C2414yes—
523C2×C42C2414yes—
524C2×C42C2412yes—
525C2×C42C2414yes—
526C2×C42C2418yes—
527C2×C42C2418yes—
528C2×C42C2418yes—
529C2×C42C2418yes—
530C2×C42C2412yes—
531C2×C42C2414yes—
532C2×C42C2414yes—
533C2×C42C2412yes—
534C2×C42C2414yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545#95C24116yes—
546#95C24116yes—
547C24—22no—
548C24—24no—
549C24—24no—
550C24—24no—
551C24—28no—
552C24—42no—
553C24—44no—
554C24—44no—
555C24C2514yes—
556C24C2514yes—
557C24C2512yes—
558C24C2511yescharacteristic
559#41—432no—
560C2×Q8—232no—
561C2×Q8—24no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8—48no—
568C2×Q8C22×D4116yes—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—216no—
573C2×D4—216no—
574C2×D4—216no—
575C2×D4—28no—
576C2×D4—24no—
577C2×D4—28no—
578C2×D4—216no—
579C2×D4—28no—
580C2×D4—24no—
581C2×D4—28no—
582C2×D4—24no—
583C2×D4—232no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—416no—
587C2×D4—416no—
588C2×D4—48no—
589C2×D4—432no—
590C2×D4—416no—
591C22×C4—28no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—28no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—216no—
612C22×C4—28no—
613C22×C4—216no—
614C22×C4—28no—
615C22×C4—42no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—48no—
619C22×C4—44no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—44no—
623C22×C4—48no—
624C22×C4—416no—
625C22×C4—432no—
626C22×C4—416no—
627C22×C4—416no—
628C22×C4C22×D414yes—
629C22×C4C22×D418yes—
630C22×C4C22×D414yes—
631C22×C4C22×D418yes—
632C22×C4C22×D414yes—
633C22×C4C2×#4118yes—
634C22×C4C2518yes—
635C22×C4C2512yes—
636C22×C4C2512yes—
637C22×C4C2512yes—
638C22×C4C2514yes—
639C22×C4C2514yes—
640C22×C4C2514yes—
641C22×C4C2514yes—
642C22×C4C2511yescharacteristic
643C22×C4C2512yes—
644C22×C4C2514yes—
645C22×C4C2514yes—
646C22×C4C2518yes—
647C22×C4C2512yes—
648C22×C4C2511yescharacteristic
649C4⋊C4—216no—
650C4⋊C4—216no—
651C4⋊C4—28no—
652C4⋊C4—216no—
653C4⋊C4—24no—
654C4⋊C4—28no—
655C4⋊C4—24no—
656C4⋊C4—28no—
657C4⋊C4—216no—
658C4⋊C4—216no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—216no—
662C4⋊C4—232no—
663C4⋊C4—28no—
664C4⋊C4—216no—
665C4⋊C4—48no—
666C4⋊C4—416no—
667C4⋊C4—48no—
668C4⋊C4C22×D4116yes—
669C4⋊C4C22×D4132yes—
670C4⋊C4C2×#41116yes—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—216no—
674C22⋊C4—216no—
675C22⋊C4—216no—
676C22⋊C4—216no—
677C22⋊C4—216no—
678C22⋊C4—216no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—216no—
682C22⋊C4—216no—
683C22⋊C4—216no—
684C22⋊C4—216no—
685C22⋊C4—216no—
686C22⋊C4—232no—
687C22⋊C4—48no—
688C22⋊C4—416no—
689C22⋊C4—48no—
690C22⋊C4—416no—
691C22⋊C4—48no—
692C22⋊C4—416no—
693C22⋊C4C2×#41116yes—
694C42—24no—
695C42—24no—
696C42—28no—
697C42—28no—
698C42—28no—
699C42—28no—
700C42—28no—
701C42—232no—
702C42—28no—
703C42—216no—
704C42—48no—
705C42—48no—
706C42—48no—
707C42C22×D418yes—
708C42C22×D418yes—
709C42C22×D4116yes—
710C42C22×D4116yes—
711C42C2×#41116yes—
712C23—22no—
713C23—22no—
714C23—28no—
715C23—22no—
716C23—24no—
717C23—24no—
718C23—22no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—28no—
723C23—24no—
724C23—28no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—416no—
729C23—44no—
730C23—48no—
731C23—48no—
732C23—44no—
733C23—48no—
734C23—816no—
735C23C23×D412yes—
736C23C22×#4114yes—
737C23#58514yes—
738C23C2611yescharacteristic
739Q8—232no—
740Q8—48no—
741Q8—88no—
742D4—432no—
743D4—432no—
744D4—416no—
745D4—416no—
746D4—48no—
747D4—832no—
748D4—88no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—22no—
755C2×C4—216no—
756C2×C4—28no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—28no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—28no—
774C2×C4—24no—
775C2×C4—44no—
776C2×C4—48no—
777C2×C4—416no—
778C2×C4—48no—
779C2×C4—416no—
780C2×C4—44no—
781C2×C4—48no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—416no—
785C2×C4—416no—
786C2×C4—416no—
787C2×C4—48no—
788C2×C4—416no—
789C2×C4—88no—
790C2×C4#532116yes—
791C2×C4C23×D414yes—
792C2×C4C23×D412yes—
793C2×C4C23×D418yes—
794C2×C4C23×D418yes—
795C2×C4C23×D414yes—
796C2×C4C23×D412yes—
797C2×C4C22×#41116yes—
798C2×C4C22×#4114yes—
799C2×C4C22×#4114yes—
800C2×C4#58514yes—
801C22—22no—
802C22—28no—
803C22—22no—
804C22—28no—
805C22—24no—
806C22—416no—
807C22—42no—
808C22—44no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—48no—
813C22—48no—
814C22—416no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—816no—
820C22C2×#53214yes—
821C22C24×D411yescharacteristic
822C22C23×#4112yes—
823C22C2×#58512yes—
824C22C2×#58512yes—
825C4—22no—
826C4—216no—
827C4—24no—
828C4—28no—
829C4—28no—
830C4—44no—
831C4—42no—
832C4—44no—
833C4—48no—
834C4—42no—
835C4—44no—
836C4—42no—
837C4—44no—
838C4C2×#53218yes—
839C4#348714yes—
840C2—24no—
841C2—44no—
842C2—84no—
843C2—84no—
844C2C22×#53211yescharacteristic
845C2C2×#348711yescharacteristic
846C2#6281014yes—
847C2#6281111yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radical#35565C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3461C2semidirect
2. C22×#529C2semidirect
3. #35677C2semidirect
4. #35661C2semidirect
5. #35649C2semidirect
6. #35640C2semidirect
7. #35638C2semidirect
8. #35584C2semidirect
9. #35572C2semidirect
11. #35469C2semidirect
12. #35396C2semidirect
13. #34965C2semidirect
14. #34934C2semidirect
15. #34919C2semidirect
16. #34877C2semidirect
17. C4×#535C2semidirect
18. C4×#525C2semidirect
19. C4×#519C2semidirect
22. C2×#542C22semidirect
23. C2×#541C22semidirect
28. C2×#533C22semidirect
33. C2×#529C22semidirect
48. #2611C22semidirect
49. #2610C22semidirect
50. #2603C22semidirect
51. #2601C22semidirect
54. #2566C22semidirect
56. #2560C22semidirect
57. #2558C22semidirect
58. #2554C22semidirect
59. #2554C22semidirect
60. #2552C22semidirect
61. #2550C22semidirect
62. #2548C22semidirect
63. #2545C22semidirect
64. #2544C22semidirect
68. #2538C22semidirect
69. #2536C22semidirect
70. #2519C22semidirect
71. #2512C22semidirect
76. #2490C22semidirect
77. #2489C22semidirect
78. #2461C22semidirect
79. #2445C22semidirect
82. #2429C22semidirect
83. #2426C22semidirect
84. #2426C22semidirect
85. #2426C22semidirect
90. #2396C22semidirect
91. #2392C22semidirect
92. #2392C22semidirect
93. #2328C22semidirect
94. #2326C22semidirect
95. #2324C22semidirect
100. C4×#127C22semidirect
101. C4×#127C22semidirect
102. C4×#124C22semidirect
103. C4×#124C22semidirect
104. C4×C22⋊Q8C22semidirect
105. C4×C22⋊Q8C22semidirect
108. C4×#121C22semidirect
109. C4×#121C22semidirect
110. C4×#121C22semidirect
116. #2293C22semidirect
117. #2290C22semidirect
119. #2276C22semidirect
123. C42×Q8C22semidirect
124. C42×D4C22semidirect
190. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34612
C22×#5292
#356772
#356612
#356492
#356402
#356382
#355842
#355722
#355652
#354692
#353962
#349652
#349342
#349192
#348772
C4×#5352
C4×#5252
C4×#5192