Finite Group Databasebeta

← #7672713

Subgroups — #7672713

Order 512.

6242 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59272C218yesmaximal, complemented
2#59013C218yesmaximal, complemented
3#39736C214yesmaximal, complemented
4#39735C214yesmaximal, complemented
5#37898C214yesmaximal, complemented
6#37893C214yesmaximal, complemented
7C2×#2856C211yesmaximal, characteristic, complemented
8#36596C214yesmaximal, complemented
9#36587C214yesmaximal, complemented
10#36211C214yesmaximal, complemented
11#36182C214yesmaximal, complemented
12#35558C212yesmaximal, complemented
13#35541C212yesmaximal, complemented
14#35286C211yesmaximal, characteristic, complemented
15#35272C211yesmaximal, characteristic, complemented
16#35252C212yesmaximal, complemented
17#34210C211yesmaximal, characteristic, complemented
18#34204C212yesmaximal, complemented
19#34188C211yesmaximal, characteristic, complemented
20C4×#525C211yesmaximal, characteristic, complemented
21C2×#2285C211yesmaximal, characteristic, complemented
22C2×#553C2218yescomplemented
23C2×#535C2212yes—
24C22×#127C2211yescharacteristic
25C2×#525C2211yescharacteristic
26C22×#121C2212yes—
27C22×#121C2214yes—
28C2×#518C2212yes—
29C2×C4×#41C2211yescharacteristic
30C22×#117C2212yes—
31C23×C42C2211yescharacteristic
32#2859C2214yescomplemented
33#2856C2212yes—
34#2856C2212yes—
35#2856C2214yes—
36#2856C2212yes—
37#2856C2212yes—
38#2856C2214yes—
39#2856C2214yescomplemented
40#2856C2214yescomplemented
41#2850C2214yescomplemented
42#2761C22116yescomplemented
43#2753C22116yescomplemented
44#2703C22116yescomplemented
45#2691C22116yescomplemented
46#2647C2214yescomplemented
47#2620C2214yescomplemented
48#2619C2214yescomplemented
49#2619C2214yescomplemented
50#2597C22116yescomplemented
51#2571C2214yescomplemented
52#2566C2218yescomplemented
53#2554C22116yescomplemented
54#2552C2214yescomplemented
55#2548C2214yescomplemented
56#2543C22116yescomplemented
57#2541C2214yescomplemented
58#2535C2218yescomplemented
59#2513C2218yescomplemented
60#2513C2218yescomplemented
61#2513C2218yescomplemented
62#2512C2218yescomplemented
63#2512C2218yescomplemented
64#2512C2218yescomplemented
65#2504C2218yescomplemented
66#2500C2218yescomplemented
67#2490C2218yescomplemented
68#2490C2218yescomplemented
69#2480C22116yes—
70#2447C2218yescomplemented
71#2445C2218yescomplemented
72#2444C22116yescomplemented
73#2442C2218yes—
74#2422C2218yescomplemented
75#2422C2218yescomplemented
76#2420C2218yescomplemented
77#2420C2218yescomplemented
78#2416C2218yescomplemented
79#2416C2218yescomplemented
80#2414C2218yescomplemented
81#2414C2218yescomplemented
82#2412C22116yes—
83#2411C2218yes—
84#2410C2218yes—
85#2408C2218yes—
86#2366C2214yescomplemented
87#2366C2214yescomplemented
88#2363C2218yescomplemented
89#2363C2218yescomplemented
90#2361C2218yescomplemented
91#2361C2218yescomplemented
92#2357C2218yescomplemented
93#2355C2214yescomplemented
94#2354C2214yescomplemented
95#2352C2218yes—
96#2342C2218yes—
97D4×C22⋊C4C2218yes—
98D4×C22⋊C4C2218yes—
99#2328C2214yescomplemented
100#2324C2218yescomplemented
101#2317C2212yes—
102#2316C2212yes—
103#2314C2214yescomplemented
104#2311C2212yes—
105#2309C2212yes—
106#2309C2212yes—
107C4×#127C2214yescomplemented
108C4×C22⋊Q8C2212yescomplemented
109C4×C22⋊Q8C2212yescomplemented
110C4×#123C2214yes—
111C4×#121C2212yescomplemented
112C4×#121C2218yescomplemented
113C4×#121C2212yescomplemented
114C4×#120C2214yes—
115#2297C2211yescharacteristic
116#2296C2211yescharacteristic
117C2×#390C2214yes—
118C2×#390C2212yes—
119#2290C2212yescomplemented
120#2290C2212yescomplemented
121#2285C2214yes—
122#2285C2211yescharacteristic
123#2285C2211yescharacteristic
124#2285C2212yes—
125#2285C2212yescomplemented
126#2285C2214yescomplemented
127#2285C2214yescomplemented
128#2285C2212yescomplemented
129C2×#384C2211yescharacteristic
130C2×#384C2212yescomplemented
131C2×#382C2212yescomplemented
132#2280C2211yescharacteristic
133C2×#380C2214yes—
134#2274C2212yes—
135C42×D4C2212yescomplemented
136C42×D4C2212yescomplemented
137C4×#117C2211yescharacteristic
138C2×C4×C4⋊C4C2214yescomplemented
139C22×#41C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2314yes—
142C23×D4C2314yes—
143C24×C4C2312yes—
144C24×C4C2311yescharacteristic
145#553—432no—
146#535—48no—
147C2×#127—28no—
148C2×#127C2312yes—
149C2×#127C2312yes—
150C2×#127C2314yes—
151C2×#127C2314yes—
152C2×#126C23116yes—
153C2×#125C2318yes—
154C2×#124C2314yes—
155#525—28no—
156C2×#123C2312yes—
157C2×#123C23116yes—
158C2×C22⋊Q8C2311yescharacteristic
159C2×C22⋊Q8C2311yescharacteristic
160C2×#121—216no—
161C2×#121—416no—
162C2×#121C2314yes—
163C2×#121C2314yes—
164C2×#121C2314yes—
165C2×#121C2318yes—
166C2×#121C2314yes—
167C2×#121C2311yescharacteristic
168C2×#121C2311yescharacteristic
169C2×#121C2318yes—
170C2×#121C2318yes—
171C2×#121C2318yes—
172C2×#121C2318yes—
173C2×#121C2318yes—
174C2×#121C2318yes—
175C2×#121C23116yes—
176C2×#120C2312yes—
177C2×#120C2318yes—
178#518—48no—
179C4×#41—28no—
180C2×C4×Q8C2312yes—
181C2×C4×D4C2314yes—
182C2×C4×D4C2312yes—
183C2×C4×D4C2312yes—
184C2×C4×D4C2312yes—
185C2×C4×D4C2314yes—
186C2×C4×D4C2318yes—
187C2×C4×D4C2318yes—
188C2×C4×D4C2318yes—
189C2×C4×D4C2318yes—
190C2×C4×D4C23116yes—
191C2×C4×D4C2314yes—
192C2×#117—48no—
193C2×#117C2311yescharacteristic
194C2×#117C2311yescharacteristic
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2311yescharacteristic
199C2×#117C2314yes—
200C2×#117C2314yes—
201C2×#117C2318yes—
202C2×#117C2314yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2314yes—
205C22×C4⋊C4C2314yes—
206C22×C4⋊C4C2314yes—
207C22×C4⋊C4C2314yes—
208C22×C22⋊C4C2314yes—
209C22×C22⋊C4C2318yes—
210C22×C22⋊C4C2314yes—
211C22×C22⋊C4C2318yes—
212C22×C42—28no—
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2314yes—
223C22×C42C2311yescharacteristic
224#400C23116yes—
225#398C23116yes—
226#397C23116yes—
227#397C23116yes—
228#397C23116yes—
229#397C23116yes—
230#397C23116yes—
231#396C23116yes—
232#396C23116yes—
233#394C23116yes—
234#394C23116yes—
235#394C23116yes—
236#394C23116yes—
237#394C23116yes—
238#392C23116yes—
239#392C23116yes—
240#391C2314yes—
241#391C2312yes—
242#390C2318yes—
243#390C2318yes—
244#390C2318yes—
245#390C2318yes—
246#390C2314yes—
247#390C2318yes—
248#390C2314yes—
249#390C2318yes—
250#390C2318yes—
251#390C2314yes—
252#390C23116yes—
253#390C2318yes—
254#390C2318yes—
255#390C2314yes—
256#390C2314yes—
257#390C2318yes—
258#390C2318yes—
259#390C2318yes—
260#390C23116yes—
261#390C2312yes—
262#389C2318yes—
263#389C2318yes—
264#389C2318yes—
265#389C2318yes—
266#389C2318yes—
267#389C2312yes—
268#389C2312yes—
269#388C23116yes—
270#388C23116yes—
271#388C23116yes—
272#388C23116yes—
273#388C23116yes—
274#388C23116yes—
275#388C23116yes—
276#388C2314yes—
277#388C2314yes—
278#387C23116yes—
279#387C2314yes—
280#387C2314yes—
281#386C2318yes—
282#386C23116yes—
283#386C23116yes—
284#386C23116yes—
285#386C23116yes—
286#386C23116yes—
287#386C23116yes—
288#386C2314yes—
289#386C2314yes—
290#386C2314yes—
291#385C23116yes—
292#385C23116yes—
293#385C2318yes—
294#385C2314yes—
295#385C2314yes—
296#385C2314yes—
297#384C2312yes—
298#384C2314yes—
299#384C2312yes—
300#384C2314yes—
301#384C2314yes—
302#384C2312yes—
303#384C2312yes—
304#384C2314yes—
305#384C2314yes—
306#382C2318yes—
307#382C2312yes—
308#382C2314yes—
309#382C2318yes—
310#382C2312yes—
311#382C2314yes—
312#382C2318yes—
313#381C2312yes—
314#381C23116yes—
315#380C2318yes—
316#380C2318yes—
317#380C2312yes—
318#380C2314yes—
319#380C2318yes—
320#380C2314yes—
321#380C2318yes—
322#380C2314yes—
323#380C2318yes—
324#380C2314yes—
325#380C2312yes—
326#379C2318yes—
327#379C2318yes—
328#379C2312yes—
329C4×C4⋊C4C2314yes—
330C4×C4⋊C4C2318yes—
331C4×C4⋊C4C2312yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2318yes—
334C4×C4⋊C4C2318yes—
335C4×C4⋊C4C2318yes—
336C4×C4⋊C4C2314yes—
337C4×C4⋊C4C2314yes—
338C4×C4⋊C4C2314yes—
339C4×C4⋊C4C2314yes—
340C4×C4⋊C4C2312yes—
341C4×C4⋊C4C2318yes—
342C4×C4⋊C4C2312yes—
343C4×C4⋊C4C2312yes—
344C4×C22⋊C4C2314yes—
345C4×C22⋊C4C2318yes—
346C4×C22⋊C4C23116yes—
347C4×C22⋊C4C2312yes—
348C4×C22⋊C4C2314yes—
349C4×C22⋊C4C2312yes—
350C4×C22⋊C4C2314yes—
351C4×C22⋊C4C2312yes—
352C4×C22⋊C4C2314yes—
353C4×C22⋊C4C2312yes—
354C4×C22⋊C4C2314yes—
355#376C2312yes—
356C2×#95C2318yes—
357C43C2312yes—
358C25C2411yescharacteristic
359C25C2414yes—
360C2×#41—24no—
361C2×#41—24no—
362C2×#41—24no—
363C22×Q8C2411yescharacteristic
364C22×D4—216no—
365C22×D4—28no—
366C22×D4—28no—
367C22×D4—216no—
368C22×D4—28no—
369C22×D4—48no—
370C22×D4—48no—
371C22×D4—416no—
372C22×D4C2412yes—
373C22×D4C2412yes—
374C22×D4C2418yes—
375C22×D4C2414yes—
376C22×D4C2418yes—
377C22×D4C2414yes—
378C22×D4C2411yescharacteristic
379C22×D4C2412yes—
380C22×D4C2418yes—
381C22×D4C2418yes—
382C22×D4C24116yes—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—28no—
386C23×C4—28no—
387C23×C4—44no—
388C23×C4#4118yes—
389C23×C4C2414yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2414yes—
403C23×C4C2418yes—
404C23×C4C24116yes—
405C23×C4C2411yescharacteristic
406#127—28no—
407#127—28no—
408#127—216no—
409#127—48no—
410#126—432no—
411#125—416no—
412#124—48no—
413#123—28no—
414#123—432no—
415C22⋊Q8—24no—
416C22⋊Q8—24no—
417#121—216no—
418#121—216no—
419#121—216no—
420#121—216no—
421#121—24no—
422#121—24no—
423#121—232no—
424#121—416no—
425#121—416no—
426#121—416no—
427#121—416no—
428#121—416no—
429#121—416no—
430#121—432no—
431#120—28no—
432#120—416no—
433C4×Q8—28no—
434C4×D4—216no—
435C4×D4—28no—
436C4×D4—28no—
437C4×D4—216no—
438C4×D4—28no—
439C4×D4—416no—
440C4×D4—416no—
441C4×D4—416no—
442C4×D4—416no—
443C4×D4—48no—
444C4×D4—432no—
445#117—24no—
446#117—24no—
447#117—28no—
448#117—28no—
449#117—24no—
450#117—28no—
451#117—48no—
452#117—48no—
453#117—48no—
454#117—416no—
455C2×C4⋊C4—28no—
456C2×C4⋊C4—216no—
457C2×C4⋊C4—48no—
458C2×C4⋊C4—48no—
459C2×C4⋊C4—48no—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2411yescharacteristic
475C2×C4⋊C4C2412yes—
476C2×C4⋊C4C2412yes—
477C2×C4⋊C4C2414yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C24116yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C24116yes—
484C2×C22⋊C4—216no—
485C2×C22⋊C4—416no—
486C2×C22⋊C4—48no—
487C2×C22⋊C4—416no—
488C2×C22⋊C4C2412yes—
489C2×C22⋊C4C2414yes—
490C2×C22⋊C4C2414yes—
491C2×C22⋊C4C24116yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C2412yes—
495C2×C22⋊C4C2414yes—
496C2×C22⋊C4C2412yes—
497C2×C22⋊C4C2414yes—
498C2×C22⋊C4C2412yes—
499C2×C22⋊C4C2412yes—
500C2×C22⋊C4C2412yes—
501C2×C22⋊C4C2412yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C24116yes—
505C2×C22⋊C4C24116yes—
506C2×C22⋊C4C24116yes—
507C2×C22⋊C4C24116yes—
508C2×C22⋊C4C24116yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C24116yes—
512C2×C22⋊C4C24116yes—
513C2×C22⋊C4C24116yes—
514C2×C42—28no—
515C2×C42—24no—
516C2×C42—28no—
517C2×C42—24no—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—24no—
521C2×C42—28no—
522C2×C42—28no—
523C2×C42—48no—
524C2×C42#4118yes—
525C2×C42C2414yes—
526C2×C42C2414yes—
527C2×C42C2412yes—
528C2×C42C2412yes—
529C2×C42C2412yes—
530C2×C42C2414yes—
531C2×C42C2414yes—
532C2×C42C2414yes—
533C2×C42C2412yes—
534C2×C42C2411yescharacteristic
535C2×C42C2412yes—
536C2×C42C2411yescharacteristic
537C2×C42C2412yes—
538C2×C42C2412yes—
539C2×C42C2412yes—
540C2×C42C2418yes—
541C2×C42C24116yes—
542C2×C42C2411yescharacteristic
543C2×C42C2412yes—
544C2×C42C2411yescharacteristic
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2414yes—
550#95C2414yes—
551#95C2414yes—
552#95C2414yes—
553#95C2414yes—
554#95C2414yes—
555#95C2414yes—
556#95C2414yes—
557#95C24116yes—
558#95C24116yes—
559#95C24116yes—
560#95C24116yes—
561C24—22no—
562C24—22no—
563C24—24no—
564C24—28no—
565C24—28no—
566C24—28no—
567C24—42no—
568C24—48no—
569C24—48no—
570C24C2×#4114yes—
571C24C2518yes—
572C24C2512yes—
573C24C2511yescharacteristic
574C24C2511yescharacteristic
575C24C2511yescharacteristic
576#41—416no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—216no—
585C2×D4—28no—
586C2×D4—232no—
587C2×D4—24no—
588C2×D4—216no—
589C2×D4—22no—
590C2×D4—28no—
591C2×D4—28no—
592C2×D4—22no—
593C2×D4—28no—
594C2×D4—28no—
595C2×D4—216no—
596C2×D4—216no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—216no—
600C2×D4—22no—
601C2×D4—216no—
602C2×D4—44no—
603C2×D4—48no—
604C2×D4—416no—
605C2×D4—48no—
606C2×D4—416no—
607C2×D4—416no—
608C2×D4—416no—
609C2×D4—432no—
610C2×D4—832no—
611C2×D4—832no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—232no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—24no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—28no—
630C22×C4—216no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—28no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—28no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—28no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—432no—
648C22×C4—48no—
649C22×C4—48no—
650C22×C4—48no—
651C22×C4—416no—
652C22×C4—416no—
653C22×C4—416no—
654C22×C4C2×#4118yes—
655C22×C4C2×#4114yes—
656C22×C4C2×#4114yes—
657C22×C4C2×#4114yes—
658C22×C4C2×#4114yes—
659C22×C4C2×#4114yes—
660C22×C4C2×#4114yes—
661C22×C4C2×#4114yes—
662C22×C4H(5,𝔽2)18yes—
663C22×C4H(5,𝔽2)14yes—
664C22×C4C2512yes—
665C22×C4C2512yes—
666C22×C4C2512yes—
667C22×C4C2514yes—
668C22×C4C2514yes—
669C22×C4C2518yes—
670C22×C4C2518yes—
671C22×C4C2518yes—
672C22×C4C2512yes—
673C22×C4C2512yes—
674C22×C4C2511yescharacteristic
675C22×C4C2511yescharacteristic
676C22×C4C2512yes—
677C22×C4C2511yescharacteristic
678C22×C4C2511yescharacteristic
679C22×C4C2512yes—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—24no—
683C4⋊C4—28no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—216no—
691C4⋊C4—28no—
692C4⋊C4—28no—
693C4⋊C4—216no—
694C4⋊C4—24no—
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—28no—
698C4⋊C4—48no—
699C4⋊C4—48no—
700C4⋊C4—48no—
701C4⋊C4—44no—
702C4⋊C4—416no—
703C4⋊C4—416no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4—24no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—216no—
713C22⋊C4—216no—
714C22⋊C4—28no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—232no—
718C22⋊C4—28no—
719C22⋊C4—48no—
720C22⋊C4—416no—
721C22⋊C4—416no—
722C22⋊C4—416no—
723C22⋊C4—416no—
724C22⋊C4—44no—
725C22⋊C4—44no—
726C22⋊C4—416no—
727C22⋊C4—416no—
728C22⋊C4—416no—
729C22⋊C4—416no—
730C42—24no—
731C42—22no—
732C42—24no—
733C42—24no—
734C42—24no—
735C42—24no—
736C42—22no—
737C42—24no—
738C42—28no—
739C42—24no—
740C42—28no—
741C42—28no—
742C42—24no—
743C42—28no—
744C42—28no—
745C42—48no—
746C42—416no—
747C42C2×#4114yes—
748C42C2×#4114yes—
749C42C2×#4118yes—
750C23—21no—
751C23—21no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—21no—
756C23—21no—
757C23—22no—
758C23—22no—
759C23—28no—
760C23—28no—
761C23—22no—
762C23—22no—
763C23—28no—
764C23—28no—
765C23—24no—
766C23—216no—
767C23—28no—
768C23—22no—
769C23—216no—
770C23—24no—
771C23—44no—
772C23—48no—
773C23—48no—
774C23—416no—
775C23—816no—
776C23—88no—
777C23—88no—
778C23—816no—
779C23C22×#4112yes—
780C23C22×#4112yes—
781C23C22×#4112yes—
782C23C22×#4112yes—
783C23C2×H(5,𝔽2)12yes—
784C23C2×H(5,𝔽2)14yes—
785C23C2611yescharacteristic
786Q8—44no—
787D4—48no—
788D4—48no—
789D4—48no—
790D4—432no—
791D4—416no—
792D4—416no—
793D4—44no—
794D4—432no—
795D4—816no—
796D4—816no—
797D4—1616no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—216no—
812C2×C4—216no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—28no—
819C2×C4—22no—
820C2×C4—28no—
821C2×C4—28no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—28no—
827C2×C4—216no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—28no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—48no—
838C2×C4—48no—
839C2×C4—48no—
840C2×C4—48no—
841C2×C4—416no—
842C2×C4—48no—
843C2×C4—816no—
844C2×C4—88no—
845C2×C4—1616no—
846C2×C4#553116yescomplemented
847C2×C4C22×#4114yes—
848C2×C4C22×#4112yes—
849C2×C4C22×#4112yes—
850C2×C4C22×#4112yes—
851C2×C4C22×#4112yes—
852C2×C4C22×#4112yes—
853C2×C4C22×#4112yes—
854C2×C4C22×#4114yes—
855C2×C4C2×H(5,𝔽2)14yes—
856C2×C4C2×H(5,𝔽2)12yes—
857C2×C4C2×H(5,𝔽2)12yes—
858C2×C4C2×H(5,𝔽2)14yes—
859C2×C4#58514yes—
860C22—24no—
861C22—24no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—24no—
866C22—24no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—416no—
872C22—42no—
873C22—42no—
874C22—44no—
875C22—416no—
876C22—48no—
877C22—42no—
878C22—42no—
879C22—48no—
880C22—416no—
881C22—44no—
882C22—42no—
883C22—48no—
884C22—1616no—
885C22C2×#55314yes—
886C22#350814yes—
887C22C23×#4111yescharacteristic
888C22C23×#4111yescharacteristic
889C22C22×H(5,𝔽2)12yes—
890C22C22×H(5,𝔽2)11yescharacteristic
891C22C2×#58512yes—
892C4—24no—
893C4—24no—
894C4—22no—
895C4—22no—
896C4—44no—
897C4—42no—
898C4—48no—
899C4—42no—
900C4—42no—
901C4—48no—
902C4—48no—
903C4—44no—
904C4—42no—
905C4C2×#55314yes—
906C4C2×#55314yes—
907C4#349418yes—
908C2—24no—
909C2—24no—
910C2—42no—
911C2—82no—
912C2—88no—
913C2C22×#55311yescharacteristic
914C2C2×#349412yes—
915C2C2×#350811yescharacteristic
916C2#6281511yescharacteristic
917C2#6283412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59272C2semidirect
2. #59013C2semidirect
3. #39736C2semidirect
4. #39735C2semidirect
5. #37898C2semidirect
6. #37893C2semidirect
7. C2×#2856C2semidirect
8. #36596C2semidirect
9. #36587C2semidirect
10. #36211C2semidirect
11. #36182C2semidirect
12. #35558C2semidirect
13. #35541C2semidirect
14. #35286C2semidirect
15. #35272C2semidirect
16. #35252C2semidirect
17. #34210C2semidirect
18. #34204C2semidirect
19. #34188C2semidirect
20. C4×#525C2semidirect
21. C2×#2285C2semidirect
22. C2×#553C22semidirect
32. #2859C22semidirect
39. #2856C22semidirect
40. #2856C22semidirect
41. #2850C22semidirect
42. #2761C22semidirect
43. #2753C22semidirect
44. #2703C22semidirect
45. #2691C22semidirect
46. #2647C22semidirect
47. #2620C22semidirect
48. #2619C22semidirect
49. #2619C22semidirect
50. #2597C22semidirect
51. #2571C22semidirect
52. #2566C22semidirect
53. #2554C22semidirect
54. #2552C22semidirect
55. #2548C22semidirect
56. #2543C22semidirect
57. #2541C22semidirect
58. #2535C22semidirect
59. #2513C22semidirect
60. #2513C22semidirect
61. #2513C22semidirect
62. #2512C22semidirect
63. #2512C22semidirect
64. #2512C22semidirect
65. #2504C22semidirect
66. #2500C22semidirect
67. #2490C22semidirect
68. #2490C22semidirect
70. #2447C22semidirect
71. #2445C22semidirect
72. #2444C22semidirect
74. #2422C22semidirect
75. #2422C22semidirect
76. #2420C22semidirect
77. #2420C22semidirect
78. #2416C22semidirect
79. #2416C22semidirect
80. #2414C22semidirect
81. #2414C22semidirect
86. #2366C22semidirect
87. #2366C22semidirect
88. #2363C22semidirect
89. #2363C22semidirect
90. #2361C22semidirect
91. #2361C22semidirect
92. #2357C22semidirect
93. #2355C22semidirect
94. #2354C22semidirect
99. #2328C22semidirect
100. #2324C22semidirect
103. #2314C22semidirect
107. C4×#127C22semidirect
108. C4×C22⋊Q8C22semidirect
109. C4×C22⋊Q8C22semidirect
111. C4×#121C22semidirect
112. C4×#121C22semidirect
113. C4×#121C22semidirect
119. #2290C22semidirect
120. #2290C22semidirect
125. #2285C22semidirect
126. #2285C22semidirect
127. #2285C22semidirect
128. #2285C22semidirect
130. C2×#384C22semidirect
131. C2×#382C22semidirect
135. C42×D4C22semidirect
136. C42×D4C22semidirect
138. C2×C4×C4⋊C4C22semidirect
846. C2×C4#553semidirect

Maximal subgroups

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

subgroupindex
#592722
#590132
#397362
#397352
#378982
#378932
C2×#28562
#365962
#365872
#362112
#361822
#355582
#355412
#352862
#352722
#352522
#342102
#342042
#341882
C4×#5252
C2×#22852