Finite Group Databasebeta

← #7672712

Subgroups — #7672712

Order 512.

5242 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59289C218yesmaximal, complemented
2#59197C218yesmaximal, complemented
3#39737C214yesmaximal, complemented
4#39734C214yesmaximal, complemented
5#37897C214yesmaximal, complemented
6#37894C214yesmaximal, complemented
7C2×#2857C211yesmaximal, characteristic, complemented
8#36599C214yesmaximal, complemented
9#36586C214yesmaximal, complemented
10#36210C214yesmaximal, complemented
11#36189C214yesmaximal, complemented
12#35673C212yesmaximal, complemented
13#35630C212yesmaximal, complemented
14#35316C211yesmaximal, characteristic, complemented
15#35306C212yesmaximal
16#35286C211yesmaximal, characteristic, complemented
17#34209C211yesmaximal, characteristic, complemented
18#34203C212yesmaximal, complemented
19#34188C211yesmaximal, characteristic, complemented
20C4×#525C211yesmaximal, characteristic
21C2×#2285C211yesmaximal, characteristic, complemented
22C2×#536C2212yes—
23C22×C4⋊Q8C2211yescharacteristic
24C2×#525C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C2×#519C2212yes—
27C2×C4×#41C2211yescharacteristic
28C22×#117C2212yes—
29C23×C42C2211yescharacteristic
30#2859C2214yescomplemented
31#2857C2212yes—
32#2857C2212yes—
33#2857C2214yes—
34#2857C2212yes—
35#2857C2212yes—
36#2857C2214yes—
37#2857C2214yes—
38#2857C2214yescomplemented
39#2850C2214yes—
40#2772C22116yescomplemented
41#2766C22116yescomplemented
42#2747C22116yes—
43#2741C22116yes—
44#2647C2214yescomplemented
45#2621C2214yes—
46#2621C2214yescomplemented
47#2620C2214yes—
48#2596C22116yescomplemented
49#2585C22116yescomplemented
50#2571C2214yescomplemented
51#2570C2218yescomplemented
52#2569C22116yes—
53#2562C2218yes—
54#2552C2214yescomplemented
55#2547C2214yescomplemented
56#2546C2214yescomplemented
57#2514C2218yescomplemented
58#2514C2218yescomplemented
59#2511C2218yescomplemented
60#2511C2218yescomplemented
61#2510C22116yes—
62#2509C2218yescomplemented
63#2507C2218yescomplemented
64#2498C22116yes—
65#2497C2218yescomplemented
66#2495C2218yes—
67#2494C2218yes—
68#2494C2218yescomplemented
69#2493C22116yes—
70#2487C2218yes—
71#2486C2218yes—
72#2485C2218yes—
73#2448C2218yescomplemented
74#2446C2218yescomplemented
75#2442C2218yes—
76#2442C2218yes—
77#2441C2218yescomplemented
78#2423C2218yescomplemented
79#2421C2218yescomplemented
80#2417C2218yes—
81#2415C2218yes—
82#2413C2218yes—
83#2412C2218yes—
84#2370C2218yescomplemented
85#2365C2214yescomplemented
86#2365C2214yescomplemented
87#2362C2218yes—
88#2360C2218yes—
89#2355C2214yescomplemented
90#2354C2214yescomplemented
91#2352C2218yes—
92#2352C2218yes—
93#2347C2218yescomplemented
94#2345C2218yes—
95#2344C2218yes—
96#2344C2218yes—
97#2342C2218yes—
98#2327C2214yescomplemented
99#2323C2218yes—
100#2317C2212yes—
101#2316C2212yes—
102#2314C2214yescomplemented
103#2311C2212yes—
104#2310C2212yes—
105#2310C2212yes—
106C4×C4⋊Q8C2214yescomplemented
107C4×C22⋊Q8C2212yes—
108C4×C22⋊Q8C2218yes—
109C4×C22⋊Q8C2212yes—
110C4×#123C2214yes—
111C4×#121C2212yes—
112C4×#121C2212yes—
113C4×#120C2214yes—
114#2297C2211yescharacteristic
115#2296C2211yescharacteristic
116C2×#391C2212yes—
117C2×#389C2214yes—
118#2290C2212yes—
119#2290C2212yes—
120#2285C2212yes—
121#2285C2212yes—
122#2285C2214yes—
123#2285C2212yes—
124#2285C2211yescharacteristic
125#2285C2214yes—
126#2285C2211yescharacteristic
127#2285C2214yescomplemented
128C2×#384C2211yescharacteristic
129C2×#384C2212yes—
130C2×#382C2212yes—
131#2280C2211yescharacteristic
132C2×#380C2214yes—
133C2×#380C2214yes—
134#2274C2212yes—
135C42×D4C2212yes—
136C42×D4C2212yes—
137C4×#117C2211yescharacteristic
138C2×C4×C4⋊C4C2214yes—
139C22×#41C2311yescharacteristic
140C23×Q8C2312yes—
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143#536—48no—
144C2×C4⋊Q8—28no—
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2312yes—
147C2×C4⋊Q8C2314yes—
148C2×C4⋊Q8C2314yes—
149C2×#125C2318yes—
150C2×#124C2314yes—
151#525—28no—
152C2×#123C2312yes—
153C2×#123C2318yes—
154C2×C22⋊Q8—216no—
155C2×C22⋊Q8C2314yes—
156C2×C22⋊Q8C2314yes—
157C2×C22⋊Q8C2311yescharacteristic
158C2×C22⋊Q8C2314yes—
159C2×C22⋊Q8C2314yes—
160C2×C22⋊Q8C2311yescharacteristic
161C2×C22⋊Q8C2318yes—
162C2×#121C2311yescharacteristic
163C2×#121C2311yescharacteristic
164C2×#120C2312yes—
165#519—48no—
166C4×#41—28no—
167C2×C4×Q8C2312yes—
168C2×C4×Q8C2318yes—
169C2×C4×Q8C2318yes—
170C2×C4×D4C2314yes—
171C2×C4×D4C2314yes—
172C2×C4×D4C2312yes—
173C2×C4×D4C2312yes—
174C2×C4×D4C2312yes—
175C2×C4×D4C2314yes—
176C2×#117—48no—
177C2×#117C2311yescharacteristic
178C2×#117C2311yescharacteristic
179C2×#117C2312yes—
180C2×#117C2312yes—
181C2×#117C2312yes—
182C2×#117C2311yescharacteristic
183C2×#117C2314yes—
184C2×#117C2318yes—
185C2×#117C2314yes—
186C2×#117C2318yes—
187C2×#117C2314yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2314yes—
190C22×C4⋊C4C2314yes—
191C22×C4⋊C4C2314yes—
192C22×C4⋊C4C2314yes—
193C22×C4⋊C4C2314yes—
194C22×C4⋊C4C2314yes—
195C22×C22⋊C4C2314yes—
196C22×C22⋊C4C2314yes—
197C22×C42—28no—
198C22×C42C2312yes—
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2312yes—
204C22×C42C2312yes—
205C22×C42C2312yes—
206C22×C42C2311yescharacteristic
207C22×C42C2314yes—
208C22×C42C2311yescharacteristic
209#401C23116yes—
210#400C23116yes—
211#400C23116yes—
212#400C23116yes—
213#400C23116yes—
214#400C23116yes—
215#399C23116yes—
216#398C23116yes—
217#398C23116yes—
218#398C23116yes—
219#398C23116yes—
220#397C23116yes—
221#397C23116yes—
222#397C23116yes—
223#396C23116yes—
224#394C23116yes—
225#391C2318yes—
226#391C2318yes—
227#391C2314yes—
228#391C2314yes—
229#391C2318yes—
230#391C2314yes—
231#391C2314yes—
232#391C2314yes—
233#391C2318yes—
234#391C2312yes—
235#390C2314yes—
236#390C2312yes—
237#389C2318yes—
238#389C2318yes—
239#389C2318yes—
240#389C2318yes—
241#389C2318yes—
242#389C2318yes—
243#389C2318yes—
244#389C2318yes—
245#389C23116yes—
246#389C2318yes—
247#389C23116yes—
248#389C2318yes—
249#389C2318yes—
250#389C2318yes—
251#389C2318yes—
252#389C2312yes—
253#389C2312yes—
254#388C23116yes—
255#388C23116yes—
256#388C23116yes—
257#388C23116yes—
258#388C23116yes—
259#388C2314yes—
260#388C23116yes—
261#388C2314yes—
262#387C23116yes—
263#387C23116yes—
264#387C23116yes—
265#387C23116yes—
266#387C23116yes—
267#387C23116yes—
268#387C23116yes—
269#387C2314yes—
270#387C23116yes—
271#387C23116yes—
272#387C23116yes—
273#387C2314yes—
274#386C2318yes—
275#386C23116yes—
276#386C2314yes—
277#386C2314yes—
278#386C2314yes—
279#385C2314yes—
280#385C23116yes—
281#385C2318yes—
282#385C2314yes—
283#385C2314yes—
284#384C2312yes—
285#384C2312yes—
286#384C2314yes—
287#384C2314yes—
288#384C2314yes—
289#384C2312yes—
290#384C2312yes—
291#384C2314yes—
292#384C2314yes—
293#383C23116yes—
294#382C2312yes—
295#382C2318yes—
296#382C2318yes—
297#382C2314yes—
298#382C2312yes—
299#382C2314yes—
300#382C2318yes—
301#381C2318yes—
302#381C2318yes—
303#381C2312yes—
304#380C2314yes—
305#380C2318yes—
306#380C2318yes—
307#380C2318yes—
308#380C2318yes—
309#380C23116yes—
310#380C2318yes—
311#380C2318yes—
312#380C2312yes—
313#380C2314yes—
314#380C2318yes—
315#380C2318yes—
316#380C2318yes—
317#380C2314yes—
318#380C2314yes—
319#380C2318yes—
320#380C2318yes—
321#380C2312yes—
322#379C2312yes—
323C4×C4⋊C4C2318yes—
324C4×C4⋊C4C2318yes—
325C4×C4⋊C4C2318yes—
326C4×C4⋊C4C2314yes—
327C4×C4⋊C4C2312yes—
328C4×C4⋊C4C2314yes—
329C4×C4⋊C4C2318yes—
330C4×C4⋊C4C2318yes—
331C4×C4⋊C4C23116yes—
332C4×C4⋊C4C2318yes—
333C4×C4⋊C4C2314yes—
334C4×C4⋊C4C2314yes—
335C4×C4⋊C4C2312yes—
336C4×C4⋊C4C2314yes—
337C4×C4⋊C4C2314yes—
338C4×C4⋊C4C2318yes—
339C4×C4⋊C4C2312yes—
340C4×C4⋊C4C2312yes—
341C4×C22⋊C4C23116yes—
342C4×C22⋊C4C2318yes—
343C4×C22⋊C4C2314yes—
344C4×C22⋊C4C2314yes—
345C4×C22⋊C4C2314yes—
346C4×C22⋊C4C2312yes—
347C4×C22⋊C4C2312yes—
348C4×C22⋊C4C2312yes—
349C4×C22⋊C4C2312yes—
350C4×C22⋊C4C2314yes—
351C4×C22⋊C4C2314yes—
352#376C2312yes—
353C2×#95C2318yes—
354C2×#95C2318yes—
355C43C2312yes—
356C25C2411yescharacteristic
357C2×#41—24no—
358C2×#41—24no—
359C2×#41—24no—
360C22×Q8—28no—
361C22×Q8—28no—
362C22×Q8—28no—
363C22×Q8C2414yes—
364C22×Q8C2414yes—
365C22×Q8C2411yescharacteristic
366C22×D4C2412yes—
367C22×D4C2412yes—
368C22×D4C2411yescharacteristic
369C22×D4C2412yes—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—28no—
373C23×C4—28no—
374C23×C4—44no—
375C23×C4#4118yes—
376C23×C4C2414yes—
377C23×C4C2414yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2414yes—
391C23×C4C2418yes—
392C23×C4C2411yescharacteristic
393C4⋊Q8—28no—
394C4⋊Q8—28no—
395C4⋊Q8—216no—
396C4⋊Q8—48no—
397#125—416no—
398#124—48no—
399#123—28no—
400#123—416no—
401C22⋊Q8—216no—
402C22⋊Q8—216no—
403C22⋊Q8—216no—
404C22⋊Q8—216no—
405C22⋊Q8—24no—
406C22⋊Q8—24no—
407C22⋊Q8—416no—
408#121—24no—
409#121—24no—
410#120—28no—
411C4×Q8—28no—
412C4×Q8—416no—
413C4×Q8—416no—
414C4×D4—216no—
415C4×D4—28no—
416C4×D4—28no—
417C4×D4—216no—
418C4×D4—28no—
419C4×D4—48no—
420#117—24no—
421#117—24no—
422#117—28no—
423#117—28no—
424#117—24no—
425#117—28no—
426#117—48no—
427#117—48no—
428#117—416no—
429#117—48no—
430#117—416no—
431C2×C4⋊C4—216no—
432C2×C4⋊C4—28no—
433C2×C4⋊C4—216no—
434C2×C4⋊C4—216no—
435C2×C4⋊C4—48no—
436C2×C4⋊C4—48no—
437C2×C4⋊C4—48no—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2418yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C24116yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C24116yes—
466C2×C4⋊C4C24116yes—
467C2×C4⋊C4C24116yes—
468C2×C22⋊C4—216no—
469C2×C22⋊C4—48no—
470C2×C22⋊C4C2414yes—
471C2×C22⋊C4C2414yes—
472C2×C22⋊C4C2418yes—
473C2×C22⋊C4C2418yes—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2412yes—
476C2×C22⋊C4C2414yes—
477C2×C22⋊C4C2412yes—
478C2×C22⋊C4C2412yes—
479C2×C22⋊C4C2412yes—
480C2×C22⋊C4C2412yes—
481C2×C22⋊C4C2412yes—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2418yes—
485C2×C22⋊C4C24116yes—
486C2×C22⋊C4C2414yes—
487C2×C22⋊C4C2414yes—
488C2×C22⋊C4C24116yes—
489C2×C42—28no—
490C2×C42—24no—
491C2×C42—28no—
492C2×C42—24no—
493C2×C42—24no—
494C2×C42—24no—
495C2×C42—24no—
496C2×C42—28no—
497C2×C42—28no—
498C2×C42—48no—
499C2×C42#4118yes—
500C2×C42C2414yes—
501C2×C42C2414yes—
502C2×C42C2412yes—
503C2×C42C2412yes—
504C2×C42C2412yes—
505C2×C42C2414yes—
506C2×C42C2414yes—
507C2×C42C2414yes—
508C2×C42C2412yes—
509C2×C42C2411yescharacteristic
510C2×C42C2412yes—
511C2×C42C2411yescharacteristic
512C2×C42C2412yes—
513C2×C42C2412yes—
514C2×C42C2412yes—
515C2×C42C2418yes—
516C2×C42C24116yes—
517C2×C42C24116yes—
518C2×C42C2411yescharacteristic
519C2×C42C2412yes—
520C2×C42C2411yescharacteristic
521#95C2418yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525#95C24116yes—
526#95C24116yes—
527#95C2414yes—
528#95C2414yes—
529#95C2414yes—
530#95C2414yes—
531#95C2414yes—
532#95C2414yes—
533#95C2414yes—
534#95C2414yes—
535#95C24116yes—
536#95C24116yes—
537#95C24116yes—
538#95C24116yes—
539#95C24116yes—
540#95C24116yes—
541#95C24116yes—
542#95C24116yes—
543C24—22no—
544C24—22no—
545C24—24no—
546C24—42no—
547C24C2×#4114yes—
548C24C2512yes—
549C24C2511yescharacteristic
550C24C2511yescharacteristic
551C24C2511yescharacteristic
552#41—416no—
553C2×Q8—22no—
554C2×Q8—28no—
555C2×Q8—28no—
556C2×Q8—22no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—22no—
562C2×Q8—432no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—28no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—232no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—24no—
593C22×C4—28no—
594C22×C4—216no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—28no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—28no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—28no—
607C22×C4—24no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—432no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4C2×#4118yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4114yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4114yes—
623C22×C4H(5,𝔽2)14yes—
624C22×C42−1+418yes—
625C22×C4C2512yes—
626C22×C4C2512yes—
627C22×C4C2514yes—
628C22×C4C2518yes—
629C22×C4C2512yes—
630C22×C4C2518yes—
631C22×C4C2518yes—
632C22×C4C2518yes—
633C22×C4C2512yes—
634C22×C4C2514yes—
635C22×C4C2512yes—
636C22×C4C2511yescharacteristic
637C22×C4C2511yescharacteristic
638C22×C4C2512yes—
639C22×C4C2511yescharacteristic
640C22×C4C2511yescharacteristic
641C22×C4C2512yes—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—216no—
645C4⋊C4—216no—
646C4⋊C4—216no—
647C4⋊C4—216no—
648C4⋊C4—24no—
649C4⋊C4—28no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—28no—
655C4⋊C4—28no—
656C4⋊C4—24no—
657C4⋊C4—216no—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—216no—
663C4⋊C4—28no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—416no—
668C4⋊C4—44no—
669C4⋊C4—416no—
670C4⋊C4—416no—
671C4⋊C4—416no—
672C22⋊C4—216no—
673C22⋊C4—216no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—24no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—28no—
686C22⋊C4—48no—
687C22⋊C4—416no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—416no—
691C42—24no—
692C42—22no—
693C42—24no—
694C42—24no—
695C42—24no—
696C42—24no—
697C42—22no—
698C42—24no—
699C42—28no—
700C42—24no—
701C42—28no—
702C42—28no—
703C42—24no—
704C42—28no—
705C42—28no—
706C42—48no—
707C42—416no—
708C42—416no—
709C42C2×#4114yes—
710C42C2×#4114yes—
711C42C2×#4118yes—
712C23—21no—
713C23—21no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—28no—
722C23—28no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—24no—
727C23—24no—
728C23—44no—
729C23—48no—
730C23—48no—
731C23C22×#4112yes—
732C23C22×#4112yes—
733C23C22×#4112yes—
734C23C22×#4112yes—
735C23C2×H(5,𝔽2)12yes—
736C23C2×2−1+414yes—
737C23C2611yescharacteristic
738Q8—416no—
739Q8—416no—
740Q8—44no—
741D4—48no—
742D4—48no—
743D4—48no—
744D4—44no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—216no—
759C2×C4—216no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—24no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—216no—
785C2×C4—22no—
786C2×C4—28no—
787C2×C4—48no—
788C2×C4—48no—
789C2×C4—48no—
790C2×C4—416no—
791C2×C4—48no—
792C2×C4—416no—
793C2×C4—48no—
794C2×C4—88no—
795C2×C4—816no—
796C2×C4#553116yes—
797C2×C4C22×#4114yes—
798C2×C4C22×#4112yes—
799C2×C4C22×#4112yes—
800C2×C4C22×#4112yes—
801C2×C4C22×#4112yes—
802C2×C4C22×#4112yes—
803C2×C4C22×#4112yes—
804C2×C4C22×#4114yes—
805C2×C4C2×H(5,𝔽2)12yes—
806C2×C4C2×H(5,𝔽2)12yes—
807C2×C4C2×2−1+414yes—
808C2×C4C2×2−1+414yes—
809C2×C4#58514yes—
810C22—24no—
811C22—24no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—24no—
816C22—24no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—42no—
829C22C2×#55314yes—
830C22#350914yes—
831C22C23×#4111yescharacteristic
832C22C23×#4111yescharacteristic
833C22C22×H(5,𝔽2)11yescharacteristic
834C22C22×2−1+412yes—
835C22C2×#58512yes—
836C4—24no—
837C4—24no—
838C4—22no—
839C4—22no—
840C4—44no—
841C4—42no—
842C4—42no—
843C4—48no—
844C4—42no—
845C4—44no—
846C4—48no—
847C4—48no—
848C4—42no—
849C4—48no—
850C4C2×#55314yes—
851C4C2×#55314yes—
852C4#349518yes—
853C2—24no—
854C2—24no—
855C2—42no—
856C2—82no—
857C2C22×#55311yescharacteristic
858C2C2×#349512yes—
859C2C2×#350911yescharacteristic
860C2#6281511yescharacteristic
861C2#6283512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59289C2semidirect
2. #59197C2semidirect
3. #39737C2semidirect
4. #39734C2semidirect
5. #37897C2semidirect
6. #37894C2semidirect
7. C2×#2857C2semidirect
8. #36599C2semidirect
9. #36586C2semidirect
10. #36210C2semidirect
11. #36189C2semidirect
12. #35673C2semidirect
13. #35630C2semidirect
14. #35316C2semidirect
16. #35286C2semidirect
17. #34209C2semidirect
18. #34203C2semidirect
19. #34188C2semidirect
21. C2×#2285C2semidirect
30. #2859C22semidirect
38. #2857C22semidirect
40. #2772C22semidirect
41. #2766C22semidirect
44. #2647C22semidirect
46. #2621C22semidirect
48. #2596C22semidirect
49. #2585C22semidirect
50. #2571C22semidirect
51. #2570C22semidirect
54. #2552C22semidirect
55. #2547C22semidirect
56. #2546C22semidirect
57. #2514C22semidirect
58. #2514C22semidirect
59. #2511C22semidirect
60. #2511C22semidirect
62. #2509C22semidirect
63. #2507C22semidirect
65. #2497C22semidirect
68. #2494C22semidirect
73. #2448C22semidirect
74. #2446C22semidirect
77. #2441C22semidirect
78. #2423C22semidirect
79. #2421C22semidirect
84. #2370C22semidirect
85. #2365C22semidirect
86. #2365C22semidirect
89. #2355C22semidirect
90. #2354C22semidirect
93. #2347C22semidirect
98. #2327C22semidirect
102. #2314C22semidirect
106. C4×C4⋊Q8C22semidirect
127. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#592892
#591972
#397372
#397342
#378972
#378942
C2×#28572
#365992
#365862
#362102
#361892
#356732
#356302
#353162
#353062
#352862
#342092
#342032
#341882
C4×#5252
C2×#22852