Finite Group Databasebeta

← #7632737

Subgroups — #7632737

Order 512.

5936 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36458C212yesmaximal, complemented
2#36458C212yesmaximal, complemented
3#36240C216yesmaximal, complemented
4D4×#126C216yesmaximal, complemented
5#35914C216yesmaximal, complemented
6#35898C212yesmaximal, complemented
7#35898C212yesmaximal, complemented
8#35873C216yesmaximal, complemented
9#35558C213yesmaximal, complemented
10#35558C213yesmaximal, complemented
11#35557C213yesmaximal, complemented
12#35545C213yesmaximal, complemented
13#35266C213yesmaximal, complemented
14#35160C213yesmaximal, complemented
15#34816C213yesmaximal, complemented
16C2×#2512C213yesmaximal, complemented
17#34258C211yesmaximal, characteristic
18#34258C211yesmaximal, characteristic
19#34258C211yesmaximal, characteristic
20#34250C211yesmaximal, characteristic, complemented
21#34183C211yesmaximal, characteristic, complemented
22C4⋊C4×#41C211yesmaximal, characteristic, complemented
23C4×#520C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25C22×#126C2216yescomplemented
26C2×#520C2211yescharacteristic
27C2×#520C2211yescharacteristic
28C2×#520C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2860C2216yescomplemented
33#2860C2216yescomplemented
34#2852C22112yescomplemented
35#2644C2216yescomplemented
36#2644C2216yescomplemented
37#2643C22112yescomplemented
38#2514C2213yescomplemented
39#2514C2213yescomplemented
40#2513C2213yescomplemented
41#2513C2213yescomplemented
42#2513C2216yescomplemented
43#2513C2216yescomplemented
44#2513C2216yescomplemented
45#2513C2216yescomplemented
46#2513C2216yescomplemented
47#2513C2216yescomplemented
48#2512C2213yescomplemented
49#2512C2213yescomplemented
50#2512C2216yescomplemented
51#2512C2216yescomplemented
52#2512C2216yescomplemented
53#2512C2216yescomplemented
54#2512C2216yescomplemented
55#2512C2216yescomplemented
56#2512C2216yescomplemented
57#2512C2216yescomplemented
58#2512C2216yescomplemented
59#2512C2216yescomplemented
60#2512C2216yescomplemented
61#2512C2216yescomplemented
62#2511C2211yescharacteristic, complemented
63#2511C2213yescomplemented
64#2511C2216yescomplemented
65#2510C2216yescomplemented
66#2510C2216yescomplemented
67#2510C22112yescomplemented
68#2497C2216yescomplemented
69#2497C2216yescomplemented
70#2497C2216yescomplemented
71#2497C2216yescomplemented
72#2496C2216yescomplemented
73#2496C2216yescomplemented
74#2496C2216yescomplemented
75#2496C2216yescomplemented
76#2495C2216yescomplemented
77#2495C2216yescomplemented
78#2494C2216yescomplemented
79#2494C2216yescomplemented
80#2481C2216yescomplemented
81#2481C2216yescomplemented
82#2481C22112yescomplemented
83#2481C22112yescomplemented
84#2481C22112yescomplemented
85#2480C22112yescomplemented
86#2480C22112yescomplemented
87#2480C22112yescomplemented
88#2480C22112yescomplemented
89#2480C22112yescomplemented
90#2480C22112yescomplemented
91#2401C2216yescomplemented
92#2401C2216yescomplemented
93C2×#397C2216yescomplemented
94C2×#396C2216yescomplemented
95#2351C2211yescharacteristic, complemented
96#2351C2212yescomplemented
97#2351C2211yescharacteristic, complemented
98Q8×C4⋊C4C2211yescharacteristic, complemented
99Q8×C4⋊C4C2212yescomplemented
100Q8×C4⋊C4C2212yescomplemented
101Q8×C4⋊C4C2212yescomplemented
102Q8×C4⋊C4C2211yescharacteristic, complemented
103#2349C2213yescomplemented
104#2349C2216yescomplemented
105#2349C2213yescomplemented
106D4×C4⋊C4C2213yescomplemented
107D4×C4⋊C4C2216yescomplemented
108D4×C4⋊C4C2216yescomplemented
109D4×C4⋊C4C2213yescomplemented
110D4×C4⋊C4C2216yescomplemented
111#2341C2212yes—
112#2341C2212yes—
113#2341C2212yes—
114#2341C2212yes—
115#2341C2212yes—
116#2341C2212yes—
117D4×C22⋊C4C2216yes—
118D4×C22⋊C4C2216yes—
119D4×C22⋊C4C2216yes—
120D4×C22⋊C4C2216yes—
121D4×C22⋊C4C2216yes—
122D4×C22⋊C4C2216yes—
123#2317C2213yescomplemented
124#2317C2213yescomplemented
125#2317C2213yescomplemented
126#2316C2213yescomplemented
127#2311C2213yes—
128#2311C2213yes—
129#2311C2213yes—
130#2309C2213yes—
131#2309C2213yes—
132#2309C2213yes—
133C4×#126C2216yescomplemented
134C4×#126C2216yescomplemented
135#2297C2213yes—
136#2297C2213yes—
137#2297C2213yes—
138#2296C2213yescomplemented
139#2296C2213yescomplemented
140#2296C2213yescomplemented
141C2×#390C2213yes—
142C2×#390C2213yes—
143C2×#390C2213yes—
144C2×#389C2213yescomplemented
145C2×#388C2216yescomplemented
146#2285C2213yescomplemented
147#2285C2213yescomplemented
148C2×#384C2213yescomplemented
149#2276C2212yescomplemented
150#2275C2216yescomplemented
151#2274C2213yescomplemented
152#2274C2213yescomplemented
153C42×Q8C2212yescomplemented
154C42×D4C2216yescomplemented
155C4×#117C2213yescomplemented
156C2×C4×C4⋊C4C2213yescomplemented
157C2×C4×C4⋊C4C2213yescomplemented
158C2×H(5,𝔽2)—28no—
159C2×H(5,𝔽2)—28no—
160C2×H(5,𝔽2)—28no—
161C22×#41C2313yes—
162C22×#41C2312yes—
163C22×#41C2311yescharacteristic
164C23×D4C2313yes—
165C23×D4C2316yes—
166C2×#126—424no—
167C2×#126C2316yes—
168C2×#126C2316yes—
169C2×#126C23112yes—
170C2×#126C23112yes—
171C2×#126C23112yes—
172C2×#126C23112yes—
173#520—28no—
174#520—28no—
175#520—28no—
176C4×#41—28no—
177C4×#41—28no—
178C4×#41—28no—
179C2×C4×Q8C2311yescharacteristic
180C2×C4×Q8C2311yescharacteristic
181C2×C4×Q8C2312yes—
182C2×C4×Q8C2311yescharacteristic
183C2×C4×Q8C2311yescharacteristic
184C2×C4×Q8C2312yes—
185C2×C4×Q8C2311yescharacteristic
186C2×C4×Q8C2311yescharacteristic
187C2×C4×Q8C2312yes—
188C2×C4×D4C2313yes—
189C2×C4×D4C2313yes—
190C2×C4×D4C2313yes—
191C2×C4×D4C2316yes—
192C2×C4×D4C2316yes—
193C2×C4×D4C2313yes—
194C2×C4×D4C2313yes—
195C2×C4×D4C2316yes—
196C2×C4×D4C2313yes—
197C2×#117C2313yes—
198C2×#117C2313yes—
199C2×#117C2313yes—
200C2×#117C2313yes—
201C2×#117C2313yes—
202C2×#117C2313yes—
203C22×C4⋊C4C2313yes—
204C22×C4⋊C4C2313yes—
205C22×C4⋊C4C2313yes—
206C22×C4⋊C4C2313yes—
207C22×C4⋊C4C2313yes—
208C22×C4⋊C4C2316yes—
209C22×C4⋊C4C2316yes—
210C22×C4⋊C4C2316yes—
211C22×C22⋊C4C2316yes—
212C22×C22⋊C4C2316yes—
213C22×C22⋊C4C2316yes—
214C22×C22⋊C4C2316yes—
215C22×C22⋊C4C2316yes—
216C22×C22⋊C4C2316yes—
217C22×C42C2313yes—
218C22×C42C2313yes—
219C22×C42C2313yes—
220C22×C42C2316yes—
221#401C2316yes—
222#401C2316yes—
223#400C2316yes—
224#400C23112yes—
225#400C23112yes—
226#400C2312yes—
227#400C2312yes—
228#400C2316yes—
229#400C2316yes—
230#400C2316yes—
231#397C23112yes—
232#397C23112yes—
233#397C23112yes—
234#397C2316yes—
235#397C2316yes—
236#397C23112yes—
237#397C23112yes—
238#397C23112yes—
239#397C2316yes—
240#397C23112yes—
241#397C23112yes—
242#397C2316yes—
243#397C2316yes—
244#397C2316yes—
245#396C23112yes—
246#396C23112yes—
247#396C2316yes—
248#396C23112yes—
249#396C23112yes—
250#396C2316yes—
251#391C2313yes—
252#391C2313yes—
253#391C2313yes—
254#391C2311yescharacteristic
255#391C2311yescharacteristic
256#391C2311yescharacteristic
257#390C2313yes—
258#390C2313yes—
259#390C2313yes—
260#390C2316yes—
261#390C2316yes—
262#390C2316yes—
263#390C2316yes—
264#390C2316yes—
265#390C2316yes—
266#390C2316yes—
267#390C2316yes—
268#390C2316yes—
269#390C2316yes—
270#390C2316yes—
271#390C2316yes—
272#390C2316yes—
273#390C2316yes—
274#390C2316yes—
275#390C2313yes—
276#390C2313yes—
277#390C2313yes—
278#389C2313yes—
279#389C2316yes—
280#389C2316yes—
281#389C2316yes—
282#389C2313yes—
283#389C2316yes—
284#389C2316yes—
285#389C2316yes—
286#389C2316yes—
287#389C2313yes—
288#389C2313yes—
289#389C2313yes—
290#389C2316yes—
291#389C2313yes—
292#389C2313yes—
293#389C2313yes—
294#389C2316yes—
295#389C2313yes—
296#389C2313yes—
297#389C2311yescharacteristic
298#389C2313yes—
299#388C2316yes—
300#388C2316yes—
301#388C2316yes—
302#388C2316yes—
303#388C2316yes—
304#388C2316yes—
305#388C23112yes—
306#388C23112yes—
307#388C23112yes—
308#388C23112yes—
309#388C23112yes—
310#388C23112yes—
311#388C23112yes—
312#388C23112yes—
313#387C2312yes—
314#387C2312yes—
315#387C2316yes—
316#387C2316yes—
317#387C2316yes—
318#387C2316yes—
319#387C23112yes—
320#387C23112yes—
321#386C23112yes—
322#386C23112yes—
323#386C23112yes—
324#386C2316yes—
325#386C2316yes—
326#386C2316yes—
327#386C2316yes—
328#386C2316yes—
329#386C2316yes—
330#385C23112yes—
331#385C23112yes—
332#385C23112yes—
333#385C2316yes—
334#385C2316yes—
335#385C2316yes—
336#385C2316yes—
337#385C2316yes—
338#385C2316yes—
339#384C2316yes—
340#384C2316yes—
341#384C2316yes—
342#384C2313yes—
343#384C2316yes—
344#384C2313yes—
345#384C2313yes—
346#384C2311yescharacteristic
347#383C2316yes—
348#383C2316yes—
349#382C2313yes—
350#382C2313yes—
351#382C2316yes—
352#382C2313yes—
353#382C2313yes—
354#380C2316yes—
355#380C2316yes—
356#380C2316yes—
357#380C2316yes—
358#380C2316yes—
359#380C2316yes—
360#380C23112yes—
361#380C2316yes—
362#380C2316yes—
363#380C2316yes—
364#380C2316yes—
365#379C23112yes—
366#379C23112yes—
367#379C23112yes—
368C4×C4⋊C4C2313yes—
369C4×C4⋊C4C2313yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2313yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2316yes—
377C4×C4⋊C4C2316yes—
378C4×C4⋊C4C2316yes—
379C4×C4⋊C4C2316yes—
380C4×C4⋊C4C2316yes—
381C4×C4⋊C4C2316yes—
382C4×C4⋊C4C2311yescharacteristic
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2316yes—
385C4×C4⋊C4C2313yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2311yescharacteristic
388C4×C4⋊C4C2313yes—
389C4×C4⋊C4C2313yes—
390C4×C4⋊C4C2313yes—
391C4×C4⋊C4C2313yes—
392C4×C22⋊C4C2316yes—
393C4×C22⋊C4C2316yes—
394C4×C22⋊C4C2316yes—
395C4×C22⋊C4C2316yes—
396C4×C22⋊C4C2316yes—
397C4×C22⋊C4C2316yes—
398C4×C22⋊C4C23112yes—
399C4×C22⋊C4C2316yes—
400C4×C22⋊C4C2316yes—
401C4×C22⋊C4C23112yes—
402#376C2316yes—
403C2×#95C2313yes—
404C2×#95C2316yes—
405C2×#95C2313yes—
406C2×#95C2316yes—
407C43C2316yes—
408C25C2416yes—
409H(5,𝔽2)—464no—
410C2×#41—28no—
411C2×#41—28no—
412C2×#41—28no—
413C2×#41—212no—
414C2×#41—212no—
415C2×#41—212no—
416C2×#41#4118yes—
417C2×#41#4118yes—
418C2×#41#4118yes—
419C22×Q8C2411yescharacteristic
420C22×Q8C2411yescharacteristic
421C22×D4—224no—
422C22×D4—224no—
423C22×D4—224no—
424C22×D4—212no—
425C22×D4—212no—
426C22×D4—212no—
427C22×D4C2416yes—
428C22×D4C2413yes—
429C22×D4C2416yes—
430C22×D4C2413yes—
431C23×C4C2416yes—
432C23×C4C2413yes—
433C23×C4C2413yes—
434C23×C4C2413yes—
435C23×C4C2413yes—
436C23×C4C2416yes—
437C23×C4C2416yes—
438C23×C4C2416yes—
439C23×C4C2413yes—
440C23×C4C2413yes—
441C23×C4C2413yes—
442#126—224no—
443#126—424no—
444#126—424no—
445#126—424no—
446#126—412no—
447#126—812no—
448C4×Q8—24no—
449C4×Q8—24no—
450C4×Q8—24no—
451C4×Q8—24no—
452C4×Q8—24no—
453C4×Q8—24no—
454C4×Q8—28no—
455C4×Q8—28no—
456C4×Q8—28no—
457C4×D4—212no—
458C4×D4—212no—
459C4×D4—212no—
460C4×D4—212no—
461C4×D4—212no—
462C4×D4—212no—
463C4×D4—224no—
464C4×D4—224no—
465C4×D4—224no—
466#117—212no—
467#117—212no—
468#117—212no—
469#117—212no—
470#117—212no—
471#117—212no—
472C2×C4⋊C4—212no—
473C2×C4⋊C4—212no—
474C2×C4⋊C4—212no—
475C2×C4⋊C4—212no—
476C2×C4⋊C4—46no—
477C2×C4⋊C4—412no—
478C2×C4⋊C4—412no—
479C2×C4⋊C4—86no—
480C2×C4⋊C4C2411yescharacteristic
481C2×C4⋊C4C2413yes—
482C2×C4⋊C4C2413yes—
483C2×C4⋊C4C2413yes—
484C2×C4⋊C4C2416yes—
485C2×C4⋊C4C2416yes—
486C2×C4⋊C4C2416yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2413yes—
490C2×C4⋊C4C2413yes—
491C2×C4⋊C4C2413yes—
492C2×C4⋊C4C2413yes—
493C2×C4⋊C4C2411yescharacteristic
494C2×C4⋊C4C2411yescharacteristic
495C2×C4⋊C4C2411yescharacteristic
496C2×C4⋊C4C2413yes—
497C2×C4⋊C4C2413yes—
498C2×C4⋊C4C2413yes—
499C2×C4⋊C4C2413yes—
500C2×C4⋊C4C2413yes—
501C2×C4⋊C4C2413yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C24112yes—
505C2×C4⋊C4C24112yes—
506C2×C4⋊C4C24112yes—
507C2×C4⋊C4C2413yes—
508C2×C4⋊C4C2413yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2411yescharacteristic
516C2×C22⋊C4—412no—
517C2×C22⋊C4—412no—
518C2×C22⋊C4—412no—
519C2×C22⋊C4—412no—
520C2×C22⋊C4—86no—
521C2×C22⋊C4—86no—
522C2×C22⋊C4C2416yes—
523C2×C22⋊C4C2416yes—
524C2×C22⋊C4C2416yes—
525C2×C22⋊C4C2416yes—
526C2×C22⋊C4C2416yes—
527C2×C22⋊C4C2416yes—
528C2×C22⋊C4C2416yes—
529C2×C22⋊C4C2416yes—
530C2×C22⋊C4C2416yes—
531C2×C22⋊C4C2416yes—
532C2×C22⋊C4C2416yes—
533C2×C22⋊C4C2416yes—
534C2×C22⋊C4C24112yes—
535C2×C22⋊C4C24112yes—
536C2×C22⋊C4C24112yes—
537C2×C22⋊C4C24112yes—
538C2×C22⋊C4C24112yes—
539C2×C22⋊C4C24112yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2416yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C42—212no—
547C2×C42—212no—
548C2×C42—212no—
549C2×C42—412no—
550C2×C42C2413yes—
551C2×C42C2413yes—
552C2×C42C2413yes—
553C2×C42C2416yes—
554C2×C42C2416yes—
555C2×C42C2416yes—
556C2×C42C2413yes—
557C2×C42C2413yes—
558C2×C42C2413yes—
559C2×C42C2413yes—
560C2×C42C2413yes—
561C2×C42C2413yes—
562C2×C42C2416yes—
563C2×C42C2411yescharacteristic
564C2×C42C2411yescharacteristic
565C2×C42C2411yescharacteristic
566C2×C42C2416yes—
567C2×C42C24112yes—
568C2×C42C2416yes—
569C2×C42C2412yes—
570#95C2411yescharacteristic
571#95C2411yescharacteristic
572#95C2416yes—
573#95C2416yes—
574#95C24112yes—
575#95C2413yes—
576#95C2413yes—
577#95C2413yes—
578#95C2413yes—
579#95C2413yes—
580#95C2413yes—
581#95C24112yes—
582#95C2412yes—
583#95C2416yes—
584#95C2416yes—
585#95C2412yes—
586#95C2412yes—
587#95C2412yes—
588#95C2412yes—
589#95C2412yes—
590#95C2412yes—
591#95C2416yes—
592#95C2416yes—
593#95C2416yes—
594#95C2416yes—
595#95C2416yes—
596#95C2416yes—
597#95C2412yes—
598#95C2416yes—
599#95C2416yes—
600#95C2416yes—
601#95C2416yes—
602#95C2416yes—
603#95C2416yes—
604#95C2416yes—
605#95C2416yes—
606C24—212no—
607C24—212no—
608C24—212no—
609C24—46no—
610C24—46no—
611C24—46no—
612C24—46no—
613C24C2516yes—
614C24C2513yes—
615#41—432no—
616#41—448no—
617#41#126164yescomplemented
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8C2×#4114yes—
622C2×Q8C2×#4114yes—
623C2×Q8C2×#4114yes—
624C2×D4—212no—
625C2×D4—212no—
626C2×D4—212no—
627C2×D4—26no—
628C2×D4—212no—
629C2×D4—212no—
630C2×D4—212no—
631C2×D4—26no—
632C2×D4—26no—
633C2×D4—496no—
634C2×D4—448no—
635C2×D4C2×#41112yes—
636C2×D4C2×#41112yes—
637C2×D4C2×#41112yes—
638C22×C4—26no—
639C22×C4—26no—
640C22×C4—26no—
641C22×C4—26no—
642C22×C4—26no—
643C22×C4—26no—
644C22×C4—212no—
645C22×C4—212no—
646C22×C4—212no—
647C22×C4—212no—
648C22×C4—212no—
649C22×C4—212no—
650C22×C4—26no—
651C22×C4—26no—
652C22×C4—26no—
653C22×C4—26no—
654C22×C4—43no—
655C22×C4—43no—
656C22×C4—43no—
657C22×C4—43no—
658C22×C4—46no—
659C22×C4—46no—
660C22×C4—46no—
661C22×C4—46no—
662C22×C4—43no—
663C22×C4—43no—
664C22×C4—46no—
665C22×C4—46no—
666C22×C4—43no—
667C22×C4—43no—
668C22×C4C2×#41112yes—
669C22×C4C2×#41112yes—
670C22×C4C2×#41112yes—
671C22×C4C2512yes—
672C22×C4C2511yescharacteristic
673C22×C4C2511yescharacteristic
674C22×C4C2512yes—
675C22×C4C2512yes—
676C22×C4C2513yes—
677C22×C4C2512yes—
678C22×C4C2513yes—
679C22×C4C2513yes—
680C22×C4C2516yes—
681C22×C4C2513yes—
682C22×C4C2513yes—
683C22×C4C2516yes—
684C22×C4C2513yes—
685C22×C4C2516yes—
686C22×C4C2511yescharacteristic
687C22×C4C2511yescharacteristic
688C22×C4C2511yescharacteristic
689C22×C4C2511yescharacteristic
690C22×C4C2511yescharacteristic
691C22×C4C2513yes—
692C4⋊C4—26no—
693C4⋊C4—26no—
694C4⋊C4—26no—
695C4⋊C4—212no—
696C4⋊C4—212no—
697C4⋊C4—212no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—26no—
702C4⋊C4—26no—
703C4⋊C4—26no—
704C4⋊C4—26no—
705C4⋊C4—26no—
706C4⋊C4—26no—
707C4⋊C4—26no—
708C4⋊C4—26no—
709C4⋊C4—26no—
710C4⋊C4—212no—
711C4⋊C4—212no—
712C4⋊C4—22no—
713C4⋊C4—26no—
714C4⋊C4—24no—
715C4⋊C4—43no—
716C4⋊C4—43no—
717C4⋊C4—412no—
718C4⋊C4—412no—
719C4⋊C4—46no—
720C4⋊C4—412no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—46no—
724C4⋊C4—46no—
725C4⋊C4—46no—
726C4⋊C4—46no—
727C4⋊C4H(5,𝔽2)14yescomplemented
728C22⋊C4—212no—
729C22⋊C4—212no—
730C22⋊C4—212no—
731C22⋊C4—212no—
732C22⋊C4—212no—
733C22⋊C4—212no—
734C22⋊C4—212no—
735C22⋊C4—212no—
736C22⋊C4—212no—
737C22⋊C4—212no—
738C22⋊C4—412no—
739C22⋊C4—412no—
740C22⋊C4—412no—
741C22⋊C4—412no—
742C22⋊C4—46no—
743C22⋊C4—46no—
744C22⋊C4—412no—
745C22⋊C4—412no—
746C22⋊C4—46no—
747C22⋊C4—46no—
748C22⋊C4—46no—
749C22⋊C4—46no—
750C22⋊C4—46no—
751C22⋊C4—46no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—26no—
756C42—26no—
757C42—26no—
758C42—26no—
759C42—26no—
760C42—26no—
761C42—26no—
762C42—26no—
763C42—26no—
764C42—212no—
765C42—212no—
766C42—212no—
767C42—212no—
768C42—412no—
769C42—42no—
770C42—46no—
771C42—46no—
772C23—23no—
773C23—23no—
774C23—23no—
775C23—23no—
776C23—26no—
777C23—26no—
778C23—26no—
779C23—26no—
780C23—26no—
781C23—26no—
782C23—26no—
783C23—424no—
784C23—812no—
785C23—812no—
786C23—812no—
787C23—812no—
788C23—812no—
789C23—812no—
790C23C22×#4116yes—
791C23C22×#4116yes—
792C23C22×#4116yes—
793C23C2611yescharacteristic
794Q8—44no—
795Q8C2×#126116yescomplemented
796D4—424no—
797D4—424no—
798D4—412no—
799D4C2×#126148yescomplemented
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—23no—
814C2×C4—23no—
815C2×C4—23no—
816C2×C4—23no—
817C2×C4—23no—
818C2×C4—23no—
819C2×C4—26no—
820C2×C4—26no—
821C2×C4—26no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—26no—
826C2×C4—26no—
827C2×C4—23no—
828C2×C4—26no—
829C2×C4—23no—
830C2×C4—23no—
831C2×C4—22no—
832C2×C4—23no—
833C2×C4—26no—
834C2×C4—23no—
835C2×C4—22no—
836C2×C4—23no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—23no—
840C2×C4—26no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—23no—
844C2×C4—26no—
845C2×C4—23no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—23no—
850C2×C4—23no—
851C2×C4—23no—
852C2×C4—21no—
853C2×C4—412no—
854C2×C4—412no—
855C2×C4—412no—
856C2×C4—412no—
857C2×C4—424no—
858C2×C4—812no—
859C2×C4—812no—
860C2×C4—86no—
861C2×C4—812no—
862C2×C4—86no—
863C2×C4C2×#126148yescomplemented
864C2×C4C22×#4112yes—
865C2×C4C22×#4116yes—
866C2×C4C22×#4116yes—
867C2×C4C22×#4116yes—
868C2×C4C22×#4112yes—
869C2×C4C22×#4112yes—
870C2×C4C2×H(5,𝔽2)12yes—
871C2×C4C2×H(5,𝔽2)12yes—
872C2×C4C2×H(5,𝔽2)12yes—
873C2×C4#58512yes—
874C22—26no—
875C22—26no—
876C22—26no—
877C22—26no—
878C22—26no—
879C22—26no—
880C22—46no—
881C22—46no—
882C22—46no—
883C22—46no—
884C22—46no—
885C22—46no—
886C22—46no—
887C22—1624no—
888C22C22×#126112yes—
889C22C23×#4111yescharacteristic
890C22C23×#4111yescharacteristic
891C22C23×#4111yescharacteristic
892C22C22×H(5,𝔽2)11yescharacteristic
893C22C2×#58511yescharacteristic
894C22H(7,𝔽2)11yescharacteristic
895C222−1+611yescharacteristic
896C4—22no—
897C4—22no—
898C4—22no—
899C4—22no—
900C4—43no—
901C4—43no—
902C4—46no—
903C4—46no—
904C4—42no—
905C4—42no—
906C4—43no—
907C4—43no—
908C4—41no—
909C4—43no—
910C4—46no—
911C4—42no—
912C4—43no—
913C4—41no—
914C4—42no—
915C4C22×#126112yes—
916C4C22×#12614yes—
917C2—212no—
918C2—86no—
919C2C23×#12611yescharacteristic
920C2#6280011yescharacteristic
921C2#6285711yescharacteristic
922C2#6298511yescharacteristic
923C2#6298611yescharacteristic
924C2#6299511yescharacteristic
925C2#6300811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×H(5,𝔽2)C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36458C2semidirect
2. #36458C2semidirect
3. #36240C2semidirect
4. D4×#126C2semidirect
5. #35914C2semidirect
6. #35898C2semidirect
7. #35898C2semidirect
8. #35873C2semidirect
9. #35558C2semidirect
10. #35558C2semidirect
11. #35557C2semidirect
12. #35545C2semidirect
13. #35266C2semidirect
14. #35160C2semidirect
15. #34816C2semidirect
16. C2×#2512C2semidirect
20. #34250C2semidirect
21. #34183C2semidirect
22. C4⋊C4×#41C2semidirect
23. C4×#520C2semidirect
25. C22×#126C22semidirect
32. #2860C22semidirect
33. #2860C22semidirect
34. #2852C22semidirect
35. #2644C22semidirect
36. #2644C22semidirect
37. #2643C22semidirect
38. #2514C22semidirect
39. #2514C22semidirect
40. #2513C22semidirect
41. #2513C22semidirect
42. #2513C22semidirect
43. #2513C22semidirect
44. #2513C22semidirect
45. #2513C22semidirect
46. #2513C22semidirect
47. #2513C22semidirect
48. #2512C22semidirect
49. #2512C22semidirect
50. #2512C22semidirect
51. #2512C22semidirect
52. #2512C22semidirect
53. #2512C22semidirect
54. #2512C22semidirect
55. #2512C22semidirect
56. #2512C22semidirect
57. #2512C22semidirect
58. #2512C22semidirect
59. #2512C22semidirect
60. #2512C22semidirect
61. #2512C22semidirect
62. #2511C22semidirect
63. #2511C22semidirect
64. #2511C22semidirect
65. #2510C22semidirect
66. #2510C22semidirect
67. #2510C22semidirect
68. #2497C22semidirect
69. #2497C22semidirect
70. #2497C22semidirect
71. #2497C22semidirect
72. #2496C22semidirect
73. #2496C22semidirect
74. #2496C22semidirect
75. #2496C22semidirect
76. #2495C22semidirect
77. #2495C22semidirect
78. #2494C22semidirect
79. #2494C22semidirect
80. #2481C22semidirect
81. #2481C22semidirect
82. #2481C22semidirect
83. #2481C22semidirect
84. #2481C22semidirect
85. #2480C22semidirect
86. #2480C22semidirect
87. #2480C22semidirect
88. #2480C22semidirect
89. #2480C22semidirect
90. #2480C22semidirect
91. #2401C22semidirect
92. #2401C22semidirect
93. C2×#397C22semidirect
94. C2×#396C22semidirect
95. #2351C22semidirect
96. #2351C22semidirect
97. #2351C22semidirect
98. Q8×C4⋊C4C22semidirect
99. Q8×C4⋊C4C22semidirect
100. Q8×C4⋊C4C22semidirect
101. Q8×C4⋊C4C22semidirect
102. Q8×C4⋊C4C22semidirect
103. #2349C22semidirect
104. #2349C22semidirect
105. #2349C22semidirect
106. D4×C4⋊C4C22semidirect
107. D4×C4⋊C4C22semidirect
108. D4×C4⋊C4C22semidirect
109. D4×C4⋊C4C22semidirect
110. D4×C4⋊C4C22semidirect
123. #2317C22semidirect
124. #2317C22semidirect
125. #2317C22semidirect
126. #2316C22semidirect
133. C4×#126C22semidirect
134. C4×#126C22semidirect
138. #2296C22semidirect
139. #2296C22semidirect
140. #2296C22semidirect
144. C2×#389C22semidirect
145. C2×#388C22semidirect
146. #2285C22semidirect
147. #2285C22semidirect
148. C2×#384C22semidirect
149. #2276C22semidirect
150. #2275C22semidirect
151. #2274C22semidirect
152. #2274C22semidirect
153. C42×Q8C22semidirect
154. C42×D4C22semidirect
155. C4×#117C22semidirect
156. C2×C4×C4⋊C4C22semidirect
157. C2×C4×C4⋊C4C22semidirect
617. #41#126semidirect
727. C4⋊C4H(5,𝔽2)semidirect
795. Q8C2×#126semidirect
799. D4C2×#126semidirect
863. C2×C4C2×#126semidirect

Maximal subgroups

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

subgroupindex
#364582
#362402
D4×#1262
#359142
#358982
#358732
#355582
#355572
#355452
#352662
#351602
#348162
C2×#25122
#342582
#342502
#341832
C4⋊C4×#412
C4×#5202