Finite Group Databasebeta

← #7626951

Subgroups — #7626951

Order 512.

8236 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic
2#34495C216yesmaximal, complemented
3#34478C216yesmaximal, complemented
4#34476C216yesmaximal, complemented
5#34415C216yesmaximal, complemented
6#34412C216yesmaximal, complemented
7#34377C213yesmaximal, complemented
8#34367C213yesmaximal, complemented
9#34320C216yesmaximal, complemented
10#34312C212yesmaximal, complemented
11#34294C212yesmaximal, complemented
12#34293C212yesmaximal, complemented
13#34258C212yesmaximal, complemented
14#34257C212yesmaximal, complemented
15#34240C213yesmaximal, complemented
16#34197C211yesmaximal, characteristic, complemented
17C4×#548C212yesmaximal, complemented
18#34129C211yesmaximal, characteristic, complemented
19#34086C213yesmaximal, complemented
20C22×2−1+4C2211yescharacteristic
21C22×H(5,𝔽2)C2211yescharacteristic
22#3500C4132yescomplemented
23C2×#548C2212yes—
24C2×#548C2212yes—
25C2×#546C2216yes—
26C2×#546C2216yes—
27C2×#536C2213yes—
28C2×#535C2213yes—
29C2×#532C2213yes—
30C22×#124C2213yes—
31C2×#520C2212yes—
32C2×#519C2212yescomplemented
33C2×C4×#41C2212yes—
34C2×C4×#41C2211yescharacteristic
35C22×C4×Q8C2212yescomplemented
36#2379C22112yescomplemented
37#2377C22112yescomplemented
38#2376C22112yescomplemented
39#2375C22112yescomplemented
40#2374C22112yescomplemented
41#2372C22112yescomplemented
42#2367C2216yescomplemented
43#2367C2216yescomplemented
44#2367C2216yescomplemented
45#2367C2216yescomplemented
46#2363C2216yescomplemented
47#2363C22112yescomplemented
48#2363C2216yescomplemented
49#2362C2216yescomplemented
50#2362C2216yescomplemented
51#2361C2216yescomplemented
52#2361C2216yescomplemented
53#2360C2216yescomplemented
54#2360C2216yescomplemented
55#2358C22112yescomplemented
56#2357C2216yescomplemented
57#2354C2216yescomplemented
58#2354C2216yescomplemented
59#2352C2216yescomplemented
60#2352C2216yescomplemented
61#2351C2212yescomplemented
62Q8×C4⋊C4C2212yescomplemented
63D4×C4⋊C4C2216yescomplemented
64#2346C2216yescomplemented
65#2346C2216yescomplemented
66#2342C22112yescomplemented
67#2342C22112yescomplemented
68#2341C2212yes—
69#2341C2212yes—
70#2341C2212yes—
71#2341C2212yes—
72#2341C2216yescomplemented
73#2341C2216yescomplemented
74Q8×C22⋊C4C2212yescomplemented
75Q8×C22⋊C4C2216yescomplemented
76Q8×C22⋊C4C2216yescomplemented
77Q8×C22⋊C4C2212yescomplemented
78D4×C22⋊C4C2216yes—
79D4×C22⋊C4C2216yes—
80D4×C22⋊C4C2216yes—
81D4×C22⋊C4C2216yes—
82#2337C2211yescharacteristic, complemented
83#2337C2213yescomplemented
84#2337C2213yescomplemented
85#2337C2213yescomplemented
86#2337C2216yescomplemented
87#2335C22112yescomplemented
88#2335C22112yescomplemented
89#2333C2216yescomplemented
90#2333C2216yescomplemented
91#2331C2216yescomplemented
92#2331C2216yescomplemented
93#2328C2216yescomplemented
94#2328C2216yescomplemented
95#2326C2216yescomplemented
96#2326C2216yescomplemented
97#2324C2216yescomplemented
98#2324C2216yescomplemented
99#2324C2216yescomplemented
100#2324C2216yescomplemented
101#2323C2216yescomplemented
102#2323C2216yescomplemented
103#2321C22112yescomplemented
104#2321C22112yescomplemented
105#2319C2213yescomplemented
106#2319C2213yescomplemented
107#2315C2216yescomplemented
108#2312C2216yescomplemented
109#2312C2216yescomplemented
110#2311C2216yes—
111#2311C2216yescomplemented
112#2311C2216yescomplemented
113#2309C2216yes—
114C4×#124C2216yescomplemented
115C4×#124C2216yescomplemented
116C4×C22⋊Q8C2216yescomplemented
117C4×C22⋊Q8C2216yescomplemented
118C4×#121C2216yescomplemented
119C4×#121C2216yescomplemented
120#2297C2216yes—
121#2297C2216yescomplemented
122#2297C2216yescomplemented
123#2293C2216yescomplemented
124#2293C2213yescomplemented
125#2293C2213yescomplemented
126C2×#390C2216yes—
127#2290C2216yescomplemented
128#2290C2216yescomplemented
129#2285C2213yescomplemented
130#2283C2213yescomplemented
131#2283C2213yescomplemented
132#2276C2211yescharacteristic, complemented
133#2276C2211yescharacteristic, complemented
134#2273C2216yescomplemented
135C42×Q8C2211yescharacteristic, complemented
136C42×Q8C2211yescharacteristic, complemented
137C42×D4C2216yescomplemented
138C4×#117C2213yescomplemented
139C2×2−1+4—48no—
140C2×2−1+4C2×C4116yescomplemented
141C2×H(5,𝔽2)—48no—
142C2×H(5,𝔽2)C2×C4116yescomplemented
143C22×#41C2311yescharacteristic
144C22×#41C2312yes—
145C22×#41C2313yes—
146C22×#41C2313yes—
147C22×#41C2316yes—
148C23×Q8C2312yes—
149C23×Q8C2313yes—
150C23×D4C2316yes—
151C23×D4C2313yes—
152#548C2×C4132yescomplemented
153#548C2×C4132yescomplemented
154#546C2×C4196yescomplemented
155#546C2×C4196yescomplemented
156#536C2×C4148yescomplemented
157#535C2×C4148yescomplemented
158#532C2×C4148yescomplemented
159C2×C4⋊Q8C2313yes—
160C2×#127C2313yes—
161C2×#124C2×C4148yescomplemented
162C2×#124C2316yes—
163C2×#124C2313yes—
164C2×#124C2311yescharacteristic
165C2×#124C2316yes—
166C2×#124C2316yes—
167C2×#123C23112yes—
168C2×C22⋊Q8C2316yes—
169C2×C22⋊Q8C2316yes—
170C2×#121C2316yes—
171C2×#121C2316yes—
172C2×#121C2316yes—
173C2×#121C2316yes—
174C2×#120C23112yes—
175#520—48no—
176#519—48no—
177C4×#41—48no—
178C4×#41C2×C4116yescomplemented
179C2×C4×Q8—48no—
180C2×C4×Q8C2312yes—
181C2×C4×Q8C2312yes—
182C2×C4×Q8C2312yes—
183C2×C4×Q8C2312yes—
184C2×C4×Q8C2316yes—
185C2×C4×Q8C2316yes—
186C2×C4×Q8C2316yes—
187C2×C4×Q8C2316yes—
188C2×C4×Q8C2311yescharacteristic
189C2×C4×Q8C2311yescharacteristic
190C2×C4×D4C2316yes—
191C2×C4×D4C2316yes—
192C2×C4×D4C2316yes—
193C2×C4×D4C2316yes—
194C2×C4×D4C2316yes—
195C2×C4×D4C2316yes—
196C2×C4×D4C23112yes—
197C2×C4×D4C2313yes—
198C2×C4×D4C2316yes—
199C2×C4×D4C2316yes—
200C2×C4×D4C2313yes—
201C2×#117C2316yes—
202C2×#117C2316yes—
203C2×#117C2316yes—
204C2×#117C2316yes—
205C2×#117C2316yes—
206C2×#117C2316yes—
207C2×#117C2313yes—
208C22×C4⋊C4C2316yes—
209C22×C4⋊C4C2316yes—
210C22×C22⋊C4C23112yes—
211C22×C22⋊C4C23112yes—
212C22×C22⋊C4C2316yes—
213C22×C22⋊C4C2316yes—
214C22×C42C2316yes—
215C22×C42C2316yes—
216C22×C42C2313yes—
217#391C2316yes—
218#391C2316yes—
219#391C2316yes—
220#391C23112yes—
221#391C2316yes—
222#391C2312yes—
223#391C2316yes—
224#391C2316yes—
225#391C2316yes—
226#390C2316yes—
227#390C23112yes—
228#390C2316yes—
229#390C2316yes—
230#390C2316yes—
231#390C2316yes—
232#390C2316yes—
233#390C23112yes—
234#390C2316yes—
235#390C23112yes—
236#390C2316yes—
237#390C2316yes—
238#390C2316yes—
239#390C2316yes—
240#390C2316yes—
241#390C2316yes—
242#390C2316yes—
243#389C2316yes—
244#389C2316yes—
245#389C2316yes—
246#389C2316yes—
247#389C23112yes—
248#389C2316yes—
249#389C2316yes—
250#388C2316yes—
251#388C2316yes—
252#388C23112yes—
253#388C23112yes—
254#388C23112yes—
255#388C23112yes—
256#388C23112yes—
257#388C23112yes—
258#388C23112yes—
259#388C23112yes—
260#388C23112yes—
261#388C23112yes—
262#388C23112yes—
263#388C23112yes—
264#388C23112yes—
265#388C23112yes—
266#388C2312yes—
267#388C2316yes—
268#388C2316yes—
269#388C2312yes—
270#388C2316yes—
271#388C2316yes—
272#387C2316yes—
273#387C23112yes—
274#387C2316yes—
275#387C2316yes—
276#387C2316yes—
277#387C23112yes—
278#386C23112yes—
279#386C23112yes—
280#386C2316yes—
281#386C2316yes—
282#386C23112yes—
283#386C2316yes—
284#386C2316yes—
285#386C2316yes—
286#386C23112yes—
287#386C23112yes—
288#386C2316yes—
289#386C2316yes—
290#386C2312yes—
291#386C2316yes—
292#386C2316yes—
293#386C2316yes—
294#386C2316yes—
295#385C2316yes—
296#385C23112yes—
297#385C23112yes—
298#385C23112yes—
299#385C23112yes—
300#385C2312yes—
301#385C23112yes—
302#385C2316yes—
303#385C2316yes—
304#384C2316yes—
305#383C2311yescharacteristic
306#383C2313yes—
307#382C2316yes—
308#382C2316yes—
309#382C2316yes—
310#381C2316yes—
311#381C2316yes—
312#380C2316yes—
313#380C2316yes—
314#380C2316yes—
315#380C2316yes—
316#380C23112yes—
317#380C23112yes—
318#380C2316yes—
319#380C2316yes—
320#380C2313yes—
321#380C2316yes—
322#380C2313yes—
323#379C23112yes—
324#379C23112yes—
325C4×C4⋊C4C2313yes—
326C4×C4⋊C4C2313yes—
327C4×C4⋊C4C2316yes—
328C4×C4⋊C4C2316yes—
329C4×C4⋊C4C2316yes—
330C4×C4⋊C4C2316yes—
331C4×C4⋊C4C2316yes—
332C4×C4⋊C4C23112yes—
333C4×C4⋊C4C2311yescharacteristic
334C4×C4⋊C4C2313yes—
335C4×C4⋊C4C2316yes—
336C4×C4⋊C4C2316yes—
337C4×C4⋊C4C2316yes—
338C4×C4⋊C4C2313yes—
339C4×C4⋊C4C2313yes—
340C4×C22⋊C4C2313yes—
341C4×C22⋊C4C23112yes—
342C4×C22⋊C4C2316yes—
343C4×C22⋊C4C23112yes—
344C4×C22⋊C4C23112yes—
345C4×C22⋊C4C2312yes—
346C4×C22⋊C4C2313yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C23112yes—
351C4×C22⋊C4C23112yes—
352C4×C22⋊C4C23112yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2316yes—
357C4×C22⋊C4C2316yes—
358C4×C22⋊C4C2316yes—
359C4×C22⋊C4C23112yes—
360#376C2313yes—
361#376C2313yes—
362#376C2316yes—
363#376C2316yes—
364C43C2313yes—
365C43C2313yes—
366C25C2416yes—
3672−1+4—464no—
368H(5,𝔽2)—464no—
369C2×#41—28no—
370C2×#41—28no—
371C2×#41—28no—
372C2×#41—412no—
373C2×#41—412no—
374C2×#41—412no—
375C2×#41—412no—
376C2×#41C22×C418yes—
377C2×#41C22×C4116yes—
378C2×#41C22×C4124yes—
379C2×#41C22×C4124yes—
380C2×#41C22×C4148yes—
381C22×Q8—28no—
382C22×Q8—28no—
383C22×Q8—412no—
384C22×Q8C22×C4116yes—
385C22×Q8C22×C4124yes—
386C22×Q8C2416yes—
387C22×Q8C2413yes—
388C22×Q8C2411yescharacteristic
389C22×Q8C2411yescharacteristic
390C22×D4—412no—
391C22×D4—412no—
392C22×D4—412no—
393C22×D4C22×C4124yes—
394C22×D4C22×C4148yes—
395C22×D4C2416yes—
396C22×D4C2413yes—
397C22×D4C2416yes—
398C22×D4C2416yes—
399C22×D4C2416yes—
400C22×D4C2416yes—
401C22×D4C2413yes—
402C22×D4C2411yescharacteristic
403C23×C4C2416yes—
404C23×C4C2416yes—
405C23×C4C2413yes—
406C23×C4C2416yes—
407C23×C4C2412yes—
408C23×C4C24112yes—
409C23×C4C2416yes—
410C23×C4C2416yes—
411C23×C4C2413yes—
412C23×C4C2413yes—
413C23×C4C2416yes—
414C4⋊Q8C22×C4124yes—
415#127C22×C4124yes—
416#124C22×C4124yes—
417#124C22×C4148yes—
418#124C22×C4148yes—
419#124C22×C4148yes—
420#124C22×C418yes—
421#123C22×C4196yes—
422C22⋊Q8C22×C4148yes—
423C22⋊Q8C22×C4148yes—
424#121C22×C4148yes—
425#121C22×C4148yes—
426#121C22×C4148yes—
427#121C22×C4148yes—
428#120C22×C4196yes—
429C4×Q8—28no—
430C4×Q8—28no—
431C4×Q8—28no—
432C4×Q8—28no—
433C4×Q8—412no—
434C4×Q8—412no—
435C4×Q8—412no—
436C4×Q8—412no—
437C4×Q8C22×C418yes—
438C4×Q8C22×C418yes—
439C4×D4—412no—
440C4×D4—412no—
441C4×D4—412no—
442C4×D4—412no—
443C4×D4—412no—
444C4×D4—412no—
445C4×D4—812no—
446C4×D4C22×C4124yes—
447C4×D4C22×C4124yes—
448C4×D4C22×C4148yes—
449C4×D4C22×C4148yes—
450#117—412no—
451#117—412no—
452#117—412no—
453#117—412no—
454#117—412no—
455#117—86no—
456#117C22×C4124yes—
457C2×C4⋊C4—412no—
458C2×C4⋊C4—412no—
459C2×C4⋊C4C2416yes—
460C2×C4⋊C4C2416yes—
461C2×C4⋊C4C2416yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2416yes—
464C2×C4⋊C4C2416yes—
465C2×C4⋊C4C24112yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C24112yes—
468C2×C4⋊C4C2416yes—
469C2×C4⋊C4C2416yes—
470C2×C4⋊C4C2416yes—
471C2×C4⋊C4C2416yes—
472C2×C4⋊C4C2416yes—
473C2×C4⋊C4C2413yes—
474C2×C4⋊C4C2413yes—
475C2×C4⋊C4C2416yes—
476C2×C4⋊C4C2416yes—
477C2×C22⋊C4—424no—
478C2×C22⋊C4—812no—
479C2×C22⋊C4C22×C4148yes—
480C2×C22⋊C4C22×C4148yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2412yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2416yes—
486C2×C22⋊C4C24112yes—
487C2×C22⋊C4C24112yes—
488C2×C22⋊C4C24112yes—
489C2×C22⋊C4C24112yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2412yes—
492C2×C22⋊C4C24112yes—
493C2×C22⋊C4C2416yes—
494C2×C22⋊C4C2416yes—
495C2×C22⋊C4C2416yes—
496C2×C22⋊C4C2416yes—
497C2×C22⋊C4C2416yes—
498C2×C22⋊C4C2416yes—
499C2×C22⋊C4C2416yes—
500C2×C22⋊C4C2416yes—
501C2×C22⋊C4C2412yes—
502C2×C22⋊C4C2416yes—
503C2×C22⋊C4C2416yes—
504C2×C22⋊C4C24112yes—
505C2×C22⋊C4C24112yes—
506C2×C22⋊C4C2416yes—
507C2×C22⋊C4C2412yes—
508C2×C22⋊C4C2412yes—
509C2×C42—412no—
510C2×C42—412no—
511C2×C42C22×C4124yes—
512C2×C42C2416yes—
513C2×C42C2416yes—
514C2×C42C2416yes—
515C2×C42C2416yes—
516C2×C42C2416yes—
517C2×C42C2413yes—
518C2×C42C2413yes—
519C2×C42C2416yes—
520C2×C42C24112yes—
521C2×C42C2416yes—
522C2×C42C2416yes—
523C2×C42C2416yes—
524C2×C42C2416yes—
525C2×C42C2411yescharacteristic
526C2×C42C2411yescharacteristic
527C2×C42C2416yes—
528C2×C42C2412yes—
529C2×C42C2413yes—
530C2×C42C2413yes—
531C2×C42C2413yes—
532C2×C42C2411yescharacteristic
533#95C2412yes—
534#95C2411yescharacteristic
535#95C2411yescharacteristic
536#95C2416yes—
537#95C2416yes—
538#95C24112yes—
539#95C2416yes—
540#95C2416yes—
541#95C2413yes—
542#95C2413yes—
543#95C2416yes—
544#95C2416yes—
545#95C2416yes—
546#95C2416yes—
547#95C2412yes—
548#95C2412yes—
549#95C24112yes—
550#95C2416yes—
551#95C2412yes—
552#95C2416yes—
553#95C2412yes—
554#95C2416yes—
555#95C2416yes—
556#95C24112yes—
557#95C2416yes—
558#95C2416yes—
559#95C2416yes—
560C24—412no—
561C24—46no—
562C24—412no—
563C24—46no—
564C24C23×C4124yes—
565C24C2516yes—
566C24C2513yes—
567C24C2512yes—
568#41—264no—
569#41—232no—
570#41—448no—
571#41—448no—
572#41—496no—
573C2×Q8—264no—
574C2×Q8—212no—
575C2×Q8—212no—
576C2×Q8—46no—
577C2×Q8—42no—
578C2×Q8—448no—
579C2×Q8C23×C4124yes—
580C2×Q8C23×C4112yes—
581C2×Q8C23×C414yes—
582C2×Q8C23×C414yes—
583C2×Q8H(5,𝔽2)18yes—
584C2×D4—212no—
585C2×D4—212no—
586C2×D4—212no—
587C2×D4—448no—
588C2×D4—496no—
589C2×D4—46no—
590C2×D4—46no—
591C2×D4—46no—
592C2×D4—46no—
593C2×D4—46no—
594C2×D4—46no—
595C2×D4—46no—
596C2×D4—46no—
597C2×D4—46no—
598C2×D4—42no—
599C2×D4C23×C4112yes—
600C2×D4C23×C4124yes—
601C2×D4C23×C4124yes—
602C2×D4C23×C4124yes—
603C2×D4C23×C4124yes—
604C2×D4C23×C4124yes—
605C2×D4C23×C4112yes—
606C2×D4C23×C414yes—
607C22×C4—212no—
608C22×C4—212no—
609C22×C4—212no—
610C22×C4—212no—
611C22×C4—212no—
612C22×C4—24no—
613C22×C4—212no—
614C22×C4—42no—
615C22×C4—46no—
616C22×C4—43no—
617C22×C4—43no—
618C22×C4—42no—
619C22×C4—412no—
620C22×C4—46no—
621C22×C4—46no—
622C22×C4—46no—
623C22×C4—46no—
624C22×C4—46no—
625C22×C4—46no—
626C22×C4—46no—
627C22×C4—46no—
628C22×C4—412no—
629C22×C4—412no—
630C22×C4—412no—
631C22×C4C23×C4112yes—
632C22×C4C23×C4124yes—
633C22×C4C23×C4124yes—
634C22×C4C23×C4112yes—
635C22×C4C23×C4112yes—
636C22×C4C23×C4124yes—
637C22×C4C2512yes—
638C22×C4C2516yes—
639C22×C4C2512yes—
640C22×C4C2516yes—
641C22×C4C2512yes—
642C22×C4C2516yes—
643C22×C4C2516yes—
644C22×C4C2511yescharacteristic
645C22×C4C2511yescharacteristic
646C22×C4C2513yes—
647C22×C4C2513yes—
648C22×C4C2511yescharacteristic
649C22×C4C2516yes—
650C22×C4C2512yes—
651C22×C4C2512yes—
652C22×C4C2513yes—
653C4⋊C4—212no—
654C4⋊C4—212no—
655C4⋊C4—212no—
656C4⋊C4—212no—
657C4⋊C4—24no—
658C4⋊C4—46no—
659C4⋊C4—412no—
660C4⋊C4—46no—
661C4⋊C4—42no—
662C4⋊C4—46no—
663C4⋊C4—46no—
664C4⋊C4—412no—
665C4⋊C4—46no—
666C4⋊C4—46no—
667C4⋊C4C23×C4112yes—
668C4⋊C4C23×C4112yes—
669C4⋊C4C23×C4124yes—
670C4⋊C4C23×C4124yes—
671C22⋊C4—212no—
672C22⋊C4—212no—
673C22⋊C4—24no—
674C22⋊C4—412no—
675C22⋊C4—412no—
676C22⋊C4—46no—
677C22⋊C4—46no—
678C22⋊C4—412no—
679C22⋊C4—412no—
680C22⋊C4—46no—
681C22⋊C4—46no—
682C22⋊C4—42no—
683C22⋊C4—46no—
684C22⋊C4—42no—
685C22⋊C4—46no—
686C22⋊C4—46no—
687C22⋊C4—46no—
688C22⋊C4—412no—
689C22⋊C4—46no—
690C22⋊C4—46no—
691C22⋊C4—46no—
692C22⋊C4C23×C4124yes—
693C22⋊C4C23×C4124yes—
694C22⋊C4C23×C4148yes—
695C22⋊C4C23×C4148yes—
696C22⋊C4C23×C4124yes—
697C22⋊C4C23×C418yes—
698C22⋊C4C23×C418yes—
699C42—212no—
700C42—212no—
701C42—212no—
702C42—212no—
703C42—212no—
704C42—42no—
705C42—46no—
706C42—46no—
707C42—46no—
708C42—41no—
709C42—41no—
710C42—46no—
711C42—46no—
712C42—412no—
713C42—43no—
714C42—43no—
715C42—46no—
716C42C23×C414yes—
717C42C23×C4112yes—
718C42C23×C4112yes—
719C42C23×C4112yes—
720C23—22no—
721C23—26no—
722C23—26no—
723C23—22no—
724C23—26no—
725C23—26no—
726C23—26no—
727C23—22no—
728C23—22no—
729C23—26no—
730C23—23no—
731C23—22no—
732C23—26no—
733C23—23no—
734C23—22no—
735C23—26no—
736C23—424no—
737C23—424no—
738C23—424no—
739C23—1612no—
740C23—1612no—
741C23C24×C4112yes—
742C23C24×C416yes—
743C23C24×C414yes—
744C23C2611yescharacteristic
745Q8—248no—
746Q8—412no—
747Q8—44no—
748Q8#518116yes—
749D4—248no—
750D4—224no—
751D4—412no—
752D4—424no—
753D4—424no—
754D4—424no—
755D4—44no—
756D4—424no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—26no—
760C2×C4—26no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—23no—
767C2×C4—21no—
768C2×C4—23no—
769C2×C4—22no—
770C2×C4—224no—
771C2×C4—248no—
772C2×C4—248no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—26no—
777C2×C4—26no—
778C2×C4—26no—
779C2×C4—26no—
780C2×C4—26no—
781C2×C4—22no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—22no—
785C2×C4—26no—
786C2×C4—22no—
787C2×C4—26no—
788C2×C4—26no—
789C2×C4—26no—
790C2×C4—22no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—412no—
795C2×C4—412no—
796C2×C4—424no—
797C2×C4—48no—
798C2×C4—812no—
799C2×C4—812no—
800C2×C4—812no—
801C2×C4—1612no—
802C2×C4C24×C412yes—
803C2×C4C24×C412yes—
804C2×C4C24×C412yes—
805C2×C4C24×C416yes—
806C2×C4C24×C416yes—
807C2×C4C24×C4112yes—
808C2×C4C24×C414yes—
809C2×C4C24×C416yes—
810C2×C4C2×H(5,𝔽2)112yes—
811C2×C4#58514yes—
812C22—24no—
813C22—26no—
814C22—212no—
815C22—26no—
816C22—24no—
817C22—212no—
818C22—26no—
819C22—24no—
820C22—212no—
821C22—42no—
822C22—46no—
823C22—42no—
824C22—46no—
825C22—46no—
826C22—42no—
827C22—46no—
828C22—46no—
829C22—42no—
830C22—46no—
831C22—1624no—
832C22C25×C411yescharacteristic
833C22C22×H(5,𝔽2)12yes—
834C22C2×#58512yes—
835C22H(7,𝔽2)11yescharacteristic
836C222−1+611yescharacteristic
837C4—22no—
838C4—24no—
839C4—212no—
840C4—22no—
841C4—26no—
842C4—22no—
843C4—26no—
844C4—24no—
845C4—42no—
846C4—42no—
847C4—46no—
848C4—46no—
849C4—42no—
850C4—46no—
851C4—46no—
852C4C2×#518112yes—
853C2—44no—
854C2—46no—
855C2—412no—
856C2C22×#51811yescharacteristic
857C2C4×#58511yescharacteristic
858C2#6265411yescharacteristic
859C2#6291912yes—
860C2#6292312yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3500C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34495C2semidirect
3. #34478C2semidirect
4. #34476C2semidirect
5. #34415C2semidirect
6. #34412C2semidirect
7. #34377C2semidirect
8. #34367C2semidirect
9. #34320C2semidirect
10. #34312C2semidirect
11. #34294C2semidirect
12. #34293C2semidirect
13. #34258C2semidirect
14. #34257C2semidirect
15. #34240C2semidirect
16. #34197C2semidirect
17. C4×#548C2semidirect
18. #34129C2semidirect
19. #34086C2semidirect
22. #3500C4semidirect
32. C2×#519C22semidirect
35. C22×C4×Q8C22semidirect
36. #2379C22semidirect
37. #2377C22semidirect
38. #2376C22semidirect
39. #2375C22semidirect
40. #2374C22semidirect
41. #2372C22semidirect
42. #2367C22semidirect
43. #2367C22semidirect
44. #2367C22semidirect
45. #2367C22semidirect
46. #2363C22semidirect
47. #2363C22semidirect
48. #2363C22semidirect
49. #2362C22semidirect
50. #2362C22semidirect
51. #2361C22semidirect
52. #2361C22semidirect
53. #2360C22semidirect
54. #2360C22semidirect
55. #2358C22semidirect
56. #2357C22semidirect
57. #2354C22semidirect
58. #2354C22semidirect
59. #2352C22semidirect
60. #2352C22semidirect
61. #2351C22semidirect
62. Q8×C4⋊C4C22semidirect
63. D4×C4⋊C4C22semidirect
64. #2346C22semidirect
65. #2346C22semidirect
66. #2342C22semidirect
67. #2342C22semidirect
72. #2341C22semidirect
73. #2341C22semidirect
74. Q8×C22⋊C4C22semidirect
75. Q8×C22⋊C4C22semidirect
76. Q8×C22⋊C4C22semidirect
77. Q8×C22⋊C4C22semidirect
82. #2337C22semidirect
83. #2337C22semidirect
84. #2337C22semidirect
85. #2337C22semidirect
86. #2337C22semidirect
87. #2335C22semidirect
88. #2335C22semidirect
89. #2333C22semidirect
90. #2333C22semidirect
91. #2331C22semidirect
92. #2331C22semidirect
93. #2328C22semidirect
94. #2328C22semidirect
95. #2326C22semidirect
96. #2326C22semidirect
97. #2324C22semidirect
98. #2324C22semidirect
99. #2324C22semidirect
100. #2324C22semidirect
101. #2323C22semidirect
102. #2323C22semidirect
103. #2321C22semidirect
104. #2321C22semidirect
105. #2319C22semidirect
106. #2319C22semidirect
107. #2315C22semidirect
108. #2312C22semidirect
109. #2312C22semidirect
111. #2311C22semidirect
112. #2311C22semidirect
114. C4×#124C22semidirect
115. C4×#124C22semidirect
116. C4×C22⋊Q8C22semidirect
117. C4×C22⋊Q8C22semidirect
118. C4×#121C22semidirect
119. C4×#121C22semidirect
121. #2297C22semidirect
122. #2297C22semidirect
123. #2293C22semidirect
124. #2293C22semidirect
125. #2293C22semidirect
127. #2290C22semidirect
128. #2290C22semidirect
129. #2285C22semidirect
130. #2283C22semidirect
131. #2283C22semidirect
132. #2276C22semidirect
133. #2276C22semidirect
134. #2273C22semidirect
135. C42×Q8C22semidirect
136. C42×Q8C22semidirect
137. C42×D4C22semidirect
138. C4×#117C22semidirect
140. C2×2−1+4C2×C4semidirect
142. C2×H(5,𝔽2)C2×C4semidirect
152. #548C2×C4semidirect
153. #548C2×C4semidirect
154. #546C2×C4semidirect
155. #546C2×C4semidirect
156. #536C2×C4semidirect
157. #535C2×C4semidirect
158. #532C2×C4semidirect
161. C2×#124C2×C4semidirect
178. C4×#41C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
#344952
#344782
#344762
#344152
#344122
#343772
#343672
#343202
#343122
#342942
#342932
#342582
#342572
#342402
#341972
C4×#5482
#341292
#340862