Finite Group Databasebeta

← #7626923

Subgroups — #7626923

Order 512.

6730 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic
2#34488C213yesmaximal, complemented
3#34482C216yesmaximal, complemented
4#34481C213yesmaximal, complemented
5#34462C216yesmaximal, complemented
6#34430C216yesmaximal, complemented
7#34421C216yesmaximal, complemented
8#34383C213yesmaximal
9#34374C213yesmaximal, complemented
10#34337C213yesmaximal, complemented
11#34337C211yesmaximal, characteristic, complemented
12#34324C213yesmaximal, complemented
13#34311C212yesmaximal, complemented
14#34311C211yesmaximal, characteristic, complemented
15#34291C212yesmaximal, complemented
16#34262C212yesmaximal, complemented
17#34249C212yesmaximal, complemented
18#34225C213yesmaximal, complemented
19#34182C211yesmaximal, characteristic, complemented
20C4×#557C211yesmaximal, characteristic, complemented
21C4×D4×Q8C211yesmaximal, characteristic, complemented
22Q8×#117C211yesmaximal, characteristic, complemented
23#34084C213yesmaximal
24#3523C4132yescomplemented
25C2×#557C2211yescharacteristic
26C2×#557C2213yes—
27C2×#556C2213yes—
28C2×#552C2216yes—
29C2×D4×Q8C2211yescharacteristic
30C2×D4×Q8C2212yes—
31C2×#541C2216yes—
32C2×#533C2213yes—
33C2×#529C2213yes—
34C2×#519C2212yes—
35C2×#519C2212yes—
36C2×#519C2212yes—
37C22×C4×Q8C2212yes—
38C22×C4×Q8C2211yescharacteristic
39#2383C22112yes—
40#2382C22112yes—
41#2382C22112yes—
42#2376C22112yes—
43#2373C22112yes—
44#2370C2216yes—
45#2370C22112yes—
46#2370C2216yes—
47#2370C2216yes—
48#2370C2216yes—
49#2370C2216yes—
50#2367C2216yes—
51#2365C2213yes—
52#2365C2216yes—
53#2365C2213yes—
54#2365C2216yes—
55#2365C2213yes—
56#2365C2213yes—
57#2362C2216yes—
58#2362C2216yes—
59#2362C2216yes—
60#2362C2216yes—
61#2360C2216yes—
62#2360C2216yes—
63#2356C2216yes—
64#2355C2216yes—
65#2355C2216yes—
66#2355C2213yes—
67#2355C2213yes—
68#2355C2213yes—
69#2354C2213yes—
70#2354C2216yes—
71#2352C2216yes—
72#2351C2216yes—
73#2351C2216yes—
74#2351C2212yes—
75#2351C2212yes—
76#2351C2216yes—
77Q8×C4⋊C4C2212yes—
78Q8×C4⋊C4C2211yescharacteristic
79Q8×C4⋊C4C2213yes—
80Q8×C4⋊C4C2213yes—
81Q8×C4⋊C4C2216yes—
82Q8×C4⋊C4C2211yescharacteristic
83Q8×C4⋊C4C2213yes—
84Q8×C4⋊C4C2216yes—
85Q8×C4⋊C4C2216yes—
86Q8×C4⋊C4C2211yescharacteristic
87Q8×C4⋊C4C2211yescharacteristic
88D4×C4⋊C4C2213yes—
89#2347C2216yes—
90#2347C2216yes—
91#2346C2216yes—
92#2346C2216yes—
93#2345C2213yes—
94#2345C2213yes—
95Q8×C22⋊C4C2211yescharacteristic
96Q8×C22⋊C4C2212yes—
97Q8×C22⋊C4C2212yes—
98Q8×C22⋊C4C2211yescharacteristic
99#2336C22112yes—
100#2335C2216yes—
101#2335C2216yes—
102#2334C22112yes—
103#2334C2216yes—
104#2334C2216yes—
105#2334C22112yes—
106#2334C22112yes—
107#2330C2213yes—
108#2330C2216yes—
109#2330C22112yes—
110#2330C2213yes—
111#2327C2216yes—
112#2326C2213yes—
113#2326C2213yes—
114#2324C2211yescharacteristic
115#2324C2213yes—
116#2323C2216yes—
117#2323C2216yes—
118#2323C2216yes—
119#2323C2213yes—
120#2323C2213yes—
121#2323C2216yes—
122#2323C2216yes—
123#2320C2216yes—
124#2320C2216yes—
125#2317C2216yes—
126#2317C2216yes—
127#2316C2216yes—
128#2314C22112yes—
129#2314C2216yes—
130C4×C4⋊Q8C2216yes—
131C4×C4⋊Q8C2213yes—
132C4×C4⋊Q8C2213yes—
133C4×C4⋊Q8C2213yes—
134C4×C4⋊Q8C2213yes—
135C4×#125C2216yes—
136C4×C22⋊Q8C2216yes—
137C4×C22⋊Q8C2216yes—
138#2298C2216yes—
139#2296C2216yes—
140#2296C2216yes—
141#2295C2213yes—
142#2295C2213yes—
143#2295C2216yes—
144#2295C2213yes—
145#2293C2213yes—
146#2293C2216yes—
147#2290C2216yes—
148#2285C2213yes—
149#2285C2213yes—
150#2285C2213yes—
151#2276C2216yes—
152#2276C2212yes—
153C42×Q8C2211yescharacteristic
154C42×Q8C2212yes—
155C42×Q8C2213yes—
156C42×Q8C2211yescharacteristic
157C42×D4C2213yes—
158C4×#117C2213yes—
159C23×Q8C2312yes—
160C23×Q8C2311yescharacteristic
161#557C2×C4116yescomplemented
162#557C2×C4148yescomplemented
163#556C2×C4148yes—
164#552C2×C4196yescomplemented
165D4×Q8C2×C4116yes—
166D4×Q8C2×C4132yescomplemented
167#541C2×C4196yescomplemented
168#533C2×C4148yescomplemented
169C2×C4⋊Q8C2313yes—
170C2×C4⋊Q8C2313yes—
171C2×C4⋊Q8C2316yes—
172#529C2×C4148yes—
173C2×#126C2316yes—
174C2×#126C23112yes—
175C2×#125C2316yes—
176C2×#125C2313yes—
177C2×#125C23112yes—
178C2×#125C2316yes—
179C2×#124C2313yes—
180C2×#123C2316yes—
181C2×C22⋊Q8C2313yes—
182C2×C22⋊Q8C2316yes—
183C2×C22⋊Q8C2316yes—
184C2×C22⋊Q8C2316yes—
185C2×#121C2311yescharacteristic
186#519—48no—
187#519—48no—
188#519C2×C4132yescomplemented
189C2×C4×Q8—48no—
190C2×C4×Q8C2×C4116yescomplemented
191C2×C4×Q8C2313yes—
192C2×C4×Q8C2311yescharacteristic
193C2×C4×Q8C2311yescharacteristic
194C2×C4×Q8C2311yescharacteristic
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2311yescharacteristic
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2316yes—
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2316yes—
201C2×C4×Q8C2316yes—
202C2×C4×Q8C2316yes—
203C2×C4×Q8C2313yes—
204C2×C4×Q8C2316yes—
205C2×C4×Q8C2316yes—
206C2×C4×Q8C2316yes—
207C2×C4×Q8C2316yes—
208C2×C4×Q8C2311yescharacteristic
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2313yes—
211C2×C4×Q8C2316yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2313yes—
214C2×C4×Q8C2313yes—
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2313yes—
217C2×C4×D4C2313yes—
218C2×C4×D4C2316yes—
219C2×#117C2311yescharacteristic
220C2×#117C2316yes—
221C2×#117C2316yes—
222C2×#117C2316yes—
223C2×#117C2316yes—
224C2×#117C2313yes—
225C2×#117C2316yes—
226C2×#117C2316yes—
227C2×#117C2316yes—
228C22×C4⋊C4C2316yes—
229C22×C4⋊C4C2313yes—
230C22×C42C2316yes—
231C22×C42C2313yes—
232#391C2313yes—
233#391C2313yes—
234#391C2316yes—
235#391C2316yes—
236#391C2316yes—
237#391C2316yes—
238#391C2313yes—
239#391C2316yes—
240#391C2313yes—
241#391C2313yes—
242#391C2313yes—
243#390C2311yescharacteristic
244#390C2313yes—
245#390C2312yes—
246#390C2316yes—
247#389C2316yes—
248#389C2316yes—
249#389C2313yes—
250#389C2316yes—
251#389C2316yes—
252#389C2316yes—
253#389C2316yes—
254#389C23112yes—
255#389C2316yes—
256#389C2316yes—
257#389C2316yes—
258#389C2316yes—
259#389C2316yes—
260#389C2316yes—
261#389C23112yes—
262#389C2316yes—
263#389C23112yes—
264#389C2313yes—
265#389C23112yes—
266#389C23112yes—
267#389C2313yes—
268#389C23112yes—
269#389C2316yes—
270#389C2313yes—
271#389C2316yes—
272#389C2316yes—
273#389C2311yescharacteristic
274#389C2313yes—
275#389C23112yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C2313yes—
280#389C2313yes—
281#388C2316yes—
282#388C2316yes—
283#388C2316yes—
284#388C23112yes—
285#388C23112yes—
286#388C23112yes—
287#388C2316yes—
288#388C2316yes—
289#388C23112yes—
290#388C23112yes—
291#388C2316yes—
292#388C2316yes—
293#388C2312yes—
294#388C2316yes—
295#388C2316yes—
296#388C2316yes—
297#388C2316yes—
298#387C23112yes—
299#387C23112yes—
300#387C23112yes—
301#387C23112yes—
302#387C23112yes—
303#387C23112yes—
304#387C23112yes—
305#387C2316yes—
306#387C23112yes—
307#387C23112yes—
308#387C23112yes—
309#387C23112yes—
310#387C2316yes—
311#387C2316yes—
312#387C2316yes—
313#387C23112yes—
314#387C2316yes—
315#387C2316yes—
316#387C2316yes—
317#387C2316yes—
318#387C2316yes—
319#387C2316yes—
320#387C2316yes—
321#387C2316yes—
322#386C2312yes—
323#386C2316yes—
324#385C2316yes—
325#385C2316yes—
326#385C23112yes—
327#385C2312yes—
328#385C2316yes—
329#385C2316yes—
330#385C2316yes—
331#385C23112yes—
332#384C2313yes—
333#384C2313yes—
334#384C2316yes—
335#384C2313yes—
336#384C23112yes—
337#384C2313yes—
338#384C2313yes—
339#384C2313yes—
340#383C23112yes—
341#382C2316yes—
342#382C2316yes—
343#382C23112yes—
344#382C23112yes—
345#382C2316yes—
346#382C2316yes—
347#380C2316yes—
348#380C2316yes—
349#380C2316yes—
350#380C2316yes—
351#380C2316yes—
352#380C2313yes—
353#380C2311yescharacteristic
354#380C2313yes—
355#380C2313yes—
356C4×C4⋊C4C2316yes—
357C4×C4⋊C4C2316yes—
358C4×C4⋊C4C2313yes—
359C4×C4⋊C4C2316yes—
360C4×C4⋊C4C2313yes—
361C4×C4⋊C4C2316yes—
362C4×C4⋊C4C2316yes—
363C4×C4⋊C4C23112yes—
364C4×C4⋊C4C2316yes—
365C4×C4⋊C4C23112yes—
366C4×C4⋊C4C2316yes—
367C4×C4⋊C4C2316yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C23112yes—
370C4×C4⋊C4C23112yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2313yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2316yes—
377C4×C4⋊C4C2311yescharacteristic
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2313yes—
380C4×C4⋊C4C2316yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2313yes—
383C4×C4⋊C4C2316yes—
384C4×C4⋊C4C23112yes—
385C4×C4⋊C4C23112yes—
386C4×C4⋊C4C2313yes—
387C4×C4⋊C4C2313yes—
388C4×C4⋊C4C2313yes—
389C4×C4⋊C4C2313yes—
390C4×C4⋊C4C2313yes—
391C4×C4⋊C4C2316yes—
392C4×C4⋊C4C2316yes—
393C4×C4⋊C4C2316yes—
394C4×C4⋊C4C2313yes—
395C4×C4⋊C4C2313yes—
396C4×C4⋊C4C2316yes—
397C4×C22⋊C4C2316yes—
398C4×C22⋊C4C23112yes—
399C4×C22⋊C4C2316yes—
400C4×C22⋊C4C2313yes—
401C4×C22⋊C4C2313yes—
402C4×C22⋊C4C2313yes—
403C4×C22⋊C4C2313yes—
404C4×C22⋊C4C2316yes—
405C4×C22⋊C4C2316yes—
406#376C2313yes—
407#376C2316yes—
408#376C2313yes—
409#376C23112yes—
410C43C2316yes—
411C43C2313yes—
412C43C2313yes—
413C22×Q8—28no—
414C22×Q8—24no—
415C22×Q8—28no—
416C22×Q8—24no—
417C22×Q8C22×C418yes—
418C22×Q8C22×C4116yes—
419C22×Q8C2413yes—
420C22×Q8C2416yes—
421C22×Q8C2413yes—
422C22×Q8C2411yescharacteristic
423C22×D4C2411yescharacteristic
424C22×D4C2412yes—
425C23×C4C2416yes—
426C23×C4C2413yes—
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2416yes—
430C23×C4C2413yes—
431C4⋊Q8C22×C4124yes—
432C4⋊Q8C22×C4124yes—
433C4⋊Q8C22×C4148yes—
434#126C22×C4148yes—
435#126C22×C4196yes—
436#125C22×C4124yes—
437#125C22×C4148yes—
438#125C22×C4196yes—
439#125C22×C4148yes—
440#124C22×C4124yes—
441#123C22×C4148yes—
442C22⋊Q8C22×C4124yes—
443C22⋊Q8C22×C4148yes—
444C22⋊Q8C22×C4148yes—
445C22⋊Q8C22×C4148yes—
446#121C22×C418yes—
447C4×Q8—24no—
448C4×Q8—28no—
449C4×Q8—24no—
450C4×Q8—28no—
451C4×Q8—24no—
452C4×Q8—24no—
453C4×Q8—212no—
454C4×Q8—412no—
455C4×Q8—412no—
456C4×Q8—46no—
457C4×Q8—412no—
458C4×Q8—412no—
459C4×Q8—412no—
460C4×Q8—412no—
461C4×Q8—412no—
462C4×Q8C22×C418yes—
463C4×Q8C22×C4124yes—
464C4×Q8C22×C418yes—
465C4×Q8C22×C4124yes—
466C4×Q8C22×C4148yes—
467C4×Q8C22×C4116yes—
468C4×Q8C22×C4148yes—
469C4×Q8C22×C4124yes—
470C4×Q8C22×C4148yes—
471C4×D4—24no—
472C4×D4—46no—
473C4×D4C22×C4124yes—
474C4×D4C22×C4148yes—
475#117—24no—
476#117—46no—
477#117—412no—
478#117—412no—
479#117—412no—
480#117—412no—
481#117C22×C4148yes—
482#117C22×C4148yes—
483#117C22×C4148yes—
484C2×C4⋊C4—412no—
485C2×C4⋊C4C22×C4124yes—
486C2×C4⋊C4C2413yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2413yes—
490C2×C4⋊C4C2411yescharacteristic
491C2×C4⋊C4C2411yescharacteristic
492C2×C4⋊C4C2413yes—
493C2×C4⋊C4C2411yescharacteristic
494C2×C4⋊C4C2411yescharacteristic
495C2×C4⋊C4C2413yes—
496C2×C4⋊C4C2413yes—
497C2×C4⋊C4C2413yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C24112yes—
500C2×C4⋊C4C2416yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2413yes—
505C2×C4⋊C4C2413yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C24112yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2416yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2413yes—
517C2×C4⋊C4C2413yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C2416yes—
521C2×C4⋊C4C2416yes—
522C2×C4⋊C4C2416yes—
523C2×C4⋊C4C2416yes—
524C2×C4⋊C4C2413yes—
525C2×C4⋊C4C2416yes—
526C2×C4⋊C4C2411yescharacteristic
527C2×C4⋊C4C24112yes—
528C2×C4⋊C4C2416yes—
529C2×C22⋊C4C2411yescharacteristic
530C2×C22⋊C4C2411yescharacteristic
531C2×C22⋊C4C2412yes—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2416yes—
534C2×C22⋊C4C2412yes—
535C2×C22⋊C4C2416yes—
536C2×C22⋊C4C2413yes—
537C2×C22⋊C4C2413yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C42—412no—
547C2×C42C22×C4124yes—
548C2×C42C2416yes—
549C2×C42C2413yes—
550C2×C42C2413yes—
551C2×C42C2416yes—
552C2×C42C2413yes—
553C2×C42C2411yescharacteristic
554C2×C42C2413yes—
555C2×C42C2413yes—
556C2×C42C2413yes—
557C2×C42C2416yes—
558C2×C42C24112yes—
559C2×C42C24112yes—
560C2×C42C2416yes—
561C2×C42C2416yes—
562C2×C42C2416yes—
563C2×C42C24112yes—
564C2×C42C2412yes—
565C2×C42C2413yes—
566C2×C42C2413yes—
567C2×C42C2413yes—
568C2×C42C2413yes—
569C2×C42C2416yes—
570C2×C42C2413yes—
571C2×C42C24112yes—
572C2×C42C2416yes—
573C2×C42C2413yes—
574C2×C42C2413yes—
575C2×C42C2413yes—
576C2×C42C2411yescharacteristic
577#95C2413yes—
578#95C2412yes—
579#95C2416yes—
580#95C2413yes—
581#95C2413yes—
582#95C2413yes—
583#95C2413yes—
584#95C2413yes—
585#95C2413yes—
586#95C2413yes—
587#95C24112yes—
588#95C24112yes—
589#95C2416yes—
590#95C2416yes—
591#95C2416yes—
592#95C2416yes—
593#95C2416yes—
594#95C2416yes—
595#95C24112yes—
596#95C2416yes—
597#95C2416yes—
598#95C2412yes—
599#95C2412yes—
600#95C2416yes—
601#95C2416yes—
602#95C2416yes—
603#95C2416yes—
604#95C2416yes—
605#95C24112yes—
606#95C2416yes—
607#95C2416yes—
608#95C24112yes—
609#95C2416yes—
610C24C2511yescharacteristic
611C24C2512yes—
612C2×Q8—264no—
613C2×Q8—232no—
614C2×Q8—212no—
615C2×Q8—26no—
616C2×Q8—26no—
617C2×Q8—212no—
618C2×Q8—26no—
619C2×Q8—26no—
620C2×Q8C23×C4112yes—
621C2×Q8C23×C4112yes—
622C2×Q8C23×C4124yes—
623C2×Q8C23×C414yes—
624C2×Q8H(5,𝔽2)14yes—
625C2×Q82−1+414yes—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4C23×C414yes—
631C2×D4C23×C418yes—
632C22×C4—212no—
633C22×C4—26no—
634C22×C4—22no—
635C22×C4—212no—
636C22×C4—26no—
637C22×C4—22no—
638C22×C4—24no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—43no—
642C22×C4—43no—
643C22×C4—46no—
644C22×C4—46no—
645C22×C4—46no—
646C22×C4C23×C414yes—
647C22×C4C23×C4112yes—
648C22×C4C23×C4124yes—
649C22×C4C23×C4112yes—
650C22×C4C2511yescharacteristic
651C22×C4C2513yes—
652C22×C4C2513yes—
653C22×C4C2512yes—
654C22×C4C2511yescharacteristic
655C22×C4C2516yes—
656C22×C4C2513yes—
657C22×C4C2516yes—
658C22×C4C2512yes—
659C22×C4C2513yes—
660C22×C4C2516yes—
661C22×C4C2512yes—
662C22×C4C2511yescharacteristic
663C22×C4C2513yes—
664C22×C4C2513yes—
665C22×C4C2516yes—
666C22×C4C2513yes—
667C22×C4C2511yescharacteristic
668C22×C4C2511yescharacteristic
669C22×C4C2513yes—
670C22×C4C2511yescharacteristic
671C4⋊C4—26no—
672C4⋊C4—212no—
673C4⋊C4—212no—
674C4⋊C4—26no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—212no—
679C4⋊C4—26no—
680C4⋊C4—26no—
681C4⋊C4—26no—
682C4⋊C4—26no—
683C4⋊C4—22no—
684C4⋊C4—412no—
685C4⋊C4—42no—
686C4⋊C4—46no—
687C4⋊C4—46no—
688C4⋊C4—46no—
689C4⋊C4—46no—
690C4⋊C4—46no—
691C4⋊C4—46no—
692C4⋊C4—46no—
693C4⋊C4—43no—
694C4⋊C4—43no—
695C4⋊C4—46no—
696C4⋊C4—46no—
697C4⋊C4—46no—
698C4⋊C4—46no—
699C4⋊C4—412no—
700C4⋊C4—46no—
701C4⋊C4C23×C4112yes—
702C4⋊C4C23×C4112yes—
703C4⋊C4C23×C4124yes—
704C4⋊C4C23×C4124yes—
705C4⋊C4C23×C4124yes—
706C4⋊C4C23×C4124yes—
707C4⋊C4C23×C4124yes—
708C4⋊C4C23×C4124yes—
709C4⋊C4C23×C4112yes—
710C4⋊C4C23×C4124yes—
711C4⋊C4C23×C414yes—
712C4⋊C4C23×C4148yes—
713C4⋊C4C23×C4124yes—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—24no—
717C22⋊C4—42no—
718C22⋊C4—46no—
719C22⋊C4—43no—
720C22⋊C4—43no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—46no—
724C22⋊C4—46no—
725C22⋊C4—46no—
726C22⋊C4C23×C418yes—
727C22⋊C4C23×C4124yes—
728C22⋊C4C23×C4124yes—
729C22⋊C4C23×C4124yes—
730C22⋊C4C23×C4124yes—
731C42—26no—
732C42—212no—
733C42—26no—
734C42—212no—
735C42—22no—
736C42—26no—
737C42—212no—
738C42—26no—
739C42—26no—
740C42—26no—
741C42—46no—
742C42—46no—
743C42—43no—
744C42—42no—
745C42—46no—
746C42—43no—
747C42—43no—
748C42—43no—
749C42—412no—
750C42—412no—
751C42—412no—
752C42—46no—
753C42C23×C4112yes—
754C42C23×C4112yes—
755C42C23×C4112yes—
756C42C23×C4112yes—
757C42C23×C4148yes—
758C42C23×C4124yes—
759C422−1+414yes—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—22no—
766C23—21no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—21no—
772C23C24×C414yes—
773C23C24×C412yes—
774C23C2611yescharacteristic
775Q8—248no—
776Q8—224no—
777Q8—224no—
778Q8#520116yes—
779D4—28no—
780D4—48no—
781C2×C4—21no—
782C2×C4—26no—
783C2×C4—23no—
784C2×C4—21no—
785C2×C4—26no—
786C2×C4—21no—
787C2×C4—26no—
788C2×C4—23no—
789C2×C4—26no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—23no—
795C2×C4—23no—
796C2×C4—22no—
797C2×C4—23no—
798C2×C4—23no—
799C2×C4—248no—
800C2×C4—224no—
801C2×C4—28no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—26no—
806C2×C4—23no—
807C2×C4—26no—
808C2×C4—23no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—26no—
813C2×C4—23no—
814C2×C4—23no—
815C2×C4—22no—
816C2×C4—23no—
817C2×C4—23no—
818C2×C4—23no—
819C2×C4—23no—
820C2×C4—22no—
821C2×C4—26no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—23no—
825C2×C4—23no—
826C2×C4—26no—
827C2×C4—22no—
828C2×C4—23no—
829C2×C4—23no—
830C2×C4—22no—
831C2×C4—26no—
832C2×C4—412no—
833C2×C4—48no—
834C2×C4—812no—
835C2×C4C24×C412yes—
836C2×C4C24×C416yes—
837C2×C4C24×C4112yes—
838C2×C4C24×C414yes—
839C2×C4C24×C416yes—
840C2×C4C24×C416yes—
841C2×C4C24×C4112yes—
842C2×C4C24×C416yes—
843C2×C4C24×C412yes—
844C2×C4C2×H(5,𝔽2)16yes—
845C2×C4C2×2−1+412yes—
846C2×C4C2×2−1+412yes—
847C2×C4C2×2−1+416yes—
848C2×C4C2×2−1+412yes—
849C2×C4#58512yes—
850C22—22no—
851C22—24no—
852C22—22no—
853C22—24no—
854C22—22no—
855C22—24no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—42no—
864C22C25×C411yescharacteristic
865C22C22×H(5,𝔽2)11yescharacteristic
866C22C22×2−1+411yescharacteristic
867C22C22×2−1+411yescharacteristic
868C22C2×#58511yescharacteristic
869C222−1+611yescharacteristic
870C222−1+611yescharacteristic
871C4—212no—
872C4—26no—
873C4—22no—
874C4—212no—
875C4—26no—
876C4—26no—
877C4—24no—
878C4—22no—
879C4—22no—
880C4—41no—
881C4—46no—
882C4—42no—
883C4—42no—
884C4—43no—
885C4—46no—
886C4—43no—
887C4—41no—
888C4—43no—
889C4—43no—
890C4C2×#520112yes—
891C4C4×2−1+414yes—
892C2—42no—
893C2—44no—
894C2C22×#52011yescharacteristic
895C2C2×C4×2−1+411yescharacteristic
896C2#6265311yescharacteristic
897C2#6291311yescharacteristic
898C2#6292211yescharacteristic
899C2#6294711yescharacteristic
900C2#6295311yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#121C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34488C2semidirect
3. #34482C2semidirect
4. #34481C2semidirect
5. #34462C2semidirect
6. #34430C2semidirect
7. #34421C2semidirect
9. #34374C2semidirect
10. #34337C2semidirect
11. #34337C2semidirect
12. #34324C2semidirect
13. #34311C2semidirect
14. #34311C2semidirect
15. #34291C2semidirect
16. #34262C2semidirect
17. #34249C2semidirect
18. #34225C2semidirect
19. #34182C2semidirect
20. C4×#557C2semidirect
21. C4×D4×Q8C2semidirect
22. Q8×#117C2semidirect
24. #3523C4semidirect
161. #557C2×C4semidirect
162. #557C2×C4semidirect
164. #552C2×C4semidirect
166. D4×Q8C2×C4semidirect
167. #541C2×C4semidirect
168. #533C2×C4semidirect
188. #519C2×C4semidirect
190. C2×C4×Q8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
#344882
#344822
#344812
#344622
#344302
#344212
#343832
#343742
#343372
#343242
#343112
#342912
#342622
#342492
#342252
#341822
C4×#5572
C4×D4×Q82
Q8×#1172
#340842