Finite Group Databasebeta

← #7626945

Subgroups — #7626945

Order 512.

8108 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3497C211yesmaximal, characteristic
2#34494C213yesmaximal, complemented
3#34487C213yesmaximal, complemented
4#34474C216yesmaximal, complemented
5#34472C216yesmaximal, complemented
6#34414C216yesmaximal, complemented
7#34410C216yesmaximal, complemented
8#34393C213yesmaximal, complemented
9#34368C213yesmaximal, complemented
10#34334C213yesmaximal, complemented
11#34330C213yesmaximal, complemented
12#34313C211yesmaximal, characteristic, complemented
13#34311C211yesmaximal, characteristic, complemented
14#34294C212yesmaximal, complemented
15#34293C212yesmaximal, complemented
16#34259C212yesmaximal, complemented
17#34257C212yesmaximal, complemented
18#34226C213yesmaximal, complemented
19#34196C211yesmaximal, characteristic, complemented
20C4×D4×Q8C211yesmaximal, characteristic, complemented
21C4×#550C211yesmaximal, characteristic, complemented
22Q8×#117C211yesmaximal, characteristic, complemented
23#34086C213yesmaximal, complemented
24C22×2−1+4C2212yes—
25#3497C4132yescomplemented
26C2×#550C2211yescharacteristic
27C2×#550C2213yes—
28C2×D4×Q8C2211yescharacteristic
29C2×D4×Q8C2213yes—
30C2×#548C2216yes—
31C2×#548C2212yes—
32C2×#537C2216yes—
33C2×#532C2213yes—
34C2×#532C2213yes—
35C2×#520C2212yes—
36C2×#519C2212yes—
37C2×C4×#41C2212yes—
38C22×C4×Q8C2212yes—
39C22×C4×Q8C2211yescharacteristic
40#2379C22112yes—
41#2378C22112yes—
42#2377C22112yes—
43#2377C22112yes—
44#2369C2216yes—
45#2368C22112yes—
46#2367C2216yes—
47#2367C2216yes—
48#2366C2213yes—
49#2366C2216yes—
50#2366C2213yes—
51#2365C2213yes—
52#2365C2213yes—
53#2364C22112yes—
54#2363C2216yes—
55#2363C2216yes—
56#2363C2216yes—
57#2363C2216yes—
58#2362C2216yes—
59#2362C2216yes—
60#2361C2216yes—
61#2361C2216yes—
62#2360C2216yes—
63#2360C2216yes—
64#2357C2216yes—
65#2357C2216yes—
66#2355C2213yes—
67#2355C2213yes—
68#2355C2213yes—
69#2355C2213yes—
70#2354C2213yes—
71#2354C2213yes—
72#2354C2216yes—
73Q8×C4⋊C4C2211yescharacteristic
74Q8×C4⋊C4C2211yescharacteristic
75Q8×C4⋊C4C2211yescharacteristic
76Q8×C4⋊C4C2211yescharacteristic
77#2349C2216yes—
78#2349C2216yes—
79D4×C4⋊C4C2213yes—
80D4×C4⋊C4C2213yes—
81D4×C4⋊C4C2216yes—
82#2345C2213yes—
83#2345C2213yes—
84#2344C2216yes—
85#2341C2212yes—
86#2341C2216yes—
87#2341C2216yes—
88#2341C2212yes—
89Q8×C22⋊C4C2212yes—
90Q8×C22⋊C4C2216yes—
91Q8×C22⋊C4C2211yescharacteristic
92Q8×C22⋊C4C2211yescharacteristic
93Q8×C22⋊C4C2212yes—
94Q8×C22⋊C4C2212yes—
95Q8×C22⋊C4C2216yes—
96#2339C2216yes—
97#2339C2216yes—
98#2339C2216yes—
99#2339C2216yes—
100#2337C2216yes—
101#2337C2216yes—
102#2333C22112yes—
103#2333C2216yes—
104#2333C2216yes—
105#2332C22112yes—
106#2331C2213yes—
107#2331C2213yes—
108#2329C22112yes—
109#2328C2213yes—
110#2328C2213yes—
111#2326C2216yes—
112#2326C2216yes—
113#2325C22112yes—
114#2324C2216yes—
115#2324C2211yescharacteristic
116#2324C2213yes—
117#2324C2213yes—
118#2324C2213yes—
119#2324C2216yes—
120#2324C22112yes—
121#2324C2216yes—
122#2323C2216yes—
123#2323C2216yes—
124#2320C2216yes—
125#2319C2216yes—
126#2318C22112yes—
127#2311C2216yes—
128#2311C2216yes—
129#2311C2216yes—
130#2310C2216yes—
131C4×C4⋊Q8C2213yes—
132C4×C4⋊Q8C2213yes—
133C4×#127C2213yes—
134C4×#127C2213yes—
135C4×C22⋊Q8C2216yes—
136C4×C22⋊Q8C2216yes—
137C4×#121C2216yes—
138C4×#121C2216yes—
139#2297C2216yes—
140#2297C2216yes—
141#2297C2216yes—
142#2295C2213yes—
143#2295C2213yes—
144C2×#391C2216yes—
145#2293C2213yes—
146#2293C2213yes—
147#2290C2216yes—
148#2290C2216yes—
149#2285C2213yes—
150#2285C2213yes—
151#2283C2213yes—
152#2276C2212yes—
153#2275C2216yes—
154C42×Q8C2211yescharacteristic
155C42×Q8C2211yescharacteristic
156C42×D4C2213yes—
157C42×D4C2213yes—
158C4×#117C2213yes—
159C2×2−1+4—48no—
160C2×2−1+4—48no—
161C2×2−1+4C2×C4132yescomplemented
162C22×#41C2312yes—
163C22×#41C2316yes—
164C22×#41C2316yes—
165C22×#41C2316yes—
166C23×Q8C2311yescharacteristic
167C23×Q8C2312yes—
168C23×Q8C2316yes—
169#550C2×C4116yescomplemented
170#550C2×C4148yescomplemented
171D4×Q8C2×C4116yescomplemented
172D4×Q8C2×C4148yescomplemented
173#548C2×C4132yescomplemented
174#548C2×C4196yescomplemented
175#537C2×C4196yescomplemented
176#532C2×C4148yescomplemented
177#532C2×C4148yescomplemented
178C2×C4⋊Q8C2313yes—
179C2×C4⋊Q8C2313yes—
180C2×#127C2313yes—
181C2×#127C2313yes—
182C2×#124C2316yes—
183C2×#124C2316yes—
184C2×C22⋊Q8C2316yes—
185C2×C22⋊Q8C2316yes—
186C2×C22⋊Q8C23112yes—
187C2×#121C2311yescharacteristic
188C2×#121C2313yes—
189C2×#121C2316yes—
190C2×#121C2316yes—
191C2×#121C2316yes—
192C2×#121C23112yes—
193C2×#121C2316yes—
194#520—48no—
195#519—48no—
196C4×#41—48no—
197C2×C4×Q8—48no—
198C2×C4×Q8C2×C4116yescomplemented
199C2×C4×Q8C2311yescharacteristic
200C2×C4×Q8C2311yescharacteristic
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2311yescharacteristic
204C2×C4×Q8C2311yescharacteristic
205C2×C4×Q8C2316yes—
206C2×C4×Q8C2316yes—
207C2×C4×Q8C2316yes—
208C2×C4×Q8C2316yes—
209C2×C4×Q8C2313yes—
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2313yes—
213C2×C4×D4C2313yes—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2316yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C2316yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2313yes—
220C2×C4×D4C2313yes—
221C2×C4×D4C2316yes—
222C2×C4×D4C2316yes—
223C2×C4×D4C2316yes—
224C2×C4×D4C23112yes—
225C2×C4×D4C2316yes—
226C2×C4×D4C2316yes—
227C2×C4×D4C2316yes—
228C2×C4×D4C2313yes—
229C2×C4×D4C2313yes—
230C2×#117C2311yescharacteristic
231C2×#117C2316yes—
232C2×#117C2316yes—
233C2×#117C2316yes—
234C2×#117C2316yes—
235C2×#117C2313yes—
236C2×#117C2316yes—
237C22×C4⋊C4C2316yes—
238C22×C4⋊C4C2316yes—
239C22×C4⋊C4C2313yes—
240C22×C42C2316yes—
241C22×C42C2316yes—
242C22×C42C2313yes—
243#391C2316yes—
244#391C2316yes—
245#391C2316yes—
246#391C2313yes—
247#391C23112yes—
248#391C2316yes—
249#391C2316yes—
250#391C2313yes—
251#391C2316yes—
252#391C23112yes—
253#391C2316yes—
254#391C2316yes—
255#391C2316yes—
256#391C2316yes—
257#391C2313yes—
258#391C2313yes—
259#390C2313yes—
260#390C2316yes—
261#390C2316yes—
262#390C2316yes—
263#390C2316yes—
264#390C2316yes—
265#390C2316yes—
266#390C23112yes—
267#390C2316yes—
268#390C23112yes—
269#390C2316yes—
270#390C2311yescharacteristic
271#390C2313yes—
272#390C2313yes—
273#390C2312yes—
274#390C2316yes—
275#390C2316yes—
276#389C2313yes—
277#389C2316yes—
278#389C2316yes—
279#389C2316yes—
280#389C2316yes—
281#389C2316yes—
282#389C2313yes—
283#389C23112yes—
284#389C2313yes—
285#389C2311yescharacteristic
286#389C2313yes—
287#389C2313yes—
288#389C2313yes—
289#389C2313yes—
290#388C2316yes—
291#388C23112yes—
292#388C23112yes—
293#388C23112yes—
294#388C2316yes—
295#388C23112yes—
296#388C23112yes—
297#388C2316yes—
298#388C23112yes—
299#388C2312yes—
300#388C2316yes—
301#388C2316yes—
302#388C23112yes—
303#388C2316yes—
304#388C2316yes—
305#387C23112yes—
306#387C23112yes—
307#387C23112yes—
308#387C23112yes—
309#387C2316yes—
310#387C2316yes—
311#387C2316yes—
312#387C2316yes—
313#387C2316yes—
314#387C2316yes—
315#387C2316yes—
316#387C2316yes—
317#386C2316yes—
318#386C2316yes—
319#386C23112yes—
320#386C23112yes—
321#386C23112yes—
322#386C23112yes—
323#386C23112yes—
324#386C2316yes—
325#386C2312yes—
326#386C2316yes—
327#386C2316yes—
328#386C2316yes—
329#386C2316yes—
330#386C2316yes—
331#386C2316yes—
332#386C2316yes—
333#386C2316yes—
334#385C2316yes—
335#385C23112yes—
336#385C23112yes—
337#385C23112yes—
338#385C23112yes—
339#385C2312yes—
340#385C2316yes—
341#385C2316yes—
342#385C23112yes—
343#384C2313yes—
344#384C2313yes—
345#384C2313yes—
346#384C2313yes—
347#383C2316yes—
348#382C2316yes—
349#382C2316yes—
350#382C2313yes—
351#382C2313yes—
352#381C23112yes—
353#381C23112yes—
354#381C2316yes—
355#380C2313yes—
356#380C2316yes—
357#380C2313yes—
358#380C23112yes—
359#380C23112yes—
360#380C2316yes—
361#380C2316yes—
362#380C2316yes—
363#380C2316yes—
364#380C2311yescharacteristic
365#380C2313yes—
366#380C2316yes—
367C4×C4⋊C4C2313yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2316yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2313yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2311yescharacteristic
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C23112yes—
380C4×C4⋊C4C2316yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2313yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2313yes—
386C4×C4⋊C4C2313yes—
387C4×C4⋊C4C2316yes—
388C4×C4⋊C4C2313yes—
389C4×C4⋊C4C2313yes—
390C4×C4⋊C4C2313yes—
391C4×C4⋊C4C2313yes—
392C4×C22⋊C4C23112yes—
393C4×C22⋊C4C2316yes—
394C4×C22⋊C4C23112yes—
395C4×C22⋊C4C2316yes—
396C4×C22⋊C4C2313yes—
397C4×C22⋊C4C2313yes—
398C4×C22⋊C4C2316yes—
399C4×C22⋊C4C2316yes—
400C4×C22⋊C4C23112yes—
401C4×C22⋊C4C23112yes—
402C4×C22⋊C4C2313yes—
403C4×C22⋊C4C2316yes—
404C4×C22⋊C4C2316yes—
405C4×C22⋊C4C2316yes—
406C4×C22⋊C4C2313yes—
407C4×C22⋊C4C2316yes—
408C4×C22⋊C4C2316yes—
409#376C2313yes—
410#376C2316yes—
411#376C2313yes—
412C2×#95C23112yes—
413C2×#95C23112yes—
414C43C2313yes—
415C43C2313yes—
4162−1+4—4128no—
417C2×#41—28no—
418C2×#41—28no—
419C2×#41—412no—
420C2×#41—412no—
421C2×#41—412no—
422C2×#41—412no—
423C2×#41—412no—
424C2×#41—412no—
425C2×#41C22×C4116yes—
426C2×#41C22×C4148yes—
427C2×#41C22×C4148yes—
428C2×#41C22×C4148yes—
429C22×Q8—28no—
430C22×Q8—28no—
431C22×Q8—24no—
432C22×Q8—24no—
433C22×Q8—412no—
434C22×Q8—412no—
435C22×Q8C22×C418yes—
436C22×Q8C22×C4116yes—
437C22×Q8C22×C4148yes—
438C22×Q8C2416yes—
439C22×Q8C2413yes—
440C22×Q8C2416yes—
441C22×Q8C2411yescharacteristic
442C22×D4C2413yes—
443C22×D4C2411yescharacteristic
444C22×D4C2416yes—
445C22×D4C2416yes—
446C22×D4C2416yes—
447C22×D4C2412yes—
448C22×D4C2416yes—
449C22×D4C2416yes—
450C23×C4C2416yes—
451C23×C4C2416yes—
452C23×C4C2413yes—
453C23×C4C2411yescharacteristic
454C23×C4C2416yes—
455C23×C4C2412yes—
456C23×C4C2416yes—
457C23×C4C24112yes—
458C23×C4C2416yes—
459C23×C4C2413yes—
460C23×C4C24112yes—
461C4⋊Q8C22×C4124yes—
462C4⋊Q8C22×C4124yes—
463#127C22×C4124yes—
464#127C22×C4124yes—
465#124C22×C4148yes—
466#124C22×C4148yes—
467C22⋊Q8C22×C4148yes—
468C22⋊Q8C22×C4148yes—
469C22⋊Q8C22×C4196yes—
470#121C22×C418yes—
471#121C22×C4124yes—
472#121C22×C4148yes—
473#121C22×C4148yes—
474#121C22×C4148yes—
475#121C22×C4148yes—
476#121C22×C4196yes—
477C4×Q8—24no—
478C4×Q8—28no—
479C4×Q8—24no—
480C4×Q8—28no—
481C4×Q8—24no—
482C4×Q8—24no—
483C4×Q8—412no—
484C4×Q8—412no—
485C4×Q8—412no—
486C4×Q8—412no—
487C4×Q8C22×C4124yes—
488C4×Q8C22×C418yes—
489C4×Q8C22×C4124yes—
490C4×Q8C22×C418yes—
491C4×D4—24no—
492C4×D4—212no—
493C4×D4—46no—
494C4×D4—46no—
495C4×D4—412no—
496C4×D4—412no—
497C4×D4—412no—
498C4×D4—412no—
499C4×D4—412no—
500C4×D4—812no—
501C4×D4—86no—
502C4×D4—86no—
503C4×D4C22×C4148yes—
504C4×D4C22×C4148yes—
505C4×D4C22×C4124yes—
506C4×D4C22×C4124yes—
507C4×D4C22×C4148yes—
508#117—24no—
509#117—46no—
510#117—412no—
511#117—412no—
512#117—412no—
513#117—412no—
514#117—86no—
515C2×C4⋊C4—412no—
516C2×C4⋊C4—412no—
517C2×C4⋊C4C22×C4124yes—
518C2×C4⋊C4C2413yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C2413yes—
521C2×C4⋊C4C2413yes—
522C2×C4⋊C4C2416yes—
523C2×C4⋊C4C2413yes—
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2411yescharacteristic
526C2×C4⋊C4C2411yescharacteristic
527C2×C4⋊C4C2413yes—
528C2×C4⋊C4C2411yescharacteristic
529C2×C4⋊C4C2413yes—
530C2×C4⋊C4C2416yes—
531C2×C4⋊C4C24112yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2416yes—
534C2×C4⋊C4C2416yes—
535C2×C4⋊C4C2416yes—
536C2×C4⋊C4C2416yes—
537C2×C4⋊C4C2413yes—
538C2×C4⋊C4C2413yes—
539C2×C4⋊C4C2416yes—
540C2×C4⋊C4C2416yes—
541C2×C4⋊C4C2413yes—
542C2×C4⋊C4C2413yes—
543C2×C4⋊C4C2416yes—
544C2×C4⋊C4C2413yes—
545C2×C4⋊C4C2411yescharacteristic
546C2×C4⋊C4C2416yes—
547C2×C4⋊C4C2416yes—
548C2×C22⋊C4C2411yescharacteristic
549C2×C22⋊C4C2411yescharacteristic
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2416yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2416yes—
554C2×C22⋊C4C2416yes—
555C2×C22⋊C4C2416yes—
556C2×C22⋊C4C2416yes—
557C2×C22⋊C4C24112yes—
558C2×C22⋊C4C2413yes—
559C2×C22⋊C4C2413yes—
560C2×C22⋊C4C2416yes—
561C2×C22⋊C4C24112yes—
562C2×C22⋊C4C2416yes—
563C2×C22⋊C4C2416yes—
564C2×C22⋊C4C2416yes—
565C2×C22⋊C4C24112yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2416yes—
569C2×C22⋊C4C2416yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C24112yes—
572C2×C22⋊C4C2416yes—
573C2×C22⋊C4C2416yes—
574C2×C42—412no—
575C2×C42—412no—
576C2×C42C22×C4124yes—
577C2×C42C2413yes—
578C2×C42C2413yes—
579C2×C42C2413yes—
580C2×C42C2413yes—
581C2×C42C2416yes—
582C2×C42C2416yes—
583C2×C42C2411yescharacteristic
584C2×C42C2413yes—
585C2×C42C2413yes—
586C2×C42C2416yes—
587C2×C42C24112yes—
588C2×C42C24112yes—
589C2×C42C2413yes—
590C2×C42C2413yes—
591C2×C42C2416yes—
592C2×C42C2416yes—
593C2×C42C2413yes—
594C2×C42C2413yes—
595C2×C42C2412yes—
596C2×C42C2413yes—
597C2×C42C2413yes—
598C2×C42C2413yes—
599C2×C42C2413yes—
600C2×C42C2411yescharacteristic
601#95C2413yes—
602#95C2416yes—
603#95C2416yes—
604#95C2416yes—
605#95C2416yes—
606#95C24112yes—
607#95C24112yes—
608#95C24112yes—
609#95C2412yes—
610#95C2413yes—
611#95C2413yes—
612#95C2413yes—
613#95C2413yes—
614#95C2413yes—
615#95C2413yes—
616#95C2413yes—
617#95C2416yes—
618#95C2416yes—
619#95C2416yes—
620#95C2412yes—
621#95C2416yes—
622#95C2412yes—
623#95C2416yes—
624#95C2416yes—
625#95C2416yes—
626#95C2416yes—
627#95C2416yes—
628#95C2416yes—
629#95C2416yes—
630#95C2416yes—
631#95C2416yes—
632C24C2512yes—
633C24C2516yes—
634C24C2511yescharacteristic
635#41—264no—
636#41—496no—
637#41—496no—
638#41—496no—
639C2×Q8—264no—
640C2×Q8—232no—
641C2×Q8—212no—
642C2×Q8—212no—
643C2×Q8—26no—
644C2×Q8—26no—
645C2×Q8—46no—
646C2×Q8—46no—
647C2×Q8—496no—
648C2×Q8C23×C4112yes—
649C2×Q8C23×C4124yes—
650C2×Q8C23×C4124yes—
651C2×Q8C23×C414yes—
652C2×Q8H(5,𝔽2)14yes—
653C2×Q8H(5,𝔽2)14yes—
654C2×D4—212no—
655C2×D4—212no—
656C2×D4—22no—
657C2×D4—26no—
658C2×D4—26no—
659C2×D4—22no—
660C2×D4—46no—
661C2×D4—46no—
662C2×D4—46no—
663C2×D4—46no—
664C2×D4—42no—
665C2×D4—46no—
666C2×D4—46no—
667C2×D4—42no—
668C2×D4—46no—
669C2×D4—46no—
670C2×D4C23×C414yes—
671C2×D4C23×C4112yes—
672C2×D4C23×C4124yes—
673C2×D4C23×C4124yes—
674C2×D4C23×C4124yes—
675C2×D4C23×C418yes—
676C2×D4C23×C4124yes—
677C2×D4C23×C4124yes—
678C22×C4—212no—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—212no—
682C22×C4—26no—
683C22×C4—26no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—24no—
687C22×C4—212no—
688C22×C4—42no—
689C22×C4—43no—
690C22×C4—42no—
691C22×C4—43no—
692C22×C4—412no—
693C22×C4—412no—
694C22×C4—46no—
695C22×C4—46no—
696C22×C4—46no—
697C22×C4—46no—
698C22×C4—46no—
699C22×C4—46no—
700C22×C4—46no—
701C22×C4—46no—
702C22×C4—412no—
703C22×C4—412no—
704C22×C4—412no—
705C22×C4C23×C414yes—
706C22×C4C23×C4112yes—
707C22×C4C23×C4124yes—
708C22×C4C23×C4124yes—
709C22×C4C23×C4112yes—
710C22×C4C23×C4148yes—
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2511yescharacteristic
714C22×C4C2513yes—
715C22×C4C2513yes—
716C22×C4C2516yes—
717C22×C4C2516yes—
718C22×C4C2511yescharacteristic
719C22×C4C2513yes—
720C22×C4C2513yes—
721C22×C4C2513yes—
722C22×C4C2511yescharacteristic
723C22×C4C2513yes—
724C22×C4C2513yes—
725C22×C4C2512yes—
726C22×C4C2516yes—
727C22×C4C2511yescharacteristic
728C22×C4C2511yescharacteristic
729C22×C4C2513yes—
730C22×C4C2511yescharacteristic
731C4⋊C4—26no—
732C4⋊C4—212no—
733C4⋊C4—26no—
734C4⋊C4—26no—
735C4⋊C4—212no—
736C4⋊C4—26no—
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—26no—
741C4⋊C4—22no—
742C4⋊C4—26no—
743C4⋊C4—46no—
744C4⋊C4—412no—
745C4⋊C4—46no—
746C4⋊C4—43no—
747C4⋊C4—43no—
748C4⋊C4—42no—
749C4⋊C4—46no—
750C4⋊C4—46no—
751C4⋊C4—46no—
752C4⋊C4—46no—
753C4⋊C4—46no—
754C4⋊C4C23×C4124yes—
755C4⋊C4C23×C4112yes—
756C4⋊C4C23×C4112yes—
757C4⋊C4C23×C414yes—
758C4⋊C4C23×C4112yes—
759C4⋊C4C23×C4124yes—
760C4⋊C4C23×C4124yes—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—212no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—46no—
767C22⋊C4—42no—
768C22⋊C4—43no—
769C22⋊C4—43no—
770C22⋊C4—42no—
771C22⋊C4—46no—
772C22⋊C4—46no—
773C22⋊C4—46no—
774C22⋊C4—412no—
775C22⋊C4—46no—
776C22⋊C4—412no—
777C22⋊C4—46no—
778C22⋊C4—46no—
779C22⋊C4—46no—
780C22⋊C4—412no—
781C22⋊C4—46no—
782C22⋊C4C23×C418yes—
783C22⋊C4C23×C4124yes—
784C22⋊C4C23×C4124yes—
785C22⋊C4C23×C4124yes—
786C22⋊C4C23×C4148yes—
787C42—26no—
788C42—26no—
789C42—212no—
790C42—212no—
791C42—26no—
792C42—26no—
793C42—22no—
794C42—26no—
795C42—26no—
796C42—42no—
797C42—46no—
798C42—46no—
799C42—46no—
800C42—43no—
801C42—43no—
802C42—412no—
803C42—412no—
804C42—43no—
805C42—43no—
806C42C23×C4112yes—
807C42C23×C4112yes—
808C42C23×C4112yes—
809C42C23×C4112yes—
810C422−1+414yescomplemented
811C23—22no—
812C23—26no—
813C23—26no—
814C23—22no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—22no—
819C23—26no—
820C23—21no—
821C23—26no—
822C23—22no—
823C23—21no—
824C23—26no—
825C23—22no—
826C23—21no—
827C23—22no—
828C23—26no—
829C23C24×C414yes—
830C23C24×C4112yes—
831C23C24×C412yes—
832C23C2611yescharacteristic
833Q8—224no—
834Q8—248no—
835Q8—424no—
836Q8#518116yes—
837D4—248no—
838D4—28no—
839D4—224no—
840D4—424no—
841D4—424no—
842D4—48no—
843D4—424no—
844D4—424no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—26no—
849C2×C4—26no—
850C2×C4—22no—
851C2×C4—23no—
852C2×C4—23no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—23no—
856C2×C4—21no—
857C2×C4—23no—
858C2×C4—21no—
859C2×C4—23no—
860C2×C4—23no—
861C2×C4—248no—
862C2×C4—224no—
863C2×C4—248no—
864C2×C4—28no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—23no—
870C2×C4—26no—
871C2×C4—23no—
872C2×C4—23no—
873C2×C4—26no—
874C2×C4—23no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—26no—
879C2×C4—23no—
880C2×C4—23no—
881C2×C4—23no—
882C2×C4—23no—
883C2×C4—22no—
884C2×C4—26no—
885C2×C4—21no—
886C2×C4—26no—
887C2×C4—26no—
888C2×C4—23no—
889C2×C4—23no—
890C2×C4—21no—
891C2×C4—23no—
892C2×C4—23no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—412no—
896C2×C4—448no—
897C2×C4—48no—
898C2×C4—812no—
899C2×C4—812no—
900C2×C4—812no—
901C2×C4—1612no—
902C2×C4C24×C412yes—
903C2×C4C24×C416yes—
904C2×C4C24×C416yes—
905C2×C4C24×C416yes—
906C2×C4C24×C414yes—
907C2×C4C24×C4112yes—
908C2×C4C24×C416yes—
909C2×C4C24×C412yes—
910C2×C4C2×H(5,𝔽2)16yes—
911C2×C4C2×H(5,𝔽2)16yes—
912C2×C4C2×2−1+412yes—
913C2×C4C2×2−1+412yes—
914C2×C4C2×2−1+412yes—
915C2×C4#58512yes—
916C22—22no—
917C22—24no—
918C22—212no—
919C22—22no—
920C22—24no—
921C22—212no—
922C22—22no—
923C22—24no—
924C22—212no—
925C22—42no—
926C22—46no—
927C22—41no—
928C22—46no—
929C22—42no—
930C22—41no—
931C22—46no—
932C22—42no—
933C22—41no—
934C22—42no—
935C22—46no—
936C22—41no—
937C22C25×C411yescharacteristic
938C22C22×H(5,𝔽2)11yescharacteristic
939C22C22×H(5,𝔽2)11yescharacteristic
940C22C22×2−1+411yescharacteristic
941C22C2×#58511yescharacteristic
942C22H(7,𝔽2)11yescharacteristic
943C222−1+611yescharacteristic
944C4—24no—
945C4—26no—
946C4—212no—
947C4—22no—
948C4—26no—
949C4—26no—
950C4—22no—
951C4—22no—
952C4—41no—
953C4—42no—
954C4—41no—
955C4—46no—
956C4—43no—
957C4—43no—
958C4—42no—
959C4—43no—
960C4—46no—
961C4—43no—
962C4C2×#518112yes—
963C4C4×2−1+414yes—
964C2—42no—
965C2—44no—
966C2—412no—
967C2C22×#51811yescharacteristic
968C2C2×C4×2−1+411yescharacteristic
969C2#6265411yescharacteristic
970C2#6291311yescharacteristic
971C2#6291711yescharacteristic
972C2#6292211yescharacteristic
973C2#6292311yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3497C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34494C2semidirect
3. #34487C2semidirect
4. #34474C2semidirect
5. #34472C2semidirect
6. #34414C2semidirect
7. #34410C2semidirect
8. #34393C2semidirect
9. #34368C2semidirect
10. #34334C2semidirect
11. #34330C2semidirect
12. #34313C2semidirect
13. #34311C2semidirect
14. #34294C2semidirect
15. #34293C2semidirect
16. #34259C2semidirect
17. #34257C2semidirect
18. #34226C2semidirect
19. #34196C2semidirect
20. C4×D4×Q8C2semidirect
21. C4×#550C2semidirect
22. Q8×#117C2semidirect
23. #34086C2semidirect
25. #3497C4semidirect
161. C2×2−1+4C2×C4semidirect
169. #550C2×C4semidirect
170. #550C2×C4semidirect
171. D4×Q8C2×C4semidirect
172. D4×Q8C2×C4semidirect
173. #548C2×C4semidirect
174. #548C2×C4semidirect
175. #537C2×C4semidirect
176. #532C2×C4semidirect
177. #532C2×C4semidirect
198. C2×C4×Q8C2×C4semidirect
810. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34972
#344942
#344872
#344742
#344722
#344142
#344102
#343932
#343682
#343342
#343302
#343132
#343112
#342942
#342932
#342592
#342572
#342262
#341962
C4×D4×Q82
C4×#5502
Q8×#1172
#340862