Finite Group Databasebeta

← #7692192

Subgroups — #7692192

Order 512.

8441 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#59420C213yesmaximal, complemented
4#59064C213yesmaximal, complemented
5#59041C213yesmaximal, complemented
6#59023C216yesmaximal, complemented
7#45353C216yesmaximal, complemented
8#45108C216yesmaximal, complemented
9#38955C213yesmaximal, complemented
10#38908C213yesmaximal, complemented
11#37668C216yesmaximal, complemented
12Q8×#124C211yesmaximal, characteristic, complemented
13Q8×#121C211yesmaximal, characteristic, complemented
14#36456C211yesmaximal, characteristic, complemented
15#36428C212yesmaximal, complemented
16#36154C213yesmaximal, complemented
17#36149C213yesmaximal, complemented
18#35983C212yesmaximal, complemented
19#35737C212yesmaximal, complemented
20#34700C213yesmaximal, complemented
21#34313C211yesmaximal, characteristic, complemented
22#34175C212yesmaximal, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C23×#41C2212yes—
25#3522—216no—
26C2×#559C2213yescomplemented
27C2×Q82C2211yescharacteristic, complemented
28C2×#554C2213yescomplemented
29D4×#41—216no—
30C2×#550C2211yescharacteristic
31C2×D4×Q8C2211yescharacteristic
32C2×D4×Q8C2212yescomplemented
33C2×#548C2211yescharacteristic
34C2×#548C2212yes—
35C2×#548C2212yescomplemented
36C2×#547C2213yes—
37C2×#547C2216yescomplemented
38C2×#546C2216yes—
39C2×D42C2213yes—
40C2×#542C2216yescomplemented
41C2×#532C2213yes—
42C2×#532C2213yescomplemented
43C2×#529C2213yescomplemented
44C2×#525C2216yes—
45C2×#520C2212yescomplemented
46C2×#520C2212yescomplemented
47C2×C4×#41C2211yescharacteristic
48C22×C4×Q8C2211yescharacteristic, complemented
49C22×C4×D4C2213yes—
50#2862C2213yescomplemented
51#2857C2213yescomplemented
52#2857C2213yescomplemented
53#2848C2216yescomplemented
54#2708C22112yescomplemented
55#2697C22112yescomplemented
56#2695C22112yescomplemented
57#2693C22112yescomplemented
58#2687C22112yescomplemented
59#2687C22112yescomplemented
60#2684C22112yescomplemented
61#2625C2216yescomplemented
62#2621C2216yescomplemented
63#2568C2213yescomplemented
64#2563C2213yes—
65#2563C2213yescomplemented
66#2547C2216yescomplemented
67#2546C2213yescomplemented
68#2538C2213yes—
69#2538C2213yescomplemented
70#2535C2216yescomplemented
71#2535C2216yescomplemented
72#2534C22112yescomplemented
73#2503C2216yescomplemented
74#2492C2216yescomplemented
75#2492C2216yescomplemented
76#2487C2216yescomplemented
77#2480C2216yescomplemented
78#2468C2216yescomplemented
79#2457C2216yescomplemented
80#2454C2213yes—
81#2452C2216yescomplemented
82#2450C22112yescomplemented
83#2447C2216yescomplemented
84#2447C2216yescomplemented
85#2447C2216yescomplemented
86#2447C2213yescomplemented
87#2442C2213yescomplemented
88#2442C2216yescomplemented
89#2439C2216yescomplemented
90#2437C22112yescomplemented
91#2435C2213yes—
92#2435C2216yescomplemented
93#2432C2216yescomplemented
94#2432C2216yescomplemented
95#2429C2216yescomplemented
96#2427C2211yescharacteristic
97#2427C2216yescomplemented
98#2427C2216yescomplemented
99#2427C2216yescomplemented
100#2427C2216yescomplemented
101#2420C2216yescomplemented
102#2420C2216yescomplemented
103#2420C2216yescomplemented
104#2420C2216yescomplemented
105#2420C2213yescomplemented
106#2419C22112yescomplemented
107#2418C2216yescomplemented
108#2417C2216yescomplemented
109#2417C2216yescomplemented
110#2417C2213yescomplemented
111#2417C2216yescomplemented
112#2408C2213yes—
113#2408C2216yescomplemented
114#2407C2216yescomplemented
115#2407C2216yescomplemented
116#2407C2216yescomplemented
117#2404C22112yescomplemented
118#2395C2216yescomplemented
119#2392C2216yescomplemented
120#2367C2213yescomplemented
121#2366C2213yescomplemented
122#2362C2213yescomplemented
123#2361C2216yescomplemented
124#2361C2213yescomplemented
125#2352C2213yescomplemented
126#2351C2212yescomplemented
127#2351C2211yescharacteristic, complemented
128Q8×C4⋊C4C2211yescharacteristic, complemented
129#2349C2216yescomplemented
130D4×C4⋊C4C2213yescomplemented
131#2341C2212yes—
132#2341C2211yescharacteristic
133#2341C2212yescomplemented
134Q8×C22⋊C4C2212yescomplemented
135Q8×C22⋊C4C2211yescharacteristic, complemented
136Q8×C22⋊C4C2212yescomplemented
137Q8×C22⋊C4C2212yescomplemented
138#2339C2216yescomplemented
139#2339C2216yescomplemented
140#2339C2216yescomplemented
141D4×C22⋊C4C2216yes—
142D4×C22⋊C4C2216yescomplemented
143D4×C22⋊C4C2216yescomplemented
144#2324C2216yescomplemented
145#2311C2216yescomplemented
146#2311C2216yescomplemented
147C4×#127C2213yescomplemented
148C4×#124C2213yes—
149C4×#124C2213yescomplemented
150C4×C22⋊Q8C2213yescomplemented
151C4×C22⋊Q8C2213yescomplemented
152C4×#121C2213yes—
153C4×#121C2213yescomplemented
154C4×#120C2216yescomplemented
155#2293C2213yescomplemented
156#2280C2216yescomplemented
157C2×#380C2216yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C42×D4C2213yescomplemented
160C22×#41—216no—
161C22×#41—216no—
162C22×#41—48no—
163C22×#41C2316yes—
164C22×#41C2316yes—
165C22×#41C2312yes—
166C22×#41C2311yescharacteristic
167C22×#41C2316yes—
168C23×Q8C2312yes—
169C23×Q8C2311yescharacteristic
170C23×D4C2316yes—
171C23×D4C2313yes—
172C24×C4C2316yes—
173#559—224no—
174Q82—28no—
175#554—224no—
176#550D4116yescomplemented
177D4×Q8—28no—
178D4×Q8—48no—
179#548—216no—
180#548—216no—
181#548—28no—
182#547—248no—
183#547—224no—
184#546—248no—
185D42—224no—
186#542—248no—
187#532—224no—
188#532—224no—
189C2×C4⋊Q8C2313yes—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2316yes—
192C2×C4⋊Q8C2316yes—
193C2×#127C2313yes—
194#529—224no—
195C2×#126C2316yes—
196C2×#125C2313yes—
197C2×#124C2313yes—
198C2×#124C2313yes—
199C2×#124C2316yes—
200C2×#124C2316yes—
201C2×#124C2311yescharacteristic
202C2×#124C2316yes—
203#525—248no—
204C2×#123C23112yes—
205C2×#123C2316yes—
206C2×#123C23112yes—
207C2×C22⋊Q8C2313yes—
208C2×C22⋊Q8C2316yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2311yescharacteristic
212C2×C22⋊Q8C23112yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2313yes—
216C2×C22⋊Q8C2316yes—
217C2×#121C2313yes—
218C2×#121C2316yes—
219C2×#121C2316yes—
220C2×#121C2311yescharacteristic
221C2×#121C2313yes—
222C2×#121C2316yes—
223C2×#121C2316yes—
224C2×#121C2316yes—
225C2×#120C23112yes—
226C2×#120C2316yes—
227#520—216no—
228#520—48no—
229C4×#41—28no—
230C2×C4×Q8—28no—
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2313yes—
239C2×C4×Q8C2313yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—224no—
242C2×C4×D4C2313yes—
243C2×C4×D4C2313yes—
244C2×C4×D4C2316yes—
245C2×C4×D4C2316yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2313yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2316yes—
262C2×C4×D4C2313yes—
263C2×#117C2316yes—
264C2×#117C2313yes—
265C2×#117C2316yes—
266C22×C4⋊C4C2316yes—
267C22×C4⋊C4C2313yes—
268C22×C4⋊C4C2313yes—
269C22×C4⋊C4C2316yes—
270C22×C22⋊C4C2316yes—
271C22×C22⋊C4C23112yes—
272C22×C42C2313yes—
273C22×C42C2313yes—
274#400C23112yes—
275#400C23112yes—
276#400C2316yes—
277#399C2316yes—
278#398C2316yes—
279#398C23112yes—
280#398C2316yes—
281#398C23112yes—
282#397C23112yes—
283#397C23112yes—
284#397C23112yes—
285#397C23112yes—
286#397C2316yes—
287#397C2312yes—
288#397C2316yes—
289#397C2316yes—
290#396C2316yes—
291#396C2316yes—
292#396C23112yes—
293#396C23112yes—
294#394C2312yes—
295#394C2316yes—
296#394C2316yes—
297#394C2316yes—
298#394C2316yes—
299#394C23112yes—
300#394C23112yes—
301#394C23112yes—
302#393C23112yes—
303#393C23112yes—
304#392C2316yes—
305#392C23112yes—
306#391C2316yes—
307#391C2316yes—
308#391C2316yes—
309#391C2316yes—
310#391C2313yes—
311#391C2316yes—
312#391C2316yes—
313#391C2316yes—
314#391C2316yes—
315#391C2313yes—
316#391C2313yes—
317#391C2316yes—
318#391C2311yescharacteristic
319#390C2313yes—
320#390C2316yes—
321#390C2316yes—
322#390C2313yes—
323#390C2316yes—
324#390C2313yes—
325#390C2313yes—
326#390C2316yes—
327#390C2316yes—
328#390C2313yes—
329#390C2313yes—
330#389C2316yes—
331#389C2313yes—
332#389C2316yes—
333#389C2316yes—
334#389C2316yes—
335#389C2313yes—
336#389C2313yes—
337#389C2313yes—
338#389C2316yes—
339#389C2313yes—
340#389C2311yescharacteristic
341#388C2316yes—
342#388C2316yes—
343#388C2316yes—
344#388C2316yes—
345#388C2316yes—
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#387C2316yes—
350#387C2316yes—
351#386C23112yes—
352#386C23112yes—
353#386C23112yes—
354#386C23112yes—
355#386C23112yes—
356#386C23112yes—
357#386C23112yes—
358#386C2316yes—
359#386C23112yes—
360#386C2316yes—
361#386C2316yes—
362#386C2316yes—
363#386C2312yes—
364#385C23112yes—
365#385C2316yes—
366#385C23112yes—
367#385C23112yes—
368#385C23112yes—
369#385C2316yes—
370#385C2316yes—
371#385C2316yes—
372#385C2316yes—
373#384C2313yes—
374#382C2316yes—
375#382C2316yes—
376#382C2313yes—
377#382C2313yes—
378#381C2316yes—
379#381C2316yes—
380#381C23112yes—
381#381C23112yes—
382#380C2316yes—
383#380C2316yes—
384#380C2313yes—
385#380C2316yes—
386#380C2316yes—
387#380C2316yes—
388#380C23112yes—
389#380C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2313yes—
393#380C2316yes—
394#380C2313yes—
395#380C2313yes—
396#380C23112yes—
397#380C23112yes—
398#380C2312yes—
399#380C2316yes—
400#379C23112yes—
401#379C2316yes—
402#379C2316yes—
403#379C2316yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2316yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2313yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2313yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2311yescharacteristic
423C4×C22⋊C4C2313yes—
424C2×#95C23112yes—
425C43C2313yes—
426C25C2416yes—
427C2×#41—24no—
428C2×#41—28no—
429C2×#41—28no—
430C2×#41—24no—
431C2×#41—224no—
432C2×#41—224no—
433C2×#41—224no—
434C2×#41—224no—
435C2×#41—224no—
436C2×#41—412no—
437C2×#41—412no—
438C2×#41—412no—
439C2×#41—4128no—
440C2×#41—86no—
441C2×#41C2×D4116yes—
442C2×#41#4118yescomplemented
443C22×Q8—24no—
444C22×Q8—28no—
445C22×Q8—24no—
446C22×Q8—28no—
447C22×Q8—24no—
448C22×Q8—28no—
449C22×Q8C2411yescharacteristic
450C22×Q8C2413yes—
451C22×Q8C2416yes—
452C22×Q8C2416yes—
453C22×Q8C2411yescharacteristic
454C22×D4—212no—
455C22×D4—224no—
456C22×D4—224no—
457C22×D4—212no—
458C22×D4—46no—
459C22×D4—412no—
460C22×D4C2412yes—
461C22×D4C2413yes—
462C22×D4C2416yes—
463C22×D4C2416yes—
464C22×D4C24112yes—
465C22×D4C2413yes—
466C22×D4C2416yes—
467C22×D4C2413yes—
468C22×D4C2411yescharacteristic
469C22×D4C2416yes—
470C23×C4—224no—
471C23×C4—224no—
472C23×C4—412no—
473C23×C4C2413yes—
474C23×C4C2413yes—
475C23×C4C2411yescharacteristic
476C23×C4C2416yes—
477C23×C4C2416yes—
478C23×C4C2413yes—
479C23×C4C2412yes—
480C23×C4C2416yes—
481C23×C4C2416yes—
482C23×C4C2413yes—
483C23×C4C2413yes—
484C23×C4C24112yes—
485C23×C4C24112yes—
486C4⋊Q8—224no—
487C4⋊Q8—212no—
488C4⋊Q8—212no—
489C4⋊Q8—412no—
490#127C2×D4124yes—
491#126—224no—
492#125—212no—
493#124—212no—
494#124—224no—
495#124—224no—
496#124—224no—
497#124—212no—
498#124—24no—
499#123—248no—
500#123—248no—
501#123—224no—
502C22⋊Q8—224no—
503C22⋊Q8—224no—
504C22⋊Q8—212no—
505C22⋊Q8—224no—
506C22⋊Q8—24no—
507C22⋊Q8—248no—
508C22⋊Q8—46no—
509C22⋊Q8—412no—
510C22⋊Q8—412no—
511C22⋊Q8—86no—
512#121—224no—
513#121—212no—
514#121—224no—
515#121—224no—
516#121—224no—
517#121—212no—
518#121—24no—
519#121C2×D4148yes—
520#120—248no—
521#120—412no—
522C4×Q8—24no—
523C4×Q8—24no—
524C4×Q8—28no—
525C4×Q8—24no—
526C4×Q8—24no—
527C4×Q8—28no—
528C4×Q8—212no—
529C4×Q8—212no—
530C4×Q8—212no—
531C4×Q8C2×D418yes—
532C4×D4—212no—
533C4×D4—224no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—224no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—212no—
540C4×D4—24no—
541C4×D4—212no—
542C4×D4—224no—
543C4×D4—212no—
544C4×D4—212no—
545C4×D4—412no—
546C4×D4—412no—
547C4×D4—412no—
548C4×D4—46no—
549C4×D4—412no—
550C4×D4—46no—
551C4×D4—86no—
552C4×D4C2×D4124yes—
553#117—224no—
554#117—212no—
555#117—412no—
556C2×C4⋊C4—224no—
557C2×C4⋊C4—212no—
558C2×C4⋊C4—212no—
559C2×C4⋊C4—412no—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C24112yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2413yes—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—812no—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2411yescharacteristic
599C2×C22⋊C4C2411yescharacteristic
600C2×C22⋊C4C24112yes—
601C2×C22⋊C4C24112yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C24112yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2413yes—
620C2×C22⋊C4C24112yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C42—212no—
627C2×C42—212no—
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2416yes—
632C2×C42C2416yes—
633C2×C42C2411yescharacteristic
634C2×C42C2413yes—
635C2×C42C2413yes—
636C2×C42C2413yes—
637C2×C42C2413yes—
638C2×C42C2413yes—
639C2×C42C2411yescharacteristic
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2413yes—
643#95C2413yes—
644#95C2416yes—
645#95C24112yes—
646#95C24112yes—
647#95C2411yescharacteristic
648#95C2411yescharacteristic
649#95C2412yes—
650#95C2412yes—
651#95C2413yes—
652#95C2413yes—
653#95C2413yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2412yes—
665#95C2416yes—
666#95C2416yes—
667#95C24112yes—
668#95C24112yes—
669C24—212no—
670C24—212no—
671C24—212no—
672C24—46no—
673C24—46no—
674C24—46no—
675C24—46no—
676C24C2516yes—
677C24C2513yes—
678C24C2512yes—
679C24C2511yescharacteristic
680#41—232no—
681#41—264no—
682#41—496no—
683#41—496no—
684#41—848no—
685C2×Q8—22no—
686C2×Q8—26no—
687C2×Q8—212no—
688C2×Q8—212no—
689C2×Q8—26no—
690C2×Q8—212no—
691C2×Q8—26no—
692C2×Q8—212no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—46no—
696C2×Q8—46no—
697C2×Q8—416no—
698C2×Q8—432no—
699C2×Q8C22×D414yes—
700C2×Q8C2×#4114yes—
701C2×Q8H(5,𝔽2)14yes—
702C2×D4—212no—
703C2×D4—212no—
704C2×D4—224no—
705C2×D4—26no—
706C2×D4—224no—
707C2×D4—24no—
708C2×D4—212no—
709C2×D4—26no—
710C2×D4—24no—
711C2×D4—212no—
712C2×D4—22no—
713C2×D4—26no—
714C2×D4—212no—
715C2×D4—212no—
716C2×D4—26no—
717C2×D4—26no—
718C2×D4—26no—
719C2×D4—22no—
720C2×D4—42no—
721C2×D4—43no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—412no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—448no—
728C2×D4—496no—
729C2×D4C22×D4112yes—
730C2×D4C22×D4124yes—
731C2×D4C22×D4124yes—
732C2×D4C2×#41112yes—
733C2×D42−1+414yes—
734C22×C4—26no—
735C22×C4—212no—
736C22×C4—212no—
737C22×C4—26no—
738C22×C4—212no—
739C22×C4—212no—
740C22×C4—26no—
741C22×C4—224no—
742C22×C4—22no—
743C22×C4—26no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—212no—
747C22×C4—24no—
748C22×C4—212no—
749C22×C4—26no—
750C22×C4—24no—
751C22×C4—212no—
752C22×C4—212no—
753C22×C4—26no—
754C22×C4—212no—
755C22×C4—22no—
756C22×C4—26no—
757C22×C4—22no—
758C22×C4—26no—
759C22×C4—26no—
760C22×C4—42no—
761C22×C4—46no—
762C22×C4—46no—
763C22×C4—43no—
764C22×C4—496no—
765C22×C4—412no—
766C22×C4—43no—
767C22×C4—43no—
768C22×C4—412no—
769C22×C4—412no—
770C22×C4—412no—
771C22×C4—412no—
772C22×C4C22×D4124yes—
773C22×C4C2×#41112yes—
774C22×C4C2511yescharacteristic
775C22×C4C2513yes—
776C22×C4C2512yes—
777C22×C4C2513yes—
778C22×C4C2513yes—
779C22×C4C2516yes—
780C22×C4C2511yescharacteristic
781C22×C4C2513yes—
782C22×C4C2516yes—
783C22×C4C2511yescharacteristic
784C22×C4C2512yes—
785C22×C4C2516yes—
786C22×C4C2511yescharacteristic
787C22×C4C2513yes—
788C22×C4C2513yes—
789C22×C4C2512yes—
790C22×C4C2511yescharacteristic
791C22×C4C2513yes—
792C22×C4C2511yescharacteristic
793C4⋊C4—26no—
794C4⋊C4—212no—
795C4⋊C4—26no—
796C4⋊C4—212no—
797C4⋊C4—212no—
798C4⋊C4—212no—
799C4⋊C4—24no—
800C4⋊C4—26no—
801C4⋊C4—26no—
802C4⋊C4—212no—
803C4⋊C4—212no—
804C4⋊C4—212no—
805C4⋊C4—26no—
806C4⋊C4—26no—
807C4⋊C4—26no—
808C4⋊C4—212no—
809C4⋊C4—22no—
810C4⋊C4—26no—
811C4⋊C4—46no—
812C4⋊C4—42no—
813C4⋊C4—43no—
814C4⋊C4—43no—
815C4⋊C4—46no—
816C4⋊C4—46no—
817C4⋊C4—46no—
818C4⋊C4—412no—
819C4⋊C4—46no—
820C4⋊C4C22×D414yes—
821C4⋊C4C22×D4112yes—
822C22⋊C4—212no—
823C22⋊C4—212no—
824C22⋊C4—212no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C22⋊C4—212no—
828C22⋊C4—26no—
829C22⋊C4—212no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—22no—
834C22⋊C4—24no—
835C22⋊C4—212no—
836C22⋊C4—212no—
837C22⋊C4—24no—
838C22⋊C4—22no—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C4—46no—
842C22⋊C4—412no—
843C22⋊C4—46no—
844C22⋊C4—46no—
845C22⋊C4—412no—
846C22⋊C4—43no—
847C22⋊C4—43no—
848C22⋊C4—43no—
849C22⋊C4—46no—
850C22⋊C4—46no—
851C22⋊C4—46no—
852C22⋊C4—46no—
853C22⋊C4—46no—
854C22⋊C4—46no—
855C22⋊C4—46no—
856C22⋊C4C22×D4124yes—
857C42—22no—
858C42—26no—
859C42—26no—
860C42—26no—
861C42—26no—
862C42—26no—
863C42—212no—
864C42—26no—
865C42—26no—
866C42—212no—
867C42—22no—
868C42—26no—
869C42—43no—
870C42—43no—
871C42C22×D4112yes—
872C23—22no—
873C23—21no—
874C23—23no—
875C23—21no—
876C23—22no—
877C23—26no—
878C23—21no—
879C23—22no—
880C23—26no—
881C23—23no—
882C23—21no—
883C23—23no—
884C23—26no—
885C23—21no—
886C23—23no—
887C23—23no—
888C23—22no—
889C23—26no—
890C23—26no—
891C23—22no—
892C23—23no—
893C23—22no—
894C23—26no—
895C23—21no—
896C23—424no—
897C23—424no—
898C23—424no—
899C23—812no—
900C23—812no—
901C23—812no—
902C23—812no—
903C23C23×D4112yes—
904C23C22×#4116yes—
905C23C2×2−1+414yes—
906C23#58512yes—
907C23C2611yescharacteristic
908Q8—412no—
909Q8—424no—
910Q8—44no—
911Q8—812no—
912Q8#546116yes—
913D4—224no—
914D4—248no—
915D4—28no—
916D4—224no—
917D4—424no—
918D4—48no—
919D4—412no—
920D4—424no—
921D4—448no—
922D4—424no—
923C2×C4—21no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—23no—
928C2×C4—23no—
929C2×C4—224no—
930C2×C4—248no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—23no—
935C2×C4—23no—
936C2×C4—23no—
937C2×C4—26no—
938C2×C4—26no—
939C2×C4—21no—
940C2×C4—23no—
941C2×C4—23no—
942C2×C4—26no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—26no—
946C2×C4—23no—
947C2×C4—23no—
948C2×C4—26no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—23no—
955C2×C4—23no—
956C2×C4—23no—
957C2×C4—21no—
958C2×C4—23no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—26no—
965C2×C4—23no—
966C2×C4—23no—
967C2×C4—21no—
968C2×C4—23no—
969C2×C4—26no—
970C2×C4—23no—
971C2×C4—26no—
972C2×C4—21no—
973C2×C4—48no—
974C2×C4—424no—
975C2×C4—424no—
976C2×C4—412no—
977C2×C4—424no—
978C2×C4—412no—
979C2×C4—44no—
980C2×C4—412no—
981C2×C4—86no—
982C2×C4—824no—
983C2×C4—1612no—
984C2×C4C23×D416yes—
985C2×C4C23×D414yes—
986C2×C4C23×D416yes—
987C2×C4C23×D412yes—
988C2×C4C22×#4112yes—
989C2×C4C22×#4116yes—
990C2×C4C2×H(5,𝔽2)16yes—
991C2×C4C2×2−1+412yes—
992C2×C4#58512yes—
993C22—22no—
994C22—212no—
995C22—24no—
996C22—26no—
997C22—22no—
998C22—24no—
999C22—24no—
1000C22—212no—
1001C22—22no—
1002C22—26no—
1003C22—26no—
1004C22—212no—
1005C22—43no—
1006C22—42no—
1007C22—41no—
1008C22—46no—
1009C22—46no—
1010C22—43no—
1011C22—41no—
1012C22—43no—
1013C22—46no—
1014C22—42no—
1015C22—46no—
1016C22—41no—
1017C22—43no—
1018C22—42no—
1019C22—42no—
1020C22—41no—
1021C22—848no—
1022C22C24×D411yescharacteristic
1023C22C23×#4111yescharacteristic
1024C22C22×H(5,𝔽2)11yescharacteristic
1025C22C22×2−1+411yescharacteristic
1026C22C2×#58511yescharacteristic
1027C22C2×#58511yescharacteristic
1028C22H(7,𝔽2)11yescharacteristic
1029C4—26no—
1030C4—22no—
1031C4—24no—
1032C4—43no—
1033C4—41no—
1034C4—46no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—43no—
1040C4—42no—
1041C4—43no—
1042C4—46no—
1043C4—43no—
1044C4—46no—
1045C4—43no—
1046C4C2×#546112yes—
1047C4#348914yes—
1048C2—42no—
1049C2—412no—
1050C2—46no—
1051C2—44no—
1052C2C22×#54611yescharacteristic
1053C2C2×#348911yescharacteristic
1054C2#6281611yescharacteristic
1055C2#6292311yescharacteristic
1056C2#6298711yescharacteristic
1057C2#6300011yescharacteristic
1058C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3522C2semidirect
2. C2×D4×#41C2semidirect
3. #59420C2semidirect
4. #59064C2semidirect
5. #59041C2semidirect
6. #59023C2semidirect
7. #45353C2semidirect
8. #45108C2semidirect
9. #38955C2semidirect
10. #38908C2semidirect
11. #37668C2semidirect
12. Q8×#124C2semidirect
13. Q8×#121C2semidirect
14. #36456C2semidirect
15. #36428C2semidirect
16. #36154C2semidirect
17. #36149C2semidirect
18. #35983C2semidirect
19. #35737C2semidirect
20. #34700C2semidirect
21. #34313C2semidirect
22. #34175C2semidirect
23. C4×#548C2semidirect
26. C2×#559C22semidirect
27. C2×Q82C22semidirect
28. C2×#554C22semidirect
32. C2×D4×Q8C22semidirect
35. C2×#548C22semidirect
37. C2×#547C22semidirect
40. C2×#542C22semidirect
42. C2×#532C22semidirect
43. C2×#529C22semidirect
45. C2×#520C22semidirect
46. C2×#520C22semidirect
48. C22×C4×Q8C22semidirect
50. #2862C22semidirect
51. #2857C22semidirect
52. #2857C22semidirect
53. #2848C22semidirect
54. #2708C22semidirect
55. #2697C22semidirect
56. #2695C22semidirect
57. #2693C22semidirect
58. #2687C22semidirect
59. #2687C22semidirect
60. #2684C22semidirect
61. #2625C22semidirect
62. #2621C22semidirect
63. #2568C22semidirect
65. #2563C22semidirect
66. #2547C22semidirect
67. #2546C22semidirect
69. #2538C22semidirect
70. #2535C22semidirect
71. #2535C22semidirect
72. #2534C22semidirect
73. #2503C22semidirect
74. #2492C22semidirect
75. #2492C22semidirect
76. #2487C22semidirect
77. #2480C22semidirect
78. #2468C22semidirect
79. #2457C22semidirect
81. #2452C22semidirect
82. #2450C22semidirect
83. #2447C22semidirect
84. #2447C22semidirect
85. #2447C22semidirect
86. #2447C22semidirect
87. #2442C22semidirect
88. #2442C22semidirect
89. #2439C22semidirect
90. #2437C22semidirect
92. #2435C22semidirect
93. #2432C22semidirect
94. #2432C22semidirect
95. #2429C22semidirect
97. #2427C22semidirect
98. #2427C22semidirect
99. #2427C22semidirect
100. #2427C22semidirect
101. #2420C22semidirect
102. #2420C22semidirect
103. #2420C22semidirect
104. #2420C22semidirect
105. #2420C22semidirect
106. #2419C22semidirect
107. #2418C22semidirect
108. #2417C22semidirect
109. #2417C22semidirect
110. #2417C22semidirect
111. #2417C22semidirect
113. #2408C22semidirect
114. #2407C22semidirect
115. #2407C22semidirect
116. #2407C22semidirect
117. #2404C22semidirect
118. #2395C22semidirect
119. #2392C22semidirect
120. #2367C22semidirect
121. #2366C22semidirect
122. #2362C22semidirect
123. #2361C22semidirect
124. #2361C22semidirect
125. #2352C22semidirect
126. #2351C22semidirect
127. #2351C22semidirect
128. Q8×C4⋊C4C22semidirect
129. #2349C22semidirect
130. D4×C4⋊C4C22semidirect
133. #2341C22semidirect
134. Q8×C22⋊C4C22semidirect
135. Q8×C22⋊C4C22semidirect
136. Q8×C22⋊C4C22semidirect
137. Q8×C22⋊C4C22semidirect
138. #2339C22semidirect
139. #2339C22semidirect
140. #2339C22semidirect
142. D4×C22⋊C4C22semidirect
143. D4×C22⋊C4C22semidirect
144. #2324C22semidirect
145. #2311C22semidirect
146. #2311C22semidirect
147. C4×#127C22semidirect
149. C4×#124C22semidirect
150. C4×C22⋊Q8C22semidirect
151. C4×C22⋊Q8C22semidirect
153. C4×#121C22semidirect
154. C4×#120C22semidirect
155. #2293C22semidirect
156. #2280C22semidirect
157. C2×#380C22semidirect
158. C42×Q8C22semidirect
159. C42×D4C22semidirect
176. #550D4semidirect
442. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C2×D4×#412
#594202
#590642
#590412
#590232
#453532
#451082
#389552
#389082
#376682
Q8×#1242
Q8×#1212
#364562
#364282
#361542
#361492
#359832
#357372
#347002
#343132
#341752
C4×#5482