Finite Group Databasebeta

← #7685552

Subgroups — #7685552

Order 512.

7985 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×#3497C211yesmaximal, characteristic, complemented
3#59813C216yesmaximal, complemented
4#59413C213yesmaximal, complemented
5#59078C213yesmaximal, complemented
6#59042C213yesmaximal, complemented
7#45246C216yesmaximal, complemented
8#44913C216yesmaximal, complemented
9#39468C213yesmaximal, complemented
10#39437C216yesmaximal, complemented
11#38909C213yesmaximal, complemented
12#36583C211yesmaximal, characteristic, complemented
13#36577C211yesmaximal, characteristic, complemented
14#36576C211yesmaximal, characteristic, complemented
15#36434C212yesmaximal, complemented
16#36419C213yesmaximal, complemented
17#36150C213yesmaximal, complemented
18#35801C212yesmaximal, complemented
19#35687C212yesmaximal, complemented
20#34889C213yesmaximal, complemented
21#34257C212yesmaximal, complemented
22C4×D4×Q8C211yesmaximal, characteristic, complemented
23C4×D4×Q8C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yes—
25#3523—216no—
26#3497—216no—
27C2×#557C2213yes—
28C2×#557C2211yescharacteristic
29C2×#556C2213yes—
30C2×#552C2216yes—
31C2×#550C2213yes—
32C2×#550C2211yescharacteristic
33C2×D4×Q8C2213yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2212yes—
38C2×#548C2216yes—
39C2×#548C2212yes—
40C2×#541C2216yes—
41C2×#537C2216yes—
42C2×#533C2213yes—
43C2×#532C2213yes—
44C2×#532C2213yes—
45C2×#529C2213yes—
46C2×#519C2212yes—
47C22×C4×Q8C2211yescharacteristic
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2212yes—
50#2858C2213yes—
51#2857C2213yes—
52#2856C2213yes—
53#2850C2216yes—
54#2715C22112yes—
55#2711C22112yes—
56#2704C22112yes—
57#2691C22112yes—
58#2691C22112yes—
59#2690C22112yes—
60#2671C22112yes—
61#2624C2216yes—
62#2616C2216yes—
63#2582C2213yes—
64#2568C2213yes—
65#2559C2216yes—
66#2559C22112yes—
67#2559C22112yes—
68#2557C2216yes—
69#2556C22112yes—
70#2550C2213yes—
71#2548C2213yes—
72#2548C2213yes—
73#2547C2213yes—
74#2545C2216yes—
75#2544C2216yes—
76#2544C2213yes—
77#2540C2213yes—
78#2538C2213yes—
79#2536C2216yes—
80#2535C2211yescharacteristic
81#2521C2216yes—
82#2500C2216yes—
83#2492C2213yes—
84#2490C2216yes—
85#2490C2216yes—
86#2490C2213yes—
87#2490C2216yes—
88#2485C2216yes—
89#2477C22112yes—
90#2464C2216yes—
91#2460C22112yes—
92#2454C2216yes—
93#2454C2216yes—
94#2453C2216yes—
95#2451C2216yes—
96#2448C2216yes—
97#2448C2216yes—
98#2442C2216yes—
99#2434C2216yes—
100#2432C2216yes—
101#2432C2216yes—
102#2429C2216yes—
103#2428C2213yes—
104#2427C2213yes—
105#2427C2216yes—
106#2426C2216yes—
107#2426C2216yes—
108#2426C2216yes—
109#2423C2216yes—
110#2421C2216yes—
111#2417C2216yes—
112#2416C2216yes—
113#2416C2216yes—
114#2414C2216yes—
115#2409C2216yes—
116#2407C2216yes—
117#2407C2216yes—
118#2395C2216yes—
119#2388C2216yes—
120#2367C2216yes—
121#2367C2216yes—
122#2365C2213yes—
123#2365C2213yes—
124#2363C2216yes—
125#2360C2213yes—
126#2360C2216yes—
127#2360C2213yes—
128#2351C2212yes—
129Q8×C4⋊C4C2211yescharacteristic
130Q8×C4⋊C4C2211yescharacteristic
131D4×C4⋊C4C2213yes—
132D4×C4⋊C4C2213yes—
133#2341C2216yes—
134#2341C2212yes—
135#2341C2212yes—
136#2341C2216yes—
137#2341C2212yes—
138Q8×C22⋊C4C2216yes—
139Q8×C22⋊C4C2211yescharacteristic
140Q8×C22⋊C4C2212yes—
141Q8×C22⋊C4C2212yes—
142Q8×C22⋊C4C2211yescharacteristic
143Q8×C22⋊C4C2216yes—
144#2311C2216yes—
145#2311C2216yes—
146C4×C4⋊Q8C2213yes—
147C4×C4⋊Q8C2213yes—
148C4×#124C2213yes—
149C4×C22⋊Q8C2216yes—
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2213yes—
152C4×C22⋊Q8C2213yes—
153C4×#121C2216yes—
154C4×#121C2213yes—
155#2297C2216yes—
156#2297C2216yes—
157C42×Q8C2211yescharacteristic
158C42×D4C2213yes—
159C42×D4C2213yes—
160C2×2−1+4—216no—
161C2×2−1+4—216no—
162C2×2−1+4—48no—
163C22×#41C2312yes—
164C22×#41C2316yes—
165C22×#41C2316yes—
166C22×#41C2316yes—
167C23×Q8C2311yescharacteristic
168C23×Q8C2316yes—
169C23×Q8C2312yes—
170C23×Q8C2311yescharacteristic
171#557—224no—
172#557—28no—
173#556—224no—
174#552—248no—
175#550—28no—
176#550—224no—
177D4×Q8—216no—
178D4×Q8—28no—
179D4×Q8—224no—
180D4×Q8D4116yescomplemented
181#548—216no—
182#548—248no—
183#548—48no—
184#541—248no—
185#537—248no—
186#533—224no—
187#532—224no—
188#532—224no—
189C2×C4⋊Q8C2313yes—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2313yes—
192C2×C4⋊Q8C2316yes—
193C2×C4⋊Q8C2313yes—
194C2×#127C2313yes—
195C2×#127C2313yes—
196#529—224no—
197C2×#126C2316yes—
198C2×#126C23112yes—
199C2×#125C2313yes—
200C2×#125C2316yes—
201C2×#125C2316yes—
202C2×#125C23112yes—
203C2×#124C2313yes—
204C2×#124C2313yes—
205C2×#124C2316yes—
206C2×#124C2316yes—
207C2×#124C2316yes—
208C2×#124C2316yes—
209C2×#123C2316yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2313yes—
212C2×C22⋊Q8C2313yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C2313yes—
215C2×C22⋊Q8C2316yes—
216C2×C22⋊Q8C23112yes—
217C2×C22⋊Q8C2313yes—
218C2×C22⋊Q8C2316yes—
219C2×C22⋊Q8C2316yes—
220C2×#121C2316yes—
221C2×#121C2316yes—
222C2×#121C23112yes—
223C2×#121C2311yescharacteristic
224C2×#121C2316yes—
225C2×#121C2313yes—
226C2×#121C2311yescharacteristic
227C2×#121C2316yes—
228C2×#121C2313yes—
229C2×#121C2316yes—
230C2×#121C2316yes—
231C2×#121C2316yes—
232#519—216no—
233C2×C4×Q8—28no—
234C2×C4×Q8—28no—
235C2×C4×Q8—48no—
236C2×C4×Q8C2313yes—
237C2×C4×Q8C2313yes—
238C2×C4×Q8C2313yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2316yes—
245C2×C4×Q8C2316yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2313yes—
248C2×C4×Q8C2313yes—
249C2×C4×Q8C2316yes—
250C2×C4×Q8C2316yes—
251C2×C4×Q8C2316yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2313yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2313yes—
262C2×C4×D4C2313yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2313yes—
265C2×#117C2316yes—
266C2×#117C2316yes—
267C2×#117C2316yes—
268C22×C4⋊C4C2313yes—
269C22×C4⋊C4C2313yes—
270C22×C4⋊C4C2316yes—
271C22×C42C2313yes—
272C22×C42C2313yes—
273C22×C42C2316yes—
274#400C23112yes—
275#400C2316yes—
276#399C23112yes—
277#399C2316yes—
278#398C23112yes—
279#398C2316yes—
280#398C23112yes—
281#397C23112yes—
282#397C2312yes—
283#397C2316yes—
284#397C2316yes—
285#397C23112yes—
286#396C23112yes—
287#396C23112yes—
288#396C23112yes—
289#395C23112yes—
290#395C2316yes—
291#394C2316yes—
292#394C23112yes—
293#394C23112yes—
294#394C2316yes—
295#394C23112yes—
296#394C2316yes—
297#394C2316yes—
298#394C2316yes—
299#394C23112yes—
300#394C23112yes—
301#394C23112yes—
302#393C2316yes—
303#392C2312yes—
304#392C2316yes—
305#392C2316yes—
306#391C2313yes—
307#391C2313yes—
308#391C2316yes—
309#391C2313yes—
310#391C2316yes—
311#391C23112yes—
312#391C2313yes—
313#391C2316yes—
314#391C2316yes—
315#391C2316yes—
316#391C2316yes—
317#391C2316yes—
318#391C2313yes—
319#391C2313yes—
320#390C2316yes—
321#390C23112yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2316yes—
334#390C2313yes—
335#390C2313yes—
336#389C2316yes—
337#389C2316yes—
338#389C2316yes—
339#389C2316yes—
340#389C2313yes—
341#389C2316yes—
342#389C2316yes—
343#389C2316yes—
344#389C2313yes—
345#389C2316yes—
346#389C2313yes—
347#389C2313yes—
348#389C2316yes—
349#388C23112yes—
350#388C23112yes—
351#388C23112yes—
352#388C23112yes—
353#388C23112yes—
354#388C2316yes—
355#388C2316yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#387C2316yes—
360#387C23112yes—
361#387C2316yes—
362#387C23112yes—
363#387C2316yes—
364#386C23112yes—
365#386C2316yes—
366#386C2316yes—
367#386C2316yes—
368#386C23112yes—
369#386C23112yes—
370#386C2316yes—
371#386C2312yes—
372#386C2312yes—
373#386C2316yes—
374#385C2316yes—
375#385C23112yes—
376#385C2316yes—
377#385C23112yes—
378#385C23112yes—
379#385C23112yes—
380#385C2316yes—
381#384C2313yes—
382#384C2313yes—
383#382C2316yes—
384#382C2311yescharacteristic
385#380C2313yes—
386#380C2316yes—
387#380C23112yes—
388#380C2316yes—
389#380C2316yes—
390#380C23112yes—
391#380C2316yes—
392#380C2313yes—
393#380C2316yes—
394#380C2316yes—
395#380C2316yes—
396#380C2311yescharacteristic
397#380C2311yescharacteristic
398C4×C4⋊C4C2313yes—
399C4×C4⋊C4C2313yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C22⋊C4C2313yes—
411C4×C22⋊C4C23112yes—
412C4×C22⋊C4C23112yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2313yes—
424C4×C22⋊C4C2316yes—
425C43C2313yes—
4262−1+4—4128no—
427C2×#41—224no—
428C2×#41—28no—
429C2×#41—224no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—224no—
433C2×#41—224no—
434C2×#41—224no—
435C2×#41—224no—
436C2×#41—412no—
437C2×#41—412no—
438C2×#41—412no—
439C22×Q8—24no—
440C22×Q8—28no—
441C22×Q8—28no—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—224no—
445C22×Q8—24no—
446C22×Q8—224no—
447C22×Q8—24no—
448C22×Q8—412no—
449C22×Q8C2×D4116yes—
450C22×Q8#4118yes—
451C22×Q8C2413yes—
452C22×Q8C2413yes—
453C22×Q8C2416yes—
454C22×Q8C2416yes—
455C22×Q8C2413yes—
456C22×Q8C2411yescharacteristic
457C22×D4C2411yescharacteristic
458C22×D4C2413yes—
459C22×D4C2416yes—
460C22×D4C2412yes—
461C22×D4C2412yes—
462C22×D4C2416yes—
463C22×D4C2416yes—
464C22×D4C2411yescharacteristic
465C22×D4C2416yes—
466C22×D4C2416yes—
467C22×D4C2416yes—
468C23×C4C2413yes—
469C23×C4C2416yes—
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2413yes—
473C23×C4C24112yes—
474C23×C4C2416yes—
475C23×C4C2413yes—
476C23×C4C2413yes—
477C23×C4C2412yes—
478C23×C4C2416yes—
479C4⋊Q8—224no—
480C4⋊Q8—212no—
481C4⋊Q8—212no—
482C4⋊Q8—212no—
483C4⋊Q8C2×D4124yes—
484#127—212no—
485#127—212no—
486#126—224no—
487#126—248no—
488#125—212no—
489#125—224no—
490#125—248no—
491#125—224no—
492#124—224no—
493#124—212no—
494#124—224no—
495#124—212no—
496#124—412no—
497#124—412no—
498#123—224no—
499C22⋊Q8—224no—
500C22⋊Q8—224no—
501C22⋊Q8—212no—
502C22⋊Q8—224no—
503C22⋊Q8—212no—
504C22⋊Q8—212no—
505C22⋊Q8—248no—
506C22⋊Q8—46no—
507C22⋊Q8—412no—
508C22⋊Q8C2×D4148yes—
509#121—24no—
510#121—24no—
511#121—224no—
512#121—212no—
513#121—224no—
514#121—224no—
515#121—224no—
516#121—248no—
517#121—412no—
518#121—46no—
519#121—412no—
520#121—412no—
521C4×Q8—24no—
522C4×Q8—24no—
523C4×Q8—224no—
524C4×Q8—28no—
525C4×Q8—224no—
526C4×Q8—24no—
527C4×Q8—24no—
528C4×Q8—28no—
529C4×Q8—212no—
530C4×Q8—212no—
531C4×Q8—224no—
532C4×Q8—212no—
533C4×Q8—212no—
534C4×Q8—212no—
535C4×Q8—412no—
536C4×Q8—412no—
537C4×Q8C2×D418yes—
538C4×D4—224no—
539C4×D4—224no—
540C4×D4—212no—
541C4×D4—224no—
542C4×D4—224no—
543C4×D4—212no—
544C4×D4—24no—
545C4×D4—24no—
546C4×D4—46no—
547C4×D4—412no—
548C4×D4—46no—
549C4×D4C2×D4124yes—
550#117—224no—
551#117—224no—
552#117—224no—
553C2×C4⋊C4—212no—
554C2×C4⋊C4—212no—
555C2×C4⋊C4—412no—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2413yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C24112yes—
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C24112yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2413yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2413yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C24112yes—
595C2×C22⋊C4C2413yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2413yes—
598C2×C22⋊C4C2413yes—
599C2×C22⋊C4C2411yescharacteristic
600C2×C22⋊C4C2411yescharacteristic
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C24112yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C24112yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C24112yes—
614C2×C22⋊C4C24112yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C42—212no—
620C2×C42—212no—
621C2×C42—412no—
622C2×C42C2413yes—
623C2×C42C24112yes—
624C2×C42C2416yes—
625C2×C42C2413yes—
626C2×C42C2413yes—
627C2×C42C2413yes—
628C2×C42C2416yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2413yes—
632C2×C42C2413yes—
633C2×C42C2413yes—
634C2×C42C2413yes—
635C2×C42C2416yes—
636C2×C42C2416yes—
637C2×C42C2413yes—
638C2×C42C2413yes—
639C2×C42C2411yescharacteristic
640#95C2413yes—
641#95C2412yes—
642#95C2412yes—
643#95C2412yes—
644#95C2416yes—
645#95C2413yes—
646#95C2416yes—
647#95C2413yes—
648#95C2416yes—
649#95C2416yes—
650#95C2416yes—
651#95C2413yes—
652#95C2413yes—
653#95C2413yes—
654#95C2416yes—
655#95C2416yes—
656#95C24112yes—
657#95C2416yes—
658#95C2416yes—
659#95C2412yes—
660#95C2416yes—
661#95C24112yes—
662#95C2416yes—
663#95C2416yes—
664#95C24112yes—
665C24C2516yes—
666C24C2512yes—
667C24C2511yescharacteristic
668C24C2511yescharacteristic
669#41—496no—
670#41—496no—
671#41—496no—
672#41—432no—
673C2×Q8—264no—
674C2×Q8—232no—
675C2×Q8—26no—
676C2×Q8—26no—
677C2×Q8—26no—
678C2×Q8—212no—
679C2×Q8—212no—
680C2×Q8—26no—
681C2×Q8—212no—
682C2×Q8—212no—
683C2×Q8—26no—
684C2×Q8—26no—
685C2×Q8—26no—
686C2×Q8—26no—
687C2×Q8—46no—
688C2×Q8—496no—
689C2×Q8—416no—
690C2×Q8C22×D4124yes—
691C2×Q8C22×D414yes—
692C2×Q8C2×#41112yes—
693C2×Q8C2×#4114yes—
694C2×Q8H(5,𝔽2)14yes—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—212no—
700C2×D4—212no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—212no—
704C2×D4—212no—
705C2×D4—26no—
706C2×D4—212no—
707C2×D4—212no—
708C2×D4—212no—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—212no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—26no—
715C2×D4—22no—
716C2×D4—26no—
717C2×D4—42no—
718C2×D4—46no—
719C2×D4—46no—
720C2×D4—42no—
721C2×D4—46no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4C22×D414yes—
728C22×C4—26no—
729C22×C4—212no—
730C22×C4—212no—
731C22×C4—26no—
732C22×C4—26no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—224no—
738C22×C4—212no—
739C22×C4—26no—
740C22×C4—224no—
741C22×C4—212no—
742C22×C4—26no—
743C22×C4—212no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—26no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—43no—
753C22×C4—412no—
754C22×C4—46no—
755C22×C4—43no—
756C22×C4—46no—
757C22×C4—46no—
758C22×C4—43no—
759C22×C4C22×D4124yes—
760C22×C4C2×#41112yes—
761C22×C4C2512yes—
762C22×C4C2513yes—
763C22×C4C2512yes—
764C22×C4C2513yes—
765C22×C4C2516yes—
766C22×C4C2513yes—
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C22×C4C2516yes—
770C22×C4C2513yes—
771C22×C4C2512yes—
772C22×C4C2513yes—
773C22×C4C2513yes—
774C22×C4C2516yes—
775C22×C4C2513yes—
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2513yes—
779C22×C4C2511yescharacteristic
780C4⋊C4—26no—
781C4⋊C4—212no—
782C4⋊C4—26no—
783C4⋊C4—212no—
784C4⋊C4—212no—
785C4⋊C4—212no—
786C4⋊C4—212no—
787C4⋊C4—212no—
788C4⋊C4—22no—
789C4⋊C4—212no—
790C4⋊C4—212no—
791C4⋊C4—22no—
792C4⋊C4—224no—
793C4⋊C4—212no—
794C4⋊C4—26no—
795C4⋊C4—26no—
796C4⋊C4—212no—
797C4⋊C4—26no—
798C4⋊C4—212no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—26no—
802C4⋊C4—412no—
803C4⋊C4—46no—
804C4⋊C4—43no—
805C4⋊C4—46no—
806C4⋊C4—46no—
807C4⋊C4—46no—
808C4⋊C4—46no—
809C4⋊C4C22×D4112yes—
810C4⋊C4C22×D4124yes—
811C4⋊C4C22×D4112yes—
812C22⋊C4—24no—
813C22⋊C4—212no—
814C22⋊C4—24no—
815C22⋊C4—212no—
816C22⋊C4—26no—
817C22⋊C4—26no—
818C22⋊C4—212no—
819C22⋊C4—212no—
820C22⋊C4—224no—
821C22⋊C4—212no—
822C22⋊C4—26no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—212no—
827C22⋊C4—212no—
828C22⋊C4—46no—
829C22⋊C4—42no—
830C22⋊C4—46no—
831C22⋊C4—46no—
832C22⋊C4—43no—
833C22⋊C4—42no—
834C22⋊C4—46no—
835C22⋊C4—46no—
836C22⋊C4—46no—
837C22⋊C4—412no—
838C22⋊C4—412no—
839C22⋊C4—46no—
840C22⋊C4—412no—
841C22⋊C4—412no—
842C22⋊C4C22×D4124yes—
843C42—26no—
844C42—26no—
845C42—26no—
846C42—26no—
847C42—26no—
848C42—26no—
849C42—224no—
850C42—212no—
851C42—26no—
852C42—26no—
853C42—212no—
854C42—26no—
855C42—46no—
856C42—46no—
857C42—43no—
858C42—43no—
859C42C22×D4112yes—
860C422−1+414yescomplemented
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—21no—
866C23—22no—
867C23—21no—
868C23—22no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—22no—
873C23—21no—
874C23—21no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—22no—
879C23—26no—
880C23—26no—
881C23—26no—
882C23—26no—
883C23—26no—
884C23—26no—
885C23—26no—
886C23C23×D414yes—
887C23C22×#4112yes—
888C23#58512yes—
889C23C2611yescharacteristic
890Q8—224no—
891Q8—248no—
892Q8—424no—
893Q8—412no—
894Q8—412no—
895Q8#546116yes—
896D4—28no—
897D4—28no—
898D4—424no—
899D4—424no—
900D4—48no—
901D4—48no—
902D4—424no—
903D4—412no—
904D4—812no—
905D4—812no—
906D4—812no—
907C2×C4—23no—
908C2×C4—21no—
909C2×C4—26no—
910C2×C4—21no—
911C2×C4—26no—
912C2×C4—23no—
913C2×C4—21no—
914C2×C4—23no—
915C2×C4—21no—
916C2×C4—23no—
917C2×C4—248no—
918C2×C4—224no—
919C2×C4—21no—
920C2×C4—23no—
921C2×C4—21no—
922C2×C4—26no—
923C2×C4—22no—
924C2×C4—23no—
925C2×C4—23no—
926C2×C4—22no—
927C2×C4—23no—
928C2×C4—23no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—23no—
932C2×C4—26no—
933C2×C4—23no—
934C2×C4—22no—
935C2×C4—26no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—23no—
940C2×C4—23no—
941C2×C4—23no—
942C2×C4—23no—
943C2×C4—21no—
944C2×C4—23no—
945C2×C4—26no—
946C2×C4—26no—
947C2×C4—22no—
948C2×C4—26no—
949C2×C4—21no—
950C2×C4—23no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—23no—
954C2×C4—23no—
955C2×C4—448no—
956C2×C4—412no—
957C2×C4—48no—
958C2×C4—412no—
959C2×C4—424no—
960C2×C4—44no—
961C2×C4—44no—
962C2×C4—86no—
963C2×C4—812no—
964C2×C4C23×D416yes—
965C2×C4C23×D4112yes—
966C2×C4C23×D416yes—
967C2×C4C23×D412yes—
968C2×C4C22×#4116yes—
969C2×C4C22×#4116yes—
970C2×C4C2×H(5,𝔽2)16yes—
971C2×C4C2×2−1+412yes—
972C2×C4C2×2−1+412yes—
973C2×C4C2×2−1+412yes—
974C2×C4#58512yes—
975C22—22no—
976C22—24no—
977C22—22no—
978C22—22no—
979C22—24no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—24no—
984C22—41no—
985C22—41no—
986C22—42no—
987C22—42no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—46no—
997C22—46no—
998C22—46no—
999C22—46no—
1000C22—46no—
1001C22—46no—
1002C22—46no—
1003C22C24×D411yescharacteristic
1004C22C23×#4111yescharacteristic
1005C22C22×H(5,𝔽2)11yescharacteristic
1006C22C22×2−1+411yescharacteristic
1007C22C2×#58511yescharacteristic
1008C22C2×#58511yescharacteristic
1009C222−1+611yescharacteristic
1010C4—26no—
1011C4—22no—
1012C4—22no—
1013C4—26no—
1014C4—212no—
1015C4—43no—
1016C4—43no—
1017C4—42no—
1018C4—43no—
1019C4—43no—
1020C4—46no—
1021C4—41no—
1022C4—41no—
1023C4—46no—
1024C4—42no—
1025C4—42no—
1026C4—43no—
1027C4C2×#546112yes—
1028C4#349714yes—
1029C2—42no—
1030C2—44no—
1031C2—42no—
1032C2—86no—
1033C2C22×#54611yescharacteristic
1034C2C2×#349711yescharacteristic
1035C2#6278811yescharacteristic
1036C2#6291311yescharacteristic
1037C2#6300211yescharacteristic
1038C2#6300711yescharacteristic
1039C2#6301911yescharacteristic
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×#3523C2semidirect
2. C2×#3497C2semidirect
3. #59813C2semidirect
4. #59413C2semidirect
5. #59078C2semidirect
6. #59042C2semidirect
7. #45246C2semidirect
8. #44913C2semidirect
9. #39468C2semidirect
10. #39437C2semidirect
11. #38909C2semidirect
12. #36583C2semidirect
13. #36577C2semidirect
14. #36576C2semidirect
15. #36434C2semidirect
16. #36419C2semidirect
17. #36150C2semidirect
18. #35801C2semidirect
19. #35687C2semidirect
20. #34889C2semidirect
21. #34257C2semidirect
22. C4×D4×Q8C2semidirect
23. C4×D4×Q8C2semidirect
180. D4×Q8D4semidirect
860. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C2×#34972
#598132
#594132
#590782
#590422
#452462
#449132
#394682
#394372
#389092
#365832
#365772
#365762
#364342
#364192
#361502
#358012
#356872
#348892
#342572
C4×D4×Q82