Finite Group Databasebeta

← #7686122

Subgroups — #7686122

Order 512.

8052 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C22×D4×Q8C211yesmaximal, characteristic, complemented
3#59421C213yesmaximal, complemented
4#59134C213yesmaximal, complemented
5#59036C213yesmaximal, complemented
6#59025C216yesmaximal, complemented
7#45291C216yesmaximal, complemented
8#45289C216yesmaximal, complemented
9#38958C213yesmaximal, complemented
10#38911C213yesmaximal, complemented
11#37665C216yesmaximal, complemented
12#36575C212yesmaximal, complemented
13Q8×#124C211yesmaximal, characteristic, complemented
14Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
15#36444C211yesmaximal, characteristic, complemented
16#36160C213yesmaximal, complemented
17#36129C213yesmaximal, complemented
18#35771C212yesmaximal, complemented
19#35723C212yesmaximal, complemented
20#34700C213yesmaximal, complemented
21#34311C211yesmaximal, characteristic, complemented
22#34173C212yesmaximal, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C24×Q8C2212yes—
25#3518—216no—
26C2×Q82C2211yescharacteristic, complemented
27C2×#556C2213yescomplemented
28C2×#556C2216yescomplemented
29C2×#555C2213yes—
30C2×D4×Q8—216no—
31C2×D4×Q8C2213yes—
32C2×D4×Q8C2213yes—
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2216yes—
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2212yescomplemented
39C2×#548C2212yescomplemented
40C2×#542C2216yescomplemented
41C2×#533C2213yescomplemented
42C22×C4⋊Q8C2213yes—
43C2×#529C2213yes—
44C22×C22⋊Q8C2216yes—
45C2×#519C2212yescomplemented
46C2×#519C2212yescomplemented
47C2×C4×#41C2211yescharacteristic, complemented
48C22×C4×Q8C2211yescharacteristic
49C22×C4×D4C2213yes—
50#2862C2213yescomplemented
51#2857C2213yes—
52#2857C2213yescomplemented
53#2847C2216yes—
54#2716C22112yescomplemented
55#2702C22112yescomplemented
56#2700C22112yescomplemented
57#2700C22112yescomplemented
58#2692C22112yescomplemented
59#2689C22112yescomplemented
60#2687C22112yescomplemented
61#2625C2216yescomplemented
62#2620C2216yescomplemented
63#2582C2213yescomplemented
64#2568C2213yescomplemented
65#2567C2213yescomplemented
66#2563C2213yes—
67#2560C22112yescomplemented
68#2550C2216yescomplemented
69#2547C2213yescomplemented
70#2545C2216yescomplemented
71#2538C2216yescomplemented
72#2537C2213yes—
73#2499C2216yescomplemented
74#2492C2216yescomplemented
75#2492C2216yescomplemented
76#2492C2216yescomplemented
77#2492C2216yescomplemented
78#2485C2216yes—
79#2481C22112yes—
80#2480C2216yes—
81#2472C22112yes—
82#2468C2216yes—
83#2465C22112yescomplemented
84#2459C22112yes—
85#2457C2216yes—
86#2454C2213yes—
87#2451C2216yescomplemented
88#2451C2216yescomplemented
89#2447C2213yes—
90#2446C2216yescomplemented
91#2446C2216yescomplemented
92#2442C2213yes—
93#2440C2216yes—
94#2439C2216yescomplemented
95#2439C2216yescomplemented
96#2436C2216yes—
97#2436C2216yescomplemented
98#2436C2216yescomplemented
99#2435C2211yescharacteristic
100#2429C2216yescomplemented
101#2427C2213yes—
102#2427C2216yescomplemented
103#2426C2216yescomplemented
104#2423C2216yescomplemented
105#2421C2216yescomplemented
106#2420C2213yes—
107#2420C2216yes—
108#2418C2216yes—
109#2417C2216yes—
110#2417C2213yes—
111#2415C2216yescomplemented
112#2415C2216yescomplemented
113#2414C2216yes—
114#2409C2216yes—
115#2409C2216yescomplemented
116#2409C2216yescomplemented
117#2408C2213yes—
118#2395C2216yes—
119#2392C2216yes—
120#2367C2213yescomplemented
121#2365C2213yescomplemented
122#2363C2216yes—
123#2362C2216yescomplemented
124#2362C2213yescomplemented
125#2361C2213yes—
126#2360C2216yes—
127#2354C2213yes—
128#2352C2216yes—
129#2352C2213yes—
130#2351C2211yescharacteristic, complemented
131Q8×C4⋊C4C2211yescharacteristic, complemented
132Q8×C4⋊C4C2212yescomplemented
133#2341C2211yescharacteristic, complemented
134Q8×C22⋊C4C2216yes—
135Q8×C22⋊C4C2211yescharacteristic
136Q8×C22⋊C4C2216yes—
137Q8×C22⋊C4C2212yes—
138Q8×C22⋊C4C2212yescomplemented
139Q8×C22⋊C4C2216yescomplemented
140Q8×C22⋊C4C2212yescomplemented
141Q8×C22⋊C4C2216yescomplemented
142Q8×C22⋊C4C2212yescomplemented
143Q8×C22⋊C4C2212yescomplemented
144#2323C2216yescomplemented
145#2310C2216yescomplemented
146#2310C2216yescomplemented
147C4×C4⋊Q8C2213yescomplemented
148C4×#124C2213yes—
149C4×#124C2213yescomplemented
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2213yescomplemented
152C4×#121C2213yes—
153C4×#121C2213yes—
154C4×#120C2216yes—
155#2293C2213yes—
156#2280C2216yes—
157#2280C2216yes—
158C42×Q8C2211yescharacteristic, complemented
159C42×D4C2213yes—
160C22×#41C2311yescharacteristic
161C23×Q8—216no—
162C23×Q8—216no—
163C23×Q8—48no—
164C23×Q8C2312yes—
165C23×Q8C2316yes—
166C23×Q8C2316yes—
167C23×Q8C2316yes—
168C23×Q8C2312yes—
169C23×Q8C2311yescharacteristic
170C23×D4C2311yescharacteristic
171C24×C4C2316yes—
172Q82—28no—
173#556—224no—
174#556—248no—
175#555—224no—
176D4×Q8—216no—
177D4×Q8—224no—
178D4×Q8—248no—
179D4×Q8—28no—
180D4×Q8—224no—
181D4×Q8D4116yescomplemented
182#548—216no—
183#548—28no—
184#548—48no—
185#542—248no—
186#533—224no—
187C2×C4⋊Q8—224no—
188C2×C4⋊Q8C2313yes—
189C2×C4⋊Q8C2313yes—
190C2×C4⋊Q8C2316yes—
191C2×C4⋊Q8C2316yes—
192C2×C4⋊Q8C2316yes—
193C2×C4⋊Q8C2316yes—
194C2×C4⋊Q8C2313yes—
195#529—224no—
196C2×#126C23112yes—
197C2×#126C2316yes—
198C2×#125C2313yes—
199C2×#124C2313yes—
200C2×#124C2311yescharacteristic
201C2×#124C2316yes—
202C2×#124C2311yescharacteristic
203C2×#124C23112yes—
204C2×#124C2316yes—
205C2×#123C2316yes—
206C2×C22⋊Q8—248no—
207C2×C22⋊Q8C23112yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C23112yes—
214C2×C22⋊Q8C2313yes—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2316yes—
218C2×C22⋊Q8C2316yes—
219C2×C22⋊Q8C2316yes—
220C2×#121C2313yes—
221C2×#121C2316yes—
222C2×#121C2313yes—
223C2×#121C2313yes—
224C2×#121C2316yes—
225C2×#120C2316yes—
226#519—216no—
227#519—48no—
228C4×#41—28no—
229C2×C4×Q8—28no—
230C2×C4×Q8C2313yes—
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2316yes—
237C2×C4×Q8C2316yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2316yes—
241C2×C4×Q8C2313yes—
242C2×C4×Q8C2316yes—
243C2×C4×Q8C2316yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—224no—
246C2×C4×D4C2313yes—
247C2×C4×D4C2313yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2313yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2313yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2313yes—
259C2×#117C2316yes—
260C2×#117C2316yes—
261C2×#117C2313yes—
262C2×#117C2316yes—
263C2×#117C2316yes—
264C2×#117C2316yes—
265C22×C4⋊C4C2313yes—
266C22×C4⋊C4C2313yes—
267C22×C4⋊C4C2316yes—
268C22×C22⋊C4C2316yes—
269C22×C42C2313yes—
270C22×C42C2313yes—
271#400C23112yes—
272#400C23112yes—
273#400C2316yes—
274#399C2316yes—
275#398C23112yes—
276#398C23112yes—
277#398C2316yes—
278#398C2316yes—
279#397C2316yes—
280#397C2316yes—
281#397C23112yes—
282#397C2316yes—
283#397C2316yes—
284#397C23112yes—
285#396C23112yes—
286#396C23112yes—
287#396C2316yes—
288#396C2316yes—
289#395C23112yes—
290#395C23112yes—
291#394C23112yes—
292#394C2316yes—
293#394C23112yes—
294#394C2312yes—
295#394C2316yes—
296#394C2312yes—
297#394C2316yes—
298#393C23112yes—
299#393C23112yes—
300#393C23112yes—
301#393C23112yes—
302#392C2316yes—
303#391C23112yes—
304#391C2316yes—
305#391C2313yes—
306#391C2313yes—
307#391C2316yes—
308#391C2316yes—
309#391C2316yes—
310#391C2316yes—
311#391C2316yes—
312#391C2316yes—
313#391C23112yes—
314#391C23112yes—
315#391C23112yes—
316#391C2313yes—
317#391C2316yes—
318#391C2316yes—
319#391C2313yes—
320#391C2316yes—
321#391C2316yes—
322#391C2316yes—
323#391C2316yes—
324#390C23112yes—
325#390C2313yes—
326#390C2313yes—
327#390C2313yes—
328#390C2313yes—
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#389C2313yes—
332#389C2316yes—
333#389C2313yes—
334#389C2316yes—
335#389C2316yes—
336#389C2316yes—
337#389C2316yes—
338#389C2313yes—
339#389C2316yes—
340#389C2313yes—
341#389C2313yes—
342#389C23112yes—
343#389C2313yes—
344#388C2316yes—
345#388C2316yes—
346#388C23112yes—
347#388C2316yes—
348#388C23112yes—
349#388C23112yes—
350#388C2316yes—
351#388C2316yes—
352#388C2316yes—
353#388C23112yes—
354#388C2316yes—
355#388C2316yes—
356#387C23112yes—
357#387C23112yes—
358#387C2316yes—
359#387C23112yes—
360#387C23112yes—
361#387C2316yes—
362#386C2316yes—
363#386C23112yes—
364#386C23112yes—
365#386C23112yes—
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#385C2316yes—
371#385C2316yes—
372#385C2316yes—
373#385C2316yes—
374#385C2316yes—
375#384C2313yes—
376#384C2316yes—
377#382C2316yes—
378#382C2313yes—
379#382C2313yes—
380#381C23112yes—
381#381C2316yes—
382#381C2316yes—
383#380C2316yes—
384#380C2316yes—
385#380C2316yes—
386#380C2316yes—
387#380C2313yes—
388#380C2316yes—
389#380C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2313yes—
394#380C2313yes—
395#380C2316yes—
396#380C2316yes—
397#380C2313yes—
398#379C2316yes—
399#379C2312yes—
400#379C2312yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C22⋊C4C23112yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C23112yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2313yes—
424C4×C22⋊C4C2311yescharacteristic
425C43C2313yes—
426C25C2412yes—
427C2×#41—24no—
428C2×#41—24no—
429C2×#41—24no—
430C22×Q8—24no—
431C22×Q8—28no—
432C22×Q8—28no—
433C22×Q8—24no—
434C22×Q8—224no—
435C22×Q8—224no—
436C22×Q8—28no—
437C22×Q8—224no—
438C22×Q8—224no—
439C22×Q8—28no—
440C22×Q8—28no—
441C22×Q8—224no—
442C22×Q8—224no—
443C22×Q8—412no—
444C22×Q8—412no—
445C22×Q8—412no—
446C22×Q8—4128no—
447C22×Q8C2×D4116yes—
448C22×Q8#4118yes—
449C22×Q8C2411yescharacteristic
450C22×Q8C2416yes—
451C22×Q8C24112yes—
452C22×Q8C2416yes—
453C22×Q8C2413yes—
454C22×Q8C2416yes—
455C22×Q8C2411yescharacteristic
456C22×D4—24no—
457C22×D4—24no—
458C22×D4—24no—
459C22×D4C2412yes—
460C22×D4C2413yes—
461C22×D4C2413yes—
462C22×D4C2411yescharacteristic
463C22×D4C2411yescharacteristic
464C22×D4C2416yes—
465C22×D4C2416yes—
466C23×C4—224no—
467C23×C4—224no—
468C23×C4—412no—
469C23×C4C2413yes—
470C23×C4C2413yes—
471C23×C4C2416yes—
472C23×C4C2413yes—
473C23×C4C2416yes—
474C23×C4C2416yes—
475C23×C4C2416yes—
476C23×C4C2416yes—
477C23×C4C2413yes—
478C23×C4C2411yescharacteristic
479C23×C4C2413yes—
480C4⋊Q8—224no—
481C4⋊Q8—224no—
482C4⋊Q8—224no—
483C4⋊Q8—224no—
484C4⋊Q8—212no—
485C4⋊Q8—212no—
486C4⋊Q8C2×D4124yes—
487#126—248no—
488#126—224no—
489#125—212no—
490#124—224no—
491#124—212no—
492#124—24no—
493#124—24no—
494#124—248no—
495#124—412no—
496#123—224no—
497C22⋊Q8—224no—
498C22⋊Q8—224no—
499C22⋊Q8—212no—
500C22⋊Q8—224no—
501C22⋊Q8—24no—
502C22⋊Q8—248no—
503C22⋊Q8—224no—
504C22⋊Q8—212no—
505C22⋊Q8—224no—
506C22⋊Q8—248no—
507C22⋊Q8—412no—
508C22⋊Q8—412no—
509C22⋊Q8C2×D4148yes—
510#121—212no—
511#121—212no—
512#121—224no—
513#121—212no—
514#121—412no—
515#120—412no—
516C4×Q8—24no—
517C4×Q8—24no—
518C4×Q8—224no—
519C4×Q8—28no—
520C4×Q8—224no—
521C4×Q8—24no—
522C4×Q8—24no—
523C4×Q8—28no—
524C4×Q8—212no—
525C4×Q8—224no—
526C4×Q8—212no—
527C4×Q8—212no—
528C4×Q8—412no—
529C4×Q8—412no—
530C4×Q8C2×D418yes—
531C4×D4—212no—
532C4×D4—224no—
533C4×D4—224no—
534C4×D4—212no—
535C4×D4—212no—
536C4×D4—212no—
537C4×D4—212no—
538C4×D4—224no—
539C4×D4—212no—
540C4×D4—212no—
541C4×D4—412no—
542C4×D4—46no—
543C4×D4C2×D4124yes—
544#117—224no—
545#117—224no—
546#117—212no—
547#117—224no—
548#117—412no—
549#117—412no—
550C2×C4⋊C4—212no—
551C2×C4⋊C4—212no—
552C2×C4⋊C4—224no—
553C2×C4⋊C4C2413yes—
554C2×C4⋊C4C2416yes—
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2416yes—
558C2×C4⋊C4C24112yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2413yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C24112yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2416yes—
584C2×C22⋊C4—224no—
585C2×C22⋊C4C2416yes—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C24112yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2411yescharacteristic
594C2×C22⋊C4C2411yescharacteristic
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2413yes—
597C2×C22⋊C4C2413yes—
598C2×C22⋊C4C2413yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C24112yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C42—212no—
619C2×C42—212no—
620C2×C42C2413yes—
621C2×C42C24112yes—
622C2×C42C2413yes—
623C2×C42C2413yes—
624C2×C42C2416yes—
625C2×C42C2416yes—
626C2×C42C2413yes—
627C2×C42C2413yes—
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C24112yes—
634C2×C42C2413yes—
635C2×C42C2413yes—
636C2×C42C2413yes—
637#95C2411yescharacteristic
638#95C2411yescharacteristic
639#95C2416yes—
640#95C2413yes—
641#95C2413yes—
642#95C2413yes—
643#95C2413yes—
644#95C2416yes—
645#95C2416yes—
646#95C2416yes—
647#95C24112yes—
648#95C24112yes—
649#95C2416yes—
650#95C2416yes—
651#95C2416yes—
652#95C24112yes—
653#95C2416yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C24112yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C24112yes—
664C24—24no—
665C24—24no—
666C24—24no—
667C24—24no—
668C24—24no—
669C24—42no—
670C24—42no—
671C24C2513yes—
672C24C2512yes—
673C24C2512yes—
674C24C2511yescharacteristic
675#41—416no—
676C2×Q8—232no—
677C2×Q8—264no—
678C2×Q8—26no—
679C2×Q8—22no—
680C2×Q8—224no—
681C2×Q8—212no—
682C2×Q8—212no—
683C2×Q8—212no—
684C2×Q8—224no—
685C2×Q8—212no—
686C2×Q8—212no—
687C2×Q8—26no—
688C2×Q8—212no—
689C2×Q8—22no—
690C2×Q8—22no—
691C2×Q8—412no—
692C2×Q8—46no—
693C2×Q8—46no—
694C2×Q8—496no—
695C2×Q8—496no—
696C2×Q8—496no—
697C2×Q8—432no—
698C2×Q8C22×D4124yes—
699C2×Q8C22×D414yes—
700C2×Q8C2×#41112yes—
701C2×Q8C2×#4114yes—
702C2×Q8H(5,𝔽2)14yes—
703C2×D4—232no—
704C2×D4—24no—
705C2×D4—24no—
706C2×D4—26no—
707C2×D4—26no—
708C2×D4—26no—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—22no—
712C2×D4—26no—
713C2×D4—26no—
714C2×D4—26no—
715C2×D4—24no—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—46no—
720C2×D4—46no—
721C2×D4—46no—
722C2×D4—46no—
723C2×D4C22×D414yes—
724C2×D42−1+414yes—
725C22×C4—22no—
726C22×C4—26no—
727C22×C4—212no—
728C22×C4—212no—
729C22×C4—26no—
730C22×C4—22no—
731C22×C4—212no—
732C22×C4—212no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—212no—
738C22×C4—212no—
739C22×C4—212no—
740C22×C4—26no—
741C22×C4—212no—
742C22×C4—212no—
743C22×C4—212no—
744C22×C4—26no—
745C22×C4—212no—
746C22×C4—26no—
747C22×C4—26no—
748C22×C4—26no—
749C22×C4—46no—
750C22×C4—46no—
751C22×C4—46no—
752C22×C4—43no—
753C22×C4—496no—
754C22×C4—43no—
755C22×C4—43no—
756C22×C4C22×D4124yes—
757C22×C4C2×#41112yes—
758C22×C42−1+414yes—
759C22×C4C2511yescharacteristic
760C22×C4C2513yes—
761C22×C4C2513yes—
762C22×C4C2513yes—
763C22×C4C2512yes—
764C22×C4C2512yes—
765C22×C4C2516yes—
766C22×C4C2516yes—
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C22×C4C2516yes—
770C22×C4C2513yes—
771C22×C4C2511yescharacteristic
772C22×C4C2513yes—
773C22×C4C2516yes—
774C22×C4C2513yes—
775C22×C4C2511yescharacteristic
776C22×C4C2513yes—
777C22×C4C2511yescharacteristic
778C4⋊C4—212no—
779C4⋊C4—26no—
780C4⋊C4—212no—
781C4⋊C4—26no—
782C4⋊C4—224no—
783C4⋊C4—212no—
784C4⋊C4—26no—
785C4⋊C4—26no—
786C4⋊C4—212no—
787C4⋊C4—212no—
788C4⋊C4—212no—
789C4⋊C4—212no—
790C4⋊C4—212no—
791C4⋊C4—26no—
792C4⋊C4—26no—
793C4⋊C4—26no—
794C4⋊C4—212no—
795C4⋊C4—26no—
796C4⋊C4—26no—
797C4⋊C4—22no—
798C4⋊C4—24no—
799C4⋊C4—46no—
800C4⋊C4—46no—
801C4⋊C4—46no—
802C4⋊C4—43no—
803C4⋊C4—46no—
804C4⋊C4—46no—
805C4⋊C4—412no—
806C4⋊C4C22×D4112yes—
807C4⋊C4C22×D4112yes—
808C4⋊C4C22×D4124yes—
809C22⋊C4—212no—
810C22⋊C4—212no—
811C22⋊C4—24no—
812C22⋊C4—24no—
813C22⋊C4—22no—
814C22⋊C4—26no—
815C22⋊C4—212no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—22no—
820C22⋊C4—212no—
821C22⋊C4—212no—
822C22⋊C4—212no—
823C22⋊C4—212no—
824C22⋊C4—224no—
825C22⋊C4—212no—
826C22⋊C4—26no—
827C22⋊C4—212no—
828C22⋊C4—26no—
829C22⋊C4—42no—
830C22⋊C4—46no—
831C22⋊C4—46no—
832C22⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4—46no—
835C22⋊C4—43no—
836C22⋊C4—42no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—412no—
841C22⋊C4C22×D4124yes—
842C42—22no—
843C42—26no—
844C42—26no—
845C42—26no—
846C42—26no—
847C42—26no—
848C42—224no—
849C42—212no—
850C42—26no—
851C42—26no—
852C42—212no—
853C42—26no—
854C42—22no—
855C42—43no—
856C42—412no—
857C42—43no—
858C42C22×D4112yes—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—216no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—23no—
877C23—23no—
878C23—23no—
879C23—23no—
880C23—23no—
881C23—23no—
882C23—23no—
883C23—48no—
884C23—48no—
885C23—48no—
886C23—48no—
887C23—48no—
888C23—48no—
889C23C23×D414yes—
890C23C22×#4112yes—
891C23C2×2−1+414yes—
892C23C2×2−1+412yes—
893C23#58512yes—
894C23C2611yescharacteristic
895Q8—224no—
896Q8—248no—
897Q8—448no—
898Q8—424no—
899Q8—44no—
900Q8—812no—
901Q8#546116yes—
902D4—216no—
903D4—28no—
904D4—28no—
905D4—412no—
906D4—412no—
907D4—812no—
908D4—812no—
909C2×C4—21no—
910C2×C4—23no—
911C2×C4—26no—
912C2×C4—26no—
913C2×C4—23no—
914C2×C4—21no—
915C2×C4—23no—
916C2×C4—23no—
917C2×C4—224no—
918C2×C4—248no—
919C2×C4—28no—
920C2×C4—23no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—26no—
925C2×C4—23no—
926C2×C4—26no—
927C2×C4—21no—
928C2×C4—23no—
929C2×C4—21no—
930C2×C4—26no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—23no—
934C2×C4—26no—
935C2×C4—26no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—23no—
940C2×C4—23no—
941C2×C4—23no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—23no—
945C2×C4—26no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—23no—
949C2×C4—26no—
950C2×C4—26no—
951C2×C4—21no—
952C2×C4—23no—
953C2×C4—21no—
954C2×C4—23no—
955C2×C4—22no—
956C2×C4—23no—
957C2×C4—21no—
958C2×C4—26no—
959C2×C4—424no—
960C2×C4—412no—
961C2×C4—424no—
962C2×C4—424no—
963C2×C4—424no—
964C2×C4—412no—
965C2×C4—412no—
966C2×C4—86no—
967C2×C4C23×D416yes—
968C2×C4C23×D4112yes—
969C2×C4C23×D416yes—
970C2×C4C23×D412yes—
971C2×C4C22×#4116yes—
972C2×C4C22×#4116yes—
973C2×C4C2×H(5,𝔽2)16yes—
974C2×C4C2×2−1+412yes—
975C2×C4C2×2−1+412yes—
976C2×C4C2×2−1+412yes—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22—432no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—43no—
999C22—43no—
1000C22—43no—
1001C22—43no—
1002C22—43no—
1003C22—43no—
1004C22—43no—
1005C22#351814yescomplemented
1006C22C24×D411yescharacteristic
1007C22C23×#4111yescharacteristic
1008C22C22×H(5,𝔽2)11yescharacteristic
1009C22C22×2−1+411yescharacteristic
1010C22C22×2−1+411yescharacteristic
1011C22C2×#58511yescharacteristic
1012C222−1+611yescharacteristic
1013C4—26no—
1014C4—22no—
1015C4—26no—
1016C4—212no—
1017C4—41no—
1018C4—43no—
1019C4—41no—
1020C4—46no—
1021C4—41no—
1022C4—46no—
1023C4—43no—
1024C4—42no—
1025C4—43no—
1026C4—42no—
1027C4—43no—
1028C4—41no—
1029C4—46no—
1030C4C2×#546112yes—
1031C4#348614yes—
1032C2—24no—
1033C2—44no—
1034C2—44no—
1035C2—83no—
1036C2C22×#54611yescharacteristic
1037C2C2×#348611yescharacteristic
1038C2C2×#351811yescharacteristic
1039C2#6291311yescharacteristic
1040C2#6299811yescharacteristic
1041C2#6300211yescharacteristic
1042C2#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×#3518C2semidirect
2. C22×D4×Q8C2semidirect
3. #59421C2semidirect
4. #59134C2semidirect
5. #59036C2semidirect
6. #59025C2semidirect
7. #45291C2semidirect
8. #45289C2semidirect
9. #38958C2semidirect
10. #38911C2semidirect
11. #37665C2semidirect
12. #36575C2semidirect
13. Q8×#124C2semidirect
14. Q8×C22⋊Q8C2semidirect
15. #36444C2semidirect
16. #36160C2semidirect
17. #36129C2semidirect
18. #35771C2semidirect
19. #35723C2semidirect
20. #34700C2semidirect
21. #34311C2semidirect
22. #34173C2semidirect
23. C4×#548C2semidirect
26. C2×Q82C22semidirect
27. C2×#556C22semidirect
28. C2×#556C22semidirect
38. C2×#548C22semidirect
39. C2×#548C22semidirect
40. C2×#542C22semidirect
41. C2×#533C22semidirect
45. C2×#519C22semidirect
46. C2×#519C22semidirect
47. C2×C4×#41C22semidirect
50. #2862C22semidirect
52. #2857C22semidirect
54. #2716C22semidirect
55. #2702C22semidirect
56. #2700C22semidirect
57. #2700C22semidirect
58. #2692C22semidirect
59. #2689C22semidirect
60. #2687C22semidirect
61. #2625C22semidirect
62. #2620C22semidirect
63. #2582C22semidirect
64. #2568C22semidirect
65. #2567C22semidirect
67. #2560C22semidirect
68. #2550C22semidirect
69. #2547C22semidirect
70. #2545C22semidirect
71. #2538C22semidirect
73. #2499C22semidirect
74. #2492C22semidirect
75. #2492C22semidirect
76. #2492C22semidirect
77. #2492C22semidirect
83. #2465C22semidirect
87. #2451C22semidirect
88. #2451C22semidirect
90. #2446C22semidirect
91. #2446C22semidirect
94. #2439C22semidirect
95. #2439C22semidirect
97. #2436C22semidirect
98. #2436C22semidirect
100. #2429C22semidirect
102. #2427C22semidirect
103. #2426C22semidirect
104. #2423C22semidirect
105. #2421C22semidirect
111. #2415C22semidirect
112. #2415C22semidirect
115. #2409C22semidirect
116. #2409C22semidirect
120. #2367C22semidirect
121. #2365C22semidirect
123. #2362C22semidirect
124. #2362C22semidirect
130. #2351C22semidirect
131. Q8×C4⋊C4C22semidirect
132. Q8×C4⋊C4C22semidirect
133. #2341C22semidirect
138. Q8×C22⋊C4C22semidirect
139. Q8×C22⋊C4C22semidirect
140. Q8×C22⋊C4C22semidirect
141. Q8×C22⋊C4C22semidirect
142. Q8×C22⋊C4C22semidirect
143. Q8×C22⋊C4C22semidirect
144. #2323C22semidirect
145. #2310C22semidirect
146. #2310C22semidirect
147. C4×C4⋊Q8C22semidirect
149. C4×#124C22semidirect
151. C4×C22⋊Q8C22semidirect
158. C42×Q8C22semidirect
181. D4×Q8D4semidirect
1005. C22#3518semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C22×D4×Q82
#594212
#591342
#590362
#590252
#452912
#452892
#389582
#389112
#376652
#365752
Q8×#1242
Q8×C22⋊Q82
#364442
#361602
#361292
#357712
#357232
#347002
#343112
#341732
C4×#5482