Finite Group Databasebeta

← #7699556

Subgroups — #7699556

Order 512.

8689 conjugacy classes of subgroups.

The subgroup lattice has 1069 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#59812C216yesmaximal, complemented
4#59420C213yesmaximal, complemented
5#59103C216yesmaximal, complemented
6#59064C213yesmaximal, complemented
7#59035C213yesmaximal, complemented
8#59020C216yesmaximal, complemented
9Q8×#121C211yesmaximal, characteristic, complemented
10#36446C211yesmaximal, characteristic, complemented
11#36445C211yesmaximal, characteristic, complemented
12#36444C212yesmaximal, complemented
13#36432C212yesmaximal, complemented
14#36428C212yesmaximal, complemented
15#36406C213yesmaximal, complemented
16#36404C213yesmaximal, complemented
17#36161C213yesmaximal, complemented
18#36149C213yesmaximal, complemented
19#36143C216yesmaximal, complemented
20C4×#550C211yesmaximal, characteristic, complemented
21C4×#548C211yesmaximal, characteristic, complemented
22C4×#546C213yesmaximal, complemented
23C22⋊C4×#41C212yesmaximal, complemented
24C23×#41C2212yes—
25#3480—216no—
26C2×#559C2213yescomplemented
27C2×#557C2211yescharacteristic, complemented
28C2×#556C2213yescomplemented
29C2×#553C2216yescomplemented
30D4×#41—216no—
31C2×#550C2211yescharacteristic
32C2×D4×Q8C2211yescharacteristic
33C2×D4×Q8C2212yescomplemented
34C2×#548C2211yescharacteristic
35C2×#548C2212yes—
36C2×#548C2212yescomplemented
37C2×#547C2213yes—
38C2×#546C2213yes—
39C2×#546C2216yes—
40C2×D42C2213yes—
41C2×#532C2213yes—
42C2×#532C2213yescomplemented
43C2×#529C2216yescomplemented
44C2×#525C2216yes—
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2213yescomplemented
47C2×C4×#41C2212yescomplemented
48C2×C4×#41C2212yescomplemented
49C22×C4×Q8C2211yescharacteristic, complemented
50C22×C4×D4C2213yes—
51#2862C2213yescomplemented
52#2857C2216yescomplemented
53#2857C2213yescomplemented
54#2857C2213yescomplemented
55#2855C2216yescomplemented
56#2848C2216yescomplemented
57#2708C22112yescomplemented
58#2697C22112yescomplemented
59#2668C22112yescomplemented
60#2568C2213yescomplemented
61#2553C22112yescomplemented
62#2553C22112yescomplemented
63#2547C2213yes—
64#2547C2216yescomplemented
65#2546C2213yescomplemented
66#2542C2213yescomplemented
67#2538C2213yes—
68#2538C2213yescomplemented
69#2537C2216yescomplemented
70#2535C2216yescomplemented
71#2534C22112yescomplemented
72#2499C2216yescomplemented
73#2489C2216yescomplemented
74#2489C2216yescomplemented
75#2485C2216yescomplemented
76#2480C22112yescomplemented
77#2470C22112yescomplemented
78#2466C22112yescomplemented
79#2457C22112yescomplemented
80#2454C2216yescomplemented
81#2447C2216yescomplemented
82#2447C2216yescomplemented
83#2447C2216yescomplemented
84#2441C2216yescomplemented
85#2435C2216yes—
86#2435C2216yescomplemented
87#2432C2216yescomplemented
88#2432C2216yescomplemented
89#2429C2216yescomplemented
90#2427C2216yescomplemented
91#2427C2216yescomplemented
92#2427C2216yescomplemented
93#2427C2216yescomplemented
94#2422C2216yescomplemented
95#2420C2216yescomplemented
96#2420C2216yescomplemented
97#2420C2216yescomplemented
98#2420C2216yescomplemented
99#2419C22112yescomplemented
100#2418C22112yescomplemented
101#2417C2216yescomplemented
102#2415C2216yescomplemented
103#2415C2216yescomplemented
104#2408C2216yescomplemented
105#2407C2216yescomplemented
106#2407C2216yescomplemented
107#2407C2216yescomplemented
108#2367C2213yes—
109#2367C2213yescomplemented
110#2366C2213yescomplemented
111#2364C2216yescomplemented
112#2363C2211yescharacteristic
113#2363C2216yescomplemented
114#2362C2213yescomplemented
115#2361C2213yescomplemented
116#2360C2216yescomplemented
117#2360C2213yescomplemented
118#2359C2216yescomplemented
119#2358C2216yescomplemented
120#2354C2213yescomplemented
121#2352C2213yescomplemented
122#2352C2213yescomplemented
123#2351C2211yescharacteristic, complemented
124Q8×C4⋊C4C2212yescomplemented
125Q8×C4⋊C4C2211yescharacteristic, complemented
126#2349C2216yescomplemented
127#2349C2213yescomplemented
128#2342C2216yescomplemented
129#2341C2211yescharacteristic
130#2341C2212yes—
131#2341C2212yescomplemented
132Q8×C22⋊C4C2212yescomplemented
133Q8×C22⋊C4C2212yescomplemented
134Q8×C22⋊C4C2212yescomplemented
135Q8×C22⋊C4C2211yescharacteristic, complemented
136#2339C2216yescomplemented
137#2339C2213yescomplemented
138#2339C2216yescomplemented
139D4×C22⋊C4C2213yes—
140D4×C22⋊C4C2216yescomplemented
141D4×C22⋊C4C2216yescomplemented
142C4×#127C2213yescomplemented
143C4×#124C2213yes—
144C4×#124C2213yescomplemented
145C4×C22⋊Q8C2213yescomplemented
146C4×C22⋊Q8C2213yescomplemented
147C4×#123C2216yescomplemented
148C4×#121C2213yes—
149C4×#121C2216yescomplemented
150C4×#121C2213yescomplemented
151C4×#121C2216yescomplemented
152C4×#120C2216yescomplemented
153#2297C2216yescomplemented
154#2297C2216yescomplemented
155#2280C2216yescomplemented
156C42×Q8C2211yescharacteristic, complemented
157C42×D4C2213yescomplemented
158C42×D4C2213yescomplemented
159C2×C4×C22⋊C4C2216yescomplemented
160C22×#41—216no—
161C22×#41—216no—
162C22×#41—48no—
163C22×#41C2316yes—
164C22×#41C2316yes—
165C22×#41C2313yes—
166C22×#41C2312yes—
167C22×#41C2311yescharacteristic
168C23×Q8C2312yes—
169C23×Q8C2311yescharacteristic
170C23×D4C2316yes—
171C23×D4C2313yes—
172C24×C4C2316yes—
173#559—224no—
174#557—28no—
175#556—224no—
176#553—248no—
177#550D4116yescomplemented
178D4×Q8—28no—
179D4×Q8—48no—
180#548—216no—
181#548—216no—
182#548—28no—
183#547—224no—
184#546—248no—
185#546—224no—
186D42—224no—
187#532—224no—
188#532—224no—
189C2×C4⋊Q8C2313yes—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2316yes—
192C2×#127C2313yes—
193#529—248no—
194C2×#126C23112yes—
195C2×#125C2316yes—
196C2×#124C2313yes—
197C2×#124C2313yes—
198C2×#124C2316yes—
199C2×#124C2316yes—
200C2×#124C2316yes—
201#525—248no—
202C2×#123C2316yes—
203C2×#123C23112yes—
204C2×#123C23112yes—
205C2×C22⋊Q8C2313yes—
206C2×C22⋊Q8C2316yes—
207C2×C22⋊Q8C2316yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2316yes—
213C2×#121C2313yes—
214C2×#121C2316yes—
215C2×#121C2316yes—
216C2×#121C2316yes—
217C2×#121C2316yes—
218C2×#121C2316yes—
219C2×#121C2316yes—
220C2×#121C2316yes—
221C2×#121C2311yescharacteristic
222C2×#120C2316yes—
223C2×#120C23112yes—
224C4×#41—216no—
225C4×#41—28no—
226C4×#41—224no—
227C4×#41—48no—
228C2×C4×Q8—28no—
229C2×C4×Q8C2313yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2313yes—
237C2×C4×Q8C2313yes—
238C2×C4×Q8C2313yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—224no—
241C2×C4×D4C2313yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2313yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2316yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2316yes—
262C2×C4×D4C2313yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2313yes—
265C2×#117C2316yes—
266C2×#117C2311yescharacteristic
267C2×#117C2313yes—
268C2×#117C2316yes—
269C2×#117C2316yes—
270C22×C4⋊C4C2313yes—
271C22×C4⋊C4C2313yes—
272C22×C22⋊C4C2316yes—
273C22×C22⋊C4C2316yes—
274C22×C22⋊C4C2316yes—
275C22×C42C2316yes—
276C22×C42C2313yes—
277C22×C42C2313yes—
278C22×C42C2316yes—
279#400C23112yes—
280#399C23112yes—
281#398C23112yes—
282#397C23112yes—
283#397C23112yes—
284#397C23112yes—
285#397C23112yes—
286#397C23112yes—
287#397C23112yes—
288#396C23112yes—
289#396C23112yes—
290#394C23112yes—
291#394C23112yes—
292#394C23112yes—
293#394C23112yes—
294#394C23112yes—
295#394C23112yes—
296#392C23112yes—
297#391C2316yes—
298#391C2316yes—
299#391C2316yes—
300#391C2316yes—
301#391C2316yes—
302#391C2316yes—
303#391C2313yes—
304#391C2313yes—
305#391C2313yes—
306#391C2316yes—
307#391C2313yes—
308#390C2316yes—
309#390C2316yes—
310#390C2316yes—
311#390C2311yescharacteristic
312#390C2313yes—
313#390C2313yes—
314#390C2313yes—
315#390C2316yes—
316#390C2316yes—
317#390C2316yes—
318#390C2312yes—
319#389C2313yes—
320#389C2316yes—
321#389C2316yes—
322#389C2316yes—
323#389C2316yes—
324#389C2316yes—
325#389C23112yes—
326#389C2316yes—
327#389C2311yescharacteristic
328#389C2313yes—
329#389C2316yes—
330#389C2313yes—
331#388C2312yes—
332#388C2316yes—
333#388C2316yes—
334#388C2316yes—
335#388C2316yes—
336#388C2316yes—
337#388C23112yes—
338#388C2316yes—
339#388C2316yes—
340#388C2316yes—
341#388C2316yes—
342#387C2316yes—
343#387C23112yes—
344#387C2316yes—
345#387C2316yes—
346#387C2316yes—
347#386C2316yes—
348#386C2316yes—
349#386C23112yes—
350#386C23112yes—
351#386C23112yes—
352#386C23112yes—
353#386C2316yes—
354#386C2316yes—
355#386C2316yes—
356#386C2316yes—
357#386C2316yes—
358#386C2312yes—
359#386C23112yes—
360#385C2316yes—
361#385C23112yes—
362#385C23112yes—
363#385C2316yes—
364#385C2316yes—
365#385C23112yes—
366#385C2316yes—
367#385C2316yes—
368#385C2316yes—
369#384C2313yes—
370#384C2316yes—
371#382C2313yes—
372#382C2316yes—
373#382C2316yes—
374#382C2313yes—
375#381C23112yes—
376#381C2316yes—
377#381C23112yes—
378#380C2316yes—
379#380C2316yes—
380#380C2316yes—
381#380C2313yes—
382#380C2316yes—
383#380C2316yes—
384#380C2313yes—
385#380C2313yes—
386#380C2313yes—
387#380C2316yes—
388#380C23112yes—
389#380C2316yes—
390#380C23112yes—
391#380C2316yes—
392#379C23112yes—
393#379C2316yes—
394#379C23112yes—
395C4×C4⋊C4C2313yes—
396C4×C4⋊C4C2313yes—
397C4×C4⋊C4C2313yes—
398C4×C4⋊C4C2313yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2313yes—
401C4×C4⋊C4C2313yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2313yes—
405C4×C22⋊C4C2313yes—
406C4×C22⋊C4C2316yes—
407C4×C22⋊C4C2316yes—
408C4×C22⋊C4C2311yescharacteristic
409C4×C22⋊C4C2313yes—
410C4×C22⋊C4C2316yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2313yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C23112yes—
423C4×C22⋊C4C2316yes—
424C2×#95C2316yes—
425C2×#95C2316yes—
426C43C2313yes—
427C25C2416yes—
428C2×#41—24no—
429C2×#41—28no—
430C2×#41—28no—
431C2×#41—24no—
432C2×#41—212no—
433C2×#41—224no—
434C2×#41—224no—
435C2×#41—224no—
436C2×#41—224no—
437C2×#41—212no—
438C2×#41—412no—
439C2×#41—412no—
440C2×#41—46no—
441C2×#41—4128no—
442C2×#41C2×D4116yes—
443C2×#41#4118yescomplemented
444C22×Q8—24no—
445C22×Q8—28no—
446C22×Q8—24no—
447C22×Q8—28no—
448C22×Q8—24no—
449C22×Q8—28no—
450C22×Q8C2413yes—
451C22×Q8C2413yes—
452C22×Q8C2416yes—
453C22×Q8C2411yescharacteristic
454C22×D4—212no—
455C22×D4—224no—
456C22×D4—212no—
457C22×D4—224no—
458C22×D4—46no—
459C22×D4—412no—
460C22×D4C2413yes—
461C22×D4C2416yes—
462C22×D4C2416yes—
463C22×D4C24112yes—
464C22×D4C2413yes—
465C22×D4C2416yes—
466C22×D4C2411yescharacteristic
467C22×D4C2413yes—
468C22×D4C2416yes—
469C22×D4C2412yes—
470C23×C4—224no—
471C23×C4—224no—
472C23×C4—412no—
473C23×C4C2413yes—
474C23×C4C2413yes—
475C23×C4C2416yes—
476C23×C4C2416yes—
477C23×C4C2416yes—
478C23×C4C2412yes—
479C23×C4C2416yes—
480C23×C4C2416yes—
481C23×C4C2413yes—
482C23×C4C2411yescharacteristic
483C23×C4C2413yes—
484C23×C4C2416yes—
485C23×C4C2416yes—
486C23×C4C2416yes—
487C23×C4C2413yes—
488C4⋊Q8—212no—
489C4⋊Q8—212no—
490C4⋊Q8—412no—
491#127C2×D4124yes—
492#126—248no—
493#125—224no—
494#124—224no—
495#124—224no—
496#124—224no—
497#124—212no—
498#124—212no—
499#123—248no—
500#123—248no—
501#123—224no—
502C22⋊Q8—224no—
503C22⋊Q8—224no—
504C22⋊Q8—212no—
505C22⋊Q8—224no—
506C22⋊Q8—212no—
507C22⋊Q8—412no—
508C22⋊Q8—412no—
509C22⋊Q8—412no—
510#121—224no—
511#121—224no—
512#121—224no—
513#121—224no—
514#121—224no—
515#121—212no—
516#121—224no—
517#121C2×D4148yes—
518#121#4118yescomplemented
519#120—248no—
520#120—224no—
521C4×Q8—24no—
522C4×Q8—24no—
523C4×Q8—28no—
524C4×Q8—24no—
525C4×Q8—24no—
526C4×Q8—28no—
527C4×Q8—212no—
528C4×Q8—212no—
529C4×Q8—212no—
530C4×Q8—212no—
531C4×Q8C2×D418yes—
532C4×D4—212no—
533C4×D4—224no—
534C4×D4—224no—
535C4×D4—212no—
536C4×D4—224no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—224no—
540C4×D4—212no—
541C4×D4—212no—
542C4×D4—24no—
543C4×D4—212no—
544C4×D4—212no—
545C4×D4—224no—
546C4×D4—224no—
547C4×D4—212no—
548C4×D4—212no—
549C4×D4—46no—
550C4×D4—46no—
551C4×D4—412no—
552C4×D4—412no—
553C4×D4—412no—
554C4×D4—412no—
555C4×D4C2×D4124yes—
556#117—224no—
557#117—24no—
558#117—212no—
559#117—224no—
560#117—412no—
561C2×C4⋊C4—212no—
562C2×C4⋊C4—212no—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2413yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2413yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C24112yes—
585C2×C4⋊C4C24112yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—412no—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2413yes—
596C2×C22⋊C4C2413yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C24112yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2411yescharacteristic
606C2×C22⋊C4C2411yescharacteristic
607C2×C22⋊C4C24112yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C24112yes—
611C2×C22⋊C4C2413yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C24112yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C24112yes—
621C2×C22⋊C4C24112yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2412yes—
626C2×C42—224no—
627C2×C42—212no—
628C2×C42—212no—
629C2×C42—412no—
630C2×C42C2412yes—
631C2×C42C2413yes—
632C2×C42C2413yes—
633C2×C42C2416yes—
634C2×C42C2411yescharacteristic
635C2×C42C2413yes—
636C2×C42C2411yescharacteristic
637C2×C42C2413yes—
638C2×C42C2416yes—
639C2×C42C2413yes—
640C2×C42C2416yes—
641C2×C42C2413yes—
642C2×C42C2413yes—
643C2×C42C2413yes—
644C2×C42C2413yes—
645C2×C42C2416yes—
646C2×C42C2413yes—
647C2×C42C2412yes—
648C2×C42C2413yes—
649#95C2411yescharacteristic
650#95C2412yes—
651#95C2413yes—
652#95C2416yes—
653#95C2416yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2412yes—
658#95C2411yescharacteristic
659#95C2413yes—
660#95C2416yes—
661#95C2413yes—
662#95C2413yes—
663#95C2416yes—
664#95C2416yes—
665#95C24112yes—
666#95C24112yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C24112yes—
674C24—212no—
675C24—212no—
676C24—212no—
677C24—46no—
678C24—46no—
679C24—46no—
680C24—46no—
681C24C2516yes—
682C24C2512yes—
683C24C2513yes—
684C24C2511yescharacteristic
685#41—232no—
686#41—264no—
687#41—448no—
688#41—496no—
689#41—496no—
690C2×Q8—26no—
691C2×Q8—26no—
692C2×Q8—212no—
693C2×Q8—26no—
694C2×Q8—26no—
695C2×Q8—212no—
696C2×Q8—26no—
697C2×Q8—212no—
698C2×Q8—26no—
699C2×Q8—416no—
700C2×Q8—432no—
701C2×Q8C22×D414yes—
702C2×Q8C2×#4114yes—
703C2×Q8H(5,𝔽2)14yes—
704C2×D4—212no—
705C2×D4—212no—
706C2×D4—224no—
707C2×D4—26no—
708C2×D4—26no—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—224no—
712C2×D4—22no—
713C2×D4—26no—
714C2×D4—26no—
715C2×D4—212no—
716C2×D4—212no—
717C2×D4—26no—
718C2×D4—26no—
719C2×D4—22no—
720C2×D4—42no—
721C2×D4—46no—
722C2×D4—43no—
723C2×D4—46no—
724C2×D4—412no—
725C2×D4—46no—
726C2×D4—42no—
727C2×D4—46no—
728C2×D4—448no—
729C2×D4—496no—
730C2×D4C22×D4112yes—
731C2×D4C22×D4124yes—
732C2×D4C22×D4124yes—
733C2×D4C2×#41112yes—
734C2×D4C2×#4114yes—
735C2×D4C2×#4118yescomplemented
736C22×C4—22no—
737C22×C4—26no—
738C22×C4—212no—
739C22×C4—212no—
740C22×C4—26no—
741C22×C4—22no—
742C22×C4—212no—
743C22×C4—212no—
744C22×C4—212no—
745C22×C4—212no—
746C22×C4—26no—
747C22×C4—26no—
748C22×C4—212no—
749C22×C4—24no—
750C22×C4—212no—
751C22×C4—212no—
752C22×C4—26no—
753C22×C4—26no—
754C22×C4—24no—
755C22×C4—212no—
756C22×C4—212no—
757C22×C4—26no—
758C22×C4—212no—
759C22×C4—26no—
760C22×C4—26no—
761C22×C4—26no—
762C22×C4—212no—
763C22×C4—212no—
764C22×C4—42no—
765C22×C4—46no—
766C22×C4—46no—
767C22×C4—46no—
768C22×C4—496no—
769C22×C4—46no—
770C22×C4—46no—
771C22×C4—46no—
772C22×C4—43no—
773C22×C4—43no—
774C22×C4—46no—
775C22×C4—43no—
776C22×C4—43no—
777C22×C4—46no—
778C22×C4—46no—
779C22×C4C22×D4124yes—
780C22×C4C2×#41112yes—
781C22×C4C2×#4114yescomplemented
782C22×C4C2511yescharacteristic
783C22×C4C2513yes—
784C22×C4C2513yes—
785C22×C4C2516yes—
786C22×C4C2511yescharacteristic
787C22×C4C2512yes—
788C22×C4C2513yes—
789C22×C4C2516yes—
790C22×C4C2516yes—
791C22×C4C2513yes—
792C22×C4C2513yes—
793C22×C4C2512yes—
794C22×C4C2513yes—
795C22×C4C2511yescharacteristic
796C22×C4C2511yescharacteristic
797C22×C4C2512yes—
798C22×C4C2511yescharacteristic
799C22×C4C2513yes—
800C22×C4C2511yescharacteristic
801C4⋊C4—26no—
802C4⋊C4—26no—
803C4⋊C4—212no—
804C4⋊C4—212no—
805C4⋊C4—22no—
806C4⋊C4—26no—
807C4⋊C4—212no—
808C4⋊C4—212no—
809C4⋊C4—212no—
810C4⋊C4—212no—
811C4⋊C4—212no—
812C4⋊C4—26no—
813C4⋊C4—26no—
814C4⋊C4—26no—
815C4⋊C4—212no—
816C4⋊C4—26no—
817C4⋊C4—212no—
818C4⋊C4—26no—
819C4⋊C4—42no—
820C4⋊C4—46no—
821C4⋊C4—43no—
822C4⋊C4—46no—
823C4⋊C4—412no—
824C4⋊C4—412no—
825C4⋊C4C22×D414yes—
826C4⋊C4C22×D4112yes—
827C4⋊C4C2×#4114yescomplemented
828C22⋊C4—212no—
829C22⋊C4—224no—
830C22⋊C4—212no—
831C22⋊C4—224no—
832C22⋊C4—224no—
833C22⋊C4—212no—
834C22⋊C4—26no—
835C22⋊C4—26no—
836C22⋊C4—212no—
837C22⋊C4—212no—
838C22⋊C4—24no—
839C22⋊C4—212no—
840C22⋊C4—24no—
841C22⋊C4—212no—
842C22⋊C4—26no—
843C22⋊C4—212no—
844C22⋊C4—22no—
845C22⋊C4—212no—
846C22⋊C4—24no—
847C22⋊C4—26no—
848C22⋊C4—22no—
849C22⋊C4—46no—
850C22⋊C4—46no—
851C22⋊C4—42no—
852C22⋊C4—46no—
853C22⋊C4—412no—
854C22⋊C4—46no—
855C22⋊C4—412no—
856C22⋊C4—46no—
857C22⋊C4—46no—
858C22⋊C4—412no—
859C22⋊C4C22×D4124yes—
860C22⋊C4C2×#4118yescomplemented
861C42—24no—
862C42—22no—
863C42—26no—
864C42—26no—
865C42—26no—
866C42—212no—
867C42—26no—
868C42—212no—
869C42—26no—
870C42—26no—
871C42—26no—
872C42—26no—
873C42—212no—
874C42—26no—
875C42—22no—
876C42—42no—
877C42—46no—
878C42—43no—
879C42C22×D4112yes—
880C23—22no—
881C23—21no—
882C23—23no—
883C23—23no—
884C23—21no—
885C23—26no—
886C23—22no—
887C23—26no—
888C23—21no—
889C23—22no—
890C23—26no—
891C23—23no—
892C23—22no—
893C23—23no—
894C23—21no—
895C23—23no—
896C23—26no—
897C23—26no—
898C23—21no—
899C23—22no—
900C23—23no—
901C23—22no—
902C23—21no—
903C23—26no—
904C23—424no—
905C23—424no—
906C23—424no—
907C23—812no—
908C23—812no—
909C23—812no—
910C23—812no—
911C23C23×D4112yes—
912C23C22×#4114yes—
913C23C22×#4116yes—
914C23C22×#4112yes—
915C23C2611yescharacteristic
916Q8—412no—
917Q8—424no—
918Q8—412no—
919Q8#546116yescomplemented
920D4—224no—
921D4—248no—
922D4—28no—
923D4—224no—
924D4—424no—
925D4—48no—
926D4—412no—
927D4—424no—
928D4—448no—
929D4—424no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—23no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—23no—
941C2×C4—22no—
942C2×C4—224no—
943C2×C4—248no—
944C2×C4—28no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—23no—
948C2×C4—23no—
949C2×C4—23no—
950C2×C4—26no—
951C2×C4—26no—
952C2×C4—21no—
953C2×C4—23no—
954C2×C4—23no—
955C2×C4—23no—
956C2×C4—26no—
957C2×C4—23no—
958C2×C4—23no—
959C2×C4—26no—
960C2×C4—23no—
961C2×C4—26no—
962C2×C4—23no—
963C2×C4—26no—
964C2×C4—21no—
965C2×C4—23no—
966C2×C4—22no—
967C2×C4—23no—
968C2×C4—21no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—26no—
972C2×C4—23no—
973C2×C4—21no—
974C2×C4—23no—
975C2×C4—23no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—48no—
979C2×C4—424no—
980C2×C4—424no—
981C2×C4—424no—
982C2×C4—424no—
983C2×C4—412no—
984C2×C4—412no—
985C2×C4—812no—
986C2×C4—86no—
987C2×C4—86no—
988C2×C4—812no—
989C2×C4—812no—
990C2×C4C23×D414yes—
991C2×C4C23×D416yes—
992C2×C4C23×D416yes—
993C2×C4C23×D412yes—
994C2×C4C22×#4114yes—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4116yes—
998C2×C4C22×#4112yes—
999C2×C4C2×H(5,𝔽2)16yes—
1000C2×C4#58512yes—
1001C2×C4#58512yes—
1002C22—22no—
1003C22—24no—
1004C22—212no—
1005C22—26no—
1006C22—26no—
1007C22—212no—
1008C22—22no—
1009C22—212no—
1010C22—24no—
1011C22—22no—
1012C22—26no—
1013C22—24no—
1014C22—46no—
1015C22—43no—
1016C22—41no—
1017C22—43no—
1018C22—42no—
1019C22—41no—
1020C22—46no—
1021C22—42no—
1022C22—46no—
1023C22—41no—
1024C22—43no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—43no—
1029C22—46no—
1030C22—848no—
1031C22C24×D411yescharacteristic
1032C22C23×#4111yescharacteristic
1033C22C23×#4111yescharacteristic
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C2×#58511yescharacteristic
1036C22C2×#58511yescharacteristic
1037C222−1+611yescharacteristic
1038C4—24no—
1039C4—26no—
1040C4—22no—
1041C4—22no—
1042C4—24no—
1043C4—22no—
1044C4—43no—
1045C4—41no—
1046C4—42no—
1047C4—43no—
1048C4—41no—
1049C4—46no—
1050C4—46no—
1051C4—43no—
1052C4—43no—
1053C4—46no—
1054C4—43no—
1055C4C2×#546112yes—
1056C4D4×#4114yes—
1057C2—42no—
1058C2—412no—
1059C2—46no—
1060C2—44no—
1061C2C22×#54611yescharacteristic
1062C2C2×D4×#4111yescharacteristic
1063C2#41211yescharacteristic
1064C2#6298411yescharacteristic
1065C2#6298811yescharacteristic
1066C2#6300911yescharacteristic
1067C2#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×#3480C2semidirect
2. C2×D4×#41C2semidirect
3. #59812C2semidirect
4. #59420C2semidirect
5. #59103C2semidirect
6. #59064C2semidirect
7. #59035C2semidirect
8. #59020C2semidirect
9. Q8×#121C2semidirect
10. #36446C2semidirect
11. #36445C2semidirect
12. #36444C2semidirect
13. #36432C2semidirect
14. #36428C2semidirect
15. #36406C2semidirect
16. #36404C2semidirect
17. #36161C2semidirect
18. #36149C2semidirect
19. #36143C2semidirect
20. C4×#550C2semidirect
21. C4×#548C2semidirect
22. C4×#546C2semidirect
23. C22⋊C4×#41C2semidirect
26. C2×#559C22semidirect
27. C2×#557C22semidirect
28. C2×#556C22semidirect
29. C2×#553C22semidirect
33. C2×D4×Q8C22semidirect
36. C2×#548C22semidirect
42. C2×#532C22semidirect
43. C2×#529C22semidirect
46. C2×C4×#41C22semidirect
47. C2×C4×#41C22semidirect
48. C2×C4×#41C22semidirect
49. C22×C4×Q8C22semidirect
51. #2862C22semidirect
52. #2857C22semidirect
53. #2857C22semidirect
54. #2857C22semidirect
55. #2855C22semidirect
56. #2848C22semidirect
57. #2708C22semidirect
58. #2697C22semidirect
59. #2668C22semidirect
60. #2568C22semidirect
61. #2553C22semidirect
62. #2553C22semidirect
64. #2547C22semidirect
65. #2546C22semidirect
66. #2542C22semidirect
68. #2538C22semidirect
69. #2537C22semidirect
70. #2535C22semidirect
71. #2534C22semidirect
72. #2499C22semidirect
73. #2489C22semidirect
74. #2489C22semidirect
75. #2485C22semidirect
76. #2480C22semidirect
77. #2470C22semidirect
78. #2466C22semidirect
79. #2457C22semidirect
80. #2454C22semidirect
81. #2447C22semidirect
82. #2447C22semidirect
83. #2447C22semidirect
84. #2441C22semidirect
86. #2435C22semidirect
87. #2432C22semidirect
88. #2432C22semidirect
89. #2429C22semidirect
90. #2427C22semidirect
91. #2427C22semidirect
92. #2427C22semidirect
93. #2427C22semidirect
94. #2422C22semidirect
95. #2420C22semidirect
96. #2420C22semidirect
97. #2420C22semidirect
98. #2420C22semidirect
99. #2419C22semidirect
100. #2418C22semidirect
101. #2417C22semidirect
102. #2415C22semidirect
103. #2415C22semidirect
104. #2408C22semidirect
105. #2407C22semidirect
106. #2407C22semidirect
107. #2407C22semidirect
109. #2367C22semidirect
110. #2366C22semidirect
111. #2364C22semidirect
113. #2363C22semidirect
114. #2362C22semidirect
115. #2361C22semidirect
116. #2360C22semidirect
117. #2360C22semidirect
118. #2359C22semidirect
119. #2358C22semidirect
120. #2354C22semidirect
121. #2352C22semidirect
122. #2352C22semidirect
123. #2351C22semidirect
124. Q8×C4⋊C4C22semidirect
125. Q8×C4⋊C4C22semidirect
126. #2349C22semidirect
127. #2349C22semidirect
128. #2342C22semidirect
131. #2341C22semidirect
132. Q8×C22⋊C4C22semidirect
133. Q8×C22⋊C4C22semidirect
134. Q8×C22⋊C4C22semidirect
135. Q8×C22⋊C4C22semidirect
136. #2339C22semidirect
137. #2339C22semidirect
138. #2339C22semidirect
140. D4×C22⋊C4C22semidirect
141. D4×C22⋊C4C22semidirect
142. C4×#127C22semidirect
144. C4×#124C22semidirect
145. C4×C22⋊Q8C22semidirect
146. C4×C22⋊Q8C22semidirect
147. C4×#123C22semidirect
149. C4×#121C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
152. C4×#120C22semidirect
153. #2297C22semidirect
154. #2297C22semidirect
155. #2280C22semidirect
156. C42×Q8C22semidirect
157. C42×D4C22semidirect
158. C42×D4C22semidirect
159. C2×C4×C22⋊C4C22semidirect
177. #550D4semidirect
443. C2×#41#41semidirect
518. #121#41semidirect
735. C2×D4C2×#41semidirect
781. C22×C4C2×#41semidirect
827. C4⋊C4C2×#41semidirect
860. C22⋊C4C2×#41semidirect
919. Q8#546semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
C2×D4×#412
#598122
#594202
#591032
#590642
#590352
#590202
Q8×#1212
#364462
#364452
#364442
#364322
#364282
#364062
#364042
#361612
#361492
#361432
C4×#5502
C4×#5482
C4×#5462
C22⋊C4×#412