Finite Group Databasebeta

← #11901815

Subgroups — #11901815

Order 1152.

2191 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596049C211yesmaximal, characteristic, complemented
2C3×#5580C212yesmaximal, complemented
3#10595438C211yesmaximal, characteristic, complemented
4#10595415C211yesmaximal, characteristic, complemented
5#10595391C212yesmaximal, complemented
6#10594660C212yesmaximal, complemented
7#10594659C211yesmaximal, characteristic, complemented
8#10594580C212yesmaximal, complemented
9#10594491C211yesmaximal, characteristic, complemented
10#10594490C212yesmaximal, complemented
11#10594488C212yesmaximal, complemented
12#10594487C212yesmaximal, complemented
13#10594006C212yesmaximal, complemented
14#10593992C211yesmaximal, characteristic, complemented
15#10593974C212yesmaximal, complemented
16#10593972C211yesmaximal, characteristic, complemented
17#10593965C212yesmaximal, complemented
18#10593910C212yesmaximal, complemented
19#10593910C212yesmaximal, complemented
20#86146—32nomaximal
21C2×C4×D32C2211yescharacteristic
22C2×#3798C2212yes—
23C32×C4×Q8C2211yescharacteristic, complemented
24#64155C2211yescharacteristic
25#64153C2211yescharacteristic, complemented
26#64106C2211yescharacteristic
27#64105C2212yes—
28#64098C2212yescomplemented
29#64097C2211yescharacteristic, complemented
30#64081C2212yes—
31C42×C3⋊D3C2211yescharacteristic
32C4×#634C2211yescharacteristic, complemented
33C4×#634C2212yescomplemented
34C3×#947C2212yes—
35C3×#946C2212yescomplemented
36C3×#898C2212yes—
37C3×#898C2212yescomplemented
38C3×#895C2212yes—
39C3×#894C2212yes—
40C3×#894C2212yescomplemented
41C3×#890C2212yescomplemented
42C3×C4×D12C2212yes—
43C3×C4×D12C2212yes—
44C3×C4×D12C2212yescomplemented
45C3×#872C2212yes—
46C3×#872C2212yescomplemented
47C3×C42×D3C2212yescomplemented
48#63922C2212yes—
49#63922C2212yes—
50#63921C2211yescharacteristic
51#63921C2211yescharacteristic
52#63919C2211yescharacteristic, complemented
53#63916C2212yes—
54#63915C2212yescomplemented
55#63914C2211yescharacteristic, complemented
56#63913C2212yes—
57#63913C2212yes—
58#63912C2211yescharacteristic
59#63912C2211yescharacteristic
60#63908C2212yes—
61#63905C2212yes—
62#63905C2212yescomplemented
63#63904C2212yes—
64#63904C2212yes—
65C4×#625C2212yes—
66C4×#625C2212yes—
67C4×#625C2211yescharacteristic, complemented
68C4×#625C2211yescharacteristic, complemented
69#63899C2212yes—
70#63899C2212yes—
71#63896C2212yescomplemented
72#63896C2212yescomplemented
73#63891C2212yes—
74#63891C2212yescomplemented
75#63885C2212yes—
76#63885C2212yes—
77#63885C2212yes—
78#63885C2212yes—
79#63884C2212yes—
80#63884C2212yescomplemented
81#63883C2211yescharacteristic
82#63883C2211yescharacteristic
83C4×#624C2211yescharacteristic
84#63880C2212yes—
85#63880C2212yes—
86#63879C2212yescomplemented
87#63879C2212yescomplemented
88#63878C2212yes—
89#63878C2212yes—
90C4×D3×Dic3C2212yescomplemented
91#63869C2212yescomplemented
92#63861C2212yes—
93#63861C2212yescomplemented
94#63860C2212yes—
95#63859C2212yes—
96#63859C2212yescomplemented
97#63858C2212yes—
98#63858C2212yescomplemented
99#63857C2212yescomplemented
100#63855C2212yes—
101#63855C2212yescomplemented
102#63854C2212yes—
103#63854C2212yes—
104#63847C2212yescomplemented
105#63847C2212yescomplemented
106#63837C2212yescomplemented
107#63837C2212yescomplemented
108C3×#529—32no—
109#5710—32no—
110#5707—32no—
111#5704—32no—
112#5701—32no—
113#5696—32no—
114#5692—32no—
115#5678—32no—
116#5669—32no—
117#5663—32no—
118#5662—32no—
119#5660—32no—
120#5657—32no—
121#5640—32no—
122#5638—32no—
123#5615—32no—
124#5613—32no—
125#5580D312yescomplemented
126#5578—32no—
127#5578—61no—
128#5557—32no—
129#5548—32no—
130#5547—32no—
131#5547—32no—
132#5538—32no—
133#5538—32no—
134#5528—32no—
135#5528—32no—
136#5522—32no—
137D3×#117—32no—
138#5479—32no—
139C4×#235—32no—
140C22×D32C2311yescharacteristic
141C2×C32×Q8C2311yescharacteristic
142C2×C4×C3⋊D3C2311yescharacteristic
143C2×C4×C3⋊D3C2311yescharacteristic
144C2×C4×C3⋊D3C2311yescharacteristic
145C2×#634C2312yes—
146C2×#634C2311yescharacteristic
147C2×C3×D12C2312yes—
148C2×C3×D12C2312yes—
149C2×C3×D12C2312yes—
150C2×C3×C4×D3C2312yes—
151C2×C3×C4×D3C2312yes—
152C2×C3×C4×D3C2312yes—
153C2×C3×C4×D3C2312yes—
154C2×C3×C4×D3C2312yes—
155C2×#627C2312yes—
156C2×#626C2312yes—
157C2×#626C2312yes—
158C2×#625C2312yes—
159C2×#625C2312yes—
160C2×#625C2311yescharacteristic
161C2×#625C2312yes—
162C2×#625C2311yescharacteristic
163C2×#624C2311yescharacteristic
164C2×#624C2311yescharacteristic
165C2×#624C2311yescharacteristic
166C2×D3×Dic3C2312yes—
167C2×D3×Dic3C2312yes—
168C2×D3×Dic3C2312yes—
169C4×D32—24no—
170#3798—28no—
171C32×C4⋊C4C2312yes—
172C32×C4⋊C4C2311yescharacteristic
173C32×C42C2311yescharacteristic
174C32×C42C2312yes—
175#3752C2312yes—
176#3752C2312yes—
177C4⋊(C3⋊Dic3)C2311yescharacteristic
178C4⋊(C3⋊Dic3)C2312yes—
179#3750C2312yes—
180#3750C2312yes—
181#3750C2312yes—
182#3750C2312yes—
183#3750C2312yes—
184C4×C3⋊Dic3C2311yescharacteristic
185C4×C3⋊Dic3C2312yes—
186C4×C3⋊Dic3C2311yescharacteristic
187C4×C3⋊Dic3C2311yescharacteristic
188C3×(C2×D3)⋊C4C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×(C2×D3)⋊C4C2312yes—
193C3×(C2×D3)⋊C4C2312yes—
194C3×(C2×D3)⋊C4C2312yes—
195C3×(C2×D3)⋊C4C2312yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×C4⋊Dic3C2312yes—
199C3×C4⋊Dic3C2312yes—
200C3×C4⋊Dic3C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×C4×Dic3C2312yes—
206C3×C4×Dic3C2312yes—
207C3×C4×Dic3C2312yes—
208#3724C2312yes—
209#3724C2311yescharacteristic
210#3724C2312yes—
211#3724C2311yescharacteristic
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216(C2×D3)⋊Dic3C2312yes—
217(C2×D3)⋊Dic3C2312yes—
218(C2×D3)⋊Dic3C2312yes—
219(C2×D3)⋊Dic3C2312yes—
220(C2×D3)⋊Dic3C2312yes—
221(C2×D3)⋊Dic3C2312yes—
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226Dic32C2312yes—
227Dic32C2312yes—
228Dic32C2312yes—
229#3455—91noSylow
230C2×#235—32no—
231C2×#235—32no—
232C22×C4×D3—32no—
233C3×#126—32no—
234C3×#126—32no—
235C3×#125—32no—
236C3×#124—32no—
237C3×#123—32no—
238C3×#123—32no—
239C3×C22⋊Q8—32no—
240C3×#121—32no—
241C3×C4×Q8—21no—
242C3×C4×Q8C2×D312yescomplemented
243C3×C4×D4—32no—
244C3×C4×D4—32no—
245C3×C4×D4—32no—
246C3×#117—32no—
247C3×#117—32no—
248C2×C3×C42—32no—
249#947C2×D312yes—
250#946—32no—
251#946—61no—
252#946C2×D312yescomplemented
253#944—32no—
254#944—61no—
255#940—32no—
256#939—32no—
257#939—32no—
258#939—32no—
259#939—32no—
260#938—32no—
261#938—32no—
262#937—32no—
263#937—32no—
264#936—32no—
265#935—32no—
266#935—32no—
267#930—32no—
268#929—32no—
269#929—32no—
270C4×#67—32no—
271C4×#67—32no—
272C4×#67—32no—
273C4×#67—32no—
274C4×#67—32no—
275C4×#67—32no—
276C4×#67—32no—
277C4×#67—32no—
278C4×#67—32no—
279C4×#67—32no—
280#926—32no—
281#926—32no—
282#924—32no—
283C2×C4×Dic3—32no—
284#898—32no—
285#898—32no—
286#898—32no—
287#898—32no—
288#898C2×D312yes—
289#898C2×D312yescomplemented
290#897—32no—
291#897—32no—
292#897—61no—
293#896—32no—
294#896—32no—
295#896—32no—
296#896—32no—
297#896—32no—
298#896—32no—
299#896—62no—
300#895—32no—
301#895C2×D312yes—
302#894—32no—
303#894—32no—
304#894—32no—
305#894—32no—
306#894C2×D312yes—
307#894C2×D312yescomplemented
308#893—32no—
309#893—32no—
310#892—32no—
311#892—32no—
312D3×C4⋊C4—32no—
313D3×C4⋊C4—32no—
314#890—32no—
315#890C2×D312yescomplemented
316#889—32no—
317#889—32no—
318#889—32no—
319#889—32no—
320#889—32no—
321#889—32no—
322#889—62no—
323#888—32no—
324#888—32no—
325#888—61no—
326#887—32no—
327#887—32no—
328#886—32no—
329#886—32no—
330#885—32no—
331#885—32no—
332#885—32no—
333#885—32no—
334#885—32no—
335#885—32no—
336#884—32no—
337#884—32no—
338#884—32no—
339#884—32no—
340#884—32no—
341#884—32no—
342#883—32no—
343#883—32no—
344#883—32no—
345#883—32no—
346#883—32no—
347#883—32no—
348#882—32no—
349#882—32no—
350#67⋊C4—32no—
351#67⋊C4—32no—
352#67⋊C4—32no—
353#67⋊C4—32no—
354D3×C22⋊C4—32no—
355D3×C22⋊C4—32no—
356#879—32no—
357#879—32no—
358#879—32no—
359#879—32no—
360#879—32no—
361#879—32no—
362#878—32no—
363#878—32no—
364#878—32no—
365#878—32no—
366#877—32no—
367#877—32no—
368#876—32no—
369#876—32no—
370#875—32no—
371C4×D12—32no—
372C4×D12—32no—
373C4×D12C2×D312yes—
374C4×D12C2×D312yes—
375C4×D12C2×D312yescomplemented
376#872—32no—
377#872—32no—
378#872—32no—
379#872—32no—
380#872—62no—
381#872C2×D312yes—
382#872C2×D312yescomplemented
383C42×D3—32no—
384C42×D3—32no—
385C42×D3—32no—
386C42×D3—61no—
387C42×D3C2×D312yescomplemented
388#870—32no—
389C4×Dic6—32no—
390C4×Dic6—32no—
391C4×Dic6—32no—
392C4×Dic6—32no—
393C4×Dic6—32no—
394C4×Dic6—62no—
395C4×Dic6—61no—
396C22×C3⋊D3C2411yescharacteristic
397C22×C3×D3C2412yes—
398C22×C3×D3C2412yes—
399C22×C3×D3C2412yes—
400C2×D32—22no—
401C2×D32—41no—
402C2×D32—41no—
403C32×Q8—41no—
404C2×C32×C4C2412yes—
405C2×C32×C4C2412yes—
406C2×C32×C4C2411yescharacteristic
407C2×C32×C4C2411yescharacteristic
408C2×C32×C4C2411yescharacteristic
409C2×C3⋊Dic3C2412yes—
410C2×C3⋊Dic3C2412yes—
411C2×C3⋊Dic3C2411yescharacteristic
412C2×C3⋊Dic3C2411yescharacteristic
413C2×C3⋊Dic3C2411yescharacteristic
414C4×C3⋊D3—41no—
415C4×C3⋊D3—41no—
416C4×C3⋊D3#4114yes—
417#634—42no—
418#634—41no—
419C2×C3×Dic3C2412yes—
420C2×C3×Dic3C2412yes—
421C2×C3×Dic3C2412yes—
422C2×C3×Dic3C2412yes—
423C2×C3×Dic3C2412yes—
424C3×D12—42no—
425C3×D12—42no—
426C3×D12—42no—
427C3×C4×D3—24no—
428C3×C4×D3—24no—
429C3×C4×D3—24no—
430C3×C4×D3—42no—
431C3×C4×D3—42no—
432#627—24no—
433#626—24no—
434#626—24no—
435#625—24no—
436#625—42no—
437#625—42no—
438#625—41no—
439#625—41no—
440#624—22no—
441#624—41no—
442#624—41no—
443D3×Dic3—24no—
444D3×Dic3—42no—
445D3×Dic3—42no—
446#542—92no—
447#542—92no—
448#541—92no—
449#540—92no—
450#539—91no—
451#539—92no—
452#539—91no—
453#538—92no—
454#538—91no—
455#538—91no—
456#533—91no—
457#532—91no—
458#529—32no—
459#529—92no—
460#529—92no—
461#529—92no—
462#525—92no—
463C4×#41—92no—
464C2×#117—91no—
465C23×D3—32no—
466C2×C3×Q8—21no—
467C2×C3×Q8C22×D312yes—
468C2×C3×D4—32no—
469C2×C3×D4—32no—
470C2×C3×D4—32no—
471C22×C3×C4—32no—
472C22×C3×C4—32no—
473C22×C3×C4—32no—
474C22×C3×C4—32no—
475C22×C3×C4—32no—
476C2×#67—32no—
477C2×#67—32no—
478C2×#67—32no—
479C2×#67—32no—
480C2×#67—32no—
481C2×#67—32no—
482C2×#67—32no—
483C2×#67—32no—
484C2×#67—32no—
485C2×#67—32no—
486C22×Dic3—32no—
487C22×Dic3—32no—
488C22×Dic3—32no—
489#235—68no—
490#235—68no—
491C2×D12—32no—
492C2×D12—32no—
493C2×D12C22×D312yes—
494C2×D12C22×D312yes—
495C2×D12C22×D312yes—
496C2×C4×D3—32no—
497C2×C4×D3—32no—
498C2×C4×D3—32no—
499C2×C4×D3—32no—
500C2×C4×D3—32no—
501C2×C4×D3—32no—
502C2×C4×D3—32no—
503C2×C4×D3—32no—
504C2×C4×D3—32no—
505C2×C4×D3—61no—
506C2×C4×D3—61no—
507C2×C4×D3—61no—
508C2×C4×D3—68no—
509C2×C4×D3C22×D312yes—
510C2×C4×D3C22×D312yes—
511C2×C4×D3C22×D312yes—
512C2×C4×D3C22×D312yes—
513C2×C4×D3C22×D312yes—
514C2×Dic6—32no—
515C2×Dic6—32no—
516C2×Dic6—32no—
517C2×Dic6—32no—
518C2×Dic6—32no—
519C2×Dic6—62no—
520C2×Dic6—61no—
521C3×C4⋊C4—21no—
522C3×C4⋊C4—22no—
523C3×C4⋊C4—32no—
524C3×C4⋊C4—32no—
525C3×C4⋊C4—32no—
526C3×C4⋊C4—32no—
527C3×C4⋊C4—32no—
528C3×C4⋊C4—32no—
529C3×C4⋊C4—32no—
530C3×C4⋊C4C22×D312yes—
531C3×C4⋊C4C22×D312yes—
532C3×C4⋊C4C22×D312yes—
533C3×C22⋊C4—32no—
534C3×C22⋊C4—32no—
535C3×C22⋊C4—32no—
536C3×C22⋊C4—32no—
537C3×C22⋊C4—32no—
538C3×C22⋊C4—32no—
539C3×C22⋊C4—32no—
540C3×C22⋊C4—32no—
541C3×C22⋊C4—32no—
542C3×C22⋊C4—32no—
543C3×C42—21no—
544C3×C42—22no—
545C3×C42—32no—
546C3×C42—32no—
547C3×C42—32no—
548C3×C42C22×D312yes—
549C3×C42C22×D312yes—
550C3×C42C22×D312yes—
551#217—32no—
552#217—32no—
553#217—32no—
554#217—32no—
555#217—32no—
556#217—32no—
557#217—32no—
558#217—32no—
559#217—32no—
560#217—32no—
561(C2×D3)⋊C4—32no—
562(C2×D3)⋊C4—32no—
563(C2×D3)⋊C4—32no—
564(C2×D3)⋊C4—32no—
565(C2×D3)⋊C4—32no—
566(C2×D3)⋊C4—32no—
567(C2×D3)⋊C4—32no—
568(C2×D3)⋊C4—32no—
569(C2×D3)⋊C4—32no—
570(C2×D3)⋊C4—32no—
571(C2×D3)⋊C4—32no—
572(C2×D3)⋊C4—32no—
573(C2×D3)⋊C4—32no—
574(C2×D3)⋊C4—32no—
575(C2×D3)⋊C4—62no—
576(C2×D3)⋊C4—62no—
577(C2×D3)⋊C4C22×D312yes—
578(C2×D3)⋊C4C22×D312yes—
579(C2×D3)⋊C4C22×D312yes—
580(C2×D3)⋊C4C22×D312yes—
581(C2×D3)⋊C4C22×D312yes—
582(C2×D3)⋊C4C22×D312yes—
583(C2×D3)⋊C4C22×D312yes—
584(C2×D3)⋊C4C22×D312yes—
585(C2×D3)⋊C4C22×D312yes—
586(C2×D3)⋊C4C22×D312yes—
587C4⋊Dic3—32no—
588C4⋊Dic3—32no—
589C4⋊Dic3—32no—
590C4⋊Dic3—32no—
591C4⋊Dic3—32no—
592C4⋊Dic3—32no—
593C4⋊Dic3—32no—
594C4⋊Dic3—61no—
595C4⋊Dic3—62no—
596C4⋊Dic3C22×D312yes—
597C4⋊Dic3C22×D312yes—
598C4⋊Dic3C22×D312yes—
599Dic3⋊C4—32no—
600Dic3⋊C4—32no—
601Dic3⋊C4—32no—
602Dic3⋊C4—32no—
603Dic3⋊C4—32no—
604Dic3⋊C4—32no—
605Dic3⋊C4—32no—
606Dic3⋊C4—32no—
607Dic3⋊C4—32no—
608Dic3⋊C4—32no—
609Dic3⋊C4—32no—
610Dic3⋊C4—32no—
611Dic3⋊C4—32no—
612Dic3⋊C4—32no—
613Dic3⋊C4—32no—
614Dic3⋊C4—32no—
615Dic3⋊C4—32no—
616Dic3⋊C4—32no—
617Dic3⋊C4—32no—
618Dic3⋊C4—32no—
619Dic3⋊C4—62no—
620Dic3⋊C4—62no—
621Dic3⋊C4—62no—
622Dic3⋊C4—62no—
623Dic3⋊C4—62no—
624Dic3⋊C4C22×D312yes—
625Dic3⋊C4C22×D312yes—
626Dic3⋊C4C22×D312yes—
627Dic3⋊C4C22×D312yes—
628C4×Dic3—32no—
629C4×Dic3—32no—
630C4×Dic3—32no—
631C4×Dic3—32no—
632C4×Dic3—32no—
633C4×Dic3—32no—
634C4×Dic3—32no—
635C4×Dic3—32no—
636C4×Dic3—32no—
637C4×Dic3—32no—
638C4×Dic3—32no—
639C4×Dic3—61no—
640C4×Dic3—62no—
641C4×Dic3—61no—
642C4×Dic3—61no—
643C4×Dic3C22×D312yes—
644C4×Dic3C22×D312yes—
645C4×Dic3C22×D312yes—
646C22×C32C2511yescharacteristic
647C2×C3⋊D3—21no—
648C2×C3⋊D3—21no—
649C2×C3⋊D3C2×#4112yes—
650C2×C3×D3—22no—
651C2×C3×D3—22no—
652C2×C3×D3—22no—
653C2×C3×D3—22no—
654C2×C3×D3—22no—
655C2×C3×D3—22no—
656C2×C3×D3—22no—
657C2×C3×D3—22no—
658C2×C3×D3—22no—
659D32—44no—
660C32×C4—21no—
661C32×C4—22no—
662C32×C4—22no—
663C32×C4—21no—
664C32×C4C2×#4112yes—
665C3⋊Dic3—21no—
666C3⋊Dic3—22no—
667C3⋊Dic3—22no—
668C3⋊Dic3—21no—
669C3⋊Dic3C2×#4112yes—
670C3×Dic3—22no—
671C3×Dic3—22no—
672C3×Dic3—22no—
673C3×Dic3—22no—
674C3×Dic3—22no—
675C2×#41—92no—
676C23×C4—91no—
677C4⋊Q8—91no—
678C4⋊Q8—91no—
679C4⋊Q8—91no—
680#127—91no—
681#126—32no—
682#126—32no—
683#126—92no—
684#126—92no—
685#126—92no—
686#126—92no—
687#126—92no—
688#126—92no—
689#125—32no—
690#125—92no—
691#125—92no—
692#125—92no—
693#125—92no—
694#124—32no—
695#124—92no—
696#124—92no—
697#124—92no—
698#124—92no—
699#123—32no—
700#123—32no—
701#123—92no—
702#123—92no—
703#123—92no—
704#123—92no—
705#123—92no—
706#123—92no—
707#123—92no—
708#123—92no—
709C22⋊Q8—32no—
710C22⋊Q8—92no—
711C22⋊Q8—92no—
712C22⋊Q8—92no—
713C22⋊Q8—92no—
714C22⋊Q8—92no—
715C22⋊Q8—91no—
716C22⋊Q8—92no—
717C22⋊Q8—91no—
718#121—32no—
719#121—91no—
720#121—91no—
721#121—92no—
722#121—92no—
723#121—92no—
724#121—92no—
725#121—92no—
726#121—92no—
727#120—92no—
728#120—92no—
729C4×Q8—92no—
730C4×Q8—92no—
731C4×Q8—92no—
732C4×Q8—91no—
733C4×Q8D3211yescharacteristic, complemented
734C4×D4—32no—
735C4×D4—32no—
736C4×D4—32no—
737C4×D4—92no—
738C4×D4—92no—
739C4×D4—92no—
740C4×D4—92no—
741C4×D4—92no—
742C4×D4—92no—
743C4×D4—92no—
744C4×D4—92no—
745C4×D4—91no—
746C4×D4—91no—
747#117—32no—
748#117—32no—
749#117—92no—
750#117—92no—
751#117—92no—
752#117—92no—
753#117—92no—
754C2×C4⋊C4—91no—
755C2×C4⋊C4—91no—
756C2×C22⋊C4—91no—
757C2×C22⋊C4—91no—
758C2×C42—32no—
759C2×C42—91no—
760C2×C42—92no—
761C2×C42—91no—
762C23×C3—32no—
763C23×C3—32no—
764C23×C3—32no—
765C22×D3—32no—
766C22×D3—61no—
767C22×D3—64no—
768C22×D3—122no—
769C22×D3—122no—
770C22×D3C23×D312yes—
771C22×D3C23×D312yes—
772C22×D3C23×D312yes—
773C3×Q8—42no—
774C3×Q8—42no—
775C3×D4—122no—
776C3×D4—122no—
777C3×D4—122no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—22no—
781C2×C3×C4—22no—
782C2×C3×C4—21no—
783C2×C3×C4—32no—
784C2×C3×C4—32no—
785C2×C3×C4—32no—
786C2×C3×C4—32no—
787C2×C3×C4—32no—
788C2×C3×C4—64no—
789C2×C3×C4—64no—
790C2×C3×C4—64no—
791C2×C3×C4—122no—
792C2×C3×C4—122no—
793C2×C3×C4C23×D312yes—
794C2×C3×C4C23×D312yes—
795C2×C3×C4C23×D312yes—
796C2×C3×C4C23×D312yes—
797C2×C3×C4C23×D312yes—
798C2×C3×C4C23×D312yes—
799C2×C3×C4C23×D312yes—
800#67—64no—
801#67—64no—
802#67—64no—
803#67—64no—
804#67—122no—
805#67—122no—
806#67—122no—
807#67—122no—
808#67—122no—
809#67—122no—
810C2×Dic3—32no—
811C2×Dic3—32no—
812C2×Dic3—32no—
813C2×Dic3—32no—
814C2×Dic3—32no—
815C2×Dic3—32no—
816C2×Dic3—32no—
817C2×Dic3—61no—
818C2×Dic3—61no—
819C2×Dic3—61no—
820C2×Dic3—62no—
821C2×Dic3—62no—
822C2×Dic3—64no—
823C2×Dic3—122no—
824C2×Dic3—122no—
825C2×Dic3C23×D312yes—
826C2×Dic3C23×D312yes—
827C2×Dic3C23×D312yes—
828C2×Dic3C23×D312yes—
829C2×Dic3C23×D312yes—
830D12—42no—
831D12—42no—
832D12—42no—
833D12—64no—
834D12—64no—
835C4×D3—24no—
836C4×D3—24no—
837C4×D3—24no—
838C4×D3—38no—
839C4×D3—42no—
840C4×D3—42no—
841C4×D3—64no—
842C4×D3—64no—
843C4×D3—64no—
844C4×D3—122no—
845C4×D3—122no—
846C4×D3—122no—
847C4×D3—122no—
848C4×D3—122no—
849C4×D3—122no—
850C4×D3—122no—
851C4×D3—122no—
852Dic6—64no—
853Dic6—64no—
854Dic6—122no—
855Dic6—122no—
856Dic6—122no—
857Dic6—124no—
858Dic6—122no—
859C2×C32C22×#4111yescharacteristic
860C2×C32#58511yescharacteristic
861C2×C32#58511yescharacteristic
862C3⋊D3—22no—
863C3×D3—42no—
864C3×D3—42no—
865C3×D3—42no—
866C24—91no—
867#41—188no—
868C2×Q8—92no—
869C2×Q8—92no—
870C2×Q8—91no—
871C2×Q8C2×D3211yescharacteristic
872C2×D4—32no—
873C2×D4—32no—
874C2×D4—32no—
875C2×D4—92no—
876C2×D4—92no—
877C2×D4—92no—
878C2×D4—92no—
879C2×D4—92no—
880C2×D4—91no—
881C2×D4—91no—
882C22×C4—32no—
883C22×C4—32no—
884C22×C4—32no—
885C22×C4—32no—
886C22×C4—32no—
887C22×C4—91no—
888C22×C4—91no—
889C22×C4—91no—
890C22×C4—92no—
891C22×C4—92no—
892C22×C4—92no—
893C22×C4—91no—
894C22×C4—91no—
895C22×C4—91no—
896C22×C4—184no—
897C4⋊C4—32no—
898C4⋊C4—32no—
899C4⋊C4—32no—
900C4⋊C4—32no—
901C4⋊C4—32no—
902C4⋊C4—32no—
903C4⋊C4—32no—
904C4⋊C4—92no—
905C4⋊C4—92no—
906C4⋊C4—92no—
907C4⋊C4—92no—
908C4⋊C4—91no—
909C4⋊C4—91no—
910C4⋊C4—92no—
911C4⋊C4—92no—
912C4⋊C4—92no—
913C4⋊C4—92no—
914C4⋊C4—92no—
915C4⋊C4—92no—
916C4⋊C4—92no—
917C4⋊C4—92no—
918C4⋊C4—91no—
919C4⋊C4C2×D3212yes—
920C4⋊C4C2×D3211yescharacteristic
921C22⋊C4—32no—
922C22⋊C4—32no—
923C22⋊C4—32no—
924C22⋊C4—32no—
925C22⋊C4—32no—
926C22⋊C4—32no—
927C22⋊C4—32no—
928C22⋊C4—32no—
929C22⋊C4—32no—
930C22⋊C4—32no—
931C22⋊C4—92no—
932C22⋊C4—92no—
933C22⋊C4—92no—
934C22⋊C4—92no—
935C22⋊C4—92no—
936C22⋊C4—92no—
937C22⋊C4—92no—
938C22⋊C4—92no—
939C22⋊C4—92no—
940C22⋊C4—92no—
941C22⋊C4—92no—
942C22⋊C4—92no—
943C42—32no—
944C42—32no—
945C42—32no—
946C42—92no—
947C42—92no—
948C42—92no—
949C42—91no—
950C42—91no—
951C42—91no—
952C42—92no—
953C42C2×D3212yes—
954C42C2×D3211yescharacteristic
955C22×C3—21no—
956C22×C3—62no—
957C22×C3—62no—
958C22×C3—62no—
959C22×C3—62no—
960C22×C3—62no—
961C22×C3—62no—
962C22×C3—62no—
963C22×C3—62no—
964C22×C3—62no—
965C22×C3C24×D312yes—
966C2×D3—22no—
967C2×D3—22no—
968C2×D3—22no—
969C2×D3—22no—
970C2×D3—22no—
971C2×D3—22no—
972C2×D3—22no—
973C2×D3—22no—
974C2×D3—22no—
975C2×D3—34no—
976C2×D3—62no—
977C2×D3—62no—
978C2×D3—62no—
979C2×D3—121no—
980C2×D3—121no—
981C2×D3—128no—
982C3×C4—22no—
983C3×C4—22no—
984C3×C4—22no—
985C3×C4—22no—
986C3×C4—22no—
987C3×C4—22no—
988C3×C4—22no—
989C3×C4—22no—
990C3×C4—42no—
991C3×C4—41no—
992C3×C4—42no—
993C3×C4—62no—
994C3×C4—62no—
995C3×C4—62no—
996C3×C4—62no—
997C3×C4—62no—
998C3×C4D3×#4114yes—
999Dic3—22no—
1000Dic3—22no—
1001Dic3—22no—
1002Dic3—22no—
1003Dic3—22no—
1004Dic3—34no—
1005Dic3—62no—
1006Dic3—62no—
1007Dic3—62no—
1008Dic3—62no—
1009Dic3—62no—
1010Dic3—62no—
1011Dic3—62no—
1012Dic3—62no—
1013Dic3—122no—
1014Dic3—122no—
1015Dic3—121no—
1016C32#345511yescharacteristic, complemented, Sylow
1017C23—32no—
1018C23—32no—
1019C23—32no—
1020C23—91no—
1021C23—182no—
1022C23—361no—
1023C23—361no—
1024Q8—41no—
1025Q8—184no—
1026Q8—361no—
1027Q8—362no—
1028D4—122no—
1029D4—122no—
1030D4—122no—
1031D4—184no—
1032D4—184no—
1033D4—184no—
1034D4—361no—
1035D4—361no—
1036D4—362no—
1037D4—362no—
1038C2×C4—32no—
1039C2×C4—32no—
1040C2×C4—32no—
1041C2×C4—32no—
1042C2×C4—32no—
1043C2×C4—64no—
1044C2×C4—64no—
1045C2×C4—64no—
1046C2×C4—91no—
1047C2×C4—94no—
1048C2×C4—91no—
1049C2×C4—92no—
1050C2×C4—92no—
1051C2×C4—91no—
1052C2×C4—122no—
1053C2×C4—122no—
1054C2×C4—182no—
1055C2×C4—184no—
1056C2×C4—361no—
1057C2×C4—361no—
1058C2×C4—361no—
1059C2×C4—361no—
1060C2×C4—362no—
1061C2×C4—362no—
1062C2×C4C22×D3212yes—
1063C2×C4C22×D3212yes—
1064C2×C4C22×D3211yescharacteristic
1065C2×C4C22×D3211yescharacteristic
1066C2×C4C22×D3211yescharacteristic
1067C2×C3—21no—
1068C2×C3—21no—
1069C2×C3—21no—
1070C2×C3—122no—
1071C2×C3—122no—
1072C2×C3—122no—
1073C2×C3C2×D3×#4112yes—
1074C2×C3#596412yes—
1075C2×C3#596412yes—
1076D3—42no—
1077D3—42no—
1078D3—42no—
1079D3—64no—
1080D3—122no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—62no—
1085C22—62no—
1086C22—62no—
1087C22—62no—
1088C22—62no—
1089C22—62no—
1090C22—92no—
1091C22—181no—
1092C22—181no—
1093C22—364no—
1094C22C23×D3211yescharacteristic
1095C4—22no—
1096C4—21no—
1097C4—22no—
1098C4—21no—
1099C4—62no—
1100C4—62no—
1101C4—62no—
1102C4—62no—
1103C4—62no—
1104C4—92no—
1105C4—181no—
1106C4—182no—
1107C4—182no—
1108C4—181no—
1109C4#6431912yes—
1110C3—21no—
1111C3#8614612yescomplemented
1112C2—122no—
1113C2—122no—
1114C2—122no—
1115C2—182no—
1116C2#1059666911yescharacteristic
1117C2C2×#6431911yescharacteristic
1118C2#1059669511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596049C2semidirect
2. C3×#5580C2semidirect
3. #10595438C2semidirect
4. #10595415C2semidirect
5. #10595391C2semidirect
6. #10594660C2semidirect
7. #10594659C2semidirect
8. #10594580C2semidirect
9. #10594491C2semidirect
10. #10594490C2semidirect
11. #10594488C2semidirect
12. #10594487C2semidirect
13. #10594006C2semidirect
14. #10593992C2semidirect
15. #10593974C2semidirect
16. #10593972C2semidirect
17. #10593965C2semidirect
18. #10593910C2semidirect
19. #10593910C2semidirect
23. C32×C4×Q8C22semidirect
25. #64153C22semidirect
28. #64098C22semidirect
29. #64097C22semidirect
32. C4×#634C22semidirect
33. C4×#634C22semidirect
35. C3×#946C22semidirect
37. C3×#898C22semidirect
40. C3×#894C22semidirect
41. C3×#890C22semidirect
44. C3×C4×D12C22semidirect
46. C3×#872C22semidirect
47. C3×C42×D3C22semidirect
52. #63919C22semidirect
54. #63915C22semidirect
55. #63914C22semidirect
62. #63905C22semidirect
67. C4×#625C22semidirect
68. C4×#625C22semidirect
71. #63896C22semidirect
72. #63896C22semidirect
74. #63891C22semidirect
80. #63884C22semidirect
86. #63879C22semidirect
87. #63879C22semidirect
90. C4×D3×Dic3C22semidirect
91. #63869C22semidirect
93. #63861C22semidirect
96. #63859C22semidirect
98. #63858C22semidirect
99. #63857C22semidirect
101. #63855C22semidirect
104. #63847C22semidirect
105. #63847C22semidirect
106. #63837C22semidirect
107. #63837C22semidirect
125. #5580D3semidirect
242. C3×C4×Q8C2×D3semidirect
252. #946C2×D3semidirect
289. #898C2×D3semidirect
307. #894C2×D3semidirect
315. #890C2×D3semidirect
375. C4×D12C2×D3semidirect
382. #872C2×D3semidirect
387. C42×D3C2×D3semidirect
733. C4×Q8D32semidirect
1016. C32#3455semidirect
1111. C3#86146semidirect

Maximal subgroups

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

subgroupindex
#105960492
C3×#55802
#105954382
#105954152
#105953912
#105946602
#105946592
#105945802
#105944912
#105944902
#105944882
#105944872
#105940062
#105939922
#105939742
#105939722
#105939652
#105939102
#861463