Finite Group Databasebeta

← #11901791

Subgroups — #11901791

Order 1152.

2235 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic, complemented
2C3×#5528C212yesmaximal, complemented
3#10595076C211yesmaximal, characteristic, complemented
4#10595033C212yesmaximal, complemented
5#10595017C211yesmaximal, characteristic, complemented
6#10594657C212yesmaximal, complemented
7#10594574C212yesmaximal, complemented
8#10594567C212yesmaximal, complemented
9#10594474C212yesmaximal, complemented
10#10594306C212yesmaximal, complemented
11#10594227C212yesmaximal, complemented
12#10594152C212yesmaximal, complemented
13#10594151C212yesmaximal, complemented
14#10594006C211yesmaximal, characteristic, complemented
15#10593992C211yesmaximal, characteristic, complemented
16#10593973C212yesmaximal, complemented
17C4×#3798C211yesmaximal, characteristic, complemented
18#10593935C211yesmaximal, characteristic, complemented
19#10593875C212yesmaximal, complemented
20#86146—32nomaximal
21C2×#3828C2211yescharacteristic
22C2×C4×D32C2211yescharacteristic
23C2×#3798C2211yescharacteristic
24C32×#117C2211yescharacteristic, complemented
25C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
26#64102C2212yes—
27#64096C2212yescomplemented
28#64090C2212yes—
29#64090C2212yescomplemented
30#64081C2211yescharacteristic
31#64081C2211yescharacteristic, complemented
32C42×C3⋊D3C2211yescharacteristic
33C42×C3⋊D3C2211yescharacteristic, complemented
34C3×C4×#67C2212yes—
35C3×C4×#67C2212yescomplemented
36C3×#898C2212yes—
37C3×#896C2212yescomplemented
38C3×#894C2212yes—
39C3×#889C2212yescomplemented
40C3×#885C2212yes—
41C3×#884C2212yes—
42C3×#883C2212yescomplemented
43C3×#879C2212yescomplemented
44C3×C4×D12C2212yes—
45C3×#872C2212yes—
46C3×C42×D3C2212yescomplemented
47C3×C4×Dic6C2212yescomplemented
48#63983C2211yescharacteristic
49#63982C2212yescomplemented
50#63980C2212yes—
51#63979C2211yescharacteristic, complemented
52#63975C2211yescharacteristic
53#63971C2212yes—
54#63962C2212yes—
55#63962C2212yescomplemented
56#63958C2212yes—
57#63953C2211yescharacteristic, complemented
58#63923C2211yescharacteristic
59#63922C2212yes—
60#63921C2212yes—
61C4×#627C2212yescomplemented
62C4×#627C2212yescomplemented
63#63916C2212yes—
64#63915C2212yes—
65#63913C2211yescharacteristic, complemented
66#63910C2212yes—
67#63906C2212yes—
68#63905C2212yes—
69C4×#626C2212yes—
70C4×#626C2212yes—
71C4×#626C2212yes—
72C4×#626C2212yescomplemented
73C4×#625C2212yes—
74C4×#625C2212yescomplemented
75#63899C2212yes—
76#63897C2211yescharacteristic
77#63896C2212yes—
78#63895C2212yes—
79#63888C2212yes—
80#63885C2212yes—
81#63883C2212yes—
82C4×#624C2211yescharacteristic
83#63878C2212yes—
84#63878C2212yes—
85#63874C2211yescharacteristic
86#63872C2212yescomplemented
87#63871C2212yescomplemented
88#63870C2212yescomplemented
89#63868C2212yescomplemented
90#63867C2212yescomplemented
91#63863C2212yes—
92#63862C2212yes—
93#63862C2212yes—
94#63862C2212yescomplemented
95#63862C2212yescomplemented
96#63859C2212yes—
97#63855C2212yes—
98#63855C2212yescomplemented
99#63854C2212yes—
100#63853C2212yes—
101#63853C2212yescomplemented
102#63852C2212yes—
103#63851C2212yescomplemented
104#63850C2212yescomplemented
105#63847C2212yescomplemented
106#63840C2211yescharacteristic, complemented
107#63839C2212yescomplemented
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#5580—32no—
126#5578—32no—
127#5557—32no—
128#5548—32no—
129#5547—32no—
130#5547—32no—
131#5538—32no—
132#5538—32no—
133#5528—32no—
134#5528D312yescomplemented
135#5522—32no—
136#5522—61no—
137D3×#117—32no—
138#5479—32no—
139C4×#235—32no—
140C22×D32C2311yescharacteristic
141C22×C32×C4C2311yescharacteristic
142C2×#638C2311yescharacteristic
143C2×#638C2311yescharacteristic
144C22×C3⋊Dic3C2312yes—
145#3828—24no—
146C2×C4⋊(C3⋊D3)C2311yescharacteristic
147C2×C4×C3⋊D3C2311yescharacteristic
148C2×C4×C3⋊D3C2312yes—
149C2×C4×C3⋊D3C2312yes—
150C2×C4×C3⋊D3C2311yescharacteristic
151C2×#634C2311yescharacteristic
152C2×C3×#67C2312yes—
153C2×C3×#67C2312yes—
154C2×C3×D12C2312yes—
155C2×C3×C4×D3C2312yes—
156C2×C3×C4×D3C2312yes—
157C2×C3×C4×D3C2312yes—
158C2×C3×C4×D3C2312yes—
159C2×C3×Dic6C2312yes—
160C2×#627C2311yescharacteristic
161C2×#627C2312yes—
162C2×#626C2312yes—
163C2×#626C2312yes—
164C2×#626C2312yes—
165C2×#625C2311yescharacteristic
166C2×#625C2312yes—
167C2×#624C2311yescharacteristic
168C2×#624C2312yes—
169C2×D3×Dic3C2312yes—
170C4×D32—24no—
171#3798—24no—
172C32×C4⋊C4C2312yes—
173C32×C22⋊C4C2312yes—
174C32×C42C2311yescharacteristic
175C32×C42C2311yescharacteristic
176#3752C2312yes—
177#3752C2312yes—
178#3750C2312yes—
179#3750C2312yes—
180C4×C3⋊Dic3C2311yescharacteristic
181C4×C3⋊Dic3C2312yes—
182C4×C3⋊Dic3C2312yes—
183C4×C3⋊Dic3C2311yescharacteristic
184C4×C3⋊Dic3C2312yes—
185C3×#217C2312yes—
186C3×#217C2312yes—
187C3×(C2×D3)⋊C4C2312yes—
188C3×(C2×D3)⋊C4C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×(C2×D3)⋊C4C2312yes—
193C3×C4⋊Dic3C2312yes—
194C3×C4⋊Dic3C2312yes—
195C3×Dic3⋊C4C2312yes—
196C3×Dic3⋊C4C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×Dic3⋊C4C2312yes—
199C3×Dic3⋊C4C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×C4×Dic3C2312yes—
202C3×C4×Dic3C2312yes—
203C3×C4×Dic3C2312yes—
204C3×C4×Dic3C2312yes—
205#3724C2312yes—
206#3724C2312yes—
207#3724C2312yes—
208Dic3⋊Dic3C2312yes—
209Dic3⋊Dic3C2312yes—
210Dic3⋊Dic3C2312yes—
211Dic3⋊Dic3C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216#3722C2312yes—
217#3722C2312yes—
218#3722C2311yescharacteristic
219#3722C2311yescharacteristic
220(C2×D3)⋊Dic3C2312yes—
221(C2×D3)⋊Dic3C2312yes—
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228Dic32C2311yescharacteristic
229Dic32C2311yescharacteristic
230#3455—91noSylow
231C2×#235—32no—
232C2×#235—32no—
233C2×#235—61no—
234C22×C4×D3—32no—
235C3×#126—32no—
236C3×#126—32no—
237C3×#125—32no—
238C3×#124—32no—
239C3×#123—32no—
240C3×#123—32no—
241C3×C22⋊Q8—32no—
242C3×#121—32no—
243C3×C4×Q8—32no—
244C3×C4×D4—32no—
245C3×C4×D4—32no—
246C3×C4×D4—32no—
247C3×#117—21no—
248C3×#117—32no—
249C3×#117C2×D312yescomplemented
250C2×C3×C42—32no—
251#947—32no—
252#946—32no—
253#946—32no—
254#944—32no—
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×#67C2×D312yes—
279C4×#67C2×D312yescomplemented
280#926—32no—
281#926—32no—
282#924—32no—
283C2×C4×Dic3—32no—
284C2×C4×Dic3—61no—
285#898—32no—
286#898—32no—
287#898—32no—
288#898—32no—
289#898—32no—
290#898C2×D312yes—
291#897—32no—
292#897—32no—
293#896—32no—
294#896—32no—
295#896—32no—
296#896—32no—
297#896—32no—
298#896C2×D312yescomplemented
299#895—32no—
300#895—32no—
301#894—32no—
302#894—32no—
303#894—32no—
304#894—32no—
305#894—32no—
306#894C2×D312yes—
307#893—32no—
308#893—32no—
309#893—62no—
310#892—32no—
311#892—32no—
312D3×C4⋊C4—32no—
313D3×C4⋊C4—32no—
314#890—32no—
315#890—32no—
316#889—32no—
317#889—32no—
318#889—32no—
319#889—32no—
320#889—32no—
321#889C2×D312yescomplemented
322#888—32no—
323#888—32no—
324#887—32no—
325#887—32no—
326#887—62no—
327#886—32no—
328#886—32no—
329#885—32no—
330#885—32no—
331#885—32no—
332#885—32no—
333#885—32no—
334#885C2×D312yes—
335#884—32no—
336#884—32no—
337#884—32no—
338#884—32no—
339#884—32no—
340#884C2×D312yes—
341#883—32no—
342#883—32no—
343#883—32no—
344#883—32no—
345#883—32no—
346#883C2×D312yescomplemented
347#882—32no—
348#882—32no—
349#67⋊C4—32no—
350#67⋊C4—32no—
351#67⋊C4—32no—
352#67⋊C4—32no—
353#67⋊C4—62no—
354#67⋊C4—62no—
355D3×C22⋊C4—32no—
356D3×C22⋊C4—32no—
357#879—32no—
358#879—32no—
359#879—32no—
360#879—32no—
361#879—32no—
362#879C2×D312yescomplemented
363#878—32no—
364#878—32no—
365#878—32no—
366#878—32no—
367#877—32no—
368#877—32no—
369#876—32no—
370#876—32no—
371#875—32no—
372C4×D12—32no—
373C4×D12—32no—
374C4×D12—32no—
375C4×D12—32no—
376C4×D12C2×D312yes—
377#872—32no—
378#872—32no—
379#872—32no—
380#872—32no—
381#872—32no—
382#872—61no—
383#872—61no—
384#872C2×D312yes—
385C42×D3—32no—
386C42×D3—32no—
387C42×D3—32no—
388C42×D3—61no—
389C42×D3—61no—
390C42×D3C2×D312yescomplemented
391#870—32no—
392C4×Dic6—32no—
393C4×Dic6—32no—
394C4×Dic6—32no—
395C4×Dic6—32no—
396C4×Dic6C2×D312yescomplemented
397C23×C32C2411yescharacteristic
398C22×C3⋊D3C2411yescharacteristic
399C22×C3⋊D3C2411yescharacteristic
400C22×C3×D3C2412yes—
401C22×C3×D3C2412yes—
402C2×D32—22no—
403C2×D32—42no—
404C2×C32×C4—22no—
405C2×C32×C4C2412yes—
406C2×C32×C4C2411yescharacteristic
407C2×C32×C4C2412yes—
408C2×C32×C4C2411yescharacteristic
409#638—22no—
410#638—22no—
411C2×C3⋊Dic3—42no—
412C2×C3⋊Dic3C2412yes—
413C2×C3⋊Dic3C2411yescharacteristic
414C2×C3⋊Dic3C2412yes—
415C2×C3⋊Dic3C2411yescharacteristic
416C4⋊(C3⋊D3)—22no—
417C4×C3⋊D3—22no—
418C4×C3⋊D3—42no—
419C4×C3⋊D3—42no—
420C4×C3⋊D3#4114yes—
421#634—22no—
422C3×#67—42no—
423C3×#67—42no—
424C2×C3×Dic3C2412yes—
425C2×C3×Dic3C2412yes—
426C2×C3×Dic3C2412yes—
427C2×C3×Dic3C2412yes—
428C2×C3×Dic3C2412yes—
429C2×C3×Dic3C2412yes—
430C3×D12—42no—
431C3×C4×D3—24no—
432C3×C4×D3—24no—
433C3×C4×D3—42no—
434C3×C4×D3—42no—
435C3×Dic6—42no—
436#627—22no—
437#627—42no—
438#626—24no—
439#626—42no—
440#626—42no—
441#625—22no—
442#625—42no—
443#624—22no—
444#624—42no—
445D3×Dic3—24no—
446#542—92no—
447#542—92no—
448#541—92no—
449#540—92no—
450#539—92no—
451#539—92no—
452#538—92no—
453#538—92no—
454#533—91no—
455#532—91no—
456#529—32no—
457#529—92no—
458#529—92no—
459#529—92no—
460#525—91no—
461#525—91no—
462C4×#41—91no—
463C4×#41—91no—
464C2×#117—91no—
465C23×D3—32no—
466C2×C3×Q8—32no—
467C2×C3×D4—32no—
468C2×C3×D4—32no—
469C2×C3×D4—32no—
470C22×C3×C4—21no—
471C22×C3×C4—32no—
472C22×C3×C4—32no—
473C22×C3×C4—32no—
474C22×C3×C4—32no—
475C22×C3×C4C22×D312yes—
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—61no—
485C2×#67—61no—
486C2×#67C22×D312yes—
487C2×#67C22×D312yes—
488C22×Dic3—32no—
489C22×Dic3—32no—
490C22×Dic3—32no—
491C22×Dic3—62no—
492#235—68no—
493#235—68no—
494#235—68no—
495C2×D12—32no—
496C2×D12—32no—
497C2×D12—32no—
498C2×D12—32no—
499C2×D12—61no—
500C2×D12C22×D312yes—
501C2×C4×D3—32no—
502C2×C4×D3—32no—
503C2×C4×D3—32no—
504C2×C4×D3—32no—
505C2×C4×D3—32no—
506C2×C4×D3—32no—
507C2×C4×D3—32no—
508C2×C4×D3—32no—
509C2×C4×D3—32no—
510C2×C4×D3—32no—
511C2×C4×D3—61no—
512C2×C4×D3—61no—
513C2×C4×D3—62no—
514C2×C4×D3—62no—
515C2×C4×D3—68no—
516C2×C4×D3C22×D312yes—
517C2×C4×D3C22×D312yes—
518C2×C4×D3C22×D312yes—
519C2×C4×D3C22×D312yes—
520C2×Dic6—32no—
521C2×Dic6—32no—
522C2×Dic6—32no—
523C2×Dic6—32no—
524C2×Dic6—61no—
525C2×Dic6C22×D312yes—
526C3×C4⋊C4—22no—
527C3×C4⋊C4—32no—
528C3×C4⋊C4—32no—
529C3×C4⋊C4—32no—
530C3×C4⋊C4—32no—
531C3×C4⋊C4—32no—
532C3×C4⋊C4—32no—
533C3×C4⋊C4—32no—
534C3×C4⋊C4—32no—
535C3×C4⋊C4C22×D312yes—
536C3×C4⋊C4C22×D312yes—
537C3×C22⋊C4—22no—
538C3×C22⋊C4—32no—
539C3×C22⋊C4—32no—
540C3×C22⋊C4—32no—
541C3×C22⋊C4—32no—
542C3×C22⋊C4—32no—
543C3×C22⋊C4—32no—
544C3×C22⋊C4—32no—
545C3×C22⋊C4—32no—
546C3×C22⋊C4C22×D312yes—
547C3×C22⋊C4C22×D312yes—
548C3×C42—21no—
549C3×C42—21no—
550C3×C42—32no—
551C3×C42—32no—
552C3×C42—32no—
553C3×C42—32no—
554C3×C42C22×D312yes—
555C3×C42C22×D312yes—
556#217—32no—
557#217—32no—
558#217—32no—
559#217—32no—
560#217—32no—
561#217—32no—
562#217—32no—
563#217—32no—
564#217C22×D312yes—
565#217C22×D312yes—
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—32no—
576(C2×D3)⋊C4—32no—
577(C2×D3)⋊C4—32no—
578(C2×D3)⋊C4—32no—
579(C2×D3)⋊C4—32no—
580(C2×D3)⋊C4—32no—
581(C2×D3)⋊C4—32no—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—62no—
585(C2×D3)⋊C4—62no—
586(C2×D3)⋊C4C22×D312yes—
587(C2×D3)⋊C4C22×D312yes—
588(C2×D3)⋊C4C22×D312yes—
589(C2×D3)⋊C4C22×D312yes—
590(C2×D3)⋊C4C22×D312yes—
591(C2×D3)⋊C4C22×D312yes—
592C4⋊Dic3—32no—
593C4⋊Dic3—32no—
594C4⋊Dic3—32no—
595C4⋊Dic3—32no—
596C4⋊Dic3—32no—
597C4⋊Dic3—32no—
598C4⋊Dic3—32no—
599C4⋊Dic3—32no—
600C4⋊Dic3C22×D312yes—
601C4⋊Dic3C22×D312yes—
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—32no—
620Dic3⋊C4—62no—
621Dic3⋊C4—62no—
622Dic3⋊C4C22×D312yes—
623Dic3⋊C4C22×D312yes—
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—61no—
639C4×Dic3—62no—
640C4×Dic3—62no—
641C4×Dic3—61no—
642C4×Dic3—62no—
643C4×Dic3C22×D312yes—
644C4×Dic3C22×D312yes—
645C4×Dic3C22×D312yes—
646C4×Dic3C22×D312yes—
647C22×C32—21no—
648C22×C32—22no—
649C22×C32C2511yescharacteristic
650C2×C3⋊D3—21no—
651C2×C3⋊D3—22no—
652C2×C3⋊D3—22no—
653C2×C3⋊D3C2×#4112yes—
654C2×C3×D3—22no—
655C2×C3×D3—22no—
656C2×C3×D3—22no—
657C2×C3×D3—22no—
658C2×C3×D3—22no—
659C2×C3×D3—22no—
660D32—44no—
661C32×C4—21no—
662C32×C4—22no—
663C32×C4—22no—
664C32×C4C2×#4112yes—
665C3⋊Dic3—21no—
666C3⋊Dic3—22no—
667C3⋊Dic3—22no—
668C3⋊Dic3C2×#4112yes—
669C3×Dic3—22no—
670C3×Dic3—22no—
671C3×Dic3—22no—
672C3×Dic3—22no—
673C3×Dic3—22no—
674C3×Dic3—22no—
675C2×#41—91no—
676C2×#41—91no—
677C23×C4—91no—
678C4⋊Q8—91no—
679C4⋊Q8—92no—
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—91no—
698#124—91no—
699#124—92no—
700#123—32no—
701#123—32no—
702#123—91no—
703#123—92no—
704#123—92no—
705#123—92no—
706#123—92no—
707#123—92no—
708#123—92no—
709#123—91no—
710#123—92no—
711C22⋊Q8—32no—
712C22⋊Q8—92no—
713C22⋊Q8—92no—
714C22⋊Q8—92no—
715C22⋊Q8—92no—
716C22⋊Q8—92no—
717C22⋊Q8—92no—
718C22⋊Q8—92no—
719#121—32no—
720#121—92no—
721#121—92no—
722#121—92no—
723#121—92no—
724#121—92no—
725#121—92no—
726#121—92no—
727#120—91no—
728#120—92no—
729#120—91no—
730C4×Q8—32no—
731C4×Q8—92no—
732C4×Q8—92no—
733C4×Q8—92no—
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—92no—
746#117—32no—
747#117—91no—
748#117—92no—
749#117—92no—
750#117—92no—
751#117—92no—
752#117—91no—
753#117—91no—
754#117D3211yescharacteristic, complemented
755C2×C4⋊C4—92no—
756C2×C22⋊C4—92no—
757C2×C42—32no—
758C2×C42—91no—
759C2×C42—91no—
760C2×C42—91no—
761C2×C42—91no—
762C23×C3—21no—
763C23×C3—32no—
764C23×C3—32no—
765C23×C3C23×D312yes—
766C22×D3—32no—
767C22×D3—32no—
768C22×D3—61no—
769C22×D3—61no—
770C22×D3—64no—
771C22×D3—122no—
772C22×D3—122no—
773C22×D3C23×D312yes—
774C22×D3C23×D312yes—
775C3×Q8—122no—
776C3×D4—122no—
777C3×D4—122no—
778C3×D4—122no—
779C2×C3×C4—24no—
780C2×C3×C4—24no—
781C2×C3×C4—21no—
782C2×C3×C4—22no—
783C2×C3×C4—22no—
784C2×C3×C4—21no—
785C2×C3×C4—32no—
786C2×C3×C4—32no—
787C2×C3×C4—32no—
788C2×C3×C4—32no—
789C2×C3×C4—32no—
790C2×C3×C4—32no—
791C2×C3×C4—64no—
792C2×C3×C4—64no—
793C2×C3×C4—122no—
794C2×C3×C4—122no—
795C2×C3×C4C23×D312yes—
796C2×C3×C4C23×D312yes—
797C2×C3×C4C23×D312yes—
798C2×C3×C4C23×D312yes—
799C2×C3×C4C23×D312yes—
800C2×C3×C4C23×D312yes—
801#67—42no—
802#67—42no—
803#67—64no—
804#67—64no—
805#67—64no—
806#67—64no—
807#67—64no—
808#67—64no—
809#67—122no—
810#67—122no—
811#67—122no—
812#67—122no—
813C2×Dic3—32no—
814C2×Dic3—32no—
815C2×Dic3—32no—
816C2×Dic3—32no—
817C2×Dic3—32no—
818C2×Dic3—32no—
819C2×Dic3—62no—
820C2×Dic3—61no—
821C2×Dic3—61no—
822C2×Dic3—62no—
823C2×Dic3—64no—
824C2×Dic3—122no—
825C2×Dic3—122no—
826C2×Dic3—124no—
827C2×Dic3C23×D312yes—
828C2×Dic3C23×D312yes—
829C2×Dic3C23×D312yes—
830C2×Dic3C23×D312yes—
831C2×Dic3C23×D312yes—
832C2×Dic3C23×D312yes—
833D12—42no—
834D12—64no—
835D12—64no—
836D12—64no—
837D12—122no—
838D12—122no—
839C4×D3—24no—
840C4×D3—24no—
841C4×D3—38no—
842C4×D3—42no—
843C4×D3—42no—
844C4×D3—64no—
845C4×D3—64no—
846C4×D3—64no—
847C4×D3—64no—
848C4×D3—64no—
849C4×D3—122no—
850C4×D3—122no—
851C4×D3—122no—
852C4×D3—122no—
853C4×D3—122no—
854C4×D3—122no—
855C4×D3—124no—
856C4×D3—124no—
857Dic6—42no—
858Dic6—64no—
859Dic6—64no—
860Dic6—64no—
861Dic6—122no—
862Dic6—122no—
863C2×C32—41no—
864C2×C32C22×#4111yescharacteristic
865C2×C32#58512yes—
866C3⋊D3—22no—
867C3⋊D3—41no—
868C3×D3—42no—
869C3×D3—42no—
870C24—91no—
871#41—184no—
872#41—184no—
873C2×Q8—32no—
874C2×Q8—91no—
875C2×Q8—92no—
876C2×Q8—91no—
877C2×D4—32no—
878C2×D4—32no—
879C2×D4—32no—
880C2×D4—92no—
881C2×D4—92no—
882C2×D4—92no—
883C2×D4—91no—
884C2×D4—91no—
885C2×D4—91no—
886C2×D4—92no—
887C2×D4—91no—
888C22×C4—32no—
889C22×C4—32no—
890C22×C4—32no—
891C22×C4—32no—
892C22×C4—91no—
893C22×C4—92no—
894C22×C4—92no—
895C22×C4—91no—
896C22×C4—92no—
897C22×C4—91no—
898C22×C4—92no—
899C22×C4—92no—
900C22×C4—184no—
901C22×C4C2×D3211yescharacteristic
902C4⋊C4—32no—
903C4⋊C4—32no—
904C4⋊C4—32no—
905C4⋊C4—32no—
906C4⋊C4—32no—
907C4⋊C4—32no—
908C4⋊C4—32no—
909C4⋊C4—32no—
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—92no—
919C4⋊C4—92no—
920C4⋊C4—92no—
921C4⋊C4—92no—
922C4⋊C4—92no—
923C4⋊C4C2×D3212yes—
924C22⋊C4—32no—
925C22⋊C4—32no—
926C22⋊C4—32no—
927C22⋊C4—32no—
928C22⋊C4—32no—
929C22⋊C4—32no—
930C22⋊C4—32no—
931C22⋊C4—32no—
932C22⋊C4—91no—
933C22⋊C4—91no—
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—
943C22⋊C4—92no—
944C22⋊C4—92no—
945C22⋊C4—92no—
946C22⋊C4C2×D3212yes—
947C42—32no—
948C42—32no—
949C42—32no—
950C42—32no—
951C42—91no—
952C42—91no—
953C42—92no—
954C42—92no—
955C42—92no—
956C42—91no—
957C42—91no—
958C42C2×D3211yescharacteristic
959C42C2×D3211yescharacteristic
960C22×C3—22no—
961C22×C3—22no—
962C22×C3—22no—
963C22×C3—22no—
964C22×C3—21no—
965C22×C3—42no—
966C22×C3—62no—
967C22×C3—62no—
968C22×C3—62no—
969C22×C3—62no—
970C22×C3—62no—
971C22×C3—62no—
972C22×C3C24×D312yes—
973C2×D3—22no—
974C2×D3—22no—
975C2×D3—22no—
976C2×D3—22no—
977C2×D3—22no—
978C2×D3—22no—
979C2×D3—34no—
980C2×D3—62no—
981C2×D3—62no—
982C2×D3—62no—
983C2×D3—62no—
984C2×D3—62no—
985C2×D3—62no—
986C2×D3—62no—
987C2×D3—122no—
988C2×D3—122no—
989C2×D3—128no—
990C3×C4—22no—
991C3×C4—22no—
992C3×C4—22no—
993C3×C4—22no—
994C3×C4—22no—
995C3×C4—22no—
996C3×C4—22no—
997C3×C4—42no—
998C3×C4—42no—
999C3×C4—62no—
1000C3×C4—62no—
1001C3×C4—62no—
1002C3×C4—62no—
1003C3×C4—62no—
1004C3×C4—62no—
1005C3×C4D3×#4114yes—
1006Dic3—22no—
1007Dic3—22no—
1008Dic3—22no—
1009Dic3—22no—
1010Dic3—22no—
1011Dic3—22no—
1012Dic3—34no—
1013Dic3—62no—
1014Dic3—62no—
1015Dic3—64no—
1016Dic3—62no—
1017Dic3—62no—
1018Dic3—62no—
1019Dic3—62no—
1020Dic3—62no—
1021Dic3—122no—
1022C32#345511yescharacteristic, complemented, Sylow
1023C23—32no—
1024C23—32no—
1025C23—91no—
1026C23—91no—
1027C23—182no—
1028C23—362no—
1029C23C22×D3211yescharacteristic
1030Q8—122no—
1031Q8—182no—
1032Q8—182no—
1033Q8—362no—
1034D4—122no—
1035D4—122no—
1036D4—122no—
1037D4—182no—
1038D4—184no—
1039D4—182no—
1040D4—182no—
1041D4—182no—
1042D4—362no—
1043D4—362no—
1044D4—362no—
1045C2×C4—22no—
1046C2×C4—32no—
1047C2×C4—32no—
1048C2×C4—32no—
1049C2×C4—32no—
1050C2×C4—32no—
1051C2×C4—32no—
1052C2×C4—64no—
1053C2×C4—64no—
1054C2×C4—91no—
1055C2×C4—94no—
1056C2×C4—92no—
1057C2×C4—91no—
1058C2×C4—92no—
1059C2×C4—122no—
1060C2×C4—122no—
1061C2×C4—182no—
1062C2×C4—184no—
1063C2×C4—182no—
1064C2×C4—362no—
1065C2×C4—362no—
1066C2×C4—362no—
1067C2×C4—362no—
1068C2×C4C22×D3212yes—
1069C2×C4C22×D3211yescharacteristic
1070C2×C4C22×D3212yes—
1071C2×C4C22×D3211yescharacteristic
1072C2×C3—21no—
1073C2×C3—22no—
1074C2×C3—42no—
1075C2×C3—42no—
1076C2×C3—122no—
1077C2×C3—122no—
1078C2×C3C2×D3×#4112yes—
1079C2×C3#596412yes—
1080C2×C3#596412yes—
1081D3—42no—
1082D3—42no—
1083D3—64no—
1084D3—122no—
1085D3—122no—
1086D3—122no—
1087C22—21no—
1088C22—22no—
1089C22—62no—
1090C22—62no—
1091C22—62no—
1092C22—62no—
1093C22—62no—
1094C22—62no—
1095C22—92no—
1096C22—182no—
1097C22—181no—
1098C22—182no—
1099C22—364no—
1100C22C23×D3211yescharacteristic
1101C4—21no—
1102C4—22no—
1103C4—22no—
1104C4—62no—
1105C4—62no—
1106C4—62no—
1107C4—62no—
1108C4—62no—
1109C4—62no—
1110C4—92no—
1111C4—181no—
1112C4—182no—
1113C4—182no—
1114C4#6430612yes—
1115C3—21no—
1116C3#8614612yescomplemented
1117C2—41no—
1118C2—122no—
1119C2—122no—
1120C2—182no—
1121C2—361no—
1122C2C2×#6430611yescharacteristic
1123C2#1059669512yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595993C2semidirect
2. C3×#5528C2semidirect
3. #10595076C2semidirect
4. #10595033C2semidirect
5. #10595017C2semidirect
6. #10594657C2semidirect
7. #10594574C2semidirect
8. #10594567C2semidirect
9. #10594474C2semidirect
10. #10594306C2semidirect
11. #10594227C2semidirect
12. #10594152C2semidirect
13. #10594151C2semidirect
14. #10594006C2semidirect
15. #10593992C2semidirect
16. #10593973C2semidirect
17. C4×#3798C2semidirect
18. #10593935C2semidirect
19. #10593875C2semidirect
24. C32×#117C22semidirect
25. C2×C4×C3⋊Dic3C22semidirect
27. #64096C22semidirect
29. #64090C22semidirect
31. #64081C22semidirect
33. C42×C3⋊D3C22semidirect
35. C3×C4×#67C22semidirect
37. C3×#896C22semidirect
39. C3×#889C22semidirect
42. C3×#883C22semidirect
43. C3×#879C22semidirect
46. C3×C42×D3C22semidirect
47. C3×C4×Dic6C22semidirect
49. #63982C22semidirect
51. #63979C22semidirect
55. #63962C22semidirect
57. #63953C22semidirect
61. C4×#627C22semidirect
62. C4×#627C22semidirect
65. #63913C22semidirect
72. C4×#626C22semidirect
74. C4×#625C22semidirect
86. #63872C22semidirect
87. #63871C22semidirect
88. #63870C22semidirect
89. #63868C22semidirect
90. #63867C22semidirect
94. #63862C22semidirect
95. #63862C22semidirect
98. #63855C22semidirect
101. #63853C22semidirect
103. #63851C22semidirect
104. #63850C22semidirect
105. #63847C22semidirect
106. #63840C22semidirect
107. #63839C22semidirect
134. #5528D3semidirect
249. C3×#117C2×D3semidirect
279. C4×#67C2×D3semidirect
298. #896C2×D3semidirect
321. #889C2×D3semidirect
346. #883C2×D3semidirect
362. #879C2×D3semidirect
390. C42×D3C2×D3semidirect
396. C4×Dic6C2×D3semidirect
754. #117D32semidirect
1022. C32#3455semidirect
1116. C3#86146semidirect

Maximal subgroups

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

subgroupindex
#105959932
C3×#55282
#105950762
#105950332
#105950172
#105946572
#105945742
#105945672
#105944742
#105943062
#105942272
#105941522
#105941512
#105940062
#105939922
#105939732
C4×#37982
#105939352
#105938752
#861463