Finite Group Databasebeta

← #11904771

Subgroups — #11904771

Order 1152.

3191 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3#10596304C211yesmaximal, characteristic, complemented
4C3×#5828C211yesmaximal, characteristic, complemented
5D3×#946C212yesmaximal, complemented
6#10595397C212yesmaximal, complemented
7#10595304C214yesmaximal, complemented
8#10595301C212yesmaximal, complemented
9#10595232C212yesmaximal, complemented
10#10595149C214yesmaximal, complemented
11#10595067C212yesmaximal, complemented
12#10594992C211yesmaximal, characteristic, complemented
13#10594902C212yesmaximal, complemented
14Dic6×#67C212yesmaximal, complemented
15#10594887C212yesmaximal, complemented
16#10594866C211yesmaximal, characteristic, complemented
17C2×#63856C211yesmaximal, characteristic, complemented
18#87295—31nomaximal
19#86042—31nomaximal
20C2×C32×#41C2211yescharacteristic, complemented
21C2×#3828C2211yescharacteristic
22C3×#1010—28no—
23C2×C3×D3×Q8C2212yescomplemented
24C2×C3×#237C2214yescomplemented
25C2×C3×#237C2212yescomplemented
26C2×C3×#235C2211yescharacteristic
27C2×C3×#235C2212yescomplemented
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×Dic6C2211yescharacteristic, complemented
30C22×C3×Dic6C2212yescomplemented
31C2×D3×#67C2212yes—
32C2×#3804C2212yes—
33D3×#235—28no—
34C2×D3×D12C2211yescharacteristic
35C2×C4×D32C2212yes—
36C2×#3799C2211yescharacteristic
37C2×#3798C2212yes—
38C2×#3795C2211yescharacteristic
39C2×D3×Dic6C2211yescharacteristic
40#64155C2212yescomplemented
41#64148C2214yescomplemented
42#64147C2212yescomplemented
43#64139C2212yescomplemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#64133C2212yescomplemented
46C3×#946C2211yescharacteristic
47C3×#946C2211yescharacteristic, complemented
48C3×#938C2211yescharacteristic
49C3×#938C2211yescharacteristic, complemented
50C3×#937C2212yes—
51C3×#935C2212yescomplemented
52C3×C4×#67C2212yes—
53C3×C4×#67C2212yescomplemented
54C3×#926C2211yescharacteristic, complemented
55#63983C2214yes—
56#63978C2214yescomplemented
57#67⋊Dic3C2214yescomplemented
58Dic3×#67C2214yes—
59#63971C2214yescomplemented
60#63970C2214yescomplemented
61#63969C2214yescomplemented
62C2×#3724C2212yescomplemented
63#63966C2214yescomplemented
64#63964C2214yescomplemented
65C2×(C2×D3)⋊Dic3C2212yes—
66#63952C2214yescomplemented
67D3×(C2×D3)⋊C4C2214yes—
68#63907C2214yescomplemented
69#63905C2214yescomplemented
70Dic3×D12C2212yescomplemented
71D3×C4⋊Dic3C2212yescomplemented
72#63888C2214yescomplemented
73#63887C2214yes—
74D3×Dic3⋊C4C2214yescomplemented
75#63871C2212yescomplemented
76#63871C2212yescomplemented
77#63866C2212yescomplemented
78#63864C2212yescomplemented
79#63856C2212yes—
80#63856C2212yes—
81#63856C2212yescomplemented
82#63856C2212yescomplemented
83#63850C2214yescomplemented
84Dic3×Dic6C2212yescomplemented
85#63841C2212yescomplemented
86#63839C2214yescomplemented
87C2×C3×2−1+4—31no—
88C2×#1010D311yescharacteristic, complemented
89C2×D3×#41—31no—
90C22×#235—31no—
91C3×#525—31no—
92#5833—31no—
93#5833—31no—
94#5833—32no—
95#5833—61no—
96#5829—34no—
97#5829—32no—
98#5828—32no—
99#5828D311yescharacteristic, complemented
100#5827—31no—
101#5824—34no—
102#5824—32no—
103#5817—32no—
104#5816—32no—
105#5816—31no—
106Q8×#67—32no—
107C2×#946—31no—
108C2×#946—32no—
109C2×#924—31no—
110#5655—34no—
111#5628—32no—
112D3×C22⋊Q8—32no—
113#5608—32no—
114#5606—32no—
115#5591—34no—
116#5552—32no—
117#5551—32no—
118#5550—32no—
119D4×Dic6—32no—
120#5526—31no—
121#5523—31no—
122C23×C3×D3C2311yescharacteristic
123C22×D32C2312yes—
124C32×#41—24no—
125C2×C32×Q8C2311yescharacteristic
126C2×C32×D4C2312yes—
127C2×C32×D4C2311yescharacteristic
128C22×C32×C4C2312yes—
129C22×C32×C4C2311yescharacteristic
130C2×#638C2312yes—
131C2×#638C2314yes—
132C22×C3⋊Dic3C2312yes—
133#3828—24no—
134C2×C4⋊(C3⋊D3)C2311yescharacteristic
135C2×C4×C3⋊D3C2312yes—
136C2×#634C2311yescharacteristic
137C2×C3×#67C2312yes—
138C2×C3×#67C2314yes—
139C2×C3×#67C2312yes—
140C2×C3×#67C2312yes—
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2314yes—
143C22×C3×Dic3C2312yes—
144C3×D3×Q8—28no—
145C3×#237—216no—
146C3×#237—28no—
147C3×#235—28no—
148C3×#235D418yescomplemented
149C2×C3×D12C2311yescharacteristic
150C2×C3×C4×D3—24no—
151C2×C3×C4×D3C2311yescharacteristic
152C2×C3×C4×D3C2311yescharacteristic
153C2×C3×C4×D3C2311yescharacteristic
154C2×C3×C4×D3C2311yescharacteristic
155C2×C3×C4×D3C2314yes—
156C2×C3×C4×D3C2312yes—
157C2×C3×Dic6—24no—
158C2×C3×Dic6—28no—
159C2×C3×Dic6C2312yes—
160C2×C3×Dic6C2314yes—
161C2×C3×Dic6C2312yes—
162C2×C3×Dic6C2311yescharacteristic
163D3×#67—28no—
164C2×#627C2312yes—
165C2×#626C2312yes—
166C2×#626C2312yes—
167C2×#625C2312yes—
168C2×#624C2312yes—
169#3804—28no—
170C2×D3×Dic3C2312yes—
171C2×D3×Dic3C2312yes—
172C2×D3×Dic3C2314yes—
173D3×D12—24no—
174C4×D32—28no—
175#3799—24no—
176#3798—28no—
177#3795—24no—
178D3×Dic6—24no—
179#3757C2314yes—
180#3752C2314yes—
181C4⋊(C3⋊Dic3)C2312yes—
182C4⋊(C3⋊Dic3)C2312yes—
183#3750C2314yes—
184C3×#217C2312yes—
185C3×#217C2312yes—
186C3×#217C2312yes—
187C3×(C2×D3)⋊C4C2312yes—
188C3×(C2×D3)⋊C4C2312yes—
189C3×C4⋊Dic3C2311yescharacteristic
190C3×C4⋊Dic3C2311yescharacteristic
191C3×Dic3⋊C4C2312yes—
192C3×Dic3⋊C4C2312yes—
193C3×C4×Dic3C2312yes—
194#3724C2314yes—
195#3724C2314yes—
196Dic3⋊Dic3C2314yes—
197Dic3⋊Dic3C2314yes—
198Dic3⋊Dic3C2314yes—
199#3722C2314yes—
200#3722C2314yes—
201(C2×D3)⋊Dic3C2314yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204Dic32C2314yes—
205#3489—91noSylow
206C3×2−1+4—68no—
207C2×C3×#41—21no—
208C2×C3×#41—34no—
209C2×C3×#41—32no—
210C2×C3×#41—31no—
211C2×C3×#41—32no—
212C2×C3×#41C2×D311yescharacteristic, complemented
213C2×C3×#41C2×D311yescharacteristic, complemented
214C22×C3×Q8—32no—
215C22×C3×Q8—31no—
216C22×C3×Q8—32no—
217C23×C3×C4—31no—
218C22×#67—32no—
219#1010—28no—
220D3×#41—68no—
221C2×#239—31no—
222C2×D3×Q8—31no—
223C2×D3×Q8C2×D312yescomplemented
224C2×#237—32no—
225C2×#237—31no—
226C2×#237C2×D314yescomplemented
227C2×#237C2×D312yescomplemented
228C2×D3×D4—32no—
229C2×D3×D4—31no—
230C2×#235—31no—
231C2×#235—31no—
232C2×#235—32no—
233C2×#235—31no—
234C2×#235—32no—
235C2×#235—32no—
236C2×#235—31no—
237C2×#235—61no—
238C2×#235—68no—
239C2×#235C2×D311yescharacteristic
240C2×#235C2×D312yescomplemented
241C22×D12—31no—
242C22×C4×D3—32no—
243C22×C4×D3—32no—
244C22×C4×D3C2×D311yescharacteristic
245C22×Dic6—31no—
246C22×Dic6C2×D311yescharacteristic, complemented
247C22×Dic6C2×D312yescomplemented
248C3×#123—32no—
249C3×C22⋊Q8—31no—
250C3×C22⋊Q8—31no—
251C3×#121—31no—
252C3×#121—31no—
253C3×#120—32no—
254C3×C4×D4—32no—
255C3×C4×D4—32no—
256C3×#117—31no—
257C2×#217—32no—
258#947—34no—
259#947—32no—
260#946—32no—
261#946—32no—
262#946—32no—
263#946—32no—
264#946—32no—
265#946—32no—
266#946—34no—
267#946—32no—
268#946—32no—
269#946—34no—
270#946—62no—
271#946C2×D311yescharacteristic
272#946C2×D311yescharacteristic, complemented
273Q8×Dic3—32no—
274#944—34no—
275#944—32no—
276#939—34no—
277#939—34no—
278#939—34no—
279#939—34no—
280#939—34no—
281#939—64no—
282#938—32no—
283#938—32no—
284#938—34no—
285#938—62no—
286#938C2×D311yescharacteristic
287#938C2×D311yescharacteristic, complemented
288#937—34no—
289#937—34no—
290#937C2×D312yes—
291#935—34no—
292#935C2×D312yescomplemented
293D4×Dic3—34no—
294D4×Dic3—34no—
295D4×Dic3—32no—
296#930—32no—
297#930—32no—
298#930—34no—
299#930—62no—
300#929—34no—
301#929—34no—
302#929—34no—
303C4×#67—34no—
304C4×#67—34no—
305C4×#67C2×D312yes—
306C4×#67C2×D312yescomplemented
307C2×(C2×D3)⋊C4—32no—
308C2×(C2×D3)⋊C4—34no—
309#926—32no—
310#926C2×D311yescharacteristic, complemented
311C2×C4⋊Dic3—31no—
312C2×C4⋊Dic3—31no—
313C2×C4⋊Dic3—32no—
314C2×C4⋊Dic3—61no—
315#924—32no—
316#924—32no—
317#924—32no—
318#924—32no—
319#924—32no—
320#924—32no—
321#924—34no—
322#924—62no—
323C2×Dic3⋊C4—32no—
324C2×Dic3⋊C4—32no—
325C2×Dic3⋊C4—34no—
326#897—32no—
327#897—32no—
328#896—34no—
329#894—34no—
330#892—32no—
331D3×C4⋊C4—34no—
332D3×C4⋊C4—32no—
333#888—34no—
334#886—34no—
335#885—34no—
336#884—34no—
337#883—34no—
338#883—34no—
339#67⋊C4—34no—
340#67⋊C4—34no—
341D3×C22⋊C4—34no—
342#878—34no—
343#878—34no—
344#875—32no—
345C4×D12—32no—
346#869—32no—
347C4×Dic6—32no—
348C23×C32C2412yes—
349C23×C32C2411yescharacteristic
350C22×C3⋊D3C2412yes—
351C22×C3×D3—22no—
352C22×C3×D3—22no—
353C22×C3×D3—41no—
354C22×C3×D3C2411yescharacteristic
355C22×C3×D3C2412yes—
356C22×C3×D3C2411yescharacteristic
357C2×D32—24no—
358C2×D32—24no—
359C2×D32—42no—
360C32×Q8—22no—
361C32×D4—24no—
362C32×D4—22no—
363C2×C32×C4—24no—
364C2×C32×C4C2×D414yes—
365C2×C32×C4C2412yes—
366C2×C32×C4C2411yescharacteristic
367C2×C32×C4C2411yescharacteristic
368#638—24no—
369#638—44no—
370C2×C3⋊Dic3—42no—
371C2×C3⋊Dic3C2414yes—
372C2×C3⋊Dic3C2412yes—
373C4⋊(C3⋊D3)—22no—
374C4×C3⋊D3—24no—
375#634—22no—
376C3×#67—28no—
377C3×#67—24no—
378C3×#67—42no—
379C3×#67C2×D418yes—
380C2×C3×Dic3—22no—
381C2×C3×Dic3—24no—
382C2×C3×Dic3—28no—
383C2×C3×Dic3C2412yes—
384C2×C3×Dic3C2414yes—
385C2×C3×Dic3C2412yes—
386C2×C3×Dic3C2411yescharacteristic
387C2×C3×Dic3C2411yescharacteristic
388C2×C3×Dic3C2412yes—
389C3×D12C2×D414yes—
390C3×C4×D3—28no—
391C3×C4×D3—22no—
392C3×C4×D3—22no—
393C3×C4×D3—22no—
394C3×C4×D3—22no—
395C3×C4×D3C2×D418yes—
396C3×Dic6—24no—
397C3×Dic6—24no—
398C3×Dic6—28no—
399C3×Dic6C2×D414yes—
400#627—24no—
401#626—24no—
402#626—24no—
403#625—24no—
404#624—24no—
405D3×Dic3—24no—
406D3×Dic3—24no—
407D3×Dic3—44no—
408C2×2−1+4—31no—
409C22×#41—91no—
410D4×Q8—92no—
411#548—92no—
412#547—92no—
413#547—94no—
414#546—92no—
415#546—94no—
416#537—92no—
417#537—91no—
418#536—91no—
419#536—92no—
420#525—31no—
421#525—92no—
422C2×C22⋊Q8—92no—
423C2×C22⋊Q8—91no—
424#520—91no—
425C24×C3—31no—
426C23×D3—32no—
427C23×D3—32no—
428C23×D3C22×D311yescharacteristic
429C3×#41—24no—
430C3×#41—24no—
431C3×#41—38no—
432C3×#41—44no—
433C3×#41—68no—
434C3×#41—68no—
435C3×#41—616no—
436C2×C3×Q8—21no—
437C2×C3×Q8—31no—
438C2×C3×Q8—34no—
439C2×C3×Q8—32no—
440C2×C3×Q8—32no—
441C2×C3×Q8—68no—
442C2×C3×Q8—68no—
443C2×C3×Q8—64no—
444C2×C3×Q8C22×D311yescharacteristic
445C2×C3×Q8C22×D311yescharacteristic
446C2×C3×D4—21no—
447C2×C3×D4—22no—
448C2×C3×D4—32no—
449C2×C3×D4—32no—
450C2×C3×D4—34no—
451C2×C3×D4—32no—
452C2×C3×D4—31no—
453C2×C3×D4C22×D312yes—
454C2×C3×D4C22×D311yescharacteristic
455C2×C3×D4C22×D311yescharacteristic
456C2×C3×D4C22×D312yes—
457C22×C3×C4—21no—
458C22×C3×C4—22no—
459C22×C3×C4—32no—
460C22×C3×C4—31no—
461C22×C3×C4—32no—
462C22×C3×C4—34no—
463C22×C3×C4—34no—
464C22×C3×C4—31no—
465C22×C3×C4—31no—
466C22×C3×C4—31no—
467C22×C3×C4—31no—
468C22×C3×C4—64no—
469C22×C3×C4C22×D312yes—
470C22×C3×C4C22×D312yes—
471C22×C3×C4C22×D311yescharacteristic
472C22×C3×C4C22×D311yescharacteristic
473C2×#67—32no—
474C2×#67—32no—
475C2×#67—32no—
476C2×#67—32no—
477C2×#67—34no—
478C2×#67—34no—
479C2×#67—32no—
480C2×#67—32no—
481C2×#67—62no—
482C2×#67—64no—
483C2×#67—68no—
484C2×#67C22×D314yes—
485C2×#67C22×D312yes—
486C2×#67C22×D312yes—
487C2×#67C22×D312yes—
488C22×Dic3—32no—
489C22×Dic3—32no—
490C22×Dic3—32no—
491C22×Dic3—32no—
492C22×Dic3—34no—
493C22×Dic3—62no—
494C22×Dic3C22×D314yes—
495C22×Dic3C22×D312yes—
496C22×Dic3C22×D311yescharacteristic
497#239—64no—
498D3×Q8—28no—
499D3×Q8—64no—
500#237—216no—
501#237—28no—
502#237—64no—
503#237—68no—
504D3×D4—64no—
505D3×D4—68no—
506#235—28no—
507#235—68no—
508#235—64no—
509#235—64no—
510#235—68no—
511#235—64no—
512#235—68no—
513#235—64no—
514#235—124no—
515#235#6718yescomplemented
516C2×D12—32no—
517C2×D12—32no—
518C2×D12—31no—
519C2×D12—31no—
520C2×D12—61no—
521C2×D12—64no—
522C2×D12C22×D311yescharacteristic
523C2×C4×D3—24no—
524C2×C4×D3—32no—
525C2×C4×D3—32no—
526C2×C4×D3—32no—
527C2×C4×D3—32no—
528C2×C4×D3—32no—
529C2×C4×D3—32no—
530C2×C4×D3—34no—
531C2×C4×D3—62no—
532C2×C4×D3—68no—
533C2×C4×D3—68no—
534C2×C4×D3C22×D314yes—
535C2×C4×D3C22×D311yescharacteristic
536C2×C4×D3C22×D311yescharacteristic
537C2×C4×D3C22×D311yescharacteristic
538C2×C4×D3C22×D311yescharacteristic
539C2×C4×D3C22×D312yes—
540C2×Dic6—24no—
541C2×Dic6—28no—
542C2×Dic6—31no—
543C2×Dic6—31no—
544C2×Dic6—32no—
545C2×Dic6—32no—
546C2×Dic6—61no—
547C2×Dic6—64no—
548C2×Dic6C22×D312yes—
549C2×Dic6C22×D314yes—
550C2×Dic6C22×D312yes—
551C2×Dic6C22×D311yescharacteristic
552C3×C4⋊C4—32no—
553C3×C4⋊C4—32no—
554C3×C4⋊C4—31no—
555C3×C4⋊C4—31no—
556C3×C22⋊C4—32no—
557C3×C22⋊C4—32no—
558C3×C22⋊C4—32no—
559C3×C22⋊C4—32no—
560C3×C22⋊C4—32no—
561C3×C42—32no—
562#217—34no—
563#217—34no—
564#217—34no—
565#217—34no—
566#217—34no—
567#217—64no—
568#217C22×D312yes—
569#217C22×D312yes—
570#217C22×D312yes—
571(C2×D3)⋊C4—34no—
572(C2×D3)⋊C4—34no—
573(C2×D3)⋊C4—34no—
574(C2×D3)⋊C4—34no—
575(C2×D3)⋊C4—34no—
576(C2×D3)⋊C4—34no—
577(C2×D3)⋊C4—34no—
578(C2×D3)⋊C4—34no—
579(C2×D3)⋊C4—34no—
580(C2×D3)⋊C4—64no—
581(C2×D3)⋊C4C22×D312yes—
582(C2×D3)⋊C4C22×D312yes—
583C4⋊Dic3—32no—
584C4⋊Dic3—32no—
585C4⋊Dic3—32no—
586C4⋊Dic3—32no—
587C4⋊Dic3—34no—
588C4⋊Dic3—34no—
589C4⋊Dic3—34no—
590C4⋊Dic3—62no—
591C4⋊Dic3—62no—
592C4⋊Dic3C22×D311yescharacteristic
593C4⋊Dic3C22×D311yescharacteristic
594Dic3⋊C4—34no—
595Dic3⋊C4—34no—
596Dic3⋊C4—34no—
597Dic3⋊C4—34no—
598Dic3⋊C4—34no—
599Dic3⋊C4—34no—
600Dic3⋊C4—34no—
601Dic3⋊C4—34no—
602Dic3⋊C4—34no—
603Dic3⋊C4—64no—
604Dic3⋊C4C22×D312yes—
605Dic3⋊C4C22×D312yes—
606C4×Dic3—34no—
607C4×Dic3—34no—
608C4×Dic3C22×D312yes—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—22no—
612C22×C32—22no—
613C22×C32—22no—
614C22×C32C22×D412yes—
615C22×C32C2511yescharacteristic
616C2×C3⋊D3—22no—
617C2×C3⋊D3—22no—
618C2×C3⋊D3—22no—
619C2×C3×D3—21no—
620C2×C3×D3—22no—
621C2×C3×D3—22no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—44no—
627C2×C3×D3C22×D414yes—
628C2×C3×D32−1+412yescomplemented
629D32—48no—
630C32×C4—22no—
631C32×C4C22×D412yes—
632C32×C4C22×D412yes—
633C3⋊Dic3—22no—
634C3⋊Dic3—24no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—24no—
638C3×Dic3—22no—
639C3×Dic3—22no—
640C3×Dic3C22×D414yes—
6412−1+4—68no—
642C2×#41—32no—
643C2×#41—34no—
644C2×#41—31no—
645C2×#41—32no—
646C2×#41—92no—
647C2×#41—92no—
648C2×#41—91no—
649C2×#41—91no—
650C2×#41—91no—
651C2×#41—188no—
652C2×#41D3211yescharacteristic, complemented
653C22×Q8—32no—
654C22×Q8—31no—
655C22×Q8—32no—
656C22×Q8—91no—
657C22×D4—91no—
658C22×D4—92no—
659C23×C4—31no—
660C23×C4—92no—
661C4⋊Q8—92no—
662C4⋊Q8—94no—
663#124—92no—
664#124—94no—
665#123—32no—
666#123—94no—
667#123—94no—
668#123—94no—
669#123—94no—
670C22⋊Q8—31no—
671C22⋊Q8—31no—
672C22⋊Q8—94no—
673C22⋊Q8—94no—
674C22⋊Q8—92no—
675C22⋊Q8—94no—
676C22⋊Q8—92no—
677C22⋊Q8—92no—
678C22⋊Q8—92no—
679C22⋊Q8—92no—
680C22⋊Q8—92no—
681C22⋊Q8—92no—
682C22⋊Q8—92no—
683#121—31no—
684#121—31no—
685#121—94no—
686#121—94no—
687#121—94no—
688#121—92no—
689#121—94no—
690#121—92no—
691#120—32no—
692#120—94no—
693C4×Q8—92no—
694C4×D4—32no—
695C4×D4—32no—
696C4×D4—92no—
697C4×D4—94no—
698C4×D4—94no—
699C4×D4—94no—
700#117—31no—
701#117—92no—
702C2×C4⋊C4—92no—
703C2×C4⋊C4—94no—
704C2×C4⋊C4—92no—
705C2×C4⋊C4—91no—
706C2×C22⋊C4—94no—
707C2×C22⋊C4—92no—
708C23×C3—21no—
709C23×C3—22no—
710C23×C3—31no—
711C23×C3—32no—
712C23×C3—31no—
713C23×C3—62no—
714C23×C3—62no—
715C23×C3—121no—
716C23×C3C23×D312yes—
717C23×C3C23×D312yes—
718C23×C3C23×D311yescharacteristic
719C23×C3C23×D311yescharacteristic
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—32no—
723C22×D3—32no—
724C22×D3—41no—
725C22×D3—62no—
726C22×D3—64no—
727C22×D3—64no—
728C22×D3—64no—
729C22×D3—64no—
730C22×D3—122no—
731C22×D3—122no—
732C22×D3C23×D311yescharacteristic
733C22×D3C23×D311yescharacteristic
734C22×D3C23×D312yes—
735C3×Q8—22no—
736C3×Q8—22no—
737C3×Q8—34no—
738C3×Q8—42no—
739C3×Q8—68no—
740C3×Q8—64no—
741C3×Q8—64no—
742C3×D4—24no—
743C3×D4—24no—
744C3×D4—22no—
745C3×D4—22no—
746C3×D4—38no—
747C3×D4—34no—
748C3×D4—42no—
749C3×D4—44no—
750C3×D4—64no—
751C3×D4—68no—
752C3×D4—122no—
753C2×C3×C4—24no—
754C2×C3×C4—24no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—22no—
758C2×C3×C4—24no—
759C2×C3×C4—32no—
760C2×C3×C4—38no—
761C2×C3×C4—32no—
762C2×C3×C4—34no—
763C2×C3×C4—31no—
764C2×C3×C4—31no—
765C2×C3×C4—32no—
766C2×C3×C4—44no—
767C2×C3×C4—68no—
768C2×C3×C4—68no—
769C2×C3×C4—64no—
770C2×C3×C4—62no—
771C2×C3×C4—62no—
772C2×C3×C4—62no—
773C2×C3×C4—62no—
774C2×C3×C4—62no—
775C2×C3×C4D3×D414yes—
776C2×C3×C4C2×#6714yes—
777C2×C3×C4C23×D312yes—
778C2×C3×C4C23×D312yes—
779C2×C3×C4C23×D311yescharacteristic
780C2×C3×C4C23×D311yescharacteristic
781C2×C3×C4C23×D311yescharacteristic
782C2×C3×C4C23×D311yescharacteristic
783#67—24no—
784#67—28no—
785#67—42no—
786#67—64no—
787#67—64no—
788#67—64no—
789#67—64no—
790#67—64no—
791#67—64no—
792#67—124no—
793#67—124no—
794#67—124no—
795#67—244no—
796#67C2×#6718yes—
797C2×Dic3—22no—
798C2×Dic3—24no—
799C2×Dic3—28no—
800C2×Dic3—34no—
801C2×Dic3—34no—
802C2×Dic3—32no—
803C2×Dic3—32no—
804C2×Dic3—62no—
805C2×Dic3—64no—
806C2×Dic3—64no—
807C2×Dic3—64no—
808C2×Dic3—124no—
809C2×Dic3—122no—
810C2×Dic3—122no—
811C2×Dic3—242no—
812C2×Dic3C23×D312yes—
813C2×Dic3C23×D312yes—
814C2×Dic3C23×D311yescharacteristic
815C2×Dic3C23×D311yescharacteristic
816C2×Dic3C23×D314yes—
817C2×Dic3C23×D312yes—
818D12—64no—
819D12—64no—
820D12—62no—
821D12—62no—
822D12—122no—
823D12C2×#6714yes—
824C4×D3—28no—
825C4×D3—22no—
826C4×D3—22no—
827C4×D3—22no—
828C4×D3—22no—
829C4×D3—64no—
830C4×D3—64no—
831C4×D3—64no—
832C4×D3—64no—
833C4×D3—64no—
834C4×D3—64no—
835C4×D3—124no—
836C4×D3—124no—
837C4×D3C2×#6718yes—
838Dic6—24no—
839Dic6—24no—
840Dic6—28no—
841Dic6—64no—
842Dic6—62no—
843Dic6—62no—
844Dic6—64no—
845Dic6—122no—
846Dic6C2×#6714yes—
847C2×C32—22no—
848C2×C32—42no—
849C2×C32C23×D411yescharacteristic
850C2×C32C2×2−1+411yescharacteristic
851C2×C32#58511yescharacteristic
852C3⋊D3—42no—
853C3×D3—22no—
854C3×D3—24no—
855C3×D3—41no—
856C24—31no—
857C24—92no—
858#41—24no—
859#41—38no—
860#41—68no—
861#41—68no—
862#41—616no—
863#41—188no—
864#41—188no—
865#41—184no—
866#41—184no—
867#41—184no—
868C2×Q8—31no—
869C2×Q8—32no—
870C2×Q8—34no—
871C2×Q8—32no—
872C2×Q8—68no—
873C2×Q8—68no—
874C2×Q8—64no—
875C2×Q8—92no—
876C2×Q8—91no—
877C2×Q8—184no—
878C2×Q8C2×D3211yescharacteristic
879C2×D4—32no—
880C2×D4—32no—
881C2×D4—34no—
882C2×D4—32no—
883C2×D4—31no—
884C2×D4—92no—
885C2×D4—92no—
886C2×D4—92no—
887C2×D4—92no—
888C2×D4—94no—
889C2×D4—91no—
890C2×D4—184no—
891C2×D4—188no—
892C2×D4C2×D3212yes—
893C2×D4C2×D3211yescharacteristic
894C22×C4—32no—
895C22×C4—32no—
896C22×C4—31no—
897C22×C4—34no—
898C22×C4—34no—
899C22×C4—31no—
900C22×C4—31no—
901C22×C4—31no—
902C22×C4—31no—
903C22×C4—64no—
904C22×C4—92no—
905C22×C4—92no—
906C22×C4—92no—
907C22×C4—94no—
908C22×C4—92no—
909C22×C4—92no—
910C22×C4—188no—
911C22×C4C2×D3212yes—
912C22×C4C2×D3211yescharacteristic
913C4⋊C4—31no—
914C4⋊C4—32no—
915C4⋊C4—31no—
916C4⋊C4—32no—
917C4⋊C4—94no—
918C4⋊C4—94no—
919C4⋊C4—94no—
920C4⋊C4—94no—
921C4⋊C4—94no—
922C4⋊C4—92no—
923C4⋊C4—92no—
924C4⋊C4—94no—
925C22⋊C4—32no—
926C22⋊C4—32no—
927C22⋊C4—32no—
928C22⋊C4—32no—
929C22⋊C4—32no—
930C22⋊C4—94no—
931C22⋊C4—94no—
932C22⋊C4—94no—
933C22⋊C4—94no—
934C22⋊C4—94no—
935C22⋊C4—94no—
936C22⋊C4—94no—
937C42—32no—
938C42—94no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—22no—
944C22×C3—22no—
945C22×C3—22no—
946C22×C3—22no—
947C22×C3—22no—
948C22×C3—22no—
949C22×C3—22no—
950C22×C3—21no—
951C22×C3—34no—
952C22×C3—32no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—42no—
956C22×C3—42no—
957C22×C3—42no—
958C22×C3—62no—
959C22×C3—62no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—61no—
963C22×C3—61no—
964C22×C3—61no—
965C22×C3—124no—
966C22×C3C2×D3×D412yes—
967C22×C3C22×#6712yes—
968C22×C3C24×D311yescharacteristic
969C22×C3C24×D311yescharacteristic
970C2×D3—21no—
971C2×D3—21no—
972C2×D3—22no—
973C2×D3—22no—
974C2×D3—21no—
975C2×D3—21no—
976C2×D3—21no—
977C2×D3—44no—
978C2×D3—62no—
979C2×D3—62no—
980C2×D3—62no—
981C2×D3—62no—
982C2×D3—62no—
983C2×D3—62no—
984C2×D3—122no—
985C2×D3—122no—
986C2×D3—122no—
987C2×D3—128no—
988C2×D3—128no—
989C2×D3#101012yescomplemented
990C2×D3C22×#6714yes—
991C3×C4—22no—
992C3×C4—22no—
993C3×C4—22no—
994C3×C4—22no—
995C3×C4—34no—
996C3×C4—42no—
997C3×C4—64no—
998C3×C4—62no—
999C3×C4—62no—
1000C3×C4—61no—
1001C3×C4—61no—
1002C3×C4C2×D3×D412yes—
1003C3×C4C2×D3×D412yes—
1004C3×C4C22×#6712yes—
1005C3×C4C22×#6712yes—
1006Dic3—21no—
1007Dic3—21no—
1008Dic3—22no—
1009Dic3—22no—
1010Dic3—24no—
1011Dic3—62no—
1012Dic3—64no—
1013Dic3—64no—
1014Dic3—62no—
1015Dic3—122no—
1016Dic3—124no—
1017Dic3C22×#6714yes—
1018C32#348911yescharacteristic, complemented, Sylow
1019C23—31no—
1020C23—32no—
1021C23—31no—
1022C23—62no—
1023C23—62no—
1024C23—92no—
1025C23—121no—
1026C23—184no—
1027C23—184no—
1028C23—362no—
1029C23C22×D3212yes—
1030C23C22×D3211yescharacteristic
1031Q8—22no—
1032Q8—34no—
1033Q8—68no—
1034Q8—64no—
1035Q8—64no—
1036Q8—184no—
1037Q8—182no—
1038D4—24no—
1039D4—22no—
1040D4—38no—
1041D4—34no—
1042D4—68no—
1043D4—64no—
1044D4—122no—
1045D4—184no—
1046D4—184no—
1047D4—184no—
1048D4—184no—
1049D4—182no—
1050D4—364no—
1051C2×C4—24no—
1052C2×C4—32no—
1053C2×C4—38no—
1054C2×C4—32no—
1055C2×C4—32no—
1056C2×C4—31no—
1057C2×C4—31no—
1058C2×C4—34no—
1059C2×C4—68no—
1060C2×C4—68no—
1061C2×C4—62no—
1062C2×C4—64no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—94no—
1068C2×C4—92no—
1069C2×C4—184no—
1070C2×C4—184no—
1071C2×C4—184no—
1072C2×C4—184no—
1073C2×C4—364no—
1074C2×C4—362no—
1075C2×C4D3×#6714yes—
1076C2×C4C22×D3212yes—
1077C2×C4C22×D3211yescharacteristic
1078C2×C4C22×D3211yescharacteristic
1079C2×C3—22no—
1080C2×C3—22no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—42no—
1085C2×C3—42no—
1086C2×C3—42no—
1087C2×C3—64no—
1088C2×C3—62no—
1089C2×C3—82no—
1090C2×C3—121no—
1091C2×C3C22×D3×D411yescharacteristic
1092C2×C3C2×#101011yescharacteristic
1093C2×C3#596411yescharacteristic
1094C2×C3D3×2−1+411yescharacteristic
1095C2×C3#596811yescharacteristic
1096C2×C3C23×#6711yescharacteristic
1097D3—22no—
1098D3—24no—
1099D3—41no—
1100D3—122no—
1101D3—122no—
1102D3—242no—
1103C22—21no—
1104C22—21no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—32no—
1109C22—34no—
1110C22—62no—
1111C22—62no—
1112C22—61no—
1113C22—61no—
1114C22—61no—
1115C22—61no—
1116C22—61no—
1117C22—124no—
1118C22—182no—
1119C22—182no—
1120C22—182no—
1121C22—368no—
1122C22C2×D3×#6712yes—
1123C22C23×D3211yescharacteristic
1124C4—22no—
1125C4—34no—
1126C4—62no—
1127C4—62no—
1128C4—61no—
1129C4—64no—
1130C4—61no—
1131C4—184no—
1132C4—182no—
1133C4C2×D3×#6712yes—
1134C4C2×D3×#6712yes—
1135C3—21no—
1136C3#8604211yescharacteristic, complemented
1137C3#8729511yescharacteristic, complemented
1138C2—22no—
1139C2—42no—
1140C2—62no—
1141C2—64no—
1142C2—121no—
1143C2—362no—
1144C2D3×#101011yescharacteristic
1145C2#1059669711yescharacteristic
1146C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×D3×#235C2semidirect
3. #10596304C2semidirect
4. C3×#5828C2semidirect
5. D3×#946C2semidirect
6. #10595397C2semidirect
7. #10595304C2semidirect
8. #10595301C2semidirect
9. #10595232C2semidirect
10. #10595149C2semidirect
11. #10595067C2semidirect
12. #10594992C2semidirect
13. #10594902C2semidirect
14. Dic6×#67C2semidirect
15. #10594887C2semidirect
16. #10594866C2semidirect
17. C2×#63856C2semidirect
20. C2×C32×#41C22semidirect
23. C2×C3×D3×Q8C22semidirect
24. C2×C3×#237C22semidirect
25. C2×C3×#237C22semidirect
27. C2×C3×#235C22semidirect
29. C22×C3×Dic6C22semidirect
30. C22×C3×Dic6C22semidirect
40. #64155C22semidirect
41. #64148C22semidirect
42. #64147C22semidirect
43. #64139C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. #64133C22semidirect
47. C3×#946C22semidirect
49. C3×#938C22semidirect
51. C3×#935C22semidirect
53. C3×C4×#67C22semidirect
54. C3×#926C22semidirect
56. #63978C22semidirect
57. #67⋊Dic3C22semidirect
59. #63971C22semidirect
60. #63970C22semidirect
61. #63969C22semidirect
62. C2×#3724C22semidirect
63. #63966C22semidirect
64. #63964C22semidirect
66. #63952C22semidirect
68. #63907C22semidirect
69. #63905C22semidirect
70. Dic3×D12C22semidirect
71. D3×C4⋊Dic3C22semidirect
72. #63888C22semidirect
74. D3×Dic3⋊C4C22semidirect
75. #63871C22semidirect
76. #63871C22semidirect
77. #63866C22semidirect
78. #63864C22semidirect
81. #63856C22semidirect
82. #63856C22semidirect
83. #63850C22semidirect
84. Dic3×Dic6C22semidirect
85. #63841C22semidirect
86. #63839C22semidirect
88. C2×#1010D3semidirect
99. #5828D3semidirect
148. C3×#235D4semidirect
212. C2×C3×#41C2×D3semidirect
213. C2×C3×#41C2×D3semidirect
223. C2×D3×Q8C2×D3semidirect
226. C2×#237C2×D3semidirect
227. C2×#237C2×D3semidirect
240. C2×#235C2×D3semidirect
246. C22×Dic6C2×D3semidirect
247. C22×Dic6C2×D3semidirect
272. #946C2×D3semidirect
287. #938C2×D3semidirect
292. #935C2×D3semidirect
306. C4×#67C2×D3semidirect
310. #926C2×D3semidirect
515. #235#67semidirect
628. C2×C3×D32−1+4semidirect
652. C2×#41D32semidirect
989. C2×D3#1010semidirect
1018. C32#3489semidirect
1136. C3#86042semidirect
1137. C3#87295semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×D3×#2352
#105963042
C3×#58282
D3×#9462
#105953972
#105953042
#105953012
#105952322
#105951492
#105950672
#105949922
#105949022
Dic6×#672
#105948872
#105948662
C2×#638562
#872953
#860423