Finite Group Databasebeta

← #11904773

Subgroups — #11904773

Order 1152.

3191 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10595994C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×#5524C211yesmaximal, characteristic, complemented
6#10595044C211yesmaximal, characteristic, complemented
7C2×#63856C211yesmaximal, characteristic, complemented
8#10594632C212yesmaximal, complemented
9#10594631C212yesmaximal, complemented
10#10594529C212yesmaximal, complemented
11#10594528C212yesmaximal, complemented
12#10594294C214yesmaximal, complemented
13#10594083C214yesmaximal, complemented
14#10594007C212yesmaximal, complemented
15#10593905C212yesmaximal, complemented
16#10593904C212yesmaximal, complemented
17#10593869C212yesmaximal, complemented
18#86356—31nomaximal
19#86042—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic, complemented
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic, complemented
25C2×D3×#67C2212yes—
26C2×#3804C2212yes—
27C2×#3804C2214yescomplemented
28D3×#235—28no—
29C2×D3×D12C2211yescharacteristic
30C2×C4×D32C2212yes—
31C2×#3799C2211yescharacteristic
32C2×#3799C2212yescomplemented
33C2×#3798C2212yes—
34C2×#3797C2212yescomplemented
35#64297—28no—
36C2×#3796C2212yescomplemented
37C2×#3795C2211yescharacteristic
38C2×D3×Dic6C2211yescharacteristic
39C2×D3×Dic6C2212yescomplemented
40C32×#117C2211yescharacteristic, complemented
41C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42#64101C2212yescomplemented
43C4⋊C4×C3⋊D3C2212yescomplemented
44#64090C2214yescomplemented
45C4×C4⋊(C3⋊D3)C2212yescomplemented
46C4×#634C2212yescomplemented
47C3×#897C2211yescharacteristic
48C3×#897C2211yescharacteristic, complemented
49C3×#897C2212yescomplemented
50C3×#897C2212yescomplemented
51C3×#895C2211yescharacteristic
52C3×#895C2211yescharacteristic, complemented
53C3×#886C2212yescomplemented
54C3×#886C2214yescomplemented
55C3×#882C2212yes—
56C3×#875C2212yescomplemented
57C3×C4×D12C2212yes—
58C3×C4×D12C2212yescomplemented
59C3×#869C2212yescomplemented
60#63980C2214yescomplemented
61C2×#3724C2212yescomplemented
62C2×(C2×D3)⋊Dic3C2212yes—
63#63922C2214yes—
64#63921C2214yes—
65#63919C2214yescomplemented
66#63916C2214yescomplemented
67#63915C2214yescomplemented
68#63912C2214yescomplemented
69#63908C2212yescomplemented
70#63908C2212yescomplemented
71#63902C2214yescomplemented
72#63900C2214yescomplemented
73#63899C2214yes—
74#63899C2214yescomplemented
75#63899C2214yescomplemented
76#63898C2214yes—
77#63885C2214yescomplemented
78#63856C2212yes—
79#63856C2212yes—
80#63856C2212yescomplemented
81#63856C2212yescomplemented
82#63856C2212yescomplemented
83#63856C2212yescomplemented
84#63854C2214yescomplemented
85#63854C2214yescomplemented
86#63854C2214yescomplemented
87C2×#1010—31no—
88C2×D3×#41—31no—
89C2×#1007—31no—
90C22×#235—31no—
91C3×#536—31no—
92C3×#525—31no—
93#5833—31no—
94#5833—31no—
95C2×#946—31no—
96C2×#924—31no—
97#5727—32no—
98#5726—32no—
99#5677—32no—
100#5676—32no—
101#5655—34no—
102#5655—34no—
103#5654—34no—
104#5629—32no—
105#5628—32no—
106#5628—32no—
107#5627—32no—
108D3×C22⋊Q8—32no—
109D3×C22⋊Q8—32no—
110#5608—32no—
111#5606—32no—
112#5591—34no—
113#5552—32no—
114#5551—32no—
115#5550—32no—
116D4×Dic6—32no—
117#5526D311yescharacteristic, complemented
118#5524D311yescharacteristic, complemented
119#5523—31no—
120#5523—31no—
121#5523—61no—
122C23×C3×D3C2311yescharacteristic
123C22×D32C2312yes—
124C22×C32×C4C2311yescharacteristic
125C2×#638C2312yes—
126C22×C3⋊Dic3C2312yes—
127#3828D418yescomplemented
128C2×C4⋊(C3⋊D3)C2311yescharacteristic
129C2×C4×C3⋊D3C2314yes—
130C2×C4×C3⋊D3C2312yes—
131C2×#634C2311yescharacteristic
132C2×C3×#67C2312yes—
133C2×C3×#67C2312yes—
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2312yes—
136C3×#235—24no—
137C3×#235—24no—
138C2×C3×D12C2312yes—
139C2×C3×D12C2311yescharacteristic
140C2×C3×D12C2311yescharacteristic
141C2×C3×D12C2312yes—
142C2×C3×C4×D3—24no—
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×C4×D3C2312yes—
146C2×C3×C4×D3C2311yescharacteristic
147C2×C3×C4×D3C2312yes—
148C2×C3×C4×D3C2311yescharacteristic
149C2×C3×Dic6—24no—
150C2×C3×Dic6C2311yescharacteristic
151C2×C3×Dic6C2312yes—
152C2×C3×Dic6C2311yescharacteristic
153C2×C3×Dic6C2312yes—
154D3×#67—28no—
155C2×#627C2312yes—
156C2×#627C2314yes—
157C2×#626C2314yes—
158C2×#626C2312yes—
159C2×#626C2312yes—
160C2×#625C2312yes—
161C2×#625C2314yes—
162C2×#624C2314yes—
163C2×#624C2312yes—
164#3804—216no—
165#3804—28no—
166C2×D3×Dic3C2312yes—
167C2×D3×Dic3C2314yes—
168C2×D3×Dic3C2312yes—
169D3×D12—24no—
170C4×D32—28no—
171#3799—28no—
172#3799—24no—
173#3798—28no—
174#3797—28no—
175#3796—28no—
176#3795—24no—
177D3×Dic6—24no—
178D3×Dic6—28no—
179C32×C4⋊C4C2311yescharacteristic
180C32×C4⋊C4C2311yescharacteristic
181C32×C22⋊C4C2312yes—
182C32×C42C2312yes—
183#3752C2314yes—
184C4⋊(C3⋊Dic3)C2312yes—
185C4⋊(C3⋊Dic3)C2312yes—
186#3750C2314yes—
187C4×C3⋊Dic3C2314yes—
188C3×(C2×D3)⋊C4C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×(C2×D3)⋊C4C2314yes—
193C3×(C2×D3)⋊C4C2314yes—
194C3×C4⋊Dic3C2312yes—
195C3×C4⋊Dic3C2314yes—
196C3×C4⋊Dic3C2312yes—
197C3×C4⋊Dic3C2314yes—
198#3724C2314yes—
199#3724C2314yes—
200#3724C2314yes—
201(C2×D3)⋊Dic3C2314yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204(C2×D3)⋊Dic3C2314yes—
205#3489—91noSylow
206C2×C3×#41—31no—
207C2×C3×#41—31no—
208C22×C3×Q8—31no—
209C23×C3×C4—31no—
210C22×#67—32no—
211#1010—68no—
212D3×#41—68no—
213#1007—68no—
214C2×#239—32no—
215C2×#239—32no—
216C2×#239—31no—
217C2×D3×Q8—31no—
218C2×D3×Q8—32no—
219C2×D3×Q8—32no—
220C2×D3×Q8—32no—
221C2×#237—32no—
222C2×#237—34no—
223C2×#237—31no—
224C2×#237—32no—
225C2×D3×D4—32no—
226C2×D3×D4—31no—
227C2×#235—31no—
228C2×#235—31no—
229C2×#235—34no—
230C2×#235—32no—
231C2×#235—31no—
232C2×#235—32no—
233C2×#235—32no—
234C2×#235—31no—
235C2×#235—32no—
236C2×#235—61no—
237C2×#235—68no—
238C2×#235C2×D311yescharacteristic
239C2×#235C2×D311yescharacteristic, complemented
240C22×D12—31no—
241C22×C4×D3—32no—
242C22×C4×D3—32no—
243C22×C4×D3C2×D311yescharacteristic
244C22×Dic6—31no—
245C22×Dic6—32no—
246C22×Dic6C2×D311yescharacteristic, complemented
247C3×C4⋊Q8—32no—
248C3×#124—32no—
249C3×#123—34no—
250C3×#123—32no—
251C3×C22⋊Q8—31no—
252C3×C22⋊Q8—31no—
253C3×C22⋊Q8—32no—
254C3×C22⋊Q8—32no—
255C3×#121—31no—
256C3×#121—31no—
257C3×#120—32no—
258C3×C4×D4—32no—
259C3×C4×D4—32no—
260C3×#117—21no—
261C3×#117C2×D311yescharacteristic, complemented
262C3×#117C2×D311yescharacteristic, complemented
263C2×#217—32no—
264#946—32no—
265#946—32no—
266#946—32no—
267#946—32no—
268#946—32no—
269#946—32no—
270#939—34no—
271#939—34no—
272#939—34no—
273#938—32no—
274#938—32no—
275#938—34no—
276#937—34no—
277D4×Dic3—34no—
278#930—32no—
279#930—32no—
280C2×(C2×D3)⋊C4—32no—
281C2×C4⋊Dic3—31no—
282C2×C4⋊Dic3—31no—
283C2×C4⋊Dic3—61no—
284#924—32no—
285#924—32no—
286#924—32no—
287#924—32no—
288#924—32no—
289#924—32no—
290C2×Dic3⋊C4—32no—
291C2×Dic3⋊C4—32no—
292#897C2×D311yescharacteristic
293#897C2×D311yescharacteristic, complemented
294#897C2×D312yescomplemented
295#897C2×D312yescomplemented
296#896—34no—
297#896—34no—
298#896—34no—
299#895—34no—
300#895C2×D311yescharacteristic
301#895C2×D311yescharacteristic, complemented
302#894—34no—
303#894—34no—
304#894—34no—
305#893—34no—
306#892—32no—
307#892—32no—
308#892—62no—
309D3×C4⋊C4—32no—
310D3×C4⋊C4—32no—
311D3×C4⋊C4—34no—
312D3×C4⋊C4—34no—
313D3×C4⋊C4—62no—
314#888—34no—
315#888—34no—
316#886C2×D312yescomplemented
317#886C2×D314yescomplemented
318#885—34no—
319#885—34no—
320#884—34no—
321#884—34no—
322#884—34no—
323#883—34no—
324#883—34no—
325#883—34no—
326#882—34no—
327#882C2×D312yes—
328#67⋊C4—34no—
329#67⋊C4—34no—
330#67⋊C4—34no—
331#67⋊C4—34no—
332#67⋊C4—64no—
333D3×C22⋊C4—34no—
334D3×C22⋊C4—34no—
335#878—34no—
336#878—34no—
337#878—34no—
338#875C2×D312yescomplemented
339C4×D12—32no—
340C4×D12—32no—
341C4×D12—62no—
342C4×D12C2×D312yes—
343C4×D12C2×D312yescomplemented
344#869C2×D312yescomplemented
345C4×Dic6—32no—
346C4×Dic6—32no—
347C4×Dic6—62no—
348C23×C32C2411yescharacteristic
349C22×C3⋊D3C2412yes—
350C22×C3×D3—22no—
351C22×C3×D3—22no—
352C22×C3×D3—41no—
353C22×C3×D3C2412yes—
354C22×C3×D3C2411yescharacteristic
355C22×C3×D3C2412yes—
356C22×C3×D3C2411yescharacteristic
357C2×D32—24no—
358C2×D32—24no—
359C2×D32—42no—
360C2×C32×C4C2×D414yes—
361C2×C32×C4C2412yes—
362C2×C32×C4C2412yes—
363C2×C32×C4C2411yescharacteristic
364C2×C32×C4C2411yescharacteristic
365#638C2×D418yes—
366C2×C3⋊Dic3—42no—
367C2×C3⋊Dic3C2414yes—
368C2×C3⋊Dic3C2412yes—
369C4⋊(C3⋊D3)C2×D414yes—
370C4×C3⋊D3—44no—
371C4×C3⋊D3C2×D418yes—
372#634C2×D414yes—
373C3×#67—24no—
374C3×#67—24no—
375C2×C3×Dic3—24no—
376C2×C3×Dic3—22no—
377C2×C3×Dic3C2412yes—
378C2×C3×Dic3C2414yes—
379C2×C3×Dic3C2412yes—
380C2×C3×Dic3C2411yescharacteristic
381C2×C3×Dic3C2411yescharacteristic
382C3×D12—24no—
383C3×D12—22no—
384C3×D12—22no—
385C3×D12—42no—
386C3×C4×D3—24no—
387C3×C4×D3—22no—
388C3×C4×D3—22no—
389C3×C4×D3—22no—
390C3×C4×D3—24no—
391C3×C4×D3—22no—
392C3×Dic6—24no—
393C3×Dic6—22no—
394C3×Dic6—24no—
395C3×Dic6—22no—
396#627—28no—
397#627—24no—
398#626—28no—
399#626—24no—
400#626—24no—
401#625—24no—
402#625—44no—
403#624—28no—
404#624—24no—
405D3×Dic3—28no—
406D3×Dic3—24no—
407D3×Dic3—24no—
408C2×2−1+4—91no—
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—31no—
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—64no—
430C3×#41—64no—
431C2×C3×Q8—31no—
432C2×C3×Q8—32no—
433C2×C3×Q8—32no—
434C2×C3×Q8—31no—
435C2×C3×Q8—64no—
436C2×C3×D4—32no—
437C2×C3×D4—32no—
438C2×C3×D4—32no—
439C2×C3×D4—31no—
440C2×C3×D4—31no—
441C2×C3×D4—32no—
442C22×C3×C4—21no—
443C22×C3×C4—31no—
444C22×C3×C4—32no—
445C22×C3×C4—31no—
446C22×C3×C4—31no—
447C22×C3×C4—31no—
448C22×C3×C4—31no—
449C22×C3×C4—32no—
450C22×C3×C4—32no—
451C22×C3×C4—64no—
452C22×C3×C4C22×D311yescharacteristic
453C22×C3×C4C22×D311yescharacteristic
454C2×#67—32no—
455C2×#67—32no—
456C2×#67—32no—
457C2×#67—32no—
458C2×#67—34no—
459C2×#67—34no—
460C2×#67—32no—
461C2×#67—32no—
462C2×#67—34no—
463C2×#67—62no—
464C2×#67—68no—
465C2×#67C22×D312yes—
466C2×#67C22×D312yes—
467C22×Dic3—32no—
468C22×Dic3—32no—
469C22×Dic3—32no—
470C22×Dic3—32no—
471C22×Dic3—34no—
472C22×Dic3—62no—
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D312yes—
475#239—68no—
476#239—64no—
477#239—68no—
478D3×Q8—68no—
479D3×Q8—68no—
480D3×Q8—68no—
481D3×Q8—64no—
482#237—68no—
483#237—64no—
484#237—68no—
485#237—616no—
486D3×D4—64no—
487D3×D4—68no—
488#235—24no—
489#235—24no—
490#235—38no—
491#235—38no—
492#235—68no—
493#235—64no—
494#235—68no—
495#235—64no—
496#235—68no—
497#235—68no—
498#235—68no—
499#235—616no—
500C2×D12—31no—
501C2×D12—31no—
502C2×D12—34no—
503C2×D12—32no—
504C2×D12—32no—
505C2×D12—61no—
506C2×D12—64no—
507C2×D12C22×D312yes—
508C2×D12C22×D311yescharacteristic
509C2×D12C22×D311yescharacteristic
510C2×D12C22×D312yes—
511C2×C4×D3—24no—
512C2×C4×D3—32no—
513C2×C4×D3—32no—
514C2×C4×D3—32no—
515C2×C4×D3—34no—
516C2×C4×D3—32no—
517C2×C4×D3—34no—
518C2×C4×D3—34no—
519C2×C4×D3—32no—
520C2×C4×D3—32no—
521C2×C4×D3—34no—
522C2×C4×D3—34no—
523C2×C4×D3—62no—
524C2×C4×D3—64no—
525C2×C4×D3—68no—
526C2×C4×D3—68no—
527C2×C4×D3C22×D311yescharacteristic
528C2×C4×D3C22×D312yes—
529C2×C4×D3C22×D311yescharacteristic
530C2×C4×D3C22×D311yescharacteristic
531C2×C4×D3C22×D311yescharacteristic
532C2×C4×D3C22×D312yes—
533C2×Dic6—24no—
534C2×Dic6—31no—
535C2×Dic6—31no—
536C2×Dic6—32no—
537C2×Dic6—34no—
538C2×Dic6—34no—
539C2×Dic6—32no—
540C2×Dic6—61no—
541C2×Dic6—64no—
542C2×Dic6—68no—
543C2×Dic6C22×D311yescharacteristic
544C2×Dic6C22×D312yes—
545C2×Dic6C22×D311yescharacteristic
546C2×Dic6C22×D312yes—
547C3×C4⋊C4—21no—
548C3×C4⋊C4—21no—
549C3×C4⋊C4—32no—
550C3×C4⋊C4—34no—
551C3×C4⋊C4—32no—
552C3×C4⋊C4—34no—
553C3×C4⋊C4C22×D311yescharacteristic
554C3×C4⋊C4C22×D311yescharacteristic
555C3×C4⋊C4C22×D311yescharacteristic
556C3×C4⋊C4C22×D311yescharacteristic
557C3×C22⋊C4—22no—
558C3×C22⋊C4—32no—
559C3×C22⋊C4—32no—
560C3×C22⋊C4—34no—
561C3×C22⋊C4—32no—
562C3×C22⋊C4—34no—
563C3×C22⋊C4—32no—
564C3×C22⋊C4C22×D312yes—
565C3×C22⋊C4C22×D312yes—
566C3×C42—22no—
567C3×C42C22×D312yes—
568C3×C42C22×D312yes—
569#217—34no—
570#217—34no—
571#217—34no—
572#217—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—64no—
580(C2×D3)⋊C4C22×D312yes—
581(C2×D3)⋊C4C22×D312yes—
582(C2×D3)⋊C4C22×D312yes—
583(C2×D3)⋊C4C22×D312yes—
584(C2×D3)⋊C4C22×D314yes—
585(C2×D3)⋊C4C22×D314yes—
586C4⋊Dic3—32no—
587C4⋊Dic3—32no—
588C4⋊Dic3—32no—
589C4⋊Dic3—32no—
590C4⋊Dic3—62no—
591C4⋊Dic3—62no—
592C4⋊Dic3C22×D314yes—
593C4⋊Dic3C22×D314yes—
594C4⋊Dic3C22×D312yes—
595C4⋊Dic3C22×D312yes—
596Dic3⋊C4—34no—
597Dic3⋊C4—34no—
598Dic3⋊C4—34no—
599Dic3⋊C4—34no—
600Dic3⋊C4—34no—
601Dic3⋊C4—34no—
602Dic3⋊C4—34no—
603Dic3⋊C4—34no—
604Dic3⋊C4—64no—
605C4×Dic3—34no—
606C4×Dic3—34no—
607C4×Dic3—64no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32C22×D412yes—
611C22×C32C2511yescharacteristic
612C2×C3⋊D3—22no—
613C2×C3⋊D3—22no—
614C2×C3⋊D3C22×D414yes—
615C2×C3×D3—21no—
616C2×C3×D3—21no—
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—22no—
624C2×C3×D3—22no—
625C2×C3×D3—21no—
626C2×C3×D3—44no—
627C2×C3×D32−1+412yescomplemented
628D32—48no—
629C32×C4—22no—
630C32×C4—22no—
631C32×C4C22×D412yes—
632C32×C4C22×D412yes—
633C3⋊Dic3—24no—
634C3⋊Dic3C22×D414yes—
635C3×Dic3—21no—
636C3×Dic3—24no—
637C3×Dic3—22no—
638C3×Dic3—22no—
639C3×Dic3—21no—
6402−1+4—188no—
641C2×#41—31no—
642C2×#41—31no—
643C2×#41—92no—
644C2×#41—94no—
645C2×#41—92no—
646C2×#41—91no—
647C2×#41—92no—
648C2×#41—91no—
649C2×#41—92no—
650C2×#41—91no—
651C2×#41—188no—
652C22×Q8—31no—
653C22×Q8—92no—
654C22×Q8—91no—
655C22×Q8—92no—
656C22×D4—91no—
657C22×D4—92no—
658C23×C4—31no—
659C23×C4—92no—
660C4⋊Q8—32no—
661C4⋊Q8—94no—
662#124—32no—
663#124—94no—
664#123—32no—
665#123—34no—
666#123—94no—
667#123—94no—
668#123—94no—
669C22⋊Q8—31no—
670C22⋊Q8—32no—
671C22⋊Q8—31no—
672C22⋊Q8—32no—
673C22⋊Q8—94no—
674C22⋊Q8—94no—
675C22⋊Q8—94no—
676C22⋊Q8—92no—
677C22⋊Q8—92no—
678C22⋊Q8—92no—
679C22⋊Q8—92no—
680C22⋊Q8—92no—
681C22⋊Q8—92no—
682#121—31no—
683#121—31no—
684#121—94no—
685#121—94no—
686#121—94no—
687#121—92no—
688#121—92no—
689#121—94no—
690#120—32no—
691#120—94no—
692C4×Q8—92no—
693C4×D4—32no—
694C4×D4—32no—
695C4×D4—94no—
696C4×D4—94no—
697C4×D4—94no—
698C4×D4—92no—
699#117—92no—
700#117D3211yescharacteristic, complemented
701C2×C4⋊C4—94no—
702C2×C4⋊C4—92no—
703C2×C4⋊C4—91no—
704C2×C4⋊C4—92no—
705C2×C22⋊C4—94no—
706C2×C22⋊C4—92no—
707C23×C3—21no—
708C23×C3—31no—
709C23×C3—31no—
710C23×C3—32no—
711C23×C3—32no—
712C23×C3—62no—
713C23×C3—62no—
714C23×C3—121no—
715C23×C3C23×D311yescharacteristic
716C23×C3C23×D311yescharacteristic
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—32no—
720C22×D3—32no—
721C22×D3—41no—
722C22×D3—62no—
723C22×D3—64no—
724C22×D3—64no—
725C22×D3—64no—
726C22×D3—64no—
727C22×D3—122no—
728C22×D3—122no—
729C22×D3C23×D311yescharacteristic
730C22×D3C23×D312yes—
731C22×D3C23×D312yes—
732C22×D3C23×D311yescharacteristic
733C3×Q8—62no—
734C3×Q8—64no—
735C3×Q8—64no—
736C3×Q8—62no—
737C3×D4—64no—
738C3×D4—64no—
739C3×D4—64no—
740C3×D4—62no—
741C3×D4—62no—
742C3×D4—122no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—22no—
746C2×C3×C4—22no—
747C2×C3×C4—24no—
748C2×C3×C4—31no—
749C2×C3×C4—31no—
750C2×C3×C4—32no—
751C2×C3×C4—34no—
752C2×C3×C4—32no—
753C2×C3×C4—62no—
754C2×C3×C4—64no—
755C2×C3×C4—62no—
756C2×C3×C4—64no—
757C2×C3×C4—62no—
758C2×C3×C4—64no—
759C2×C3×C4—62no—
760C2×C3×C4—62no—
761C2×C3×C4D3×D414yes—
762C2×C3×C4D3×D414yes—
763C2×C3×C4C23×D312yes—
764C2×C3×C4C23×D312yes—
765C2×C3×C4C23×D312yes—
766C2×C3×C4C23×D312yes—
767C2×C3×C4C23×D311yescharacteristic
768C2×C3×C4C23×D311yescharacteristic
769C2×C3×C4C23×D311yescharacteristic
770C2×C3×C4C23×D311yescharacteristic
771#67—24no—
772#67—24no—
773#67—38no—
774#67—38no—
775#67—68no—
776#67—64no—
777#67—64no—
778#67—68no—
779#67—64no—
780#67—64no—
781#67—124no—
782#67—124no—
783C2×Dic3—24no—
784C2×Dic3—22no—
785C2×Dic3—32no—
786C2×Dic3—32no—
787C2×Dic3—34no—
788C2×Dic3—34no—
789C2×Dic3—62no—
790C2×Dic3—64no—
791C2×Dic3—64no—
792C2×Dic3—68no—
793C2×Dic3—64no—
794C2×Dic3—122no—
795C2×Dic3—122no—
796C2×Dic3—242no—
797C2×Dic3C23×D311yescharacteristic
798C2×Dic3C23×D311yescharacteristic
799C2×Dic3C23×D312yes—
800C2×Dic3C23×D312yes—
801C2×Dic3C23×D314yes—
802D12—24no—
803D12—22no—
804D12—22no—
805D12—34no—
806D12—34no—
807D12—42no—
808D12—64no—
809D12—64no—
810D12—64no—
811D12—68no—
812C4×D3—22no—
813C4×D3—22no—
814C4×D3—22no—
815C4×D3—22no—
816C4×D3—24no—
817C4×D3—24no—
818C4×D3—38no—
819C4×D3—38no—
820C4×D3—68no—
821C4×D3—64no—
822C4×D3—64no—
823C4×D3—68no—
824C4×D3—68no—
825C4×D3—64no—
826C4×D3—64no—
827C4×D3—68no—
828C4×D3—124no—
829C4×D3—124no—
830C4×D3—244no—
831Dic6—24no—
832Dic6—24no—
833Dic6—22no—
834Dic6—22no—
835Dic6—34no—
836Dic6—34no—
837Dic6—64no—
838Dic6—64no—
839Dic6—68no—
840Dic6—64no—
841Dic6—68no—
842C2×C32—22no—
843C2×C32C23×D411yescharacteristic
844C2×C32C2×2−1+411yescharacteristic
845C2×C32#58511yescharacteristic
846C3⋊D3—24no—
847C3×D3—22no—
848C3×D3—42no—
849C3×D3—42no—
850C3×D3—41no—
851C24—31no—
852C24—92no—
853#41—64no—
854#41—64no—
855#41—98no—
856#41—188no—
857#41—188no—
858#41—1816no—
859#41—184no—
860#41—184no—
861#41—188no—
862#41—188no—
863C2×Q8—32no—
864C2×Q8—31no—
865C2×Q8—32no—
866C2×Q8—31no—
867C2×Q8—64no—
868C2×Q8—94no—
869C2×Q8—92no—
870C2×Q8—91no—
871C2×Q8—184no—
872C2×Q8—188no—
873C2×Q8—188no—
874C2×D4—32no—
875C2×D4—32no—
876C2×D4—32no—
877C2×D4—31no—
878C2×D4—31no—
879C2×D4—32no—
880C2×D4—94no—
881C2×D4—92no—
882C2×D4—92no—
883C2×D4—92no—
884C2×D4—92no—
885C2×D4—94no—
886C2×D4—91no—
887C2×D4—184no—
888C2×D4—188no—
889C22×C4—32no—
890C22×C4—31no—
891C22×C4—32no—
892C22×C4—31no—
893C22×C4—31no—
894C22×C4—31no—
895C22×C4—31no—
896C22×C4—32no—
897C22×C4—64no—
898C22×C4—94no—
899C22×C4—92no—
900C22×C4—94no—
901C22×C4—92no—
902C22×C4—92no—
903C22×C4—92no—
904C22×C4—92no—
905C22×C4—94no—
906C22×C4—188no—
907C22×C4C2×D3211yescharacteristic
908C4⋊C4—32no—
909C4⋊C4—34no—
910C4⋊C4—32no—
911C4⋊C4—34no—
912C4⋊C4—94no—
913C4⋊C4—94no—
914C4⋊C4—94no—
915C4⋊C4—92no—
916C4⋊C4—94no—
917C4⋊C4—92no—
918C4⋊C4C2×D3211yescharacteristic
919C4⋊C4C2×D3211yescharacteristic
920C22⋊C4—32no—
921C22⋊C4—34no—
922C22⋊C4—32no—
923C22⋊C4—32no—
924C22⋊C4—32no—
925C22⋊C4—34no—
926C22⋊C4—94no—
927C22⋊C4—94no—
928C22⋊C4—94no—
929C22⋊C4—94no—
930C22⋊C4—94no—
931C22⋊C4C2×D3212yes—
932C42—94no—
933C42C2×D3212yes—
934C22×C3—21no—
935C22×C3—21no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—22no—
939C22×C3—21no—
940C22×C3—32no—
941C22×C3—41no—
942C22×C3—41no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—62no—
946C22×C3—62no—
947C22×C3—61no—
948C22×C3—62no—
949C22×C3—62no—
950C22×C3—62no—
951C22×C3—61no—
952C22×C3—62no—
953C22×C3—61no—
954C22×C3—124no—
955C22×C3C2×D3×D412yes—
956C22×C3C2×D3×D412yes—
957C22×C3C24×D311yescharacteristic
958C22×C3C24×D311yescharacteristic
959C2×D3—21no—
960C2×D3—21no—
961C2×D3—21no—
962C2×D3—22no—
963C2×D3—22no—
964C2×D3—22no—
965C2×D3—21no—
966C2×D3—21no—
967C2×D3—22no—
968C2×D3—22no—
969C2×D3—22no—
970C2×D3—34no—
971C2×D3—34no—
972C2×D3—44no—
973C2×D3—64no—
974C2×D3—62no—
975C2×D3—62no—
976C2×D3—62no—
977C2×D3—62no—
978C2×D3—122no—
979C2×D3—122no—
980C2×D3—128no—
981C2×D3—128no—
982C2×D3#101012yescomplemented
983C3×C4—22no—
984C3×C4—22no—
985C3×C4—22no—
986C3×C4—22no—
987C3×C4—22no—
988C3×C4—22no—
989C3×C4—42no—
990C3×C4—42no—
991C3×C4—62no—
992C3×C4—61no—
993C3×C4—62no—
994C3×C4—64no—
995C3×C4—61no—
996C3×C4C2×D3×D412yes—
997C3×C4C2×D3×D412yes—
998C3×C4C2×D3×D412yes—
999C3×C4C2×D3×D412yes—
1000Dic3—24no—
1001Dic3—22no—
1002Dic3—22no—
1003Dic3—21no—
1004Dic3—21no—
1005Dic3—34no—
1006Dic3—34no—
1007Dic3—64no—
1008Dic3—64no—
1009Dic3—64no—
1010Dic3—124no—
1011C32#348911yescharacteristic, complemented, Sylow
1012C23—31no—
1013C23—32no—
1014C23—31no—
1015C23—32no—
1016C23—62no—
1017C23—62no—
1018C23—92no—
1019C23—121no—
1020C23—184no—
1021C23—184no—
1022C23—362no—
1023C23C22×D3211yescharacteristic
1024Q8—64no—
1025Q8—64no—
1026Q8—62no—
1027Q8—62no—
1028Q8—94no—
1029Q8—188no—
1030Q8—184no—
1031D4—64no—
1032D4—64no—
1033D4—64no—
1034D4—62no—
1035D4—62no—
1036D4—98no—
1037D4—94no—
1038D4—122no—
1039D4—184no—
1040D4—184no—
1041D4—188no—
1042D4—184no—
1043D4—364no—
1044C2×C4—32no—
1045C2×C4—34no—
1046C2×C4—31no—
1047C2×C4—31no—
1048C2×C4—32no—
1049C2×C4—62no—
1050C2×C4—64no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—64no—
1056C2×C4—64no—
1057C2×C4—92no—
1058C2×C4—98no—
1059C2×C4—94no—
1060C2×C4—184no—
1061C2×C4—188no—
1062C2×C4—184no—
1063C2×C4—184no—
1064C2×C4—188no—
1065C2×C4—364no—
1066C2×C4—362no—
1067C2×C4#380214yes—
1068C2×C4C22×D3212yes—
1069C2×C4C22×D3212yes—
1070C2×C4C22×D3211yescharacteristic
1071C2×C4C22×D3211yescharacteristic
1072C2×C3—22no—
1073C2×C3—22no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—42no—
1078C2×C3—62no—
1079C2×C3—122no—
1080C2×C3—121no—
1081C2×C3—122no—
1082C2×C3C22×D3×D411yescharacteristic
1083C2×C3C22×D3×D411yescharacteristic
1084C2×C3C2×#101011yescharacteristic
1085C2×C3#596411yescharacteristic
1086C2×C3D3×2−1+411yescharacteristic
1087C2×C3#596811yescharacteristic
1088D3—22no—
1089D3—41no—
1090D3—42no—
1091D3—42no—
1092D3—64no—
1093D3—64no—
1094D3—124no—
1095C22—21no—
1096C22—21no—
1097C22—32no—
1098C22—61no—
1099C22—61no—
1100C22—61no—
1101C22—62no—
1102C22—62no—
1103C22—62no—
1104C22—61no—
1105C22—62no—
1106C22—61no—
1107C22—62no—
1108C22—62no—
1109C22—94no—
1110C22—124no—
1111C22—182no—
1112C22—182no—
1113C22—368no—
1114C22C2×#380212yes—
1115C22C23×D3211yescharacteristic
1116C4—22no—
1117C4—22no—
1118C4—61no—
1119C4—61no—
1120C4—62no—
1121C4—62no—
1122C4—64no—
1123C4—94no—
1124C4—184no—
1125C4C2×#380212yes—
1126C4C2×#380212yes—
1127C3—21no—
1128C3#8604211yescharacteristic, complemented
1129C3#8635611yescharacteristic, complemented
1130C2—22no—
1131C2—62no—
1132C2—121no—
1133C2—122no—
1134C2—122no—
1135C2—184no—
1136C2C22×#380211yescharacteristic
1137C2D3×#101011yescharacteristic
1138C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. C2×#64297C2semidirect
3. #10595994C2semidirect
4. C3×#5526C2semidirect
5. C3×#5524C2semidirect
6. #10595044C2semidirect
7. C2×#63856C2semidirect
8. #10594632C2semidirect
9. #10594631C2semidirect
10. #10594529C2semidirect
11. #10594528C2semidirect
12. #10594294C2semidirect
13. #10594083C2semidirect
14. #10594007C2semidirect
15. #10593905C2semidirect
16. #10593904C2semidirect
17. #10593869C2semidirect
22. C2×C3×#235C22semidirect
24. C22×C3×Dic6C22semidirect
27. C2×#3804C22semidirect
32. C2×#3799C22semidirect
34. C2×#3797C22semidirect
36. C2×#3796C22semidirect
39. C2×D3×Dic6C22semidirect
40. C32×#117C22semidirect
41. C2×C4⋊(C3⋊Dic3)C22semidirect
42. #64101C22semidirect
43. C4⋊C4×C3⋊D3C22semidirect
44. #64090C22semidirect
45. C4×C4⋊(C3⋊D3)C22semidirect
46. C4×#634C22semidirect
48. C3×#897C22semidirect
49. C3×#897C22semidirect
50. C3×#897C22semidirect
52. C3×#895C22semidirect
53. C3×#886C22semidirect
54. C3×#886C22semidirect
56. C3×#875C22semidirect
58. C3×C4×D12C22semidirect
59. C3×#869C22semidirect
60. #63980C22semidirect
61. C2×#3724C22semidirect
65. #63919C22semidirect
66. #63916C22semidirect
67. #63915C22semidirect
68. #63912C22semidirect
69. #63908C22semidirect
70. #63908C22semidirect
71. #63902C22semidirect
72. #63900C22semidirect
74. #63899C22semidirect
75. #63899C22semidirect
77. #63885C22semidirect
80. #63856C22semidirect
81. #63856C22semidirect
82. #63856C22semidirect
83. #63856C22semidirect
84. #63854C22semidirect
85. #63854C22semidirect
86. #63854C22semidirect
117. #5526D3semidirect
118. #5524D3semidirect
127. #3828D4semidirect
239. C2×#235C2×D3semidirect
246. C22×Dic6C2×D3semidirect
261. C3×#117C2×D3semidirect
262. C3×#117C2×D3semidirect
293. #897C2×D3semidirect
294. #897C2×D3semidirect
295. #897C2×D3semidirect
301. #895C2×D3semidirect
316. #886C2×D3semidirect
317. #886C2×D3semidirect
338. #875C2×D3semidirect
343. C4×D12C2×D3semidirect
344. #869C2×D3semidirect
627. C2×C3×D32−1+4semidirect
700. #117D32semidirect
982. C2×D3#1010semidirect
1011. C32#3489semidirect
1128. C3#86042semidirect
1129. C3#86356semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×#642972
#105959942
C3×#55262
C3×#55242
#105950442
C2×#638562
#105946322
#105946312
#105945292
#105945282
#105942942
#105940832
#105940072
#105939052
#105939042
#105938692
#863563
#860423