Finite Group Databasebeta

← #11904770

Subgroups — #11904770

Order 1152.

3441 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3C3×#5833C211yesmaximal, characteristic, complemented
4C3×#5828C211yesmaximal, characteristic, complemented
5#10595429C212yesmaximal, complemented
6#10595405C212yesmaximal, complemented
7#10595307C214yesmaximal, complemented
8#10595306C212yesmaximal, complemented
9#10595240C212yesmaximal, complemented
10#10595162C214yesmaximal, complemented
11#10595078C212yesmaximal, complemented
12#10594990C211yesmaximal, characteristic, complemented
13#10594918C212yesmaximal, complemented
14#10594915C212yesmaximal, complemented
15#10594856C211yesmaximal, characteristic, complemented
16C2×#63857C211yesmaximal, characteristic, complemented
17#10594834C212yesmaximal, complemented
18#86380—31nomaximal
19#86042—31nomaximal
20C2×C32×#41C2211yescharacteristic, complemented
21#64367—28no—
22C2×Q8×C3⋊D3C2212yescomplemented
23C2×#3830C2214yescomplemented
24C2×#3830C2212yescomplemented
25C2×#3828C2211yescharacteristic
26C2×#3828C2212yescomplemented
27C22×#634C2211yescharacteristic, complemented
28C22×#634C2212yescomplemented
29C2×C3×#235C2211yescharacteristic
30C22×C3×C4×D3C2211yescharacteristic
31C2×D3×#67C2212yes—
32C2×#3804C2212yes—
33D3×#235—28no—
34C2×D3×D12C2211yescharacteristic
35C2×C4×D32C2212yes—
36C2×#3799C2211yescharacteristic
37C2×#3798C2212yes—
38C2×#3795C2211yescharacteristic
39C2×D3×Dic6C2211yescharacteristic
40C3×#946C2211yescharacteristic
41C3×#946C2211yescharacteristic, complemented
42C3×#946C2212yescomplemented
43C3×#939C2214yescomplemented
44C3×#938C2211yescharacteristic
45C3×#938C2211yescharacteristic, complemented
46C3×#938C2212yescomplemented
47C3×#937C2212yes—
48C3×#935C2212yescomplemented
49C3×#930C2212yescomplemented
50C3×C4×#67C2212yes—
51C3×C4×#67C2212yescomplemented
52C3×#926C2211yescharacteristic, complemented
53C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
54C3×#924C2212yescomplemented
55#63983C2214yes—
56#63982C2214yescomplemented
57#63980C2214yescomplemented
58#63975C2214yescomplemented
59#67⋊Dic3C2214yes—
60#67⋊Dic3C2214yescomplemented
61C2×Dic3⋊Dic3C2212yescomplemented
62#63962C2214yescomplemented
63C2×(C2×D3)⋊Dic3C2212yes—
64#63958C2214yescomplemented
65#63958C2214yescomplemented
66#63952C2214yescomplemented
67#63921C2214yes—
68#63913C2214yescomplemented
69#63900C2212yescomplemented
70#63896C2214yes—
71#63896C2214yescomplemented
72#63894C2212yescomplemented
73#63883C2214yescomplemented
74#63866C2212yescomplemented
75#63860C2212yescomplemented
76#63857C2212yes—
77#63857C2212yes—
78#63857C2212yescomplemented
79#63857C2212yescomplemented
80#63857C2212yescomplemented
81#63857C2212yescomplemented
82#63853C2214yescomplemented
83#63853C2214yescomplemented
84#63849C2212yescomplemented
85#63844C2212yescomplemented
86#63840C2214yescomplemented
87C2×#1010—31no—
88C2×#1010—31no—
89C2×#1010—61no—
90C2×D3×#41—31no—
91C22×#235—31no—
92C3×#537—31no—
93C3×#525—31no—
94#5833D311yescharacteristic, complemented
95#5828D311yescharacteristic, complemented
96#5825—31no—
97C2×#924—31no—
98#5655—34no—
99#5632—32no—
100#5631—32no—
101#5628—32no—
102#5628—32no—
103D3×C22⋊Q8—32no—
104D3×C22⋊Q8—32no—
105#5612—32no—
106#5611—34no—
107#5610—34no—
108#5608—32no—
109#5608—32no—
110#5606—32no—
111#5606—32no—
112#5598—32no—
113#5591—34no—
114#5552—32no—
115#5551—32no—
116#5550—32no—
117D4×Dic6—32no—
118#5526—31no—
119#5523—31no—
120C2×#897—31no—
121#5504—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×#638C2314yes—
131C2×#638C2312yes—
132C22×C3⋊Dic3C2312yes—
133C22×C3⋊Dic3C2314yes—
134Q8×C3⋊D3—28no—
135#3830—216no—
136#3830—28no—
137#3828—28no—
138#3828D418yescomplemented
139C2×C4⋊(C3⋊D3)C2311yescharacteristic
140C2×C4×C3⋊D3C2314yes—
141C2×C4×C3⋊D3C2312yes—
142C2×#634—24no—
143C2×#634—28no—
144C2×#634C2314yes—
145C2×#634C2312yes—
146C2×#634C2312yes—
147C2×#634C2311yescharacteristic
148C2×C3×#67C2312yes—
149C2×C3×#67C2312yes—
150C2×C3×#67C2312yes—
151C2×C3×#67C2314yes—
152C22×C3×Dic3C2311yescharacteristic
153C22×C3×Dic3C2312yes—
154C3×#235—24no—
155C2×C3×D12C2311yescharacteristic
156C2×C3×C4×D3—24no—
157C2×C3×C4×D3C2311yescharacteristic
158C2×C3×C4×D3C2311yescharacteristic
159C2×C3×C4×D3C2311yescharacteristic
160C2×C3×C4×D3C2312yes—
161C2×C3×C4×D3C2311yescharacteristic
162C2×C3×Dic6C2311yescharacteristic
163D3×#67—28no—
164C2×#627C2312yes—
165C2×#626C2312yes—
166C2×#626C2312yes—
167C2×#625C2312yes—
168C2×#624C2312yes—
169C2×#624C2314yes—
170#3804—28no—
171C2×D3×Dic3C2312yes—
172C2×D3×Dic3C2312yes—
173D3×D12—24no—
174C4×D32—28no—
175#3799—24no—
176#3798—28no—
177#3795—24no—
178D3×Dic6—24no—
179C3×#217C2314yes—
180C3×#217C2312yes—
181C3×#217C2312yes—
182C3×#217C2312yes—
183C3×(C2×D3)⋊C4C2312yes—
184C3×(C2×D3)⋊C4C2312yes—
185C3×(C2×D3)⋊C4C2314yes—
186C3×C4⋊Dic3C2312yes—
187C3×C4⋊Dic3C2312yes—
188C3×C4⋊Dic3C2311yescharacteristic
189C3×C4⋊Dic3C2311yescharacteristic
190C3×Dic3⋊C4C2314yes—
191C3×Dic3⋊C4C2312yes—
192C3×Dic3⋊C4C2312yes—
193C3×C4×Dic3C2312yes—
194#3724C2314yes—
195Dic3⋊Dic3C2314yes—
196Dic3⋊Dic3C2314yes—
197Dic3⋊Dic3C2314yes—
198Dic3⋊Dic3C2314yes—
199#3722C2314yes—
200(C2×D3)⋊Dic3C2314yes—
201(C2×D3)⋊Dic3C2314yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204Dic32C2314yes—
205#3489—91noSylow
206C2×C3×#41—21no—
207C2×C3×#41—31no—
208C2×C3×#41C2×D311yescharacteristic, complemented
209C2×C3×#41C2×D311yescharacteristic, complemented
210C23×C3×C4—31no—
211C22×#67—32no—
212#1010—68no—
213#1010—68no—
214#1010—616no—
215D3×#41—68no—
216C2×#239—31no—
217C2×D3×Q8—32no—
218C2×D3×Q8—32no—
219C2×D3×Q8—31no—
220C2×D3×Q8—62no—
221C2×#237—34no—
222C2×#237—32no—
223C2×#237—32no—
224C2×#237—34no—
225C2×#237—32no—
226C2×#237—31no—
227C2×#237—62no—
228C2×#237—64no—
229C2×D3×D4—32no—
230C2×D3×D4—31no—
231C2×#235—31no—
232C2×#235—31no—
233C2×#235—32no—
234C2×#235—32no—
235C2×#235—32no—
236C2×#235—31no—
237C2×#235—32no—
238C2×#235—32no—
239C2×#235—31no—
240C2×#235—61no—
241C2×#235—62no—
242C2×#235—68no—
243C2×#235C2×D311yescharacteristic
244C22×D12—31no—
245C22×C4×D3—32no—
246C22×C4×D3—32no—
247C22×C4×D3C2×D311yescharacteristic
248C22×Dic6—32no—
249C22×Dic6—31no—
250C22×Dic6—31no—
251C22×Dic6—32no—
252C22×Dic6—31no—
253C22×Dic6—61no—
254C22×Dic6—62no—
255C3×#123—32no—
256C3×C22⋊Q8—31no—
257C3×C22⋊Q8—31no—
258C3×C22⋊Q8—32no—
259C3×C22⋊Q8—32no—
260C3×#121—31no—
261C3×#121—31no—
262C3×#121—32no—
263C3×#121—34no—
264C3×#121—32no—
265C3×#120—32no—
266C3×C4×D4—32no—
267C3×C4×D4—32no—
268C3×#117—31no—
269C2×C3×C4⋊C4—31no—
270C2×#217—32no—
271#946C2×D311yescharacteristic
272#946C2×D311yescharacteristic, complemented
273#946C2×D312yescomplemented
274#944—32no—
275#939—34no—
276#939—34no—
277#939C2×D314yescomplemented
278#938—34no—
279#938—34no—
280#938C2×D311yescharacteristic
281#938C2×D311yescharacteristic, complemented
282#938C2×D312yescomplemented
283#937—34no—
284#937—34no—
285#937C2×D312yes—
286#936—32no—
287#935—34no—
288#935C2×D312yescomplemented
289D4×Dic3—34no—
290D4×Dic3—34no—
291#930C2×D312yescomplemented
292C4×#67—34no—
293C4×#67C2×D312yes—
294C4×#67C2×D312yescomplemented
295C2×(C2×D3)⋊C4—32no—
296#926C2×D311yescharacteristic, complemented
297C2×C4⋊Dic3—32no—
298C2×C4⋊Dic3C2×D311yescharacteristic, complemented
299#924—32no—
300#924—32no—
301#924—32no—
302#924—32no—
303#924—32no—
304#924—32no—
305#924C2×D312yescomplemented
306C2×Dic3⋊C4—32no—
307#897—32no—
308#897—32no—
309#897—32no—
310#897—32no—
311#897—32no—
312#897—32no—
313#896—34no—
314#896—34no—
315#894—34no—
316#894—34no—
317#893—32no—
318#892—32no—
319#892—32no—
320D3×C4⋊C4—32no—
321D3×C4⋊C4—32no—
322D3×C4⋊C4—34no—
323D3×C4⋊C4—34no—
324#888—34no—
325#888—34no—
326#887—32no—
327#886—34no—
328#885—34no—
329#885—34no—
330#884—34no—
331#884—34no—
332#883—34no—
333#883—34no—
334#883—34no—
335#883—34no—
336#67⋊C4—34no—
337#67⋊C4—34no—
338#67⋊C4—34no—
339D3×C22⋊C4—34no—
340D3×C22⋊C4—34no—
341#878—34no—
342#878—34no—
343#878—34no—
344#878—34no—
345#875—32no—
346C4×D12—32no—
347#869—32no—
348C4×Dic6—32no—
349C23×C32C2412yes—
350C23×C32C2411yescharacteristic
351C22×C3⋊D3C2412yes—
352C22×C3×D3—22no—
353C22×C3×D3—22no—
354C22×C3×D3—41no—
355C22×C3×D3C2412yes—
356C22×C3×D3C2411yescharacteristic
357C22×C3×D3C2411yescharacteristic
358C2×D32—24no—
359C2×D32—24no—
360C2×D32—42no—
361C32×Q8—22no—
362C32×D4—24no—
363C32×D4—22no—
364C2×C32×C4—24no—
365C2×C32×C4C2×D414yes—
366C2×C32×C4C2412yes—
367C2×C32×C4C2411yescharacteristic
368C2×C32×C4C2411yescharacteristic
369#638—28no—
370#638C2×D418yes—
371C2×C3⋊Dic3—24no—
372C2×C3⋊Dic3—28no—
373C2×C3⋊Dic3C2414yes—
374C2×C3⋊Dic3C2412yes—
375C4⋊(C3⋊D3)C2×D414yes—
376C4×C3⋊D3—28no—
377C4×C3⋊D3C2×D418yes—
378#634—24no—
379#634—24no—
380#634—28no—
381#634C2×D414yes—
382C3×#67—24no—
383C3×#67—24no—
384C3×#67—42no—
385C3×#67—44no—
386C2×C3×Dic3—22no—
387C2×C3×Dic3—42no—
388C2×C3×Dic3C2412yes—
389C2×C3×Dic3C2414yes—
390C2×C3×Dic3C2412yes—
391C2×C3×Dic3C2411yescharacteristic
392C2×C3×Dic3C2412yes—
393C2×C3×Dic3C2411yescharacteristic
394C3×D12—22no—
395C3×C4×D3—22no—
396C3×C4×D3—22no—
397C3×C4×D3—22no—
398C3×C4×D3—24no—
399C3×C4×D3—22no—
400C3×Dic6—22no—
401#627—24no—
402#626—24no—
403#626—24no—
404#625—24no—
405#624—24no—
406#624—44no—
407D3×Dic3—24no—
408D3×Dic3—24no—
409C2×2−1+4—91no—
410C22×#41—91no—
411D4×Q8—92no—
412#548—92no—
413#547—92no—
414#547—94no—
415#546—92no—
416#546—94no—
417#537—31no—
418#537—92no—
419#536—91no—
420#536—92no—
421#525—31no—
422#525—92no—
423C2×C22⋊Q8—91no—
424C2×C22⋊Q8—92no—
425#520—91no—
426C24×C3—31no—
427C23×D3—32no—
428C23×D3—32no—
429C23×D3C22×D311yescharacteristic
430C3×#41—28no—
431C3×#41—24no—
432C3×#41—24no—
433C3×#41—64no—
434C2×C3×Q8—21no—
435C2×C3×Q8—31no—
436C2×C3×Q8C22×D311yescharacteristic
437C2×C3×Q8C22×D311yescharacteristic
438C2×C3×D4—22no—
439C2×C3×D4—21no—
440C2×C3×D4—32no—
441C2×C3×D4—32no—
442C2×C3×D4—34no—
443C2×C3×D4—32no—
444C2×C3×D4—31no—
445C2×C3×D4C22×D312yes—
446C2×C3×D4C22×D311yescharacteristic
447C2×C3×D4C22×D311yescharacteristic
448C2×C3×D4C22×D312yes—
449C22×C3×C4—22no—
450C22×C3×C4—21no—
451C22×C3×C4—31no—
452C22×C3×C4—32no—
453C22×C3×C4—31no—
454C22×C3×C4—31no—
455C22×C3×C4—31no—
456C22×C3×C4—32no—
457C22×C3×C4—31no—
458C22×C3×C4—64no—
459C22×C3×C4C22×D312yes—
460C22×C3×C4C22×D312yes—
461C22×C3×C4C22×D311yescharacteristic
462C22×C3×C4C22×D311yescharacteristic
463C2×#67—32no—
464C2×#67—32no—
465C2×#67—34no—
466C2×#67—34no—
467C2×#67—32no—
468C2×#67—32no—
469C2×#67—32no—
470C2×#67—32no—
471C2×#67—62no—
472C2×#67—64no—
473C2×#67—68no—
474C2×#67C22×D312yes—
475C2×#67C22×D312yes—
476C2×#67C22×D314yes—
477C2×#67C22×D312yes—
478C22×Dic3—34no—
479C22×Dic3—34no—
480C22×Dic3—32no—
481C22×Dic3—32no—
482C22×Dic3—32no—
483C22×Dic3—32no—
484C22×Dic3—62no—
485C22×Dic3—64no—
486C22×Dic3C22×D311yescharacteristic
487C22×Dic3C22×D312yes—
488#239—64no—
489D3×Q8—64no—
490D3×Q8—68no—
491D3×Q8—68no—
492D3×Q8—616no—
493#237—64no—
494#237—68no—
495#237—68no—
496#237—68no—
497#237—616no—
498#237—616no—
499#237—616no—
500#237—632no—
501D3×D4—64no—
502D3×D4—68no—
503#235—24no—
504#235—38no—
505#235—38no—
506#235—68no—
507#235—64no—
508#235—64no—
509#235—68no—
510#235—68no—
511#235—68no—
512#235—68no—
513#235—68no—
514#235—616no—
515C2×D12—31no—
516C2×D12—31no—
517C2×D12—32no—
518C2×D12—32no—
519C2×D12—61no—
520C2×D12—64no—
521C2×D12C22×D311yescharacteristic
522C2×C4×D3—24no—
523C2×C4×D3—32no—
524C2×C4×D3—32no—
525C2×C4×D3—32no—
526C2×C4×D3—32no—
527C2×C4×D3—34no—
528C2×C4×D3—34no—
529C2×C4×D3—32no—
530C2×C4×D3—32no—
531C2×C4×D3—34no—
532C2×C4×D3—34no—
533C2×C4×D3—62no—
534C2×C4×D3—64no—
535C2×C4×D3—68no—
536C2×C4×D3—68no—
537C2×C4×D3C22×D311yescharacteristic
538C2×C4×D3C22×D311yescharacteristic
539C2×C4×D3C22×D311yescharacteristic
540C2×C4×D3C22×D312yes—
541C2×C4×D3C22×D311yescharacteristic
542C2×Dic6—31no—
543C2×Dic6—31no—
544C2×Dic6—32no—
545C2×Dic6—34no—
546C2×Dic6—34no—
547C2×Dic6—32no—
548C2×Dic6—32no—
549C2×Dic6—32no—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C2×Dic6—61no—
553C2×Dic6—62no—
554C2×Dic6—62no—
555C2×Dic6—64no—
556C2×Dic6—64no—
557C2×Dic6—68no—
558C2×Dic6—68no—
559C2×Dic6—616no—
560C2×Dic6—68no—
561C2×Dic6—64no—
562C2×Dic6—64no—
563C2×Dic6C22×D311yescharacteristic
564C3×C4⋊C4—32no—
565C3×C4⋊C4—32no—
566C3×C4⋊C4—34no—
567C3×C4⋊C4—32no—
568C3×C4⋊C4—31no—
569C3×C4⋊C4—32no—
570C3×C4⋊C4—31no—
571C3×C22⋊C4—32no—
572C3×C22⋊C4—34no—
573C3×C22⋊C4—32no—
574C3×C22⋊C4—32no—
575C3×C22⋊C4—32no—
576C3×C22⋊C4—34no—
577C3×C22⋊C4—32no—
578C3×C42—32no—
579#217—34no—
580#217—34no—
581#217—34no—
582#217—34no—
583#217C22×D312yes—
584#217C22×D314yes—
585#217C22×D312yes—
586#217C22×D312yes—
587(C2×D3)⋊C4—34no—
588(C2×D3)⋊C4—34no—
589(C2×D3)⋊C4—34no—
590(C2×D3)⋊C4—34no—
591(C2×D3)⋊C4—34no—
592(C2×D3)⋊C4—34no—
593(C2×D3)⋊C4C22×D312yes—
594(C2×D3)⋊C4C22×D314yes—
595(C2×D3)⋊C4C22×D312yes—
596C4⋊Dic3—34no—
597C4⋊Dic3—34no—
598C4⋊Dic3—34no—
599C4⋊Dic3—34no—
600C4⋊Dic3C22×D312yes—
601C4⋊Dic3C22×D311yescharacteristic
602C4⋊Dic3C22×D312yes—
603C4⋊Dic3C22×D311yescharacteristic
604Dic3⋊C4—34no—
605Dic3⋊C4—34no—
606Dic3⋊C4—34no—
607Dic3⋊C4—34no—
608Dic3⋊C4—34no—
609Dic3⋊C4—34no—
610Dic3⋊C4C22×D312yes—
611Dic3⋊C4C22×D314yes—
612Dic3⋊C4C22×D312yes—
613C4×Dic3—34no—
614C4×Dic3—34no—
615C4×Dic3C22×D312yes—
616C22×C32—22no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—22no—
620C22×C32—22no—
621C22×C32C22×D412yes—
622C22×C32C2511yescharacteristic
623C2×C3⋊D3—22no—
624C2×C3⋊D3—22no—
625C2×C3⋊D3C22×D414yes—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—22no—
629C2×C3×D3—21no—
630C2×C3×D3—22no—
631C2×C3×D3—21no—
632C2×C3×D3—22no—
633C2×C3×D3—21no—
634C2×C3×D3—44no—
635C2×C3×D32−1+412yescomplemented
636D32—48no—
637C32×C4—22no—
638C32×C4C22×D412yes—
639C32×C4C22×D412yes—
640C3⋊Dic3—24no—
641C3⋊Dic3C22×D414yes—
642C3×Dic3—21no—
643C3×Dic3—22no—
644C3×Dic3—21no—
645C3×Dic3—22no—
646C3×Dic3—22no—
647C3×Dic3—24no—
6482−1+4—188no—
649C2×#41—31no—
650C2×#41—92no—
651C2×#41—92no—
652C2×#41—91no—
653C2×#41—91no—
654C2×#41—92no—
655C2×#41—94no—
656C2×#41—91no—
657C2×#41—92no—
658C2×#41—188no—
659C2×#41D3211yescharacteristic, complemented
660C22×Q8—91no—
661C22×Q8—92no—
662C22×Q8—91no—
663C22×Q8—92no—
664C22×D4—91no—
665C22×D4—92no—
666C23×C4—31no—
667C23×C4—92no—
668C4⋊Q8—92no—
669C4⋊Q8—94no—
670#124—92no—
671#124—94no—
672#123—32no—
673#123—94no—
674#123—94no—
675#123—94no—
676#123—94no—
677C22⋊Q8—31no—
678C22⋊Q8—32no—
679C22⋊Q8—31no—
680C22⋊Q8—32no—
681C22⋊Q8—94no—
682C22⋊Q8—94no—
683C22⋊Q8—94no—
684C22⋊Q8—92no—
685C22⋊Q8—92no—
686C22⋊Q8—92no—
687C22⋊Q8—92no—
688C22⋊Q8—92no—
689C22⋊Q8—92no—
690#121—31no—
691#121—31no—
692#121—32no—
693#121—34no—
694#121—32no—
695#121—94no—
696#121—94no—
697#121—94no—
698#120—32no—
699#120—94no—
700C4×Q8—92no—
701C4×D4—32no—
702C4×D4—32no—
703C4×D4—92no—
704C4×D4—94no—
705C4×D4—94no—
706C4×D4—94no—
707#117—31no—
708#117—92no—
709C2×C4⋊C4—31no—
710C2×C4⋊C4—92no—
711C2×C4⋊C4—94no—
712C2×C4⋊C4—92no—
713C2×C22⋊C4—94no—
714C2×C22⋊C4—92no—
715C23×C3—22no—
716C23×C3—21no—
717C23×C3—31no—
718C23×C3—32no—
719C23×C3—31no—
720C23×C3—62no—
721C23×C3—62no—
722C23×C3—121no—
723C23×C3C23×D312yes—
724C23×C3C23×D312yes—
725C23×C3C23×D311yescharacteristic
726C23×C3C23×D311yescharacteristic
727C22×D3—22no—
728C22×D3—22no—
729C22×D3—32no—
730C22×D3—32no—
731C22×D3—41no—
732C22×D3—62no—
733C22×D3—64no—
734C22×D3—64no—
735C22×D3—64no—
736C22×D3—64no—
737C22×D3—122no—
738C22×D3—122no—
739C22×D3C23×D312yes—
740C22×D3C23×D311yescharacteristic
741C22×D3C23×D311yescharacteristic
742C3×Q8—24no—
743C3×Q8—22no—
744C3×Q8—22no—
745C3×Q8—62no—
746C3×D4—28no—
747C3×D4—24no—
748C3×D4—24no—
749C3×D4—24no—
750C3×D4—22no—
751C3×D4—22no—
752C3×D4—64no—
753C3×D4—64no—
754C3×D4—62no—
755C3×D4—124no—
756C3×D4—122no—
757C2×C3×C4—28no—
758C2×C3×C4—24no—
759C2×C3×C4—24no—
760C2×C3×C4—21no—
761C2×C3×C4—22no—
762C2×C3×C4—21no—
763C2×C3×C4—24no—
764C2×C3×C4—32no—
765C2×C3×C4—34no—
766C2×C3×C4—31no—
767C2×C3×C4—32no—
768C2×C3×C4—31no—
769C2×C3×C4—32no—
770C2×C3×C4—62no—
771C2×C3×C4—62no—
772C2×C3×C4—62no—
773C2×C3×C4—64no—
774C2×C3×C4—62no—
775C2×C3×C4—62no—
776C2×C3×C4—122no—
777C2×C3×C4D3×D414yes—
778C2×C3×C4D3×D414yes—
779C2×C3×C4C23×D312yes—
780C2×C3×C4C23×D312yes—
781C2×C3×C4C23×D311yescharacteristic
782C2×C3×C4C23×D311yescharacteristic
783C2×C3×C4C23×D311yescharacteristic
784C2×C3×C4C23×D311yescharacteristic
785#67—24no—
786#67—24no—
787#67—38no—
788#67—38no—
789#67—42no—
790#67—44no—
791#67—68no—
792#67—64no—
793#67—64no—
794#67—64no—
795#67—64no—
796#67—68no—
797#67—68no—
798#67—616no—
799C2×Dic3—22no—
800C2×Dic3—32no—
801C2×Dic3—32no—
802C2×Dic3—34no—
803C2×Dic3—34no—
804C2×Dic3—42no—
805C2×Dic3—62no—
806C2×Dic3—64no—
807C2×Dic3—64no—
808C2×Dic3—64no—
809C2×Dic3—68no—
810C2×Dic3—68no—
811C2×Dic3—616no—
812C2×Dic3—68no—
813C2×Dic3—64no—
814C2×Dic3—64no—
815C2×Dic3C23×D312yes—
816C2×Dic3C23×D314yes—
817C2×Dic3C23×D312yes—
818C2×Dic3C23×D311yescharacteristic
819C2×Dic3C23×D312yes—
820C2×Dic3C23×D311yescharacteristic
821D12—22no—
822D12—34no—
823D12—34no—
824D12—64no—
825D12—64no—
826D12—64no—
827C4×D3—22no—
828C4×D3—22no—
829C4×D3—22no—
830C4×D3—22no—
831C4×D3—24no—
832C4×D3—38no—
833C4×D3—38no—
834C4×D3—68no—
835C4×D3—64no—
836C4×D3—64no—
837C4×D3—64no—
838C4×D3—64no—
839C4×D3—68no—
840C4×D3—68no—
841C4×D3—616no—
842C4×D3—124no—
843C4×D3—124no—
844Dic6—22no—
845Dic6—34no—
846Dic6—34no—
847Dic6—64no—
848Dic6—64no—
849Dic6—64no—
850Dic6—68no—
851Dic6—68no—
852Dic6—68no—
853Dic6—616no—
854Dic6—68no—
855Dic6—64no—
856Dic6—64no—
857Dic6—64no—
858Dic6—64no—
859C2×C32—22no—
860C2×C32—42no—
861C2×C32C23×D411yescharacteristic
862C2×C32C2×2−1+411yescharacteristic
863C2×C32#58511yescharacteristic
864C3⋊D3—24no—
865C3×D3—22no—
866C3×D3—42no—
867C3×D3—41no—
868C24—31no—
869C24—92no—
870#41—24no—
871#41—64no—
872#41—98no—
873#41—188no—
874#41—188no—
875#41—188no—
876#41—184no—
877#41—184no—
878#41—188no—
879#41—1816no—
880C2×Q8—31no—
881C2×Q8—92no—
882C2×Q8—91no—
883C2×Q8—92no—
884C2×Q8—94no—
885C2×Q8—92no—
886C2×Q8—188no—
887C2×Q8—184no—
888C2×Q8—188no—
889C2×Q8—184no—
890C2×Q8C2×D3211yescharacteristic
891C2×D4—32no—
892C2×D4—32no—
893C2×D4—32no—
894C2×D4—34no—
895C2×D4—31no—
896C2×D4—92no—
897C2×D4—92no—
898C2×D4—92no—
899C2×D4—92no—
900C2×D4—94no—
901C2×D4—91no—
902C2×D4—184no—
903C2×D4—188no—
904C2×D4C2×D3212yes—
905C2×D4C2×D3211yescharacteristic
906C22×C4—31no—
907C22×C4—32no—
908C22×C4—31no—
909C22×C4—31no—
910C22×C4—31no—
911C22×C4—31no—
912C22×C4—32no—
913C22×C4—64no—
914C22×C4—92no—
915C22×C4—94no—
916C22×C4—92no—
917C22×C4—92no—
918C22×C4—92no—
919C22×C4—92no—
920C22×C4—94no—
921C22×C4—94no—
922C22×C4—188no—
923C22×C4C2×D3212yes—
924C22×C4C2×D3211yescharacteristic
925C4⋊C4—32no—
926C4⋊C4—32no—
927C4⋊C4—31no—
928C4⋊C4—32no—
929C4⋊C4—34no—
930C4⋊C4—31no—
931C4⋊C4—32no—
932C4⋊C4—94no—
933C4⋊C4—94no—
934C4⋊C4—94no—
935C4⋊C4—94no—
936C4⋊C4—94no—
937C22⋊C4—32no—
938C22⋊C4—32no—
939C22⋊C4—32no—
940C22⋊C4—34no—
941C22⋊C4—32no—
942C22⋊C4—34no—
943C22⋊C4—32no—
944C22⋊C4—94no—
945C22⋊C4—94no—
946C22⋊C4—94no—
947C22⋊C4—94no—
948C22⋊C4—94no—
949C42—32no—
950C42—94no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—21no—
955C22×C3—24no—
956C22×C3—22no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—22no—
960C22×C3—22no—
961C22×C3—22no—
962C22×C3—22no—
963C22×C3—21no—
964C22×C3—32no—
965C22×C3—41no—
966C22×C3—41no—
967C22×C3—42no—
968C22×C3—42no—
969C22×C3—61no—
970C22×C3—61no—
971C22×C3—62no—
972C22×C3—61no—
973C22×C3—62no—
974C22×C3—62no—
975C22×C3—61no—
976C22×C3—61no—
977C22×C3—124no—
978C22×C3C2×D3×D412yes—
979C22×C3C2×D3×D412yes—
980C22×C3C24×D311yescharacteristic
981C22×C3C24×D311yescharacteristic
982C2×D3—21no—
983C2×D3—21no—
984C2×D3—21no—
985C2×D3—22no—
986C2×D3—21no—
987C2×D3—21no—
988C2×D3—22no—
989C2×D3—22no—
990C2×D3—34no—
991C2×D3—34no—
992C2×D3—44no—
993C2×D3—64no—
994C2×D3—62no—
995C2×D3—62no—
996C2×D3—62no—
997C2×D3—62no—
998C2×D3—122no—
999C2×D3—122no—
1000C2×D3—128no—
1001C2×D3—128no—
1002C2×D3#101012yescomplemented
1003C3×C4—24no—
1004C3×C4—22no—
1005C3×C4—22no—
1006C3×C4—22no—
1007C3×C4—22no—
1008C3×C4—61no—
1009C3×C4—62no—
1010C3×C4—61no—
1011C3×C4—64no—
1012C3×C4—62no—
1013C3×C4—62no—
1014C3×C4C2×D3×D412yes—
1015C3×C4C2×D3×D412yes—
1016C3×C4C2×D3×D412yes—
1017C3×C4C2×D3×D412yes—
1018Dic3—22no—
1019Dic3—21no—
1020Dic3—21no—
1021Dic3—22no—
1022Dic3—22no—
1023Dic3—24no—
1024Dic3—34no—
1025Dic3—34no—
1026Dic3—64no—
1027Dic3—68no—
1028Dic3—64no—
1029Dic3—64no—
1030C32#348911yescharacteristic, complemented, Sylow
1031C23—31no—
1032C23—31no—
1033C23—32no—
1034C23—62no—
1035C23—62no—
1036C23—92no—
1037C23—121no—
1038C23—184no—
1039C23—184no—
1040C23—362no—
1041C23C22×D3212yes—
1042C23C22×D3211yescharacteristic
1043Q8—22no—
1044Q8—62no—
1045Q8—94no—
1046Q8—188no—
1047Q8—184no—
1048Q8—184no—
1049Q8—184no—
1050D4—24no—
1051D4—22no—
1052D4—64no—
1053D4—64no—
1054D4—62no—
1055D4—98no—
1056D4—94no—
1057D4—124no—
1058D4—122no—
1059D4—184no—
1060D4—184no—
1061D4—184no—
1062D4—188no—
1063C2×C4—24no—
1064C2×C4—32no—
1065C2×C4—32no—
1066C2×C4—34no—
1067C2×C4—31no—
1068C2×C4—31no—
1069C2×C4—32no—
1070C2×C4—62no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—64no—
1076C2×C4—92no—
1077C2×C4—98no—
1078C2×C4—94no—
1079C2×C4—122no—
1080C2×C4—188no—
1081C2×C4—184no—
1082C2×C4—184no—
1083C2×C4—184no—
1084C2×C4—188no—
1085C2×C4—184no—
1086C2×C4—364no—
1087C2×C4#381114yes—
1088C2×C4C22×D3212yes—
1089C2×C4C22×D3211yescharacteristic
1090C2×C4C22×D3211yescharacteristic
1091C2×C3—22no—
1092C2×C3—22no—
1093C2×C3—21no—
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—42no—
1097C2×C3—44no—
1098C2×C3—42no—
1099C2×C3—42no—
1100C2×C3—62no—
1101C2×C3—122no—
1102C2×C3—121no—
1103C2×C3C22×D3×D411yescharacteristic
1104C2×C3C22×D3×D411yescharacteristic
1105C2×C3C2×#101011yescharacteristic
1106C2×C3#596411yescharacteristic
1107C2×C3#596611yescharacteristic
1108C2×C3D3×2−1+411yescharacteristic
1109D3—22no—
1110D3—41no—
1111D3—42no—
1112D3—64no—
1113D3—64no—
1114D3—124no—
1115C22—21no—
1116C22—21no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—32no—
1121C22—61no—
1122C22—61no—
1123C22—61no—
1124C22—62no—
1125C22—61no—
1126C22—62no—
1127C22—61no—
1128C22—62no—
1129C22—94no—
1130C22—124no—
1131C22—182no—
1132C22—182no—
1133C22—368no—
1134C22C2×#381112yes—
1135C22C23×D3211yescharacteristic
1136C4—22no—
1137C4—62no—
1138C4—64no—
1139C4—62no—
1140C4—61no—
1141C4—61no—
1142C4—62no—
1143C4—94no—
1144C4—184no—
1145C4C2×#381112yes—
1146C4C2×#381112yes—
1147C3—21no—
1148C3#8604211yescharacteristic, complemented
1149C3#8638011yescharacteristic, complemented
1150C2—22no—
1151C2—42no—
1152C2—62no—
1153C2—121no—
1154C2—122no—
1155C2—184no—
1156C2D3×#101011yescharacteristic
1157C2#1059669611yescharacteristic
1158C2C22×#381111yescharacteristic
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×#64367C2semidirect
2. C2×D3×#235C2semidirect
3. C3×#5833C2semidirect
4. C3×#5828C2semidirect
5. #10595429C2semidirect
6. #10595405C2semidirect
7. #10595307C2semidirect
8. #10595306C2semidirect
9. #10595240C2semidirect
10. #10595162C2semidirect
11. #10595078C2semidirect
12. #10594990C2semidirect
13. #10594918C2semidirect
14. #10594915C2semidirect
15. #10594856C2semidirect
16. C2×#63857C2semidirect
17. #10594834C2semidirect
20. C2×C32×#41C22semidirect
22. C2×Q8×C3⋊D3C22semidirect
23. C2×#3830C22semidirect
24. C2×#3830C22semidirect
26. C2×#3828C22semidirect
27. C22×#634C22semidirect
28. C22×#634C22semidirect
41. C3×#946C22semidirect
42. C3×#946C22semidirect
43. C3×#939C22semidirect
45. C3×#938C22semidirect
46. C3×#938C22semidirect
48. C3×#935C22semidirect
49. C3×#930C22semidirect
51. C3×C4×#67C22semidirect
52. C3×#926C22semidirect
53. C2×C3×C4⋊Dic3C22semidirect
54. C3×#924C22semidirect
56. #63982C22semidirect
57. #63980C22semidirect
58. #63975C22semidirect
60. #67⋊Dic3C22semidirect
61. C2×Dic3⋊Dic3C22semidirect
62. #63962C22semidirect
64. #63958C22semidirect
65. #63958C22semidirect
66. #63952C22semidirect
68. #63913C22semidirect
69. #63900C22semidirect
71. #63896C22semidirect
72. #63894C22semidirect
73. #63883C22semidirect
74. #63866C22semidirect
75. #63860C22semidirect
78. #63857C22semidirect
79. #63857C22semidirect
80. #63857C22semidirect
81. #63857C22semidirect
82. #63853C22semidirect
83. #63853C22semidirect
84. #63849C22semidirect
85. #63844C22semidirect
86. #63840C22semidirect
94. #5833D3semidirect
95. #5828D3semidirect
138. #3828D4semidirect
208. C2×C3×#41C2×D3semidirect
209. C2×C3×#41C2×D3semidirect
272. #946C2×D3semidirect
273. #946C2×D3semidirect
277. #939C2×D3semidirect
281. #938C2×D3semidirect
282. #938C2×D3semidirect
288. #935C2×D3semidirect
291. #930C2×D3semidirect
294. C4×#67C2×D3semidirect
296. #926C2×D3semidirect
298. C2×C4⋊Dic3C2×D3semidirect
305. #924C2×D3semidirect
635. C2×C3×D32−1+4semidirect
659. C2×#41D32semidirect
1002. C2×D3#1010semidirect
1030. C32#3489semidirect
1148. C3#86042semidirect
1149. C3#86380semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C2×D3×#2352
C3×#58332
C3×#58282
#105954292
#105954052
#105953072
#105953062
#105952402
#105951622
#105950782
#105949902
#105949182
#105949152
#105948562
C2×#638572
#105948342
#863803
#860423