Finite Group Databasebeta

← #11904776

Subgroups — #11904776

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×#64364C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3C3×#5816C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5#10595431C212yesmaximal, complemented
6#10595430C212yesmaximal, complemented
7#10595429C212yesmaximal, complemented
8#10595405C212yesmaximal, complemented
9#10595404C212yesmaximal, complemented
10#10595362C212yesmaximal, complemented
11#10595361C212yesmaximal, complemented
12#10595341C212yesmaximal, complemented
13#10595077C214yesmaximal, complemented
14#10595043C211yesmaximal, characteristic, complemented
15#10595023C211yesmaximal, characteristic, complemented
16#10594990C211yesmaximal, characteristic, complemented
17#10594917C214yesmaximal, complemented
18#86356—31nomaximal
19#85985—31nomaximal
20C22×C32×Q8C2211yescharacteristic, complemented
21#64364—28no—
22C2×#3832C2212yescomplemented
23C2×#3832C2212yescomplemented
24C2×Q8×C3⋊D3C2212yescomplemented
25C2×Q8×C3⋊D3C2212yescomplemented
26C2×#3828C2211yescharacteristic
27C2×#3828C2214yescomplemented
28C2×#3828C2211yescharacteristic, complemented
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×#947C2212yescomplemented
41C3×#946C2212yes—
42C3×#946C2212yes—
43C3×#946C2212yescomplemented
44C3×#946C2212yescomplemented
45C3×#946C2212yescomplemented
46C3×#946C2212yescomplemented
47C3×#944C2212yescomplemented
48C3×#929C2214yescomplemented
49C2×C3×(C2×D3)⋊C4C2212yes—
50C3×#926C2211yescharacteristic, complemented
51C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2212yescomplemented
53#63978C2214yescomplemented
54#63977C2212yes—
55#63966C2212yescomplemented
56#63952C2214yescomplemented
57#63923C2214yes—
58#63921C2214yes—
59#63916C2212yescomplemented
60#63913C2214yescomplemented
61#63912C2214yescomplemented
62#63910C2214yescomplemented
63#63910C2214yescomplemented
64#63909C2211yescharacteristic
65#63909C2211yescharacteristic, complemented
66#63909C2212yescomplemented
67C4×#626C2212yes—
68C4×#626C2212yescomplemented
69#63900C2212yescomplemented
70#63897C2214yescomplemented
71#63896C2214yes—
72#63896C2214yescomplemented
73#63894C2212yescomplemented
74#63883C2214yescomplemented
75#63881C2214yes—
76#63881C2214yescomplemented
77#63871C2212yescomplemented
78#63865C2214yescomplemented
79#63857C2211yescharacteristic
80#63857C2211yescharacteristic, complemented
81#63857C2212yescomplemented
82#63853C2214yescomplemented
83#63853C2214yescomplemented
84#63849C2212yescomplemented
85#63844C2212yescomplemented
86#63840C2214yescomplemented
87C2×D3×#41—31no—
88C2×#1007—31no—
89C2×#1007—31no—
90C2×#1007—61no—
91C22×#235—31no—
92C3×#536—31no—
93C2×C3×C22⋊Q8—31no—
94#5833—31no—
95#5816D311yescharacteristic, complemented
96C2×#946D311yescharacteristic, complemented
97#5791—31no—
98#5727—32no—
99#5726—32no—
100#5677—32no—
101#5676—32no—
102#5655—34no—
103#5654—34no—
104#5633—32no—
105#5632—32no—
106#5631—32no—
107#5630—32no—
108#5629—32no—
109#5629—32no—
110#5628—32no—
111#5628—32no—
112#5627—32no—
113#5627—32no—
114D3×C22⋊Q8—32no—
115D3×C22⋊Q8—32no—
116#5524—31no—
117#5523—31no—
118#5510—31no—
119#5507—34no—
120#5504—31no—
121#5490—34no—
122C23×C3×D3C2311yescharacteristic
123C22×D32C2312yes—
124C2×C32×Q8—24no—
125C2×C32×Q8C2312yes—
126C2×C32×Q8C2312yes—
127C22×C32×C4C2312yes—
128C22×C32×C4C2311yescharacteristic
129C2×#638C2312yes—
130C2×#638C2312yes—
131#3832—28no—
132#3832—28no—
133Q8×C3⋊D3—28no—
134Q8×C3⋊D3—28no—
135#3828—24no—
136#3828—216no—
137#3828D418yescomplemented
138C2×C4⋊(C3⋊D3)C2314yes—
139C2×C4⋊(C3⋊D3)C2311yescharacteristic
140C2×C4⋊(C3⋊D3)C2311yescharacteristic
141C2×C4×C3⋊D3C2314yes—
142C2×C4×C3⋊D3C2314yes—
143C2×C4×C3⋊D3C2312yes—
144C2×C4×C3⋊D3C2312yes—
145C2×#634C2314yes—
146C2×#634C2311yescharacteristic
147C2×#634C2311yescharacteristic
148C2×C3×#67C2312yes—
149C22×C3×Dic3C2311yescharacteristic
150C22×C3×Dic3C2312yes—
151C3×#235—24no—
152C2×C3×D12C2311yescharacteristic
153C2×C3×C4×D3—24no—
154C2×C3×C4×D3C2311yescharacteristic
155C2×C3×C4×D3C2311yescharacteristic
156C2×C3×C4×D3C2311yescharacteristic
157C2×C3×C4×D3C2312yes—
158C2×C3×C4×D3C2311yescharacteristic
159C2×C3×Dic6C2311yescharacteristic
160D3×#67—28no—
161C2×#627C2312yes—
162C2×#626C2312yes—
163C2×#626C2312yes—
164C2×#626C2312yes—
165C2×#626C2314yes—
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×#217C2312yes—
180C3×(C2×D3)⋊C4C2314yes—
181C3×(C2×D3)⋊C4C2314yes—
182C3×(C2×D3)⋊C4C2314yes—
183C3×(C2×D3)⋊C4C2314yes—
184C3×C4⋊Dic3C2312yes—
185C3×C4⋊Dic3C2312yes—
186C3×C4⋊Dic3C2311yescharacteristic
187C3×C4⋊Dic3C2311yescharacteristic
188C3×Dic3⋊C4C2314yes—
189C3×Dic3⋊C4C2314yes—
190C3×Dic3⋊C4C2314yes—
191C3×Dic3⋊C4C2314yes—
192C3×C4×Dic3C2312yes—
193#3724C2314yes—
194Dic3⋊Dic3C2312yes—
195Dic3⋊Dic3C2314yes—
196Dic3⋊Dic3C2312yes—
197#3722C2314yes—
198#3722C2312yes—
199#3722C2314yes—
200#3722C2312yes—
201(C2×D3)⋊Dic3C2312yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2312yes—
204Dic32C2314yes—
205#3489—91noSylow
206C2×C3×#41—31no—
207C22×C3×Q8—21no—
208C22×C3×Q8C2×D311yescharacteristic, complemented
209C22×C3×Q8C2×D311yescharacteristic, complemented
210C23×C3×C4—31no—
211C22×#67—32no—
212D3×#41—68no—
213#1007—68no—
214#1007—68no—
215#1007—616no—
216C2×#239—32no—
217C2×#239—32no—
218C2×#239—32no—
219C2×#239—32no—
220C2×#239—31no—
221C2×#239—62no—
222C2×#239—62no—
223C2×D3×Q8—32no—
224C2×D3×Q8—32no—
225C2×D3×Q8—32no—
226C2×D3×Q8—32no—
227C2×D3×Q8—31no—
228C2×D3×Q8—62no—
229C2×D3×Q8—62no—
230C2×#237—32no—
231C2×#237—31no—
232C2×D3×D4—32no—
233C2×D3×D4—31no—
234C2×#235—31no—
235C2×#235—31no—
236C2×#235—34no—
237C2×#235—34no—
238C2×#235—31no—
239C2×#235—31no—
240C2×#235—32no—
241C2×#235—31no—
242C2×#235—32no—
243C2×#235—32no—
244C2×#235—31no—
245C2×#235—61no—
246C2×#235—61no—
247C2×#235—64no—
248C2×#235—68no—
249C2×#235C2×D311yescharacteristic
250C22×D12—31no—
251C22×C4×D3—32no—
252C22×C4×D3—32no—
253C22×C4×D3C2×D311yescharacteristic
254C22×Dic6—31no—
255C3×C4⋊Q8—32no—
256C3×#124—32no—
257C3×#123—34no—
258C3×C22⋊Q8—32no—
259C3×C22⋊Q8—32no—
260C3×C22⋊Q8—32no—
261C3×C22⋊Q8—32no—
262C3×C22⋊Q8—32no—
263C3×C22⋊Q8—32no—
264C3×#117—31no—
265C2×C3×C4⋊C4—32no—
266C2×C3×C4⋊C4—31no—
267C2×C3×C22⋊C4—32no—
268#953—32no—
269#947C2×D312yescomplemented
270#946—32no—
271#946C2×D312yes—
272#946C2×D312yes—
273#946C2×D312yescomplemented
274#946C2×D312yescomplemented
275#946C2×D312yescomplemented
276#946C2×D312yescomplemented
277#944C2×D312yescomplemented
278#939—34no—
279#938—32no—
280#930—34no—
281#930—31no—
282#930—31no—
283#930—32no—
284#929—32no—
285#929C2×D314yescomplemented
286C4×#67—34no—
287C4×#67—32no—
288C4×#67—32no—
289C2×(C2×D3)⋊C4C2×D312yes—
290#926C2×D311yescharacteristic, complemented
291C2×C4⋊Dic3C2×D311yescharacteristic, complemented
292#924—31no—
293#924—31no—
294#924—32no—
295C2×Dic3⋊C4C2×D312yescomplemented
296#897—31no—
297#897—32no—
298#897—31no—
299#897—32no—
300#896—34no—
301#896—34no—
302#896—34no—
303#896—34no—
304#895—32no—
305#895—32no—
306#895—31no—
307#895—31no—
308#895—34no—
309#895—34no—
310#894—34no—
311#894—34no—
312#894—34no—
313#894—34no—
314#893—34no—
315#893—34no—
316#893—32no—
317#892—32no—
318#892—32no—
319D3×C4⋊C4—32no—
320D3×C4⋊C4—32no—
321D3×C4⋊C4—34no—
322D3×C4⋊C4—34no—
323#888—34no—
324#888—34no—
325#887—32no—
326#886—32no—
327#885—34no—
328#885—34no—
329#884—34no—
330#884—34no—
331#884—34no—
332#884—34no—
333#883—34no—
334#883—34no—
335#882—32no—
336#882—34no—
337#882—34no—
338#67⋊C4—34no—
339#67⋊C4—34no—
340#67⋊C4—34no—
341D3×C22⋊C4—34no—
342D3×C22⋊C4—34no—
343#878—34no—
344#878—34no—
345C4×D12—32no—
346C4×D12—32no—
347C4×D12—32no—
348C4×Dic6—32no—
349C23×C32C2411yescharacteristic
350C22×C3⋊D3C2412yes—
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—24no—
362C32×Q8—24no—
363C2×C32×C4—24no—
364C2×C32×C4C2×D414yes—
365C2×C32×C4C2414yes—
366C2×C32×C4C2411yescharacteristic
367C2×C32×C4C2411yescharacteristic
368#638—24no—
369#638C2×D418yes—
370C2×C3⋊Dic3C2412yes—
371C2×C3⋊Dic3C2412yes—
372C4⋊(C3⋊D3)—28no—
373C4⋊(C3⋊D3)—22no—
374C4⋊(C3⋊D3)C2×D414yes—
375C4×C3⋊D3—28no—
376C4×C3⋊D3—24no—
377C4×C3⋊D3—28no—
378C4×C3⋊D3C2×D418yes—
379#634—22no—
380#634—28no—
381#634C2×D414yes—
382C3×#67—24no—
383C2×C3×Dic3—22no—
384C2×C3×Dic3—42no—
385C2×C3×Dic3C2412yes—
386C2×C3×Dic3C2414yes—
387C2×C3×Dic3C2412yes—
388C2×C3×Dic3C2411yescharacteristic
389C2×C3×Dic3C2412yes—
390C2×C3×Dic3C2411yescharacteristic
391C3×D12—22no—
392C3×C4×D3—22no—
393C3×C4×D3—22no—
394C3×C4×D3—22no—
395C3×C4×D3—24no—
396C3×C4×D3—22no—
397C3×Dic6—22no—
398#627—24no—
399#626—24no—
400#626—24no—
401#626—24no—
402#626—42no—
403#626—44no—
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—94no—
414#547—92no—
415#546—94no—
416#546—92no—
417#537—91no—
418#537—92no—
419#536—31no—
420#536—92no—
421#525—91no—
422#525—92no—
423C2×C22⋊Q8—31no—
424C2×C22⋊Q8—92no—
425#520—91no—
426C24×C3—31no—
427C23×D3—32no—
428C23×D3—32no—
429C23×D3C22×D311yescharacteristic
430C3×#41—64no—
431C2×C3×Q8—28no—
432C2×C3×Q8—24no—
433C2×C3×Q8—24no—
434C2×C3×Q8—22no—
435C2×C3×Q8—22no—
436C2×C3×Q8—31no—
437C2×C3×Q8C22×D312yes—
438C2×C3×Q8C22×D312yes—
439C2×C3×Q8C22×D312yes—
440C2×C3×Q8C22×D312yes—
441C2×C3×D4—32no—
442C2×C3×D4—31no—
443C22×C3×C4—22no—
444C22×C3×C4—21no—
445C22×C3×C4—31no—
446C22×C3×C4—32no—
447C22×C3×C4—31no—
448C22×C3×C4—32no—
449C22×C3×C4—31no—
450C22×C3×C4—31no—
451C22×C3×C4—31no—
452C22×C3×C4—64no—
453C22×C3×C4C22×D312yes—
454C22×C3×C4C22×D312yes—
455C22×C3×C4C22×D311yescharacteristic
456C22×C3×C4C22×D311yescharacteristic
457C2×#67—32no—
458C2×#67—32no—
459C2×#67—32no—
460C2×#67—32no—
461C2×#67—32no—
462C2×#67—32no—
463C2×#67—32no—
464C2×#67—32no—
465C2×#67—32no—
466C2×#67—34no—
467C2×#67—32no—
468C2×#67—62no—
469C2×#67—62no—
470C2×#67—68no—
471C2×#67C22×D312yes—
472C22×Dic3—32no—
473C22×Dic3—32no—
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D312yes—
476#239—64no—
477#239—68no—
478#239—68no—
479#239—68no—
480#239—68no—
481#239—616no—
482#239—616no—
483D3×Q8—64no—
484D3×Q8—68no—
485D3×Q8—68no—
486D3×Q8—68no—
487D3×Q8—68no—
488D3×Q8—616no—
489D3×Q8—616no—
490#237—64no—
491#237—68no—
492D3×D4—64no—
493D3×D4—68no—
494#235—24no—
495#235—38no—
496#235—38no—
497#235—68no—
498#235—64no—
499#235—64no—
500#235—68no—
501#235—68no—
502#235—68no—
503#235—616no—
504#235—616no—
505#235—632no—
506#235—68no—
507#235—64no—
508#235—64no—
509C2×D12—31no—
510C2×D12—31no—
511C2×D12—32no—
512C2×D12—32no—
513C2×D12—32no—
514C2×D12—34no—
515C2×D12—34no—
516C2×D12—31no—
517C2×D12—31no—
518C2×D12—32no—
519C2×D12—34no—
520C2×D12—61no—
521C2×D12—64no—
522C2×D12—61no—
523C2×D12—64no—
524C2×D12C22×D311yescharacteristic
525C2×C4×D3—24no—
526C2×C4×D3—32no—
527C2×C4×D3—32no—
528C2×C4×D3—32no—
529C2×C4×D3—32no—
530C2×C4×D3—32no—
531C2×C4×D3—34no—
532C2×C4×D3—34no—
533C2×C4×D3—34no—
534C2×C4×D3—34no—
535C2×C4×D3—32no—
536C2×C4×D3—32no—
537C2×C4×D3—32no—
538C2×C4×D3—34no—
539C2×C4×D3—34no—
540C2×C4×D3—62no—
541C2×C4×D3—64no—
542C2×C4×D3—64no—
543C2×C4×D3—62no—
544C2×C4×D3—68no—
545C2×C4×D3—68no—
546C2×C4×D3C22×D311yescharacteristic
547C2×C4×D3C22×D311yescharacteristic
548C2×C4×D3C22×D311yescharacteristic
549C2×C4×D3C22×D312yes—
550C2×C4×D3C22×D311yescharacteristic
551C2×Dic6—31no—
552C2×Dic6—31no—
553C2×Dic6—34no—
554C2×Dic6—34no—
555C2×Dic6—31no—
556C2×Dic6—31no—
557C2×Dic6—32no—
558C2×Dic6—32no—
559C2×Dic6—61no—
560C2×Dic6—61no—
561C2×Dic6—64no—
562C2×Dic6—64no—
563C2×Dic6C22×D311yescharacteristic
564C3×C4⋊C4—32no—
565C3×C4⋊C4—34no—
566C3×C4⋊C4—34no—
567C3×C4⋊C4—31no—
568C3×C4⋊C4—32no—
569C3×C4⋊C4—34no—
570C3×C4⋊C4—34no—
571C3×C4⋊C4—31no—
572C3×C22⋊C4—32no—
573C3×C22⋊C4—34no—
574C3×C22⋊C4—34no—
575C3×C22⋊C4—34no—
576C3×C22⋊C4—34no—
577C3×C42—32no—
578#217—32no—
579#217—34no—
580#217—32no—
581#217C22×D312yes—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—34no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—34no—
587(C2×D3)⋊C4—32no—
588(C2×D3)⋊C4—34no—
589(C2×D3)⋊C4—34no—
590(C2×D3)⋊C4—32no—
591(C2×D3)⋊C4—34no—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4C22×D314yes—
594(C2×D3)⋊C4C22×D314yes—
595(C2×D3)⋊C4C22×D314yes—
596(C2×D3)⋊C4C22×D314yes—
597C4⋊Dic3—32no—
598C4⋊Dic3—32no—
599C4⋊Dic3—34no—
600C4⋊Dic3C22×D312yes—
601C4⋊Dic3C22×D311yescharacteristic
602C4⋊Dic3C22×D312yes—
603C4⋊Dic3C22×D311yescharacteristic
604Dic3⋊C4—34no—
605Dic3⋊C4—34no—
606Dic3⋊C4—32no—
607Dic3⋊C4—34no—
608Dic3⋊C4—32no—
609Dic3⋊C4C22×D314yes—
610Dic3⋊C4C22×D314yes—
611Dic3⋊C4C22×D314yes—
612Dic3⋊C4C22×D314yes—
613C4×Dic3—34no—
614C4×Dic3—34no—
615C4×Dic3C22×D312yes—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32C22×D412yes—
619C22×C32C2511yescharacteristic
620C2×C3⋊D3—22no—
621C2×C3⋊D3—22no—
622C2×C3⋊D3—22no—
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—24no—
638C32×C4C22×D412yes—
639C32×C4C22×D412yes—
640C3⋊Dic3—22no—
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—92no—
656C2×#41—91no—
657C2×#41—91no—
658C2×#41—94no—
659C2×#41—188no—
660C22×Q8—91no—
661C22×Q8—92no—
662C22×Q8—92no—
663C22×Q8D3211yescharacteristic, complemented
664C22×D4—91no—
665C22×D4—92no—
666C23×C4—31no—
667C23×C4—92no—
668C4⋊Q8—32no—
669C4⋊Q8—94no—
670#124—32no—
671#124—94no—
672#123—34no—
673#123—94no—
674#123—94no—
675#123—92no—
676#123—94no—
677C22⋊Q8—32no—
678C22⋊Q8—32no—
679C22⋊Q8—32no—
680C22⋊Q8—32no—
681C22⋊Q8—32no—
682C22⋊Q8—32no—
683C22⋊Q8—94no—
684C22⋊Q8—94no—
685C22⋊Q8—94no—
686C22⋊Q8—91no—
687C22⋊Q8—92no—
688C22⋊Q8—91no—
689C22⋊Q8—92no—
690#121—94no—
691#121—94no—
692#121—94no—
693#121—91no—
694#121—92no—
695#121—91no—
696#121—92no—
697#121—94no—
698#120—94no—
699#120—92no—
700C4×Q8—92no—
701C4×D4—92no—
702C4×D4—92no—
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—32no—
711C2×C4⋊C4—92no—
712C2×C4⋊C4—94no—
713C2×C22⋊C4—32no—
714C2×C22⋊C4—94no—
715C23×C3—21no—
716C23×C3—31no—
717C23×C3—32no—
718C23×C3—31no—
719C23×C3—62no—
720C23×C3—62no—
721C23×C3—121no—
722C23×C3C23×D311yescharacteristic
723C23×C3C23×D311yescharacteristic
724C22×D3—22no—
725C22×D3—22no—
726C22×D3—32no—
727C22×D3—32no—
728C22×D3—32no—
729C22×D3—32no—
730C22×D3—41no—
731C22×D3—62no—
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—28no—
743C3×Q8—28no—
744C3×Q8—24no—
745C3×Q8—24no—
746C3×Q8—24no—
747C3×Q8—24no—
748C3×Q8—62no—
749C3×D4—64no—
750C3×D4—62no—
751C2×C3×C4—28no—
752C2×C3×C4—24no—
753C2×C3×C4—24no—
754C2×C3×C4—24no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—24no—
758C2×C3×C4—32no—
759C2×C3×C4—34no—
760C2×C3×C4—32no—
761C2×C3×C4—31no—
762C2×C3×C4—32no—
763C2×C3×C4—31no—
764C2×C3×C4—62no—
765C2×C3×C4—62no—
766C2×C3×C4—62no—
767C2×C3×C4—64no—
768C2×C3×C4—62no—
769C2×C3×C4—62no—
770C2×C3×C4—122no—
771C2×C3×C4D3×D414yes—
772C2×C3×C4D3×D414yes—
773C2×C3×C4C23×D314yes—
774C2×C3×C4C23×D314yes—
775C2×C3×C4C23×D311yescharacteristic
776C2×C3×C4C23×D311yescharacteristic
777C2×C3×C4C23×D311yescharacteristic
778C2×C3×C4C23×D311yescharacteristic
779#67—24no—
780#67—38no—
781#67—38no—
782#67—68no—
783#67—64no—
784#67—64no—
785#67—64no—
786#67—64no—
787#67—64no—
788#67—68no—
789#67—64no—
790#67—64no—
791#67—124no—
792#67—122no—
793C2×Dic3—22no—
794C2×Dic3—32no—
795C2×Dic3—32no—
796C2×Dic3—32no—
797C2×Dic3—32no—
798C2×Dic3—42no—
799C2×Dic3—62no—
800C2×Dic3—62no—
801C2×Dic3—64no—
802C2×Dic3—64no—
803C2×Dic3C23×D312yes—
804C2×Dic3C23×D314yes—
805C2×Dic3C23×D312yes—
806C2×Dic3C23×D311yescharacteristic
807C2×Dic3C23×D312yes—
808C2×Dic3C23×D311yescharacteristic
809D12—22no—
810D12—34no—
811D12—34no—
812D12—64no—
813D12—68no—
814D12—68no—
815D12—616no—
816D12—64no—
817D12—64no—
818D12—64no—
819D12—64no—
820D12—62no—
821D12—62no—
822D12—122no—
823D12—124no—
824C4×D3—22no—
825C4×D3—22no—
826C4×D3—22no—
827C4×D3—22no—
828C4×D3—24no—
829C4×D3—38no—
830C4×D3—38no—
831C4×D3—68no—
832C4×D3—64no—
833C4×D3—64no—
834C4×D3—68no—
835C4×D3—68no—
836C4×D3—64no—
837C4×D3—64no—
838C4×D3—68no—
839C4×D3—68no—
840C4×D3—616no—
841C4×D3—616no—
842C4×D3—68no—
843C4×D3—64no—
844C4×D3—64no—
845C4×D3—124no—
846C4×D3—124no—
847Dic6—22no—
848Dic6—34no—
849Dic6—34no—
850Dic6—64no—
851Dic6—64no—
852Dic6—64no—
853Dic6—68no—
854Dic6—68no—
855Dic6—616no—
856Dic6—64no—
857Dic6—62no—
858Dic6—62no—
859C2×C32—22no—
860C2×C32C23×D411yescharacteristic
861C2×C32C2×2−1+411yescharacteristic
862C2×C32#58511yescharacteristic
863C3⋊D3—24no—
864C3⋊D3—42no—
865C3×D3—22no—
866C3×D3—42no—
867C3×D3—41no—
868C24—31no—
869C24—92no—
870#41—64no—
871#41—98no—
872#41—1816no—
873#41—188no—
874#41—188no—
875#41—184no—
876#41—184no—
877#41—188no—
878#41—188no—
879#41—184no—
880C2×Q8—24no—
881C2×Q8—31no—
882C2×Q8—92no—
883C2×Q8—91no—
884C2×Q8—91no—
885C2×Q8—94no—
886C2×Q8—184no—
887C2×Q8—188no—
888C2×Q8—188no—
889C2×Q8C2×D3212yes—
890C2×Q8C2×D3212yes—
891C2×D4—32no—
892C2×D4—31no—
893C2×D4—92no—
894C2×D4—92no—
895C2×D4—92no—
896C2×D4—92no—
897C2×D4—94no—
898C2×D4—92no—
899C2×D4—92no—
900C2×D4—92no—
901C2×D4—91no—
902C2×D4—94no—
903C2×D4—91no—
904C2×D4—184no—
905C2×D4—188no—
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—94no—
920C22×C4—94no—
921C22×C4—92no—
922C22×C4—188no—
923C22×C4C2×D3212yes—
924C22×C4C2×D3211yescharacteristic
925C4⋊C4—32no—
926C4⋊C4—34no—
927C4⋊C4—32no—
928C4⋊C4—34no—
929C4⋊C4—31no—
930C4⋊C4—34no—
931C4⋊C4—31no—
932C4⋊C4—34no—
933C4⋊C4—92no—
934C4⋊C4—94no—
935C4⋊C4—94no—
936C4⋊C4—92no—
937C22⋊C4—32no—
938C22⋊C4—34no—
939C22⋊C4—34no—
940C22⋊C4—34no—
941C22⋊C4—34no—
942C22⋊C4—94no—
943C22⋊C4—92no—
944C22⋊C4—92no—
945C22⋊C4—94no—
946C22⋊C4—92no—
947C22⋊C4—94no—
948C22⋊C4—92no—
949C42—32no—
950C42—94no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—21no—
955C22×C3—22no—
956C22×C3—21no—
957C22×C3—32no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—62no—
963C22×C3—61no—
964C22×C3—62no—
965C22×C3—62no—
966C22×C3—61no—
967C22×C3—61no—
968C22×C3—124no—
969C22×C3C2×D3×D412yes—
970C22×C3C2×D3×D412yes—
971C22×C3C24×D311yescharacteristic
972C22×C3C24×D311yescharacteristic
973C2×D3—21no—
974C2×D3—21no—
975C2×D3—21no—
976C2×D3—22no—
977C2×D3—21no—
978C2×D3—21no—
979C2×D3—22no—
980C2×D3—22no—
981C2×D3—34no—
982C2×D3—34no—
983C2×D3—44no—
984C2×D3—64no—
985C2×D3—62no—
986C2×D3—62no—
987C2×D3—62no—
988C2×D3—62no—
989C2×D3—64no—
990C2×D3—62no—
991C2×D3—62no—
992C2×D3—62no—
993C2×D3—62no—
994C2×D3—62no—
995C2×D3—62no—
996C2×D3—122no—
997C2×D3—122no—
998C2×D3—122no—
999C2×D3—122no—
1000C2×D3—128no—
1001C2×D3—128no—
1002C2×D3#100712yescomplemented
1003C3×C4—28no—
1004C3×C4—24no—
1005C3×C4—24no—
1006C3×C4—22no—
1007C3×C4—22no—
1008C3×C4—61no—
1009C3×C4—62no—
1010C3×C4—61no—
1011C3×C4—62no—
1012C3×C4—62no—
1013C3×C4—64no—
1014C3×C4C2×D3×D412yes—
1015C3×C4C2×D3×D412yes—
1016C3×C4C2×D3×D412yes—
1017C3×C4C2×D3×D412yes—
1018Dic3—22no—
1019Dic3—21no—
1020Dic3—21no—
1021Dic3—24no—
1022Dic3—22no—
1023Dic3—22no—
1024Dic3—34no—
1025Dic3—34no—
1026Dic3—64no—
1027Dic3—64no—
1028Dic3—62no—
1029Dic3—62no—
1030C32#348911yescharacteristic, complemented, Sylow
1031C23—31no—
1032C23—31no—
1033C23—32no—
1034C23—62no—
1035C23—62no—
1036C23—92no—
1037C23—92no—
1038C23—121no—
1039C23—184no—
1040C23—184no—
1041C23—362no—
1042C23C22×D3211yescharacteristic
1043Q8—24no—
1044Q8—24no—
1045Q8—62no—
1046Q8—94no—
1047Q8—188no—
1048Q8—184no—
1049Q8—182no—
1050D4—64no—
1051D4—62no—
1052D4—98no—
1053D4—94no—
1054D4—188no—
1055D4—184no—
1056D4—184no—
1057D4—184no—
1058D4—184no—
1059D4—184no—
1060D4—182no—
1061D4—364no—
1062D4—362no—
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—92no—
1079C2×C4—122no—
1080C2×C4—188no—
1081C2×C4—188no—
1082C2×C4—184no—
1083C2×C4—184no—
1084C2×C4—184no—
1085C2×C4—184no—
1086C2×C4—364no—
1087C2×C4#381114yes—
1088C2×C4C22×D3214yes—
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—62no—
1098C2×C3—121no—
1099C2×C3—122no—
1100C2×C3C22×D3×D411yescharacteristic
1101C2×C3C22×D3×D411yescharacteristic
1102C2×C3C2×#100711yescharacteristic
1103C2×C3#596411yescharacteristic
1104C2×C3D3×2−1+411yescharacteristic
1105C2×C3#596811yescharacteristic
1106D3—22no—
1107D3—42no—
1108D3—41no—
1109D3—64no—
1110D3—64no—
1111D3—124no—
1112D3—124no—
1113D3—122no—
1114D3—122no—
1115C22—21no—
1116C22—21no—
1117C22—32no—
1118C22—61no—
1119C22—61no—
1120C22—61no—
1121C22—62no—
1122C22—61no—
1123C22—62no—
1124C22—61no—
1125C22—62no—
1126C22—94no—
1127C22—124no—
1128C22—182no—
1129C22—182no—
1130C22—182no—
1131C22—182no—
1132C22—182no—
1133C22—368no—
1134C22C2×#381112yes—
1135C22C23×D3211yescharacteristic
1136C4—24no—
1137C4—62no—
1138C4—64no—
1139C4—62no—
1140C4—61no—
1141C4—61no—
1142C4—62no—
1143C4—94no—
1144C4—182no—
1145C4C2×#381112yes—
1146C4C2×#381112yes—
1147C3—21no—
1148C3#8598511yescharacteristic, complemented
1149C3#8635611yescharacteristic, complemented
1150C2—22no—
1151C2—62no—
1152C2—121no—
1153C2—122no—
1154C2—184no—
1155C2—362no—
1156C2D3×#100711yescharacteristic
1157C2#1059668811yescharacteristic
1158C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64364C2semidirect
2. C2×D3×#235C2semidirect
3. C3×#5816C2semidirect
4. C2×C3×#946C2semidirect
5. #10595431C2semidirect
6. #10595430C2semidirect
7. #10595429C2semidirect
8. #10595405C2semidirect
9. #10595404C2semidirect
10. #10595362C2semidirect
11. #10595361C2semidirect
12. #10595341C2semidirect
13. #10595077C2semidirect
14. #10595043C2semidirect
15. #10595023C2semidirect
16. #10594990C2semidirect
17. #10594917C2semidirect
20. C22×C32×Q8C22semidirect
22. C2×#3832C22semidirect
23. C2×#3832C22semidirect
24. C2×Q8×C3⋊D3C22semidirect
25. C2×Q8×C3⋊D3C22semidirect
27. C2×#3828C22semidirect
28. C2×#3828C22semidirect
40. C3×#947C22semidirect
43. C3×#946C22semidirect
44. C3×#946C22semidirect
45. C3×#946C22semidirect
46. C3×#946C22semidirect
47. C3×#944C22semidirect
48. C3×#929C22semidirect
50. C3×#926C22semidirect
51. C2×C3×C4⋊Dic3C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. #63978C22semidirect
55. #63966C22semidirect
56. #63952C22semidirect
59. #63916C22semidirect
60. #63913C22semidirect
61. #63912C22semidirect
62. #63910C22semidirect
63. #63910C22semidirect
65. #63909C22semidirect
66. #63909C22semidirect
68. C4×#626C22semidirect
69. #63900C22semidirect
70. #63897C22semidirect
72. #63896C22semidirect
73. #63894C22semidirect
74. #63883C22semidirect
76. #63881C22semidirect
77. #63871C22semidirect
78. #63865C22semidirect
80. #63857C22semidirect
81. #63857C22semidirect
82. #63853C22semidirect
83. #63853C22semidirect
84. #63849C22semidirect
85. #63844C22semidirect
86. #63840C22semidirect
95. #5816D3semidirect
96. C2×#946D3semidirect
137. #3828D4semidirect
208. C22×C3×Q8C2×D3semidirect
209. C22×C3×Q8C2×D3semidirect
269. #947C2×D3semidirect
273. #946C2×D3semidirect
274. #946C2×D3semidirect
275. #946C2×D3semidirect
276. #946C2×D3semidirect
277. #944C2×D3semidirect
285. #929C2×D3semidirect
290. #926C2×D3semidirect
291. C2×C4⋊Dic3C2×D3semidirect
295. C2×Dic3⋊C4C2×D3semidirect
635. C2×C3×D32−1+4semidirect
663. C22×Q8D32semidirect
1002. C2×D3#1007semidirect
1030. C32#3489semidirect
1148. C3#85985semidirect
1149. C3#86356semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
C2×D3×#2352
C3×#58162
C2×C3×#9462
#105954312
#105954302
#105954292
#105954052
#105954042
#105953622
#105953612
#105953412
#105950772
#105950432
#105950232
#105949902
#105949172
#863563
#859853