Finite Group Databasebeta

← #11906368

Subgroups — #11906368

Order 1152.

2265 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
4#10595420C212yesmaximal, complemented
5Q8×#626C212yesmaximal, complemented
6#10595400C212yesmaximal, complemented
7#10595361C212yesmaximal, complemented
8#10594536C212yesmaximal, complemented
9#10594532C212yesmaximal, complemented
10#10594510C212yesmaximal
11#10594502C212yesmaximal, complemented
12#10594393C212yesmaximal, complemented
13#10594344C212yesmaximal, complemented
14#10594325C212yesmaximal, complemented
15#10594312C212yesmaximal, complemented
16C4×#3798C211yesmaximal, characteristic
17D3×#869C211yesmaximal, characteristic, complemented
18#10593866C211yesmaximal, characteristic, complemented
19#10593859C211yesmaximal, characteristic, complemented
20#86281—31nomaximal
21#86215—31nomaximal
22C2×Q8×C3⋊D3C2212yes—
23C2×C3×D3×Q8C2212yes—
24C2×#3798C2211yescharacteristic
25C2×D3×Dic6C2212yes—
26C32×C4⋊Q8C2211yescharacteristic
27#64153C2212yes—
28C4⋊C4×C3⋊D3C2212yes—
29C4⋊C4×C3⋊D3C2212yes—
30#64097C2212yes—
31#64097C2212yes—
32C42×C3⋊D3C2211yescharacteristic
33#64078C2211yescharacteristic
34C3×#946C2212yes—
35C3×Q8×Dic3C2212yes—
36C3×#944C2212yes—
37C3×#897C2212yes—
38C3×#892C2212yes—
39C3×D3×C4⋊C4C2212yes—
40C3×D3×C4⋊C4C2212yes—
41C3×#890C2212yes—
42C3×#888C2212yes—
43C3×#888C2212yes—
44C3×#887C2212yes—
45C3×C42×D3C2211yescharacteristic
46C3×C42×D3C2211yescharacteristic
47C3×#869C2211yescharacteristic
48C3×#869C2211yescharacteristic
49#63918C2212yes—
50#63918C2212yes—
51C4×#627C2211yescharacteristic
52C4×#627C2211yescharacteristic
53C4×#626C2211yescharacteristic
54C4×#626C2211yescharacteristic
55C4×#626C2214yes—
56C4×#626C2211yescharacteristic
57C4×#626C2211yescharacteristic
58C4×#625C2211yescharacteristic
59C4×#625C2211yescharacteristic
60#63896C2214yes—
61D3×C4⋊Dic3C2212yes—
62D3×C4⋊Dic3C2212yes—
63#63887C2214yes—
64#63881C2214yes—
65#63879C2214yes—
66#63874C2211yescharacteristic
67#63872C2212yes—
68#63871C2214yes—
69#63871C2212yes—
70#63871C2212yes—
71#63869C2212yes—
72#63867C2214yes—
73#63866C2214yes—
74#63866C2212yes—
75#63865C2214yes—
76#63857C2214yes—
77#63857C2212yes—
78#63856C2212yes—
79#63855C2211yescharacteristic
80#63855C2211yescharacteristic
81#63851C2214yes—
82#63849C2212yes—
83#63847C2214yes—
84#63846C2214yes—
85#63844C2212yes—
86#63843C2212yes—
87#63843C2212yes—
88Dic3×Dic6C2212yes—
89#63841C2212yes—
90#63840C2214yes—
91#63839C2214yes—
92#63837C2214yes—
93C3×#533—31no—
94C2×C3×C4⋊Q8—31no—
95Q8×#67—32no—
96Q8×#67—32no—
97#5730—32no—
98#5729—32no—
99#5729—32no—
100#5728—31no—
101#5728—31no—
102#5728—31no—
103#5728D311yescharacteristic, complemented
104#5727—32no—
105D3×C4⋊Q8—31no—
106D3×C4⋊Q8—31no—
107D3×C4⋊Q8—31no—
108D3×C4⋊Q8—61no—
109D3×C4⋊Q8D311yescharacteristic, complemented
110#5722—32no—
111#5721—32no—
112#5689—32no—
113#5689—32no—
114#5635—32no—
115#5635—32no—
116#5632—32no—
117#5632—32no—
118#5579—32no—
119Q8×D12—32no—
120#5567—32no—
121Q8×Dic6—32no—
122#5523—32no—
123#5519—32no—
124#5511—32no—
125#5511—32no—
126#5504—32no—
127#5500—32no—
128C4×#235—31no—
129C4×#235—31no—
130#5470—31no—
131C2×#869—31no—
132C2×C32×Q8C2312yes—
133Q8×C3⋊D3—44no—
134C2×C4×C3⋊D3C2311yescharacteristic
135C2×C4×C3⋊D3C2311yescharacteristic
136C2×C4×C3⋊D3C2314yes—
137C2×C4×C3⋊D3C2311yescharacteristic
138C2×#634C2312yes—
139C2×#634C2314yes—
140C3×D3×Q8—44no—
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×C4×D3C2314yes—
146C2×C3×C4×D3C2311yescharacteristic
147C2×C3×C4×D3C2311yescharacteristic
148C2×C3×Dic6C2312yes—
149C2×C3×Dic6C2312yes—
150C2×C3×Dic6C2314yes—
151C2×#627C2314yes—
152C2×#627C2311yescharacteristic
153C2×#626C2311yescharacteristic
154C2×#626C2311yescharacteristic
155C2×#625C2311yescharacteristic
156C2×D3×Dic3C2314yes—
157#3798Q818yescomplemented
158D3×Dic6—44no—
159C32×C4⋊C4C2312yes—
160C32×C4⋊C4C2312yes—
161C32×C42C2311yescharacteristic
162C4⋊(C3⋊Dic3)C2312yes—
163C4⋊(C3⋊Dic3)C2312yes—
164#3750C2314yes—
165#3750C2314yes—
166C4×C3⋊Dic3C2311yescharacteristic
167C4×C3⋊Dic3C2311yescharacteristic
168C4×C3⋊Dic3C2311yescharacteristic
169C3×(C2×D3)⋊C4C2314yes—
170C3×C4⋊Dic3C2312yes—
171C3×C4⋊Dic3C2312yes—
172C3×C4⋊Dic3C2312yes—
173C3×C4⋊Dic3C2314yes—
174C3×C4⋊Dic3C2312yes—
175C3×Dic3⋊C4C2314yes—
176C3×Dic3⋊C4C2314yes—
177C3×Dic3⋊C4C2314yes—
178C3×C4×Dic3C2311yescharacteristic
179C3×C4×Dic3C2314yes—
180C3×C4×Dic3C2311yescharacteristic
181C3×C4×Dic3C2311yescharacteristic
182C3×C4×Dic3C2311yescharacteristic
183C3×C4×Dic3C2311yescharacteristic
184C3×C4×Dic3C2311yescharacteristic
185#3724C2311yescharacteristic
186#3724C2314yes—
187#3724C2311yescharacteristic
188Dic3⋊Dic3C2314yes—
189Dic3⋊Dic3C2314yes—
190Dic3⋊Dic3C2311yescharacteristic
191Dic3⋊Dic3C2314yes—
192Dic3⋊Dic3C2314yes—
193Dic3⋊Dic3C2311yescharacteristic
194Dic3⋊Dic3C2314yes—
195Dic3⋊Dic3C2311yescharacteristic
196Dic3⋊Dic3C2311yescharacteristic
197#3722C2314yes—
198#3722C2311yescharacteristic
199#3722C2311yescharacteristic
200(C2×D3)⋊Dic3C2314yes—
201(C2×D3)⋊Dic3C2311yescharacteristic
202(C2×D3)⋊Dic3C2311yescharacteristic
203(C2×D3)⋊Dic3C2311yescharacteristic
204(C2×D3)⋊Dic3C2311yescharacteristic
205Dic32C2314yes—
206Dic32C2314yes—
207#3503—91noSylow
208C22×C3×Q8—32no—
209C2×D3×Q8—32no—
210C2×D3×Q8—32no—
211C2×D3×Q8—32no—
212C2×D3×Q8—62no—
213C2×D3×Q8C2×D312yes—
214C2×#235—31no—
215C2×#235—31no—
216C22×Dic6—32no—
217C3×C4⋊Q8—21no—
218C3×C4⋊Q8—32no—
219C3×C4⋊Q8—32no—
220C3×C4⋊Q8—32no—
221C3×C4⋊Q8—31no—
222C3×C4⋊Q8—31no—
223C3×C4⋊Q8C2×D311yescharacteristic
224C3×C4⋊Q8C2×D311yescharacteristic
225C3×#125—32no—
226C3×C22⋊Q8—32no—
227C3×C22⋊Q8—32no—
228C3×C4×Q8—32no—
229C3×C4×Q8—32no—
230C3×#117—32no—
231C2×C3×C4⋊C4—32no—
232C2×C3×C4⋊C4—32no—
233C2×C3×C42—31no—
234C2×C3×C42—31no—
235#946—32no—
236#946—34no—
237#946—32no—
238#946—32no—
239#946—34no—
240#946C2×D312yes—
241Q8×Dic3—32no—
242Q8×Dic3—32no—
243Q8×Dic3—32no—
244Q8×Dic3C2×D312yes—
245#944—32no—
246#944—32no—
247#944—34no—
248#944—32no—
249#944—34no—
250#944—62no—
251#944C2×D312yes—
252C4×#67—31no—
253C4×#67—31no—
254C4×#67—31no—
255C4×#67—31no—
256C4×#67—34no—
257C4×#67—31no—
258C4×#67—31no—
259C4×#67—31no—
260C4×#67—31no—
261C4×#67—34no—
262#926—32no—
263#926—31no—
264#926—31no—
265C2×C4⋊Dic3—32no—
266C2×C4⋊Dic3—32no—
267#924—32no—
268#924—32no—
269#924—34no—
270#924—34no—
271#897—32no—
272#897—34no—
273#897—32no—
274#897—34no—
275#897—32no—
276#897C2×D312yes—
277#896—34no—
278#896—34no—
279#896—34no—
280#896—34no—
281#893—34no—
282#892—32no—
283#892—32no—
284#892—32no—
285#892C2×D312yes—
286D3×C4⋊C4—32no—
287D3×C4⋊C4—32no—
288D3×C4⋊C4—32no—
289D3×C4⋊C4—32no—
290D3×C4⋊C4—32no—
291D3×C4⋊C4—32no—
292D3×C4⋊C4—62no—
293D3×C4⋊C4—62no—
294D3×C4⋊C4C2×D312yes—
295D3×C4⋊C4C2×D312yes—
296#890—32no—
297#890—34no—
298#890—32no—
299#890—32no—
300#890C2×D312yes—
301#889—34no—
302#889—34no—
303#889—34no—
304#889—34no—
305#888—34no—
306#888—32no—
307#888—32no—
308#888—32no—
309#888—32no—
310#888—34no—
311#888—34no—
312#888—32no—
313#888—32no—
314#888—62no—
315#888—62no—
316#888C2×D312yes—
317#888C2×D312yes—
318#887—32no—
319#887—32no—
320#887—32no—
321#887—34no—
322#887C2×D312yes—
323#67⋊C4—34no—
324#67⋊C4—34no—
325#878—34no—
326#878—34no—
327C4×D12—31no—
328C4×D12—31no—
329C4×D12—31no—
330C4×D12—31no—
331C4×D12—34no—
332#872—31no—
333#872—31no—
334#872—31no—
335#872—31no—
336C42×D3—31no—
337C42×D3—31no—
338C42×D3—61no—
339C42×D3C2×D311yescharacteristic
340C42×D3C2×D311yescharacteristic
341#870—32no—
342#870—34no—
343#869—32no—
344#869—34no—
345#869—31no—
346#869—31no—
347#869—32no—
348#869—32no—
349#869—61no—
350#869C2×D311yescharacteristic
351#869C2×D311yescharacteristic
352C4×Dic6—32no—
353C4×Dic6—32no—
354C4×Dic6—34no—
355C4×Dic6—31no—
356C4×Dic6—31no—
357C4×Dic6—31no—
358C4×Dic6—31no—
359C22×C3⋊D3C2411yescharacteristic
360C22×C3×D3C2411yescharacteristic
361C22×C3×D3C2411yescharacteristic
362C32×Q8—24no—
363C2×C32×C4C2414yes—
364C2×C32×C4C2411yescharacteristic
365C2×C32×C4C2411yescharacteristic
366C2×C32×C4C2411yescharacteristic
367C2×C3⋊Dic3C2414yes—
368C2×C3⋊Dic3C2411yescharacteristic
369C2×C3⋊Dic3C2411yescharacteristic
370C2×C3⋊Dic3C2411yescharacteristic
371C4×C3⋊D3—22no—
372C4×C3⋊D3—22no—
373C4×C3⋊D3—44no—
374C4×C3⋊D3C2×Q814yescomplemented
375#634—24no—
376#634—44no—
377C2×C3×Dic3C2414yes—
378C2×C3×Dic3C2414yes—
379C2×C3×Dic3C2411yescharacteristic
380C2×C3×Dic3C2411yescharacteristic
381C2×C3×Dic3C2411yescharacteristic
382C2×C3×Dic3C2411yescharacteristic
383C2×C3×Dic3C2411yescharacteristic
384C2×C3×Dic3C2411yescharacteristic
385C3×C4×D3—22no—
386C3×C4×D3—22no—
387C3×C4×D3—22no—
388C3×C4×D3—22no—
389C3×C4×D3—44no—
390C3×C4×D3C2×Q814yescomplemented
391C3×C4×D3C2×Q814yescomplemented
392C3×Dic6—24no—
393C3×Dic6—24no—
394C3×Dic6—44no—
395#627—44no—
396#627C2×Q814yescomplemented
397#626C2×Q814yescomplemented
398#626C2×Q814yescomplemented
399#625C2×Q814yescomplemented
400D3×Dic3—44no—
401Q82—92no—
402#557—92no—
403#554—92no—
404#554—92no—
405#554—92no—
406D4×Q8—92no—
407D4×Q8—92no—
408D4×Q8—92no—
409#544—92no—
410#544—92no—
411#544—92no—
412#533—31no—
413#533—91no—
414#533—91no—
415C2×C4⋊Q8—31no—
416C2×C4⋊Q8—91no—
417C2×C4⋊Q8—91no—
418#520—92no—
419C4×#41—91no—
420C2×C3×Q8—22no—
421C2×C3×Q8—32no—
422C2×C3×Q8—32no—
423C2×C3×Q8—34no—
424C2×C3×Q8—124no—
425C2×C3×Q8C22×D312yes—
426C2×C3×Q8C22×D312yes—
427C22×C3×C4—31no—
428C22×C3×C4—31no—
429C22×C3×C4—31no—
430C22×C3×C4—31no—
431C22×C3×C4—31no—
432C22×C3×C4—31no—
433C22×C3×C4—34no—
434C2×#67—31no—
435C2×#67—31no—
436C2×#67—31no—
437C2×#67—31no—
438C22×Dic3—34no—
439D3×Q8—44no—
440D3×Q8—124no—
441D3×Q8—124no—
442D3×Q8—124no—
443D3×Q8—128no—
444#235—38no—
445#235—38no—
446C2×D12—31no—
447C2×D12—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—34no—
455C2×C4×D3—34no—
456C2×C4×D3—34no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—64no—
461C2×C4×D3C22×D311yescharacteristic
462C2×C4×D3C22×D311yescharacteristic
463C2×C4×D3C22×D311yescharacteristic
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D314yes—
466C2×C4×D3C22×D311yescharacteristic
467C2×C4×D3C22×D311yescharacteristic
468C2×Dic6—31no—
469C2×Dic6—31no—
470C2×Dic6—32no—
471C2×Dic6—32no—
472C2×Dic6—34no—
473C2×Dic6—34no—
474C2×Dic6—34no—
475C2×Dic6—34no—
476C2×Dic6—62no—
477C2×Dic6—64no—
478C2×Dic6—124no—
479C2×Dic6C22×D312yes—
480C2×Dic6C22×D312yes—
481C2×Dic6C22×D314yes—
482C3×C4⋊C4—22no—
483C3×C4⋊C4—22no—
484C3×C4⋊C4—32no—
485C3×C4⋊C4—34no—
486C3×C4⋊C4—32no—
487C3×C4⋊C4—34no—
488C3×C4⋊C4—32no—
489C3×C4⋊C4—34no—
490C3×C4⋊C4—34no—
491C3×C4⋊C4—32no—
492C3×C4⋊C4C22×D312yes—
493C3×C4⋊C4C22×D312yes—
494C3×C4⋊C4C22×D312yes—
495C3×C4⋊C4C22×D312yes—
496C3×C22⋊C4—34no—
497C3×C42—21no—
498C3×C42—31no—
499C3×C42—31no—
500C3×C42—31no—
501C3×C42—31no—
502C3×C42—34no—
503C3×C42—31no—
504C3×C42—31no—
505C3×C42C22×D311yescharacteristic
506C3×C42C22×D311yescharacteristic
507#217—31no—
508#217—31no—
509#217—31no—
510#217—31no—
511#217—34no—
512(C2×D3)⋊C4—31no—
513(C2×D3)⋊C4—31no—
514(C2×D3)⋊C4—31no—
515(C2×D3)⋊C4—31no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—31no—
518(C2×D3)⋊C4—31no—
519(C2×D3)⋊C4—31no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4C22×D314yes—
524C4⋊Dic3—32no—
525C4⋊Dic3—32no—
526C4⋊Dic3—32no—
527C4⋊Dic3—32no—
528C4⋊Dic3—31no—
529C4⋊Dic3—34no—
530C4⋊Dic3—31no—
531C4⋊Dic3—31no—
532C4⋊Dic3—31no—
533C4⋊Dic3—34no—
534C4⋊Dic3—34no—
535C4⋊Dic3—34no—
536C4⋊Dic3—34no—
537C4⋊Dic3—62no—
538C4⋊Dic3—62no—
539C4⋊Dic3C22×D312yes—
540C4⋊Dic3C22×D312yes—
541C4⋊Dic3C22×D312yes—
542C4⋊Dic3C22×D312yes—
543C4⋊Dic3C22×D314yes—
544Dic3⋊C4—34no—
545Dic3⋊C4—34no—
546Dic3⋊C4—34no—
547Dic3⋊C4—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—31no—
551Dic3⋊C4—31no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—34no—
559Dic3⋊C4—34no—
560Dic3⋊C4—34no—
561Dic3⋊C4—34no—
562Dic3⋊C4—34no—
563Dic3⋊C4—64no—
564Dic3⋊C4—64no—
565Dic3⋊C4C22×D314yes—
566Dic3⋊C4C22×D314yes—
567Dic3⋊C4C22×D314yes—
568C4×Dic3—31no—
569C4×Dic3—31no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—31no—
573C4×Dic3—31no—
574C4×Dic3—34no—
575C4×Dic3—34no—
576C4×Dic3—34no—
577C4×Dic3—34no—
578C4×Dic3—61no—
579C4×Dic3—61no—
580C4×Dic3—61no—
581C4×Dic3C22×D311yescharacteristic
582C4×Dic3C22×D311yescharacteristic
583C4×Dic3C22×D311yescharacteristic
584C4×Dic3C22×D311yescharacteristic
585C4×Dic3C22×D311yescharacteristic
586C4×Dic3C22×D311yescharacteristic
587C4×Dic3C22×D314yes—
588C22×C32C2511yescharacteristic
589C2×C3⋊D3—21no—
590C2×C3⋊D3—21no—
591C2×C3⋊D3C22×Q812yes—
592C2×C3×D3—21no—
593C2×C3×D3—21no—
594C2×C3×D3—21no—
595C2×C3×D3—21no—
596C2×C3×D3C22×Q812yes—
597C2×C3×D3C22×Q812yes—
598C32×C4—24no—
599C32×C4C22×Q812yes—
600C32×C4H(5,𝔽2)12yes—
601C32×C42−1+412yes—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3⋊Dic3—24no—
605C3⋊Dic3C22×Q812yes—
606C3×Dic3—24no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—24no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3C22×Q812yes—
613C3×Dic3C22×Q812yes—
614C2×#41—91no—
615C22×Q8—32no—
616C22×Q8—92no—
617C22×Q8—92no—
618C4⋊Q8—32no—
619C4⋊Q8—32no—
620C4⋊Q8—32no—
621C4⋊Q8—31no—
622C4⋊Q8—31no—
623C4⋊Q8—92no—
624C4⋊Q8—92no—
625C4⋊Q8—92no—
626C4⋊Q8—94no—
627C4⋊Q8—94no—
628C4⋊Q8—94no—
629C4⋊Q8—92no—
630C4⋊Q8—92no—
631C4⋊Q8—92no—
632C4⋊Q8—91no—
633C4⋊Q8D3211yescharacteristic
634#125—32no—
635#125—92no—
636#125—94no—
637#125—92no—
638#125—94no—
639#125—94no—
640C22⋊Q8—32no—
641C22⋊Q8—32no—
642C22⋊Q8—94no—
643C22⋊Q8—94no—
644C22⋊Q8—94no—
645C22⋊Q8—92no—
646C22⋊Q8—94no—
647C22⋊Q8—94no—
648C22⋊Q8—92no—
649C22⋊Q8—92no—
650C22⋊Q8—94no—
651C22⋊Q8—92no—
652C4×Q8—32no—
653C4×Q8—32no—
654C4×Q8—91no—
655C4×Q8—91no—
656C4×Q8—94no—
657C4×Q8—92no—
658C4×Q8—92no—
659C4×Q8—92no—
660C4×Q8—92no—
661C4×D4—91no—
662C4×D4—91no—
663C4×D4—91no—
664C4×D4—91no—
665C4×D4—94no—
666C4×D4—94no—
667C4×D4—94no—
668C4×D4—91no—
669C4×D4—91no—
670#117—32no—
671#117—91no—
672#117—91no—
673#117—91no—
674#117—92no—
675#117—92no—
676C2×C4⋊C4—32no—
677C2×C4⋊C4—32no—
678C2×C4⋊C4—92no—
679C2×C4⋊C4—92no—
680C2×C4⋊C4—92no—
681C2×C4⋊C4—92no—
682C2×C42—31no—
683C2×C42—31no—
684C2×C42—91no—
685C23×C3—31no—
686C23×C3—31no—
687C22×D3—31no—
688C22×D3—31no—
689C22×D3—61no—
690C22×D3C23×D311yescharacteristic
691C22×D3C23×D311yescharacteristic
692C3×Q8—24no—
693C3×Q8—24no—
694C3×Q8—44no—
695C3×Q8—64no—
696C3×Q8—64no—
697C3×Q8—124no—
698C2×C3×C4—21no—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—24no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—34no—
705C2×C3×C4—34no—
706C2×C3×C4—34no—
707C2×C3×C4—34no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—62no—
713C2×C3×C4—62no—
714C2×C3×C4—62no—
715C2×C3×C4—62no—
716C2×C3×C4—124no—
717C2×C3×C4C23×D314yes—
718C2×C3×C4C23×D314yes—
719C2×C3×C4C23×D311yescharacteristic
720C2×C3×C4C23×D311yescharacteristic
721C2×C3×C4C23×D311yescharacteristic
722C2×C3×C4C23×D311yescharacteristic
723C2×C3×C4C23×D311yescharacteristic
724C2×C3×C4C23×D311yescharacteristic
725#67—34no—
726#67—34no—
727#67—34no—
728#67—34no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—34no—
736C2×Dic3—34no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—64no—
741C2×Dic3—124no—
742C2×Dic3C23×D314yes—
743C2×Dic3C23×D314yes—
744C2×Dic3C23×D311yescharacteristic
745C2×Dic3C23×D311yescharacteristic
746C2×Dic3C23×D311yescharacteristic
747C2×Dic3C23×D311yescharacteristic
748C2×Dic3C23×D311yescharacteristic
749C2×Dic3C23×D311yescharacteristic
750D12—34no—
751D12—34no—
752C4×D3—22no—
753C4×D3—22no—
754C4×D3—22no—
755C4×D3—22no—
756C4×D3—34no—
757C4×D3—34no—
758C4×D3—44no—
759C4×D3—64no—
760C4×D3—64no—
761C4×D3—64no—
762C4×D3—62no—
763C4×D3—62no—
764C4×D3—62no—
765C4×D3—62no—
766C4×D3—124no—
767C4×D3—124no—
768C4×D3—124no—
769C4×D3—128no—
770C4×D3D3×Q814yescomplemented
771C4×D3D3×Q814yescomplemented
772Dic6—24no—
773Dic6—24no—
774Dic6—34no—
775Dic6—34no—
776Dic6—44no—
777Dic6—64no—
778Dic6—64no—
779Dic6—124no—
780Dic6—124no—
781Dic6—124no—
782Dic6—124no—
783Dic6—124no—
784Dic6—128no—
785C2×C32C23×Q811yescharacteristic
786C2×C32C2×H(5,𝔽2)11yescharacteristic
787C2×C32C2×2−1+411yescharacteristic
788C3⋊D3—22no—
789C3×D3—22no—
790C3×D3—22no—
791#41—98no—
792C2×Q8—32no—
793C2×Q8—32no—
794C2×Q8—34no—
795C2×Q8—91no—
796C2×Q8—94no—
797C2×Q8—92no—
798C2×Q8—94no—
799C2×Q8—124no—
800C2×Q8—364no—
801C2×Q8—364no—
802C2×Q8C2×D3212yes—
803C2×D4—91no—
804C2×D4—91no—
805C2×D4—91no—
806C22×C4—31no—
807C22×C4—31no—
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—31no—
811C22×C4—31no—
812C22×C4—34no—
813C22×C4—94no—
814C22×C4—91no—
815C22×C4—91no—
816C22×C4—91no—
817C22×C4—94no—
818C4⋊C4—32no—
819C4⋊C4—32no—
820C4⋊C4—34no—
821C4⋊C4—34no—
822C4⋊C4—32no—
823C4⋊C4—32no—
824C4⋊C4—34no—
825C4⋊C4—34no—
826C4⋊C4—94no—
827C4⋊C4—94no—
828C4⋊C4—91no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4—91no—
832C4⋊C4—91no—
833C4⋊C4—91no—
834C4⋊C4—94no—
835C4⋊C4—94no—
836C4⋊C4—94no—
837C4⋊C4—94no—
838C4⋊C4—92no—
839C4⋊C4—92no—
840C4⋊C4—94no—
841C4⋊C4—94no—
842C4⋊C4C2×D3212yes—
843C4⋊C4C2×D3212yes—
844C22⋊C4—34no—
845C22⋊C4—91no—
846C22⋊C4—91no—
847C22⋊C4—94no—
848C22⋊C4—91no—
849C22⋊C4—91no—
850C22⋊C4—91no—
851C22⋊C4—91no—
852C22⋊C4—94no—
853C42—31no—
854C42—31no—
855C42—31no—
856C42—31no—
857C42—31no—
858C42—31no—
859C42—34no—
860C42—94no—
861C42—94no—
862C42—91no—
863C42—91no—
864C42—91no—
865C42C2×D3211yescharacteristic
866C22×C3—21no—
867C22×C3—32no—
868C22×C3—32no—
869C22×C3—61no—
870C22×C3—61no—
871C22×C3—61no—
872C22×C3—61no—
873C22×C3C24×D311yescharacteristic
874C22×C3C24×D311yescharacteristic
875C2×D3—21no—
876C2×D3—21no—
877C2×D3—21no—
878C2×D3—21no—
879C2×D3—32no—
880C2×D3—32no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—61no—
885C2×D3—61no—
886C2×D3—61no—
887C2×D3—61no—
888C2×D3C2×D3×Q812yes—
889C2×D3C2×D3×Q812yes—
890C3×C4—24no—
891C3×C4—24no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—32no—
896C3×C4—32no—
897C3×C4—44no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—64no—
901C3×C4—64no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4#100412yes—
905C3×C4C2×D3×Q812yes—
906C3×C4C2×D3×Q812yes—
907C3×C4#100712yes—
908C3×C4#100912yes—
909C3×C4#101012yes—
910Dic3—24no—
911Dic3—21no—
912Dic3—21no—
913Dic3—21no—
914Dic3—24no—
915Dic3—21no—
916Dic3—32no—
917Dic3—32no—
918Dic3—62no—
919Dic3—62no—
920Dic3—62no—
921Dic3—64no—
922Dic3—61no—
923Dic3—61no—
924Dic3—64no—
925Dic3—61no—
926Dic3—61no—
927Dic3—124no—
928Dic3C2×D3×Q812yes—
929Dic3C2×D3×Q812yes—
930C32#350311yescharacteristic, complemented, Sylow
931C23—31no—
932C23—31no—
933C23—91no—
934Q8—24no—
935Q8—64no—
936Q8—64no—
937Q8—94no—
938Q8—124no—
939Q8—184no—
940Q8—364no—
941Q8—364no—
942D4—94no—
943D4—94no—
944D4—94no—
945C2×C4—31no—
946C2×C4—31no—
947C2×C4—34no—
948C2×C4—34no—
949C2×C4—31no—
950C2×C4—31no—
951C2×C4—31no—
952C2×C4—31no—
953C2×C4—34no—
954C2×C4—34no—
955C2×C4—62no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—62no—
959C2×C4—91no—
960C2×C4—94no—
961C2×C4—91no—
962C2×C4—91no—
963C2×C4—94no—
964C2×C4—124no—
965C2×C4—182no—
966C2×C4—182no—
967C2×C4—364no—
968C2×C4—364no—
969C2×C4C22×D3214yes—
970C2×C4C22×D3211yescharacteristic
971C2×C4C22×D3211yescharacteristic
972C2×C4C22×D3211yescharacteristic
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—62no—
977C2×C3—62no—
978C2×C3C2×#100411yescharacteristic
979C2×C3C22×D3×Q811yescharacteristic
980C2×C3C22×D3×Q811yescharacteristic
981C2×C3C2×#100711yescharacteristic
982C2×C3C2×#100911yescharacteristic
983C2×C3C2×#101011yescharacteristic
984D3—22no—
985D3—22no—
986D3—64no—
987D3—62no—
988D3—62no—
989C22—32no—
990C22—32no—
991C22—61no—
992C22—61no—
993C22—61no—
994C22—61no—
995C22—92no—
996C22—181no—
997C22—181no—
998C22C23×D3211yescharacteristic
999C4—24no—
1000C4—32no—
1001C4—32no—
1002C4—61no—
1003C4—61no—
1004C4—64no—
1005C4—61no—
1006C4—61no—
1007C4—64no—
1008C4—92no—
1009C4—181no—
1010C4—184no—
1011C4—181no—
1012C4#6431412yes—
1013C4#6431512yes—
1014C4D32×Q812yes—
1015C3—21no—
1016C3#8621511yescharacteristic, complemented
1017C3#8628111yescharacteristic, complemented
1018C2—62no—
1019C2—62no—
1020C2—182no—
1021C2C2×#6431411yescharacteristic
1022C2C2×#6431511yescharacteristic
1023C2C2×D32×Q811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×#3798C22
hypercenterC4⋊Q8D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C4⋊Q8C2semidirect
2. C3×#5728C2semidirect
3. C3×D3×C4⋊Q8C2semidirect
4. #10595420C2semidirect
5. Q8×#626C2semidirect
6. #10595400C2semidirect
7. #10595361C2semidirect
8. #10594536C2semidirect
9. #10594532C2semidirect
11. #10594502C2semidirect
12. #10594393C2semidirect
13. #10594344C2semidirect
14. #10594325C2semidirect
15. #10594312C2semidirect
17. D3×#869C2semidirect
18. #10593866C2semidirect
19. #10593859C2semidirect
103. #5728D3semidirect
109. D3×C4⋊Q8D3semidirect
157. #3798Q8semidirect
374. C4×C3⋊D3C2×Q8semidirect
390. C3×C4×D3C2×Q8semidirect
391. C3×C4×D3C2×Q8semidirect
396. #627C2×Q8semidirect
397. #626C2×Q8semidirect
398. #626C2×Q8semidirect
399. #625C2×Q8semidirect
770. C4×D3D3×Q8semidirect
771. C4×D3D3×Q8semidirect
930. C32#3503semidirect
1016. C3#86215semidirect
1017. C3#86281semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C3×#57282
C3×D3×C4⋊Q82
#105954202
Q8×#6262
#105954002
#105953612
#105945362
#105945322
#105945102
#105945022
#105943932
#105943442
#105943252
#105943122
C4×#37982
D3×#8692
#105938662
#105938592
#862813
#862153