Finite Group Databasebeta

← #11906342

Subgroups — #11906342

Order 1152.

2265 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×#5727C211yesmaximal, characteristic, complemented
3C3×#5721C211yesmaximal, characteristic, complemented
4Q8×#626C212yesmaximal, complemented
5#10595367C212yesmaximal, complemented
6#10595361C212yesmaximal, complemented
7D3×#944C212yesmaximal, complemented
8#10594485C212yesmaximal, complemented
9#10594394C214yesmaximal, complemented
10#10594390C214yesmaximal, complemented
11#10594361C212yesmaximal
12#10594325C212yesmaximal, complemented
13#10594312C212yesmaximal, complemented
14Dic6×D12C211yesmaximal, characteristic, complemented
15C4×#3796C211yesmaximal, characteristic
16#10593882C211yesmaximal, characteristic, complemented
17#10593860C211yesmaximal, characteristic, complemented
18#87018—31nomaximal
19#86747—31nomaximal
20C2×Q8×C3⋊D3C2212yes—
21C2×C3×D3×Q8C2212yes—
22C2×#3796C2211yescharacteristic
23C2×D3×Dic6C2212yes—
24C32×C4⋊Q8C2211yescharacteristic
25#64153C2212yes—
26C4⋊C4×C3⋊D3C2212yes—
27C4⋊C4×C3⋊D3C2212yes—
28#64097C2212yes—
29#64097C2212yes—
30C42×C3⋊D3C2211yescharacteristic
31#64078C2211yescharacteristic
32C3×#946C2212yes—
33C3×Q8×Dic3C2212yes—
34C3×#944C2212yes—
35C3×#896C2214yes—
36C3×#893C2212yes—
37C3×#890C2212yes—
38C3×#889C2214yes—
39C3×#888C2212yes—
40C3×#887C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63919C2211yescharacteristic
46#63918C2212yes—
47C4×#627C2212yes—
48C4×#626C2212yes—
49C4×#626C2214yes—
50#63899C2214yes—
51#63898C2211yescharacteristic
52#63896C2214yes—
53#63893C2214yes—
54Dic3×D12C2212yes—
55#63881C2214yes—
56#63881C2212yes—
57#63878C2212yes—
58#63877C2214yes—
59D3×Dic3⋊C4C2214yes—
60D3×Dic3⋊C4C2214yes—
61C4×D3×Dic3C2212yes—
62#63874C2212yes—
63#63873C2211yescharacteristic
64#63871C2214yes—
65#63871C2211yescharacteristic
66#63871C2211yescharacteristic
67#63870C2212yes—
68#63869C2212yes—
69#63866C2214yes—
70#63866C2212yes—
71#63865C2214yes—
72#63865C2212yes—
73#63857C2212yes—
74#63857C2214yes—
75#63849C2211yescharacteristic
76#63847C2214yes—
77#63845C2214yes—
78#63844C2212yes—
79#63843C2211yescharacteristic
80Dic3×Dic6C2212yes—
81#63840C2214yes—
82#63839C2214yes—
83#63839C2214yes—
84#63837C2214yes—
85C3×#557—31no—
86C3×D4×Q8—31no—
87Q8×#67—32no—
88C2×#944—32no—
89#5729—32no—
90#5727—32no—
91#5727D311yescharacteristic, complemented
92D3×C4⋊Q8—32no—
93D3×C4⋊Q8—31no—
94D3×C4⋊Q8—31no—
95D3×C4⋊Q8—61no—
96#5722—32no—
97#5721D311yescharacteristic, complemented
98#5690—34no—
99#5690—32no—
100#5689—34no—
101#5689—32no—
102#5636—34no—
103#5632—32no—
104#5623—34no—
105#5622—32no—
106#5578—32no—
107#5578—31no—
108#5578—31no—
109Q8×D12—32no—
110Q8×D12—31no—
111#5574—32no—
112C4×#239—31no—
113#5570—31no—
114#5567—31no—
115Q8×Dic6—32no—
116#5546—32no—
117#5539—32no—
118D4×Dic6—31no—
119C4×#237—31no—
120C2×C32×Q8C2312yes—
121Q8×C3⋊D3—44no—
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2314yes—
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×#634C2312yes—
127C2×#634C2314yes—
128C3×D3×Q8—44no—
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2314yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×C3×Dic6C2311yescharacteristic
134C2×C3×Dic6C2314yes—
135C2×C3×Dic6C2311yescharacteristic
136C2×#627C2312yes—
137C2×#627C2314yes—
138C2×#626C2312yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2314yes—
141C2×D3×Dic3C2312yes—
142#3796Q818yescomplemented
143D3×Dic6—44no—
144C32×C4⋊C4C2312yes—
145C32×C4⋊C4C2312yes—
146C32×C42C2311yescharacteristic
147C4⋊(C3⋊Dic3)C2312yes—
148C4⋊(C3⋊Dic3)C2312yes—
149#3750C2314yes—
150#3750C2314yes—
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2311yescharacteristic
153C4×C3⋊Dic3C2311yescharacteristic
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2312yes—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4⋊Dic3C2314yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2312yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2312yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2312yes—
171#3724C2312yes—
172#3724C2312yes—
173#3724C2314yes—
174#3724C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2312yes—
181#3722C2312yes—
182#3722C2312yes—
183#3722C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Dic32C2312yes—
189#3503—91noSylow
190C22×C3×Q8—32no—
191C2×#239—31no—
192C2×D3×Q8—32no—
193C2×D3×Q8—32no—
194C2×D3×Q8—32no—
195C2×D3×Q8—62no—
196C2×D3×Q8C2×D312yes—
197C2×#237—31no—
198C22×Dic6—32no—
199C3×C4⋊Q8—21no—
200C3×C4⋊Q8—32no—
201C3×C4⋊Q8—32no—
202C3×C4⋊Q8C2×D311yescharacteristic
203C3×C4⋊Q8C2×D311yescharacteristic
204C3×#125—34no—
205C3×#125—32no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—34no—
208C3×C4×Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×Q8—31no—
211C3×C4×Q8—31no—
212C3×C4×Q8—31no—
213C3×C4×D4—32no—
214C3×C4×D4—31no—
215#946—34no—
216#946—31no—
217#946—31no—
218#946C2×D312yes—
219Q8×Dic3—31no—
220Q8×Dic3—32no—
221Q8×Dic3C2×D312yes—
222#944—32no—
223#944—32no—
224#944—31no—
225#944—31no—
226#944—34no—
227#944—34no—
228#944—34no—
229#944—32no—
230#944—62no—
231#944C2×D312yes—
232D4×Dic3—31no—
233D4×Dic3—32no—
234C4×#67—32no—
235C4×#67—34no—
236#924—32no—
237#924—34no—
238C2×Dic3⋊C4—34no—
239C2×Dic3⋊C4—34no—
240C2×C4×Dic3—32no—
241#897—34no—
242#897—32no—
243#897—31no—
244#897—34no—
245#897—31no—
246#897—34no—
247#896—34no—
248#896—34no—
249#896—34no—
250#896—32no—
251#896—34no—
252#896—32no—
253#896C2×D314yes—
254#893—31no—
255#893—32no—
256#893—34no—
257#893C2×D312yes—
258#892—32no—
259#892—31no—
260#892—31no—
261D3×C4⋊C4—34no—
262D3×C4⋊C4—34no—
263D3×C4⋊C4—32no—
264D3×C4⋊C4—32no—
265D3×C4⋊C4—32no—
266D3×C4⋊C4—32no—
267D3×C4⋊C4—62no—
268D3×C4⋊C4—62no—
269#890—34no—
270#890—32no—
271#890C2×D312yes—
272#889—34no—
273#889—34no—
274#889—34no—
275#889—32no—
276#889—32no—
277#889C2×D314yes—
278#888—34no—
279#888—34no—
280#888—32no—
281#888—32no—
282#888—32no—
283#888—32no—
284#888—31no—
285#888—31no—
286#888—34no—
287#888—34no—
288#888—32no—
289#888—62no—
290#888—62no—
291#888C2×D312yes—
292#887—31no—
293#887—32no—
294#887—34no—
295#887C2×D312yes—
296#67⋊C4—34no—
297#67⋊C4—32no—
298#878—34no—
299#878—34no—
300#878—34no—
301#877—32no—
302#877—34no—
303C4×D12—32no—
304C4×D12—34no—
305C4×D12—32no—
306C4×D12C2×D311yescharacteristic
307#872—34no—
308#872—32no—
309#872—32no—
310C42×D3—32no—
311C42×D3—31no—
312C42×D3—31no—
313C42×D3—61no—
314#870—32no—
315#869—34no—
316#869—32no—
317#869—31no—
318#869—31no—
319#869—32no—
320#869—61no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—34no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D311yescharacteristic
329C22×C3⋊D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C32×Q8—24no—
332C2×C32×C4C2414yes—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C3⋊Dic3C2414yes—
337C2×C3⋊Dic3C2411yescharacteristic
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2411yescharacteristic
340C4×C3⋊D3—22no—
341C4×C3⋊D3—22no—
342C4×C3⋊D3—44no—
343C4×C3⋊D3C2×Q814yescomplemented
344#634—24no—
345#634—44no—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C3×D12C2×Q814yescomplemented
354C3×C4×D3—24no—
355C3×C4×D3—44no—
356C3×Dic6—22no—
357C3×Dic6—22no—
358C3×Dic6—44no—
359C3×Dic6C2×Q814yescomplemented
360#627—24no—
361#627—44no—
362#626C2×Q818yescomplemented
363D3×Dic3—24no—
364D3×Dic3—44no—
365D3×Dic3C2×Q818yescomplemented
366Q82—92no—
367#557—31no—
368#557—91no—
369#554—92no—
370#554—94no—
371D4×Q8—31no—
372D4×Q8—91no—
373D4×Q8—92no—
374D4×Q8—92no—
375#544—94no—
376#544—92no—
377#533—91no—
378#533—92no—
379C2×C4⋊Q8—92no—
380C2×C4⋊Q8—91no—
381#520—92no—
382C4×#41—91no—
383C2×C3×Q8—22no—
384C2×C3×Q8—31no—
385C2×C3×Q8—31no—
386C2×C3×Q8—31no—
387C2×C3×Q8—34no—
388C2×C3×Q8—124no—
389C2×C3×Q8C22×D312yes—
390C2×C3×Q8C22×D312yes—
391C2×C3×D4—31no—
392C22×C3×C4—32no—
393C22×C3×C4—34no—
394C2×#67—32no—
395C22×Dic3—32no—
396C22×Dic3—32no—
397C22×Dic3—34no—
398#239—38no—
399D3×Q8—44no—
400D3×Q8—124no—
401D3×Q8—124no—
402D3×Q8—124no—
403D3×Q8—128no—
404#237—38no—
405C2×D12—32no—
406C2×D12C22×D311yescharacteristic
407C2×C4×D3—32no—
408C2×C4×D3—31no—
409C2×C4×D3—31no—
410C2×C4×D3—32no—
411C2×C4×D3—31no—
412C2×C4×D3—31no—
413C2×C4×D3—31no—
414C2×C4×D3—31no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—61no—
419C2×C4×D3—61no—
420C2×C4×D3—61no—
421C2×C4×D3—64no—
422C2×C4×D3C22×D312yes—
423C2×C4×D3C22×D314yes—
424C2×Dic6—32no—
425C2×Dic6—32no—
426C2×Dic6—32no—
427C2×Dic6—32no—
428C2×Dic6—34no—
429C2×Dic6—34no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—62no—
433C2×Dic6—64no—
434C2×Dic6—124no—
435C2×Dic6C22×D311yescharacteristic
436C2×Dic6C22×D311yescharacteristic
437C2×Dic6C22×D314yes—
438C2×Dic6C22×D311yescharacteristic
439C3×C4⋊C4—22no—
440C3×C4⋊C4—22no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4—34no—
445C3×C4⋊C4—34no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—32no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4C22×D312yes—
453C3×C4⋊C4C22×D312yes—
454C3×C4⋊C4C22×D312yes—
455C3×C4⋊C4C22×D312yes—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—32no—
458C3×C42—21no—
459C3×C42—32no—
460C3×C42—32no—
461C3×C42—34no—
462C3×C42—32no—
463C3×C42C22×D311yescharacteristic
464C3×C42C22×D311yescharacteristic
465#217—32no—
466#217—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4C22×D314yes—
476(C2×D3)⋊C4C22×D312yes—
477C4⋊Dic3—32no—
478C4⋊Dic3—32no—
479C4⋊Dic3—32no—
480C4⋊Dic3—32no—
481C4⋊Dic3—32no—
482C4⋊Dic3—34no—
483C4⋊Dic3—32no—
484C4⋊Dic3—32no—
485C4⋊Dic3—34no—
486C4⋊Dic3—34no—
487C4⋊Dic3—62no—
488C4⋊Dic3—62no—
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D311yescharacteristic
491C4⋊Dic3C22×D311yescharacteristic
492C4⋊Dic3C22×D311yescharacteristic
493C4⋊Dic3C22×D314yes—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—32no—
507Dic3⋊C4—32no—
508Dic3⋊C4—32no—
509Dic3⋊C4—32no—
510Dic3⋊C4—32no—
511Dic3⋊C4—34no—
512Dic3⋊C4—64no—
513Dic3⋊C4—64no—
514Dic3⋊C4C22×D314yes—
515Dic3⋊C4C22×D312yes—
516Dic3⋊C4C22×D312yes—
517Dic3⋊C4C22×D312yes—
518Dic3⋊C4C22×D314yes—
519Dic3⋊C4C22×D314yes—
520C4×Dic3—31no—
521C4×Dic3—31no—
522C4×Dic3—31no—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—31no—
526C4×Dic3—32no—
527C4×Dic3—34no—
528C4×Dic3—34no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—32no—
532C4×Dic3—61no—
533C4×Dic3—61no—
534C4×Dic3—61no—
535C4×Dic3C22×D312yes—
536C4×Dic3C22×D312yes—
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D314yes—
539C22×C32C2511yescharacteristic
540C2×C3⋊D3—21no—
541C2×C3⋊D3—21no—
542C2×C3⋊D3C22×Q812yes—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3C22×Q814yes—
546C32×C4—21no—
547C32×C4—24no—
548C32×C4C22×Q812yes—
549C32×C4H(5,𝔽2)12yes—
550C3⋊Dic3—21no—
551C3⋊Dic3—24no—
552C3⋊Dic3C22×Q812yes—
553C3⋊Dic32−1+412yes—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3—22no—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3C22×Q814yes—
561C2×#41—91no—
562C22×Q8—32no—
563C22×Q8—92no—
564C22×Q8—92no—
565C4⋊Q8—32no—
566C4⋊Q8—32no—
567C4⋊Q8—92no—
568C4⋊Q8—92no—
569C4⋊Q8—94no—
570C4⋊Q8—91no—
571C4⋊Q8—94no—
572C4⋊Q8—94no—
573C4⋊Q8—94no—
574C4⋊Q8—91no—
575C4⋊Q8—92no—
576C4⋊Q8—92no—
577C4⋊Q8—92no—
578C4⋊Q8—91no—
579C4⋊Q8D3211yescharacteristic
580#125—34no—
581#125—32no—
582#125—92no—
583#125—94no—
584#125—92no—
585#125—94no—
586C22⋊Q8—32no—
587C22⋊Q8—34no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—92no—
592C22⋊Q8—94no—
593C22⋊Q8—92no—
594C22⋊Q8—94no—
595C22⋊Q8—91no—
596C22⋊Q8—91no—
597C22⋊Q8—94no—
598C4×Q8—32no—
599C4×Q8—32no—
600C4×Q8—31no—
601C4×Q8—31no—
602C4×Q8—31no—
603C4×Q8—92no—
604C4×Q8—92no—
605C4×Q8—94no—
606C4×Q8—92no—
607C4×Q8—91no—
608C4×D4—32no—
609C4×D4—31no—
610C4×D4—92no—
611C4×D4—94no—
612C4×D4—92no—
613C4×D4—92no—
614C4×D4—94no—
615C4×D4—91no—
616#117—92no—
617#117—94no—
618#117—92no—
619#117—91no—
620C2×C4⋊C4—94no—
621C2×C4⋊C4—94no—
622C2×C4⋊C4—92no—
623C2×C4⋊C4—92no—
624C2×C42—92no—
625C2×C42—91no—
626C23×C3—32no—
627C22×D3—31no—
628C22×D3—31no—
629C22×D3—61no—
630C22×D3C23×D312yes—
631C3×Q8—24no—
632C3×Q8—24no—
633C3×Q8—34no—
634C3×Q8—44no—
635C3×Q8—62no—
636C3×Q8—62no—
637C3×Q8—124no—
638C3×D4—34no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—24no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—64no—
651C2×C3×C4—124no—
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D314yes—
655C2×C3×C4C23×D314yes—
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660#67—38no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—31no—
665C2×Dic3—38no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—34no—
669C2×Dic3—34no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—64no—
674C2×Dic3—64no—
675C2×Dic3—124no—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D312yes—
683D12—38no—
684D12D3×Q814yescomplemented
685C4×D3—24no—
686C4×D3—38no—
687C4×D3—34no—
688C4×D3—34no—
689C4×D3—44no—
690C4×D3—64no—
691C4×D3—62no—
692C4×D3—62no—
693C4×D3—64no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—62no—
697C4×D3—62no—
698C4×D3—124no—
699C4×D3—124no—
700C4×D3—124no—
701C4×D3—128no—
702Dic6—22no—
703Dic6—22no—
704Dic6—44no—
705Dic6—64no—
706Dic6—64no—
707Dic6—64no—
708Dic6—64no—
709Dic6—124no—
710Dic6—124no—
711Dic6—124no—
712Dic6—124no—
713Dic6—124no—
714Dic6—128no—
715Dic6D3×Q814yescomplemented
716C2×C32C23×Q811yescharacteristic
717C2×C32C2×H(5,𝔽2)11yescharacteristic
718C2×C32C2×2−1+411yescharacteristic
719C3⋊D3—22no—
720C3×D3—24no—
721#41—98no—
722C2×Q8—31no—
723C2×Q8—31no—
724C2×Q8—31no—
725C2×Q8—34no—
726C2×Q8—92no—
727C2×Q8—94no—
728C2×Q8—92no—
729C2×Q8—94no—
730C2×Q8—124no—
731C2×Q8—364no—
732C2×Q8—364no—
733C2×Q8C2×D3212yes—
734C2×D4—31no—
735C2×D4—92no—
736C22×C4—32no—
737C22×C4—34no—
738C22×C4—92no—
739C22×C4—92no—
740C22×C4—94no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—91no—
744C22×C4—94no—
745C4⋊C4—34no—
746C4⋊C4—34no—
747C4⋊C4—31no—
748C4⋊C4—32no—
749C4⋊C4—31no—
750C4⋊C4—31no—
751C4⋊C4—31no—
752C4⋊C4—32no—
753C4⋊C4—32no—
754C4⋊C4—34no—
755C4⋊C4—34no—
756C4⋊C4—92no—
757C4⋊C4—92no—
758C4⋊C4—94no—
759C4⋊C4—94no—
760C4⋊C4—92no—
761C4⋊C4—92no—
762C4⋊C4—94no—
763C4⋊C4—92no—
764C4⋊C4—94no—
765C4⋊C4—92no—
766C4⋊C4—94no—
767C4⋊C4—94no—
768C4⋊C4—92no—
769C4⋊C4—92no—
770C4⋊C4C2×D3212yes—
771C4⋊C4C2×D3212yes—
772C22⋊C4—34no—
773C22⋊C4—32no—
774C22⋊C4—92no—
775C22⋊C4—92no—
776C22⋊C4—92no—
777C22⋊C4—94no—
778C22⋊C4—92no—
779C42—32no—
780C42—32no—
781C42—34no—
782C42—32no—
783C42—92no—
784C42—92no—
785C42—94no—
786C42—91no—
787C42—91no—
788C42—91no—
789C42C2×D3211yescharacteristic
790C22×C3—21no—
791C22×C3—34no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3C24×D311yescharacteristic
795C22×C3C24×D311yescharacteristic
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—32no—
799C2×D3—32no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—62no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3C2×D3×Q814yes—
808C3×C4—22no—
809C3×C4—24no—
810C3×C4—24no—
811C3×C4—21no—
812C3×C4—21no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—34no—
816C3×C4—44no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—62no—
820C3×C4—62no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4#100412yes—
824C3×C4C2×D3×Q812yes—
825C3×C4C2×D3×Q812yes—
826C3×C4#100912yes—
827Dic3—22no—
828Dic3—22no—
829Dic3—22no—
830Dic3—22no—
831Dic3—22no—
832Dic3—22no—
833Dic3—32no—
834Dic3—32no—
835Dic3—32no—
836Dic3—32no—
837Dic3—62no—
838Dic3—62no—
839Dic3—62no—
840Dic3—64no—
841Dic3—61no—
842Dic3—64no—
843Dic3—61no—
844Dic3—124no—
845Dic3C2×D3×Q814yes—
846C32#350311yescharacteristic, complemented, Sylow
847C23—32no—
848C23—91no—
849Q8—24no—
850Q8—34no—
851Q8—62no—
852Q8—62no—
853Q8—124no—
854Q8—184no—
855Q8—184no—
856Q8—364no—
857Q8—364no—
858D4—34no—
859D4—98no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—64no—
868C2×C4—98no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—94no—
872C2×C4—91no—
873C2×C4—94no—
874C2×C4—124no—
875C2×C4—182no—
876C2×C4—184no—
877C2×C4—182no—
878C2×C4—364no—
879C2×C4—364no—
880C2×C4C22×D3214yes—
881C2×C4C22×D3211yescharacteristic
882C2×C4C22×D3211yescharacteristic
883C2×C4C22×D3211yescharacteristic
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—64no—
888C2×C3C2×#100411yescharacteristic
889C2×C3C22×D3×Q811yescharacteristic
890C2×C3C22×D3×Q811yescharacteristic
891C2×C3C2×#100911yescharacteristic
892C2×C3D3×2−1+411yescharacteristic
893C2×C3D3×2−1+411yescharacteristic
894D3—24no—
895D3—64no—
896D3—62no—
897D3—62no—
898C22—34no—
899C22—62no—
900C22—62no—
901C22—92no—
902C22—181no—
903C22—181no—
904C22C23×D3211yescharacteristic
905C4—24no—
906C4—21no—
907C4—34no—
908C4—62no—
909C4—62no—
910C4—62no—
911C4—62no—
912C4—62no—
913C4—62no—
914C4—92no—
915C4—92no—
916C4—181no—
917C4—184no—
918C4#6431412yes—
919C4D32×Q812yes—
920C3—21no—
921C3#8674711yescharacteristic, complemented
922C3#8701811yescharacteristic, complemented
923C2—64no—
924C2—182no—
925C2C2×#6431411yescharacteristic
926C2C2×D32×Q811yescharacteristic
927C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×#3796C22
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×#5727C2semidirect
3. C3×#5721C2semidirect
4. Q8×#626C2semidirect
5. #10595367C2semidirect
6. #10595361C2semidirect
7. D3×#944C2semidirect
8. #10594485C2semidirect
9. #10594394C2semidirect
10. #10594390C2semidirect
12. #10594325C2semidirect
13. #10594312C2semidirect
14. Dic6×D12C2semidirect
16. #10593882C2semidirect
17. #10593860C2semidirect
91. #5727D3semidirect
97. #5721D3semidirect
142. #3796Q8semidirect
343. C4×C3⋊D3C2×Q8semidirect
353. C3×D12C2×Q8semidirect
359. C3×Dic6C2×Q8semidirect
362. #626C2×Q8semidirect
365. D3×Dic3C2×Q8semidirect
684. D12D3×Q8semidirect
715. Dic6D3×Q8semidirect
846. C32#3503semidirect
921. C3#86747semidirect
922. C3#87018semidirect

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×#57272
C3×#57212
Q8×#6262
#105953672
#105953612
D3×#9442
#105944852
#105943942
#105943902
#105943612
#105943252
#105943122
Dic6×D122
C4×#37962
#105938822
#105938602
#870183
#867473