Finite Group Databasebeta

← #11901897

Subgroups — #11901897

Order 1152.

2305 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×#5729C212yesmaximal, complemented
3#10595429C212yesmaximal
4#10595369C214yesmaximal, complemented
5#10595365C212yesmaximal, complemented
6#10594624C212yesmaximal
7#10594602C211yesmaximal, characteristic
8D32×C4⋊C4C211yesmaximal, characteristic
9#10594502C212yesmaximal, complemented
10#10594482C211yesmaximal, characteristic, complemented
11#10594399C212yesmaximal, complemented
12#10594390C214yesmaximal, complemented
13#10594374C211yesmaximal, characteristic, complemented
14#10594344C212yesmaximal, complemented
15#10593992C211yesmaximal, characteristic
16#10593959C212yesmaximal, complemented
17#10593948C211yesmaximal, characteristic, complemented
18D3×#544—32nomaximal
19C2×Q8×C3⋊D3C2212yes—
20C2×C4×D32C2212yes—
21C2×C4×D32C2211yescharacteristic
22C2×#3797C2212yes—
23C32×C4⋊Q8C2211yescharacteristic, complemented
24#64153C2212yescomplemented
25C4⋊C4×C3⋊D3C2211yescharacteristic
26C4⋊C4×C3⋊D3C2211yescharacteristic
27C4⋊C4×C3⋊D3C2212yes—
28#64097C2211yescharacteristic, complemented
29#64097C2212yescomplemented
30#64097C2211yescharacteristic, complemented
31C42×C3⋊D3C2211yescharacteristic
32#64078C2211yescharacteristic, complemented
33C3×#946C2214yes—
34C3×#944C2214yescomplemented
35C3×#896C2214yes—
36C3×#892C2212yes—
37C3×D3×C4⋊C4C2212yes—
38C3×#890C2212yescomplemented
39C3×#889C2214yescomplemented
40C3×#888C2212yescomplemented
41C3×#872C2212yes—
42C3×#870C2212yescomplemented
43#63921C2212yes—
44#63921C2211yescharacteristic
45#63921C2211yescharacteristic
46#63918C2212yescomplemented
47#63900C2211yescharacteristic
48#63900C2211yescharacteristic
49#63900C2212yes—
50#63896C2214yes—
51#63896C2214yes—
52#63893C2214yes—
53D3×C4⋊Dic3C2212yes—
54#63887C2214yes—
55#63883C2211yescharacteristic
56#63883C2212yes—
57#63883C2212yes—
58#63883C2212yes—
59#63883C2212yes—
60#63883C2212yes—
61#63883C2211yescharacteristic
62C4×#624C2212yes—
63C4×#624C2211yescharacteristic
64#63878C2212yes—
65#63878C2212yes—
66#63877C2214yes—
67D3×Dic3⋊C4C2214yes—
68#63872C2212yescomplemented
69#63870C2212yescomplemented
70#63870C2212yescomplemented
71#63869C2212yescomplemented
72#63867C2214yescomplemented
73#63866C2214yescomplemented
74#63857C2214yes—
75#63855C2212yes—
76#63851C2214yes—
77#63847C2214yescomplemented
78#63846C2214yescomplemented
79#63845C2214yescomplemented
80#63841C2212yes—
81#63840C2214yescomplemented
82#63840C2214yescomplemented
83#63839C2214yescomplemented
84C3×#544—32no—
85#5729—34no—
86#5729—32no—
87#5729D312yescomplemented
88D3×C4⋊Q8—32no—
89D3×C4⋊Q8—34no—
90D3×C4⋊Q8—32no—
91D3×C4⋊Q8—61no—
92#5689—34no—
93#5689—32no—
94#5689—32no—
95D3×#125—32no—
96D3×#125—34no—
97D3×#125—32no—
98D3×C22⋊Q8—34no—
99D3×C22⋊Q8—34no—
100#5623—34no—
101#5623—34no—
102D3×#117—32no—
103D3×#117—32no—
104#5519—32no—
105#5519—32no—
106C2×D3×C4⋊C4—32no—
107#5500—32no—
108C22×D32C2311yescharacteristic
109C2×C32×Q8C2312yes—
110Q8×C3⋊D3—44no—
111C2×C4×C3⋊D3C2312yes—
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C4×C3⋊D3C2311yescharacteristic
116C2×#634C2312yes—
117C2×#634C2312yes—
118C2×#634C2312yes—
119C2×C3×C4×D3C2314yes—
120C2×C3×C4×D3C2312yes—
121C2×C3×Dic6C2314yes—
122C2×#627C2314yes—
123C2×#624C2311yescharacteristic
124C2×#624C2312yes—
125C2×#624C2312yes—
126C2×#624C2311yescharacteristic
127C2×#624C2311yescharacteristic
128C2×D3×Dic3C2314yes—
129C2×D3×Dic3C2312yes—
130C4×D32—44no—
131C4×D32Q818yescomplemented
132#3797—44no—
133C32×C4⋊C4C2311yescharacteristic
134C32×C4⋊C4C2312yes—
135C32×C4⋊C4C2311yescharacteristic
136C32×C42C2311yescharacteristic
137C4⋊(C3⋊Dic3)C2311yescharacteristic
138C4⋊(C3⋊Dic3)C2312yes—
139C4⋊(C3⋊Dic3)C2311yescharacteristic
140#3750C2312yes—
141#3750C2312yes—
142#3750C2312yes—
143#3750C2312yes—
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2311yescharacteristic
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2312yes—
149C3×(C2×D3)⋊C4C2312yes—
150C3×C4⋊Dic3C2312yes—
151C3×C4⋊Dic3C2314yes—
152C3×C4⋊Dic3C2312yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2312yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2312yes—
159C3×Dic3⋊C4C2314yes—
160C3×C4×Dic3C2312yes—
161C3×C4×Dic3C2314yes—
162#3724C2312yes—
163#3724C2314yes—
164#3724C2312yes—
165Dic3⋊Dic3C2314yes—
166Dic3⋊Dic3C2312yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2312yes—
171Dic3⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2312yes—
174(C2×D3)⋊Dic3C2312yes—
175Dic32C2312yes—
176Dic32C2314yes—
177C2×#544—91noSylow
178C2×D3×Q8—34no—
179C2×D3×Q8—34no—
180C2×D3×Q8—62no—
181C22×C4×D3—32no—
182C22×C4×D3—34no—
183C3×C4⋊Q8—21no—
184C3×C4⋊Q8—34no—
185C3×C4⋊Q8—32no—
186C3×C4⋊Q8C2×D312yescomplemented
187C3×#125—34no—
188C3×#125—32no—
189C3×#125—32no—
190C3×C22⋊Q8—34no—
191C3×C22⋊Q8—34no—
192C3×#117—32no—
193C3×#117—32no—
194C2×C3×C4⋊C4—32no—
195#946—34no—
196#946C2×D314yes—
197#944—34no—
198#944—34no—
199#944—34no—
200#944—62no—
201#944C2×D314yescomplemented
202#926—32no—
203#926—32no—
204C2×C4⋊Dic3—32no—
205#924—34no—
206#924—34no—
207C2×Dic3⋊C4—34no—
208#897—34no—
209#897—34no—
210#896—34no—
211#896—34no—
212#896—34no—
213#896C2×D314yes—
214#892—32no—
215#892—32no—
216#892—32no—
217#892C2×D312yes—
218D3×C4⋊C4—34no—
219D3×C4⋊C4—32no—
220D3×C4⋊C4—32no—
221D3×C4⋊C4—34no—
222D3×C4⋊C4—32no—
223D3×C4⋊C4—32no—
224D3×C4⋊C4—34no—
225D3×C4⋊C4—32no—
226D3×C4⋊C4—32no—
227D3×C4⋊C4—34no—
228D3×C4⋊C4—34no—
229D3×C4⋊C4—34no—
230D3×C4⋊C4—34no—
231D3×C4⋊C4—34no—
232D3×C4⋊C4—32no—
233D3×C4⋊C4—61no—
234D3×C4⋊C4—61no—
235D3×C4⋊C4—62no—
236D3×C4⋊C4C2×D312yes—
237#890—32no—
238#890—34no—
239#890—32no—
240#890—34no—
241#890—32no—
242#890C2×D312yescomplemented
243#889—34no—
244#889—34no—
245#889—34no—
246#889—34no—
247#889—34no—
248#889—34no—
249#889—34no—
250#889C2×D314yescomplemented
251#888—34no—
252#888—32no—
253#888—34no—
254#888—32no—
255#888—34no—
256#888—34no—
257#888—34no—
258#888—34no—
259#888—32no—
260#888—61no—
261#888—62no—
262#888—61no—
263#888C2×D312yescomplemented
264D3×C22⋊C4—34no—
265D3×C22⋊C4—32no—
266D3×C22⋊C4—32no—
267#878—34no—
268#878—34no—
269#878—34no—
270#878—34no—
271#877—32no—
272#877—32no—
273#877—34no—
274#872—32no—
275#872—34no—
276#872C2×D312yes—
277C42×D3—32no—
278C42×D3—34no—
279C42×D3—32no—
280C42×D3—61no—
281#870—32no—
282#870—34no—
283#870C2×D312yescomplemented
284#869—34no—
285#869—32no—
286#869—32no—
287#869—61no—
288C22×C3⋊D3C2411yescharacteristic
289C22×C3×D3C2412yes—
290C2×D32—22no—
291C2×D32—22no—
292C2×D32C2×Q814yes—
293C32×Q8—42no—
294C2×C32×C4C2412yes—
295C2×C32×C4C2411yescharacteristic
296C2×C32×C4C2411yescharacteristic
297C2×C32×C4C2412yes—
298C2×C32×C4C2411yescharacteristic
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2411yescharacteristic
301C2×C3⋊Dic3C2411yescharacteristic
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2411yescharacteristic
304C4×C3⋊D3—22no—
305C4×C3⋊D3—22no—
306C4×C3⋊D3—24no—
307C4×C3⋊D3—24no—
308C4×C3⋊D3C2×Q814yes—
309#634—42no—
310#634—42no—
311#634—42no—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2414yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2414yes—
316C2×C3×Dic3C2412yes—
317C3×C4×D3—44no—
318C3×C4×D3C2×Q818yescomplemented
319C3×Dic6—44no—
320#627—44no—
321#624—22no—
322#624—24no—
323#624—24no—
324#624—22no—
325#624C2×Q814yes—
326D3×Dic3—44no—
327D3×Dic3C2×Q818yescomplemented
328#544—32no—
329#544—92no—
330#544—92no—
331#544—92no—
332#544—94no—
333#544—94no—
334C2×C4⋊Q8—92no—
335C2×C4⋊Q8—91no—
336C2×C4⋊Q8—91no—
337C2×#125—92no—
338C2×#125—91no—
339C2×#125—91no—
340C2×C22⋊Q8—92no—
341C2×C22⋊Q8—92no—
342C2×#117—91no—
343C2×#117—91no—
344C22×C4⋊C4—91no—
345C23×D3—32no—
346C2×C3×Q8—22no—
347C2×C3×Q8—34no—
348C2×C3×Q8C22×D314yes—
349C22×C3×C4—32no—
350C22×C3×C4—34no—
351C22×Dic3—32no—
352C22×Dic3—34no—
353D3×Q8—128no—
354D3×Q8—128no—
355D3×Q8—128no—
356C2×C4×D3—32no—
357C2×C4×D3—32no—
358C2×C4×D3—32no—
359C2×C4×D3—316no—
360C2×C4×D3—32no—
361C2×C4×D3—32no—
362C2×C4×D3—34no—
363C2×C4×D3—34no—
364C2×C4×D3—34no—
365C2×C4×D3—32no—
366C2×C4×D3—32no—
367C2×C4×D3—34no—
368C2×C4×D3—34no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—128no—
375C2×C4×D3C22×D314yes—
376C2×C4×D3C22×D312yes—
377C2×Dic6—34no—
378C2×Dic6—34no—
379C2×Dic6—34no—
380C2×Dic6—34no—
381C2×Dic6—34no—
382C2×Dic6—62no—
383C2×Dic6—62no—
384C2×Dic6—62no—
385C2×Dic6C22×D314yes—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—32no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—32no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—32no—
398C3×C4⋊C4—32no—
399C3×C4⋊C4C22×D312yes—
400C3×C4⋊C4C22×D314yes—
401C3×C4⋊C4C22×D312yes—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—32no—
405C3×C42—21no—
406C3×C42—34no—
407C3×C42—32no—
408C3×C42C22×D312yes—
409#217—32no—
410#217—32no—
411#217—34no—
412(C2×D3)⋊C4—32no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—32no—
415(C2×D3)⋊C4C22×D314yes—
416(C2×D3)⋊C4C22×D312yes—
417(C2×D3)⋊C4C22×D312yes—
418C4⋊Dic3—32no—
419C4⋊Dic3—32no—
420C4⋊Dic3—34no—
421C4⋊Dic3—32no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3—34no—
426C4⋊Dic3—32no—
427C4⋊Dic3—34no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—62no—
431C4⋊Dic3C22×D312yes—
432C4⋊Dic3C22×D312yes—
433C4⋊Dic3C22×D314yes—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—32no—
443Dic3⋊C4—32no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—62no—
450Dic3⋊C4—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4—62no—
453Dic3⋊C4C22×D314yes—
454Dic3⋊C4C22×D314yes—
455Dic3⋊C4C22×D314yes—
456Dic3⋊C4C22×D312yes—
457Dic3⋊C4C22×D312yes—
458Dic3⋊C4C22×D314yes—
459Dic3⋊C4C22×D314yes—
460C4×Dic3—32no—
461C4×Dic3—32no—
462C4×Dic3—32no—
463C4×Dic3—34no—
464C4×Dic3—32no—
465C4×Dic3—34no—
466C4×Dic3—32no—
467C4×Dic3—61no—
468C4×Dic3—61no—
469C4×Dic3—61no—
470C4×Dic3C22×D312yes—
471C4×Dic3C22×D314yes—
472C22×C32C2511yescharacteristic
473C2×C3⋊D3C22×Q812yes—
474C2×C3⋊D3H(5,𝔽2)12yes—
475C2×C3⋊D32−1+412yes—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3C22×Q814yes—
479D32—28no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—22no—
483C32×C4—22no—
484C32×C4C22×Q812yes—
485C3⋊Dic3—21no—
486C3⋊Dic3—21no—
487C3⋊Dic3—22no—
488C3⋊Dic3—22no—
489C3⋊Dic3C22×Q812yes—
490C3×Dic3—24no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—24no—
494C3×Dic3C22×Q814yes—
495C22×Q8—92no—
496C22×Q8—92no—
497C23×C4—91no—
498C23×C4—92no—
499C4⋊Q8—34no—
500C4⋊Q8—32no—
501C4⋊Q8—92no—
502C4⋊Q8—94no—
503C4⋊Q8—94no—
504C4⋊Q8—94no—
505C4⋊Q8—94no—
506C4⋊Q8—92no—
507C4⋊Q8—92no—
508C4⋊Q8—91no—
509C4⋊Q8—91no—
510C4⋊Q8—91no—
511C4⋊Q8D3211yescharacteristic, complemented
512#125—34no—
513#125—32no—
514#125—32no—
515#125—94no—
516#125—92no—
517#125—94no—
518#125—92no—
519#125—92no—
520#125—94no—
521#125—94no—
522#125—92no—
523C22⋊Q8—34no—
524C22⋊Q8—34no—
525C22⋊Q8—94no—
526C22⋊Q8—94no—
527C22⋊Q8—94no—
528C22⋊Q8—94no—
529C22⋊Q8—94no—
530C22⋊Q8—94no—
531#117—32no—
532#117—32no—
533#117—94no—
534#117—92no—
535#117—92no—
536#117—92no—
537#117—92no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—92no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—92no—
545C2×C4⋊C4—92no—
546C2×C4⋊C4—92no—
547C2×C4⋊C4—92no—
548C2×C4⋊C4—92no—
549C2×C4⋊C4—94no—
550C2×C4⋊C4—92no—
551C2×C4⋊C4—91no—
552C2×C4⋊C4—91no—
553C2×C4⋊C4—92no—
554C2×C22⋊C4—92no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C42—92no—
558C2×C42—91no—
559C2×C42—91no—
560C23×C3—32no—
561C22×D3—32no—
562C22×D3—38no—
563C22×D3—61no—
564C22×D3—64no—
565C22×D3—64no—
566C22×D3C23×D312yes—
567C3×Q8—44no—
568C3×Q8—44no—
569C3×Q8—124no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—32no—
576C2×C3×C4—38no—
577C2×C3×C4—34no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—34no—
581C2×C3×C4—124no—
582C2×C3×C4C23×D312yes—
583C2×C3×C4C23×D312yes—
584C2×C3×C4C23×D314yes—
585C2×C3×C4C23×D314yes—
586C2×C3×C4C23×D312yes—
587C2×Dic3—32no—
588C2×Dic3—38no—
589C2×Dic3—32no—
590C2×Dic3—34no—
591C2×Dic3—32no—
592C2×Dic3—34no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—124no—
599C2×Dic3C23×D314yes—
600C2×Dic3C23×D312yes—
601C2×Dic3C23×D312yes—
602C2×Dic3C23×D314yes—
603C2×Dic3C23×D312yes—
604C4×D3—38no—
605C4×D3—38no—
606C4×D3—38no—
607C4×D3—44no—
608C4×D3—64no—
609C4×D3—68no—
610C4×D3—64no—
611C4×D3—68no—
612C4×D3—64no—
613C4×D3—64no—
614C4×D3—68no—
615C4×D3—64no—
616C4×D3—68no—
617C4×D3—64no—
618C4×D3—64no—
619C4×D3—124no—
620C4×D3—124no—
621C4×D3—124no—
622C4×D3D3×Q818yescomplemented
623Dic6—44no—
624Dic6—124no—
625Dic6—124no—
626Dic6—124no—
627Dic6—124no—
628Dic6—124no—
629Dic6—124no—
630Dic6—124no—
631Dic6—124no—
632C2×C32C23×Q811yescharacteristic
633C2×C32C2×H(5,𝔽2)11yescharacteristic
634C2×C32C2×2−1+411yescharacteristic
635C3⋊D3#54414yescomplemented
636C3×D3—24no—
637C24—91no—
638C2×Q8—34no—
639C2×Q8—94no—
640C2×Q8—92no—
641C2×Q8—92no—
642C2×Q8—92no—
643C2×Q8—364no—
644C2×Q8—364no—
645C2×Q8C2×D3212yes—
646C22×C4—32no—
647C22×C4—34no—
648C22×C4—91no—
649C22×C4—98no—
650C22×C4—91no—
651C22×C4—92no—
652C22×C4—91no—
653C22×C4—92no—
654C22×C4—92no—
655C22×C4—94no—
656C22×C4—91no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—92no—
660C22×C4—92no—
661C22×C4—364no—
662C4⋊C4—34no—
663C4⋊C4—32no—
664C4⋊C4—32no—
665C4⋊C4—32no—
666C4⋊C4—32no—
667C4⋊C4—34no—
668C4⋊C4—34no—
669C4⋊C4—34no—
670C4⋊C4—34no—
671C4⋊C4—34no—
672C4⋊C4—92no—
673C4⋊C4—94no—
674C4⋊C4—92no—
675C4⋊C4—92no—
676C4⋊C4—92no—
677C4⋊C4—94no—
678C4⋊C4—94no—
679C4⋊C4—94no—
680C4⋊C4—94no—
681C4⋊C4—94no—
682C4⋊C4—92no—
683C4⋊C4—91no—
684C4⋊C4—92no—
685C4⋊C4—91no—
686C4⋊C4—92no—
687C4⋊C4—92no—
688C4⋊C4—92no—
689C4⋊C4C2×D3211yescharacteristic
690C4⋊C4C2×D3211yescharacteristic
691C4⋊C4C2×D3212yes—
692C22⋊C4—34no—
693C22⋊C4—32no—
694C22⋊C4—32no—
695C22⋊C4—94no—
696C22⋊C4—92no—
697C22⋊C4—92no—
698C42—34no—
699C42—32no—
700C42—94no—
701C42—92no—
702C42—91no—
703C42—91no—
704C42—91no—
705C42C2×D3211yescharacteristic
706C22×C3—21no—
707C22×C3—34no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3C24×D312yes—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—34no—
714C2×D3—34no—
715C2×D3—34no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—616no—
720C2×D3C2×D3×Q814yes—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—24no—
724C3×C4—22no—
725C3×C4—24no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—34no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—62no—
732C3×C4—64no—
733C3×C4—64no—
734C3×C4—62no—
735C3×C4C2×D3×Q814yes—
736Dic3—22no—
737Dic3—24no—
738Dic3—24no—
739Dic3—22no—
740Dic3—34no—
741Dic3—62no—
742Dic3—62no—
743Dic3—62no—
744Dic3—62no—
745Dic3—64no—
746Dic3—64no—
747Dic3—62no—
748Dic3—122no—
749Dic3—122no—
750Dic3C2×D3×Q814yes—
751C32C2×#54411yescharacteristic, complemented, Sylow
752C23—32no—
753C23—94no—
754C23—91no—
755C23—182no—
756C23—182no—
757Q8—42no—
758Q8—124no—
759Q8—362no—
760Q8—362no—
761Q8—362no—
762Q8—364no—
763C2×C4—32no—
764C2×C4—38no—
765C2×C4—32no—
766C2×C4—34no—
767C2×C4—32no—
768C2×C4—34no—
769C2×C4—94no—
770C2×C4—98no—
771C2×C4—91no—
772C2×C4—94no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—92no—
776C2×C4—92no—
777C2×C4—124no—
778C2×C4—184no—
779C2×C4—182no—
780C2×C4—184no—
781C2×C4—182no—
782C2×C4—184no—
783C2×C4—182no—
784C2×C4—182no—
785C2×C4—184no—
786C2×C4—364no—
787C2×C4C22×D3212yes—
788C2×C4C22×D3211yescharacteristic
789C2×C4C22×D3211yescharacteristic
790C2×C4C22×D3212yes—
791C2×C4C22×D3211yescharacteristic
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—64no—
796C2×C3C22×D3×Q812yes—
797C2×C3D3×H(5,𝔽2)12yes—
798C2×C3D3×2−1+412yes—
799D3—24no—
800D3—38no—
801D3—64no—
802C22—34no—
803C22—62no—
804C22—62no—
805C22—92no—
806C22—92no—
807C22—92no—
808C22—188no—
809C22C23×D3211yescharacteristic
810C4—22no—
811C4—21no—
812C4—22no—
813C4—21no—
814C4—34no—
815C4—64no—
816C4—62no—
817C4—62no—
818C4—64no—
819C4—92no—
820C4—182no—
821C4—181no—
822C4—182no—
823C4—181no—
824C4D32×Q812yes—
825C3—21no—
826C3D3×#54412yescomplemented
827C2—64no—
828C2—94no—
829C2#1059667511yescharacteristic
830C2C2×D32×Q811yescharacteristic
831C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC22×D32C23
hypercenterC4⋊Q8D32
hypocenterC32C2×#544
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×#5729C2semidirect
4. #10595369C2semidirect
5. #10595365C2semidirect
9. #10594502C2semidirect
10. #10594482C2semidirect
11. #10594399C2semidirect
12. #10594390C2semidirect
13. #10594374C2semidirect
14. #10594344C2semidirect
16. #10593959C2semidirect
17. #10593948C2semidirect
23. C32×C4⋊Q8C22semidirect
24. #64153C22semidirect
28. #64097C22semidirect
29. #64097C22semidirect
30. #64097C22semidirect
32. #64078C22semidirect
34. C3×#944C22semidirect
38. C3×#890C22semidirect
39. C3×#889C22semidirect
40. C3×#888C22semidirect
42. C3×#870C22semidirect
46. #63918C22semidirect
68. #63872C22semidirect
69. #63870C22semidirect
70. #63870C22semidirect
71. #63869C22semidirect
72. #63867C22semidirect
73. #63866C22semidirect
77. #63847C22semidirect
78. #63846C22semidirect
79. #63845C22semidirect
81. #63840C22semidirect
82. #63840C22semidirect
83. #63839C22semidirect
87. #5729D3semidirect
131. C4×D32Q8semidirect
186. C3×C4⋊Q8C2×D3semidirect
201. #944C2×D3semidirect
242. #890C2×D3semidirect
250. #889C2×D3semidirect
263. #888C2×D3semidirect
283. #870C2×D3semidirect
318. C3×C4×D3C2×Q8semidirect
327. D3×Dic3C2×Q8semidirect
511. C4⋊Q8D32semidirect
622. C4×D3D3×Q8semidirect
635. C3⋊D3#544semidirect
751. C32C2×#544semidirect
826. C3D3×#544semidirect

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×#57292
#105954292
#105953692
#105953652
#105946242
#105946022
D32×C4⋊C42
#105945022
#105944822
#105943992
#105943902
#105943742
#105943442
#105939922
#105939592
#105939482
D3×#5443