Finite Group Databasebeta

← #11903008

Subgroups — #11903008

Order 1152.

2397 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5581C212yesmaximal, complemented
3#10595429C211yesmaximal, characteristic, complemented
4#10595429C211yesmaximal, characteristic, complemented
5#10595380C212yesmaximal, complemented
6#10594608C212yesmaximal
7#10594602C211yesmaximal, characteristic, complemented
8D32×C4⋊C4C211yesmaximal, characteristic, complemented
9#10594550C212yesmaximal, complemented
10#10594430C214yesmaximal, complemented
11#10594399C212yesmaximal, complemented
12#10594020C212yesmaximal, complemented
13C4×#3802C211yesmaximal, characteristic
14#10593992C212yesmaximal, complemented
15#10593948C211yesmaximal, characteristic, complemented
16#10593920C212yesmaximal, complemented
17#10593919C214yesmaximal, complemented
18D3×#552—32nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3802C2211yescharacteristic
21C2×C4×D32C2212yes—
22C2×C4×D32C2211yescharacteristic
23C2×C4×D32C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic, complemented
25Q8×C3⋊Dic3C2211yescharacteristic, complemented
26C4⋊C4×C3⋊D3C2211yescharacteristic
27C4⋊C4×C3⋊D3C2212yes—
28#64096C2212yescomplemented
29#64096C2211yescharacteristic, complemented
30C42×C3⋊D3C2211yescharacteristic
31C42×C3⋊D3C2212yes—
32C4×#634C2212yescomplemented
33C4×#634C2211yescharacteristic, complemented
34C3×#946C2212yescomplemented
35C3×#946C2212yescomplemented
36C3×#894C2214yes—
37C3×#892C2212yescomplemented
38C3×D3×C4⋊C4C2212yescomplemented
39C3×#889C2214yescomplemented
40C3×#876C2214yescomplemented
41C3×C4×D12C2212yes—
42C3×#872C2214yescomplemented
43C3×#870C2212yescomplemented
44#63921C2212yes—
45#63921C2212yes—
46#63921C2212yes—
47#63921C2211yescharacteristic
48#63921C2211yescharacteristic
49#63905C2214yes—
50#63902C2212yes—
51C4×#625C2212yes—
52#63900C2211yescharacteristic
53#63900C2211yescharacteristic
54#63900C2211yescharacteristic
55#63898C2212yes—
56#63896C2214yescomplemented
57#63896C2214yescomplemented
58#63891C2214yes—
59D3×C4⋊Dic3C2212yescomplemented
60#63884C2214yes—
61#63883C2212yes—
62#63883C2212yes—
63#63883C2212yes—
64#63883C2212yes—
65#63883C2212yes—
66C4×#624C2212yes—
67#63878C2214yescomplemented
68#63878C2214yescomplemented
69#63877C2214yescomplemented
70D3×Dic3⋊C4C2214yescomplemented
71#63872C2212yescomplemented
72#63870C2212yescomplemented
73#63870C2212yescomplemented
74#63867C2214yescomplemented
75#63862C2214yescomplemented
76#63862C2214yescomplemented
77#63862C2214yescomplemented
78#63857C2212yescomplemented
79#63857C2212yescomplemented
80#63855C2214yescomplemented
81#63846C2214yescomplemented
82#63845C2214yescomplemented
83#63841C2212yescomplemented
84C3×#552—32no—
85#5708—34no—
86D3×#126—34no—
87#5694—32no—
88#5693—34no—
89D3×#125—34no—
90D3×#125—32no—
91D3×#123—34no—
92#5650—34no—
93#5642—32no—
94#5639—32no—
95D3×C22⋊Q8—32no—
96D3×C22⋊Q8—32no—
97#5581D312yescomplemented
98C4×D3×Q8—32no—
99C4×D3×Q8—61no—
100C4×D3×D4—32no—
101#5541—32no—
102#5531—34no—
103#5529—32no—
104D3×#117—32no—
105D3×#117—34no—
106#5513—32no—
107C2×D3×C4⋊C4—32no—
108C22×D32C2311yescharacteristic
109C22×D32C2311yescharacteristic
110C2×C32×Q8C2311yescharacteristic
111Q8×C3⋊D3—24no—
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2311yescharacteristic
117C2×#634C2311yescharacteristic
118C2×#634C2312yes—
119C2×C3×D12C2312yes—
120C2×C3×C4×D3C2314yes—
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2312yes—
123C2×#625C2312yes—
124C2×#624C2311yescharacteristic
125C2×#624C2312yes—
126C2×#624C2311yescharacteristic
127C2×#624C2312yes—
128C2×D3×Dic3C2312yes—
129C2×D3×Dic3C2314yes—
130C2×D3×Dic3C2312yes—
131#3802—24no—
132C4×D32—28no—
133C4×D32—24no—
134C4×D32—24no—
135C32×C4⋊C4C2312yes—
136C32×C4⋊C4C2311yescharacteristic
137C32×C42C2311yescharacteristic
138C32×C42C2312yes—
139C4⋊(C3⋊Dic3)C2311yescharacteristic
140C4⋊(C3⋊Dic3)C2312yes—
141#3750C2312yes—
142#3750C2312yes—
143#3750C2312yes—
144C4×C3⋊Dic3C2312yes—
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2312yes—
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2311yescharacteristic
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×C4×Dic3C2314yes—
164#3724C2312yes—
165#3724C2312yes—
166#3724C2312yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2314yes—
171Dic3⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2312yes—
174(C2×D3)⋊Dic3C2314yes—
175(C2×D3)⋊Dic3C2314yes—
176(C2×D3)⋊Dic3C2312yes—
177Dic32C2314yes—
178C2×#552—91noSylow
179C2×D3×Q8—32no—
180C2×D3×Q8—61no—
181C2×D3×D4—32no—
182C22×C4×D3—34no—
183C22×C4×D3—32no—
184C22×C4×D3—32no—
185C3×#126—34no—
186C3×#125—34no—
187C3×#125—32no—
188C3×#123—34no—
189C3×C22⋊Q8—32no—
190C3×C22⋊Q8—32no—
191C3×C4×Q8—21no—
192C3×C4×Q8C2×D312yescomplemented
193C3×C4×D4—32no—
194C3×#117—32no—
195C3×#117—34no—
196C2×C3×C4⋊C4—32no—
197#946C2×D312yescomplemented
198#946C2×D312yescomplemented
199Q8×Dic3—32no—
200Q8×Dic3—61no—
201#935—34no—
202D4×Dic3—32no—
203#929—34no—
204C4×#67—32no—
205C4×#67—32no—
206#926—32no—
207#926—34no—
208C2×C4⋊Dic3—32no—
209#924—32no—
210#924—32no—
211C2×Dic3⋊C4—34no—
212#898—34no—
213#898—34no—
214#898—34no—
215#897—32no—
216#897—32no—
217#896—34no—
218#896—34no—
219#894—34no—
220#894C2×D314yes—
221#893—32no—
222#892—32no—
223#892—34no—
224#892—34no—
225#892C2×D312yescomplemented
226D3×C4⋊C4—32no—
227D3×C4⋊C4—34no—
228D3×C4⋊C4—34no—
229D3×C4⋊C4—32no—
230D3×C4⋊C4—32no—
231D3×C4⋊C4—32no—
232D3×C4⋊C4—32no—
233D3×C4⋊C4—34no—
234D3×C4⋊C4—34no—
235D3×C4⋊C4—34no—
236D3×C4⋊C4—34no—
237D3×C4⋊C4—34no—
238D3×C4⋊C4—61no—
239D3×C4⋊C4—62no—
240D3×C4⋊C4C2×D312yescomplemented
241#890—32no—
242#890—32no—
243#890—34no—
244#890—34no—
245#889—34no—
246#889—34no—
247#889—34no—
248#889—34no—
249#889—34no—
250#889C2×D314yescomplemented
251#887—34no—
252#887—32no—
253#887—62no—
254#887—61no—
255#886—34no—
256#883—34no—
257#883—34no—
258#67⋊C4—32no—
259#67⋊C4—32no—
260D3×C22⋊C4—34no—
261D3×C22⋊C4—34no—
262D3×C22⋊C4—34no—
263D3×C22⋊C4—32no—
264D3×C22⋊C4—32no—
265#879—34no—
266#879—34no—
267#879—34no—
268#878—34no—
269#878—34no—
270#877—34no—
271#877—34no—
272#877—34no—
273#876C2×D314yescomplemented
274C4×D12C2×D312yes—
275#872—34no—
276#872—34no—
277#872C2×D314yescomplemented
278C42×D3—32no—
279C42×D3—34no—
280C42×D3—34no—
281C42×D3—62no—
282C42×D3—61no—
283#870—34no—
284#870C2×D312yescomplemented
285C4×Dic6—32no—
286C4×Dic6—34no—
287C4×Dic6—62no—
288C4×Dic6—61no—
289C22×C3⋊D3C2411yescharacteristic
290C22×C3×D3C2412yes—
291C22×C3×D3C2412yes—
292C2×D32—22no—
293C2×D32—22no—
294C2×D32—22no—
295C2×D32—22no—
296C2×D32—22no—
297C2×D32#4114yes—
298C32×Q8—22no—
299C2×C32×C4C2412yes—
300C2×C32×C4C2411yescharacteristic
301C2×C32×C4C2411yescharacteristic
302C2×C32×C4C2412yes—
303C2×C32×C4C2411yescharacteristic
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2411yescharacteristic
306C2×C3⋊Dic3C2412yes—
307C2×C3⋊Dic3C2411yescharacteristic
308C2×C3⋊Dic3C2411yescharacteristic
309C4×C3⋊D3—24no—
310C4×C3⋊D3—22no—
311C4×C3⋊D3—24no—
312C4×C3⋊D3—22no—
313C4×C3⋊D3#4114yes—
314#634—22no—
315#634—24no—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2414yes—
318C2×C3×Dic3C2414yes—
319C2×C3×Dic3C2412yes—
320C3×D12—24no—
321C3×C4×D3—28no—
322C3×C4×D3—24no—
323C3×C4×D3—24no—
324#625—24no—
325#624—24no—
326#624—22no—
327#624—22no—
328#624—24no—
329D3×Dic3—28no—
330D3×Dic3—24no—
331D3×Dic3—24no—
332#552—32no—
333#552—92no—
334#552—94no—
335#552—92no—
336#552—92no—
337#552—94no—
338C2×#126—92no—
339C2×#125—92no—
340C2×#125—91no—
341C2×#123—92no—
342C2×C22⋊Q8—91no—
343C2×C22⋊Q8—91no—
344C2×C4×Q8—91no—
345C2×C4×D4—91no—
346C2×#117—91no—
347C2×#117—92no—
348C22×C4⋊C4—91no—
349C23×D3—32no—
350C23×D3—32no—
351C2×C3×Q8—21no—
352C2×C3×Q8C22×D312yes—
353C2×C3×D4—32no—
354C22×C3×C4—34no—
355C22×C3×C4—32no—
356C22×C3×C4—32no—
357C2×#67—32no—
358C2×#67—32no—
359C22×Dic3—32no—
360C22×Dic3—34no—
361C22×Dic3—32no—
362D3×Q8—68no—
363D3×Q8—68no—
364D3×D4—68no—
365C2×D12C22×D312yes—
366C2×C4×D3—32no—
367C2×C4×D3—32no—
368C2×C4×D3—32no—
369C2×C4×D3—34no—
370C2×C4×D3—32no—
371C2×C4×D3—34no—
372C2×C4×D3—34no—
373C2×C4×D3—32no—
374C2×C4×D3—32no—
375C2×C4×D3—34no—
376C2×C4×D3—34no—
377C2×C4×D3—32no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—61no—
383C2×C4×D3—68no—
384C2×C4×D3—68no—
385C2×C4×D3—616no—
386C2×C4×D3C22×D314yes—
387C2×C4×D3C22×D312yes—
388C2×C4×D3C22×D312yes—
389C2×Dic6—34no—
390C2×Dic6—32no—
391C2×Dic6—61no—
392C2×Dic6—62no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—22no—
395C3×C4⋊C4—32no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—32no—
401C3×C4⋊C4—32no—
402C3×C4⋊C4—34no—
403C3×C4⋊C4C22×D314yes—
404C3×C4⋊C4C22×D312yes—
405C3×C22⋊C4—32no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—32no—
410C3×C42—22no—
411C3×C42—21no—
412C3×C42—34no—
413C3×C42C22×D312yes—
414C3×C42C22×D314yes—
415#217—32no—
416#217—34no—
417#217—34no—
418#217—34no—
419#217—32no—
420(C2×D3)⋊C4—32no—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4C22×D314yes—
426(C2×D3)⋊C4C22×D312yes—
427(C2×D3)⋊C4C22×D314yes—
428(C2×D3)⋊C4C22×D312yes—
429(C2×D3)⋊C4C22×D314yes—
430C4⋊Dic3—34no—
431C4⋊Dic3—32no—
432C4⋊Dic3—34no—
433C4⋊Dic3—34no—
434C4⋊Dic3—34no—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—61no—
438C4⋊Dic3—62no—
439C4⋊Dic3C22×D312yes—
440C4⋊Dic3C22×D312yes—
441C4⋊Dic3C22×D312yes—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—32no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—32no—
453Dic3⋊C4—34no—
454Dic3⋊C4—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457Dic3⋊C4C22×D314yes—
458Dic3⋊C4C22×D314yes—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461Dic3⋊C4C22×D314yes—
462C4×Dic3—34no—
463C4×Dic3—32no—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—32no—
467C4×Dic3—32no—
468C4×Dic3—34no—
469C4×Dic3—34no—
470C4×Dic3—62no—
471C4×Dic3—61no—
472C4×Dic3—62no—
473C4×Dic3—61no—
474C4×Dic3—62no—
475C4×Dic3—61no—
476C4×Dic3C22×D314yes—
477C22×C32C2511yescharacteristic
478C2×C3⋊D3C2×#4112yes—
479C2×C3⋊D3C2×#4112yes—
480C2×C3⋊D32−1+412yes—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3C2×#4114yes—
487D32—28no—
488D32—44no—
489C32×C4—22no—
490C32×C4—21no—
491C32×C4—22no—
492C32×C4—21no—
493C32×C4C2×#4112yes—
494C3⋊Dic3—22no—
495C3⋊Dic3—21no—
496C3⋊Dic3—22no—
497C3⋊Dic3—21no—
498C3⋊Dic3C2×#4112yes—
499C3×Dic3—24no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—24no—
503C22×Q8—91no—
504C22×D4—91no—
505C23×C4—92no—
506C23×C4—91no—
507C23×C4—91no—
508#126—34no—
509#126—94no—
510#126—94no—
511#126—94no—
512#125—34no—
513#125—32no—
514#125—94no—
515#125—92no—
516#125—92no—
517#125—94no—
518#125—94no—
519#125—92no—
520#123—34no—
521#123—94no—
522#123—94no—
523#123—94no—
524C22⋊Q8—32no—
525C22⋊Q8—32no—
526C22⋊Q8—94no—
527C22⋊Q8—94no—
528C22⋊Q8—92no—
529C22⋊Q8—92no—
530C4×Q8—91no—
531C4×Q8—92no—
532C4×Q8—91no—
533C4×Q8—91no—
534C4×Q8—92no—
535C4×Q8D3211yescharacteristic, complemented
536C4×D4—32no—
537C4×D4—92no—
538C4×D4—92no—
539C4×D4—92no—
540#117—32no—
541#117—34no—
542#117—94no—
543#117—94no—
544#117—94no—
545#117—94no—
546#117—92no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—91no—
549C2×C4⋊C4—92no—
550C2×C4⋊C4—92no—
551C2×C4⋊C4—91no—
552C2×C4⋊C4—92no—
553C2×C4⋊C4—91no—
554C2×C4⋊C4—92no—
555C2×C4⋊C4—92no—
556C2×C4⋊C4—94no—
557C2×C4⋊C4—92no—
558C2×C4⋊C4—91no—
559C2×C4⋊C4—92no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—92no—
562C2×C22⋊C4—92no—
563C2×C22⋊C4—91no—
564C2×C22⋊C4—92no—
565C2×C42—92no—
566C2×C42—92no—
567C2×C42—91no—
568C23×C3—32no—
569C23×C3—32no—
570C22×D3—32no—
571C22×D3—38no—
572C22×D3—61no—
573C22×D3—64no—
574C22×D3—64no—
575C22×D3—64no—
576C22×D3—64no—
577C22×D3—64no—
578C22×D3C23×D312yes—
579C22×D3C23×D312yes—
580C3×Q8—24no—
581C3×Q8—24no—
582C3×D4—64no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—32no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—32no—
592C2×C3×C4—68no—
593C2×C3×C4—64no—
594C2×C3×C4—64no—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D314yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D314yes—
599C2×C3×C4C23×D312yes—
600#67—64no—
601#67—64no—
602C2×Dic3—32no—
603C2×Dic3—32no—
604C2×Dic3—34no—
605C2×Dic3—32no—
606C2×Dic3—34no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—62no—
610C2×Dic3—62no—
611C2×Dic3—61no—
612C2×Dic3—64no—
613C2×Dic3—64no—
614C2×Dic3—68no—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D314yes—
617C2×Dic3C23×D312yes—
618C2×Dic3C23×D314yes—
619D12—24no—
620C4×D3—28no—
621C4×D3—24no—
622C4×D3—24no—
623C4×D3—38no—
624C4×D3—64no—
625C4×D3—68no—
626C4×D3—64no—
627C4×D3—64no—
628C4×D3—68no—
629C4×D3—64no—
630C4×D3—64no—
631C4×D3—64no—
632C4×D3—68no—
633C4×D3—64no—
634C4×D3—68no—
635C4×D3—64no—
636C4×D3—68no—
637C4×D3—68no—
638C4×D3—124no—
639C4×D3—122no—
640Dic6—68no—
641Dic6—68no—
642Dic6—64no—
643Dic6—64no—
644C2×C32C22×#4111yescharacteristic
645C2×C32C22×#4111yescharacteristic
646C2×C32C2×2−1+411yescharacteristic
647C3⋊D3#55214yescomplemented
648C3×D3—24no—
649C3×D3—42no—
650C24—91no—
651C24—91no—
652C2×Q8—92no—
653C2×Q8—91no—
654C2×Q8—184no—
655C2×Q8C2×D3211yescharacteristic
656C2×D4—32no—
657C2×D4—92no—
658C2×D4—184no—
659C22×C4—34no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—91no—
663C22×C4—92no—
664C22×C4—91no—
665C22×C4—92no—
666C22×C4—94no—
667C22×C4—92no—
668C22×C4—92no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—92no—
672C22×C4—92no—
673C22×C4—91no—
674C22×C4—184no—
675C22×C4—184no—
676C22×C4—188no—
677C4⋊C4—32no—
678C4⋊C4—34no—
679C4⋊C4—34no—
680C4⋊C4—32no—
681C4⋊C4—34no—
682C4⋊C4—32no—
683C4⋊C4—34no—
684C4⋊C4—34no—
685C4⋊C4—92no—
686C4⋊C4—94no—
687C4⋊C4—92no—
688C4⋊C4—94no—
689C4⋊C4—94no—
690C4⋊C4—92no—
691C4⋊C4—94no—
692C4⋊C4—94no—
693C4⋊C4—92no—
694C4⋊C4—91no—
695C4⋊C4—92no—
696C4⋊C4—92no—
697C4⋊C4—92no—
698C4⋊C4C2×D3211yescharacteristic
699C4⋊C4C2×D3212yes—
700C22⋊C4—32no—
701C22⋊C4—34no—
702C22⋊C4—34no—
703C22⋊C4—32no—
704C22⋊C4—34no—
705C22⋊C4—92no—
706C22⋊C4—94no—
707C22⋊C4—94no—
708C22⋊C4—92no—
709C22⋊C4—94no—
710C42—34no—
711C42—94no—
712C42—92no—
713C42—92no—
714C42—92no—
715C42—91no—
716C42—91no—
717C42—91no—
718C42C2×D3212yes—
719C42C2×D3211yescharacteristic
720C22×C3—21no—
721C22×C3—34no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3C24×D312yes—
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—34no—
734C2×D3—34no—
735C2×D3—34no—
736C2×D3—62no—
737C2×D3—62no—
738C2×D3—62no—
739C2×D3—616no—
740C2×D3—128no—
741C2×D3D3×#4114yes—
742C3×C4—24no—
743C3×C4—22no—
744C3×C4—24no—
745C3×C4—24no—
746C3×C4—22no—
747C3×C4—22no—
748C3×C4—22no—
749C3×C4—42no—
750C3×C4—41no—
751C3×C4—62no—
752C3×C4—62no—
753C3×C4—64no—
754C3×C4—64no—
755C3×C4D3×#4114yes—
756Dic3—22no—
757Dic3—22no—
758Dic3—24no—
759Dic3—24no—
760Dic3—34no—
761Dic3—62no—
762Dic3—64no—
763Dic3—62no—
764Dic3—64no—
765Dic3—64no—
766Dic3—62no—
767Dic3—62no—
768Dic3—122no—
769Dic3—121no—
770C32C2×#55211yescharacteristic, complemented, Sylow
771C23—32no—
772C23—32no—
773C23—94no—
774C23—91no—
775C23—182no—
776C23—182no—
777C23—182no—
778C23—182no—
779C23—182no—
780Q8—22no—
781Q8—184no—
782Q8—182no—
783D4—64no—
784D4—184no—
785C2×C4—32no—
786C2×C4—34no—
787C2×C4—32no—
788C2×C4—34no—
789C2×C4—68no—
790C2×C4—64no—
791C2×C4—64no—
792C2×C4—91no—
793C2×C4—94no—
794C2×C4—91no—
795C2×C4—92no—
796C2×C4—92no—
797C2×C4—91no—
798C2×C4—184no—
799C2×C4—182no—
800C2×C4—184no—
801C2×C4—182no—
802C2×C4—182no—
803C2×C4—182no—
804C2×C4—184no—
805C2×C4—184no—
806C2×C4—184no—
807C2×C4—184no—
808C2×C4—188no—
809C2×C4C22×D3212yes—
810C2×C4C22×D3211yescharacteristic
811C2×C4C22×D3212yes—
812C2×C4C22×D3211yescharacteristic
813C2×C4C22×D3211yescharacteristic
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—64no—
818C2×C3—122no—
819C2×C3C2×D3×#4112yes—
820C2×C3C2×D3×#4112yes—
821C2×C3D3×2−1+412yes—
822D3—24no—
823D3—38no—
824D3—42no—
825D3—64no—
826C22—34no—
827C22—62no—
828C22—62no—
829C22—62no—
830C22—62no—
831C22—62no—
832C22—92no—
833C22—92no—
834C22—92no—
835C22—188no—
836C22—364no—
837C22C23×D3211yescharacteristic
838C4—22no—
839C4—21no—
840C4—22no—
841C4—21no—
842C4—62no—
843C4—62no—
844C4—64no—
845C4—64no—
846C4—92no—
847C4—182no—
848C4—181no—
849C4—182no—
850C4—181no—
851C4#6430612yes—
852C3—21no—
853C3D3×#55212yescomplemented
854C2—64no—
855C2—94no—
856C2—122no—
857C2C2×#6430611yescharacteristic
858C2#1059668711yescharacteristic
859C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3802C22
hypercenterC4×Q8D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5581C2semidirect
3. #10595429C2semidirect
4. #10595429C2semidirect
5. #10595380C2semidirect
7. #10594602C2semidirect
8. D32×C4⋊C4C2semidirect
9. #10594550C2semidirect
10. #10594430C2semidirect
11. #10594399C2semidirect
12. #10594020C2semidirect
14. #10593992C2semidirect
15. #10593948C2semidirect
16. #10593920C2semidirect
17. #10593919C2semidirect
24. C32×C4×Q8C22semidirect
25. Q8×C3⋊Dic3C22semidirect
28. #64096C22semidirect
29. #64096C22semidirect
32. C4×#634C22semidirect
33. C4×#634C22semidirect
34. C3×#946C22semidirect
35. C3×#946C22semidirect
37. C3×#892C22semidirect
38. C3×D3×C4⋊C4C22semidirect
39. C3×#889C22semidirect
40. C3×#876C22semidirect
42. C3×#872C22semidirect
43. C3×#870C22semidirect
56. #63896C22semidirect
57. #63896C22semidirect
59. D3×C4⋊Dic3C22semidirect
67. #63878C22semidirect
68. #63878C22semidirect
69. #63877C22semidirect
70. D3×Dic3⋊C4C22semidirect
71. #63872C22semidirect
72. #63870C22semidirect
73. #63870C22semidirect
74. #63867C22semidirect
75. #63862C22semidirect
76. #63862C22semidirect
77. #63862C22semidirect
78. #63857C22semidirect
79. #63857C22semidirect
80. #63855C22semidirect
81. #63846C22semidirect
82. #63845C22semidirect
83. #63841C22semidirect
97. #5581D3semidirect
192. C3×C4×Q8C2×D3semidirect
197. #946C2×D3semidirect
198. #946C2×D3semidirect
225. #892C2×D3semidirect
240. D3×C4⋊C4C2×D3semidirect
250. #889C2×D3semidirect
273. #876C2×D3semidirect
277. #872C2×D3semidirect
284. #870C2×D3semidirect
535. C4×Q8D32semidirect
647. C3⋊D3#552semidirect
770. C32C2×#552semidirect
853. C3D3×#552semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55812
#105954292
#105953802
#105946082
#105946022
D32×C4⋊C42
#105945502
#105944302
#105943992
#105940202
C4×#38022
#105939922
#105939482
#105939202
#105939192
D3×#5523