Finite Group Databasebeta

← #11903014

Subgroups — #11903014

Order 1152.

2457 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5513C212yesmaximal, complemented
3#10595079C212yesmaximal
4C4×#3811C211yesmaximal, characteristic
5#10594969C212yesmaximal, complemented
6#10594960C214yesmaximal, complemented
7#10594925C211yesmaximal, characteristic, complemented
8#10594853C212yesmaximal, complemented
9#10594656C212yesmaximal, complemented
10#10594631C211yesmaximal, characteristic, complemented
11#10594602C211yesmaximal, characteristic, complemented
12#10594579C212yesmaximal, complemented
13#10594482C211yesmaximal, characteristic, complemented
14#10594471C214yesmaximal, complemented
15#10594399C212yesmaximal, complemented
16#10594363C211yesmaximal, characteristic, complemented
17#10594337C212yesmaximal, complemented
18D3×#552—32nomaximal
19C22×C4×C3⋊D3C2212yes—
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×#3811C2211yescharacteristic
22C2×C4×D32C2211yescharacteristic
23C2×#3797C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C2×#3750C2212yescomplemented
27C4⋊C4×C3⋊D3C2211yescharacteristic
28C4⋊C4×C3⋊D3C2211yescharacteristic
29C4⋊C4×C3⋊D3C2212yes—
30C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
31C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
32C4⋊C4×C3⋊D3C2212yescomplemented
33C3×#929C2214yes—
34C3×C4×#67C2212yes—
35C3×#926C2214yescomplemented
36C3×#924C2212yescomplemented
37C3×#898C2214yescomplemented
38C3×#897C2212yescomplemented
39C3×#892C2212yescomplemented
40C3×#890C2212yescomplemented
41C3×#889C2214yescomplemented
42C3×#887C2212yescomplemented
43#63982C2212yescomplemented
44#63974C2212yes—
45#63974C2211yescharacteristic
46#67⋊Dic3C2212yes—
47#63962C2214yes—
48#63957C2214yescomplemented
49#63921C2212yes—
50#63921C2212yes—
51#63921C2211yescharacteristic
52C4×#626C2212yes—
53#63900C2211yescharacteristic
54#63900C2212yes—
55#63900C2212yes—
56#63899C2214yescomplemented
57#63883C2212yes—
58#63883C2212yes—
59#63883C2211yescharacteristic
60#63883C2212yes—
61C4×#624C2212yes—
62C4×#624C2212yes—
63C4×#624C2211yescharacteristic
64#63881C2212yes—
65#63877C2214yescomplemented
66#63874C2214yescomplemented
67#63871C2212yescomplemented
68#63869C2212yescomplemented
69#63867C2214yescomplemented
70#63865C2212yescomplemented
71#63861C2214yescomplemented
72#63859C2214yescomplemented
73#63858C2214yescomplemented
74#63856C2212yescomplemented
75#63853C2214yes—
76#63853C2214yes—
77#63849C2214yescomplemented
78#63847C2214yescomplemented
79#63846C2214yescomplemented
80#63845C2214yescomplemented
81Dic3×Dic6C2212yescomplemented
82#63841C2212yescomplemented
83#63837C2214yescomplemented
84C3×#552—32no—
85#5708—34no—
86D3×#126—34no—
87#5694—32no—
88#5693—34no—
89D3×#125—32no—
90D3×#125—34no—
91D3×#123—34no—
92#5650—34no—
93#5642—32no—
94#5639—32no—
95D3×C22⋊Q8—32no—
96D3×C22⋊Q8—32no—
97#5581—32no—
98C4×D3×Q8—32no—
99C4×D3×D4—32no—
100#5541—32no—
101#5531—34no—
102#5529—32no—
103D3×#117—34no—
104D3×#117—32no—
105#5513D312yescomplemented
106C2×D3×C4⋊C4—32no—
107C2×D3×C4⋊C4—61no—
108C23×C3⋊D3C2311yescharacteristic
109C22×D32C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2312yes—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2312yes—
114C2×C4×C3⋊D3—28no—
115C2×C4×C3⋊D3—24no—
116C2×C4×C3⋊D3C2312yes—
117C2×C4×C3⋊D3C2311yescharacteristic
118C2×C4×C3⋊D3C2312yes—
119C2×C4×C3⋊D3C2312yes—
120C2×C4×C3⋊D3C2312yes—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C3×#67C2312yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×Dic6C2312yes—
127#3811—24no—
128C2×#627C2312yes—
129C2×#626C2312yes—
130C2×#624C2312yes—
131C2×#624C2311yescharacteristic
132C2×#624C2311yescharacteristic
133C2×#624C2311yescharacteristic
134C2×#624C2312yes—
135C2×D3×Dic3C2312yes—
136C4×D32—24no—
137#3797—24no—
138C32×C4⋊C4C2311yescharacteristic
139C32×C4⋊C4C2312yes—
140C32×C4⋊C4C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144#3750C2312yes—
145#3750C2312yes—
146#3750C2312yes—
147#3750C2312yes—
148C3×#217C2314yes—
149C3×#217C2312yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2312yes—
153C3×C4⋊Dic3C2314yes—
154C3×C4⋊Dic3C2312yes—
155C3×C4⋊Dic3C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2312yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×C4×Dic3C2312yes—
161C3×C4×Dic3C2314yes—
162C3×C4×Dic3C2314yes—
163#3724C2314yes—
164#3724C2312yes—
165#3724C2314yes—
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2312yes—
169Dic3⋊Dic3C2314yes—
170#3722C2312yes—
171#3722C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2312yes—
175Dic32C2312yes—
176Dic32C2314yes—
177Dic32C2314yes—
178C2×#552—91noSylow
179C2×D3×Q8—32no—
180C2×D3×D4—32no—
181C22×C4×D3—34no—
182C22×C4×D3—32no—
183C22×C4×D3—32no—
184C22×C4×D3—61no—
185C22×C4×D3—62no—
186C3×#126—34no—
187C3×#125—34no—
188C3×#125—32no—
189C3×#123—34no—
190C3×C22⋊Q8—32no—
191C3×C22⋊Q8—32no—
192C3×C4×Q8—32no—
193C3×C4×D4—32no—
194C3×#117—34no—
195C3×#117—32no—
196C2×C3×C4⋊C4—21no—
197C2×C3×C4⋊C4C2×D312yescomplemented
198#946—32no—
199#946—32no—
200Q8×Dic3—32no—
201#935—34no—
202D4×Dic3—32no—
203#929C2×D314yes—
204C4×#67—32no—
205C4×#67C2×D312yes—
206#926—32no—
207#926C2×D314yescomplemented
208C2×C4⋊Dic3—32no—
209C2×C4⋊Dic3—61no—
210#924—32no—
211#924C2×D312yescomplemented
212C2×Dic3⋊C4—34no—
213C2×Dic3⋊C4—62no—
214#898—34no—
215#898—34no—
216#898C2×D314yescomplemented
217#897—32no—
218#897C2×D312yescomplemented
219#896—34no—
220#896—34no—
221#894—34no—
222#894—34no—
223#893—32no—
224#892—32no—
225#892—34no—
226#892—34no—
227#892C2×D312yescomplemented
228D3×C4⋊C4—32no—
229D3×C4⋊C4—34no—
230D3×C4⋊C4—32no—
231D3×C4⋊C4—34no—
232D3×C4⋊C4—32no—
233D3×C4⋊C4—32no—
234D3×C4⋊C4—34no—
235D3×C4⋊C4—34no—
236D3×C4⋊C4—32no—
237D3×C4⋊C4—34no—
238D3×C4⋊C4—34no—
239D3×C4⋊C4—32no—
240D3×C4⋊C4—34no—
241D3×C4⋊C4—61no—
242D3×C4⋊C4—61no—
243D3×C4⋊C4—62no—
244D3×C4⋊C4—61no—
245D3×C4⋊C4—61no—
246D3×C4⋊C4—62no—
247#890—34no—
248#890—34no—
249#890—32no—
250#890C2×D312yescomplemented
251#889—34no—
252#889—34no—
253#889—34no—
254#889—34no—
255#889—34no—
256#889C2×D314yescomplemented
257#887—34no—
258#887C2×D312yescomplemented
259#886—34no—
260#883—34no—
261#883—34no—
262#67⋊C4—32no—
263#67⋊C4—32no—
264D3×C22⋊C4—34no—
265D3×C22⋊C4—32no—
266D3×C22⋊C4—34no—
267D3×C22⋊C4—34no—
268D3×C22⋊C4—32no—
269#879—34no—
270#879—34no—
271#879—34no—
272#878—34no—
273#878—34no—
274#877—34no—
275#877—34no—
276#877—34no—
277#876—34no—
278C4×D12—32no—
279#872—34no—
280#872—34no—
281#872—34no—
282C42×D3—34no—
283C42×D3—32no—
284C42×D3—34no—
285#870—32no—
286#870—34no—
287C4×Dic6—32no—
288C4×Dic6—34no—
289C23×C32C2411yescharacteristic
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3#4114yes—
293C22×C3⋊D3C2411yescharacteristic
294C22×C3⋊D3C2411yescharacteristic
295C22×C3×D3C2412yes—
296C2×D32—22no—
297C2×D32—22no—
298C2×D32—22no—
299C2×C32×C4—22no—
300C2×C32×C4—24no—
301C2×C32×C4C2412yes—
302C2×C32×C4C2411yescharacteristic
303C2×C32×C4C2412yes—
304C2×C32×C4C2411yescharacteristic
305C2×C3⋊Dic3—22no—
306C2×C3⋊Dic3—24no—
307C2×C3⋊Dic3C2412yes—
308C2×C3⋊Dic3C2411yescharacteristic
309C2×C3⋊Dic3C2412yes—
310C2×C3⋊Dic3C2411yescharacteristic
311C4×C3⋊D3—22no—
312C4×C3⋊D3—22no—
313C4×C3⋊D3—22no—
314C4×C3⋊D3—24no—
315C4×C3⋊D3—24no—
316C4×C3⋊D3—24no—
317C4×C3⋊D3—24no—
318C4×C3⋊D3#4114yes—
319C3×#67—24no—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2414yes—
323C2×C3×Dic3C2414yes—
324C2×C3×Dic3C2412yes—
325C3×C4×D3—24no—
326C3×Dic6—24no—
327#627—24no—
328#626—24no—
329#624—24no—
330#624—22no—
331#624—22no—
332#624—22no—
333#624—24no—
334D3×Dic3—24no—
335#552—32no—
336#552—92no—
337#552—94no—
338#552—92no—
339#552—92no—
340#552—94no—
341C2×#126—92no—
342C2×#125—92no—
343C2×#125—91no—
344C2×#123—92no—
345C2×C22⋊Q8—91no—
346C2×C22⋊Q8—91no—
347C2×C4×Q8—91no—
348C2×C4×D4—91no—
349C2×#117—91no—
350C2×#117—92no—
351C22×C4⋊C4—91no—
352C23×D3—32no—
353C23×D3—32no—
354C23×D3—61no—
355C2×C3×Q8—32no—
356C2×C3×D4—32no—
357C22×C3×C4—21no—
358C22×C3×C4—22no—
359C22×C3×C4—32no—
360C22×C3×C4C22×D314yes—
361C22×C3×C4C22×D312yes—
362C2×#67—32no—
363C2×#67C22×D312yes—
364C22×Dic3—34no—
365C22×Dic3—32no—
366C22×Dic3—32no—
367C22×Dic3—61no—
368C22×Dic3—62no—
369D3×Q8—68no—
370D3×D4—68no—
371C2×D12—32no—
372C2×C4×D3—32no—
373C2×C4×D3—32no—
374C2×C4×D3—34no—
375C2×C4×D3—34no—
376C2×C4×D3—32no—
377C2×C4×D3—34no—
378C2×C4×D3—32no—
379C2×C4×D3—32no—
380C2×C4×D3—34no—
381C2×C4×D3—32no—
382C2×C4×D3—32no—
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—32no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—68no—
395C2×C4×D3—68no—
396C2×C4×D3—616no—
397C2×C4×D3—68no—
398C2×C4×D3—128no—
399C2×C4×D3C22×D312yes—
400C2×Dic6—34no—
401C2×Dic6C22×D312yes—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—21no—
404C3×C4⋊C4—22no—
405C3×C4⋊C4—34no—
406C3×C4⋊C4—32no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—32no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4C22×D312yes—
413C3×C4⋊C4C22×D314yes—
414C3×C4⋊C4C22×D312yes—
415C3×C22⋊C4—32no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—32no—
420C3×C42—32no—
421C3×C42—34no—
422C3×C42—34no—
423#217—34no—
424#217—34no—
425#217—32no—
426#217C22×D312yes—
427#217C22×D314yes—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—32no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—32no—
432(C2×D3)⋊C4—32no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4C22×D314yes—
436(C2×D3)⋊C4C22×D312yes—
437(C2×D3)⋊C4C22×D314yes—
438C4⋊Dic3—32no—
439C4⋊Dic3—32no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444C4⋊Dic3—32no—
445C4⋊Dic3—61no—
446C4⋊Dic3—61no—
447C4⋊Dic3—62no—
448C4⋊Dic3C22×D312yes—
449C4⋊Dic3C22×D314yes—
450C4⋊Dic3C22×D314yes—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—32no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—62no—
465Dic3⋊C4—62no—
466Dic3⋊C4—62no—
467Dic3⋊C4—62no—
468Dic3⋊C4C22×D314yes—
469Dic3⋊C4C22×D314yes—
470Dic3⋊C4C22×D312yes—
471Dic3⋊C4C22×D314yes—
472C4×Dic3—34no—
473C4×Dic3—32no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C4×Dic3—32no—
478C4×Dic3C22×D314yes—
479C4×Dic3C22×D314yes—
480C4×Dic3C22×D312yes—
481C22×C32—21no—
482C22×C32—21no—
483C22×C32C2×#4112yes—
484C22×C32C2511yescharacteristic
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—28no—
488C2×C3⋊D3C2×#4112yes—
489C2×C3⋊D3C2×#4112yes—
490C2×C3⋊D3C2×#4112yes—
491C2×C3⋊D32−1+412yes—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495D32—44no—
496C32×C4—21no—
497C32×C4—22no—
498C32×C4—22no—
499C32×C4C2×#4112yes—
500C3⋊Dic3—21no—
501C3⋊Dic3—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3C2×#4112yes—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—24no—
507C3×Dic3—22no—
508C3×Dic3—24no—
509C22×Q8—91no—
510C22×D4—91no—
511C23×C4—91no—
512C23×C4—92no—
513C23×C4—91no—
514#126—34no—
515#126—94no—
516#126—94no—
517#126—94no—
518#125—34no—
519#125—32no—
520#125—94no—
521#125—92no—
522#125—94no—
523#125—94no—
524#125—94no—
525#123—34no—
526#123—94no—
527#123—94no—
528#123—94no—
529C22⋊Q8—32no—
530C22⋊Q8—32no—
531C22⋊Q8—92no—
532C22⋊Q8—94no—
533C22⋊Q8—92no—
534C22⋊Q8—92no—
535C22⋊Q8—92no—
536C4×Q8—32no—
537C4×Q8—94no—
538C4×Q8—92no—
539C4×D4—32no—
540C4×D4—92no—
541C4×D4—92no—
542C4×D4—92no—
543#117—34no—
544#117—32no—
545#117—94no—
546#117—94no—
547#117—94no—
548#117—94no—
549#117—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—92no—
557C2×C4⋊C4—92no—
558C2×C4⋊C4—91no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—92no—
562C2×C4⋊C4—92no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4D3211yescharacteristic, complemented
566C2×C22⋊C4—91no—
567C2×C22⋊C4—92no—
568C2×C22⋊C4—92no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—92no—
571C2×C42—92no—
572C2×C42—92no—
573C2×C42—91no—
574C23×C3—21no—
575C23×C3—32no—
576C23×C3C23×D312yes—
577C22×D3—32no—
578C22×D3—38no—
579C22×D3—32no—
580C22×D3—64no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—64no—
584C22×D3—64no—
585C22×D3—64no—
586C22×D3—64no—
587C22×D3—64no—
588C22×D3—64no—
589C22×D3—64no—
590C22×D3C23×D312yes—
591C3×Q8—64no—
592C3×D4—64no—
593C2×C3×C4—24no—
594C2×C3×C4—28no—
595C2×C3×C4—24no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—32no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—34no—
604C2×C3×C4—34no—
605C2×C3×C4—44no—
606C2×C3×C4—64no—
607C2×C3×C4C23×D314yes—
608C2×C3×C4C23×D314yes—
609C2×C3×C4C23×D312yes—
610C2×C3×C4C23×D312yes—
611#67—24no—
612#67—64no—
613C2×Dic3—32no—
614C2×Dic3—34no—
615C2×Dic3—32no—
616C2×Dic3—34no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—64no—
622C2×Dic3—64no—
623C2×Dic3—64no—
624C2×Dic3—68no—
625C2×Dic3—124no—
626C2×Dic3C23×D312yes—
627C2×Dic3C23×D312yes—
628C2×Dic3C23×D314yes—
629C2×Dic3C23×D314yes—
630C2×Dic3C23×D312yes—
631D12—64no—
632C4×D3—24no—
633C4×D3—38no—
634C4×D3—64no—
635C4×D3—64no—
636C4×D3—68no—
637C4×D3—64no—
638C4×D3—64no—
639C4×D3—68no—
640C4×D3—64no—
641C4×D3—64no—
642C4×D3—64no—
643C4×D3—68no—
644C4×D3—68no—
645C4×D3—68no—
646C4×D3—68no—
647C4×D3—64no—
648C4×D3—64no—
649C4×D3—64no—
650C4×D3—64no—
651C4×D3—124no—
652C4×D3—124no—
653C4×D3—124no—
654C4×D3—124no—
655Dic6—24no—
656Dic6—68no—
657C2×C32—22no—
658C2×C32C22×#4111yescharacteristic
659C2×C32C22×#4111yescharacteristic
660C2×C32C2×2−1+411yescharacteristic
661C3⋊D3—22no—
662C3⋊D3#55214yescomplemented
663C3×D3—42no—
664C24—91no—
665C24—91no—
666C2×Q8—32no—
667C2×Q8—92no—
668C2×Q8—184no—
669C2×D4—32no—
670C2×D4—92no—
671C2×D4—184no—
672C22×C4—32no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—92no—
676C22×C4—92no—
677C22×C4—91no—
678C22×C4—92no—
679C22×C4—91no—
680C22×C4—92no—
681C22×C4—91no—
682C22×C4—92no—
683C22×C4—91no—
684C22×C4—92no—
685C22×C4—92no—
686C22×C4—92no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—184no—
690C22×C4—188no—
691C22×C4—184no—
692C22×C4C2×D3212yes—
693C22×C4C2×D3211yescharacteristic
694C4⋊C4—34no—
695C4⋊C4—32no—
696C4⋊C4—34no—
697C4⋊C4—32no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—94no—
702C4⋊C4—92no—
703C4⋊C4—94no—
704C4⋊C4—92no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—92no—
709C4⋊C4—91no—
710C4⋊C4—92no—
711C4⋊C4—91no—
712C4⋊C4—92no—
713C4⋊C4—92no—
714C4⋊C4—92no—
715C4⋊C4C2×D3211yescharacteristic
716C4⋊C4C2×D3211yescharacteristic
717C4⋊C4C2×D3212yes—
718C22⋊C4—32no—
719C22⋊C4—34no—
720C22⋊C4—34no—
721C22⋊C4—32no—
722C22⋊C4—34no—
723C22⋊C4—92no—
724C22⋊C4—94no—
725C22⋊C4—94no—
726C22⋊C4—92no—
727C22⋊C4—94no—
728C42—34no—
729C42—34no—
730C42—32no—
731C42—94no—
732C42—94no—
733C42—92no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—21no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3D3×#4114yes—
744C22×C3C24×D312yes—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—34no—
749C2×D3—34no—
750C2×D3—34no—
751C2×D3—34no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—616no—
757C2×D3—62no—
758C2×D3—616no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—128no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—24no—
766C3×C4—24no—
767C3×C4—22no—
768C3×C4—42no—
769C3×C4—42no—
770C3×C4—64no—
771C3×C4—62no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—64no—
775C3×C4D3×#4114yes—
776Dic3—24no—
777Dic3—22no—
778Dic3—22no—
779Dic3—22no—
780Dic3—24no—
781Dic3—34no—
782Dic3—62no—
783Dic3—62no—
784Dic3—62no—
785Dic3—64no—
786Dic3—64no—
787Dic3—122no—
788Dic3—122no—
789C32C2×#55211yescharacteristic, complemented, Sylow
790C23—32no—
791C23—91no—
792C23—94no—
793C23—91no—
794C23—182no—
795C23—182no—
796C23—182no—
797C23—182no—
798C23—182no—
799C23C22×D3211yescharacteristic
800Q8—64no—
801Q8—184no—
802D4—64no—
803D4—184no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—34no—
809C2×C4—34no—
810C2×C4—32no—
811C2×C4—64no—
812C2×C4—91no—
813C2×C4—94no—
814C2×C4—92no—
815C2×C4—91no—
816C2×C4—92no—
817C2×C4—182no—
818C2×C4—182no—
819C2×C4—184no—
820C2×C4—184no—
821C2×C4—184no—
822C2×C4—184no—
823C2×C4—182no—
824C2×C4—182no—
825C2×C4—184no—
826C2×C4—182no—
827C2×C4—184no—
828C2×C4—184no—
829C2×C4—182no—
830C2×C4—184no—
831C2×C4—182no—
832C2×C4C22×D3212yes—
833C2×C4C22×D3211yescharacteristic
834C2×C4C22×D3212yes—
835C2×C4C22×D3211yescharacteristic
836C2×C3—24no—
837C2×C3—24no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—122no—
842C2×C3C2×D3×#4112yes—
843C2×C3C2×D3×#4112yes—
844C2×C3D3×2−1+412yes—
845D3—38no—
846D3—42no—
847D3—64no—
848D3—64no—
849D3—64no—
850C22—21no—
851C22—21no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—92no—
856C22—92no—
857C22—92no—
858C22—92no—
859C22—188no—
860C22—181no—
861C22—181no—
862C22—364no—
863C22#6431212yes—
864C22C23×D3211yescharacteristic
865C4—21no—
866C4—22no—
867C4—22no—
868C4—62no—
869C4—64no—
870C4—62no—
871C4—62no—
872C4—64no—
873C4—92no—
874C4—181no—
875C4—182no—
876C4—182no—
877C4#6430612yes—
878C3—21no—
879C3D3×#55212yescomplemented
880C2—22no—
881C2—94no—
882C2—122no—
883C2—182no—
884C2C2×#6430611yescharacteristic
885C2C2×#6431211yescharacteristic
886C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
prime radicalC2×#3811C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
2. C3×#5513C2semidirect
5. #10594969C2semidirect
6. #10594960C2semidirect
7. #10594925C2semidirect
8. #10594853C2semidirect
9. #10594656C2semidirect
10. #10594631C2semidirect
11. #10594602C2semidirect
12. #10594579C2semidirect
13. #10594482C2semidirect
14. #10594471C2semidirect
15. #10594399C2semidirect
16. #10594363C2semidirect
17. #10594337C2semidirect
24. C2×C32×C4⋊C4C22semidirect
25. C2×C4⋊(C3⋊Dic3)C22semidirect
26. C2×#3750C22semidirect
30. C4⋊C4×C3⋊D3C22semidirect
31. C4⋊C4×C3⋊D3C22semidirect
32. C4⋊C4×C3⋊D3C22semidirect
35. C3×#926C22semidirect
36. C3×#924C22semidirect
37. C3×#898C22semidirect
38. C3×#897C22semidirect
39. C3×#892C22semidirect
40. C3×#890C22semidirect
41. C3×#889C22semidirect
42. C3×#887C22semidirect
43. #63982C22semidirect
48. #63957C22semidirect
56. #63899C22semidirect
65. #63877C22semidirect
66. #63874C22semidirect
67. #63871C22semidirect
68. #63869C22semidirect
69. #63867C22semidirect
70. #63865C22semidirect
71. #63861C22semidirect
72. #63859C22semidirect
73. #63858C22semidirect
74. #63856C22semidirect
77. #63849C22semidirect
78. #63847C22semidirect
79. #63846C22semidirect
80. #63845C22semidirect
81. Dic3×Dic6C22semidirect
82. #63841C22semidirect
83. #63837C22semidirect
105. #5513D3semidirect
197. C2×C3×C4⋊C4C2×D3semidirect
207. #926C2×D3semidirect
211. #924C2×D3semidirect
216. #898C2×D3semidirect
218. #897C2×D3semidirect
227. #892C2×D3semidirect
250. #890C2×D3semidirect
256. #889C2×D3semidirect
258. #887C2×D3semidirect
565. C2×C4⋊C4D32semidirect
662. C3⋊D3#552semidirect
789. C32C2×#552semidirect
879. C3D3×#552semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C3×#55132
#105950792
C4×#38112
#105949692
#105949602
#105949252
#105948532
#105946562
#105946312
#105946022
#105945792
#105944822
#105944712
#105943992
#105943632
#105943372
D3×#5523