Finite Group Databasebeta

← #11857548

Subgroups — #11857548

Order 1152.

1705 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic
2#10594182C212yesmaximal, complemented
3C3⋊D3×#99C211yesmaximal, characteristic, complemented
4C3×D3×#99C211yesmaximal, characteristic, complemented
5C3×#4740C211yesmaximal, characteristic, complemented
6#10591528C211yesmaximal, characteristic, complemented
7#10591527C211yesmaximal, characteristic, complemented
8D3×#834C211yesmaximal, characteristic, complemented
9#10590405C212yesmaximal, complemented
10#10590404C212yesmaximal, complemented
11D3×#806C212yesmaximal, complemented
12#78694—31nomaximal
13#78688—31nomaximal
14C2×D4×C3⋊D3C2211yescharacteristic
15C2×C3×#237C2211yescharacteristic
16C2×C3×D3×D4C2211yescharacteristic
17C2×#3811C411yescharacteristic, complemented
18C2×#3811C2211yescharacteristic
19C2×D3×#67C411yescharacteristic, complemented
20C2×D3×#67C2211yescharacteristic
21C22×#626C411yescharacteristic, complemented
22C22×#626C2211yescharacteristic
23C2×#3804C411yescharacteristic, complemented
24C2×#3804C2211yescharacteristic
25#64314—22no—
26#64314—22no—
27#64314—22no—
28#64314—22no—
29C2×D3×D12C411yescharacteristic, complemented
30C2×#3799C411yescharacteristic, complemented
31C2×#3798C411yescharacteristic, complemented
32C2×#3796C411yescharacteristic, complemented
33C22⋊C4×C3⋊D3C2212yescomplemented
34C3×D3×C22⋊C4C2212yescomplemented
35C3×#877C2212yescomplemented
36#63974C2212yescomplemented
37D3×#217C2212yescomplemented
38#63955C2212yescomplemented
39#63904—22no—
40C4×#626—22no—
41#63881—22no—
42#63880—22no—
43C32×#99C2211yescharacteristic, complemented
44#63661C2211yescharacteristic, complemented
45#63633C2212yescomplemented
46C3×#834C2211yescharacteristic, complemented
47C3×#834C2211yescharacteristic, complemented
48C3×#806C2212yescomplemented
49C3×#806C2212yescomplemented
50#63581C2212yescomplemented
51#63580C2212yescomplemented
52#63580C2212yescomplemented
53C2×#1009—31no—
54C2×#1004—31no—
55#5521—32no—
56#5486—32no—
57C3×#410—31no—
58C2×C3×#99—31no—
59#5240—31no—
60C2×#834—31no—
61#5006—32no—
62C2×#806—32no—
63D3×#99—31no—
64D3×#99—32no—
65D3×#99—31no—
66D3×#99—31no—
67D3×#99—31no—
68D3×#99—31no—
69D3×#99—32no—
70D3×#99—32no—
71D3×#99—61no—
72D3×#99D311yescharacteristic, complemented
73#4740—31no—
74#4740—32no—
75#4740D311yescharacteristic, complemented
76C23×C3⋊D3C2×C411yescharacteristic, complemented
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2×C411yescharacteristic, complemented
79C23×C3×D3C2311yescharacteristic
80C22×D32C2×C411yescharacteristic, complemented
81C22×D32C2×C411yescharacteristic, complemented
82C2×C32×D4C2311yescharacteristic
83C2×#638C2×C411yescharacteristic, complemented
84C2×#638C2311yescharacteristic
85D4×C3⋊D3—22no—
86D4×C3⋊D3—22no—
87C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
88C2×C4×C3⋊D3—22no—
89C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
90C2×C3×#67C2×C411yescharacteristic, complemented
91C2×C3×#67C2×C411yescharacteristic, complemented
92C2×C3×#67C2311yescharacteristic
93C2×C3×#67C2311yescharacteristic
94C22×C3×Dic3C2×C411yescharacteristic, complemented
95C22×C3×Dic3C2311yescharacteristic
96C3×#237—22no—
97C3×#237—22no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2×C411yescharacteristic, complemented
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3C2×C411yescharacteristic, complemented
103C2×C3×C4×D3C2×C411yescharacteristic, complemented
104C2×C3×Dic6C2×C411yescharacteristic, complemented
105#3811—22no—
106#3811—22no—
107#3811—22no—
108#3811—22no—
109D3×#67—22no—
110D3×#67—22no—
111D3×#67—22no—
112D3×#67—22no—
113C2×#627C2×C411yescharacteristic, complemented
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626C2×C411yescharacteristic
119C2×#626C2×C411yescharacteristic
120C2×#626C2×C411yescharacteristic
121C2×#626C2×C411yescharacteristic
122C2×#626C2×C411yescharacteristic, complemented
123C2×#626C2×C411yescharacteristic, complemented
124C2×#626C2×C411yescharacteristic, complemented
125C2×#626C2×C411yescharacteristic, complemented
126C2×#626D412yes—
127C2×#626D412yes—
128C2×#626D412yes—
129C2×#626D412yes—
130C2×#625C2×C411yescharacteristic, complemented
131C2×#624—22no—
132C2×#624C2×C411yescharacteristic, complemented
133C2×#624C2×C411yescharacteristic, complemented
134#3804—22no—
135#3804—22no—
136#3804—22no—
137#3804—22no—
138C2×D3×Dic3—22no—
139C2×D3×Dic3C2×C411yescharacteristic, complemented
140C2×D3×Dic3C2×C411yescharacteristic, complemented
141D3×D12—22no—
142D3×D12—22no—
143#3799—22no—
144#3799—22no—
145#3798—21no—
146#3798—21no—
147#3798—21no—
148#3798—21no—
149#3796—22no—
150#3796—22no—
151C32×C22⋊C4C2312yes—
152#3757C2312yes—
153#3752—22no—
154C3×#217C2312yes—
155C3×#217C2312yes—
156C3×(C2×D3)⋊C4—22no—
157C3×Dic3⋊C4—22no—
158C3×C4×Dic3—22no—
159Dic3⋊Dic3—22no—
160#3722—22no—
161(C2×D3)⋊Dic3—22no—
162Dic32—22no—
163#2883—91noSylow
164C2×C3×#41—31no—
165C22×C3×D4—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—31no—
170#1009—62no—
171#1009—62no—
172#1009—62no—
173#1009—62no—
174C2×#239—31no—
175C2×#239—31no—
176#1004—62no—
177#1004—62no—
178#1004—62no—
179#1004—62no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237C2×D311yescharacteristic
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—31no—
189C2×D3×D4—31no—
190C2×D3×D4—31no—
191C2×D3×D4—31no—
192C2×D3×D4—31no—
193C2×D3×D4—61no—
194C2×D3×D4C2×D311yescharacteristic
195C2×#235—31no—
196C2×#235—31no—
197C2×#235—31no—
198C2×#235—31no—
199C2×#235—31no—
200C22×D12—31no—
201C22×D12—31no—
202C22×D12—31no—
203C3×#117—32no—
204C2×C3×C22⋊C4—32no—
205C2×#217—32no—
206C4×#67—62no—
207C4×#67—62no—
208#926—32no—
209#893—62no—
210#893—62no—
211#67⋊C4—62no—
212#67⋊C4—62no—
213D3×C22⋊C4—32no—
214D3×C22⋊C4—32no—
215D3×C22⋊C4—32no—
216D3×C22⋊C4—32no—
217D3×C22⋊C4—32no—
218D3×C22⋊C4—62no—
219D3×C22⋊C4C2×D312yescomplemented
220#877—32no—
221#877C2×D312yescomplemented
222C4×D12—62no—
223C4×D12—62no—
224C3×#99—21no—
225C3×#99—31no—
226C3×#99—31no—
227C3×#99—32no—
228C3×#99—32no—
229C3×#99C2×D311yescharacteristic, complemented
230C3×#99C2×D311yescharacteristic, complemented
231#834—31no—
232#834—31no—
233#834—32no—
234#834—32no—
235#834—61no—
236#834C2×D311yescharacteristic, complemented
237#834C2×D311yescharacteristic, complemented
238#806—32no—
239#806—32no—
240#806—32no—
241#806—32no—
242#806—32no—
243#806—32no—
244#806—62no—
245#806C2×D312yescomplemented
246#806C2×D312yescomplemented
247C23×C32C22×C411yescharacteristic
248C23×C32C2411yescharacteristic
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—81no—
252C22×C3⋊D3—81no—
253C22×C3⋊D3C22×C411yescharacteristic
254C22×C3⋊D3C22×C411yescharacteristic
255C22×C3⋊D3C22×C411yescharacteristic
256C22×C3⋊D3C2×D412yes—
257C22×C3⋊D3C2×D412yes—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—81no—
261C22×C3×D3—81no—
262C22×C3×D3C22×C411yescharacteristic
263C22×C3×D3C22×C411yescharacteristic
264C22×C3×D3C22×C411yescharacteristic
265C22×C3×D3C22×C411yescharacteristic
266C22×C3×D3C2×D412yes—
267C22×C3×D3C2×D412yes—
268C2×D32—22no—
269C2×D32—22no—
270C2×D32—81no—
271C2×D32—81no—
272C32×D4—22no—
273C2×C32×C4—22no—
274C2×C32×C4C22×C411yescharacteristic
275#638—22no—
276#638—22no—
277C2×C3⋊Dic3—22no—
278C2×C3⋊Dic3C22×C411yescharacteristic
279C4⋊(C3⋊D3)—22no—
280C4×C3⋊D3—21no—
281C4×C3⋊D3—21no—
282C4×C3⋊D3—82no—
283C3×#67—22no—
284C3×#67—22no—
285C3×#67—22no—
286C3×#67—22no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3C22×C411yescharacteristic
292C2×C3×Dic3C22×C411yescharacteristic
293C2×C3×Dic3C22×C411yescharacteristic
294C2×C3×Dic3C22×C411yescharacteristic
295C2×C3×Dic3C2×D412yes—
296C2×C3×Dic3C2×D412yes—
297C3×D12—22no—
298C3×C4×D3—21no—
299C3×C4×D3—21no—
300C3×C4×D3—21no—
301C3×C4×D3—21no—
302C3×C4×D3—82no—
303C3×Dic6—22no—
304#627—21no—
305#627—21no—
306#626—21no—
307#626—21no—
308#626—21no—
309#626—21no—
310#626—21no—
311#626—21no—
312#626—21no—
313#626—21no—
314#626C22⋊C412yes—
315#626C22⋊C412yes—
316#626C22⋊C411yescharacteristic
317#626C22⋊C411yescharacteristic
318#626C22⋊C411yescharacteristic
319#626C22⋊C411yescharacteristic
320#626C22⋊C412yes—
321#626C22⋊C412yes—
322#626C22⋊C412yes—
323#626C22⋊C412yes—
324#625—21no—
325#625—21no—
326#624—22no—
327#624—22no—
328#624—82no—
329D3×Dic3—22no—
330D3×Dic3—22no—
331D3×Dic3—82no—
332C2×H(5,𝔽2)—91no—
333#518—92no—
334#410—31no—
335#410—92no—
336#410—91no—
337C2×#99—31no—
338C2×#99—91no—
339C2×#99—92no—
340C2×#99—92no—
341C2×#99—91no—
342C2×#99—91no—
343C24×C3—31no—
344C24×C3—31no—
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—31no—
350C23×D3—31no—
351C23×D3—31no—
352C23×D3—31no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3C4×D311yescharacteristic, complemented
356C23×D3C22×D311yescharacteristic
357C3×#41—62no—
358C3×#41—62no—
359C2×C3×Q8—31no—
360C2×C3×D4—21no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—62no—
367C2×C3×D4—62no—
368C2×C3×D4C22×D311yescharacteristic
369C2×C3×D4C22×D311yescharacteristic
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—62no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—31no—
381C2×#67—31no—
382C2×#67—31no—
383C2×#67—31no—
384C2×#67—31no—
385C2×#67—31no—
386C2×#67—31no—
387C2×#67—31no—
388C2×#67—31no—
389C2×#67—32no—
390C2×#67—32no—
391C2×#67—32no—
392C2×#67—32no—
393C2×#67—61no—
394C2×#67—61no—
395C2×#67—61no—
396C2×#67—61no—
397C2×#67—61no—
398C2×#67—61no—
399C2×#67—62no—
400C2×#67—62no—
401C2×#67—62no—
402C2×#67—62no—
403C2×#67C4×D311yescharacteristic, complemented
404C2×#67C4×D311yescharacteristic, complemented
405C2×#67C22×D311yescharacteristic
406C2×#67C22×D311yescharacteristic
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—62no—
410C22×Dic3C4×D311yescharacteristic, complemented
411C22×Dic3C22×D311yescharacteristic
412#239—62no—
413#239—62no—
414#239—62no—
415#239—62no—
416#237—22no—
417#237—22no—
418#237—62no—
419#237—62no—
420#237—62no—
421#237—62no—
422#237—62no—
423#237—62no—
424D3×D4—22no—
425D3×D4—22no—
426D3×D4—62no—
427D3×D4—62no—
428D3×D4—62no—
429D3×D4—62no—
430D3×D4—62no—
431D3×D4—62no—
432D3×D4—62no—
433D3×D4—62no—
434D3×D4—62no—
435D3×D4—62no—
436D3×D4—62no—
437D3×D4—62no—
438D3×D4—62no—
439D3×D4—62no—
440D3×D4—62no—
441D3×D4—62no—
442D3×D4—62no—
443D3×D4—62no—
444D3×D4—122no—
445D3×D4—122no—
446#235—62no—
447#235—62no—
448#235—61no—
449#235—61no—
450#235—61no—
451#235—61no—
452#235—61no—
453#235—61no—
454#235—61no—
455#235—61no—
456#235—62no—
457#235—62no—
458#235—62no—
459#235—62no—
460C2×D12—31no—
461C2×D12—31no—
462C2×D12—31no—
463C2×D12—31no—
464C2×D12—32no—
465C2×D12—32no—
466C2×D12—32no—
467C2×D12—32no—
468C2×D12—31no—
469C2×D12—31no—
470C2×D12—31no—
471C2×D12—31no—
472C2×D12—31no—
473C2×D12—31no—
474C2×D12—61no—
475C2×D12—62no—
476C2×D12—62no—
477C2×D12—61no—
478C2×D12—61no—
479C2×D12—61no—
480C2×D12—61no—
481C2×D12C4×D311yescharacteristic, complemented
482C2×C4×D3—22no—
483C2×C4×D3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—31no—
486C2×C4×D3—31no—
487C2×C4×D3—31no—
488C2×C4×D3—31no—
489C2×C4×D3—31no—
490C2×C4×D3—31no—
491C2×C4×D3—61no—
492C2×C4×D3—62no—
493C2×C4×D3—62no—
494C2×C4×D3—62no—
495C2×C4×D3—62no—
496C2×C4×D3—62no—
497C2×C4×D3—122no—
498C2×C4×D3C4×D311yescharacteristic, complemented
499C2×C4×D3C4×D311yescharacteristic, complemented
500C2×Dic6—31no—
501C2×Dic6—31no—
502C2×Dic6C4×D311yescharacteristic, complemented
503C3×C4⋊C4—62no—
504C3×C22⋊C4—22no—
505C3×C22⋊C4—32no—
506C3×C22⋊C4—32no—
507C3×C22⋊C4—62no—
508C3×C22⋊C4C22×D312yes—
509C3×C22⋊C4C22×D312yes—
510C3×C42—62no—
511#217—32no—
512#217—32no—
513#217—62no—
514#217—62no—
515#217C22×D312yes—
516#217C22×D312yes—
517(C2×D3)⋊C4—22no—
518(C2×D3)⋊C4—62no—
519(C2×D3)⋊C4—62no—
520(C2×D3)⋊C4—62no—
521(C2×D3)⋊C4—62no—
522(C2×D3)⋊C4—62no—
523(C2×D3)⋊C4—122no—
524C4⋊Dic3—62no—
525Dic3⋊C4—22no—
526Dic3⋊C4—62no—
527C4×Dic3—22no—
528C4×Dic3—62no—
529C4×Dic3—62no—
530C22×C32—21no—
531C22×C32—41no—
532C22×C32—41no—
533C22×C32C23×C411yescharacteristic
534C22×C32C22×D412yes—
535C2×C3⋊D3—21no—
536C2×C3⋊D3—42no—
537C2×C3⋊D3—41no—
538C2×C3⋊D3—42no—
539C2×C3⋊D3—41no—
540C2×C3⋊D3—41no—
541C2×C3⋊D3—81no—
542C2×C3⋊D3—81no—
543C2×C3⋊D3C2×C22⋊C412yes—
544C2×C3⋊D3C2×C22⋊C411yescharacteristic
545C2×C3⋊D3C2×C22⋊C411yescharacteristic
546C2×C3×D3—21no—
547C2×C3×D3—21no—
548C2×C3×D3—42no—
549C2×C3×D3—42no—
550C2×C3×D3—41no—
551C2×C3×D3—41no—
552C2×C3×D3—41no—
553C2×C3×D3—41no—
554C2×C3×D3—81no—
555C2×C3×D3—81no—
556C2×C3×D3C2×C22⋊C412yes—
557C2×C3×D3C2×C22⋊C411yescharacteristic
558C2×C3×D3C2×C22⋊C411yescharacteristic
559D32—82no—
560D32—82no—
561C32×C4—21no—
562C32×C4—42no—
563C3⋊Dic3—21no—
564C3⋊Dic3—42no—
565C3×Dic3—21no—
566C3×Dic3—21no—
567C3×Dic3—42no—
568C3×Dic3—42no—
569C3×Dic3C2×C22⋊C412yes—
570C3×Dic3C2×C22⋊C411yescharacteristic
571C3×Dic3C2×C22⋊C411yescharacteristic
572H(5,𝔽2)—182no—
573H(5,𝔽2)—182no—
574H(5,𝔽2)—182no—
575H(5,𝔽2)—182no—
576C2×#41—31no—
577C2×#41—91no—
578C2×#41—91no—
579C2×#41—91no—
580C2×#41—91no—
581C2×#41—91no—
582C22×D4—31no—
583C22×D4—91no—
584C22×D4—91no—
585C22×D4—91no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C4×D4—182no—
592C4×D4—182no—
593C4×D4—182no—
594C4×D4—182no—
595#117—32no—
596#117—92no—
597C2×C22⋊C4—32no—
598C2×C22⋊C4—92no—
599C2×C22⋊C4—92no—
600C2×C22⋊C4—92no—
601#99—31no—
602#99—31no—
603#99—32no—
604#99—32no—
605#99—92no—
606#99—92no—
607#99—92no—
608#99—91no—
609#99—92no—
610#99D3211yescharacteristic, complemented
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—31no—
614C23×C3—31no—
615C23×C3—32no—
616C23×C3—32no—
617C23×C3—31no—
618C23×C3—31no—
619C23×C3—61no—
620C23×C3—61no—
621C23×C3—241no—
622C23×C3—241no—
623C23×C3C2×C4×D311yescharacteristic
624C23×C3C2×C4×D311yescharacteristic
625C23×C3C23×D311yescharacteristic
626C23×C3C23×D311yescharacteristic
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—31no—
630C22×D3—31no—
631C22×D3—31no—
632C22×D3—31no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—32no—
636C22×D3—32no—
637C22×D3—31no—
638C22×D3—31no—
639C22×D3—61no—
640C22×D3—62no—
641C22×D3—61no—
642C22×D3—62no—
643C22×D3—61no—
644C22×D3—62no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—61no—
648C22×D3—61no—
649C22×D3—61no—
650C22×D3—61no—
651C22×D3—62no—
652C22×D3—81no—
653C22×D3—81no—
654C22×D3—121no—
655C22×D3—121no—
656C22×D3—241no—
657C22×D3—241no—
658C22×D3—241no—
659C22×D3—241no—
660C22×D3—241no—
661C22×D3—241no—
662C22×D3—242no—
663C22×D3—241no—
664C22×D3—241no—
665C22×D3—242no—
666C22×D3C2×C4×D311yescharacteristic
667C22×D3C2×C4×D311yescharacteristic
668C22×D3C2×C4×D311yescharacteristic
669C22×D3C2×C4×D311yescharacteristic
670C22×D3D3×D412yes—
671C22×D3D3×D412yes—
672C3×Q8—62no—
673C3×D4—22no—
674C3×D4—22no—
675C3×D4—42no—
676C3×D4—62no—
677C3×D4—62no—
678C3×D4—62no—
679C3×D4—62no—
680C3×D4—62no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—21no—
684C2×C3×C4—31no—
685C2×C3×C4—31no—
686C2×C3×C4—32no—
687C2×C3×C4—32no—
688C2×C3×C4—31no—
689C2×C3×C4—31no—
690C2×C3×C4—42no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—62no—
698C2×C3×C4—62no—
699C2×C3×C4—242no—
700C2×C3×C4C2×C4×D311yescharacteristic
701C2×C3×C4C2×C4×D311yescharacteristic
702#67—22no—
703#67—22no—
704#67—22no—
705#67—22no—
706#67—32no—
707#67—32no—
708#67—31no—
709#67—31no—
710#67—31no—
711#67—31no—
712#67—32no—
713#67—32no—
714#67—32no—
715#67—32no—
716#67—61no—
717#67—61no—
718#67—61no—
719#67—61no—
720#67—61no—
721#67—61no—
722#67—61no—
723#67—61no—
724#67—62no—
725#67—62no—
726#67—62no—
727#67—62no—
728#67—61no—
729#67—61no—
730#67—61no—
731#67—61no—
732#67—122no—
733#67—122no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—22no—
737C2×Dic3—22no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—61no—
741C2×Dic3—62no—
742C2×Dic3—62no—
743C2×Dic3—62no—
744C2×Dic3—62no—
745C2×Dic3—122no—
746C2×Dic3—242no—
747C2×Dic3C2×C4×D311yescharacteristic
748C2×Dic3C2×C4×D311yescharacteristic
749C2×Dic3C2×C4×D311yescharacteristic
750C2×Dic3C2×C4×D311yescharacteristic
751C2×Dic3D3×D412yes—
752C2×Dic3D3×D412yes—
753D12—22no—
754D12—31no—
755D12—31no—
756D12—31no—
757D12—31no—
758D12—32no—
759D12—32no—
760D12—32no—
761D12—32no—
762D12—32no—
763D12—32no—
764D12—62no—
765D12—62no—
766D12—61no—
767D12—61no—
768D12—61no—
769D12—61no—
770D12—61no—
771D12—61no—
772D12—61no—
773D12—61no—
774D12—122no—
775C4×D3—21no—
776C4×D3—21no—
777C4×D3—21no—
778C4×D3—21no—
779C4×D3—62no—
780C4×D3—62no—
781C4×D3—62no—
782C4×D3—61no—
783C4×D3—61no—
784C4×D3—61no—
785C4×D3—61no—
786C4×D3—62no—
787C4×D3—62no—
788C4×D3—62no—
789C4×D3—82no—
790C4×D3—121no—
791C4×D3—121no—
792C4×D3—242no—
793C4×D3—242no—
794C4×D3—242no—
795C4×D3—242no—
796C4×D3—242no—
797C4×D3—244no—
798Dic6—22no—
799Dic6—61no—
800Dic6—61no—
801Dic6—61no—
802Dic6—61no—
803C2×C32—22no—
804C2×C32—21no—
805C2×C32—41no—
806C2×C32C22×C22⋊C411yescharacteristic
807C3⋊D3—21no—
808C3⋊D3—22no—
809C3⋊D3—21no—
810C3⋊D3—41no—
811C3×D3—22no—
812C3×D3—21no—
813C3×D3—21no—
814C3×D3—41no—
815C3×D3—41no—
816C24—31no—
817C24—31no—
818C24—91no—
819C24—91no—
820C24—91no—
821C24—91no—
822#41—62no—
823#41—62no—
824#41—182no—
825#41—182no—
826#41—181no—
827#41—181no—
828#41—181no—
829#41—181no—
830#41—182no—
831#41—182no—
832#41—182no—
833#41—182no—
834#41—182no—
835#41—182no—
836C2×Q8—31no—
837C2×Q8—91no—
838C2×D4—31no—
839C2×D4—31no—
840C2×D4—31no—
841C2×D4—31no—
842C2×D4—31no—
843C2×D4—62no—
844C2×D4—62no—
845C2×D4—92no—
846C2×D4—92no—
847C2×D4—92no—
848C2×D4—92no—
849C2×D4—91no—
850C2×D4—91no—
851C2×D4—91no—
852C2×D4—91no—
853C2×D4—91no—
854C2×D4—91no—
855C2×D4—91no—
856C2×D4—91no—
857C2×D4—91no—
858C2×D4—91no—
859C2×D4—91no—
860C2×D4—91no—
861C2×D4—182no—
862C2×D4—182no—
863C2×D4—181no—
864C2×D4—181no—
865C2×D4—181no—
866C2×D4—181no—
867C2×D4—182no—
868C2×D4—182no—
869C2×D4—182no—
870C2×D4—182no—
871C2×D4—182no—
872C2×D4—182no—
873C2×D4—182no—
874C2×D4—182no—
875C2×D4—182no—
876C2×D4—182no—
877C2×D4C2×D3211yescharacteristic
878C22×C4—31no—
879C22×C4—31no—
880C22×C4—31no—
881C22×C4—31no—
882C22×C4—62no—
883C22×C4—91no—
884C22×C4—91no—
885C22×C4—91no—
886C22×C4—91no—
887C22×C4—91no—
888C22×C4—182no—
889C22×C4—182no—
890C22×C4—182no—
891C4⋊C4—62no—
892C4⋊C4—182no—
893C22⋊C4—32no—
894C22⋊C4—32no—
895C22⋊C4—62no—
896C22⋊C4—92no—
897C22⋊C4—182no—
898C22⋊C4—182no—
899C22⋊C4—182no—
900C22⋊C4C2×D3212yes—
901C42—62no—
902C42—182no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—22no—
907C22×C3—32no—
908C22×C3—31no—
909C22×C3—31no—
910C22×C3—41no—
911C22×C3—41no—
912C22×C3—41no—
913C22×C3—41no—
914C22×C3—41no—
915C22×C3—61no—
916C22×C3—61no—
917C22×C3—81no—
918C22×C3—81no—
919C22×C3—122no—
920C22×C3—122no—
921C22×C3—121no—
922C22×C3—121no—
923C22×C3—121no—
924C22×C3—121no—
925C22×C3—241no—
926C22×C3—241no—
927C22×C3C22×C4×D311yescharacteristic
928C22×C3C22×C4×D311yescharacteristic
929C22×C3C2×D3×D412yes—
930C22×C3C2×D3×D412yes—
931C2×D3—21no—
932C2×D3—21no—
933C2×D3—32no—
934C2×D3—31no—
935C2×D3—31no—
936C2×D3—32no—
937C2×D3—31no—
938C2×D3—31no—
939C2×D3—42no—
940C2×D3—42no—
941C2×D3—41no—
942C2×D3—41no—
943C2×D3—41no—
944C2×D3—41no—
945C2×D3—61no—
946C2×D3—61no—
947C2×D3—62no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—81no—
951C2×D3—81no—
952C2×D3—121no—
953C2×D3—122no—
954C2×D3—122no—
955C2×D3—122no—
956C2×D3—122no—
957C2×D3—121no—
958C2×D3—121no—
959C2×D3—121no—
960C2×D3—121no—
961C2×D3—124no—
962C2×D3—122no—
963C2×D3—121no—
964C2×D3—121no—
965C2×D3—242no—
966C2×D3—241no—
967C2×D3—241no—
968C2×D3—242no—
969C2×D3—242no—
970C2×D3—242no—
971C2×D3—242no—
972C2×D3—241no—
973C2×D3—241no—
974C2×D3—241no—
975C2×D3—241no—
976C2×D3—242no—
977C2×D3—242no—
978C2×D3D3×C22⋊C411yescharacteristic
979C2×D3D3×C22⋊C411yescharacteristic
980C2×D3D3×C22⋊C412yes—
981C3×C4—21no—
982C3×C4—21no—
983C3×C4—31no—
984C3×C4—31no—
985C3×C4—32no—
986C3×C4—41no—
987C3×C4—42no—
988C3×C4—42no—
989C3×C4—61no—
990C3×C4—61no—
991C3×C4—82no—
992C3×C4—122no—
993C3×C4—122no—
994Dic3—21no—
995Dic3—21no—
996Dic3—42no—
997Dic3—42no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—121no—
1001Dic3—122no—
1002Dic3—122no—
1003Dic3—242no—
1004Dic3D3×C22⋊C412yes—
1005Dic3D3×C22⋊C411yescharacteristic
1006Dic3D3×C22⋊C411yescharacteristic
1007C32#288311yescharacteristic, complemented, Sylow
1008C23—31no—
1009C23—31no—
1010C23—32no—
1011C23—32no—
1012C23—31no—
1013C23—31no—
1014C23—61no—
1015C23—61no—
1016C23—91no—
1017C23—91no—
1018C23—92no—
1019C23—92no—
1020C23—91no—
1021C23—181no—
1022C23—181no—
1023C23—182no—
1024C23—182no—
1025C23—241no—
1026C23—241no—
1027C23—721no—
1028C23—721no—
1029C23—721no—
1030C23—721no—
1031C23C4×D3211yescharacteristic
1032C23C22×D3211yescharacteristic
1033Q8—62no—
1034Q8—181no—
1035Q8—181no—
1036D4—22no—
1037D4—62no—
1038D4—62no—
1039D4—62no—
1040D4—62no—
1041D4—62no—
1042D4—91no—
1043D4—91no—
1044D4—91no—
1045D4—91no—
1046D4—92no—
1047D4—92no—
1048D4—92no—
1049D4—92no—
1050D4—92no—
1051D4—92no—
1052D4—182no—
1053D4—181no—
1054D4—181no—
1055D4—181no—
1056D4—181no—
1057D4—181no—
1058D4—181no—
1059D4—181no—
1060D4—181no—
1061D4—182no—
1062D4—181no—
1063D4—181no—
1064D4—182no—
1065C2×C4—22no—
1066C2×C4—31no—
1067C2×C4—31no—
1068C2×C4—32no—
1069C2×C4—32no—
1070C2×C4—31no—
1071C2×C4—31no—
1072C2×C4—61no—
1073C2×C4—61no—
1074C2×C4—61no—
1075C2×C4—61no—
1076C2×C4—61no—
1077C2×C4—61no—
1078C2×C4—62no—
1079C2×C4—62no—
1080C2×C4—91no—
1081C2×C4—181no—
1082C2×C4—181no—
1083C2×C4—182no—
1084C2×C4—182no—
1085C2×C4—182no—
1086C2×C4—182no—
1087C2×C4—182no—
1088C2×C4—242no—
1089C2×C4—722no—
1090C2×C4—722no—
1091C2×C4—722no—
1092C2×C4C4×D3211yescharacteristic
1093C2×C3—22no—
1094C2×C3—21no—
1095C2×C3—22no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—42no—
1099C2×C3—41no—
1100C2×C3—41no—
1101C2×C3—41no—
1102C2×C3—62no—
1103C2×C3—61no—
1104C2×C3—61no—
1105C2×C3—81no—
1106C2×C3—121no—
1107C2×C3—121no—
1108C2×C3C2×D3×C22⋊C411yescharacteristic
1109C2×C3C2×D3×C22⋊C411yescharacteristic
1110D3—21no—
1111D3—21no—
1112D3—22no—
1113D3—41no—
1114D3—41no—
1115D3—62no—
1116D3—61no—
1117D3—62no—
1118D3—61no—
1119D3—61no—
1120D3—62no—
1121D3—61no—
1122D3—121no—
1123D3—122no—
1124D3—121no—
1125D3—121no—
1126D3—241no—
1127C22—21no—
1128C22—31no—
1129C22—31no—
1130C22—32no—
1131C22—41no—
1132C22—41no—
1133C22—61no—
1134C22—61no—
1135C22—91no—
1136C22—91no—
1137C22—92no—
1138C22—122no—
1139C22—122no—
1140C22—121no—
1141C22—121no—
1142C22—121no—
1143C22—121no—
1144C22—181no—
1145C22—241no—
1146C22—241no—
1147C22—362no—
1148C22—362no—
1149C22—361no—
1150C22—361no—
1151C22—361no—
1152C22—721no—
1153C22—721no—
1154C22—722no—
1155C22—722no—
1156C22C2×C4×D3211yescharacteristic
1157C22D32×D412yes—
1158C4—21no—
1159C4—31no—
1160C4—31no—
1161C4—32no—
1162C4—42no—
1163C4—61no—
1164C4—61no—
1165C4—122no—
1166C4—122no—
1167C4—181no—
1168C4—362no—
1169C3—21no—
1170C3#7868811yescharacteristic, complemented
1171C3#7869411yescharacteristic, complemented
1172C2—22no—
1173C2—21no—
1174C2—41no—
1175C2—61no—
1176C2—61no—
1177C2—62no—
1178C2—121no—
1179C2—121no—
1180C2—181no—
1181C2—182no—
1182C2—181no—
1183C2—361no—
1184C2D32×C22⋊C411yescharacteristic
subgroupG/H
centerC2D32×C22⋊C4
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC32×#99C22
socleC2×C32C22×C22⋊C4
prime radicalC2×#64314C2
cosocleC23×C32C24
hypercenter#99D32
hypocenterC32#2883
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #10594182C2semidirect
3. C3⋊D3×#99C2semidirect
4. C3×D3×#99C2semidirect
5. C3×#4740C2semidirect
6. #10591528C2semidirect
7. #10591527C2semidirect
8. D3×#834C2semidirect
9. #10590405C2semidirect
10. #10590404C2semidirect
11. D3×#806C2semidirect
17. C2×#3811C4semidirect
19. C2×D3×#67C4semidirect
21. C22×#626C4semidirect
23. C2×#3804C4semidirect
29. C2×D3×D12C4semidirect
30. C2×#3799C4semidirect
31. C2×#3798C4semidirect
32. C2×#3796C4semidirect
33. C22⋊C4×C3⋊D3C22semidirect
34. C3×D3×C22⋊C4C22semidirect
35. C3×#877C22semidirect
36. #63974C22semidirect
37. D3×#217C22semidirect
38. #63955C22semidirect
43. C32×#99C22semidirect
44. #63661C22semidirect
45. #63633C22semidirect
46. C3×#834C22semidirect
47. C3×#834C22semidirect
48. C3×#806C22semidirect
49. C3×#806C22semidirect
50. #63581C22semidirect
51. #63580C22semidirect
52. #63580C22semidirect
72. D3×#99D3semidirect
75. #4740D3semidirect
76. C23×C3⋊D3C2×C4semidirect
78. C23×C3×D3C2×C4semidirect
80. C22×D32C2×C4semidirect
81. C22×D32C2×C4semidirect
83. C2×#638C2×C4semidirect
87. C2×C4⋊(C3⋊D3)C2×C4semidirect
89. C2×C4×C3⋊D3C2×C4semidirect
90. C2×C3×#67C2×C4semidirect
91. C2×C3×#67C2×C4semidirect
94. C22×C3×Dic3C2×C4semidirect
100. C2×C3×D12C2×C4semidirect
102. C2×C3×C4×D3C2×C4semidirect
103. C2×C3×C4×D3C2×C4semidirect
104. C2×C3×Dic6C2×C4semidirect
113. C2×#627C2×C4semidirect
122. C2×#626C2×C4semidirect
123. C2×#626C2×C4semidirect
124. C2×#626C2×C4semidirect
125. C2×#626C2×C4semidirect
130. C2×#625C2×C4semidirect
132. C2×#624C2×C4semidirect
133. C2×#624C2×C4semidirect
139. C2×D3×Dic3C2×C4semidirect
140. C2×D3×Dic3C2×C4semidirect
219. D3×C22⋊C4C2×D3semidirect
221. #877C2×D3semidirect
229. C3×#99C2×D3semidirect
230. C3×#99C2×D3semidirect
236. #834C2×D3semidirect
237. #834C2×D3semidirect
245. #806C2×D3semidirect
246. #806C2×D3semidirect
355. C23×D3C4×D3semidirect
403. C2×#67C4×D3semidirect
404. C2×#67C4×D3semidirect
410. C22×Dic3C4×D3semidirect
481. C2×D12C4×D3semidirect
498. C2×C4×D3C4×D3semidirect
499. C2×C4×D3C4×D3semidirect
502. C2×Dic6C4×D3semidirect
610. #99D32semidirect
1007. C32#2883semidirect
1170. C3#78688semidirect
1171. C3#78694semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
#105941822
C3⋊D3×#992
C3×D3×#992
C3×#47402
#105915282
#105915272
D3×#8342
#105904052
#105904042
D3×#8062
#786943
#786883