Finite Group Databasebeta

← #11860957

Subgroups — #11860957

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic, complemented
2#10594992C211yesmaximal, characteristic, complemented
3C2×#63822C211yesmaximal, characteristic
4C2×#63635C211yesmaximal, characteristic, complemented
5C3×#4966C211yesmaximal, characteristic, complemented
6#10591088C211yesmaximal, characteristic, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10590477C212yesmaximal, complemented
9#10590475C212yesmaximal, complemented
10#10590455C212yesmaximal, complemented
11#10590453C212yesmaximal, complemented
12#82558—31nomaximal
13#78869—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×#67—22no—
20C3×#926C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#893C2212yes—
23C3×#892—21no—
24C3×D3×C4⋊C4—21no—
25C3×#887C2212yes—
26#67⋊Dic3—22no—
27Dic3×D12C2212yes—
28D3×C4⋊Dic3—21no—
29Dic3×Dic6C2212yes—
30#63841—21no—
31C2×#3718C2211yescharacteristic
32C2×#3715C2211yescharacteristic
33C2×#3715C2211yescharacteristic
34#63822C418yescomplemented
35C2×#3713C2211yescharacteristic
36#63635C2212yes—
37#63635C2212yes—
38C3×#810C2212yes—
39C3×#809C2212yes—
40#63566C2212yes—
41#63563C2212yes—
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#520—31no—
45#5827—31no—
46C2×#950—31no—
47C2×#950—31no—
48#5523—31no—
49#5504D311yescharacteristic, complemented
50C3×#417—31no—
51#5232—31no—
52#5133—31no—
53#5122—31no—
54#5030—32no—
55C4×#215—32no—
56C4×#214—32no—
57#5014—32no—
58#4997—31no—
59#4966D311yescharacteristic, complemented
60C2×#808—31no—
61C2×#808—31no—
62C2×#808—61no—
63#4789—32no—
64#4788—32no—
65#4785—32no—
66#4758—32no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—21no—
70C2×C3×#67—21no—
71C2×C3×#67—21no—
72C3×#235—22no—
73C3×#235—22no—
74C3×#235C2×C414yescomplemented
75C3×#235C2×C414yescomplemented
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—22no—
81C2×C3×Dic6C2311yescharacteristic
82C2×C3×Dic6C2311yescharacteristic
83C2×D3×Dic3—22no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C2×C3⋊(C3⋊C8)C2×C414yescomplemented
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C3×#217D412yes—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3D411yescharacteristic
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C3×#208—22no—
99C2×C3×C3⋊C8C2312yes—
100Dic3⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102Dic32—22no—
103#3718C2×C414yescomplemented
104#3715C2×C414yescomplemented
105#3715C2×C414yescomplemented
106#3713C2×C414yescomplemented
107#2952—91noSylow
108C2×C3×#41—31no—
109C2×C3×#41—31no—
110C2×#235C2×D311yescharacteristic
111C2×#235C2×D311yescharacteristic
112C2×C3×M16—31no—
113C3×C4×Q8—32no—
114C3×C4×D4—32no—
115C3×C4×D4—62no—
116C3×#117—31no—
117C3×#117—61no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—61no—
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C4⋊C4C2×D311yescharacteristic
122#950—38no—
123#950—38no—
124Q8×Dic3—32no—
125C2×#216—31no—
126C2×#216—31no—
127C2×#215—31no—
128C2×#215—31no—
129D4×Dic3—32no—
130D4×Dic3—62no—
131C2×#214—31no—
132C2×#214—31no—
133C2×#213—31no—
134C2×#213—31no—
135C4×#67—22no—
136#926—61no—
137#926C2×D311yescharacteristic
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—61no—
141C2×C4⋊Dic3—61no—
142C2×#208C2×D311yescharacteristic
143C22×C3⋊C8—31no—
144C22×C3⋊C8—31no—
145C22×C3⋊C8—61no—
146#893C2×D312yes—
147#892—21no—
148#892—61no—
149D3×C4⋊C4—21no—
150D3×C4⋊C4—61no—
151#887C2×D312yes—
152#67⋊C4—62no—
153C4×D12—32no—
154C4×Dic6—32no—
155C3×#103—32no—
156C3×#102—32no—
157#835—32no—
158#832—32no—
159#821—32no—
160#816—32no—
161#815—32no—
162C8×Dic3—32no—
163#810C2×D312yes—
164#809C2×D312yes—
165#808—32no—
166#808—32no—
167#808—32no—
168#808—32no—
169#808—62no—
170#808—62no—
171#803—32no—
172C4×C3⋊C8—32no—
173C23×C32C2×D411yescharacteristic
174C22×C3×D3—21no—
175C22×C3×D3—21no—
176C2×C32×C4—22no—
177C2×C32×C4—81no—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—81no—
184C3×#67—24no—
185C3×#67—24no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D412yes—
189C2×C3×Dic3C2×D412yes—
190C3×D12—21no—
191C3×D12—21no—
192C3×D12C22×C412yes—
193C3×D12C22×C412yes—
194C3×C4×D3—24no—
195C3×C4×D3—24no—
196C3×C4×D3—82no—
197C3×Dic6—21no—
198C3×Dic6—21no—
199C3×Dic6C22×C412yes—
200C3×Dic6C22×C412yes—
201D3×Dic3—82no—
202C3⋊(C3⋊C8)C22×C412yes—
203C3⋊(C3⋊C8)C22×C412yes—
204C3×C3⋊C8—22no—
205C2×#135—91no—
206#520—31no—
207#520—91no—
208#442—92no—
209#441—92no—
210C4×SD16—92no—
211C4×SD16—92no—
212C2×#106—91no—
213#417—31no—
214#417—91no—
215#405—91no—
216C3×#41—34no—
217C3×#41—34no—
218C3×#41—62no—
219C3×#41—62no—
220C2×C3×Q8—31no—
221C2×C3×Q8—31no—
222C2×C3×D4—31no—
223C2×C3×D4—31no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—41no—
230C22×C3×C4—62no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—21no—
236C2×#67—21no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—62no—
240C22×Dic3—121no—
241#235—22no—
242#235—22no—
243#235C4×D314yescomplemented
244#235C4×D314yescomplemented
245C2×D12C22×D311yescharacteristic
246C2×D12C22×D311yescharacteristic
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—22no—
250C2×C4×D3—62no—
251C2×Dic6C22×D311yescharacteristic
252C2×Dic6C22×D311yescharacteristic
253C3×M16—62no—
254C2×C3×C8—32no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—41no—
261C3×C4⋊C4—62no—
262C3×C4⋊C4C22×D312yes—
263C3×C4⋊C4C22×D312yes—
264C3×C22⋊C4—32no—
265C3×C22⋊C4—62no—
266C3×C42—32no—
267C3×C42—62no—
268#217—62no—
269#217#6712yes—
270#216—34no—
271#216—34no—
272#215—34no—
273#215—34no—
274#214—34no—
275#214—34no—
276#213—34no—
277#213—34no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—62no—
280C4⋊Dic3—32no—
281C4⋊Dic3—32no—
282C4⋊Dic3—62no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—62no—
286C4⋊Dic3—121no—
287C4⋊Dic3#6711yescharacteristic
288C4⋊Dic3#6711yescharacteristic
289Dic3⋊C4—22no—
290Dic3⋊C4—62no—
291C4×Dic3—22no—
292C4×Dic3—62no—
293C4×Dic3—62no—
294C4×Dic3C22×D312yes—
295#208—22no—
296C2×C3⋊C8—34no—
297C2×C3⋊C8—34no—
298C2×C3⋊C8—31no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—31no—
301C2×C3⋊C8—31no—
302C2×C3⋊C8—61no—
303C2×C3⋊C8—61no—
304C2×C3⋊C8—64no—
305C2×C3⋊C8C22×D312yes—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32C4×D412yes—
309C22×C32C22×D411yescharacteristic
310C2×C3×D3—22no—
311C2×C3×D3—22no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C32×C4—42no—
317C32×C4C4×D412yes—
318C32×C4C23×C411yescharacteristic
319C32×C4C2×#4111yescharacteristic
320C3⋊Dic3—42no—
321C3×Dic3—22no—
322C3×Dic3—22no—
323C3×Dic3—22no—
324C3×Dic3—22no—
325C2×#41—31no—
326C2×#41—31no—
327#135—98no—
328C2×Q16—91no—
329C2×SD16—91no—
330C2×SD16—91no—
331C2×D8—91no—
332C2×M16—31no—
333C22×C8—91no—
334C4×Q8—32no—
335C4×Q8—92no—
336C4×D4—32no—
337C4×D4—62no—
338C4×D4—92no—
339C4×D4—182no—
340#117—31no—
341#117—61no—
342#117—181no—
343C2×C4⋊C4—61no—
344C2×C4⋊C4—91no—
345C2×C4⋊C4—181no—
346C2×C4⋊C4D3211yescharacteristic
347#106—92no—
348#106—92no—
349#103—32no—
350#103—92no—
351#102—32no—
352#102—92no—
353#97—92no—
354C4×C8—92no—
355C23×C3—21no—
356C23×C3—61no—
357C23×C3—61no—
358C23×C3D3×D411yescharacteristic
359C23×C3C2×#6711yescharacteristic
360C22×D3—21no—
361C22×D3—21no—
362C3×Q8—32no—
363C3×Q8—32no—
364C3×Q8—61no—
365C3×Q8—61no—
366C3×D4—32no—
367C3×D4—32no—
368C3×D4—64no—
369C3×D4—64no—
370C3×D4—61no—
371C3×D4—61no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—32no—
379C2×C3×C4—32no—
380C2×C3×C4—42no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—64no—
384C2×C3×C4—64no—
385C2×C3×C4—81no—
386C2×C3×C4—81no—
387C2×C3×C4—82no—
388C2×C3×C4—242no—
389C2×C3×C4C2×C4×D312yes—
390C2×C3×C4C2×C4×D312yes—
391C2×C3×C4#23512yes—
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4#23712yes—
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—24no—
398#67—24no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—122no—
404C2×Dic3—242no—
405C2×Dic3—241no—
406C2×Dic3—241no—
407C2×Dic3—242no—
408C2×Dic3C2×#6712yes—
409C2×Dic3C2×#6712yes—
410D12—21no—
411D12—21no—
412D12C2×C4×D312yes—
413D12C2×C4×D312yes—
414C4×D3—24no—
415C4×D3—24no—
416C4×D3—82no—
417C4×D3—242no—
418Dic6—21no—
419Dic6—21no—
420Dic6C2×C4×D312yes—
421Dic6C2×C4×D312yes—
422C3×C8—62no—
423C3⋊C8—22no—
424C3⋊C8—32no—
425C3⋊C8—32no—
426C3⋊C8—32no—
427C3⋊C8—32no—
428C3⋊C8—62no—
429C3⋊C8—62no—
430C2×C32—22no—
431C2×C32C2×C4×D411yescharacteristic
432C2×C32#57711yescharacteristic
433C2×C32#57711yescharacteristic
434C3×D3—42no—
435C3×D3—42no—
436#41—34no—
437#41—34no—
438#41—62no—
439#41—62no—
440C2×Q8—31no—
441C2×Q8—31no—
442C2×D4—31no—
443C2×D4—31no—
444C2×D4—61no—
445C2×D4—61no—
446C22×C4—21no—
447C22×C4—62no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—182no—
451C22×C4—181no—
452C22×C4C2×D3211yescharacteristic
453Q16—94no—
454SD16—94no—
455SD16—94no—
456D8—94no—
457M16—62no—
458C2×C8—32no—
459C2×C8—91no—
460C2×C8—91no—
461C2×C8—94no—
462C4⋊C4—21no—
463C4⋊C4—31no—
464C4⋊C4—31no—
465C4⋊C4—62no—
466C4⋊C4—92no—
467C4⋊C4—182no—
468C4⋊C4—181no—
469C4⋊C4C2×D3212yes—
470C22⋊C4—32no—
471C22⋊C4—62no—
472C22⋊C4—182no—
473C42—32no—
474C42—62no—
475C42—182no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—22no—
484C22×C3—62no—
485C22×C3—62no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3#67⋊C412yes—
491C22×C3C4×#6712yes—
492C22×C3C2×D3×D411yescharacteristic
493C22×C3C22×#6711yescharacteristic
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—41no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—22no—
503C3×C4—42no—
504C3×C4—42no—
505C3×C4—62no—
506C3×C4—62no—
507C3×C4—62no—
508C3×C4—62no—
509C3×C4—82no—
510C3×C4#67⋊C412yes—
511C3×C4C4×#6712yes—
512C3×C4C22×C4×D311yescharacteristic
513C3×C4C22×C4×D311yescharacteristic
514C3×C4C2×#23511yescharacteristic
515C3×C4C2×#23711yescharacteristic
516Dic3—22no—
517Dic3—22no—
518Dic3—22no—
519Dic3—22no—
520Dic3—122no—
521Dic3—122no—
522Dic3—242no—
523C32#295211yescharacteristic, complemented, Sylow
524C23—61no—
525C23—61no—
526C23D3×#6711yescharacteristic
527Q8—32no—
528Q8—32no—
529Q8—61no—
530Q8—61no—
531D4—32no—
532D4—32no—
533D4—64no—
534D4—64no—
535D4—61no—
536D4—61no—
537C2×C4—22no—
538C2×C4—32no—
539C2×C4—32no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—64no—
543C2×C4—64no—
544C2×C4—81no—
545C2×C4—182no—
546C2×C4—242no—
547C2×C4—722no—
548C2×C4—721no—
549C2×C4#379512yes—
550C2×C4C4×D3212yes—
551C2×C4D3×#6711yescharacteristic
552C2×C4C22×D3211yescharacteristic
553C8—62no—
554C8—92no—
555C8—92no—
556C2×C3—24no—
557C2×C3—22no—
558C2×C3—22no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—122no—
563C2×C3—122no—
564C2×C3C2×#67⋊C411yescharacteristic
565C2×C3#577511yescharacteristic
566C2×C3#577811yescharacteristic
567C2×C3C2×C4×#6711yescharacteristic
568C2×C3#583611yescharacteristic
569C2×C3#583711yescharacteristic
570D3—42no—
571D3—42no—
572C22—21no—
573C22—21no—
574C22—62no—
575C22—62no—
576C22—121no—
577C22—121no—
578C22—121no—
579C22—121no—
580C22#6387912yes—
581C22C2×D3×#6711yescharacteristic
582C4—42no—
583C4—62no—
584C4—62no—
585C4—62no—
586C4—62no—
587C4—362no—
588C4#6387912yes—
589C4C2×#379511yescharacteristic
590C4C2×C4×D3211yescharacteristic
591C3—21no—
592C3#7886911yescharacteristic, complemented
593C3#8255811yescharacteristic, complemented
594C2—22no—
595C2—122no—
596C2—122no—
597C2C2×#6387911yescharacteristic
598C2#1059510611yescharacteristic
599C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#63822C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5504C2semidirect
2. #10594992C2semidirect
4. C2×#63635C2semidirect
5. C3×#4966C2semidirect
6. #10591088C2semidirect
7. #10591057C2semidirect
8. #10590477C2semidirect
9. #10590475C2semidirect
10. #10590455C2semidirect
11. #10590453C2semidirect
34. #63822C4semidirect
49. #5504D3semidirect
59. #4966D3semidirect
74. C3×#235C2×C4semidirect
75. C3×#235C2×C4semidirect
88. C2×C3⋊(C3⋊C8)C2×C4semidirect
103. #3718C2×C4semidirect
104. #3715C2×C4semidirect
105. #3715C2×C4semidirect
106. #3713C2×C4semidirect
243. #235C4×D3semidirect
244. #235C4×D3semidirect
523. C32#2952semidirect
592. C3#78869semidirect
593. C3#82558semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105949922
C2×#638222
C2×#636352
C3×#49662
#105910882
#105910572
#105904772
#105904752
#105904552
#105904532
#825583
#788693