Finite Group Databasebeta

← #11882280

Subgroups — #11882280

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic
2#10593873C211yesmaximal, characteristic, complemented
3#10592793C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5#10590578C212yesmaximal, complemented
6#10590559C212yesmaximal, complemented
7#10590558C212yesmaximal, complemented
8#10590514C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10#10590364C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#83320—31nomaximal
13#81002—31nomaximal
14C2×C3×#239—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#947—21no—
18C3×#895—21no—
19C3×#895C2212yes—
20C3×#893—21no—
21C3×#893C2212yes—
22C3×#874C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918C2211yescharacteristic
26C4×#627—21no—
27#63867—21no—
28#63866C2211yescharacteristic
29#63857C2211yescharacteristic
30#63856C2211yescharacteristic
31#63855—21no—
32#63851—21no—
33C2×#3716C2212yes—
34C2×#3715C2212yes—
35C2×D3×C3⋊C8C2212yes—
36#63637C2212yes—
37#63635C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#810C2212yes—
40C3×#808C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42Dic3⋊(C3⋊C8)C2212yes—
43#63563C2212yes—
44#63562C2212yes—
45C3×#532—31no—
46#5725D311yescharacteristic
47#5578—31no—
48#5470—31no—
49C3×#475—31no—
50#5094—31no—
51#5094—31no—
52#5094—61no—
53#5094D311yescharacteristic, complemented
54#5075—31no—
55#5075—31no—
56#5041—32no—
57#5041—32no—
58#5027—31no—
59#5019—32no—
60#5008—32no—
61C2×C4⋊(C3⋊C8)—31no—
62#4870—32no—
63#4864—32no—
64#4848—31no—
65D3×C4⋊C8—31no—
66#4818—32no—
67#4807—32no—
68C2×C32×Q8—21no—
69C2×#634C2311yescharacteristic
70C3×#239—44no—
71C2×C3×D12—22no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6C2311yescharacteristic
80C2×#627—21no—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2312yes—
83C32×C42C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C4×C3⋊Dic3—21no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3—21no—
93C3×C4×Dic3D411yescharacteristic
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97#3724—21no—
98Dic3⋊Dic3—21no—
99Dic3⋊Dic3—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102(C2×D3)⋊Dic3—21no—
103(C2×D3)⋊Dic3—21no—
104#3716—42no—
105#3715—42no—
106D3×C3⋊C8—42no—
107#3246—91noSylow
108C2×C3×#41—61no—
109C2×#239—21no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8C2×D311yescharacteristic
112C3×C4⋊Q8C2×D311yescharacteristic
113C3×#127—31no—
114C3×#124—61no—
115C3×#121—32no—
116C3×#121—61no—
117C3×C4×Q8—31no—
118C3×C4×D4—32no—
119C3×C4×D4—61no—
120C2×C3×C42—31no—
121#947—21no—
122#946—31no—
123#944—31no—
124C2×#215—32no—
125C2×#214—32no—
126C2×#214—32no—
127#926—61no—
128#924—31no—
129#924—31no—
130#924—61no—
131C22×C3⋊C8—32no—
132C2×#204—32no—
133C2×D3×C8—32no—
134#897—31no—
135#896—61no—
136#895—21no—
137#895C2×D312yes—
138#893—21no—
139#893C2×D312yes—
140#889—61no—
141#888—31no—
142#874C2×D311yescharacteristic
143#872—61no—
144C42×D3C2×D311yescharacteristic
145#870—61no—
146#869—31no—
147#869—31no—
148C4×Dic6—31no—
149C4×Dic6—31no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C4×Dic6C2×D311yescharacteristic
154C3×#106—32no—
155C3×C4⋊C8—31no—
156C3×#103—32no—
157#832—32no—
158#832—32no—
159#821—32no—
160Dic3⋊C8—32no—
161#810—32no—
162#810—32no—
163#810—62no—
164#810C2×D312yes—
165#809—32no—
166#808—32no—
167#808—32no—
168#808—62no—
169#808C2×D312yes—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3×D3—22no—
176C22×C3×D3C2×D411yescharacteristic
177C32×Q8—42no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184#634—21no—
185#634—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—42no—
194C3×D12—44no—
195C3×D12—42no—
196C3×C4×D3—21no—
197C3×C4×D3—21no—
198C3×C4×D3—41no—
199C3×C4×D3—44no—
200C3×C4×D3SD1614yescomplemented
201C3×Dic6—21no—
202C3×Dic6—21no—
203#627—42no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207#532—31no—
208#476—92no—
209#475—31no—
210#475—91no—
211#465—92no—
212#465—92no—
213#461—92no—
214#460—91no—
215#460—91no—
216C2×C4⋊C8—91no—
217C3×#41—124no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—31no—
221C2×C3×Q8—41no—
222C2×C3×D4—32no—
223C2×C3×D4—62no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—62no—
230#239—44no—
231C2×D12—22no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12C22×D312yes—
235C2×C4×D3—22no—
236C2×C4×D3#6711yescharacteristic
237C2×C4×D3#6711yescharacteristic
238C2×C4×D3C22×D311yescharacteristic
239C2×Dic6—31no—
240C2×Dic6—31no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6C22×D311yescharacteristic
245C2×C3×C8—32no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—41no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4C22×D312yes—
253C3×C4⋊C4C22×D312yes—
254C3×C22⋊C4—62no—
255C3×C22⋊C4—62no—
256C3×C42—21no—
257C3×C42—31no—
258C3×C42—31no—
259C3×C42—31no—
260C3×C42—61no—
261C3×C42C22×D311yescharacteristic
262C3×C42C22×D311yescharacteristic
263#217—61no—
264#217—61no—
265#215—122no—
266#214—122no—
267#214—122no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—22no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3C22×D311yescharacteristic
280Dic3⋊C4—21no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—121no—
290C4×Dic3—21no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—121no—
294C4×Dic3#6711yescharacteristic
295C4×Dic3#6711yescharacteristic
296C4×Dic3C22×D311yescharacteristic
297C2×C3⋊C8—32no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8—122no—
301C2×C3⋊C8C22×D312yes—
302#204—122no—
303D3×C8—122no—
304C22×C32C22×D411yescharacteristic
305C2×C3×D3—21no—
306C2×C3×D3—21no—
307C2×C3×D3—42no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3C2×SD1612yes—
311C32×C4—21no—
312C32×C4—42no—
313C32×C4C2×SD1612yes—
314C32×C4H(5,𝔽2)11yescharacteristic
315C32×C42−1+411yescharacteristic
316C3⋊Dic3—41no—
317C3⋊Dic3—41no—
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—41no—
322C3×Dic3C2×SD1612yes—
323C2×#41—61no—
324C2×SD16—92no—
325C2×SD16—92no—
326C22×C8—92no—
327C4⋊Q8—91no—
328C4⋊Q8—91no—
329C4⋊Q8D3211yescharacteristic
330#127—31no—
331#125—181no—
332#124—61no—
333C22⋊Q8—91no—
334C22⋊Q8—91no—
335C22⋊Q8—181no—
336#121—32no—
337#121—61no—
338C4×Q8—31no—
339C4×Q8—91no—
340C4×Q8—181no—
341C4×D4—32no—
342C4×D4—61no—
343#117—181no—
344C2×C42—31no—
345#106—32no—
346#106—92no—
347C4⋊C8—31no—
348C4⋊C8—92no—
349C4⋊C8—91no—
350#103—32no—
351#103—92no—
352#102—92no—
353#102—92no—
354C23×C3—31no—
355C23×C3—62no—
356C22×D3—22no—
357C22×D3C2×#6711yescharacteristic
358C3×Q8—42no—
359C3×Q8—42no—
360C3×Q8—61no—
361C3×Q8—61no—
362C3×Q8—82no—
363C3×D4—62no—
364C3×D4—62no—
365C3×D4—122no—
366C3×D4—124no—
367C3×D4—122no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—31no—
374C2×C3×C4—34no—
375C2×C3×C4—31no—
376C2×C3×C4—31no—
377C2×C3×C4—42no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—121no—
383C2×C3×C4—124no—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3C2×#6711yescharacteristic
399C2×Dic3C2×#6711yescharacteristic
400C2×Dic3C2×#6711yescharacteristic
401D12—22no—
402D12—22no—
403D12—42no—
404D12—44no—
405D12—42no—
406C4×D3—21no—
407C4×D3—21no—
408C4×D3—41no—
409C4×D3—44no—
410C4×D3#21414yescomplemented
411Dic6—21no—
412Dic6—21no—
413Dic6—62no—
414Dic6—61no—
415Dic6—61no—
416Dic6—61no—
417Dic6—61no—
418Dic6—121no—
419Dic6—122no—
420Dic6—122no—
421C3×C8—62no—
422C3⋊C8—22no—
423C3⋊C8—62no—
424C3⋊C8—62no—
425C3⋊C8—122no—
426C2×C32#53711yescharacteristic
427C2×C32C22×SD1611yescharacteristic
428C2×C32#57511yescharacteristic
429C3×D3—22no—
430C3×D3—82no—
431#41—124no—
432C2×Q8—21no—
433C2×Q8—31no—
434C2×Q8—91no—
435C2×Q8—181no—
436C2×D4—32no—
437C2×D4—62no—
438C2×D4—61no—
439C2×D4—61no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—62no—
444SD16—362no—
445SD16—362no—
446C2×C8—32no—
447C2×C8—92no—
448C2×C8—362no—
449C4⋊C4—21no—
450C4⋊C4—31no—
451C4⋊C4—61no—
452C4⋊C4—91no—
453C4⋊C4—181no—
454C4⋊C4—181no—
455C4⋊C4—181no—
456C4⋊C4—181no—
457C4⋊C4—181no—
458C4⋊C4—181no—
459C4⋊C4C2×D3212yes—
460C22⋊C4—62no—
461C22⋊C4—62no—
462C22⋊C4—181no—
463C22⋊C4—181no—
464C42—31no—
465C42—31no—
466C42—31no—
467C42—61no—
468C42—181no—
469C42C2×D3211yescharacteristic
470C22×C3—21no—
471C22×C3—32no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—122no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C22×#6711yescharacteristic
479C2×D3—21no—
480C2×D3—21no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3C2×#21412yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—32no—
491C3×C4—41no—
492C3×C4—42no—
493C3×C4—42no—
494C3×C4—61no—
495C3×C4—61no—
496C3×C4—82no—
497C3×C4—121no—
498C3×C4—121no—
499C3×C4D3×SD1612yes—
500C3×C4C2×#21412yes—
501C3×C4#100711yescharacteristic
502C3×C4#100911yescharacteristic
503C3×C4#100911yescharacteristic
504C3×C4#101011yescharacteristic
505Dic3—21no—
506Dic3—21no—
507Dic3—41no—
508Dic3—41no—
509Dic3—122no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513Dic3—121no—
514Dic3—241no—
515Dic3C2×#21412yes—
516C32#324611yescharacteristic, complemented, Sylow
517C23—31no—
518C23—62no—
519Q8—42no—
520Q8—61no—
521Q8—61no—
522Q8—181no—
523Q8—181no—
524Q8—362no—
525D4—62no—
526D4—62no—
527D4—122no—
528D4—124no—
529D4—122no—
530C2×C4—22no—
531C2×C4—31no—
532C2×C4—34no—
533C2×C4—31no—
534C2×C4—31no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—121no—
540C2×C4—124no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4D3×#6711yescharacteristic
544C2×C4D3×#6711yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—62no—
547C8—182no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—62no—
552C2×C3—242no—
553C2×C3#562911yescharacteristic
554C2×C3C2×D3×SD1611yescharacteristic
555C2×C3#577711yescharacteristic
556C2×C3C22×#21411yescharacteristic
557C2×C3#582211yescharacteristic
558C2×C3#583311yescharacteristic
559D3—22no—
560D3—82no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—122no—
565C22—122no—
566C22—122no—
567C22C2×D3×#6711yescharacteristic
568C4—21no—
569C4—32no—
570C4—42no—
571C4—61no—
572C4—61no—
573C4—121no—
574C4—121no—
575C4—361no—
576C4—361no—
577C4D3×#21412yes—
578C4#6431511yescharacteristic
579C4#6432011yescharacteristic
580C3—21no—
581C3#8100211yescharacteristic, complemented
582C3#8332011yescharacteristic, complemented
583C2—62no—
584C2—242no—
585C2C2×D3×#21411yescharacteristic
586C2#1059531711yescharacteristic
587C2#1059539811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC3×#5725C2
hypercenterC4⋊Q8D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10593873C2semidirect
3. #10592793C2semidirect
4. C3×#5094C2semidirect
5. #10590578C2semidirect
6. #10590559C2semidirect
7. #10590558C2semidirect
8. #10590514C2semidirect
9. #10590377C2semidirect
10. #10590364C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
53. #5094D3semidirect
200. C3×C4×D3SD16semidirect
410. C4×D3#214semidirect
516. C32#3246semidirect
581. C3#81002semidirect
582. C3#83320semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
#105938732
#105927932
C3×#50942
#105905782
#105905592
#105905582
#105905142
#105903772
#105903642
D3×C4⋊(C3⋊C8)2
#833203
#810023