Finite Group Databasebeta

← #11895425

Subgroups — #11895425

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593900C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590879C212yesmaximal, complemented
7#10590878C212yesmaximal, complemented
8#10590757C212yesmaximal, complemented
9#10590744C212yesmaximal, complemented
10#10590377C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81588—31nomaximal
13#79932—31nomaximal
14C2×#3796—21no—
15C2×#3744C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#874C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63919—21no—
22#63918C2212yes—
23#63916—21no—
24#63911C2212yes—
25Dic3×D12C2212yes—
26#63886—22no—
27#63844C2212yes—
28#63843—21no—
29#63839—22no—
30C2×#3716C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63644C2211yescharacteristic
34#63643C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63564C2212yes—
42#63563C2212yes—
43#5722—31no—
44#5718—31no—
45#5577—31no—
46Q8×Dic6—31no—
47C3×#486—31no—
48C3×C8×Q8—31no—
49#5084—31no—
50#5075—31no—
51#4848—31no—
52#4848—32no—
53#4842—31no—
54#4842—32no—
55#4762—32no—
56#4761—32no—
57#4760—32no—
58#4758—32no—
59#4694—32no—
60#4694D311yescharacteristic, complemented
61C4×#204—31no—
62C4×#204—31no—
63C4×#204—32no—
64C4×#204—61no—
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2311yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#627—22no—
75C2×#626—22no—
76C2×#626—22no—
77C2×D3×Dic3—22no—
78#3796—44no—
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C32×C42C2311yescharacteristic
82#3752—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C4×C3⋊Dic3—21no—
87#3744—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3716—24no—
99#3362—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C3×C4⋊Q8—31no—
103C3×#127—31no—
104C3×C4×Q8—31no—
105Q8×Dic3—61no—
106#944—62no—
107#940—32no—
108#939—62no—
109#938—61no—
110D4×Dic3—32no—
111C2×#214—32no—
112C2×#204—32no—
113C2×#204—31no—
114C2×#204—31no—
115C2×#204—61no—
116#895—62no—
117#895—61no—
118#888—32no—
119#888—61no—
120#888—62no—
121#888—61no—
122#887—32no—
123#887—61no—
124#874—32no—
125#874C2×D311yescharacteristic
126C4×D12—32no—
127C4×D12—31no—
128C4×D12—31no—
129C4×D12—61no—
130#869—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—32no—
135C4×Dic6—61no—
136C4×Dic6C2×D311yescharacteristic
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#102—32no—
140C3×#102—32no—
141C3×C4×C8—21no—
142C3×C4×C8—32no—
143C3×C4×C8C2×D311yescharacteristic
144C3×C4×C8C2×D311yescharacteristic
145#832—32no—
146#821—32no—
147#821—31no—
148#821—31no—
149#821—32no—
150#821—61no—
151#821C2×D312yes—
152#821C2×D312yes—
153#817—31no—
154#817—31no—
155#817—32no—
156#817—61no—
157#816—31no—
158#816—31no—
159#816—61no—
160Dic3⋊C8C2×D312yes—
161C8×Dic3C2×D312yes—
162#809—32no—
163#808—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)—21no—
175C4×C3⋊D3—42no—
176#634—21no—
177#634#4112yescomplemented
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—22no—
182C3×D12—22no—
183C3×D12—42no—
184C3×D12—81no—
185C3×Dic6—81no—
186C3×Dic6SD1614yescomplemented
187#627—82no—
188#626—44no—
189#626—82no—
190D3×Dic3—44no—
191C32×C8—21no—
192C32×C8—21no—
193C3×C3⋊C8—22no—
194Q82—91no—
195#550—91no—
196#486—31no—
197#486—92no—
198#476—92no—
199#476—91no—
200#460—92no—
201#460—91no—
202C8×Q8—31no—
203C4×SD16—92no—
204C4×SD16—91no—
205C2×C3×Q8—31no—
206C2×C3×Q8—61no—
207C2×C3×D4—32no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C2×#67—62no—
211C2×#67—62no—
212C22×Dic3—62no—
213#239—124no—
214#237—124no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—31no—
218C2×D12—31no—
219C2×D12—61no—
220C2×D12—62no—
221C2×D12—62no—
222C2×D12C22×D312yes—
223C2×C4×D3—62no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—121no—
227C2×Dic6—21no—
228C2×Dic6—31no—
229C2×Dic6—31no—
230C2×Dic6—61no—
231C2×Dic6—62no—
232C2×Dic6—62no—
233C2×Dic6D1211yescharacteristic
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—32no—
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C22×D311yescharacteristic
241C3×C4⋊C4—32no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—61no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#217—62no—
250#214—64no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—121no—
255C4⋊Dic3—21no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3D1211yescharacteristic
264C4⋊Dic3C22×D312yes—
265Dic3⋊C4—62no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—121no—
271Dic3⋊C4D1212yes—
272C4×Dic3—62no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—62no—
276C4×Dic3—121no—
277C4×Dic3C22×D312yes—
278C2×C3⋊C8C22×D312yes—
279#204—62no—
280#204—62no—
281#204—64no—
282#204—64no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C32×C4—21no—
291C32×C4C2×SD1612yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C3×Dic3C2×SD1614yes—
300C2×#41—181no—
301C2×SD16—92no—
302C2×SD16—91no—
303C4⋊Q8—31no—
304C4⋊Q8—92no—
305C4⋊Q8—181no—
306C4⋊Q8—182no—
307#127—31no—
308#127—92no—
309#121—181no—
310#121—182no—
311C4×Q8—31no—
312C4×Q8—92no—
313C4×Q8—91no—
314C4×Q8—181no—
315C4×D4—92no—
316C4×D4—91no—
317#106—92no—
318#106—91no—
319C4⋊C8—32no—
320C4⋊C8—31no—
321#103—91no—
322#102—32no—
323#102—32no—
324#102—92no—
325#102—92no—
326#102—91no—
327C4×C8—32no—
328C4×C8D3211yescharacteristic
329C23×C3—62no—
330C22×D3—22no—
331C22×D3—61no—
332C22×D3—61no—
333C22×D3—121no—
334C3×Q8—34no—
335C3×Q8—241no—
336C3×D4—62no—
337C3×D4—62no—
338C3×D4—122no—
339C3×D4—241no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—62no—
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352#67—124no—
353#67—242no—
354C2×Dic3—22no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—124no—
365C2×Dic3C2×D1212yes—
366C2×Dic3C2×D1212yes—
367D12—22no—
368D12—22no—
369D12—42no—
370D12—62no—
371D12—61no—
372D12—61no—
373D12—61no—
374D12—61no—
375D12—81no—
376D12—121no—
377D12—124no—
378D12—242no—
379C4×D3—124no—
380C4×D3—122no—
381C4×D3—122no—
382C4×D3—242no—
383Dic6—32no—
384Dic6—32no—
385Dic6—62no—
386Dic6—61no—
387Dic6—61no—
388Dic6—81no—
389Dic6—121no—
390Dic6—242no—
391Dic6—242no—
392Dic6#20414yescomplemented
393C3×C8—22no—
394C3×C8—21no—
395C3×C8—21no—
396C3×C8—21no—
397C3×C8—21no—
398C3×C8—41no—
399C3×C8—62no—
400C3⋊C8—22no—
401C2×C32#54811yescharacteristic
402C2×C32C22×SD1611yescharacteristic
403C2×C32#57611yescharacteristic
404C3⋊D3—81no—
405C3×D3—82no—
406#41—364no—
407C2×Q8—31no—
408C2×Q8—61no—
409C2×Q8—91no—
410C2×Q8—182no—
411C2×D4—32no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—91no—
415C2×D4—182no—
416C2×D4—182no—
417C22×C4—182no—
418C22×C4—181no—
419SD16—182no—
420SD16—184no—
421C2×C8—32no—
422C2×C8C2×D3211yescharacteristic
423C2×C8C2×D3211yescharacteristic
424C4⋊C4—32no—
425C4⋊C4—31no—
426C4⋊C4—32no—
427C4⋊C4—61no—
428C4⋊C4—91no—
429C4⋊C4—91no—
430C4⋊C4—182no—
431C4⋊C4—182no—
432C4⋊C4—181no—
433C22⋊C4—182no—
434C22⋊C4—181no—
435C42—32no—
436C42—182no—
437C42—181no—
438C42C2×D3211yescharacteristic
439C22×C3—21no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3C22×D1211yescharacteristic
444C22×C3C2×D3×D411yescharacteristic
445C2×D3—42no—
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—122no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—241no—
456C2×D3—241no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—21no—
462C3×C4—34no—
463C3×C4—41no—
464C3×C4—62no—
465C3×C4—122no—
466C3×C4C2×#20412yes—
467C3×C4D3×SD1612yes—
468C3×C4#100711yescharacteristic
469C3×C4D3×#4111yescharacteristic
470C3×C4D3×#4111yescharacteristic
471C3×C4#101011yescharacteristic
472Dic3—22no—
473Dic3—42no—
474Dic3—62no—
475Dic3—62no—
476Dic3—122no—
477Dic3—121no—
478Dic3—121no—
479Dic3—121no—
480Dic3—121no—
481Dic3—241no—
482Dic3—241no—
483Dic3C2×#20414yes—
484C32#336211yescharacteristic, complemented, Sylow
485C23—62no—
486C23—181no—
487Q8—34no—
488Q8—92no—
489Q8—181no—
490Q8—241no—
491Q8—722no—
492D4—62no—
493D4—62no—
494D4—122no—
495D4—181no—
496D4—181no—
497D4—241no—
498D4—364no—
499D4—722no—
500C2×C4—32no—
501C2×C4—32no—
502C2×C4—62no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—364no—
507C2×C4—362no—
508C2×C4D3×D1211yescharacteristic
509C2×C4D3×D1211yescharacteristic
510C2×C4C22×D3211yescharacteristic
511C8—21no—
512C8—21no—
513C8—62no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—242no—
518C2×C3#557611yescharacteristic
519C2×C3#567711yescharacteristic
520C2×C3C22×#20411yescharacteristic
521C2×C3#575211yescharacteristic
522C2×C3#575711yescharacteristic
523C2×C3C2×D3×SD1611yescharacteristic
524D3—82no—
525D3—242no—
526D3—241no—
527D3—241no—
528C22—122no—
529C22—122no—
530C22—122no—
531C22—361no—
532C22—361no—
533C22—361no—
534C22C2×D3×D1211yescharacteristic
535C4—21no—
536C4—34no—
537C4—62no—
538C4—122no—
539C4—182no—
540C4—361no—
541C4—361no—
542C4D3×#20412yes—
543C4#6429711yescharacteristic
544C4#6430611yescharacteristic
545C3—21no—
546C3#7993211yescharacteristic, complemented
547C3#8158811yescharacteristic, complemented
548C2—242no—
549C2—721no—
550C2#1059390111yescharacteristic
551C2C2×D3×#20411yescharacteristic
552C2#1059467811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4×C8D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. C4×#3744C2semidirect
4. C3×#4694C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590879C2semidirect
7. #10590878C2semidirect
8. #10590757C2semidirect
9. #10590744C2semidirect
10. #10590377C2semidirect
11. #10590300C2semidirect
60. #4694D3semidirect
65. C8×Dic6D3semidirect
177. #634#41semidirect
186. C3×Dic6SD16semidirect
392. Dic6#204semidirect
484. C32#3362semidirect
546. C3#79932semidirect
547. C3#81588semidirect

Maximal subgroups

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

subgroupindex
#105939002
#105938562
C4×#37442
C3×#46942
C3×C8×Dic62
#105908792
#105908782
#105907572
#105907442
#105903772
#105903002
#815883
#799323