Finite Group Databasebeta

← #11895976

Subgroups — #11895976

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593900C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590882C212yesmaximal, complemented
7#10590879C212yesmaximal, complemented
8#10590772C212yesmaximal, complemented
9#10590747C212yesmaximal, complemented
10#10590377C211yesmaximal, characteristic, complemented
11#10590313C211yesmaximal, characteristic, complemented
12#81590—31nomaximal
13#79980—31nomaximal
14C2×#3796—21no—
15C2×#3744C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#874C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63916—21no—
22#63911C2212yes—
23Dic3×D12C2212yes—
24#63886—22no—
25#63873—21no—
26#63869C2212yes—
27#63847—22no—
28#63844C2212yes—
29#63843—21no—
30C2×#3716C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63644C2211yescharacteristic
34#63643C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×#815C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63564C2212yes—
42#63563C2212yes—
43#5721—31no—
44#5718—31no—
45#5577—31no—
46#5567—31no—
47C3×#486—31no—
48C3×#446—31no—
49#5087—31no—
50#5075—31no—
51#4848—31no—
52#4848—32no—
53#4847—32no—
54#4846—31no—
55#4764—32no—
56#4763—32no—
57#4762—32no—
58#4757—32no—
59#4713—32no—
60#4710—32no—
61#4694D311yescharacteristic, complemented
62C4×#204—31no—
63C4×#204—31no—
64C4×#204—61no—
65#4679D311yescharacteristic, 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×#626—22no—
75C2×#626—22no—
76C2×D3×Dic3—22no—
77#3796—44no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C42C2311yescharacteristic
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3—21no—
86#3744—22no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3724—22no—
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3716—24no—
99#3368—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C3×C4⋊Q8—31no—
103C3×#127—31no—
104C3×C4×Q8—31no—
105Q8×Dic3—61no—
106#944—61no—
107#944—61no—
108#940—32no—
109#939—62no—
110#938—61no—
111D4×Dic3—32no—
112C2×#214—32no—
113C2×#204—32no—
114C2×#204—31no—
115C2×#204—31no—
116C2×#204—61no—
117#895—62no—
118#895—61no—
119#890—32no—
120#889—62no—
121#889—62no—
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#870—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×#97—32no—
142C3×C4×C8—21no—
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#818—32no—
154#817—31no—
155#817—31no—
156#817—61no—
157#816—31no—
158#816—31no—
159#816—61no—
160#815C2×D312yes—
161Dic3⋊C8C2×D312yes—
162#809—32no—
163#807—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—22no—
186C3×Dic6—42no—
187#626—44no—
188#626—82no—
189D3×Dic3—44no—
190C32×C8—21no—
191C32×C8—21no—
192C3×C3⋊C8—22no—
193#557—91no—
194#550—91no—
195#490—92no—
196#486—31no—
197#478—92no—
198#474—91no—
199#460—92no—
200#460—91no—
201#446—31no—
202#440—92no—
203C4×SD16—91no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C2×C3×D4—32no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C2×#67—62no—
210C2×#67—62no—
211C22×Dic3—62no—
212#239—124no—
213#237—124no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—31no—
217C2×D12—31no—
218C2×D12—61no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12C22×D312yes—
222C2×C4×D3—62no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—121no—
226C2×Dic6—21no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—61no—
230C2×Dic6D1211yescharacteristic
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—32no—
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C2×C3×C8C22×D311yescharacteristic
238C3×C4⋊C4—31no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—61no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—62no—
247#214—64no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—121no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3D1211yescharacteristic
261C4⋊Dic3C22×D312yes—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—121no—
270Dic3⋊C4D1212yes—
271C4×Dic3—62no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—62no—
275C4×Dic3—121no—
276C4×Dic3C22×D312yes—
277C2×C3⋊C8C22×D312yes—
278#204—62no—
279#204—62no—
280#204—64no—
281#204—64no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C32×C4—21no—
290C32×C4AGL(1,ℤ/8)12yes—
291C32×C4C2×#4111yescharacteristic
292C32×C42−1+411yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C3×Dic3—22no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C2×#41—181no—
300C2×SD16—92no—
301C2×SD16—91no—
302C4⋊Q8—31no—
303C4⋊Q8—181no—
304#127—31no—
305#127—92no—
306#125—92no—
307#125—182no—
308#121—181no—
309#121—182no—
310C4×Q8—31no—
311C4×Q8—92no—
312C4×Q8—91no—
313C4×Q8—181no—
314C4×D4—92no—
315C4×D4—91no—
316#107—92no—
317#106—91no—
318C4⋊C8—32no—
319C4⋊C8—31no—
320#103—91no—
321#102—32no—
322#102—32no—
323#102—92no—
324#102—92no—
325#102—91no—
326#97—32no—
327C4×C8D3211yescharacteristic
328C23×C3—62no—
329C22×D3—22no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—121no—
333C3×Q8—62no—
334C3×Q8—122no—
335C3×D4—62no—
336C3×D4—62no—
337C3×D4—122no—
338C3×D4—241no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—62no—
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351#67—124no—
352#67—242no—
353C2×Dic3—22no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—124no—
364C2×Dic3C2×D1212yes—
365C2×Dic3C2×D1212yes—
366D12—22no—
367D12—22no—
368D12—42no—
369D12—62no—
370D12—61no—
371D12—61no—
372D12—61no—
373D12—61no—
374D12—81no—
375D12—121no—
376D12—124no—
377D12—242no—
378C4×D3—124no—
379C4×D3—122no—
380C4×D3—122no—
381C4×D3—242no—
382Dic6—22no—
383Dic6—32no—
384Dic6—32no—
385Dic6—42no—
386Dic6—62no—
387Dic6—61no—
388Dic6—61no—
389Dic6—121no—
390C3×C8—22no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—41no—
396C3×C8—62no—
397C3⋊C8—22no—
398C2×C32#54811yescharacteristic
399C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
400C2×C32#57711yescharacteristic
401C3⋊D3—81no—
402C3×D3—82no—
403#41—364no—
404C2×Q8—31no—
405C2×Q8—61no—
406C2×Q8—91no—
407C2×D4—32no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—91no—
411C2×D4—182no—
412C2×D4—182no—
413C22×C4—182no—
414C22×C4—181no—
415SD16—182no—
416SD16—184no—
417C2×C8—32no—
418C2×C8C2×D3211yescharacteristic
419C2×C8C2×D3211yescharacteristic
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—32no—
423C4⋊C4—61no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—182no—
427C4⋊C4—182no—
428C4⋊C4—182no—
429C4⋊C4—181no—
430C22⋊C4—182no—
431C22⋊C4—181no—
432C42—32no—
433C42—182no—
434C42—181no—
435C42C2×D3211yescharacteristic
436C22×C3—21no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3C22×D1211yescharacteristic
441C22×C3C2×D3×D411yescharacteristic
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—122no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—241no—
453C2×D3—241no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—41no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—122no—
463C3×C4#90812yes—
464C3×C4#91112yes—
465C3×C4#100711yescharacteristic
466C3×C4D3×#4111yescharacteristic
467C3×C4D3×#4111yescharacteristic
468C3×C4#101011yescharacteristic
469Dic3—22no—
470Dic3—22no—
471Dic3—42no—
472Dic3—62no—
473Dic3—62no—
474Dic3—122no—
475Dic3—121no—
476Dic3—121no—
477Dic3—121no—
478Dic3—121no—
479Dic3—241no—
480Dic3—241no—
481C32#336811yescharacteristic, complemented, Sylow
482C23—62no—
483C23—181no—
484Q8—62no—
485Q8—92no—
486Q8—122no—
487Q8—181no—
488D4—62no—
489D4—62no—
490D4—122no—
491D4—181no—
492D4—181no—
493D4—241no—
494D4—364no—
495D4—722no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—364no—
503C2×C4—362no—
504C2×C4D3×D1211yescharacteristic
505C2×C4D3×D1211yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—21no—
508C8—21no—
509C8—62no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—242no—
514C2×C3#557611yescharacteristic
515C2×C3#567711yescharacteristic
516C2×C3C2×#90811yescharacteristic
517C2×C3#575111yescharacteristic
518C2×C3C2×#91111yescharacteristic
519C2×C3#576211yescharacteristic
520D3—82no—
521D3—242no—
522D3—241no—
523D3—241no—
524C22—122no—
525C22—122no—
526C22—122no—
527C22—361no—
528C22—361no—
529C22—361no—
530C22C2×D3×D1211yescharacteristic
531C4—21no—
532C4—62no—
533C4—62no—
534C4—122no—
535C4—182no—
536C4—361no—
537C4—361no—
538C4#6379512yes—
539C4#6429711yescharacteristic
540C4#6430611yescharacteristic
541C3—21no—
542C3#7998011yescharacteristic, complemented
543C3#8159011yescharacteristic, complemented
544C2—242no—
545C2—721no—
546C2#1059390111yescharacteristic
547C2C2×#6379511yescharacteristic
548C2#1059467711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4×C8D32
hypocenterC32#3368
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. #10593864C2semidirect
3. C4×#3744C2semidirect
4. C3×#4694C2semidirect
5. C3×#4679C2semidirect
6. #10590882C2semidirect
7. #10590879C2semidirect
8. #10590772C2semidirect
9. #10590747C2semidirect
10. #10590377C2semidirect
11. #10590313C2semidirect
61. #4694D3semidirect
65. #4679D3semidirect
177. #634#41semidirect
481. C32#3368semidirect
542. C3#79980semidirect
543. C3#81590semidirect

Maximal subgroups

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

subgroupindex
#105939002
#105938642
C4×#37442
C3×#46942
C3×#46792
#105908822
#105908792
#105907722
#105907472
#105903772
#105903132
#815903
#799803