Finite Group Databasebeta

← #11868791

Subgroups — #11868791

Order 1152.

1248 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic
2C2×#64097C211yesmaximal, characteristic, complemented
3C32×#428C211yesmaximal, characteristic, complemented
4#10592832C211yesmaximal, characteristic
5#10592817C211yesmaximal, characteristic, complemented
6#10592694C211yesmaximal, characteristic, complemented
7#10592665C211yesmaximal, characteristic
8#10592589C212yesmaximal, complemented
9#10592574C212yesmaximal, complemented
10#10592569C212yesmaximal, complemented
11#10592553C212yesmaximal, complemented
12#79240—34nomaximal
13C2×#3828C2211yescharacteristic
14C22×#634—21no—
15C2×C32×M16C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750—21no—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22#64102C2211yescharacteristic
23#64102C2211yescharacteristic
24#64097—21no—
25#64097—21no—
26#64097C2212yes—
27#64097C2212yes—
28#64096C2211yescharacteristic
29#64096C2211yescharacteristic
30#64090—21no—
31#64090—21no—
32#64081—21no—
33C42×C3⋊D3—21no—
34C32×#107C2212yes—
35C32×#106C2212yes—
36#63648C2212yes—
37#63643C2212yes—
38#63641C2212yes—
39#63641C2212yes—
40#63637C2212yes—
41#63636C2212yes—
42#63635C2212yes—
43#63634C2212yes—
44#5522—34no—
45C2×#888—34no—
46C3×#428D314yescomplemented
47#5133—34no—
48#5118—34no—
49#4995—34no—
50#4966—34no—
51#4890—38no—
52#4875—38no—
53#4870—38no—
54#4854—38no—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—21no—
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3D411yescharacteristic
60C22×C3⋊Dic3D411yescharacteristic
61#3828—22no—
62#3828Q814yescomplemented
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×#634—22no—
68C2×#634—22no—
69C2×#634—44no—
70C2×#634C2311yescharacteristic
71C32×M16—22no—
72C2×C32×C8C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77C32×C22⋊C4—21no—
78C32×C42—21no—
79#3752—21no—
80#3752—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83#3750—21no—
84#3750—21no—
85#3750—22no—
86#3750—22no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93#3748—22no—
94C2×C3⋊(C3⋊C8)C2312yes—
95#3079—91noSylow
96C2×#235—34no—
97C22×Dic6—64no—
98C2×C3×M16C2×D314yes—
99C3×#117C2×D314yes—
100C2×C3×C4⋊C4C2×D314yes—
101C2×C4⋊Dic3—34no—
102C2×Dic3⋊C4—64no—
103C2×C4×Dic3—34no—
104C2×#208—34no—
105#893—34no—
106#893—34no—
107#888—38no—
108#888—38no—
109#888—64no—
110#888—64no—
111#887—34no—
112#887—34no—
113#67⋊C4—64no—
114#67⋊C4—64no—
115#872—64no—
116C42×D3—64no—
117C3×#107C2×D318yes—
118C3×#106C2×D318yes—
119#821—38no—
120#816—38no—
121Dic3⋊C8—38no—
122Dic3⋊C8—38no—
123#810—38no—
124#809—38no—
125#808—38no—
126#807—38no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—22no—
132C2×C32×C4—42no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×Q812yes—
135C2×C32×C4#4112yes—
136C2×C32×C4C2411yescharacteristic
137#638—24no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—42no—
143C2×C3⋊Dic3C2×D411yescharacteristic
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C2×Q812yescomplemented
149C4×C3⋊D3—24no—
150C4×C3⋊D3—42no—
151C4×C3⋊D3—42no—
152#634—21no—
153#634—44no—
154#634—44no—
155#634C2×Q812yescomplemented
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158C2×C4⋊Q8—91no—
159C4×#41—91no—
160#477—92no—
161#476—92no—
162#475—92no—
163#474—92no—
164#428—91no—
165#428C3⋊D311yescharacteristic, complemented
166#423—91no—
167#417—91no—
168#417—91no—
169C22×C3×C4—24no—
170C22×C3×C4C22×D314yes—
171C2×#67—64no—
172C22×Dic3—34no—
173C22×Dic3—34no—
174C22×Dic3—64no—
175#235—316no—
176#235—68no—
177C2×D12—34no—
178C2×C4×D3—64no—
179C2×C4×D3—64no—
180C2×C4×D3—64no—
181C2×Dic6—34no—
182C2×Dic6—68no—
183C2×Dic6—68no—
184C2×Dic6—1216no—
185C3×M16—28no—
186C2×C3×C8C22×D318yes—
187C3×C4⋊C4—24no—
188C3×C4⋊C4C22×D314yes—
189C3×C4⋊C4C22×D314yes—
190C3×C4⋊C4C22×D318yes—
191C3×C22⋊C4—24no—
192C3×C42—24no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—64no—
195C4⋊Dic3—38no—
196C4⋊Dic3—64no—
197Dic3⋊C4—64no—
198Dic3⋊C4—64no—
199Dic3⋊C4—68no—
200Dic3⋊C4—68no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—34no—
205C4×Dic3—64no—
206C4×Dic3—64no—
207#208—68no—
208C2×C3⋊C8—38no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32C22⋊Q812yes—
212C22×C32C22×D411yescharacteristic
213C2×C3⋊D3—22no—
214C2×C3⋊D3—41no—
215C2×C3⋊D3—41no—
216C32×C4—42no—
217C32×C4—41no—
218C32×C4—41no—
219C32×C4C22⋊Q812yes—
220C32×C4C22×Q811yescharacteristic
221C32×C4C2×#4111yescharacteristic
222C3⋊Dic3—22no—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—42no—
226C3⋊Dic3AGL(1,ℤ/8)12yes—
227C3⋊Dic3#13712yes—
228C2×#41—91no—
229C22×Q8—181no—
230C2×M16—91no—
231C2×M16C2×C3⋊D311yescharacteristic
232C4⋊Q8—92no—
233C4⋊Q8—92no—
234C4⋊Q8—181no—
235C4⋊Q8—181no—
236C4×Q8—91no—
237C4×Q8—91no—
238C4×D4—91no—
239C4×D4—91no—
240C4×D4—181no—
241C4×D4—181no—
242#117—181no—
243#117C2×C3⋊D311yescharacteristic
244C2×C4⋊C4—91no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4C2×C3⋊D311yescharacteristic
247C2×C42—91no—
248C2×C42—181no—
249#107—92no—
250#107C2×C3⋊D312yes—
251#106—92no—
252#106C2×C3⋊D312yes—
253C4⋊C8—92no—
254C4⋊C8—92no—
255#103—92no—
256#103—92no—
257#102—92no—
258#102—92no—
259C23×C3D3×D414yes—
260C22×D3—64no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—28no—
264C2×C3×C4—48no—
265C2×C3×C4#23518yes—
266C2×C3×C4D3×D414yes—
267C2×C3×C4D3×Q818yes—
268C2×C3×C4C23×D314yes—
269#67—616no—
270C2×Dic3—34no—
271C2×Dic3—34no—
272C2×Dic3—34no—
273C2×Dic3—34no—
274C2×Dic3—68no—
275C2×Dic3—68no—
276C2×Dic3—64no—
277C2×Dic3—68no—
278C2×Dic3—128no—
279D12—38no—
280D12—64no—
281C4×D3—616no—
282C4×D3—128no—
283C4×D3—128no—
284Dic6—38no—
285Dic6—64no—
286Dic6—1216no—
287Dic6—1216no—
288C3×C8—28no—
289C3⋊C8—68no—
290C2×C32—22no—
291C2×C32C2×C22⋊Q811yescharacteristic
292C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
293C2×C32C2×#13711yescharacteristic
294C3⋊D3—42no—
295#41—94no—
296#41—182no—
297C2×Q8—91no—
298C2×Q8—182no—
299C2×Q8—182no—
300C2×Q8—364no—
301C2×D4—91no—
302C2×D4—181no—
303C22×C4—21no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—181no—
307C22×C4—181no—
308C22×C4—181no—
309C22×C4—181no—
310C22×C4C22×C3⋊D311yescharacteristic
311M16—22no—
312M16—182no—
313C2×C8—92no—
314C2×C8C22×C3⋊D312yes—
315C4⋊C4—21no—
316C4⋊C4—92no—
317C4⋊C4—182no—
318C4⋊C4—182no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4C22×C3⋊D312yes—
323C4⋊C4C22×C3⋊D311yescharacteristic
324C4⋊C4C22×C3⋊D311yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C42—21no—
329C42—91no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—181no—
334C42—181no—
335C22×C3—24no—
336C22×C3—24no—
337C22×C3#89618yes—
338C22×C3C2×D3×D414yes—
339C2×D3—68no—
340C2×D3—124no—
341C2×D3—124no—
342C3×C4—48no—
343C3×C4—44no—
344C3×C4—44no—
345C3×C4#89618yes—
346C3×C4C2×#23514yes—
347C3×C4C2×D3×Q814yes—
348Dic3—38no—
349Dic3—38no—
350Dic3—68no—
351Dic3—64no—
352Dic3—64no—
353Dic3—128no—
354C32#307911yescharacteristic, complemented, Sylow
355C23—181no—
356C23D4×C3⋊D311yescharacteristic
357Q8—92no—
358Q8—181no—
359Q8—364no—
360Q8—364no—
361D4—92no—
362D4—184no—
363D4—181no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—42no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—181no—
375C2×C4—184no—
376C2×C4—182no—
377C2×C4—362no—
378C2×C4—362no—
379C2×C4—362no—
380C2×C4#382812yes—
381C2×C4D4×C3⋊D311yescharacteristic
382C2×C4Q8×C3⋊D312yes—
383C2×C4C23×C3⋊D311yescharacteristic
384C8—22no—
385C8—182no—
386C2×C3—28no—
387C2×C3C2×#89614yes—
388C2×C3D3×AGL(1,ℤ/8)14yes—
389C2×C3D3×#13714yes—
390D3—128no—
391C22—21no—
392C22—21no—
393C22—182no—
394C22—361no—
395C22—361no—
396C22#6410512yes—
397C22C2×D4×C3⋊D311yescharacteristic
398C4—42no—
399C4—41no—
400C4—41no—
401C4—92no—
402C4—92no—
403C4—182no—
404C4—181no—
405C4—181no—
406C4—362no—
407C4#6410512yes—
408C4C2×#382811yescharacteristic
409C4C2×Q8×C3⋊D311yescharacteristic
410C3#7924014yescomplemented
411C2—22no—
412C2—362no—
413C2C2×#6410511yescharacteristic
414C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
415C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenter#428C3⋊D3
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. C2×#64097C2semidirect
3. C32×#428C2semidirect
5. #10592817C2semidirect
6. #10592694C2semidirect
8. #10592589C2semidirect
9. #10592574C2semidirect
10. #10592569C2semidirect
11. #10592553C2semidirect
46. C3×#428D3semidirect
62. #3828Q8semidirect
148. C4⋊(C3⋊D3)C2×Q8semidirect
155. #634C2×Q8semidirect
165. #428C3⋊D3semidirect
354. C32#3079semidirect
410. C3#79240semidirect

Maximal subgroups

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

subgroupindex
#105959932
C2×#640972
C32×#4282
#105928322
#105928172
#105926942
#105926652
#105925892
#105925742
#105925692
#105925532
#792403