Finite Group Databasebeta

← #11868648

Subgroups — #11868648

Order 1152.

1320 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#10595988C211yesmaximal, characteristic, complemented
2C2×#64102C211yesmaximal, characteristic
3C32×#428C211yesmaximal, characteristic, complemented
4#10592830C211yesmaximal, characteristic
5#10592817C211yesmaximal, characteristic, complemented
6#10592700C211yesmaximal, characteristic
7#10592663C211yesmaximal, characteristic, complemented
8#10592590C212yesmaximal, complemented
9#10592589C212yesmaximal, complemented
10#10592570C212yesmaximal, complemented
11#10592569C212yesmaximal, complemented
12#79239—34nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C2×C32×M16C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3752—21no—
19#64135C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22#64102—21no—
23#64102—21no—
24#64102C2212yes—
25#64102C2212yes—
26#64099C2211yescharacteristic, complemented
27#64099C2211yescharacteristic, complemented
28#64097C2211yescharacteristic, complemented
29#64097C2211yescharacteristic, complemented
30#64087—21no—
31#64087—21no—
32C4×#634—21no—
33C4×#634—21no—
34C32×#107C2212yescomplemented
35C32×#106C2212yescomplemented
36#63648C2212yes—
37#63648C2212yes—
38#63641C2212yescomplemented
39#63641C2212yescomplemented
40#63636C2212yes—
41#63636C2212yes—
42#63635C2212yescomplemented
43#63634C2212yescomplemented
44#5517—34no—
45C2×#893—34no—
46C3×#428D314yescomplemented
47#5131—34no—
48#5118—34no—
49#5001—34no—
50#4964—34no—
51#4891—38no—
52#4890—38no—
53#4871—38no—
54#4870—38no—
55C23×C3⋊D3—21no—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3D411yescharacteristic
59C22×C3⋊Dic3D411yescharacteristic
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)Q814yescomplemented
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—44no—
67C2×#634—21no—
68C2×#634—21no—
69C32×M16—22no—
70C2×C32×C8C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2311yescharacteristic
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—21no—
76C32×C42—21no—
77#3757—21no—
78#3752—22no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85#3750—21no—
86#3750—21no—
87#3750—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#3077—91noSylow
96C22×D12—34no—
97C22×C4×D3—64no—
98C2×C3×M16C2×D314yes—
99C3×#117C2×D314yes—
100C2×C3×C4⋊C4C2×D314yes—
101C2×(C2×D3)⋊C4—64no—
102#926—34no—
103C2×C4×Dic3—34no—
104C2×#208—34no—
105#893—38no—
106#893—38no—
107#893—64no—
108#893—64no—
109#890—34no—
110#890—34no—
111#888—34no—
112#888—34no—
113#878—64no—
114#878—64no—
115C4×Dic6—64no—
116C4×Dic6—64no—
117C3×#107C2×D318yescomplemented
118C3×#106C2×D318yescomplemented
119#821—38no—
120#821—38no—
121Dic3⋊C8—38no—
122Dic3⋊C8—38no—
123#809—38no—
124#809—38no—
125#808—38no—
126#807—38no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—24no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—22no—
135C2×C32×C4—42no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×Q812yes—
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)C2×Q814yes—
151C4×C3⋊D3—44no—
152C4×C3⋊D3—44no—
153#634—42no—
154#634—42no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157#533—91no—
158C2×C4×D4—91no—
159#478—92no—
160#478—92no—
161#476—92no—
162#474—92no—
163#428—91no—
164#428C3⋊D311yescharacteristic, complemented
165#423—91no—
166#418—91no—
167#418—91no—
168C23×D3—64no—
169C22×C3×C4—24no—
170C22×C3×C4C22×D314yes—
171C22×Dic3—34no—
172C22×Dic3—34no—
173C2×D12—316no—
174C2×D12—38no—
175C2×D12—68no—
176C2×D12—64no—
177C2×C4×D3—68no—
178C2×C4×D3—68no—
179C2×C4×D3—1216no—
180C2×Dic6—64no—
181C2×Dic6—64no—
182C3×M16—28no—
183C2×C3×C8C22×D318yes—
184C3×C4⋊C4—24no—
185C3×C4⋊C4C22×D318yes—
186C3×C4⋊C4C22×D314yes—
187C3×C4⋊C4C22×D314yes—
188C3×C22⋊C4—24no—
189C3×C42—24no—
190#217—64no—
191(C2×D3)⋊C4—68no—
192(C2×D3)⋊C4—68no—
193C4⋊Dic3—34no—
194C4⋊Dic3—34no—
195C4⋊Dic3—64no—
196C4⋊Dic3—64no—
197Dic3⋊C4—64no—
198Dic3⋊C4—64no—
199Dic3⋊C4—64no—
200Dic3⋊C4—64no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—34no—
205C4×Dic3—64no—
206#208—68no—
207C2×C3⋊C8—38no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32C22⋊Q812yes—
211C22×C32C22×D411yescharacteristic
212C2×C3⋊D3—24no—
213C2×C3⋊D3—48no—
214C2×C3⋊D3—42no—
215C2×C3⋊D3—42no—
216C32×C4—41no—
217C32×C4—42no—
218C32×C4—41no—
219C32×C4C22⋊Q812yes—
220C32×C4C22×Q811yescharacteristic
221C32×C4C2×#4111yescharacteristic
222C3⋊Dic3—21no—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—41no—
226C3⋊Dic3—41no—
227C3⋊Dic3AGL(1,ℤ/8)12yes—
228C22×D4—91no—
229C23×C4—181no—
230C2×M16—91no—
231C2×M16C2×C3⋊D311yescharacteristic
232C4⋊Q8—91no—
233C4⋊Q8—91no—
234#125—91no—
235#125—91no—
236C22⋊Q8—181no—
237C22⋊Q8—181no—
238C4×Q8—181no—
239C4×Q8—181no—
240C4×D4—92no—
241C4×D4—92no—
242C4×D4—181no—
243C4×D4—181no—
244#117—91no—
245#117C2×C3⋊D311yescharacteristic
246C2×C4⋊C4C2×C3⋊D311yescharacteristic
247C2×C22⋊C4—181no—
248C2×C42—91no—
249#107—92no—
250#107C2×C3⋊D312yescomplemented
251#106—92no—
252#106C2×C3⋊D312yescomplemented
253C4⋊C8—92no—
254C4⋊C8—92no—
255#102—92no—
256#102—92no—
257#102—92no—
258#102—92no—
259C23×C3D3×D414yes—
260C22×D3—616no—
261C22×D3—68no—
262C22×D3—128no—
263C22×D3—128no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—28no—
267C2×C3×C4—48no—
268C2×C3×C4#23518yes—
269C2×C3×C4D3×D414yes—
270C2×C3×C4D3×Q818yes—
271C2×C3×C4C23×D314yes—
272C2×Dic3—34no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—68no—
277C2×Dic3—64no—
278C2×Dic3—64no—
279C2×Dic3—124no—
280D12—316no—
281D12—616no—
282D12—68no—
283C4×D3—1216no—
284C4×D3—1216no—
285Dic6—128no—
286Dic6—128no—
287C3×C8—28no—
288C3⋊C8—68no—
289C2×C32—22no—
290C2×C32C2×C22⋊Q811yescharacteristic
291C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
292C2×C32#57511yescharacteristic
293C3⋊D3—44no—
294C24—181no—
295C2×Q8—181no—
296C2×Q8—181no—
297C2×D4—92no—
298C2×D4—94no—
299C2×D4—182no—
300C2×D4—181no—
301C22×C4—21no—
302C22×C4—91no—
303C22×C4—91no—
304C22×C4—182no—
305C22×C4—182no—
306C22×C4—364no—
307C22×C4C22×C3⋊D311yescharacteristic
308M16—22no—
309M16—182no—
310C2×C8—92no—
311C2×C8C22×C3⋊D312yes—
312C4⋊C4—21no—
313C4⋊C4—91no—
314C4⋊C4—91no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4C22×C3⋊D311yescharacteristic
322C4⋊C4C22×C3⋊D311yescharacteristic
323C4⋊C4C22×C3⋊D312yes—
324C22⋊C4—21no—
325C22⋊C4—182no—
326C22⋊C4—182no—
327C22⋊C4—181no—
328C42—21no—
329C42—91no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—181no—
334C22×C3—24no—
335C22×C3—24no—
336C22×C3#89618yes—
337C22×C3C2×D3×D414yes—
338C2×D3—616no—
339C2×D3—1232no—
340C2×D3—128no—
341C2×D3—128no—
342C3×C4—44no—
343C3×C4—48no—
344C3×C4—44no—
345C3×C4#89618yes—
346C3×C4C2×#23514yes—
347C3×C4C2×D3×Q814yes—
348Dic3—38no—
349Dic3—64no—
350Dic3—64no—
351Dic3—64no—
352Dic3—124no—
353Dic3—124no—
354C32#307711yescharacteristic, complemented, Sylow
355C23—182no—
356C23—184no—
357C23—362no—
358C23—362no—
359C23D4×C3⋊D311yescharacteristic
360Q8—362no—
361Q8—362no—
362D4—94no—
363D4—182no—
364D4—184no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—42no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—91no—
373C2×C4—182no—
374C2×C4—181no—
375C2×C4—181no—
376C2×C4—364no—
377C2×C4—364no—
378C2×C4—361no—
379C2×C4#382812yes—
380C2×C4D4×C3⋊D311yescharacteristic
381C2×C4Q8×C3⋊D312yes—
382C2×C4C23×C3⋊D311yescharacteristic
383C8—22no—
384C8—182no—
385C2×C3—28no—
386C2×C3C2×#89614yes—
387C2×C3D3×AGL(1,ℤ/8)14yes—
388C2×C3#577714yes—
389D3—1216no—
390C22—21no—
391C22—21no—
392C22—184no—
393C22—368no—
394C22—362no—
395C22—362no—
396C22#6410512yes—
397C22C2×D4×C3⋊D311yescharacteristic
398C4—42no—
399C4—41no—
400C4—41no—
401C4—92no—
402C4—181no—
403C4—181no—
404C4—181no—
405C4—361no—
406C4—361no—
407C4#6410512yes—
408C4C2×#382811yescharacteristic
409C4C2×Q8×C3⋊D311yescharacteristic
410C3#7923914yescomplemented
411C2—22no—
412C2—364no—
413C2C2×#6410511yescharacteristic
414C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
415C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#428C3⋊D3
hypocenterC32#3077
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
1. #10595988C2semidirect
3. C32×#428C2semidirect
5. #10592817C2semidirect
7. #10592663C2semidirect
8. #10592590C2semidirect
9. #10592589C2semidirect
10. #10592570C2semidirect
11. #10592569C2semidirect
26. #64099C22semidirect
27. #64099C22semidirect
28. #64097C22semidirect
29. #64097C22semidirect
34. C32×#107C22semidirect
35. C32×#106C22semidirect
38. #63641C22semidirect
39. #63641C22semidirect
42. #63635C22semidirect
43. #63634C22semidirect
46. C3×#428D3semidirect
62. C2×C4⋊(C3⋊D3)Q8semidirect
117. C3×#107C2×D3semidirect
118. C3×#106C2×D3semidirect
164. #428C3⋊D3semidirect
250. #107C2×C3⋊D3semidirect
252. #106C2×C3⋊D3semidirect
354. C32#3077semidirect
410. C3#79239semidirect

Maximal subgroups

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

subgroupindex
#105959882
C2×#641022
C32×#4282
#105928302
#105928172
#105927002
#105926632
#105925902
#105925892
#105925702
#105925692
#792393