Finite Group Databasebeta

← #13078980

Subgroups — #13078980

Order 1408.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623220C211yesmaximal, characteristic, complemented
2#10623206C211yesmaximal, characteristic
3C11×#488C211yesmaximal, characteristic, complemented
4#10622682C211yesmaximal, characteristic, complemented
5#10622668C211yesmaximal, characteristic, complemented
6#10622415C211yesmaximal, characteristic, complemented
7D11×#103C211yesmaximal, characteristic, complemented
8#10622410C211yesmaximal, characteristic, complemented
9#10622405C211yesmaximal, characteristic, complemented
10#10622385C211yesmaximal, characteristic
11#10622384C211yesmaximal, characteristic
12#10622381C211yesmaximal, characteristic, complemented
13#10622378C211yesmaximal, characteristic, complemented
14#10622302C211yesmaximal, characteristic, complemented
15#10622294C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C11×#125C2211yescharacteristic
19C11×#124C2211yescharacteristic
20#66997C2211yescharacteristic
21#66989C2211yescharacteristic
22C2×#4313C2211yescharacteristic
23C2×C8×D11C2211yescharacteristic
24#66950—21no—
25#66949—21no—
26#66945C2211yescharacteristic
27C4⋊C4×D11C2211yescharacteristic
28#66943C2211yescharacteristic
29#66942—21no—
30#66941—21no—
31#66941C2211yescharacteristic
32#66936—21no—
33#66936—21no—
34#66931—21no—
35#66931—21no—
36#66925C2211yescharacteristic
37#66922C2211yescharacteristic
38#66922C2211yescharacteristic
39C11×#103C2211yescharacteristic
40C11×#103C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C4×C8×C11C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66874C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C22×Dic11—21no—
63Q8×D11—22no—
64Q8×D11—22no—
65#4341—22no—
66#4341—22no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11C2311yescharacteristic
70C2×Dic22—21no—
71C2×Dic22—21no—
72C2×Dic22—21no—
73C2×Dic22C2311yescharacteristic
74C2×Dic22C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C42×C11C2311yescharacteristic
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4D411yescharacteristic
88(C2×D11)⋊C4D411yescharacteristic
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3137—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113D4×C11—21no—
114D4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—42no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—42no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C4×D11—42no—
131C4×D11—81no—
132C4×D11#4112yes—
133C4×D11#4112yes—
134Dic22—21no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22—42no—
139Dic22—81no—
140Dic22—81no—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145#544—111no—
146#536—111no—
147#491—111no—
148#491—111no—
149#489—111no—
150#489—111no—
151#488—111no—
152#488D1111yescharacteristic, complemented
153#487—111no—
154#487—111no—
155#419—111no—
156#417—111no—
157#416—111no—
158C2×#103—111no—
159#405—111no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11#12412yes—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11C2×#4111yescharacteristic
173C4×C11C2×#4111yescharacteristic
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180Dic11#12412yes—
181C2×#41—111no—
182C22×Q8—111no—
183C2×M16—111no—
184C22×C8—111no—
185C4⋊Q8—111no—
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188C4⋊Q8—111no—
189C4⋊Q8—221no—
190#125—111no—
191#125—221no—
192#125C2×D1111yescharacteristic
193#124—111no—
194#124C2×D1111yescharacteristic
195#123—221no—
196#123—221no—
197C22⋊Q8—221no—
198C22⋊Q8—221no—
199C22⋊Q8—221no—
200C22⋊Q8—221no—
201#117—111no—
202#117—111no—
203C2×C4⋊C4—111no—
204#103—111no—
205#103—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#103C2×D1111yescharacteristic
215#103C2×D1111yescharacteristic
216#102—111no—
217#102—111no—
218#102C2×D1111yescharacteristic
219#102C2×D1111yescharacteristic
220#97—111no—
221#97—111no—
222C4×C8—111no—
223C4×C8C2×D1111yescharacteristic
224C2×C11—81no—
225C2×C11C2×#12411yescharacteristic
226C2×C11#57711yescharacteristic
227C2×C11#57811yescharacteristic
228D11—22no—
229#41—222no—
230#41—222no—
231C2×Q8—111no—
232C2×Q8—111no—
233C2×Q8—221no—
234C2×Q8—221no—
235C2×Q8—222no—
236C2×Q8—222no—
237C2×Q8—221no—
238C2×Q8C22×D1111yescharacteristic
239C2×D4—221no—
240C2×D4C22×D1111yescharacteristic
241C22×C4—111no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245M16—222no—
246C2×C8—111no—
247C2×C8—111no—
248C2×C8—222no—
249C2×C8C22×D1111yescharacteristic
250C2×C8C22×D1111yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4C22×D1111yescharacteristic
267C4⋊C4C22×D1111yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—111no—
271C22⋊C4—111no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C42—111no—
276C42—221no—
277C42C22×D1111yescharacteristic
278C11#313711yescharacteristic, complemented, Sylow
279C23—21no—
280C23—111no—
281Q8—21no—
282Q8—21no—
283Q8—221no—
284Q8—221no—
285Q8—221no—
286Q8—221no—
287Q8—442no—
288Q8—881no—
289Q8—881no—
290D4—21no—
291D4—21no—
292D4—442no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—111no—
297C2×C4—112no—
298C2×C4—112no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—881no—
308C2×C4D4×D1111yescharacteristic
309C2×C4D4×D1111yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—21no—
312C8—21no—
313C8—221no—
314C8—221no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—112no—
319C22—221no—
320C22—221no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—112no—
328C4—221no—
329C4—221no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4—441no—
334C4#41×D1111yescharacteristic
335C4#41×D1111yescharacteristic
336C2—81no—
337C2—222no—
338C2D11×#12411yescharacteristic
339C2#1062330111yescharacteristic
340C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#488C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
hypercenter#488D11
hypocenterC11#3137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #10623220C2semidirect
3. C11×#488C2semidirect
4. #10622682C2semidirect
5. #10622668C2semidirect
6. #10622415C2semidirect
7. D11×#103C2semidirect
8. #10622410C2semidirect
9. #10622405C2semidirect
12. #10622381C2semidirect
13. #10622378C2semidirect
14. #10622302C2semidirect
15. #10622294C2semidirect
152. #488D11semidirect
278. C11#3137semidirect

Maximal subgroups

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

subgroupindex
#106232202
#106232062
C11×#4882
#106226822
#106226682
#106224152
D11×#1032
#106224102
#106224052
#106223852
#106223842
#106223812
#106223782
#106223022
#106222942
#313711