Finite Group Databasebeta

← #13081431

Subgroups — #13081431

Order 1408.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic22C211yesmaximal, characteristic, complemented
2#10623090C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622779C211yesmaximal, characteristic, complemented
5#10622776C211yesmaximal, characteristic
6#10622641C211yesmaximal, characteristic, complemented
7#10622620C211yesmaximal, characteristic, complemented
8#10622503C211yesmaximal, characteristic, complemented
9#10622488C211yesmaximal, characteristic, complemented
10#10622430C211yesmaximal, characteristic, complemented
11#10622403C211yesmaximal, characteristic, complemented
12#10622378C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic
14#10622327C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993C2211yescharacteristic
24#66989C2211yescharacteristic
25#66982—21no—
26C4×C22⋊D11—21no—
27#66946C2211yescharacteristic
28#66941—21no—
29#66941—21no—
30#66941C2211yescharacteristic
31#66941C2211yescharacteristic
32#66940C2211yescharacteristic
33#66938—21no—
34#66936—21no—
35#66928C2211yescharacteristic
36#66922—21no—
37#66922C2211yescharacteristic
38C4×Dic22—21no—
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22D411yescharacteristic
70C2×Dic22C2311yescharacteristic
71C11×SD16—22no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C42×C11—21no—
79C42×C11C2311yescharacteristic
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82#4326—22no—
83#4325—22no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11D411yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3375—111nomaximal, Sylow
106C23×C11—21no—
107C22×D11—21no—
108Q8×C11—21no—
109Q8×C11#4112yes—
110D4×C11—21no—
111D4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—81no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—42no—
120C22⋊D11—81no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128D44—21no—
129D44—21no—
130C4×D11—81no—
131Dic22—22no—
132Dic22—21no—
133Dic22—21no—
134Dic22—81no—
135Dic22—81no—
136Dic22—81no—
137C8×C11—21no—
138C8×C11—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141#559—111no—
142Q82—111no—
143#489—111no—
144#489—111no—
145#486—111no—
146#477—111no—
147#474—111no—
148#474—111no—
149#464—111no—
150#464—111no—
151#460—111no—
152#446—111no—
153#440—111no—
154#440D1111yescharacteristic, complemented
155C4×Q16—111no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11C22×D411yescharacteristic
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C4×C11—22no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11C2×#4111yescharacteristic
169C4×C112−1+411yescharacteristic
170Dic11—21no—
171Dic11—21no—
172Dic11—21no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11#13712yes—
177C2×Q16—111no—
178C2×SD16—111no—
179C2×SD16C2×D1111yescharacteristic
180C4⋊Q8—111no—
181C4⋊Q8—111no—
182C4⋊Q8—111no—
183C4⋊Q8—221no—
184C4⋊Q8—221no—
185C4⋊Q8—221no—
186#127—111no—
187#124—111no—
188#124—111no—
189#124—221no—
190#123—221no—
191#123—221no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×Q8—221no—
197C4×Q8C2×D1111yescharacteristic
198C4×D4—111no—
199C4×D4—221no—
200C4×D4C2×D1111yescharacteristic
201#107—111no—
202#107—111no—
203#107C2×D1111yescharacteristic
204C4⋊C8—111no—
205C4⋊C8—111no—
206C4⋊C8—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103C2×D1111yescharacteristic
211#102—111no—
212#102—111no—
213#102—111no—
214#102—111no—
215#102—111no—
216#102C2×D1111yescharacteristic
217#97—111no—
218#97C2×D1111yescharacteristic
219C4×C8—111no—
220C2×C11—81no—
221C2×C11#54811yescharacteristic
222C2×C11C2×#13711yescharacteristic
223C2×C11#57611yescharacteristic
224D11—81no—
225C2×Q8—111no—
226C2×Q8—111no—
227C2×Q8—221no—
228C2×Q8—221no—
229C2×Q8—221no—
230C2×Q8C22×D1111yescharacteristic
231C2×D4—111no—
232C2×D4—221no—
233C2×D4—221no—
234C2×D4C22×D1111yescharacteristic
235C22×C4—21no—
236C22×C4—221no—
237Q16—222no—
238SD16—22no—
239SD16—222no—
240C2×C8—111no—
241C2×C8—111no—
242C2×C8C22×D1111yescharacteristic
243C2×C8C22×D1111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4C22×D1111yescharacteristic
257C4⋊C4C22×D1111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—21no—
265C42—111no—
266C42—111no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42C22×D1111yescharacteristic
271C11#337511yescharacteristic, complemented, Sylow
272C23—21no—
273C23—221no—
274Q8—21no—
275Q8—222no—
276Q8—221no—
277Q8—221no—
278Q8—881no—
279Q8—881no—
280Q8—881no—
281Q8#433912yes—
282D4—21no—
283D4—21no—
284D4—221no—
285D4—221no—
286D4—442no—
287D4—881no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—881no—
300C2×C4D4×D1111yescharacteristic
301C2×C4D4×D1111yescharacteristic
302C2×C4C23×D1111yescharacteristic
303C8—21no—
304C8—21no—
305C8—221no—
306C8—221no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—441no—
311C22—441no—
312C22—441no—
313C22C2×D4×D1111yescharacteristic
314C4—21no—
315C4—21no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—112no—
320C4—221no—
321C4—221no—
322C4—221no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4C2×#433911yescharacteristic
327C4#6704311yescharacteristic
328C2—81no—
329C2—881no—
330C2#1062308311yescharacteristic
331C2#1062330511yescharacteristic
332C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#66993C22
hypercenter#440D11
hypocenterC11#3375
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. Q8×Dic22C2semidirect
3. C11×#440C2semidirect
4. #10622779C2semidirect
6. #10622641C2semidirect
7. #10622620C2semidirect
8. #10622503C2semidirect
9. #10622488C2semidirect
10. #10622430C2semidirect
11. #10622403C2semidirect
12. #10622378C2semidirect
14. #10622327C2semidirect
15. #10622314C2semidirect
154. #440D11semidirect
271. C11#3375semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic222
#106230902
C11×#4402
#106227792
#106227762
#106226412
#106226202
#106225032
#106224882
#106224302
#106224032
#106223782
#106223732
#106223272
#106223142
#337511