Finite Group Databasebeta

← #13081670

Subgroups — #13081670

Order 1408.

362 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623098C211yesmaximal, characteristic, complemented
2#10623090C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622788C211yesmaximal, characteristic
5#10622780C211yesmaximal, characteristic, complemented
6#10622641C211yesmaximal, characteristic, complemented
7#10622632C211yesmaximal, characteristic, complemented
8#10622502C211yesmaximal, characteristic, complemented
9#10622486C211yesmaximal, characteristic, complemented
10#10622431C211yesmaximal, characteristic, complemented
11#10622406C211yesmaximal, characteristic, complemented
12#10622380C211yesmaximal, characteristic, complemented
13#10622375C211yesmaximal, characteristic
14#10622328C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66997C2211yescharacteristic
20#66997C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993C2211yescharacteristic
24#66989C2211yescharacteristic
25C2×#4324C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27#66982—21no—
28C4×C22⋊D11—21no—
29C2×Dic44C2211yescharacteristic
30C2×Dic44C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32C2×#4314C2211yescharacteristic
33#66946C2211yescharacteristic
34#66942—21no—
35#66942—21no—
36#66940C2211yescharacteristic
37#66940C2211yescharacteristic
38#66940C2211yescharacteristic
39#66938—21no—
40#66936—21no—
41#66928C2211yescharacteristic
42#66923—21no—
43#66922C2211yescharacteristic
44C4×Dic22—21no—
45C4×Dic22C2211yescharacteristic
46C11×#107C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#102C2211yescharacteristic
49C11×#97C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66873C2211yescharacteristic
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×Dic22D411yescharacteristic
67C2×Dic22C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C11×SD16—22no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81#4326—41no—
82#4325—41no—
83#4324—41no—
84#4324—41no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11D411yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107Dic44—22no—
108Dic44—41no—
109#4314—22no—
110#4314—41no—
111#3400—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114Q8×C11—21no—
115Q8×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—81no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—42no—
126C22⋊D11—81no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136C4×D11—81no—
137Dic22—22no—
138Dic22—21no—
139Dic22—21no—
140Dic22—21no—
141Dic22—21no—
142Dic22—21no—
143Dic22—21no—
144C8×C11—21no—
145C8×C11#4112yes—
146C11⋊C8—21no—
147C11⋊C8—21no—
148#559—111no—
149#557—111no—
150#497—111no—
151#497—111no—
152#492—111no—
153#464—111no—
154#464—111no—
155#462—111no—
156#461—111no—
157#461—111no—
158#460—111no—
159#446—111no—
160#440—111no—
161#440D1111yescharacteristic, complemented
162C4×Q16—111no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×D411yescharacteristic
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C11H(5,𝔽2)11yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11#13712yes—
184C2×Q16—111no—
185C2×Q16—111no—
186C2×Q16—111no—
187C2×SD16—111no—
188C2×SD16—111no—
189C2×SD16—111no—
190C2×SD16—111no—
191C2×SD16—111no—
192C2×SD16C2×D1111yescharacteristic
193C4⋊Q8—111no—
194C4⋊Q8—111no—
195C4⋊Q8—111no—
196#127—111no—
197#125—221no—
198#125—221no—
199#125—221no—
200#124—111no—
201#124—111no—
202#124—221no—
203#123—221no—
204#123—221no—
205C4×Q8—111no—
206C4×Q8—111no—
207C4×Q8—111no—
208C4×Q8—111no—
209C4×Q8—221no—
210C4×Q8C2×D1111yescharacteristic
211C4×D4—111no—
212C4×D4—221no—
213C4×D4C2×D1111yescharacteristic
214#107C2×D1111yescharacteristic
215C4⋊C8—111no—
216C4⋊C8—111no—
217C4⋊C8—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103C2×D1111yescharacteristic
222#102—111no—
223#102C2×D1111yescharacteristic
224#97—111no—
225#97C2×D1111yescharacteristic
226C4×C8—111no—
227C2×C11—81no—
228C2×C11#55011yescharacteristic
229C2×C11C2×#13711yescharacteristic
230C2×C11#57711yescharacteristic
231D11—81no—
232C2×Q8—111no—
233C2×Q8—111no—
234C2×Q8—111no—
235C2×Q8—111no—
236C2×Q8C22×D1111yescharacteristic
237C2×D4—111no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4C22×D1111yescharacteristic
241C22×C4—21no—
242C22×C4—221no—
243Q16—222no—
244Q16—441no—
245Q16—441no—
246SD16—22no—
247SD16—222no—
248SD16—441no—
249SD16—441no—
250SD16—441no—
251SD16—441no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4C22×D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C42—21no—
278C42—111no—
279C42—111no—
280C42—221no—
281C42—221no—
282C42—221no—
283C42C22×D1111yescharacteristic
284C11#340011yescharacteristic, complemented, Sylow
285C23—21no—
286C23—221no—
287Q8—21no—
288Q8—21no—
289Q8—222no—
290Q8—221no—
291Q8—221no—
292Q8—221no—
293Q8—221no—
294Q8—221no—
295Q8—221no—
296D4—21no—
297D4—21no—
298D4—221no—
299D4—221no—
300D4—442no—
301D4—881no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—81no—
306C2×C4—111no—
307C2×C4—111no—
308C2×C4—111no—
309C2×C4—111no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—881no—
314C2×C4D4×D1111yescharacteristic
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—221no—
319C8—221no—
320C8#433912yes—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22C2×D4×D1111yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—112no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4—441no—
338C4—441no—
339C4—441no—
340C4C2×#433911yescharacteristic
341C4#6704211yescharacteristic
342C2—81no—
343C2—881no—
344C2#1062308411yescharacteristic
345C2#1062330611yescharacteristic
346C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#66993C22
hypercenter#440D11
hypocenterC11#3400
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. #10623098C2semidirect
3. C11×#440C2semidirect
5. #10622780C2semidirect
6. #10622641C2semidirect
7. #10622632C2semidirect
8. #10622502C2semidirect
9. #10622486C2semidirect
10. #10622431C2semidirect
11. #10622406C2semidirect
12. #10622380C2semidirect
14. #10622328C2semidirect
15. #10622314C2semidirect
161. #440D11semidirect
284. C11#3400semidirect

Maximal subgroups

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

subgroupindex
#106230982
#106230902
C11×#4402
#106227882
#106227802
#106226412
#106226322
#106225022
#106224862
#106224312
#106224062
#106223802
#106223752
#106223282
#106223142
#340011