Finite Group Databasebeta

← #13080892

Subgroups — #13080892

Order 1408.

374 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D11C211yesmaximal, characteristic
2#10623172C211yesmaximal, characteristic
3C11×#451C211yesmaximal, characteristic, complemented
4#10622838C211yesmaximal, characteristic, complemented
5#10622802C211yesmaximal, characteristic, complemented
6#10622799C211yesmaximal, characteristic, complemented
7Q16×Dic11C211yesmaximal, characteristic, complemented
8#10622795C211yesmaximal, characteristic, complemented
9#10622665C211yesmaximal, characteristic, complemented
10#10622427C211yesmaximal, characteristic, complemented
11#10622415C211yesmaximal, characteristic, complemented
12#10622405C211yesmaximal, characteristic, complemented
13#10622404C211yesmaximal, characteristic, complemented
14#10622342C211yesmaximal, characteristic
15#10622336C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21#66999—21no—
22#66999C2211yescharacteristic
23#66999C2211yescharacteristic
24Q8×Dic11C2211yescharacteristic
25Q8×Dic11C2211yescharacteristic
26#66997—21no—
27#66997C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29C4×C22⋊D11—21no—
30C4×C22⋊D11C2211yescharacteristic
31#66979C2211yescharacteristic
32#66977—21no—
33#66977C2211yescharacteristic
34C2×#4318C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36#66951—21no—
37#66945C2211yescharacteristic
38#66941C2211yescharacteristic
39#66940—21no—
40#66938—21no—
41#66932—21no—
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66881C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66874C2211yescharacteristic
58#66872C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C2×Q8×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11D411yescharacteristic
68Q8×D11—22no—
69Q8×D11—41no—
70C2×C4×D11—21no—
71C2×C4×D11C2311yescharacteristic
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22C2311yescharacteristic
75C11×Q16—22no—
76C11×Q16—41no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11D411yescharacteristic
85#4326—41no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4D411yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107#4318—41no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3328—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11C2×D411yescharacteristic
114Q8×C11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—42no—
120Q8×C11#4112yes—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—42no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—22no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—42no—
141Dic22—21no—
142Dic22—21no—
143Dic22—42no—
144Dic22—42no—
145C8×C11—21no—
146C8×C11—21no—
147C11⋊C8—21no—
148C11⋊C8—21no—
149#556—111no—
150D4×Q8—111no—
151#487—111no—
152#485—111no—
153#485—111no—
154#475—111no—
155#470—111no—
156#470—111no—
157#462—111no—
158#451—111no—
159#451D1111yescharacteristic, complemented
160C4×Q16—111no—
161#436—111no—
162#419—111no—
163#419—111no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11C22×D411yescharacteristic
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11C2×#4111yescharacteristic
177C4×C11H(5,𝔽2)11yescharacteristic
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11#13712yes—
185C22×Q8—111no—
186C22×Q8C2×D1111yescharacteristic
187C2×Q16—111no—
188C2×Q16C2×D1111yescharacteristic
189C2×Q16C2×D1111yescharacteristic
190C2×M16—111no—
191C2×M16—111no—
192C4⋊Q8—111no—
193C4⋊Q8—111no—
194C4⋊Q8—221no—
195#126—221no—
196#126—221no—
197#124—221no—
198C22⋊Q8—111no—
199C22⋊Q8—111no—
200C22⋊Q8—111no—
201C22⋊Q8—221no—
202C22⋊Q8—221no—
203C22⋊Q8C2×D1111yescharacteristic
204C4×Q8—111no—
205C4×Q8—111no—
206C4×Q8—221no—
207C4×D4—111no—
208C4×D4—221no—
209#117—111no—
210#117—111no—
211#107—111no—
212#106—111no—
213#106—111no—
214C4⋊C8—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103C2×D1111yescharacteristic
224#103C2×D1111yescharacteristic
225C22⋊C8—111no—
226C22⋊C8C2×D1111yescharacteristic
227C4×C8—111no—
228C2×C11—41no—
229C2×C11#54611yescharacteristic
230C2×C11C2×#13711yescharacteristic
231C2×C11#57811yescharacteristic
232D11—41no—
233C2×Q8—21no—
234C2×Q8—22no—
235C2×Q8—41no—
236C2×Q8—111no—
237C2×Q8—221no—
238C2×Q8—221no—
239C2×Q8—222no—
240C2×Q8—441no—
241C2×Q8C22×D1111yescharacteristic
242C2×Q8C22×D1111yescharacteristic
243C2×Q8C22×D1111yescharacteristic
244C2×D4—111no—
245C22×C4—21no—
246C22×C4—111no—
247C22×C4—221no—
248C22×C4C22×D1111yescharacteristic
249Q16—22no—
250Q16—41no—
251Q16—441no—
252M16—441no—
253M16—441no—
254C2×C8—111no—
255C2×C8—111no—
256C2×C8C22×D1111yescharacteristic
257C2×C8C22×D1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4C22×D1111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—111no—
274C22⋊C4—111no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C42—111no—
281C42—221no—
282C42—221no—
283C42—221no—
284C42—221no—
285C11#332811yescharacteristic, complemented, Sylow
286C23—111no—
287C23D4×D1111yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—221no—
295Q8—221no—
296Q8—442no—
297Q8—442no—
298Q8#434112yes—
299D4—222no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—111no—
308C2×C4—111no—
309C2×C4—111no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—442no—
317C2×C4D4×D1111yescharacteristic
318C2×C4C23×D1111yescharacteristic
319C8—21no—
320C8—21no—
321C8—221no—
322C8—221no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—221no—
327C22—221no—
328C22—221no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—112no—
336C4—221no—
337C4—221no—
338C4—441no—
339C4—441no—
340C4—441no—
341C4—441no—
342C4C2×#434111yescharacteristic
343C4#6703711yescharacteristic
344C2—41no—
345C2—441no—
346C2#1062312211yescharacteristic
347C2#1062329711yescharacteristic
348C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
prime radicalC2×C22⋊D11D4
hypercenter#451D11
hypocenterC11#3328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. C11×#451C2semidirect
4. #10622838C2semidirect
5. #10622802C2semidirect
6. #10622799C2semidirect
7. Q16×Dic11C2semidirect
8. #10622795C2semidirect
9. #10622665C2semidirect
10. #10622427C2semidirect
11. #10622415C2semidirect
12. #10622405C2semidirect
13. #10622404C2semidirect
15. #10622336C2semidirect
159. #451D11semidirect
285. C11#3328semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D112
#106231722
C11×#4512
#106228382
#106228022
#106227992
Q16×Dic112
#106227952
#106226652
#106224272
#106224152
#106224052
#106224042
#106223422
#106223362
#332811