Finite Group Databasebeta

← #13081162

Subgroups — #13081162

Order 1408.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623064C211yesmaximal, characteristic, complemented
2#10623045C211yesmaximal, characteristic
3C11×#428C211yesmaximal, characteristic, complemented
4#10622747C211yesmaximal, characteristic, complemented
5#10622740C211yesmaximal, characteristic, complemented
6#10622616C211yesmaximal, characteristic, complemented
7#10622584C211yesmaximal, characteristic, complemented
8#10622502C211yesmaximal, characteristic, complemented
9#10622498C211yesmaximal, characteristic, complemented
10#10622493C211yesmaximal, characteristic, complemented
11#10622490C211yesmaximal, characteristic, complemented
12#10622483C211yesmaximal, characteristic, complemented
13#10622480C211yesmaximal, characteristic, complemented
14#10622477C211yesmaximal, characteristic, complemented
15#10622469C211yesmaximal, characteristic, complemented
16C2×C11×M16C2211yescharacteristic
17C11×#117C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19#66983—21no—
20#66983C2211yescharacteristic
21C4×C22⋊D11—21no—
22C4×C22⋊D11C2211yescharacteristic
23#66977C2211yescharacteristic
24C2×#4314C2211yescharacteristic
25C2×C8×D11C2211yescharacteristic
26#66951—21no—
27#66950C2211yescharacteristic
28#66948C2211yescharacteristic
29#66947—21no—
30#66946C2211yescharacteristic
31#66945C2211yescharacteristic
32#66945C2211yescharacteristic
33#66943C2211yescharacteristic
34#66941C2211yescharacteristic
35#66940C2211yescharacteristic
36#66938—21no—
37#66932—21no—
38#66929—21no—
39C4×Dic22—21no—
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66882C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51#66874C2211yescharacteristic
52#66874C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C2×C22⋊D11D411yescharacteristic
63C2×D44—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11C2311yescharacteristic
67C2×Dic22—21no—
68C2×Dic22C2311yescharacteristic
69C11×M16—22no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C42×C11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11D411yescharacteristic
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4D411yescharacteristic
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#4314—22no—
104C8×D11—22no—
105#3350—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C22×D11—21no—
108C22×D11C2×D411yescharacteristic
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—81no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2411yescharacteristic
118C22⋊D11—41no—
119C22⋊D11—42no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126D44—21no—
127D44—21no—
128D44—81no—
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—81no—
132Dic22—21no—
133Dic22—21no—
134Dic22—42no—
135C8×C11—21no—
136C8×C11#4112yes—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#556—111no—
140#553—111no—
141#501—111no—
142#485—111no—
143#483—111no—
144#482—111no—
145#482—111no—
146#479—111no—
147#476—111no—
148#468—111no—
149#465—111no—
150#440—111no—
151#435—111no—
152#428D1111yescharacteristic, complemented
153#427—111no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11C22×D411yescharacteristic
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11C2×#4111yescharacteristic
170C4×C112−1+411yescharacteristic
171Dic11—21no—
172Dic11—21no—
173Dic11—21no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16—111no—
178C2×M16C2×D1111yescharacteristic
179C22×C8—111no—
180C4⋊Q8—111no—
181#126—221no—
182#126—221no—
183#126—221no—
184#125—111no—
185#124—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189#121—111no—
190#121—111no—
191#121—221no—
192C4×Q8—111no—
193C4×Q8—221no—
194C4×D4—111no—
195C4×D4—111no—
196C4×D4—221no—
197#117—111no—
198#117—111no—
199#117C2×D1111yescharacteristic
200C2×C4⋊C4C2×D1111yescharacteristic
201#107—111no—
202#107—111no—
203#107C2×D1111yescharacteristic
204#107C2×D1111yescharacteristic
205#106—111no—
206#106—111no—
207#106—111no—
208#106C2×D1111yescharacteristic
209#106C2×D1111yescharacteristic
210C4⋊C8—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#102—111no—
215#102—111no—
216#102—111no—
217C22⋊C8—111no—
218C22⋊C8—111no—
219#97—111no—
220C2×C11—41no—
221C2×C11#54711yescharacteristic
222C2×C11#57511yescharacteristic
223C2×C11#57711yescharacteristic
224D11—41no—
225D11—81no—
226C2×Q8—111no—
227C2×Q8—221no—
228C2×D4—111no—
229C2×D4—111no—
230C2×D4—221no—
231C2×D4—221no—
232C22×C4—21no—
233C22×C4—111no—
234C22×C4—221no—
235C22×C4C22×D1111yescharacteristic
236SD16—222no—
237M16—22no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—111no—
259C22⋊C4—111no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C42—21no—
268C42—111no—
269C42—221no—
270C42—221no—
271C42—221no—
272C11#335011yescharacteristic, complemented, Sylow
273C23—111no—
274C23—221no—
275C23D4×D1111yescharacteristic
276Q8—221no—
277Q8—221no—
278Q8—442no—
279D4—221no—
280D4—221no—
281D4—441no—
282D4—442no—
283D4—881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—81no—
291C2×C4—111no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—881no—
300C2×C4D4×D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—21no—
303C8—221no—
304C8—221no—
305C8#433912yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—221no—
310C22—221no—
311C22—221no—
312C22—441no—
313C22—441no—
314C22—441no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—221no—
322C4—221no—
323C4—221no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4C2×#433911yescharacteristic
328C4#6704011yescharacteristic
329C2—41no—
330C2—441no—
331C2—881no—
332C2#1062303811yescharacteristic
333C2#1062330611yescharacteristic
334C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
prime radical#10623045C2
hypercenter#428D11
hypocenterC11#3350
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #10623064C2semidirect
3. C11×#428C2semidirect
4. #10622747C2semidirect
5. #10622740C2semidirect
6. #10622616C2semidirect
7. #10622584C2semidirect
8. #10622502C2semidirect
9. #10622498C2semidirect
10. #10622493C2semidirect
11. #10622490C2semidirect
12. #10622483C2semidirect
13. #10622480C2semidirect
14. #10622477C2semidirect
15. #10622469C2semidirect
152. #428D11semidirect
272. C11#3350semidirect

Maximal subgroups

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

subgroupindex
#106230642
#106230452
C11×#4282
#106227472
#106227402
#106226162
#106225842
#106225022
#106224982
#106224932
#106224902
#106224832
#106224802
#106224772
#106224692
#335011