Finite Group Databasebeta

← #13080085

Subgroups — #13080085

Order 1408.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623264C211yesmaximal, characteristic, complemented
2#10623113C211yesmaximal, characteristic, complemented
3C11×#475C211yesmaximal, characteristic, complemented
4#10622697C211yesmaximal, characteristic, complemented
5#10622641C211yesmaximal, characteristic, complemented
6#10622483C211yesmaximal, characteristic, complemented
7#10622478C211yesmaximal, characteristic
8#10622477C211yesmaximal, characteristic, complemented
9#10622467C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic, complemented
13#10622429C211yesmaximal, characteristic, complemented
14#10622420C211yesmaximal, characteristic, complemented
15#10622411C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#67000—21no—
19#67000C2211yescharacteristic
20#66999—21no—
21#66999C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24C2×D88C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26C2×#4313C2211yescharacteristic
27C2×C8×D11C2211yescharacteristic
28#66951—21no—
29#66950C2211yescharacteristic
30#66949—21no—
31#66948C2211yescharacteristic
32#66948C2211yescharacteristic
33#66947—21no—
34#66947—21no—
35#66946C2211yescharacteristic
36#66941C2211yescharacteristic
37#66940C2211yescharacteristic
38#66929—21no—
39#66928—21no—
40#66928C2211yescharacteristic
41C4×D44C2211yescharacteristic
42#66925C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#103C2211yescharacteristic
48#66885C2211yescharacteristic
49#66880C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66874C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D44—21no—
62C2×D44—21no—
63C2×D44C2311yescharacteristic
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11C2311yescharacteristic
68C2×Dic22—21no—
69C2×Dic22C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79#4326—41no—
80#4325—41no—
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)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4D411yescharacteristic
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104D88—41no—
105#4314—41no—
106#4313—41no—
107C8×D11—41no—
108#3263—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—81no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—21no—
128D44—21no—
129D44—21no—
130D44—21no—
131D44—81no—
132D44—81no—
133C4×D11—21no—
134C4×D11—21no—
135C4×D11—81no—
136C4×D11—81no—
137Dic22—21no—
138Dic22—21no—
139Dic22—81no—
140C8×C11—21no—
141C8×C11—21no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144#542—111no—
145#542—111no—
146#476—111no—
147#476—111no—
148#475—111no—
149#475D1111yescharacteristic, complemented
150#470—111no—
151#469—111no—
152#465—111no—
153#465—111no—
154#464—111no—
155#464—111no—
156#463—111no—
157#463—111no—
158#424—111no—
159C22×C11C22×D411yescharacteristic
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11H(5,𝔽2)11yescharacteristic
176C4×C112−1+411yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16—111no—
183C2×SD16—111no—
184C2×SD16—111no—
185C2×D8—111no—
186C2×M16—111no—
187C22×C8—111no—
188C4⋊Q8—111no—
189C4⋊Q8C2×D1111yescharacteristic
190#126—221no—
191#126—221no—
192#124—111no—
193#124—111no—
194#124—221no—
195#124—221no—
196#123—221no—
197#123—221no—
198C22⋊Q8—111no—
199C22⋊Q8—111no—
200C22⋊Q8—221no—
201C22⋊Q8—221no—
202#121—111no—
203#121—111no—
204C4×Q8—111no—
205C4×Q8C2×D1111yescharacteristic
206C4×D4—111no—
207C4×D4—111no—
208#117—111no—
209#106—111no—
210#106—111no—
211#106C2×D1111yescharacteristic
212#106C2×D1111yescharacteristic
213C4⋊C8—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216C4⋊C8C2×D1111yescharacteristic
217#103—111no—
218#103—111no—
219#103C2×D1111yescharacteristic
220#103C2×D1111yescharacteristic
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225C2×C11#53711yescharacteristic
226C2×C11#57711yescharacteristic
227C2×C11#57711yescharacteristic
228D11—41no—
229D11—81no—
230D11—81no—
231C2×Q8—21no—
232C2×Q8—111no—
233C2×Q8—221no—
234C2×Q8C22×D1111yescharacteristic
235C2×D4—111no—
236C2×D4—111no—
237C2×D4—221no—
238C2×D4—221no—
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—221no—
242Q16—441no—
243SD16—441no—
244SD16—441no—
245D8—441no—
246M16—441no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—441no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—111no—
265C22⋊C4—111no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C42—21no—
277C42—111no—
278C42—221no—
279C42C22×D1111yescharacteristic
280C11#326311yescharacteristic, complemented, Sylow
281C23—111no—
282C23—221no—
283C23—221no—
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—221no—
288Q8—221no—
289Q8—881no—
290D4—221no—
291D4—221no—
292D4—221no—
293D4—221no—
294D4—881no—
295D4—881no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4D4×D1111yescharacteristic
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—21no—
314C8—221no—
315C8—221no—
316C22—221no—
317C22—221no—
318C22—221no—
319C22—441no—
320C22—441no—
321C22—441no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—221no—
333C4—221no—
334C4—221no—
335C4—441no—
336C4—441no—
337C4#6704011yescharacteristic
338C4#6704211yescharacteristic
339C2—441no—
340C2—881no—
341C2—881no—
342C2#1062316011yescharacteristic
343C2#1062329311yescharacteristic
344C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#475C2
socleC22×C11C22×D4
prime radical#10622478C2
hypercenter#475D11
hypocenterC11#3263
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #10623264C2semidirect
2. #10623113C2semidirect
3. C11×#475C2semidirect
4. #10622697C2semidirect
5. #10622641C2semidirect
6. #10622483C2semidirect
8. #10622477C2semidirect
9. #10622467C2semidirect
10. #10622457C2semidirect
11. #10622452C2semidirect
12. #10622432C2semidirect
13. #10622429C2semidirect
14. #10622420C2semidirect
15. #10622411C2semidirect
149. #475D11semidirect
280. C11#3263semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106231132
C11×#4752
#106226972
#106226412
#106224832
#106224782
#106224772
#106224672
#106224572
#106224522
#106224322
#106224292
#106224202
#106224112
#326311