Finite Group Databasebeta

← #13080026

Subgroups — #13080026

Order 1408.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623264C211yesmaximal, characteristic, complemented
2#10623093C211yesmaximal, characteristic, complemented
3C11×#476C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622629C211yesmaximal, characteristic, complemented
6#10622484C211yesmaximal, characteristic, complemented
7#10622478C211yesmaximal, characteristic, complemented
8#10622477C211yesmaximal, characteristic, complemented
9#10622470C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622399C211yesmaximal, characteristic, complemented
13#10622393C211yesmaximal, characteristic, complemented
14#10622388C211yesmaximal, characteristic, complemented
15#10622375C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18#67000—21no—
19#66999—21no—
20#66993C2211yescharacteristic
21#66991C2211yescharacteristic
22C2×#4324C2211yescharacteristic
23C2×#4323C2211yescharacteristic
24#66983—21no—
25#66982—21no—
26C2×D88C2211yescharacteristic
27C2×#4314C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66950C2211yescharacteristic
32#66948C2211yescharacteristic
33#66948C2211yescharacteristic
34#66947—21no—
35#66946C2211yescharacteristic
36#66943C2211yescharacteristic
37#66940C2211yescharacteristic
38#66937—21no—
39#66936—21no—
40#66928C2211yescharacteristic
41C4×D44C2211yescharacteristic
42#66925C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×#102C2211yescharacteristic
48#66885C2211yescharacteristic
49#66880C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66874C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11C2311yescharacteristic
72C2×Dic22C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C42×C11C2311yescharacteristic
81C22⋊Dic11—21no—
82#4324—41no—
83#4323—41no—
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⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
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#3257—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11C2×D411yescharacteristic
113Q8×C11—81no—
114D4×C11—21no—
115D4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—81no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—81no—
124C22⋊D11—81no—
125C22⋊D11—81no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131D44—21no—
132D44—21no—
133D44—21no—
134D44—21no—
135D44—81no—
136D44—81no—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—81no—
140C4×D11—81no—
141Dic22—21no—
142Dic22—21no—
143C8×C11—21no—
144C8×C11—21no—
145C11⋊C8—21no—
146C11⋊C8—21no—
147#542—111no—
148#540—111no—
149#479—111no—
150#478—111no—
151#476D1111yescharacteristic, complemented
152#474—111no—
153#469—111no—
154#468—111no—
155#466—111no—
156#465—111no—
157#463—111no—
158#463—111no—
159#460—111no—
160#459—111no—
161#424—111no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11C22×D411yescharacteristic
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11H(5,𝔽2)11yescharacteristic
181C4×C112−1+411yescharacteristic
182Dic11—21no—
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187C2×SD16—111no—
188C2×SD16—111no—
189C2×D8—111no—
190C2×D8—111no—
191C2×M16—111no—
192C22×C8—111no—
193C4⋊Q8C2×D1111yescharacteristic
194#127—111no—
195#126—221no—
196#125—111no—
197#124—111no—
198#124—221no—
199#123—221no—
200#123—221no—
201#123—221no—
202C22⋊Q8—111no—
203C22⋊Q8—221no—
204#121—111no—
205#121—111no—
206#121—111no—
207#121—221no—
208#121—221no—
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4C2×D1111yescharacteristic
213#117—111no—
214#107—111no—
215#107—111no—
216#106C2×D1111yescharacteristic
217#106C2×D1111yescharacteristic
218C4⋊C8—111no—
219C4⋊C8—111no—
220C4⋊C8—111no—
221C4⋊C8C2×D1111yescharacteristic
222#103—111no—
223#103—111no—
224#102—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228#102C2×D1111yescharacteristic
229#102C2×D1111yescharacteristic
230C2×C11—81no—
231C2×C11#53711yescharacteristic
232C2×C11#57611yescharacteristic
233C2×C11#57711yescharacteristic
234D11—41no—
235D11—81no—
236D11—81no—
237C2×Q8—21no—
238C2×Q8—111no—
239C2×D4—111no—
240C2×D4—111no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4C22×D1111yescharacteristic
247C22×C4—21no—
248C22×C4—111no—
249C22×C4—221no—
250C22×C4—221no—
251SD16—441no—
252SD16—441no—
253D8—441no—
254D8—441no—
255M16—441no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—441no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4C22×D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
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—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C42—111no—
284C42—221no—
285C42C22×D1111yescharacteristic
286C11#325711yescharacteristic, complemented, Sylow
287C23—21no—
288C23—111no—
289C23—221no—
290C23—221no—
291Q8—81no—
292Q8—221no—
293Q8—221no—
294D4—21no—
295D4—21no—
296D4—221no—
297D4—221no—
298D4—221no—
299D4—221no—
300D4—881no—
301D4—881no—
302D4—881no—
303D4—881no—
304D4—881no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4D4×D1111yescharacteristic
319C2×C4D4×D1111yescharacteristic
320C2×C4C23×D1111yescharacteristic
321C8—21no—
322C8—21no—
323C8—221no—
324C8—221no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—221no—
329C22—221no—
330C22—221no—
331C22—441no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—221no—
344C4—221no—
345C4—221no—
346C4—441no—
347C4—441no—
348C4#6704011yescharacteristic
349C4#6704211yescharacteristic
350C2—81no—
351C2—441no—
352C2—881no—
353C2—881no—
354C2#1062316011yescharacteristic
355C2#1062329311yescharacteristic
356C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#476C2
socleC22×C11C22×D4
hypercenter#476D11
hypocenterC11#3257
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10623264C2semidirect
2. #10623093C2semidirect
3. C11×#476C2semidirect
4. #10622700C2semidirect
5. #10622629C2semidirect
6. #10622484C2semidirect
7. #10622478C2semidirect
8. #10622477C2semidirect
9. #10622470C2semidirect
10. #10622457C2semidirect
11. #10622452C2semidirect
12. #10622399C2semidirect
13. #10622393C2semidirect
14. #10622388C2semidirect
15. #10622375C2semidirect
151. #476D11semidirect
286. C11#3257semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106230932
C11×#4762
#106227002
#106226292
#106224842
#106224782
#106224772
#106224702
#106224572
#106224522
#106223992
#106223932
#106223882
#106223752
#325711