Finite Group Databasebeta

← #13081571

Subgroups — #13081571

Order 1408.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623261C211yesmaximal, characteristic, complemented
2#10623221C211yesmaximal, characteristic, complemented
3C11×#501C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622679C211yesmaximal, characteristic, complemented
6#10622504C211yesmaximal, characteristic, complemented
7#10622503C211yesmaximal, characteristic, complemented
8#10622489C211yesmaximal, characteristic, complemented
9#10622485C211yesmaximal, characteristic
10#10622484C211yesmaximal, characteristic, complemented
11#10622484C211yesmaximal, characteristic, complemented
12#10622482C211yesmaximal, characteristic
13#10622471C211yesmaximal, characteristic, complemented
14#10622324C211yesmaximal, characteristic
15#10622314C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#66999—21no—
19#66999—21no—
20C2×D88C2211yescharacteristic
21#66950—21no—
22#66950—21no—
23#66949—21no—
24#66949—21no—
25#66946C2211yescharacteristic
26#66946C2211yescharacteristic
27#66946C2211yescharacteristic
28#66946C2211yescharacteristic
29C4⋊C4×D11—21no—
30C4⋊C4×D11—21no—
31#66943C2211yescharacteristic
32#66943C2211yescharacteristic
33#66943C2211yescharacteristic
34#66941C2211yescharacteristic
35C4×D44C2211yescharacteristic
36C4×D44C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#107C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#97C2211yescharacteristic
43#66885C2211yescharacteristic
44#66885C2211yescharacteristic
45#66881C2211yescharacteristic
46#66879C2211yescharacteristic
47Dic11⋊C8C2211yescharacteristic
48Dic11⋊C8C2211yescharacteristic
49C8×Dic11C2211yescharacteristic
50#66873C2211yescharacteristic
51#66873C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D44C2311yescharacteristic
61C2×D44C2311yescharacteristic
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×Dic22—21no—
69C2×Dic22D411yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C42×C11C2311yescharacteristic
80(C2×D11)⋊C4—21no—
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—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11D411yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97Dic11⋊C4D411yescharacteristic
98C4×Dic11C2311yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102D88Q814yescomplemented
103#3389—111nomaximal, Sylow
104C22×D11—21no—
105C22×D11—21no—
106Q8×C11—81no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2411yescharacteristic
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11C2×D411yescharacteristic
117C2×Dic11C2×D411yescharacteristic
118C2×Dic11C2×D411yescharacteristic
119C2×Dic11C2×D411yescharacteristic
120D44—21no—
121D44—21no—
122D44C2×Q812yes—
123D44C2×Q812yes—
124C4×D11—42no—
125C4×D11—42no—
126C4×D11—81no—
127C4×D11—81no—
128C4×D11—81no—
129C4×D11—81no—
130Dic22—41no—
131Dic22—81no—
132C8×C11—21no—
133C8×C11C2×Q812yes—
134C11⋊C8—21no—
135C11⋊C8—21no—
136#554—111no—
137#554—111no—
138#501—111no—
139#501D1111yescharacteristic, complemented
140#499—111no—
141#478—111no—
142#478—111no—
143#478—111no—
144#478—111no—
145#474—111no—
146#474—111no—
147#446—111no—
148#442—111no—
149#442—111no—
150C4×D8—111no—
151C22×C11C22×D411yescharacteristic
152C2×D11—22no—
153C2×D11—22no—
154C2×D11—41no—
155C2×D11—41no—
156C2×D11—41no—
157C2×D11—41no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11C22×Q811yescharacteristic
165C4×C112−1+411yescharacteristic
166Dic11—21no—
167Dic11—21no—
168Dic11—21no—
169Dic11—21no—
170Dic11—41no—
171Dic11—41no—
172C2×D8—111no—
173C4⋊Q8—111no—
174C4⋊Q8C2×D1111yescharacteristic
175#125—111no—
176#125—111no—
177#125—111no—
178#125C2×D1111yescharacteristic
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181C22⋊Q8—221no—
182C22⋊Q8—221no—
183C22⋊Q8—221no—
184C22⋊Q8—221no—
185C4×Q8—111no—
186C4×D4—111no—
187C4×D4—111no—
188C4×D4—111no—
189C4×D4—111no—
190C4×D4—111no—
191C4×D4—111no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4—221no—
194#107—111no—
195#107—111no—
196#107—111no—
197#107C2×D1111yescharacteristic
198#107C2×D1111yescharacteristic
199#106—111no—
200#106—111no—
201#106C2×D1111yescharacteristic
202#106C2×D1111yescharacteristic
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206#102—111no—
207#102—111no—
208#102—111no—
209#102—111no—
210#102—111no—
211#102—111no—
212#97—111no—
213#97C2×D1111yescharacteristic
214C4×C8—111no—
215C2×C11D4×Q811yescharacteristic
216C2×C11#57511yescharacteristic
217C2×C11#57611yescharacteristic
218D11—42no—
219D11—42no—
220C2×Q8—21no—
221C2×Q8—111no—
222C2×Q8—221no—
223C2×D4—111no—
224C2×D4—111no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231D8—114no—
232C2×C8—111no—
233C2×C8—111no—
234C2×C8C22×D1111yescharacteristic
235C2×C8C22×D1111yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4C22×D1111yescharacteristic
252C4⋊C4C22×D1111yescharacteristic
253C4⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C22⋊C4—221no—
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C42—111no—
262C42—111no—
263C42C22×D1111yescharacteristic
264C11#338911yescharacteristic, complemented, Sylow
265C23—221no—
266C23—221no—
267Q8—81no—
268Q8—441no—
269Q8—881no—
270D4—112no—
271D4—112no—
272D4—221no—
273D4—221no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—111no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4D4×D1111yescharacteristic
291C2×C4D4×D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—21no—
294C8—221no—
295C8—221no—
296C8Q8×D1112yes—
297C22—222no—
298C22—222no—
299C22—441no—
300C22—441no—
301C22—441no—
302C22—441no—
303C22C2×D4×D1111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—221no—
311C4—221no—
312C4—221no—
313C4—221no—
314C4—441no—
315C4—441no—
316C4C2×Q8×D1111yescharacteristic
317C4#6704011yescharacteristic
318C2—442no—
319C2—442no—
320C2#1062325811yescharacteristic
321C2#1062330511yescharacteristic
322C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radicalC2×D88C22
hypercenter#501D11
hypocenterC11#3389
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #10623261C2semidirect
2. #10623221C2semidirect
3. C11×#501C2semidirect
4. #10622700C2semidirect
5. #10622679C2semidirect
6. #10622504C2semidirect
7. #10622503C2semidirect
8. #10622489C2semidirect
10. #10622484C2semidirect
11. #10622484C2semidirect
13. #10622471C2semidirect
15. #10622314C2semidirect
102. D88Q8semidirect
139. #501D11semidirect
264. C11#3389semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106232212
C11×#5012
#106227002
#106226792
#106225042
#106225032
#106224892
#106224852
#106224842
#106224822
#106224712
#106223242
#106223142
#338911