Finite Group Databasebeta

← #13081445

Subgroups — #13081445

Order 1408.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623115C211yesmaximal, characteristic, complemented
2#10623110C211yesmaximal, characteristic, complemented
3C11×#446C211yesmaximal, characteristic, complemented
4#10622464C211yesmaximal, characteristic, complemented
5#10622460C211yesmaximal, characteristic, complemented
6#10622457C211yesmaximal, characteristic
7#10622457C211yesmaximal, characteristic
8#10622454C211yesmaximal, characteristic, complemented
9#10622442C211yesmaximal, characteristic, complemented
10#10622327C211yesmaximal, characteristic, complemented
11#10622324C211yesmaximal, characteristic
12#10622323C211yesmaximal, characteristic, complemented
13#10622316C211yesmaximal, characteristic, complemented
14#10622310C211yesmaximal, characteristic, complemented
15C4×#4314C211yesmaximal, characteristic, complemented
16C4×Q8×C11C2211yescharacteristic
17#66999—21no—
18#66999—21no—
19C2×D88C2211yescharacteristic
20C2×#4314C2211yescharacteristic
21C2×#4314C2211yescharacteristic
22#66951—21no—
23#66951—21no—
24#66949—21no—
25#66949—21no—
26#66945—21no—
27C4⋊C4×D11—21no—
28#66928C2211yescharacteristic
29#66928C2211yescharacteristic
30C4×D44C2211yescharacteristic
31C4×D44C2211yescharacteristic
32C4×D44C2211yescharacteristic
33C4×D44C2211yescharacteristic
34#66923C2211yescharacteristic
35#66923C2211yescharacteristic
36#66922C2211yescharacteristic
37#66922C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#97C2211yescharacteristic
44C11×#97C2211yescharacteristic
45C4×C8×C11C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×Q8×C11D411yescharacteristic
60C2×D44C2311yescharacteristic
61C2×D44C2311yescharacteristic
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4D411yescharacteristic
74C11×C4⋊C4D411yescharacteristic
75C11×C4⋊C4D411yescharacteristic
76C42×C11C2311yescharacteristic
77C42×C11C2311yescharacteristic
78C42×C11C2311yescharacteristic
79(C2×D11)⋊C4—21no—
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—
86(C2×D11)⋊C4—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102D88—22no—
103#4314—22no—
104#4314—22no—
105#3376—111nomaximal, Sylow
106C22×D11—21no—
107C22×D11—21no—
108Q8×C11—41no—
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2411yescharacteristic
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122D44—21no—
123D44—21no—
124D44—21no—
125D44#4112yes—
126C4×D11—42no—
127C4×D11—42no—
128C4×D11—81no—
129C4×D11—81no—
130Dic22—21no—
131Dic22—21no—
132Dic22—21no—
133Dic22—21no—
134Dic22—81no—
135C8×C11—21no—
136C8×C11—21no—
137C8×C11—21no—
138C8×C11—21no—
139#556—111no—
140#554—111no—
141#491—111no—
142#489—111no—
143#488—111no—
144#479—111no—
145#478—111no—
146#475—111no—
147#463—111no—
148#463—111no—
149#461—111no—
150#446D1111yescharacteristic, complemented
151#442—111no—
152#440—111no—
153C4×SD16—111no—
154C22×C11C22×D411yescharacteristic
155C2×D11—22no—
156C2×D11—41no—
157C2×D11—41no—
158C2×D11—41no—
159C2×D11—41no—
160C2×D11—41no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11C2×#4111yescharacteristic
168C4×C112−1+411yescharacteristic
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C2×SD16—111no—
176C2×SD16—111no—
177C2×D8—111no—
178C4⋊Q8—111no—
179C4⋊Q8—111no—
180#126—221no—
181#126—221no—
182#125—111no—
183#125—111no—
184#124—111no—
185#124—111no—
186C22⋊Q8—221no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C22⋊Q8—221no—
190C4×Q8—111no—
191C4×Q8—111no—
192C4×Q8C2×D1111yescharacteristic
193C4×D4—111no—
194C4×D4—111no—
195C4×D4—111no—
196C4×D4—111no—
197#117—221no—
198C2×C4⋊C4—221no—
199#107—111no—
200#106—111no—
201#106—111no—
202C4⋊C8C2×D1111yescharacteristic
203C4⋊C8C2×D1111yescharacteristic
204C4⋊C8C2×D1111yescharacteristic
205#103—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#102—111no—
212#102—111no—
213#102—111no—
214#102—111no—
215#97C2×D1111yescharacteristic
216#97C2×D1111yescharacteristic
217C4×C8C2×D1111yescharacteristic
218C2×C11#54811yescharacteristic
219C2×C11#57511yescharacteristic
220C2×C11#57711yescharacteristic
221D11—42no—
222D11—81no—
223C2×Q8—111no—
224C2×Q8—111no—
225C2×Q8—221no—
226C2×Q8D4411yescharacteristic
227C2×D4—111no—
228C2×D4—111no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—221no—
233SD16—222no—
234SD16—222no—
235D8—222no—
236C2×C8C22×D1111yescharacteristic
237C2×C8C22×D1111yescharacteristic
238C2×C8C22×D1111yescharacteristic
239C2×C8C22×D1111yescharacteristic
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⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4D4411yescharacteristic
254C4⋊C4D4411yescharacteristic
255C4⋊C4D4411yescharacteristic
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—221no—
265C42—221no—
266C42C22×D1111yescharacteristic
267C42C22×D1111yescharacteristic
268C42C22×D1111yescharacteristic
269C11#337611yescharacteristic, complemented, Sylow
270C23—221no—
271C23—221no—
272Q8—41no—
273Q8—221no—
274Q8—221no—
275Q8—221no—
276Q8—221no—
277Q8—881no—
278D4—112no—
279D4—221no—
280D4—221no—
281D4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4C2×D4411yescharacteristic
293C2×C4C2×D4411yescharacteristic
294C2×C4C2×D4411yescharacteristic
295C2×C4C2×D4411yescharacteristic
296C2×C4C2×D4411yescharacteristic
297C2×C4C2×D4411yescharacteristic
298C2×C4C23×D1111yescharacteristic
299C8—21no—
300C8—21no—
301C8—21no—
302C8—21no—
303C22—222no—
304C22—441no—
305C22—441no—
306C22—441no—
307C22—441no—
308C22—441no—
309C22C22×D4411yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—441no—
317C4—441no—
318C4—441no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4#6704011yescharacteristic
323C4#41×D1111yescharacteristic
324C2—442no—
325C2—881no—
326C2#1062310711yescharacteristic
327C2#1062327911yescharacteristic
328C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#446C2
socleC22×C11C22×D4
prime radicalC2×D88C22
hypercenter#446D11
hypocenterC11#3376
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #10623115C2semidirect
2. #10623110C2semidirect
3. C11×#446C2semidirect
4. #10622464C2semidirect
5. #10622460C2semidirect
8. #10622454C2semidirect
9. #10622442C2semidirect
10. #10622327C2semidirect
12. #10622323C2semidirect
13. #10622316C2semidirect
14. #10622310C2semidirect
15. C4×#4314C2semidirect
150. #446D11semidirect
269. C11#3376semidirect

Maximal subgroups

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

subgroupindex
#106231152
#106231102
C11×#4462
#106224642
#106224602
#106224572
#106224542
#106224422
#106223272
#106223242
#106223232
#106223162
#106223102
C4×#43142
#337611