Finite Group Databasebeta

← #13081510

Subgroups — #13081510

Order 1408.

374 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#10623258C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic, complemented
3C11×#476C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622627C211yesmaximal, characteristic
6#10622484C211yesmaximal, characteristic, complemented
7#10622483C211yesmaximal, characteristic, complemented
8#10622469C211yesmaximal, characteristic, complemented
9#10622468C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622398C211yesmaximal, characteristic
13#10622374C211yesmaximal, characteristic, complemented
14#10622372C211yesmaximal, characteristic, complemented
15#10622369C211yesmaximal, characteristic
16C2×Q8×D11—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66999—21no—
20D4×Dic11C2211yescharacteristic
21D4×Dic11C2211yescharacteristic
22C2×#4323C2211yescharacteristic
23#66977—21no—
24C2×Dic11⋊C4—21no—
25#66949—21no—
26#66949—21no—
27#66946C2211yescharacteristic
28#66946C2211yescharacteristic
29#66943C2211yescharacteristic
30#66941C2211yescharacteristic
31#66941C2211yescharacteristic
32#66941C2211yescharacteristic
33#66931—21no—
34#66931—21no—
35C4×D44C2211yescharacteristic
36#66923C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×#106C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66896C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66882C2211yescharacteristic
47#66881C2211yescharacteristic
48#66879C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66873C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×Dic11—21no—
63C22×Dic11—21no—
64Q8×D11—44no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22—21no—
72C2×Dic22D411yescharacteristic
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—
82C22⋊Dic11—21no—
83#4323Q814yescomplemented
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11D411yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11C2311yescharacteristic
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#3384—111nomaximal, Sylow
105C23×C11—21no—
106C22×D11—21no—
107Q8×C11—42no—
108D4×C11—21no—
109D4×C11C2×Q812yescomplemented
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—81no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—42no—
121C2×Dic11—81no—
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126D44—21no—
127D44C2×Q812yes—
128C4×D11—42no—
129C4×D11—42no—
130C4×D11—42no—
131Dic22—22no—
132Dic22—42no—
133Dic22—42no—
134Dic22—81no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8C2×Q812yescomplemented
139#554—111no—
140D4×Q8—111no—
141#501—111no—
142#501—111no—
143#498—111no—
144#478—111no—
145#478—111no—
146#476—111no—
147#476—111no—
148#476D1111yescharacteristic, complemented
149#474—111no—
150#446—111no—
151#442—111no—
152#442—111no—
153C4×D8—111no—
154C22×C11—22no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11C22×D411yescharacteristic
158C2×D11—22no—
159C2×D11—41no—
160C2×D11—41no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11C22×Q811yescharacteristic
167C4×C112−1+411yescharacteristic
168Dic11—21no—
169Dic11—21no—
170Dic11—21no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11AGL(1,ℤ/8)12yes—
175C22×Q8—221no—
176C2×D8—111no—
177C4⋊Q8—111no—
178C4⋊Q8—111no—
179C4⋊Q8—111no—
180C4⋊Q8C2×D1111yescharacteristic
181#125—111no—
182#125—111no—
183C22⋊Q8—221no—
184C22⋊Q8—221no—
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C4×Q8—111no—
190C4×D4—111no—
191C4×D4—111no—
192C4×D4—111no—
193C4×D4—111no—
194C4×D4—111no—
195C4×D4C2×D1111yescharacteristic
196C2×C4⋊C4—221no—
197#107—111no—
198#107—111no—
199#107—111no—
200#106—111no—
201#106—111no—
202#106—111no—
203#106—111no—
204#106C2×D1111yescharacteristic
205#106C2×D1111yescharacteristic
206C4⋊C8—111no—
207C4⋊C8—111no—
208C4⋊C8C2×D1111yescharacteristic
209#102—111no—
210#102—111no—
211#102—111no—
212#102—111no—
213#102C2×D1111yescharacteristic
214#102C2×D1111yescharacteristic
215#97—111no—
216#97—111no—
217C4×C8—111no—
218C2×C11—42no—
219C2×C11D4×Q811yescharacteristic
220C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C11#57711yescharacteristic
222D11—42no—
223C2×Q8—21no—
224C2×Q8—111no—
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—444no—
229C2×D4—111no—
230C2×D4C22×D1111yescharacteristic
231C22×C4—21no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237D8—114no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8C22×D1111yescharacteristic
241C2×C8C22×D1111yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4C22×D1111yescharacteristic
257C4⋊C4C22×D1111yescharacteristic
258C4⋊C4C22×D1111yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C42—111no—
266C42—111no—
267C42C22×D1111yescharacteristic
268C11#338411yescharacteristic, complemented, Sylow
269C23—21no—
270C23—221no—
271Q8—42no—
272Q8—222no—
273Q8—442no—
274Q8—442no—
275Q8—881no—
276D4—21no—
277D4—112no—
278D4—221no—
279D4Q8×D1112yescomplemented
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—81no—
284C2×C4—111no—
285C2×C4—111no—
286C2×C4—111no—
287C2×C4—111no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—881no—
296C2×C4D4×D1111yescharacteristic
297C2×C4D4×D1111yescharacteristic
298C2×C4C23×D1111yescharacteristic
299C8—21no—
300C8—21no—
301C8—112no—
302C8—221no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—222no—
307C22—441no—
308C22—441no—
309C22C2×D4×D1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—112no—
316C4—221no—
317C4—221no—
318C4—221no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4C2×Q8×D1111yescharacteristic
323C4#6704311yescharacteristic
324C2—42no—
325C2—442no—
326C2#1062316311yescharacteristic
327C2#1062329311yescharacteristic
328C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#476C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#476D11
hypocenterC11#3384
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. #10623258C2semidirect
2. #10623070C2semidirect
3. C11×#476C2semidirect
4. #10622693C2semidirect
6. #10622484C2semidirect
7. #10622483C2semidirect
8. #10622469C2semidirect
9. #10622468C2semidirect
10. #10622460C2semidirect
11. #10622441C2semidirect
13. #10622374C2semidirect
14. #10622372C2semidirect
83. #4323Q8semidirect
109. D4×C11C2×Q8semidirect
138. C11⋊C8C2×Q8semidirect
148. #476D11semidirect
268. C11#3384semidirect
279. D4Q8×D11semidirect

Maximal subgroups

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

subgroupindex
#106232582
#106230702
C11×#4762
#106226932
#106226272
#106224842
#106224832
#106224692
#106224682
#106224602
#106224412
#106223982
#106223742
#106223722
#106223692
#338411