Finite Group Databasebeta

← #13078468

Subgroups — #13078468

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623220C211yesmaximal, characteristic, complemented
2#10623077C211yesmaximal, characteristic
3C11×#478C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622620C211yesmaximal, characteristic, complemented
6D11×#107C211yesmaximal, characteristic, complemented
7#10622488C211yesmaximal, characteristic, complemented
8#10622474C211yesmaximal, characteristic, complemented
9#10622470C211yesmaximal, characteristic, complemented
10#10622463C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622385C211yesmaximal, characteristic
13#10622384C211yesmaximal, characteristic
14#10622379C211yesmaximal, characteristic, complemented
15#10622372C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C11×#125C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19D4×Dic11C2211yescharacteristic
20C4×C22⋊D11—21no—
21C2×Dic11⋊C4—21no—
22C2×#4313C2211yescharacteristic
23C2×C8×D11C2211yescharacteristic
24#66950—21no—
25#66949—21no—
26#66945C2211yescharacteristic
27C4⋊C4×D11C2211yescharacteristic
28C4⋊C4×D11C2211yescharacteristic
29#66943C2211yescharacteristic
30#66942—21no—
31#66941—21no—
32#66941C2211yescharacteristic
33#66940C2211yescharacteristic
34(C22⋊D11)⋊C4—21no—
35#66930—21no—
36#66925C2211yescharacteristic
37#66922C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C11×#107C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66882C2211yescharacteristic
47#66882C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C2×C22⋊D11—21no—
62C22×Dic11—21no—
63C22×Dic11—21no—
64#4341—22no—
65#4341Q814yescomplemented
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11C2311yescharacteristic
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C42×C11C2311yescharacteristic
81C22⋊Dic11—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4D411yescharacteristic
84(C2×D11)⋊C4D411yescharacteristic
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105C8×D11—22no—
106#3083—111nomaximal, Sylow
107C23×C11—21no—
108C22×D11C2×D411yescharacteristic
109D4×C11—21no—
110D4×C11C2×Q812yes—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—81no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2411yescharacteristic
118C22⋊D11—24no—
119C2×Dic11—21no—
120C2×Dic11—24no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—81no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C4×D11—81no—
129C4×D11—81no—
130C4×D11C2×Q812yes—
131C4×D11#4112yes—
132Dic22—21no—
133Dic22—81no—
134Dic22—81no—
135Dic22C2×Q812yes—
136C8×C11—21no—
137C8×C11—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140#544—111no—
141#520—111no—
142#479—111no—
143#479—111no—
144#478—111no—
145#478D1111yescharacteristic, complemented
146#477—111no—
147#477—111no—
148#474—111no—
149#474—111no—
150#428—111no—
151C2×#107—111no—
152#424—111no—
153#417—111no—
154#416—111no—
155C22×C11—22no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11C22×D411yescharacteristic
159C2×D11—21no—
160C2×D11—21no—
161C2×D11C22⋊Q812yes—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11C22×Q811yescharacteristic
168C4×C11C2×#4111yescharacteristic
169Dic11—22no—
170Dic11—21no—
171Dic11—21no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175Dic11C22⋊Q812yes—
176C2×#41—111no—
177C2×M16—111no—
178C22×C8—111no—
179C4⋊Q8—111no—
180C4⋊Q8—111no—
181C4⋊Q8—221no—
182#125—111no—
183#125—221no—
184#125C2×D1111yescharacteristic
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187C4×Q8—111no—
188C4×Q8—111no—
189C4×D4—111no—
190C4×D4—221no—
191C4×D4—221no—
192C4×D4C2×D1111yescharacteristic
193#117—111no—
194#117—111no—
195#117—221no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—221no—
199#107—111no—
200#107—111no—
201#107—111no—
202#107—111no—
203#107—111no—
204#107C2×D1111yescharacteristic
205#106—111no—
206#106C2×D1111yescharacteristic
207C4⋊C8—111no—
208C4⋊C8—111no—
209C4⋊C8—111no—
210C4⋊C8C2×D1111yescharacteristic
211#103—111no—
212#103—111no—
213#103—111no—
214#103—111no—
215#102—111no—
216#102—111no—
217#102C2×D1111yescharacteristic
218#102C2×D1111yescharacteristic
219C2×C11—42no—
220C2×C11C2×C22⋊Q811yescharacteristic
221C2×C11#57611yescharacteristic
222C2×C11#57811yescharacteristic
223D11—22no—
224#41—114no—
225#41—222no—
226C2×Q8—111no—
227C2×Q8—221no—
228C2×Q8—221no—
229C2×D4—221no—
230C2×D4C22×D1111yescharacteristic
231C22×C4—21no—
232C22×C4—111no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—111no—
263C22⋊C4—111no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C42—111no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42C22×D1111yescharacteristic
271C11#308311yescharacteristic, complemented, Sylow
272C23—21no—
273C23—111no—
274Q8—112no—
275Q8—221no—
276Q8—881no—
277Q8—881no—
278D4—21no—
279D4—224no—
280D4Q8×D1112yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—111no—
286C2×C4—112no—
287C2×C4—112no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—224no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4D4×D1111yescharacteristic
299C2×C4D4×D1111yescharacteristic
300C2×C4C23×D1111yescharacteristic
301C8—21no—
302C8—21no—
303C8—221no—
304C8—221no—
305C22—22no—
306C22—41no—
307C22—41no—
308C22—112no—
309C22—221no—
310C22—221no—
311C22C2×D4×D1111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—112no—
318C4—221no—
319C4—221no—
320C4—222no—
321C4—441no—
322C4—441no—
323C4—441no—
324C4C2×Q8×D1111yescharacteristic
325C4#41×D1111yescharacteristic
326C2—42no—
327C2—222no—
328C2D11×C22⋊Q811yescharacteristic
329C2#1062330211yescharacteristic
330C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
hypercenter#478D11
hypocenterC11#3083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10623220C2semidirect
3. C11×#478C2semidirect
4. #10622676C2semidirect
5. #10622620C2semidirect
6. D11×#107C2semidirect
7. #10622488C2semidirect
8. #10622474C2semidirect
9. #10622470C2semidirect
10. #10622463C2semidirect
11. #10622452C2semidirect
14. #10622379C2semidirect
15. #10622372C2semidirect
65. #4341Q8semidirect
145. #478D11semidirect
271. C11#3083semidirect

Maximal subgroups

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

subgroupindex
#106232202
#106230772
C11×#4782
#106226762
#106226202
D11×#1072
#106224882
#106224742
#106224702
#106224632
#106224522
#106223852
#106223842
#106223792
#106223722
#308311