Finite Group Databasebeta

← #13078837

Subgroups — #13078837

Order 1408.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623228C211yesmaximal, characteristic, complemented
2#10623105C211yesmaximal, characteristic
3C11×#479C211yesmaximal, characteristic, complemented
4#10622679C211yesmaximal, characteristic, complemented
5#10622644C211yesmaximal, characteristic, complemented
6#10622502C211yesmaximal, characteristic, complemented
7#10622497C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic, complemented
9#10622465C211yesmaximal, characteristic, complemented
10#10622454C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622423C211yesmaximal, characteristic
13#10622423C211yesmaximal, characteristic
14#10622403C211yesmaximal, characteristic, complemented
15#10622402C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C11×#125C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20C2×#4326C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22C2×#4314C2211yescharacteristic
23C2×#4314C2211yescharacteristic
24#66951—21no—
25#66951—21no—
26#66950C2211yescharacteristic
27#66950C2211yescharacteristic
28#66946—21no—
29#66946C2211yescharacteristic
30C4⋊C4×D11—21no—
31C4⋊C4×D11C2211yescharacteristic
32#66943—21no—
33#66943—21no—
34#66940C2211yescharacteristic
35#66940C2211yescharacteristic
36C4×D44—21no—
37C4×D44C2211yescharacteristic
38#66925—21no—
39#66925C2211yescharacteristic
40#66922C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60#4343—22no—
61#4343—22no—
62C2×D44—21no—
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C42×C11—21no—
80C42×C11C2311yescharacteristic
81#4326—22no—
82#4326—22no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4D411yescharacteristic
88(C2×D11)⋊C4D411yescharacteristic
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4314—22no—
107#4314—22no—
108#3120—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11#4112yes—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126D44—24no—
127D44—21no—
128D44#4112yes—
129C4×D11—24no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—81no—
133C4×D11—81no—
134C4×D11—81no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22—21no—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#541—111no—
144#520—111no—
145#484—111no—
146#483—111no—
147#479D1111yescharacteristic, complemented
148#478—111no—
149#462—111no—
150#461—111no—
151#452—111no—
152#452—111no—
153#441—111no—
154#440—111no—
155C4×Q16—111no—
156C4×SD16—111no—
157#433—111no—
158C22×C11C22×D411yescharacteristic
159C2×D11—22no—
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—41no—
164C2×D11—41no—
165C4×C11—22no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C11C2×#4111yescharacteristic
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×#41—111no—
180C2×Q16—111no—
181C2×Q16—111no—
182C2×SD16—111no—
183C2×SD16—111no—
184C4⋊Q8—111no—
185#126—221no—
186#126—221no—
187#125—221no—
188#125—221no—
189#125C2×D1111yescharacteristic
190C22⋊Q8—111no—
191C22⋊Q8—111no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8C2×D1111yescharacteristic
196C4×D4—111no—
197C4×D4—111no—
198C4×D4—221no—
199C4×D4—221no—
200#117—111no—
201#117—221no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204#107—111no—
205#107C2×D1111yescharacteristic
206#106—111no—
207#106C2×D1111yescharacteristic
208C4⋊C8—111no—
209C4⋊C8C2×D1111yescharacteristic
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#103C2×D1111yescharacteristic
215#103C2×D1111yescharacteristic
216#102—111no—
217#102—111no—
218C22⋊C8—111no—
219C22⋊C8—111no—
220#97—111no—
221C4×C8—111no—
222C2×C11#52511yescharacteristic
223C2×C11#57711yescharacteristic
224C2×C11#57811yescharacteristic
225D11—41no—
226D11—42no—
227#41—222no—
228#41—222no—
229C2×Q8—111no—
230C2×Q8—111no—
231C2×Q8C22×D1111yescharacteristic
232C2×D4—111no—
233C2×D4—221no—
234C22×C4—111no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239Q16—222no—
240Q16—222no—
241SD16—222no—
242SD16—222no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—111no—
265C22⋊C4—111no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C42—21no—
271C42—111no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#312011yescharacteristic, complemented, Sylow
277C23—111no—
278C23—221no—
279Q8—21no—
280Q8—221no—
281Q8—221no—
282Q8—221no—
283Q8—221no—
284Q8#434312yes—
285D4—112no—
286D4—224no—
287D4—221no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—224no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—881no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4D4×D1111yescharacteristic
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8—221no—
310C8—221no—
311C22—221no—
312C22—221no—
313C22—222no—
314C22—221no—
315C22—441no—
316C22—441no—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—221no—
325C4—221no—
326C4—221no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4C2×#434311yescharacteristic
331C4#41×D1111yescharacteristic
332C2—441no—
333C2—442no—
334C2#1062315811yescharacteristic
335C2#1062330111yescharacteristic
336C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radicalC2×#4343C22
hypercenter#479D11
hypocenterC11#3120
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #10623228C2semidirect
3. C11×#479C2semidirect
4. #10622679C2semidirect
5. #10622644C2semidirect
6. #10622502C2semidirect
7. #10622497C2semidirect
8. #10622475C2semidirect
9. #10622465C2semidirect
10. #10622454C2semidirect
11. #10622453C2semidirect
14. #10622403C2semidirect
15. #10622402C2semidirect
147. #479D11semidirect
276. C11#3120semidirect

Maximal subgroups

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

subgroupindex
#106232282
#106231052
C11×#4792
#106226792
#106226442
#106225022
#106224972
#106224752
#106224652
#106224542
#106224532
#106224232
#106224032
#106224022
#312011