Finite Group Databasebeta

← #13078774

Subgroups — #13078774

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623109C211yesmaximal, characteristic, complemented
2C4×#4341C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622786C211yesmaximal, characteristic
5#10622775C211yesmaximal, characteristic, complemented
6#10622643C211yesmaximal, characteristic, complemented
7#10622631C211yesmaximal, characteristic, complemented
8#10622501C211yesmaximal, characteristic, complemented
9#10622488C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622406C211yesmaximal, characteristic, complemented
12#10622396C211yesmaximal, characteristic
13#10622374C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15#10622318C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23D4×Dic11C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25C4×C22⋊D11—21no—
26C2×C4×Dic11—21no—
27C2×Dic44C2211yescharacteristic
28#66950C2211yescharacteristic
29#66949—21no—
30#66945C2211yescharacteristic
31#66942—21no—
32#66941C2211yescharacteristic
33#66940C2211yescharacteristic
34(C22⋊D11)⋊C4—21no—
35#66930—21no—
36#66925—21no—
37C42×D11C2211yescharacteristic
38C4×Dic22—21no—
39C4×Dic22C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66881C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65#4341—22no—
66#4341—22no—
67C2×C4×D11D411yescharacteristic
68C2×C4×D11D411yescharacteristic
69C2×C4×D11C2311yescharacteristic
70C2×Dic22—21no—
71C2×Dic22C2311yescharacteristic
72C2×Dic22C2311yescharacteristic
73C11×SD16—22no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C42×C11—21no—
81C42×C11C2311yescharacteristic
82C22⋊Dic11—21no—
83#4326—22no—
84#4324—22no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11D411yescharacteristic
103C4×Dic11D411yescharacteristic
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107Dic44—22no—
108#3116—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113D4×C11—21no—
114D4×C11#4112yes—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C22⋊D11—24no—
123C2×Dic11—24no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—42no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—22no—
135C4×D11—41no—
136Dic22—21no—
137Dic22—21no—
138Dic22—21no—
139Dic22—42no—
140Dic22#4112yes—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145#533—111no—
146C4×#41—111no—
147#485—111no—
148#485—111no—
149#477—111no—
150#476—111no—
151#462—111no—
152#461—111no—
153#452—111no—
154#452—111no—
155#441—111no—
156#441—111no—
157#440—111no—
158#440D1111yescharacteristic, complemented
159#432—111no—
160C22×C11—22no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11C2×#4111yescharacteristic
173C4×C11C2×#4111yescharacteristic
174Dic11—22no—
175Dic11—21no—
176Dic11—21no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180Dic11#13712yes—
181C2×#41—111no—
182C2×Q16—111no—
183C2×Q16—111no—
184C2×SD16—111no—
185C2×SD16C2×D1111yescharacteristic
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188#125—221no—
189C22⋊Q8—111no—
190C22⋊Q8—111no—
191C22⋊Q8—221no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8—221no—
196C4×Q8C2×D1111yescharacteristic
197C4×D4—111no—
198C4×D4—221no—
199C4×D4—221no—
200C4×D4C2×D1111yescharacteristic
201#117—111no—
202#117—221no—
203#117—221no—
204C2×C42—111no—
205C2×C42—221no—
206#107—111no—
207#107C2×D1111yescharacteristic
208#106—111no—
209#106—111no—
210C4⋊C8—111no—
211C4⋊C8—111no—
212#103—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#103C2×D1111yescharacteristic
218#102—111no—
219#102C2×D1111yescharacteristic
220C22⋊C8—111no—
221C22⋊C8—111no—
222#97—111no—
223#97C2×D1111yescharacteristic
224C2×C11—42no—
225C2×C11#52511yescharacteristic
226C2×C11C2×#13711yescharacteristic
227C2×C11#57511yescharacteristic
228D11—41no—
229#41—222no—
230#41—222no—
231C2×Q8—111no—
232C2×Q8—111no—
233C2×Q8—221no—
234C2×Q8C22×D1111yescharacteristic
235C2×D4—221no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—221no—
242C22×C4—221no—
243Q16—222no—
244Q16—222no—
245SD16—22no—
246SD16—222no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8C22×D1111yescharacteristic
250C2×C8C22×D1111yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—21no—
270C42—111no—
271C42—111no—
272C42—111no—
273C42—221no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42C22×D1111yescharacteristic
278C11#311611yescharacteristic, complemented, Sylow
279C23—21no—
280C23—111no—
281Q8—21no—
282Q8—21no—
283Q8—112no—
284Q8—221no—
285Q8—221no—
286Q8—221no—
287Q8—442no—
288D4—21no—
289D4—224no—
290D4#433912yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—222no—
299C2×C4—224no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—441no—
307C2×C4—442no—
308C2×C4D4×D1111yescharacteristic
309C2×C4D4×D1111yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—21no—
312C8—21no—
313C8—221no—
314C8—221no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—221no—
319C22—221no—
320C22—221no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—112no—
328C4—221no—
329C4—221no—
330C4—222no—
331C4—441no—
332C4—441no—
333C4—441no—
334C4C2×#433911yescharacteristic
335C4#41×D1111yescharacteristic
336C2—42no—
337C2—441no—
338C2#1062307811yescharacteristic
339C2#1062330411yescharacteristic
340C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
hypercenter#440D11
hypocenterC11#3116
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623109C2semidirect
3. C11×#440C2semidirect
5. #10622775C2semidirect
6. #10622643C2semidirect
7. #10622631C2semidirect
8. #10622501C2semidirect
9. #10622488C2semidirect
10. #10622428C2semidirect
11. #10622406C2semidirect
13. #10622374C2semidirect
14. #10622329C2semidirect
15. #10622318C2semidirect
158. #440D11semidirect
278. C11#3116semidirect

Maximal subgroups

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

subgroupindex
#106231092
C4×#43412
C11×#4402
#106227862
#106227752
#106226432
#106226312
#106225012
#106224882
#106224282
#106224062
#106223962
#106223742
#106223292
#106223182
#311611