Finite Group Databasebeta

← #13080908

Subgroups — #13080908

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623163C211yesmaximal, characteristic, complemented
2#10623063C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic, complemented
4#10622662C211yesmaximal, characteristic, complemented
5#10622617C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622488C211yesmaximal, characteristic, complemented
8#10622480C211yesmaximal, characteristic, complemented
9#10622465C211yesmaximal, characteristic, complemented
10#10622431C211yesmaximal, characteristic, complemented
11#10622419C211yesmaximal, characteristic, complemented
12#10622415C211yesmaximal, characteristic, complemented
13#10622405C211yesmaximal, characteristic, complemented
14#10622351C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#66997C2211yescharacteristic
21C2×#4325C2211yescharacteristic
22#66983C2211yescharacteristic
23C4×C22⋊D11C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26C2×#4314C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28#66950C2211yescharacteristic
29#66949—21no—
30#66948C2211yescharacteristic
31#66946C2211yescharacteristic
32#66945C2211yescharacteristic
33#66941—21no—
34#66941C2211yescharacteristic
35#66940C2211yescharacteristic
36#66938—21no—
37#66937—21no—
38(C22⋊D11)⋊C4—21no—
39#66931—21no—
40#66928—21no—
41#66925—21no—
42C11×#107C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×C22⋊C8C2211yescharacteristic
47#66899C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66873C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C2×C22⋊D11D411yescharacteristic
63C22×Dic11—21no—
64Q8×D11—22no—
65Q8×D11—41no—
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×Dic22—22no—
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22—41no—
76C2×Dic22C2311yescharacteristic
77C2×Dic22C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C42×C11—21no—
87C22⋊Dic11D411yescharacteristic
88#4325—41no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4D411yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105#4318—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#4314—22no—
109#4314—41no—
110#4313—41no—
111#3329—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11—21no—
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—22no—
126C22⋊D11—81no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—42no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136D44—81no—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—42no—
140C4×D11—42no—
141Dic22—21no—
142Dic22—21no—
143Dic22—21no—
144Dic22—42no—
145Dic22—42no—
146Dic22—81no—
147Dic22#4112yes—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#555—111no—
153D4×Q8—111no—
154#487—111no—
155#485—111no—
156#485D1111yescharacteristic, complemented
157#477—111no—
158#468—111no—
159#468—111no—
160#461—111no—
161#448—111no—
162#448—111no—
163C4×SD16—111no—
164#436—111no—
165#419—111no—
166#419—111no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11C22×D411yescharacteristic
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C4×C11—21no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11C2×#4111yescharacteristic
183C4×C11H(5,𝔽2)11yescharacteristic
184Dic11—22no—
185Dic11—21no—
186Dic11—21no—
187Dic11—41no—
188Dic11—41no—
189Dic11#13712yes—
190C22×Q8—111no—
191C22×Q8—111no—
192C2×SD16—111no—
193C2×SD16—111no—
194C2×SD16—111no—
195C2×M16—111no—
196C2×M16—111no—
197C4⋊Q8—111no—
198C4⋊Q8—111no—
199C4⋊Q8—221no—
200#124—221no—
201#124—221no—
202C22⋊Q8—111no—
203C22⋊Q8—221no—
204C22⋊Q8—221no—
205C22⋊Q8C2×D1111yescharacteristic
206#121—111no—
207#121—111no—
208#121—221no—
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—221no—
213#117—111no—
214#117—221no—
215#117C2×D1111yescharacteristic
216#107—111no—
217#107C2×D1111yescharacteristic
218#106C2×D1111yescharacteristic
219C4⋊C8—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103C2×D1111yescharacteristic
228#103C2×D1111yescharacteristic
229#102—111no—
230C22⋊C8—111no—
231C22⋊C8C2×D1111yescharacteristic
232C4×C8—111no—
233C2×C11—41no—
234C2×C11#54611yescharacteristic
235C2×C11C2×#13711yescharacteristic
236C2×C11#57711yescharacteristic
237D11—41no—
238D11—81no—
239C2×Q8—111no—
240C2×Q8—111no—
241C2×Q8—221no—
242C2×Q8—221no—
243C2×Q8—222no—
244C2×Q8—221no—
245C2×Q8—222no—
246C2×Q8—441no—
247C2×Q8—441no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—111no—
250C2×D4—111no—
251C2×D4—221no—
252C2×D4—221no—
253C22×C4—111no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4C22×D1111yescharacteristic
258SD16—222no—
259SD16—441no—
260SD16—441no—
261M16—441no—
262M16—441no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—111no—
269C4⋊C4—111no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4C22×D1111yescharacteristic
276C4⋊C4C22×D1111yescharacteristic
277C4⋊C4C22×D1111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—111no—
281C22⋊C4—111no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C42—21no—
288C42—111no—
289C42—221no—
290C42—221no—
291C11#332911yescharacteristic, complemented, Sylow
292C23—111no—
293C23—221no—
294C23D4×D1111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—112no—
298Q8—221no—
299Q8—221no—
300Q8—221no—
301Q8—442no—
302Q8—442no—
303Q8—881no—
304D4—222no—
305D4—221no—
306D4—221no—
307D4—881no—
308D4—881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—111no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4D4×D1111yescharacteristic
327C2×C4C23×D1111yescharacteristic
328C8—21no—
329C8—21no—
330C8—221no—
331C8—221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—221no—
336C22—221no—
337C22—221no—
338C22—441no—
339C22—441no—
340C22—441no—
341C22C2×D4×D1111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—112no—
348C4—221no—
349C4—221no—
350C4—222no—
351C4—441no—
352C4—441no—
353C4#41×D1111yescharacteristic
354C4#6704211yescharacteristic
355C2—41no—
356C2—441no—
357C2—881no—
358C2#1062318511yescharacteristic
359C2#1062330111yescharacteristic
360C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radical#10623063C2
hypercenter#485D11
hypocenterC11#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #10623163C2semidirect
3. C11×#485C2semidirect
4. #10622662C2semidirect
5. #10622617C2semidirect
6. #10622499C2semidirect
7. #10622488C2semidirect
8. #10622480C2semidirect
9. #10622465C2semidirect
10. #10622431C2semidirect
11. #10622419C2semidirect
12. #10622415C2semidirect
13. #10622405C2semidirect
14. #10622351C2semidirect
15. #10622342C2semidirect
156. #485D11semidirect
291. C11#3329semidirect

Maximal subgroups

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

subgroupindex
#106231632
#106230632
C11×#4852
#106226622
#106226172
#106224992
#106224882
#106224802
#106224652
#106224312
#106224192
#106224152
#106224052
#106223512
#106223422
#332911