Finite Group Databasebeta

← #13079510

Subgroups — #13079510

Order 1408.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623159C211yesmaximal, characteristic
2#10623057C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic, complemented
4#10622663C211yesmaximal, characteristic, complemented
5#10622609C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622500C211yesmaximal, characteristic, complemented
8#10622481C211yesmaximal, characteristic, complemented
9#10622480C211yesmaximal, characteristic, complemented
10#10622429C211yesmaximal, characteristic, complemented
11#10622426C211yesmaximal, characteristic, complemented
12#10622421C211yesmaximal, characteristic, complemented
13#10622421C211yesmaximal, characteristic, complemented
14#10622352C211yesmaximal, characteristic, complemented
15#10622340C211yesmaximal, characteristic
16C2×Q8×D11C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20C11×#117C2211yescharacteristic
21#66999C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24#66977C2211yescharacteristic
25C2×Dic44C2211yescharacteristic
26C2×Dic44C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29#66950C2211yescharacteristic
30#66950C2211yescharacteristic
31#66950C2211yescharacteristic
32#66950C2211yescharacteristic
33#66950C2211yescharacteristic
34#66947—21no—
35#66945C2211yescharacteristic
36#66941—21no—
37#66939—21no—
38#66939—21no—
39#66938—21no—
40#66936—21no—
41#66928—21no—
42#66922—21no—
43C11×#107C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×C22⋊C8C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11D411yescharacteristic
62C2×C22⋊D11D411yescharacteristic
63C22×Dic11—21no—
64Q8×D11—41no—
65Q8×D11—41no—
66#4339—41no—
67#4339—41no—
68C2×D44D411yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×C4×D11C2311yescharacteristic
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22D411yescharacteristic
77C2×Dic22C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C42×C11—21no—
89C22⋊Dic11—21no—
90#4326—41no—
91#4326—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110Dic44—41no—
111Dic44—41no—
112#4313—41no—
113C8×D11—41no—
114#3202—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C22×D11C2×D411yescharacteristic
117C22×D11C2×D411yescharacteristic
118Q8×C11—21no—
119Q8×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—41no—
129C22⋊D11—41no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—42no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137D44—41no—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—42no—
143Dic22—21no—
144Dic22—21no—
145Dic22—21no—
146Dic22—21no—
147Dic22—21no—
148Dic22—21no—
149Dic22—41no—
150Dic22—42no—
151Dic22—42no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#536—111no—
157#536—111no—
158#485—111no—
159#485—111no—
160#485—111no—
161#485D1111yescharacteristic, complemented
162#470—111no—
163#470—111no—
164#467—111no—
165#467—111no—
166#451—111no—
167#451—111no—
168#451—111no—
169#451—111no—
170#408—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11H(5,𝔽2)11yescharacteristic
187C4×C11H(5,𝔽2)11yescharacteristic
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194C2×#41—111no—
195C22×Q8—111no—
196C22×Q8—111no—
197C2×Q16—111no—
198C2×Q16—111no—
199C2×Q16—111no—
200C2×Q16—111no—
201C2×M16—111no—
202C22×C8—111no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205#124—221no—
206#124—221no—
207#123—221no—
208#123—221no—
209#123—221no—
210#123—221no—
211C22⋊Q8—111no—
212C22⋊Q8—111no—
213C22⋊Q8—111no—
214C22⋊Q8—111no—
215C22⋊Q8—111no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218C22⋊Q8C2×D1111yescharacteristic
219#117—111no—
220#117C2×D1111yescharacteristic
221#107—111no—
222#107C2×D1111yescharacteristic
223#106—111no—
224#106C2×D1111yescharacteristic
225#103—111no—
226#103—111no—
227#103—111no—
228#103—111no—
229#103—111no—
230#103—111no—
231#103C2×D1111yescharacteristic
232#103C2×D1111yescharacteristic
233C22⋊C8—111no—
234C22⋊C8—111no—
235C22⋊C8—111no—
236C22⋊C8C2×D1111yescharacteristic
237C2×C11—41no—
238C2×C11#53411yescharacteristic
239C2×C11#57811yescharacteristic
240C2×C11#57811yescharacteristic
241D11—41no—
242D11—41no—
243#41—441no—
244#41—441no—
245C2×Q8—111no—
246C2×Q8—111no—
247C2×Q8—111no—
248C2×Q8—111no—
249C2×Q8—221no—
250C2×Q8—221no—
251C2×Q8—441no—
252C2×Q8—441no—
253C2×Q8—441no—
254C2×Q8—441no—
255C2×Q8C22×D1111yescharacteristic
256C2×D4—111no—
257C2×D4—111no—
258C2×D4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4C22×D1111yescharacteristic
264Q16—441no—
265Q16—441no—
266Q16—441no—
267Q16—441no—
268M16—441no—
269C2×C8—111no—
270C2×C8—111no—
271C2×C8—441no—
272C2×C8C22×D1111yescharacteristic
273C2×C8C22×D1111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4C22×D1111yescharacteristic
284C4⋊C4C22×D1111yescharacteristic
285C4⋊C4C22×D1111yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C42—21no—
297C42—221no—
298C11#320211yescharacteristic, complemented, Sylow
299C23—111no—
300C23—111no—
301C23D4×D1111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—221no—
305Q8—221no—
306Q8—221no—
307Q8—221no—
308Q8—221no—
309Q8—221no—
310Q8—441no—
311Q8—442no—
312Q8—442no—
313D4—441no—
314D4—441no—
315D4—441no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—111no—
323C2×C4—111no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4D4×D1111yescharacteristic
335C2×C4C23×D1111yescharacteristic
336C8—21no—
337C8—21no—
338C8—221no—
339C8—221no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—221no—
344C22—221no—
345C22—221no—
346C22—221no—
347C22—221no—
348C22—221no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—221no—
356C4—221no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4—441no—
361C4#6704211yescharacteristic
362C4#6704211yescharacteristic
363C2—41no—
364C2—441no—
365C2—441no—
366C2#1062318411yescharacteristic
367C2#1062330211yescharacteristic
368C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#485D11
hypocenterC11#3202
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
3. C11×#485C2semidirect
4. #10622663C2semidirect
5. #10622609C2semidirect
6. #10622501C2semidirect
7. #10622500C2semidirect
8. #10622481C2semidirect
9. #10622480C2semidirect
10. #10622429C2semidirect
11. #10622426C2semidirect
12. #10622421C2semidirect
13. #10622421C2semidirect
14. #10622352C2semidirect
161. #485D11semidirect
298. C11#3202semidirect

Maximal subgroups

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

subgroupindex
#106231592
#106230572
C11×#4852
#106226632
#106226092
#106225012
#106225002
#106224812
#106224802
#106224292
#106224262
#106224212
#106223522
#106223402
#320211