Finite Group Databasebeta

← #13079509

Subgroups — #13079509

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#10623347C211yesmaximal, characteristic
2#10623159C211yesmaximal, characteristic
3C11×#451C211yesmaximal, characteristic, complemented
4#10622841C211yesmaximal, characteristic, complemented
5#10622802C211yesmaximal, characteristic, complemented
6#10622801C211yesmaximal, characteristic, complemented
7#10622799C211yesmaximal, characteristic, complemented
8#10622799C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622429C211yesmaximal, characteristic, complemented
11#10622428C211yesmaximal, characteristic, complemented
12#10622427C211yesmaximal, characteristic, complemented
13#10622426C211yesmaximal, characteristic, complemented
14#10622340C211yesmaximal, characteristic
15#10622336C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22#67000—21no—
23#66999C2211yescharacteristic
24#66999C2211yescharacteristic
25#66999C2211yescharacteristic
26#66999C2211yescharacteristic
27#66999C2211yescharacteristic
28#66997—21no—
29C2×#4326C2211yescharacteristic
30C2×#4326C2211yescharacteristic
31#66982—21no—
32#66982—21no—
33#66979C2211yescharacteristic
34#66977C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36C2×C8×D11C2211yescharacteristic
37#66950C2211yescharacteristic
38#66947—21no—
39#66945C2211yescharacteristic
40#66941—21no—
41#66938—21no—
42#66936—21no—
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66882C2211yescharacteristic
54#66881C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C2×Q8×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11D411yescharacteristic
68C2×C22⋊D11D411yescharacteristic
69Q8×D11—41no—
70Q8×D11—41no—
71#4339—41no—
72#4339—41no—
73C2×D44D411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11C2311yescharacteristic
76C2×C4×D11C2311yescharacteristic
77C2×Dic22—21no—
78C2×Dic22D411yescharacteristic
79C2×Dic22C2311yescharacteristic
80C11×Q16—41no—
81C11×Q16—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4—21no—
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89#4326—41no—
90#4326—41no—
91(C2×D11)⋊C4—21no—
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—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
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—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123Q8×C11—21no—
124Q8×C11—42no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C22⋊D11—41no—
135C22⋊D11—41no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142D44—41no—
143C4×D11—21no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—42no—
148Dic22—21no—
149Dic22—21no—
150Dic22—41no—
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#485—111no—
162#470—111no—
163#470—111no—
164#467—111no—
165#467—111no—
166#451—111no—
167#451—111no—
168#451—111no—
169#451D1111yescharacteristic, complemented
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×Q8C2×D1111yescharacteristic
197C2×Q16—111no—
198C2×Q16—111no—
199C2×Q16C2×D1111yescharacteristic
200C2×Q16C2×D1111yescharacteristic
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#117—111no—
221#107—111no—
222#107—111no—
223#106—111no—
224#106—111no—
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—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—111no—
249C2×Q8—111no—
250C2×Q8—221no—
251C2×Q8—441no—
252C2×Q8—441no—
253C2×Q8C22×D1111yescharacteristic
254C2×Q8C22×D1111yescharacteristic
255C2×Q8C22×D1111yescharacteristic
256C2×D4—111no—
257C2×D4—111no—
258C2×D4—111no—
259C22×C4—21no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—221no—
263C22×C4C22×D1111yescharacteristic
264Q16—41no—
265Q16—41no—
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—111no—
277C4⋊C4—111no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4C22×D1111yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—221no—
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—221no—
297C42—221no—
298C11#320211yescharacteristic, complemented, Sylow
299C23—111no—
300C23—111no—
301C23D4×D1111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309Q8—221no—
310Q8—221no—
311Q8—441no—
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—42no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
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#6703711yescharacteristic
362C4#6703711yescharacteristic
363C2—41no—
364C2—441no—
365C2—441no—
366C2#1062312011yescharacteristic
367C2#1062329711yescharacteristic
368C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#451D11
hypocenterC11#3202
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. C11×#451C2semidirect
4. #10622841C2semidirect
5. #10622802C2semidirect
6. #10622801C2semidirect
7. #10622799C2semidirect
8. #10622799C2semidirect
9. #10622658C2semidirect
10. #10622429C2semidirect
11. #10622428C2semidirect
12. #10622427C2semidirect
13. #10622426C2semidirect
15. #10622336C2semidirect
169. #451D11semidirect
298. C11#3202semidirect

Maximal subgroups

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

subgroupindex
#106233472
#106231592
C11×#4512
#106228412
#106228022
#106228012
#106227992
#106226582
#106224292
#106224282
#106224272
#106224262
#106223402
#106223362
#320211