Finite Group Databasebeta

← #13079500

Subgroups — #13079500

Order 1408.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623364C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic, complemented
3C11×#408C211yesmaximal, characteristic, complemented
4#10622750C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622729C211yesmaximal, characteristic, complemented
7#10622727C211yesmaximal, characteristic, complemented
8#10622352C211yesmaximal, characteristic, complemented
9#10622351C211yesmaximal, characteristic, complemented
10#10622350C211yesmaximal, characteristic, complemented
11#10622346C211yesmaximal, characteristic, complemented
12#10622346C211yesmaximal, characteristic, complemented
13#10622336C211yesmaximal, characteristic, complemented
14#10622335C211yesmaximal, characteristic, complemented
15#10622334C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C2×C11×M16C2211yescharacteristic
20C22×C8×C11C2211yescharacteristic
21#66999—21no—
22#66997—21no—
23#66992—21no—
24#66992—21no—
25#66991—21no—
26#66989—21no—
27#66988—21no—
28#66988—21no—
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic
31#66979C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33#66977C2211yescharacteristic
34#66977C2211yescharacteristic
35#66977C2211yescharacteristic
36#66977C2211yescharacteristic
37#66977C2211yescharacteristic
38#66977C2211yescharacteristic
39C2×Dic44C2211yescharacteristic
40C2×Dic44C2211yescharacteristic
41C2×#4314C2211yescharacteristic
42C2×#4314C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46C11×C22⋊C8C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C2×Q8×C11D411yescharacteristic
62C2×D4×C11D411yescharacteristic
63C2×D4×C11D411yescharacteristic
64C2×D4×C11D411yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73#4339—41no—
74#4339—41no—
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×Dic22—21no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22C2311yescharacteristic
81C2×Dic22C2311yescharacteristic
82C2×Dic22C2311yescharacteristic
83C11×M16—41no—
84C2×C8×C11—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C2×C8×C11C2311yescharacteristic
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110Dic44—41no—
111Dic44—41no—
112#4314—41no—
113#4314—41no—
114#3201—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C23×C11C2×D411yescharacteristic
117C23×C11C2×D411yescharacteristic
118C22×D11—21no—
119Q8×C11—41no—
120D4×C11—41no—
121D4×C11—41no—
122D4×C11—41no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—42no—
134C22⋊D11—81no—
135C22⋊D11—81no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—42no—
144C2×Dic11—81no—
145D44—21no—
146D44—21no—
147C4×D11—42no—
148Dic22—21no—
149Dic22—21no—
150Dic22—21no—
151Dic22—21no—
152Dic22—21no—
153Dic22—21no—
154Dic22—42no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—21no—
159#537—111no—
160#536—111no—
161#485—111no—
162#484—111no—
163#483—111no—
164#482—111no—
165#470—111no—
166#468—111no—
167#467—111no—
168#465—111no—
169#452—111no—
170#452—111no—
171#451—111no—
172#448—111no—
173#408D1111yescharacteristic, complemented
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11C22×D411yescharacteristic
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11H(5,𝔽2)11yescharacteristic
191C4×C11H(5,𝔽2)11yescharacteristic
192Dic11—41no—
193Dic11—41no—
194Dic11—41no—
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C2×#41C2×D1111yescharacteristic
201C22×Q8—111no—
202C2×Q16—111no—
203C2×Q16—111no—
204C2×SD16—111no—
205C2×SD16—111no—
206C2×M16C2×D1111yescharacteristic
207C22×C8C2×D1111yescharacteristic
208C4⋊Q8—221no—
209#124—221no—
210#123—221no—
211#123—221no—
212C22⋊Q8—111no—
213C22⋊Q8—111no—
214C22⋊Q8—111no—
215C22⋊Q8—111no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218C22⋊Q8—221no—
219#121—111no—
220#121—111no—
221#121—221no—
222#121—221no—
223#121—221no—
224#117—111no—
225C2×C4⋊C4—111no—
226#107—111no—
227#107—111no—
228#106—111no—
229#106—111no—
230#103—111no—
231#103—111no—
232#103—111no—
233#103—111no—
234#103—111no—
235#103—111no—
236#102—111no—
237#102—111no—
238C22⋊C8C2×D1111yescharacteristic
239C22⋊C8C2×D1111yescharacteristic
240C22⋊C8C2×D1111yescharacteristic
241C22⋊C8C2×D1111yescharacteristic
242C2×C11—41no—
243C2×C11—41no—
244C2×C11—41no—
245C2×C11#53411yescharacteristic
246C2×C11#57711yescharacteristic
247C2×C11#57811yescharacteristic
248D11—81no—
249#41—41no—
250#41—41no—
251#41—441no—
252#41—441no—
253C2×Q8—111no—
254C2×Q8—111no—
255C2×Q8—111no—
256C2×Q8—221no—
257C2×Q8—441no—
258C2×Q8—441no—
259C2×Q8D4411yescharacteristic
260C2×D4—111no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4D4411yescharacteristic
265C2×D4D4411yescharacteristic
266C2×D4D4411yescharacteristic
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273Q16—441no—
274Q16—441no—
275SD16—441no—
276SD16—441no—
277M16—41no—
278C2×C8—41no—
279C2×C8C22×D1111yescharacteristic
280C2×C8C22×D1111yescharacteristic
281C2×C8C22×D1111yescharacteristic
282C2×C8C22×D1111yescharacteristic
283C4⋊C4—111no—
284C4⋊C4—111no—
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C42—221no—
304C11#320111yescharacteristic, complemented, Sylow
305C23—221no—
306C23C2×D4411yescharacteristic
307C23C2×D4411yescharacteristic
308C23C2×D4411yescharacteristic
309Q8—41no—
310Q8—221no—
311Q8—221no—
312Q8—221no—
313Q8—221no—
314Q8—221no—
315Q8—221no—
316Q8—442no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—221no—
321D4—221no—
322D4—442no—
323D4—881no—
324D4—881no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—881no—
341C2×C4C2×D4411yescharacteristic
342C2×C4C2×D4411yescharacteristic
343C2×C4C2×D4411yescharacteristic
344C2×C4C23×D1111yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22C22×D4411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—441no—
366C4—441no—
367C4—441no—
368C4—441no—
369C4—441no—
370C4—441no—
371C4—441no—
372C4#6703711yescharacteristic
373C4#6703711yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—881no—
378C2#1062302411yescharacteristic
379C2#1062328211yescharacteristic
380C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#408C2
socleC22×C11C22×D4
prime radical#10623364C2
hypercenter#408D11
hypocenterC11#3201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #10623356C2semidirect
3. C11×#408C2semidirect
4. #10622750C2semidirect
5. #10622747C2semidirect
6. #10622729C2semidirect
7. #10622727C2semidirect
8. #10622352C2semidirect
9. #10622351C2semidirect
10. #10622350C2semidirect
11. #10622346C2semidirect
12. #10622346C2semidirect
13. #10622336C2semidirect
14. #10622335C2semidirect
15. #10622334C2semidirect
173. #408D11semidirect
304. C11#3201semidirect

Maximal subgroups

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

subgroupindex
#106233642
#106233562
C11×#4082
#106227502
#106227472
#106227292
#106227272
#106223522
#106223512
#106223502
#106223462
#106223362
#106223352
#106223342
#320111