Finite Group Databasebeta

← #13079495

Subgroups — #13079495

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#10623159C211yesmaximal, characteristic, complemented
3C11×#452C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622802C211yesmaximal, characteristic, complemented
6#10622799C211yesmaximal, characteristic, complemented
7#10622784C211yesmaximal, characteristic, complemented
8#10622783C211yesmaximal, characteristic, complemented
9#10622657C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622426C211yesmaximal, characteristic, complemented
12#10622393C211yesmaximal, characteristic, complemented
13#10622392C211yesmaximal, characteristic, complemented
14#10622340C211yesmaximal, characteristic, complemented
15#10622334C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22#66999C2211yescharacteristic
23#66999C2211yescharacteristic
24#66999C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26#66992—21no—
27#66992—21no—
28#66991C2211yescharacteristic
29#66991C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31#66983—21no—
32C2×C4⋊Dic11C2211yescharacteristic
33#66977—21no—
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×#102C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66881C2211yescharacteristic
54#66881C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11D411yescharacteristic
70C2×C22⋊D11D411yescharacteristic
71C22×Dic11—21no—
72Q8×D11—41no—
73Q8×D11—41no—
74#4339—41no—
75#4339—41no—
76C2×D44D411yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C2×Dic22—21no—
81C2×Dic22D411yescharacteristic
82C2×Dic22C2311yescharacteristic
83C11×Q16—41no—
84C11×SD16—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4—21no—
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93#4326—41no—
94#4324—41no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11C2311yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#4313—41no—
113C8×D11—41no—
114#3201—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11C2×D411yescharacteristic
118C22×D11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—42no—
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—
136C22⋊D11—81no—
137C22⋊D11—81no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—81no—
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145D44—41no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—42no—
151Dic22—21no—
152Dic22—21no—
153Dic22—41no—
154Dic22—42no—
155C8×C11—21no—
156C8×C11—21no—
157C11⋊C8—21no—
158C11⋊C8—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#452D1111yescharacteristic, complemented
171#451—111no—
172#448—111no—
173#408—111no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11H(5,𝔽2)11yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193Dic11—21no—
194Dic11—21no—
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C2×#41C2×D1111yescharacteristic
201C22×Q8—111no—
202C2×Q16—111no—
203C2×Q16C2×D1111yescharacteristic
204C2×SD16—111no—
205C2×SD16C2×D1111yescharacteristic
206C2×M16—111no—
207C22×C8—111no—
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—221no—
218C22⋊Q8C2×D1111yescharacteristic
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#103C2×D1111yescharacteristic
236#102—111no—
237#102C2×D1111yescharacteristic
238C22⋊C8—111no—
239C22⋊C8—111no—
240C22⋊C8—111no—
241C22⋊C8C2×D1111yescharacteristic
242C2×C11—41no—
243C2×C11—81no—
244C2×C11#53411yescharacteristic
245C2×C11#57711yescharacteristic
246C2×C11#57811yescharacteristic
247D11—41no—
248D11—41no—
249#41—41no—
250#41—41no—
251#41—441no—
252#41—441no—
253C2×Q8—111no—
254C2×Q8—111no—
255C2×Q8—221no—
256C2×Q8—441no—
257C2×Q8—441no—
258C2×Q8C22×D1111yescharacteristic
259C2×Q8C22×D1111yescharacteristic
260C2×D4—21no—
261C2×D4—111no—
262C2×D4—111no—
263C2×D4—111no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4C22×D1111yescharacteristic
267C22×C4—21no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4C22×D1111yescharacteristic
273Q16—41no—
274Q16—441no—
275SD16—41no—
276SD16—441no—
277M16—441no—
278C2×C8—111no—
279C2×C8—111no—
280C2×C8—441no—
281C2×C8C22×D1111yescharacteristic
282C2×C8C22×D1111yescharacteristic
283C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
294C22⋊C4—21no—
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—21no—
306C23—111no—
307C23—111no—
308C23D4×D1111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—221no—
314Q8—221no—
315Q8—441no—
316Q8—442no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—441no—
321D4—441no—
322D4—441no—
323D4—881no—
324D4—881no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—442no—
342C2×C4—881no—
343C2×C4D4×D1111yescharacteristic
344C2×C4C23×D1111yescharacteristic
345C8—21no—
346C8—21no—
347C8—221no—
348C8—221no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—221no—
356C22—221no—
357C22—221no—
358C22—221no—
359C22—221no—
360C22—221no—
361C22C2×D4×D1111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—221no—
367C4—221no—
368C4—441no—
369C4—441no—
370C4—441no—
371C4—441no—
372C4#6703711yescharacteristic
373C4#6703711yescharacteristic
374C2—41no—
375C2—81no—
376C2—441no—
377C2—441no—
378C2#1062312011yescharacteristic
379C2#1062330111yescharacteristic
380C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
prime radical#10623364C2
hypercenter#452D11
hypocenterC11#3201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10623159C2semidirect
3. C11×#452C2semidirect
4. #10622852C2semidirect
5. #10622802C2semidirect
6. #10622799C2semidirect
7. #10622784C2semidirect
8. #10622783C2semidirect
9. #10622657C2semidirect
10. #10622428C2semidirect
11. #10622426C2semidirect
12. #10622393C2semidirect
13. #10622392C2semidirect
14. #10622340C2semidirect
15. #10622334C2semidirect
170. #452D11semidirect
304. C11#3201semidirect

Maximal subgroups

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

subgroupindex
#106233642
#106231592
C11×#4522
#106228522
#106228022
#106227992
#106227842
#106227832
#106226572
#106224282
#106224262
#106223932
#106223922
#106223402
#106223342
#320111