Finite Group Databasebeta

← #13079501

Subgroups — #13079501

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#10623160C211yesmaximal, characteristic
2#10623159C211yesmaximal, characteristic, complemented
3C11×#467C211yesmaximal, characteristic, complemented
4#10622800C211yesmaximal, characteristic, complemented
5#10622799C211yesmaximal, characteristic, complemented
6#10622727C211yesmaximal, characteristic, complemented
7#10622723C211yesmaximal, characteristic, complemented
8#10622665C211yesmaximal, characteristic, complemented
9#10622662C211yesmaximal, characteristic, complemented
10#10622498C211yesmaximal, characteristic, complemented
11#10622497C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic, complemented
13#10622423C211yesmaximal, characteristic, complemented
14#10622419C211yesmaximal, characteristic, complemented
15#10622418C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C22×C8×C11C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic
23#66999C2211yescharacteristic
24#66999C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27#66983C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×#4318C2211yescharacteristic
30C2×#4314C2211yescharacteristic
31#66950C2211yescharacteristic
32#66949—21no—
33#66948—21no—
34#66948C2211yescharacteristic
35#66947—21no—
36#66945C2211yescharacteristic
37C4⋊C4×D11C2211yescharacteristic
38#66941—21no—
39#66938—21no—
40#66937—21no—
41#66937—21no—
42#66936—21no—
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66881C2211yescharacteristic
54#66880C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64C2×C22⋊D11D411yescharacteristic
65#4343—41no—
66#4343—41no—
67Q8×D11—41no—
68Q8×D11—41no—
69#4339—41no—
70#4339—41no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44D411yescharacteristic
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C2×Dic22—21no—
81C2×Dic22D411yescharacteristic
82C2×Dic22C2311yescharacteristic
83C11×Q16—41no—
84C2×C8×C11—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C22⋊Dic11—21no—
94#4326—41no—
95#4325—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110#4318—41no—
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113#4314—41no—
114#3201—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117C22×D11C2×D411yescharacteristic
118C22×D11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
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×C11C2411yescharacteristic
131C22⋊D11—41no—
132C22⋊D11—41no—
133C22⋊D11—81no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139D44—21no—
140D44—21no—
141D44—41no—
142D44—42no—
143D44—81no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—42no—
149C4×D11—42no—
150C4×D11—81no—
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#467D1111yescharacteristic, complemented
168#465—111no—
169#452—111no—
170#452—111no—
171#451—111no—
172#448—111no—
173#408—111no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11H(5,𝔽2)11yescharacteristic
193C4×C11H(5,𝔽2)11yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41—111no—
200C2×#41—111no—
201C22×Q8—111no—
202C2×Q16—111no—
203C2×Q16C2×D1111yescharacteristic
204C2×SD16—111no—
205C2×SD16—111no—
206C2×M16—111no—
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—221no—
217C22⋊Q8C2×D1111yescharacteristic
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#107C2×D1111yescharacteristic
228#106—111no—
229#106—111no—
230#103—111no—
231#103—111no—
232#103—111no—
233#103—111no—
234#103C2×D1111yescharacteristic
235#103C2×D1111yescharacteristic
236#102—111no—
237#102—111no—
238C22⋊C8—111no—
239C22⋊C8—111no—
240C22⋊C8—111no—
241C22⋊C8—111no—
242C2×C11—41no—
243C2×C11#53411yescharacteristic
244C2×C11#57711yescharacteristic
245C2×C11#57811yescharacteristic
246D11—41no—
247D11—41no—
248D11—81no—
249#41—441no—
250#41—441no—
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—111no—
261C2×D4—111no—
262C2×D4—111no—
263C2×D4—111no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4C22×D1111yescharacteristic
273Q16—41no—
274Q16—441no—
275SD16—441no—
276SD16—441no—
277M16—441no—
278C2×C8—41no—
279C2×C8—111no—
280C2×C8—111no—
281C2×C8C22×D1111yescharacteristic
282C2×C8C22×D1111yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4C22×D1111yescharacteristic
293C4⋊C4C22×D1111yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—21no—
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—111no—
306C23—111no—
307C23—221no—
308C23D4×D1111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—221no—
314Q8—221no—
315Q8—441no—
316Q8—442no—
317D4—221no—
318D4—221no—
319D4—441no—
320D4—442no—
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—21no—
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—442no—
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—221no—
353C22—221no—
354C22—221no—
355C22—221no—
356C22—221no—
357C22—221no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22C2×D4×D1111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—221no—
368C4—221no—
369C4—441no—
370C4—441no—
371C4—441no—
372C4#6703711yescharacteristic
373C4#6704211yescharacteristic
374C2—41no—
375C2—441no—
376C2—441no—
377C2—881no—
378C2#1062313611yescharacteristic
379C2#1062329711yescharacteristic
380C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#467C2
socleC22×C11C22×D4
prime radical#10623160C2
hypercenter#467D11
hypocenterC11#3201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #10623159C2semidirect
3. C11×#467C2semidirect
4. #10622800C2semidirect
5. #10622799C2semidirect
6. #10622727C2semidirect
7. #10622723C2semidirect
8. #10622665C2semidirect
9. #10622662C2semidirect
10. #10622498C2semidirect
11. #10622497C2semidirect
12. #10622428C2semidirect
13. #10622423C2semidirect
14. #10622419C2semidirect
15. #10622418C2semidirect
167. #467D11semidirect
304. C11#3201semidirect

Maximal subgroups

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

subgroupindex
#106231602
#106231592
C11×#4672
#106228002
#106227992
#106227272
#106227232
#106226652
#106226622
#106224982
#106224972
#106224282
#106224232
#106224192
#106224182
#320111