Finite Group Databasebeta

← #13078906

Subgroups — #13078906

Order 1408.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623103C211yesmaximal, characteristic, complemented
2#10623093C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622783C211yesmaximal, characteristic, complemented
5#10622776C211yesmaximal, characteristic, complemented
6C4×#4325C211yesmaximal, characteristic, complemented
7C4×#4324C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic, complemented
9#10622490C211yesmaximal, characteristic, complemented
10#10622419C211yesmaximal, characteristic, complemented
11#10622409C211yesmaximal, characteristic, complemented
12#10622397C211yesmaximal, characteristic, complemented
13#10622375C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622322C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21C2×#4325C2211yescharacteristic
22#66993C2211yescharacteristic
23#66991C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25#66983—21no—
26#66982—21no—
27C2×#4314C2211yescharacteristic
28#66948C2211yescharacteristic
29#66945—21no—
30#66945C2211yescharacteristic
31#66943C2211yescharacteristic
32#66940—21no—
33#66940C2211yescharacteristic
34#66937—21no—
35#66936—21no—
36C4×D44C2211yescharacteristic
37#66925—21no—
38#66925C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65Q8×D11—22no—
66Q8×D11—22no—
67C2×D44—21no—
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11C2311yescharacteristic
72C2×Dic22—21no—
73C2×Dic22C2311yescharacteristic
74C11×SD16—22no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C42×C11—21no—
82C42×C11C2311yescharacteristic
83C22⋊Dic11—21no—
84#4325—22no—
85#4324—22no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4D411yescharacteristic
90(C2×D11)⋊C4D411yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107#4314—22no—
108#3126—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11#4112yes—
114D4×C11—21no—
115D4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—81no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—81no—
124C22⋊D11—81no—
125C22⋊D11—81no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132D44—21no—
133D44—21no—
134D44—81no—
135C4×D11—24no—
136C4×D11—21no—
137C4×D11—21no—
138C4×D11—81no—
139Dic22—24no—
140Dic22—21no—
141Dic22#4112yes—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#540—111no—
147#519—111no—
148#482—111no—
149#482—111no—
150#479—111no—
151#479—111no—
152#460—111no—
153#460—111no—
154#448—111no—
155#448—111no—
156#440—111no—
157#440D1111yescharacteristic, complemented
158C4×SD16—111no—
159C4×SD16—111no—
160#433—111no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11C22×D411yescharacteristic
165C2×D11—21no—
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C4×C11—22no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11C2×#4111yescharacteristic
177C4×C11C2×#4111yescharacteristic
178Dic11—21no—
179Dic11—22no—
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184C22×Q8—111no—
185C2×SD16—111no—
186C2×SD16—111no—
187C2×SD16—111no—
188C2×SD16C2×D1111yescharacteristic
189#127—111no—
190#125—111no—
191#123—221no—
192#123—221no—
193#121—111no—
194#121—111no—
195#121—221no—
196#121—221no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—111no—
200C4×Q8—221no—
201C4×Q8—221no—
202C4×Q8C2×D1111yescharacteristic
203C4×D4—111no—
204C4×D4C2×D1111yescharacteristic
205#117—111no—
206#117—111no—
207#117—221no—
208#117—221no—
209#107—111no—
210#107C2×D1111yescharacteristic
211#106—111no—
212#106—111no—
213C4⋊C8—111no—
214C4⋊C8—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103C2×D1111yescharacteristic
219#102—111no—
220#102—111no—
221#102—111no—
222#102C2×D1111yescharacteristic
223C22⋊C8—111no—
224C22⋊C8—111no—
225#97C2×D1111yescharacteristic
226C4×C8—111no—
227C2×C11—81no—
228C2×C11#52511yescharacteristic
229C2×C11#57711yescharacteristic
230C2×C11#57711yescharacteristic
231D11—41no—
232D11—81no—
233C2×Q8—111no—
234C2×Q8—221no—
235C2×Q8—222no—
236C2×Q8—222no—
237C2×Q8C22×D1111yescharacteristic
238C2×D4—111no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4C22×D1111yescharacteristic
244C22×C4—21no—
245C22×C4—111no—
246C22×C4—221no—
247C22×C4—221no—
248SD16—22no—
249SD16—222no—
250SD16—222no—
251SD16—222no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4C22×D1111yescharacteristic
267C4⋊C4C22×D1111yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—111no—
270C22⋊C4—111no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C42—21no—
276C42—111no—
277C42—221no—
278C42—221no—
279C42—221no—
280C42—221no—
281C42C22×D1111yescharacteristic
282C11#312611yescharacteristic, complemented, Sylow
283C23—21no—
284C23—111no—
285C23—221no—
286Q8—21no—
287Q8—112no—
288Q8—224no—
289Q8—221no—
290Q8#433912yes—
291D4—21no—
292D4—21no—
293D4—221no—
294D4—221no—
295D4—881no—
296D4—881no—
297D4—881no—
298D4—881no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—224no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—881no—
313C2×C4D4×D1111yescharacteristic
314C2×C4D4×D1111yescharacteristic
315C2×C4C23×D1111yescharacteristic
316C8—21no—
317C8—21no—
318C8—221no—
319C8—221no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—221no—
324C22—221no—
325C22—221no—
326C22—441no—
327C22—441no—
328C22—441no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—221no—
336C4—221no—
337C4—221no—
338C4—222no—
339C4—441no—
340C4—441no—
341C4C2×#433911yescharacteristic
342C4#41×D1111yescharacteristic
343C2—81no—
344C2—441no—
345C2—881no—
346C2#1062307811yescharacteristic
347C2#1062330611yescharacteristic
348C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#10623093C2
hypercenter#440D11
hypocenterC11#3126
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623103C2semidirect
3. C11×#440C2semidirect
4. #10622783C2semidirect
5. #10622776C2semidirect
6. C4×#4325C2semidirect
7. C4×#4324C2semidirect
8. #10622498C2semidirect
9. #10622490C2semidirect
10. #10622419C2semidirect
11. #10622409C2semidirect
12. #10622397C2semidirect
13. #10622375C2semidirect
14. #10622323C2semidirect
15. #10622322C2semidirect
157. #440D11semidirect
282. C11#3126semidirect

Maximal subgroups

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

subgroupindex
#106231032
#106230932
C11×#4402
#106227832
#106227762
C4×#43252
C4×#43242
#106224982
#106224902
#106224192
#106224092
#106223972
#106223752
#106223232
#106223222
#312611