Finite Group Databasebeta

← #13079242

Subgroups — #13079242

Order 1408.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623114C211yesmaximal, characteristic, complemented
2#10623093C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622788C211yesmaximal, characteristic, complemented
5#10622787C211yesmaximal, characteristic, complemented
6C4×#4325C211yesmaximal, characteristic, complemented
7C4×#4324C211yesmaximal, characteristic, complemented
8#10622499C211yesmaximal, characteristic, complemented
9#10622491C211yesmaximal, characteristic, complemented
10#10622420C211yesmaximal, characteristic, complemented
11#10622410C211yesmaximal, characteristic, complemented
12#10622391C211yesmaximal, characteristic, complemented
13#10622377C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622321C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66999C2211yescharacteristic
20#66997C2211yescharacteristic
21C2×#4325C2211yescharacteristic
22#66993C2211yescharacteristic
23#66991C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25#66983—21no—
26#66982—21no—
27C2×#4314C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66950C2211yescharacteristic
32#66948C2211yescharacteristic
33#66943C2211yescharacteristic
34#66943C2211yescharacteristic
35#66942—21no—
36#66937—21no—
37#66936—21no—
38#66929—21no—
39C4×D44C2211yescharacteristic
40#66925C2211yescharacteristic
41#66923—21no—
42C4×Dic22C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66885C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
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—
65C2×D44—21no—
66C2×D44C2311yescharacteristic
67C2×C4×D11—21no—
68C2×C4×D11C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C11×SD16—22no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
80#4325—22no—
81#4324—22no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4D411yescharacteristic
87(C2×D11)⋊C4D411yescharacteristic
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100Dic11⋊C4D411yescharacteristic
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#4314—22no—
106#4313—22no—
107C8×D11—22no—
108#3174—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
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—21no—
136C4×D11—21no—
137C4×D11—81no—
138Dic22—21no—
139Dic22—21no—
140C8×C11—21no—
141C8×C11#4112yes—
142C11⋊C8—21no—
143C11⋊C8#4112yes—
144#541—111no—
145#540—111no—
146#499—111no—
147#492—111no—
148#491—111no—
149#490—111no—
150#468—111no—
151#468—111no—
152#465—111no—
153#465—111no—
154#440—111no—
155#440D1111yescharacteristic, complemented
156C4×SD16—111no—
157C4×SD16—111no—
158#405—111no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11C22×D411yescharacteristic
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11C2×#4111yescharacteristic
175C4×C11C2×#4111yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×SD16—111no—
183C2×SD16—111no—
184C2×SD16—111no—
185C2×SD16C2×D1111yescharacteristic
186C2×M16—111no—
187C22×C8—111no—
188C4⋊Q8—111no—
189#127—111no—
190#126—221no—
191#126—221no—
192#125—111no—
193#125—111no—
194#125—221no—
195#125—221no—
196#123—221no—
197#123—221no—
198C22⋊Q8—111no—
199C22⋊Q8—111no—
200#121—111no—
201#121—111no—
202#121—221no—
203#121—221no—
204C4×Q8—111no—
205C4×Q8C2×D1111yescharacteristic
206C4×D4—111no—
207C4×D4C2×D1111yescharacteristic
208#117—111no—
209#107—111no—
210#107C2×D1111yescharacteristic
211#106—111no—
212#106—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#103C2×D1111yescharacteristic
217#102—111no—
218#102—111no—
219#102—111no—
220#102C2×D1111yescharacteristic
221#97—111no—
222#97C2×D1111yescharacteristic
223C4×C8—111no—
224C4×C8—111no—
225C2×C11—81no—
226C2×C11#53211yescharacteristic
227C2×C11#57711yescharacteristic
228C2×C11#57711yescharacteristic
229D11—41no—
230D11—81no—
231C2×Q8—111no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—111no—
234C2×D4—221no—
235C2×D4—221no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4C22×D1111yescharacteristic
239C22×C4—21no—
240C22×C4—111no—
241C22×C4—221no—
242SD16—22no—
243SD16—222no—
244SD16—222no—
245SD16—222no—
246M16—222no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—222no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
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—
275C22⋊C4—221no—
276C42—21no—
277C42—111no—
278C42—221no—
279C42C22×D1111yescharacteristic
280C11#317411yescharacteristic, complemented, Sylow
281C23—21no—
282C23—111no—
283C23—221no—
284Q8—21no—
285Q8—21no—
286Q8—221no—
287Q8—221no—
288D4—21no—
289D4—21no—
290D4—221no—
291D4—221no—
292D4—881no—
293D4—881no—
294D4—881no—
295D4—881no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—881no—
309C2×C4D4×D1111yescharacteristic
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—112no—
314C8—221no—
315C8#433912yes—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—221no—
320C22—221no—
321C22—221no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—221no—
332C4—221no—
333C4—221no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4C2×#433911yescharacteristic
338C4#41×D1111yescharacteristic
339C2—81no—
340C2—441no—
341C2—881no—
342C2#1062307911yescharacteristic
343C2#1062330611yescharacteristic
344C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#10623093C2
hypercenter#440D11
hypocenterC11#3174
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. #10623114C2semidirect
3. C11×#440C2semidirect
4. #10622788C2semidirect
5. #10622787C2semidirect
6. C4×#4325C2semidirect
7. C4×#4324C2semidirect
8. #10622499C2semidirect
9. #10622491C2semidirect
10. #10622420C2semidirect
11. #10622410C2semidirect
12. #10622391C2semidirect
13. #10622377C2semidirect
14. #10622323C2semidirect
15. #10622321C2semidirect
155. #440D11semidirect
280. C11#3174semidirect

Maximal subgroups

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

subgroupindex
#106231142
#106230932
C11×#4402
#106227882
#106227872
C4×#43252
C4×#43242
#106224992
#106224912
#106224202
#106224102
#106223912
#106223772
#106223232
#106223212
#317411