Finite Group Databasebeta

← #13081666

Subgroups — #13081666

Order 1408.

362 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623252C211yesmaximal, characteristic, complemented
2#10623212C211yesmaximal, characteristic
3C11×#497C211yesmaximal, characteristic, complemented
4#10622803C211yesmaximal, characteristic, complemented
5#10622798C211yesmaximal, characteristic, complemented
6Q16×Dic11C211yesmaximal, characteristic, complemented
7#10622795C211yesmaximal, characteristic, complemented
8#10622788C211yesmaximal, characteristic
9#10622777C211yesmaximal, characteristic, complemented
10#10622776C211yesmaximal, characteristic
11#10622775C211yesmaximal, characteristic, complemented
12#10622696C211yesmaximal, characteristic, complemented
13#10622667C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×C4⋊Q8C2211yescharacteristic
21C11×#124C2211yescharacteristic
22#67000C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24Q8×Dic11C2211yescharacteristic
25Q8×Dic11C2211yescharacteristic
26#66997C2211yescharacteristic
27#66997C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30C2×#4325C2211yescharacteristic
31#66993C2211yescharacteristic
32D4×Dic11C2211yescharacteristic
33C2×#4324C2211yescharacteristic
34C2×#4314C2211yescharacteristic
35#66943—21no—
36#66942—21no—
37#66942—21no—
38#66940—21no—
39#66939—21no—
40#66938—21no—
41#66936—21no—
42(C22⋊D11)⋊C4—21no—
43C4×D44C2211yescharacteristic
44C4×Dic22C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50#66896C2211yescharacteristic
51#66885C2211yescharacteristic
52#66882C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57C8×Dic11C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C22×Dic11—21no—
66C2×D44C2311yescharacteristic
67C2×C4×D11—21no—
68C2×Dic22D411yescharacteristic
69C2×Dic22C2311yescharacteristic
70C11×Q16—22no—
71C11×Q16—41no—
72C11×SD16—22no—
73C11×SD16—41no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C42×C11C2311yescharacteristic
81C22⋊Dic11—21no—
82#4326—41no—
83#4325—41no—
84#4325—41no—
85#4324—41no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11D411yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4314—22no—
111#3400—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114Q8×C11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—42no—
129C22⋊D11—81no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—81no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138D44—21no—
139D44—21no—
140C4×D11—81no—
141Dic22—22no—
142Dic22—21no—
143Dic22—21no—
144C8×C11—21no—
145C8×C11#4112yes—
146C11⋊C8—21no—
147C11⋊C8—21no—
148#559—111no—
149#557—111no—
150#497—111no—
151#497D1111yescharacteristic, complemented
152#492—111no—
153#464—111no—
154#464—111no—
155#462—111no—
156#461—111no—
157#461—111no—
158#460—111no—
159#446—111no—
160#440—111no—
161#440—111no—
162C4×Q16—111no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×D411yescharacteristic
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C11H(5,𝔽2)11yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11#13712yes—
184C2×Q16—111no—
185C2×Q16C2×D1111yescharacteristic
186C2×Q16C2×D1111yescharacteristic
187C2×SD16—111no—
188C2×SD16—111no—
189C2×SD16—111no—
190C2×SD16—111no—
191C2×SD16C2×D1111yescharacteristic
192C2×SD16C2×D1111yescharacteristic
193C4⋊Q8—111no—
194C4⋊Q8—111no—
195C4⋊Q8C2×D1111yescharacteristic
196#127—111no—
197#125—221no—
198#125—221no—
199#125—221no—
200#124—111no—
201#124—221no—
202#124C2×D1111yescharacteristic
203#123—221no—
204#123—221no—
205C4×Q8—111no—
206C4×Q8—111no—
207C4×Q8—111no—
208C4×Q8—111no—
209C4×Q8—111no—
210C4×Q8—221no—
211C4×D4—111no—
212C4×D4—111no—
213C4×D4—221no—
214#107—111no—
215C4⋊C8—111no—
216C4⋊C8—111no—
217C4⋊C8—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#102—111no—
223#102—111no—
224#97—111no—
225#97C2×D1111yescharacteristic
226C4×C8—111no—
227C2×C11—81no—
228C2×C11#55011yescharacteristic
229C2×C11C2×#13711yescharacteristic
230C2×C11#57711yescharacteristic
231D11—81no—
232C2×Q8—111no—
233C2×Q8—111no—
234C2×Q8C22×D1111yescharacteristic
235C2×Q8C22×D1111yescharacteristic
236C2×Q8C22×D1111yescharacteristic
237C2×D4—111no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4C22×D1111yescharacteristic
241C22×C4—221no—
242C22×C4—221no—
243Q16—22no—
244Q16—41no—
245Q16—441no—
246SD16—22no—
247SD16—41no—
248SD16—222no—
249SD16—441no—
250SD16—441no—
251SD16—441no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C42—111no—
278C42—111no—
279C42—221no—
280C42—221no—
281C42—221no—
282C42—221no—
283C42C22×D1111yescharacteristic
284C11#340011yescharacteristic, complemented, Sylow
285C23—21no—
286C23—221no—
287Q8—21no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—222no—
294Q8—221no—
295Q8—221no—
296D4—21no—
297D4—21no—
298D4—221no—
299D4—221no—
300D4—442no—
301D4—881no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—111no—
306C2×C4—111no—
307C2×C4—111no—
308C2×C4—111no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—881no—
313C2×C4—881no—
314C2×C4D4×D1111yescharacteristic
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—221no—
319C8—221no—
320C8#434112yes—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22C2×D4×D1111yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—112no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4—441no—
338C4—441no—
339C4—441no—
340C4C2×#434111yescharacteristic
341C4#6703711yescharacteristic
342C2—81no—
343C2—881no—
344C2#1062324911yescharacteristic
345C2D11×#13711yescharacteristic
346C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#497C2
socleC22×C11C22×D4
prime radical#66993C22
hypercenter#497D11
hypocenterC11#3400
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #10623252C2semidirect
3. C11×#497C2semidirect
4. #10622803C2semidirect
5. #10622798C2semidirect
6. Q16×Dic11C2semidirect
7. #10622795C2semidirect
9. #10622777C2semidirect
11. #10622775C2semidirect
12. #10622696C2semidirect
13. #10622667C2semidirect
14. #10622323C2semidirect
15. #10622314C2semidirect
151. #497D11semidirect
284. C11#3400semidirect

Maximal subgroups

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

subgroupindex
#106232522
#106232122
C11×#4972
#106228032
#106227982
Q16×Dic112
#106227952
#106227882
#106227772
#106227762
#106227752
#106226962
#106226672
#106223232
#106223142
#340011