Finite Group Databasebeta

← #13075592

Subgroups — #13075592

Order 1408.

480 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic
3#10622844C211yesmaximal, characteristic
4#10622843C211yesmaximal, characteristic, complemented
5#10622842C211yesmaximal, characteristic, complemented
6#10622607C211yesmaximal, characteristic
7#10622603C211yesmaximal, characteristic
8#10622602C211yesmaximal, characteristic
9#10622602C211yesmaximal, characteristic
10#10622599C211yesmaximal, characteristic, complemented
11#10622597C211yesmaximal, characteristic, complemented
12#10622596C211yesmaximal, characteristic, complemented
13#10622585C211yesmaximal, characteristic, complemented
14#10622553C211yesmaximal, characteristic
15#10622546C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C11×C4⋊Q8—24no—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C42×C11C2211yescharacteristic
25#66999—24no—
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C23×D11C2311yescharacteristic
54C2×Q8×C11—22no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11—41no—
58C2×Q8×C11—41no—
59C2×Q8×C11D414yes—
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C2×C4×D11—22no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C42×C11—22no—
82(C2×D11)⋊C4—22no—
83(C2×D11)⋊C4—22no—
84(C2×D11)⋊C4—22no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4Q814yescomplemented
88C4⋊Dic11—22no—
89C4⋊Dic11—41no—
90Dic11⋊C4—22no—
91Dic11⋊C4—22no—
92Dic11⋊C4—22no—
93Dic11⋊C4—22no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96C4×Dic11—41no—
97#2729—111nomaximal, Sylow
98C23×C11C2411yescharacteristic
99C22×D11—21no—
100C22×D11—21no—
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—21no—
105C22×D11C2×Q812yes—
106Q8×C11—44no—
107Q8×C11—44no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D412yes—
125C2×C4×C11C2×D412yes—
126C2×C4×C11C2×D412yes—
127C2×C4×C11C2×Q812yes—
128C2×C4×C11#4112yes—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11C2×Q812yes—
150C4×D11—44no—
151C2×C4⋊Q8D1111yescharacteristic, complemented
152C2×C22⋊Q8—111no—
153#400—111no—
154#398—111no—
155#398—111no—
156#396—111no—
157#395—111no—
158#393—111no—
159#391—111no—
160#389—111no—
161#388—111no—
162#388—111no—
163#387—111no—
164#385—111no—
165#385—111no—
166C22×C11C22×D411yescharacteristic
167C22×C11C22×Q811yescharacteristic
168C22×C11C2×#4111yescharacteristic
169C22×C11H(5,𝔽2)11yescharacteristic
170C22×C11H(5,𝔽2)11yescharacteristic
171C22×C112−1+411yescharacteristic
172C22×C112−1+411yescharacteristic
173C2×D11—22no—
174C2×D11—22no—
175C2×D11—22no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—22no—
184C4×C11—22no—
185C4×C11—41no—
186C4×C11—41no—
187Dic11—22no—
188Dic11—41no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194C22×Q8C2×D1111yescharacteristic
195C22×Q8C2×D1111yescharacteristic
196C23×C4—111no—
197C4⋊Q8—24no—
198C22⋊Q8—224no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4C2×D1111yescharacteristic
208C2×C4⋊C4C2×D1111yescharacteristic
209C2×C4⋊C4C2×D1111yescharacteristic
210C2×C4⋊C4C2×D1111yescharacteristic
211C2×C22⋊C4—111no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—111no—
215C2×C22⋊C4—111no—
216C2×C22⋊C4—111no—
217C2×C42—111no—
218C2×C42C2×D1111yescharacteristic
219#95—111no—
220#95—111no—
221#95—111no—
222#95—111no—
223#95—111no—
224#95—111no—
225#95—111no—
226#95—111no—
227#95—111no—
228#95—111no—
229#95—111no—
230#95—111no—
231C2×C11#53411yescharacteristic
232C2×C11#54211yescharacteristic
233C2×C11#54411yescharacteristic
234C2×C11#54811yescharacteristic
235C2×C11D4×Q811yescharacteristic
236C2×C11#55411yescharacteristic
237C2×C11#56311yescharacteristic
238D11—42no—
239C24—111no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8C22⋊D1114yes—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—111no—
252C22×C4—111no—
253C22×C4—222no—
254C22×C4—441no—
255C22×C4—441no—
256C22×C4C22×D1111yescharacteristic
257C22×C4C22×D1111yescharacteristic
258C22×C4C22×D1111yescharacteristic
259C22×C4C22×D1111yescharacteristic
260C22×C4C22×D1111yescharacteristic
261C22×C4C22×D1111yescharacteristic
262C22×C4C22×D1111yescharacteristic
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—222no—
268C4⋊C4—222no—
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C22⋊C4—114no—
276C22⋊C4—222no—
277C22⋊C4—222no—
278C22⋊C4—222no—
279C22⋊C4—441no—
280C22⋊C4—441no—
281C42—22no—
282C42—441no—
283C11#272911yescharacteristic, complemented, Sylow
284C23—112no—
285C23—221no—
286C23—221no—
287C23—221no—
288C23—221no—
289C23—221no—
290C23—221no—
291C23C23×D1111yescharacteristic
292Q8—44no—
293Q8—44no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—112no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—444no—
332C2×C4Q8×D1112yes—
333C2×C4#434312yes—
334C2×C4C2×C22⋊D1112yes—
335C2×C4C2×C22⋊D1112yes—
336C2×C4C2×C22⋊D1112yes—
337C22—222no—
338C22—222no—
339C22—222no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22—441no—
344C22#6703711yescharacteristic
345C22#6703711yescharacteristic
346C22C2×Q8×D1111yescharacteristic
347C22C2×#434311yescharacteristic
348C22#6704011yescharacteristic
349C22#6704011yescharacteristic
350C22C22×C22⋊D1111yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—222no—
359C4—441no—
360C4—441no—
361C4—441no—
362C4—441no—
363C4—441no—
364C4—441no—
365C2—442no—
366C2#1062326011yescharacteristic
367C2#1062326111yescharacteristic
368C2#1062326411yescharacteristic
369C2#1062326611yescharacteristic
370C2#1062333511yescharacteristic
371C2Q8×C22⋊D1111yescharacteristic
372C2#1062334811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C4⋊Q8C2
prime radicalC23×D11C23
hypercenterC2×C4⋊Q8D11
hypocenterC11#2729
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C4⋊Q8C2semidirect
4. #10622843C2semidirect
5. #10622842C2semidirect
10. #10622599C2semidirect
11. #10622597C2semidirect
12. #10622596C2semidirect
13. #10622585C2semidirect
15. #10622546C2semidirect
87. (C2×D11)⋊C4Q8semidirect
151. C2×C4⋊Q8D11semidirect
283. C11#2729semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
C2×#669992
#106228442
#106228432
#106228422
#106226072
#106226032
#106226022
#106225992
#106225972
#106225962
#106225852
#106225532
#106225462
#272911