Finite Group Databasebeta

← #13075595

Subgroups — #13075595

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×#66941C211yesmaximal, characteristic, complemented
2C2×#66931C211yesmaximal, characteristic
3C11×#388C211yesmaximal, characteristic
4#10622597C211yesmaximal, characteristic, complemented
5#10622564C211yesmaximal, characteristic
6#10622563C211yesmaximal, characteristic
7#10622561C211yesmaximal, characteristic
8#10622560C211yesmaximal, characteristic
9#10622559C211yesmaximal, characteristic
10#10622542C211yesmaximal, characteristic, complemented
11#10622541C211yesmaximal, characteristic, complemented
12#10622273C211yesmaximal, characteristic, complemented
13#10622270C211yesmaximal, characteristic, complemented
14#10622269C211yesmaximal, characteristic, complemented
15#10622268C211yesmaximal, characteristic, complemented
16C23×Dic11C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C42×C11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39#66941—24no—
40#66931—24no—
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×Dic11—22no—
61C22×Dic11—41no—
62C22×Dic11—41no—
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22D414yes—
77C11×C4⋊C4—22no—
78C11×C22⋊C4—22no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4Q814yescomplemented
81C42×C11—41no—
82C22⋊Dic11—22no—
83C22⋊Dic11—22no—
84C22⋊Dic11—41no—
85C4⋊Dic11—22no—
86C4⋊Dic11—22no—
87C4⋊Dic11—22no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90Dic11⋊C4—22no—
91Dic11⋊C4—22no—
92Dic11⋊C4—22no—
93Dic11⋊C4—22no—
94Dic11⋊C4—22no—
95Dic11⋊C4—41no—
96C4×Dic11—22no—
97#2729—111nomaximal, Sylow
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11C2×Q812yes—
105C23×C11C2411yescharacteristic
106C2×C4×C11—21no—
107C2×C4×C11—21no—
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×C11C2×D412yes—
122C2×C4×C11C2×Q812yes—
123C2×C4×C11C2×Q812yes—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
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—44no—
146C2×Dic11C2×D412yes—
147C2×Dic11C2×D412yes—
148C2×Dic11#4112yes—
149Dic22—44no—
150Dic22—44no—
151C2×C4⋊Q8—111no—
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#388D1111yescharacteristic
163#387—111no—
164#385—111no—
165#385—111no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C22×D411yescharacteristic
174C22×C11C22×Q811yescharacteristic
175C22×C11C2×#4111yescharacteristic
176C22×C11H(5,𝔽2)11yescharacteristic
177C22×C11H(5,𝔽2)11yescharacteristic
178C22×C112−1+411yescharacteristic
179C22×C112−1+411yescharacteristic
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186Dic11—22no—
187Dic11—22no—
188Dic11—22no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194C22×Q8—111no—
195C22×Q8—111no—
196C23×C4—111no—
197C4⋊Q8—224no—
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⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4C2×D1111yescharacteristic
211C2×C22⋊C4—111no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4C2×D1111yescharacteristic
215C2×C22⋊C4C2×D1111yescharacteristic
216C2×C22⋊C4C2×D1111yescharacteristic
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#95C2×D1111yescharacteristic
230#95C2×D1111yescharacteristic
231C2×C11—42no—
232C2×C11#53411yescharacteristic
233C2×C11#54211yescharacteristic
234C2×C11#54411yescharacteristic
235C2×C11#54811yescharacteristic
236C2×C11D4×Q811yescharacteristic
237C2×C11#55411yescharacteristic
238C2×C11#56311yescharacteristic
239C24C22×D1111yescharacteristic
240C2×Q8—114no—
241C2×Q8—222no—
242C2×Q8—441no—
243C2×Q8—441no—
244C2×Q8—441no—
245C2×Q8—441no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—111no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—222no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4C22×D1111yescharacteristic
258C22×C4C22×D1111yescharacteristic
259C22×C4C22×D1111yescharacteristic
260C22×C4C22×D1111yescharacteristic
261C22×C4C22×D1111yescharacteristic
262C22×C4C22×D1111yescharacteristic
263C4⋊C4—22no—
264C4⋊C4—222no—
265C4⋊C4—222no—
266C4⋊C4—222no—
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—22no—
276C22⋊C4—41no—
277C22⋊C4—222no—
278C22⋊C4—222no—
279C22⋊C4—441no—
280C22⋊C4Dic2214yescomplemented
281C42—41no—
282C42—222no—
283C11#272911yescharacteristic, complemented, Sylow
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23C2×Dic2212yes—
291C23C23×D1111yescharacteristic
292Q8—444no—
293Q8—444no—
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—112no—
310C2×C4—112no—
311C2×C4—112no—
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—221no—
332C2×C4—221no—
333C2×C4—444no—
334C2×C4C2×Dic2212yes—
335C2×C4C2×Dic2212yes—
336C2×C4D4×D1112yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22C22×Dic2211yescharacteristic
345C22C2×D4×D1111yescharacteristic
346C22#6703711yescharacteristic
347C22#41×D1111yescharacteristic
348C22#6704211yescharacteristic
349C22#6704311yescharacteristic
350C22#6704311yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—222no—
358C4—222no—
359C4—222no—
360C4—441no—
361C4—441no—
362C4—441no—
363C4—441no—
364C4—441no—
365C2—42no—
366C2#1062305011yescharacteristic
367C2D4×Dic2211yescharacteristic
368C2#1062307011yescharacteristic
369C2#1062313611yescharacteristic
370C2#1062318211yescharacteristic
371C2#1062320811yescharacteristic
372C2#1062324111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC24×C11C23
hypercenter#388D11
hypocenterC11#2729
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66941C2semidirect
4. #10622597C2semidirect
10. #10622542C2semidirect
11. #10622541C2semidirect
12. #10622273C2semidirect
13. #10622270C2semidirect
14. #10622269C2semidirect
15. #10622268C2semidirect
80. C11×C22⋊C4Q8semidirect
280. C22⋊C4Dic22semidirect
283. C11#2729semidirect

Maximal subgroups

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

subgroupindex
C2×#669412
C2×#669312
C11×#3882
#106225972
#106225642
#106225632
#106225612
#106225602
#106225592
#106225422
#106225412
#106222732
#106222702
#106222692
#106222682
#272911