Finite Group Databasebeta

← #13074445

Subgroups — #13074445

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66942C211yesmaximal, characteristic, complemented
2C2×#66930C211yesmaximal, characteristic
3C11×#396C211yesmaximal, characteristic
4#10622597C211yesmaximal, characteristic, complemented
5#10622596C211yesmaximal, characteristic, complemented
6#10622593C211yesmaximal, characteristic, complemented
7#10622589C211yesmaximal, characteristic, complemented
8#10622585C211yesmaximal, characteristic, complemented
9#10622561C211yesmaximal, characteristic
10#10622561C211yesmaximal, characteristic
11#10622561C211yesmaximal, characteristic
12#10622555C211yesmaximal, characteristic
13#10622555C211yesmaximal, characteristic
14#10622270C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C23×Dic11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×C4×Dic11C2211yescharacteristic
42C2×C4×Dic11C2211yescharacteristic
43#66942—24no—
44#66930—24no—
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—22no—
62C22×Dic11Q814yes—
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C11×C4⋊C4—22no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C22⋊C4—22no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—41no—
77C22⋊Dic11—22no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80C4⋊Dic11—22no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83Dic11⋊C4—22no—
84Dic11⋊C4—22no—
85Dic11⋊C4—22no—
86Dic11⋊C4—22no—
87Dic11⋊C4—22no—
88Dic11⋊C4—22no—
89Dic11⋊C4—22no—
90Dic11⋊C4—22no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95C4×Dic11—22no—
96C4×Dic11D414yes—
97#2629—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×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×D412yes—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—28no—
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×Dic11C2×D412yes—
145C2×Dic11C2×D412yes—
146C2×Dic11C2×Q812yes—
147C2×Dic11C2×Q812yes—
148C2×Dic11#4112yes—
149C2×#125—111no—
150C2×#117—111no—
151#398—111no—
152#398—111no—
153#398—111no—
154#398—111no—
155#396—111no—
156#396—111no—
157#396—111no—
158#396D1111yescharacteristic
159#389—111no—
160#389—111no—
161#384—111no—
162#380—111no—
163#380—111no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11C22×D411yescharacteristic
172C22×C11C22×Q811yescharacteristic
173C22×C11C2×#4111yescharacteristic
174C22×C11H(5,𝔽2)11yescharacteristic
175C22×C11H(5,𝔽2)11yescharacteristic
176C22×C112−1+411yescharacteristic
177C22×C112−1+411yescharacteristic
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184Dic11—22no—
185Dic11—22no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189Dic11—41no—
190Dic11—41no—
191Dic11C22⋊Q814yes—
192C23×C4—111no—
193#125—224no—
194#117—224no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
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×C4⋊C4C2×D1111yescharacteristic
212C2×C4⋊C4C2×D1111yescharacteristic
213C2×C22⋊C4—111no—
214C2×C22⋊C4—111no—
215C2×C22⋊C4—111no—
216C2×C22⋊C4C2×D1111yescharacteristic
217C2×C22⋊C4C2×D1111yescharacteristic
218C2×C22⋊C4C2×D1111yescharacteristic
219C2×C42—111no—
220C2×C42—111no—
221#95—111no—
222#95—111no—
223#95—111no—
224#95—111no—
225#95—111no—
226#95—111no—
227#95—111no—
228#95C2×D1111yescharacteristic
229C2×C11—42no—
230C2×C11C2×C22⋊Q811yescharacteristic
231C2×C11#53711yescharacteristic
232C2×C11#53711yescharacteristic
233C2×C11#54011yescharacteristic
234C2×C11#54111yescharacteristic
235C2×C11#54411yescharacteristic
236C2×C11#54411yescharacteristic
237C24C22×D1111yescharacteristic
238C22×C4—111no—
239C22×C4—114no—
240C22×C4—111no—
241C22×C4—111no—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—222no—
248C22×C4—222no—
249C22×C4C22×D1111yescharacteristic
250C22×C4C22×D1111yescharacteristic
251C22×C4C22×D1111yescharacteristic
252C22×C4C22×D1111yescharacteristic
253C22×C4C22×D1111yescharacteristic
254C22×C4C22×D1111yescharacteristic
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—222no—
262C4⋊C4—222no—
263C4⋊C4—222no—
264C4⋊C4—222no—
265C4⋊C4—222no—
266C4⋊C4—222no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—222no—
277C22⋊C4—441no—
278C22⋊C4—441no—
279C42—114no—
280C42—222no—
281C11#262911yescharacteristic, complemented, Sylow
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23Q8×D1112yes—
289C23C23×D1111yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
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—112no—
308C2×C4—112no—
309C2×C4—112no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—228no—
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×C4D4×D1112yes—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22C2×D4×D1111yescharacteristic
341C22#6703711yescharacteristic
342C22#6703711yescharacteristic
343C22C2×Q8×D1111yescharacteristic
344C22#41×D1111yescharacteristic
345C22#6704311yescharacteristic
346C22#6704311yescharacteristic
347C4—22no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—114no—
354C4—222no—
355C4—222no—
356C4—441no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4—441no—
361C2—42no—
362C2#1062312811yescharacteristic
363C2#1062313911yescharacteristic
364C2#1062314611yescharacteristic
365C2#1062315411yescharacteristic
366C2#1062315411yescharacteristic
367C2D11×C22⋊Q811yescharacteristic
368C2#1062323211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
prime radicalC24×C11C23
hypercenter#396D11
hypocenterC11#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#66942C2semidirect
4. #10622597C2semidirect
5. #10622596C2semidirect
6. #10622593C2semidirect
7. #10622589C2semidirect
8. #10622585C2semidirect
14. #10622270C2semidirect
15. #10622260C2semidirect
281. C11#2629semidirect

Maximal subgroups

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

subgroupindex
C2×#669422
C2×#669302
C11×#3962
#106225972
#106225962
#106225932
#106225892
#106225852
#106225612
#106225552
#106222702
#106222602
#262911