Finite Group Databasebeta

← #13075403

Subgroups — #13075403

Order 1408.

432 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66942C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic
4#10622597C211yesmaximal, characteristic
5#10622592C211yesmaximal, characteristic
6#10622592C211yesmaximal, characteristic
7#10622591C211yesmaximal, characteristic
8#10622591C211yesmaximal, characteristic
9#10622587C211yesmaximal, characteristic
10#10622273C211yesmaximal, characteristic
11#10622271C211yesmaximal, characteristic
12#10622268C211yesmaximal, characteristic
13#10622265C211yesmaximal, characteristic
14#10622260C211yesmaximal, characteristic
15#10622259C211yesmaximal, characteristic
16C22×Dic22C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×C4×Dic11C2211yescharacteristic
33C2×C4×Dic11C2211yescharacteristic
34C2×C4×Dic11C2211yescharacteristic
35#66942—24no—
36#66941—24no—
37C11×#95C2211yescharacteristic
38C11×#95C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C2×Dic22—22no—
69C2×Dic22—22no—
70C2×Dic22—22no—
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80Dic11⋊C4—22no—
81Dic11⋊C4—22no—
82Dic11⋊C4—22no—
83Dic11⋊C4—22no—
84Dic11⋊C4—22no—
85Dic11⋊C4—41no—
86Dic11⋊C4D414yes—
87Dic11⋊C4Q814yescomplemented
88C4×Dic11—22no—
89C4×Dic11—22no—
90C4×Dic11—41no—
91#2713—111nomaximal, Sylow
92C23×C11C2411yescharacteristic
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
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×C11C2×D412yes—
113C2×C4×C11C2×Q812yes—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
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×Dic11C2×D412yes—
134C2×Dic11C2×D412yes—
135C2×Dic11C2×Q812yes—
136C2×Dic11C2×Q812yes—
137C2×Dic11#4112yes—
138Dic22—44no—
139Dic22—44no—
140C2×C4⋊Q8—111no—
141C2×#125—111no—
142#400—111no—
143#400—111no—
144#398—111no—
145#398D1111yescharacteristic
146#395—111no—
147#395—111no—
148#391—111no—
149#391—111no—
150#389—111no—
151#387—111no—
152#387—111no—
153#387—111no—
154#387—111no—
155C22×C11C22×D411yescharacteristic
156C22×C11C22×Q811yescharacteristic
157C22×C11C2×#4111yescharacteristic
158C22×C11H(5,𝔽2)11yescharacteristic
159C22×C112−1+411yescharacteristic
160C22×C112−1+411yescharacteristic
161C22×C112−1+411yescharacteristic
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169Dic11—22no—
170Dic11—22no—
171Dic11—22no—
172Dic11—22no—
173Dic11—22no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C22×Q8—111no—
178C22×Q8—111no—
179C4⋊Q8—224no—
180#125—224no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4C2×D1111yescharacteristic
192C2×C4⋊C4C2×D1111yescharacteristic
193C2×C4⋊C4C2×D1111yescharacteristic
194C2×C4⋊C4C2×D1111yescharacteristic
195C2×C42—111no—
196C2×C42—111no—
197C2×C42—111no—
198#95—111no—
199#95—111no—
200#95—111no—
201#95—111no—
202#95—111no—
203#95—111no—
204#95—111no—
205#95—111no—
206#95—111no—
207#95—111no—
208#95—111no—
209#95—111no—
210#95—111no—
211#95C2×D1111yescharacteristic
212#95C2×D1111yescharacteristic
213#95C2×D1111yescharacteristic
214C2×C11#53611yescharacteristic
215C2×C11#54111yescharacteristic
216C2×C11#54411yescharacteristic
217C2×C11#54611yescharacteristic
218C2×C11D4×Q811yescharacteristic
219C2×C11#55711yescharacteristic
220C2×C11#56311yescharacteristic
221C2×Q8—222no—
222C2×Q8—222no—
223C2×Q8—222no—
224C2×Q8—222no—
225C2×Q8—441no—
226C2×Q8—441no—
227C22×C4—111no—
228C22×C4—111no—
229C22×C4—111no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4C22×D1111yescharacteristic
236C22×C4C22×D1111yescharacteristic
237C22×C4C22×D1111yescharacteristic
238C22×C4C22×D1111yescharacteristic
239C22×C4C22×D1111yescharacteristic
240C22×C4C22×D1111yescharacteristic
241C22×C4C22×D1111yescharacteristic
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—114no—
247C4⋊C4—114no—
248C4⋊C4—222no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—441no—
256C42—222no—
257C42—222no—
258C42—441no—
259C11#271311yescharacteristic, complemented, Sylow
260C23C23×D1111yescharacteristic
261Q8—444no—
262Q8—444no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—112no—
283C2×C4—112no—
284C2×C4—112no—
285C2×C4—112no—
286C2×C4—112no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4D4×D1112yes—
307C2×C4Q8×D1112yes—
308C22C2×D4×D1111yescharacteristic
309C22#6703711yescharacteristic
310C22C2×Q8×D1111yescharacteristic
311C22#6704011yescharacteristic
312C22#41×D1111yescharacteristic
313C22#6704311yescharacteristic
314C22#6704311yescharacteristic
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—222no—
323C4—222no—
324C4—222no—
325C4—222no—
326C4—222no—
327C4—441no—
328C4—441no—
329C4—441no—
330C2#1062314111yescharacteristic
331C2#1062315911yescharacteristic
332C2#1062316311yescharacteristic
333C2#1062318211yescharacteristic
334C2#1062321611yescharacteristic
335C2#1062322711yescharacteristic
336C2#1062326011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#398C2
hypercenter#398D11
hypocenterC11#2713
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
87. Dic11⋊C4Q8semidirect
259. C11#2713semidirect

Maximal subgroups

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

subgroupindex
C2×#669422
C2×#669412
C11×#3982
#106225972
#106225922
#106225912
#106225872
#106222732
#106222712
#106222682
#106222652
#106222602
#106222592
#271311