Finite Group Databasebeta

← #13076647

Subgroups — #13076647

Order 1408.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66991C211yesmaximal, characteristic
2C2×#66949C211yesmaximal, characteristic, complemented
3C11×#394C211yesmaximal, characteristic, complemented
4#10622835C211yesmaximal, characteristic, complemented
5#10622596C211yesmaximal, characteristic, complemented
6#10622574C212yesmaximal, complemented
7#10622572C212yesmaximal, complemented
8#10622562C212yesmaximal, complemented
9#10622560C212yesmaximal, complemented
10#10622277C211yesmaximal, characteristic, complemented
11#10622274C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×C4×D11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22#66991—24no—
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2212yes—
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31#66949—24no—
32C11×#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C23×D11C2311yescharacteristic
39C2×D4×C11—22no—
40C2×D4×C11—42no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—24no—
46C2×C22⋊D11—42no—
47C2×C22⋊D11—42no—
48C22×Dic11C2312yes—
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C2×C4×D11—42no—
54C2×C4×D11D414yes—
55C2×Dic22—22no—
56C2×Dic22—42no—
57C11×C4⋊C4—22no—
58C11×C22⋊C4—42no—
59C11×C22⋊C4—42no—
60C22⋊Dic11—24no—
61C22⋊Dic11—42no—
62C22⋊Dic11—42no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—42no—
66C4⋊Dic11—22no—
67C4⋊Dic11—42no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—42no—
71#2816—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11C2411yescharacteristic
80C22×D11—22no—
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—22no—
84C22×D11C2×D412yes—
85D4×C11—44no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11C2×D412yes—
96C22⋊D11—48no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11C2×D412yes—
110C4×D11—44no—
111Dic22—44no—
112C2×C22⋊Q8—111no—
113C2×#121—111no—
114#399—112no—
115#398—111no—
116#398—111no—
117#394—111no—
118#394—112no—
119#394—112no—
120#394D1111yescharacteristic, complemented
121#393—112no—
122#381—111no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11C22×D411yescharacteristic
131C22×C11H(5,𝔽2)12yes—
132C22×C11H(5,𝔽2)11yescharacteristic
133C22×C11H(5,𝔽2)11yescharacteristic
134C22×C112−1+412yes—
135C2×D11—22no—
136C2×D11—22no—
137C2×D11—22no—
138C2×D11—42no—
139C2×D11—42no—
140C4×C11—22no—
141C4×C11—41no—
142C4×C11—41no—
143C4×C11—42no—
144Dic11—22no—
145Dic11—41no—
146Dic11—41no—
147Dic11—42no—
148Dic11—42no—
149C22×Q8—111no—
150C22×D4—112no—
151C22×D4C2×D1111yescharacteristic
152C23×C4—111no—
153C22⋊Q8—224no—
154#121—224no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—111no—
157C2×C4⋊C4—111no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4C2×D1111yescharacteristic
161C2×C22⋊C4—112no—
162C2×C22⋊C4—111no—
163C2×C22⋊C4—111no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4C2×D1112yes—
168C2×C22⋊C4C2×D1112yes—
169#95—112no—
170#95—111no—
171#95—112no—
172#95—112no—
173#95C2×D1111yescharacteristic
174C2×C11—82no—
175C2×C11#53411yescharacteristic
176C2×C11#53511yescharacteristic
177C2×C11#53611yescharacteristic
178C2×C11#56212yes—
179C2×C11#56212yes—
180D11—42no—
181C24—111no—
182C24C22×D1112yes—
183C2×Q8—222no—
184C2×Q8—442no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—224no—
188C2×D4—442no—
189C2×D4—442no—
190C22×C4—111no—
191C22×C4—114no—
192C22×C4—112no—
193C22×C4—111no—
194C22×C4—112no—
195C22×C4—111no—
196C22×C4—442no—
197C22×C4C22×D1112yes—
198C22×C4C22×D1111yescharacteristic
199C22×C4C22×D1111yescharacteristic
200C22×C4C22×D1111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—222no—
203C4⋊C4—222no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C4⋊C4—442no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—222no—
210C22⋊C4—222no—
211C22⋊C4—224no—
212C22⋊C4—442no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C11#281611yescharacteristic, complemented, Sylow
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—112no—
224C23—222no—
225C23—221no—
226C23—221no—
227C23—222no—
228C23C23×D1111yescharacteristic
229Q8—444no—
230D4—44no—
231D4—448no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—112no—
242C2×C4—222no—
243C2×C4—221no—
244C2×C4—222no—
245C2×C4—221no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—221no—
249C2×C4—222no—
250C2×C4—221no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—444no—
255C2×C4D4×D1112yes—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—222no—
264C22—222no—
265C22—222no—
266C22—442no—
267C22—442no—
268C22C2×D4×D1111yescharacteristic
269C22#6703712yes—
270C22#6703711yescharacteristic
271C22#6704211yescharacteristic
272C22#6704312yes—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—42no—
277C4—222no—
278C4—441no—
279C4—442no—
280C4—441no—
281C4—442no—
282C2—82no—
283C2—442no—
284C2#1062312011yescharacteristic
285C2#1062313811yescharacteristic
286C2#1062315212yes—
287C2#1062319812yes—
288C2#1062320611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC2×#66991C2
hypercenter#394D11
hypocenterC11#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66949C2semidirect
3. C11×#394C2semidirect
4. #10622835C2semidirect
5. #10622596C2semidirect
6. #10622574C2semidirect
7. #10622572C2semidirect
8. #10622562C2semidirect
9. #10622560C2semidirect
10. #10622277C2semidirect
11. #10622274C2semidirect
120. #394D11semidirect
215. C11#2816semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×#669492
C11×#3942
#106228352
#106225962
#106225742
#106225722
#106225622
#106225602
#106222772
#106222742
#281611