Finite Group Databasebeta

← #13073614

Subgroups — #13073614

Order 1408.

676 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 151 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×#66993C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic, complemented
3C2×#66938C212yesmaximal, complemented
4C11×#394C211yesmaximal, characteristic, complemented
5#10622835C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622570C212yesmaximal, complemented
8#10622570C212yesmaximal, complemented
9#10622570C212yesmaximal, complemented
10#10622285C211yesmaximal, characteristic, complemented
11#10622262C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×C22⋊D11C2212yes—
15C22×D44C2211yescharacteristic
16C22×Dic22C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22#66993—24no—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2212yes—
31C2×C4×Dic11C2211yescharacteristic
32C2×C4×Dic11C2211yescharacteristic
33C2×C4×Dic11C2211yescharacteristic
34#66940—24no—
35#66938—28no—
36C11×#95C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C24×C11C2312yes—
39C23×D11C2312yes—
40C2×D4×C11—22no—
41C2×D4×C11—42no—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—24no—
50C2×C22⋊D11—24no—
51C2×C22⋊D11—24no—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C2×D44—22no—
58C2×D44—42no—
59C2×Dic22—22no—
60C2×Dic22—22no—
61C2×Dic22D414yescomplemented
62C11×C4⋊C4—22no—
63C11×C22⋊C4—24no—
64C11×C22⋊C4—42no—
65C22⋊Dic11—24no—
66C22⋊Dic11—42no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—42no—
70(C2×D11)⋊C4—42no—
71Dic11⋊C4—22no—
72Dic11⋊C4—24no—
73Dic11⋊C4—22no—
74C4×Dic11—24no—
75C4×Dic11—22no—
76C4×Dic11—22no—
77C4×Dic11D414yes—
78#2548—111nomaximal, Sylow
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11C2411yescharacteristic
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94D4×C11—44no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11C2×D412yes—
104C2×C4×C11C2×D412yes—
105C22⋊D11—48no—
106C22⋊D11—48no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11C2×D412yes—
115C2×Dic11C2×D412yes—
116C2×Dic11C2×D412yes—
117C2×Dic11C2×D412yes—
118C2×Dic11#4112yes—
119C2×Dic11#4114yes—
120D44—44no—
121Dic22—28no—
122C2×#127—111no—
123C2×#124—112no—
124C2×C4×Q8—111no—
125#394—111no—
126#394—111no—
127#394—111no—
128#394D1111yescharacteristic, complemented
129#390—112no—
130#390—112no—
131#390—112no—
132C4×C4⋊C4—111no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—42no—
140C22×C11C22×D411yescharacteristic
141C22×C11C22×D411yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11C2×#4112yes—
144C22×C11H(5,𝔽2)12yes—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C4×C11—22no—
153C4×C11—22no—
154C4×C11—41no—
155C4×C11—42no—
156Dic11—22no—
157Dic11—41no—
158Dic11—42no—
159Dic11#12114yes—
160Dic11#12414yescomplemented
161C22×Q8—111no—
162C22×D4—112no—
163C22×D4—112no—
164C22×D4—111no—
165C22×D4C2×D1111yescharacteristic
166#127—224no—
167#124—228no—
168C4×Q8—224no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—112no—
172C2×C4⋊C4C2×D1111yescharacteristic
173C2×C22⋊C4—112no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4—112no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4C2×D1112yes—
180C2×C22⋊C4C2×D1112yes—
181C2×C42—111no—
182C2×C42—111no—
183C2×C42—111no—
184C2×C42—112no—
185#95—111no—
186#95C2×D1111yescharacteristic
187C2×C11—82no—
188C2×C11C2×#12111yescharacteristic
189C2×C11C2×#12411yescharacteristic
190C2×C11#53511yescharacteristic
191C2×C11#55012yes—
192C2×C11#55912yes—
193D11—82no—
194C24—112no—
195C24C22×D1112yes—
196C2×Q8—114no—
197C2×Q8—222no—
198C2×Q8—222no—
199C2×D4—22no—
200C2×D4—42no—
201C2×D4—224no—
202C2×D4—224no—
203C2×D4—224no—
204C2×D4—224no—
205C2×D4—224no—
206C2×D4—224no—
207C2×D4—222no—
208C2×D4—442no—
209C22×C4—111no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4—112no—
213C22×C4—111no—
214C22×C4C22×D1112yes—
215C22×C4C22×D1111yescharacteristic
216C22×C4C22×D1111yescharacteristic
217C22×C4C22×D1111yescharacteristic
218C4⋊C4—22no—
219C4⋊C4—222no—
220C4⋊C4—224no—
221C4⋊C4—222no—
222C22⋊C4—24no—
223C22⋊C4—42no—
224C22⋊C4—224no—
225C22⋊C4—224no—
226C22⋊C4—224no—
227C22⋊C4—442no—
228C22⋊C4—442no—
229C22⋊C4—442no—
230C42—114no—
231C42—222no—
232C42—222no—
233C42—224no—
234C11#254811yescharacteristic, complemented, Sylow
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—222no—
243C23—222no—
244C23—222no—
245C23—222no—
246C23—222no—
247C23—222no—
248C23—222no—
249C23C23×D1111yescharacteristic
250Q8—228no—
251D4—44no—
252D4—444no—
253D4—448no—
254D4—448no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—112no—
264C2×C4—112no—
265C2×C4—112no—
266C2×C4—114no—
267C2×C4—112no—
268C2×C4—112no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—222no—
272C2×C4—221no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—222no—
276C2×C4D4×D1112yes—
277C2×C4D4×D1112yes—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—442no—
286C22—442no—
287C22—442no—
288C22—442no—
289C22—442no—
290C22—442no—
291C22—442no—
292C22C2×D4×D1111yescharacteristic
293C22C2×D4×D1111yescharacteristic
294C22#6703712yes—
295C22#41×D1112yes—
296C22#41×D1111yescharacteristic
297C4—22no—
298C4—22no—
299C4—41no—
300C4—42no—
301C4—114no—
302C4—114no—
303C4—222no—
304C4—441no—
305C4—442no—
306C2—82no—
307C2—882no—
308C2#1062312311yescharacteristic
309C2#1062313012yes—
310C2D11×#12111yescharacteristic
311C2#1062319512yes—
312C2D11×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC2×#66993C2
hypercenter#394D11
hypocenterC11#2548
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66940C2semidirect
3. C2×#66938C2semidirect
4. C11×#394C2semidirect
5. #10622835C2semidirect
6. #10622604C2semidirect
7. #10622570C2semidirect
8. #10622570C2semidirect
9. #10622570C2semidirect
10. #10622285C2semidirect
11. #10622262C2semidirect
61. C2×Dic22D4semidirect
128. #394D11semidirect
160. Dic11#124semidirect
234. C11#2548semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669402
C2×#669382
C11×#3942
#106228352
#106226042
#106225702
#106222852
#106222622
#254811