Finite Group Databasebeta

← #13071952

Subgroups — #13071952

Order 1408.

864 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 159 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
1C22×#4343C211yesmaximal, characteristic
2C2×#66947C212yesmaximal, complemented
3C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4C11×#395C211yesmaximal, characteristic, complemented
5#10622842C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622602C212yesmaximal, complemented
8#10622285C211yesmaximal, characteristic, complemented
9#10622281C212yesmaximal, complemented
10#10622278C212yesmaximal, complemented
11#10622277C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×#4343—28no—
14C2×#4343—24no—
15C22×D44C2211yescharacteristic
16C22×D44C2212yes—
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×C4×D11C2212yes—
20C22×C4×D11C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2212yes—
32#66947—28no—
33C4⋊C4×D11—24no—
34C11×#95C2211yescharacteristic
35C11×#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2212yes—
39C23×D11C2312yes—
40C23×D11C2311yescharacteristic
41C2×Q8×C11—24no—
42C2×Q8×C11—22no—
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52#4343—232no—
53C2×D44—24no—
54C2×D44—24no—
55C2×D44—24no—
56C2×D44—22no—
57C2×D44D418yes—
58C2×C4×D11—24no—
59C2×C4×D11—22no—
60C2×C4×D11—22no—
61C2×C4×D11—24no—
62C2×C4×D11—24no—
63C2×C4×D11—22no—
64C2×C4×D11—24no—
65C2×C4×D11—24no—
66C2×C4×D11—22no—
67C2×C4×D11D414yes—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—24no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—24no—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—24no—
74(C2×D11)⋊C4—24no—
75C4⋊Dic11—22no—
76Dic11⋊C4—22no—
77Dic11⋊C4—22no—
78Dic11⋊C4—24no—
79#2406—111nomaximal, Sylow
80C23×C11C2411yescharacteristic
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11C2×D414yes—
91C22×D11C2×D414yes—
92C22×D11C2×D412yes—
93Q8×C11—28no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11C2×D414yes—
105C2×C4×C11C2×D412yes—
106C2×C4×C11#4112yescomplemented
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11C2×D412yes—
116C2×Dic11#4112yescomplemented
117D44—28no—
118D44—216no—
119C4×D11—28no—
120C4×D11—216no—
121C4×D11—28no—
122C4×D11—44no—
123C22×#41—111no—
124C2×#123—112no—
125C22×C4⋊C4—111no—
126#395—111no—
127#395D1111yescharacteristic, complemented
128#394—111no—
129#394—111no—
130#386—112no—
131#385—112no—
132#385—112no—
133#381—111no—
134C22×C11C22×D411yescharacteristic
135C22×C11C22×D412yes—
136C22×C11C2×#4111yescharacteristic
137C22×C11C2×#4111yescharacteristic
138C22×C112−1+412yes—
139C2×D11—22no—
140C2×D11—22no—
141C2×D11—24no—
142C2×D11—24no—
143C2×D11—24no—
144C2×D11—24no—
145C2×D11—24no—
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11#12014yes—
151C4×C11—24no—
152C4×C11—22no—
153C4×C11—22no—
154C4×C11—41no—
155C4×C11—42no—
156Dic11—22no—
157Dic11—22no—
158Dic11—41no—
159Dic11—42no—
160C2×#41—224no—
161C2×#41—228no—
162C22×Q8C2×D1111yescharacteristic
163C22×D4—112no—
164C22×D4—111no—
165C23×C4—111no—
166C23×C4—111no—
167C23×C4—111no—
168C23×C4—112no—
169#123—228no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—111no—
172C2×C4⋊C4—111no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4—224no—
175C2×C4⋊C4C2×D1111yescharacteristic
176C2×C4⋊C4C2×D1112yes—
177C2×C22⋊C4—112no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182#95—112no—
183#95—111no—
184#95—112no—
185#95C2×D1111yescharacteristic
186#95C2×D1112yes—
187C2×C11C2×#12011yescharacteristic
188C2×C11#52511yescharacteristic
189C2×C11#53611yescharacteristic
190C2×C11#54712yes—
191C2×C11#54712yes—
192D11—24no—
193D11—44no—
194C24—111no—
195C24—112no—
196#41—2232no—
197C2×Q8—22no—
198C2×Q8—24no—
199C2×D4—118no—
200C2×D4—224no—
201C2×D4—224no—
202C2×D4—224no—
203C2×D4—222no—
204C22×C4—111no—
205C22×C4—111no—
206C22×C4—114no—
207C22×C4—112no—
208C22×C4—111no—
209C22×C4—224no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—224no—
213C22×C4—224no—
214C22×C4—222no—
215C22×C4—224no—
216C22×C4—224no—
217C22×C4—222no—
218C22×C4C22×D1112yes—
219C22×C4C22×D1111yescharacteristic
220C22×C4C22×D1111yescharacteristic
221C22×C4C22×D1112yes—
222C22×C4C22×D1111yescharacteristic
223C4⋊C4—22no—
224C4⋊C4—24no—
225C4⋊C4—222no—
226C4⋊C4—222no—
227C4⋊C4—222no—
228C4⋊C4—224no—
229C22⋊C4—224no—
230C22⋊C4—224no—
231C22⋊C4—224no—
232C22⋊C4—224no—
233C22⋊C4—224no—
234C11#240611yescharacteristic, complemented, Sylow
235C23—114no—
236C23—112no—
237C23—114no—
238C23—221no—
239C23—222no—
240C23—221no—
241C23—222no—
242C23—222no—
243C23—222no—
244C23—222no—
245C23—222no—
246C23—222no—
247C23C23×D1111yescharacteristic
248Q8—28no—
249D4—2216no—
250D4—228no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—112no—
262C2×C4—112no—
263C2×C4—228no—
264C2×C4—2216no—
265C2×C4—228no—
266C2×C4—221no—
267C2×C4—222no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—221no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—444no—
275C2×C4D4×D1112yes—
276C2×C4D4×D1114yes—
277C2×C4#434312yescomplemented
278C22—114no—
279C22—222no—
280C22—224no—
281C22—222no—
282C22—224no—
283C22—224no—
284C22—224no—
285C22—224no—
286C22—442no—
287C22—442no—
288C22—442no—
289C22—442no—
290C22C2×D4×D1111yescharacteristic
291C22C2×D4×D1112yes—
292C22C2×#434311yescharacteristic
293C22#6704012yes—
294C22#41×D1111yescharacteristic
295C4—22no—
296C4—24no—
297C4—22no—
298C4—41no—
299C4—42no—
300C4—222no—
301C4—222no—
302C4—442no—
303C4—441no—
304C2—224no—
305C2—444no—
306C2D11×#12011yescharacteristic
307C2#1062315811yescharacteristic
308C2#1062316212yes—
309C2#1062325511yescharacteristic
310C2#1062325712yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radicalC22×#4343C2
hypercenter#395D11
hypocenterC11#2406
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#66947C2semidirect
3. C2×C4⋊C4×D11C2semidirect
4. C11×#395C2semidirect
5. #10622842C2semidirect
6. #10622604C2semidirect
7. #10622602C2semidirect
8. #10622285C2semidirect
9. #10622281C2semidirect
10. #10622278C2semidirect
11. #10622277C2semidirect
106. C2×C4×C11#41semidirect
116. C2×Dic11#41semidirect
127. #395D11semidirect
234. C11#2406semidirect
277. C2×C4#4343semidirect

Maximal subgroups

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

subgroupindex
C22×#43432
C2×#669472
C2×C4⋊C4×D112
C11×#3952
#106228422
#106226042
#106226022
#106222852
#106222812
#106222782
#106222772
#240611