Finite Group Databasebeta

← #13076639

Subgroups — #13076639

Order 1408.

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

normal subgroups only

This group has 644 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×#66948C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic, complemented
3C11×#397C211yesmaximal, characteristic, complemented
4#10622606C211yesmaximal, characteristic, complemented
5#10622573C212yesmaximal, complemented
6#10622573C211yesmaximal, characteristic, complemented
7#10622573C212yesmaximal, complemented
8#10622288C212yesmaximal, complemented
9#10622284C211yesmaximal, characteristic, complemented
10#10622284C212yesmaximal, complemented
11#10622277C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C22×D44C2211yescharacteristic
16C22×D44C2212yes—
17C22×D44C2211yescharacteristic
18C22×D44C2212yes—
19C22×C4×D11C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×Dic11⋊C4C2211yescharacteristic
30#66948—24no—
31#66937—24no—
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2312yes—
39C23×D11C2311yescharacteristic
40C23×D11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—22no—
46C2×C22⋊D11—22no—
47C2×C22⋊D11—42no—
48C2×C22⋊D11—42no—
49C2×C22⋊D11—42no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11—42no—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C2×D44—22no—
56C2×D44—24no—
57C2×D44—22no—
58C2×D44—42no—
59C2×D44—42no—
60C2×D44—42no—
61C2×D44—42no—
62C2×D44—42no—
63C2×D44—42no—
64C2×D44—42no—
65C2×C4×D11—42no—
66C2×C4×D11D414yescomplemented
67C11×C4⋊C4—22no—
68C11×C22⋊C4—22no—
69C11×C22⋊C4—42no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—42no—
76Dic11⋊C4—22no—
77#2815—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—22no—
81C23×C11—21no—
82C23×C11—22no—
83C23×C11C2411yescharacteristic
84C22×D11—22no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—22no—
92C22×D11—21no—
93C22×D11—22no—
94C22×D11—22no—
95C22×D11—22no—
96C22×D11—22no—
97C22×D11—22no—
98C22×D11—22no—
99C22×D11—22no—
100C22×D11C2×D412yes—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11C2×D412yes—
111C22⋊D11—44no—
112C22⋊D11—44no—
113C22⋊D11—48no—
114C2×Dic11—22no—
115C2×Dic11—21no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—22no—
119C2×Dic11—22no—
120C2×Dic11C2×D412yes—
121D44—44no—
122D44—48no—
123D44—44no—
124D44—48no—
125C4×D11—44no—
126C2×#121—111no—
127C2×#121—111no—
128#397—111no—
129#397—112no—
130#397D1111yescharacteristic, complemented
131#392—112no—
132#392—111no—
133#392—112no—
134#392—111no—
135#392—112no—
136#381—111no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11C22×D411yescharacteristic
143C22×C11H(5,𝔽2)11yescharacteristic
144C22×C11H(5,𝔽2)12yes—
145C22×C11H(5,𝔽2)11yescharacteristic
146C22×C11H(5,𝔽2)12yes—
147C2×D11—22no—
148C2×D11—22no—
149C2×D11—22no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—42no—
156C2×D11—42no—
157C2×D11—41no—
158C2×D11—42no—
159C2×D11—42no—
160C2×D11—42no—
161C2×D11—42no—
162C2×D11—42no—
163C2×D11—42no—
164C4×C11—22no—
165C4×C11—42no—
166C4×C11—41no—
167C4×C11—42no—
168Dic11—22no—
169Dic11—41no—
170Dic11—42no—
171C22×D4—111no—
172C22×D4—111no—
173C22×D4—112no—
174C22×D4—112no—
175C22×D4—111no—
176C22×D4—111no—
177C22×D4—112no—
178C23×C4—111no—
179#121—224no—
180#121—224no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4C2×D1111yescharacteristic
183C2×C22⋊C4—112no—
184C2×C22⋊C4—111no—
185C2×C22⋊C4—112no—
186C2×C22⋊C4—112no—
187C2×C22⋊C4—112no—
188C2×C22⋊C4—112no—
189C2×C22⋊C4C2×D1111yescharacteristic
190C2×C22⋊C4C2×D1112yes—
191#95—112no—
192#95—111no—
193#95—112no—
194#95C2×D1111yescharacteristic
195#95C2×D1112yes—
196C2×C11—81no—
197C2×C11#53411yescharacteristic
198C2×C11#53511yescharacteristic
199C2×C11#53511yescharacteristic
200C2×C11#56012yes—
201C2×C11#56012yes—
202D11—42no—
203D11—82no—
204D11—81no—
205C24—111no—
206C24—111no—
207C24—112no—
208C24C22×D1111yescharacteristic
209C2×D4—222no—
210C2×D4—224no—
211C2×D4—222no—
212C2×D4—222no—
213C2×D4—222no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—442no—
219C2×D4—442no—
220C2×D4—442no—
221C2×D4—442no—
222C2×D4—442no—
223C2×D4—442no—
224C2×D4—442no—
225C2×D4—442no—
226C22×C4—111no—
227C22×C4—114no—
228C22×C4—112no—
229C22×C4—111no—
230C22×C4—442no—
231C22×C4C22×D1112yes—
232C22×C4C22×D1112yes—
233C22×C4C22×D1111yescharacteristic
234C22×C4C22×D1111yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—222no—
237C22⋊C4—22no—
238C22⋊C4—42no—
239C22⋊C4—224no—
240C22⋊C4—222no—
241C22⋊C4—442no—
242C22⋊C4—442no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C11#281511yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—21no—
249C23—22no—
250C23—22no—
251C23—112no—
252C23—221no—
253C23—222no—
254C23—221no—
255C23—222no—
256C23—222no—
257C23—221no—
258C23—222no—
259C23—221no—
260C23—221no—
261C23—222no—
262C23—222no—
263C23—222no—
264C23—222no—
265C23—222no—
266C23—222no—
267C23—222no—
268C23C23×D1111yescharacteristic
269D4—444no—
270D4—448no—
271D4—444no—
272D4—448no—
273D4—444no—
274D4—444no—
275D4—448no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—112no—
286C2×C4—222no—
287C2×C4—221no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—444no—
293C2×C4D4×D1112yes—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—222no—
300C22—222no—
301C22—222no—
302C22—442no—
303C22—442no—
304C22—442no—
305C22—442no—
306C22—442no—
307C22—442no—
308C22—441no—
309C22—442no—
310C22—441no—
311C22—442no—
312C22—442no—
313C22—442no—
314C22—441no—
315C22—442no—
316C22C2×D4×D1111yescharacteristic
317C22#6703711yescharacteristic
318C22#6704211yescharacteristic
319C22#6704212yes—
320C22#6704212yes—
321C4—22no—
322C4—42no—
323C4—42no—
324C4—41no—
325C4—222no—
326C4—442no—
327C4—441no—
328C2—81no—
329C2—442no—
330C2—882no—
331C2—881no—
332C2#1062313811yescharacteristic
333C2#1062318411yescharacteristic
334C2#1062319712yes—
335C2#1062320511yescharacteristic
336C2#1062324212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
hypercenter#397D11
hypocenterC11#2815
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66937C2semidirect
3. C11×#397C2semidirect
4. #10622606C2semidirect
5. #10622573C2semidirect
6. #10622573C2semidirect
7. #10622573C2semidirect
8. #10622288C2semidirect
9. #10622284C2semidirect
10. #10622284C2semidirect
11. #10622277C2semidirect
66. C2×C4×D11D4semidirect
130. #397D11semidirect
245. C11#2815semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669372
C11×#3972
#106226062
#106225732
#106222882
#106222842
#106222772
#281511