Finite Group Databasebeta

← #13073551

Subgroups — #13073551

Order 1408.

760 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 157 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×#66949C212yesmaximal, complemented
2C2×#66946C211yesmaximal, characteristic, complemented
3C2×#66938C211yesmaximal, characteristic, complemented
4C2×#66937C212yesmaximal, complemented
5C11×#399C211yesmaximal, characteristic, complemented
6#10622605C211yesmaximal, characteristic, complemented
7#10622601C212yesmaximal, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622570C212yesmaximal, complemented
10#10622284C211yesmaximal, characteristic, complemented
11#10622262C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×D44C2211yescharacteristic
15C22×D44C2212yes—
16C22×C4×D11C2212yes—
17C22×Dic22C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2212yes—
20C2×C11×C22⋊C4C2212yes—
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2212yes—
32C2×C4×Dic11C2211yescharacteristic
33#66949—28no—
34#66946—24no—
35#66938—24no—
36#66937—28no—
37C11×#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C24×C11C2311yescharacteristic
40C23×D11C2311yescharacteristic
41C23×D11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—22no—
49C2×C22⋊D11—24no—
50C2×C22⋊D11—42no—
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C2×D44—24no—
56C2×D44—24no—
57C2×D44—22no—
58C2×D44—24no—
59C2×D44—42no—
60C2×C4×D11—24no—
61C2×C4×D11—24no—
62C2×C4×D11—24no—
63C2×Dic22—22no—
64C2×Dic22—24no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—24no—
67C11×C22⋊C4—24no—
68C11×C22⋊C4—22no—
69C22⋊Dic11—22no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—24no—
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—24no—
76Dic11⋊C4—24no—
77Dic11⋊C4D418yescomplemented
78C4×Dic11—42no—
79C4×Dic11D414yescomplemented
80#2540—111nomaximal, Sylow
81C23×C11—21no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—21no—
85C23×C11—21no—
86C23×C11C2411yescharacteristic
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—21no—
94C22×D11—22no—
95C22×D11—22no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11#4114yes—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11C2×D412yes—
108C2×C4×C11C2×D414yes—
109C22⋊D11—48no—
110C22⋊D11—44no—
111C2×Dic11—22no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11C2×D412yes—
118C2×Dic11C2×D414yes—
119C2×Dic11C2×D412yes—
120C2×Dic11C2×D414yes—
121D44—28no—
122D44—48no—
123C4×D11—48no—
124Dic22—44no—
125C2×#124—111no—
126C2×C22⋊Q8—112no—
127C2×#121—112no—
128C2×C4×D4—111no—
129#399—111no—
130#399D1111yescharacteristic, complemented
131#392—111no—
132#392—111no—
133#390—112no—
134#390—112no—
135C4×C4⋊C4—111no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11C22×D411yescharacteristic
142C22×C11C22×D412yes—
143C22×C11C2×#4112yes—
144C22×C11H(5,𝔽2)11yescharacteristic
145C22×C112−1+411yescharacteristic
146C2×D11—24no—
147C2×D11—24no—
148C2×D11—24no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—41no—
156C2×D11—42no—
157C2×D11—42no—
158C4×C11—22no—
159C4×C11—24no—
160C4×C11—41no—
161C4×C11—42no—
162Dic11—22no—
163Dic11—24no—
164Dic11—41no—
165Dic11#12714yes—
166C22×Q8—111no—
167C22×D4—111no—
168C22×D4—112no—
169C22×D4—111no—
170C22×D4—112no—
171C23×C4—112no—
172#124—224no—
173C22⋊Q8—228no—
174#121—228no—
175C4×D4—224no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4C2×D1111yescharacteristic
179C2×C4⋊C4C2×D1112yes—
180C2×C22⋊C4—111no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—111no—
186C2×C22⋊C4—111no—
187C2×C22⋊C4C2×D1112yes—
188C2×C22⋊C4C2×D1111yescharacteristic
189C2×C42—111no—
190C2×C42—112no—
191#95—111no—
192#95C2×D1111yescharacteristic
193C2×C11—81no—
194C2×C11#52511yescharacteristic
195C2×C11C2×#12711yescharacteristic
196C2×C11#53711yescharacteristic
197C2×C11#54612yes—
198C2×C11#54812yes—
199D11—44no—
200D11—81no—
201C24—112no—
202C24—111no—
203C24C22×D1111yescharacteristic
204C2×Q8—224no—
205C2×Q8—222no—
206C2×D4—224no—
207C2×D4—224no—
208C2×D4—224no—
209C2×D4—224no—
210C2×D4—222no—
211C2×D4—224no—
212C2×D4—222no—
213C2×D4—224no—
214C2×D4—442no—
215C2×D4—442no—
216C22×C4—111no—
217C22×C4—112no—
218C22×C4—111no—
219C22×C4—111no—
220C22×C4—224no—
221C22×C4—224no—
222C22×C4—224no—
223C22×C4C22×D1111yescharacteristic
224C22×C4C22×D1112yes—
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1112yes—
227C4⋊C4—22no—
228C4⋊C4—24no—
229C4⋊C4—118no—
230C4⋊C4—224no—
231C22⋊C4—24no—
232C22⋊C4—22no—
233C22⋊C4—224no—
234C22⋊C4—224no—
235C22⋊C4—224no—
236C22⋊C4—222no—
237C22⋊C4—222no—
238C22⋊C4—224no—
239C22⋊C4—222no—
240C42—114no—
241C42—442no—
242C11#254011yescharacteristic, complemented, Sylow
243C23—21no—
244C23—22no—
245C23—21no—
246C23—22no—
247C23—21no—
248C23—114no—
249C23—222no—
250C23—222no—
251C23—222no—
252C23—222no—
253C23—222no—
254C23—222no—
255C23—221no—
256C23—222no—
257C23—221no—
258C23—222no—
259C23—221no—
260C23C23×D1111yescharacteristic
261Q8—444no—
262D4—228no—
263D4—448no—
264D4—444no—
265D4—448no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—112no—
275C2×C4—114no—
276C2×C4—112no—
277C2×C4—114no—
278C2×C4—221no—
279C2×C4—222no—
280C2×C4—221no—
281C2×C4—222no—
282C2×C4—221no—
283C2×C4—222no—
284C2×C4—448no—
285C2×C4D4×D1112yes—
286C2×C4D4×D1114yes—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—224no—
293C22—224no—
294C22—224no—
295C22—442no—
296C22—442no—
297C22—442no—
298C22—442no—
299C22—441no—
300C22—441no—
301C22—442no—
302C22—442no—
303C22—441no—
304C22C2×D4×D1111yescharacteristic
305C22C2×D4×D1112yes—
306C22#6704011yescharacteristic
307C22#41×D1112yes—
308C22#6704211yescharacteristic
309C4—24no—
310C4—22no—
311C4—42no—
312C4—41no—
313C4—114no—
314C4—222no—
315C4—224no—
316C4—441no—
317C2—81no—
318C2—444no—
319C2—881no—
320C2#1062316011yescharacteristic
321C2#1062316412yes—
322C2#1062318512yes—
323C2#1062318711yescharacteristic
324C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
hypercenter#399D11
hypocenterC11#2540
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66949C2semidirect
2. C2×#66946C2semidirect
3. C2×#66938C2semidirect
4. C2×#66937C2semidirect
5. C11×#399C2semidirect
6. #10622605C2semidirect
7. #10622601C2semidirect
8. #10622573C2semidirect
9. #10622570C2semidirect
10. #10622284C2semidirect
11. #10622262C2semidirect
77. Dic11⋊C4D4semidirect
79. C4×Dic11D4semidirect
130. #399D11semidirect
242. C11#2540semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×#669462
C2×#669382
C2×#669372
C11×#3992
#106226052
#106226012
#106225732
#106225702
#106222842
#106222622
#254011