Finite Group Databasebeta

← #13072026

Subgroups — #13072026

Order 1408.

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

normal subgroups only

This group has 610 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×#66988C211yesmaximal, characteristic
2C2×#66988C211yesmaximal, characteristic
3C22×C4⋊Dic11C211yesmaximal, characteristic, complemented
4C2×#66930C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic
6#10622823C211yesmaximal, characteristic, complemented
7#10622564C212yesmaximal, complemented
8#10622561C212yesmaximal, complemented
9#10622556C211yesmaximal, characteristic, complemented
10#10622270C212yesmaximal, complemented
11#10622260C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C23×Dic11C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23#66988—24no—
24#66988—24no—
25C2×C4⋊Dic11—24no—
26C2×C4⋊Dic11C2212yes—
27C2×C4⋊Dic11C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2212yes—
32C2×Dic11⋊C4C2211yescharacteristic
33C2×C4×Dic11C2212yes—
34#66930—24no—
35C11×#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2311yescharacteristic
40C24×C11C2311yescharacteristic
41C2×D4×C11—22no—
42C2×D4×C11—22no—
43C2×D4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—24no—
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2312yes—
49C22×Dic11—22no—
50C22×Dic11—22no—
51C22×Dic11—22no—
52C22×Dic11—22no—
53C22×Dic11—22no—
54C22×Dic11D414yes—
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2312yes—
58C22×Dic11C2312yes—
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C11×C22⋊C4—22no—
62C11×C22⋊C4—24no—
63C22⋊Dic11—22no—
64C22⋊Dic11—22no—
65C22⋊Dic11—24no—
66C22⋊Dic11—22no—
67C22⋊Dic11D414yes—
68C4⋊Dic11—24no—
69C4⋊Dic11—24no—
70Dic11⋊C4—24no—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73Dic11⋊C4—24no—
74Dic11⋊C4—24no—
75C4×Dic11—24no—
76#2413—111nomaximal, Sylow
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—22no—
82C23×C11—21no—
83C23×C11—22no—
84C23×C11C2×D412yes—
85C23×C11C2×D412yes—
86C23×C11#4112yes—
87C23×C11C2411yescharacteristic
88D4×C11—44no—
89C2×C4×C11—28no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11#4114yes—
99C2×Dic11—28no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—22no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—44no—
114C2×Dic11C2×D414yes—
115C2×Dic11C2×D412yes—
116C2×Dic11C2×D412yes—
117C2×#123—111no—
118C2×#123—111no—
119C2×#117—111no—
120C22×C4⋊C4—111no—
121#398—112no—
122#396—112no—
123#389—112no—
124#388—112no—
125#386D1111yescharacteristic
126#385—111no—
127#381—111no—
128C22×C11—22no—
129C22×C11—22no—
130C22×C11—24no—
131C22×C11—24no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11#12114yes—
138C22×C11C22×D411yescharacteristic
139C22×C11C22×D411yescharacteristic
140C22×C11C2×#4111yescharacteristic
141C22×C11C2×#4112yes—
142C22×C112−1+412yes—
143C4×C11—24no—
144C4×C11—41no—
145C4×C11—42no—
146Dic11—22no—
147Dic11—22no—
148Dic11—24no—
149Dic11—42no—
150Dic11—41no—
151Dic11—41no—
152C22×D4C2×D1111yescharacteristic
153C23×C4—111no—
154C23×C4—111no—
155C23×C4C2×D1111yescharacteristic
156#123—224no—
157#123—224no—
158#117—224no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—112no—
162C2×C4⋊C4—111no—
163C2×C4⋊C4—112no—
164C2×C4⋊C4—111no—
165C2×C4⋊C4—112no—
166C2×C4⋊C4—224no—
167C2×C22⋊C4—111no—
168C2×C22⋊C4—111no—
169C2×C22⋊C4—111no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—111no—
172C2×C22⋊C4C2×D1111yescharacteristic
173C2×C22⋊C4C2×D1112yes—
174C2×C42—112no—
175#95—112no—
176#95—112no—
177#95—112no—
178#95C2×D1112yes—
179C2×C11—24no—
180C2×C11—81no—
181C2×C11C2×#12111yescharacteristic
182C2×C11#52511yescharacteristic
183C2×C11#53611yescharacteristic
184C2×C11#54712yes—
185C2×C11#55212yes—
186C24C22×D1111yescharacteristic
187C24C22×D1111yescharacteristic
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—22no—
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—114no—
194C22×C4—112no—
195C22×C4—111no—
196C22×C4—111no—
197C22×C4—111no—
198C22×C4—111no—
199C22×C4—112no—
200C22×C4—222no—
201C22×C4—222no—
202C22×C4—222no—
203C22×C4—222no—
204C22×C4—222no—
205C22×C4C22×D1112yes—
206C22×C4C22×D1111yescharacteristic
207C22×C4C22×D1112yes—
208C4⋊C4—224no—
209C4⋊C4—224no—
210C4⋊C4—224no—
211C4⋊C4—224no—
212C4⋊C4—222no—
213C4⋊C4—222no—
214C4⋊C4—224no—
215C22⋊C4—22no—
216C22⋊C4—24no—
217C22⋊C4—114no—
218C22⋊C4—224no—
219C22⋊C4—222no—
220C22⋊C4—222no—
221C22⋊C4—222no—
222C42—224no—
223C11#241311yescharacteristic, complemented, Sylow
224C23—22no—
225C23—22no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—22no—
230C23—22no—
231C23#433912yes—
232C23D4×D1112yes—
233C23D4×D1112yes—
234C23C23×D1111yescharacteristic
235D4—44no—
236C2×C4—28no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—114no—
246C2×C4—112no—
247C2×C4—112no—
248C2×C4—228no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4—221no—
252C2×C4—221no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—221no—
257C2×C4—221no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—444no—
263C2×C4#434114yes—
264C22—24no—
265C22—22no—
266C22—24no—
267C22—22no—
268C22—41no—
269C22—42no—
270C22—41no—
271C22—42no—
272C22—41no—
273C22#6693714yes—
274C22C2×#433911yescharacteristic
275C22C2×D4×D1111yescharacteristic
276C22C2×D4×D1111yescharacteristic
277C22C2×#434112yes—
278C22#6704312yes—
279C4—24no—
280C4—41no—
281C4—42no—
282C4—222no—
283C4—222no—
284C4—224no—
285C4—442no—
286C4—441no—
287C4—441no—
288C2—24no—
289C2—81no—
290C2C2×#6693711yescharacteristic
291C2#1062307212yes—
292C2#1062311711yescharacteristic
293C2#1062314212yes—
294C2#1062317911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC22×D4×C11C22
hypercenter#386D11
hypocenterC11#2413
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic11C2semidirect
4. C2×#66930C2semidirect
6. #10622823C2semidirect
7. #10622564C2semidirect
8. #10622561C2semidirect
9. #10622556C2semidirect
10. #10622270C2semidirect
11. #10622260C2semidirect
223. C11#2413semidirect

Maximal subgroups

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

subgroupindex
C2×#669882
C22×C4⋊Dic112
C2×#669302
C11×#3862
#106228232
#106225642
#106225612
#106225562
#106222702
#106222602
#241311