Finite Group Databasebeta

← #13076944

Subgroups — #13076944

Order 1408.

688 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 165 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×#66992C211yesmaximal, characteristic
2C2×#66988C211yesmaximal, characteristic, complemented
3C22×C4×Dic11C211yesmaximal, characteristic, complemented
4C2×#66939C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622570C212yesmaximal, complemented
8#10622564C212yesmaximal, complemented
9#10622555C211yesmaximal, characteristic, complemented
10#10622282C212yesmaximal, complemented
11#10622260C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×C22⋊D11C2211yescharacteristic
16C23×Dic11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2211yescharacteristic
23#66992—24no—
24#66988—24no—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2212yes—
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2212yes—
32C2×C4×Dic11—24no—
33C2×C4×Dic11C2212yes—
34C2×C4×Dic11C2212yes—
35#66939—24no—
36C11×#95C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2311yescharacteristic
40C24×C11C2311yescharacteristic
41C23×D11C2311yescharacteristic
42C2×D4×C11—22no—
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—24no—
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2312yes—
50C2×C22⋊D11—22no—
51C2×C22⋊D11—24no—
52C2×C22⋊D11—22no—
53C2×C22⋊D11—22no—
54C2×C22⋊D11—22no—
55C22×Dic11—24no—
56C22×Dic11—22no—
57C22×Dic11—22no—
58C22×Dic11D414yes—
59C22×Dic11D414yescomplemented
60C22×Dic11C2312yes—
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2312yes—
64C22×Dic11C2311yescharacteristic
65C11×C22⋊C4—22no—
66C11×C22⋊C4—24no—
67C22⋊Dic11—24no—
68C22⋊Dic11—22no—
69C22⋊Dic11—22no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—24no—
73C4⋊Dic11—24no—
74Dic11⋊C4—24no—
75Dic11⋊C4—22no—
76Dic11⋊C4—24no—
77C4×Dic11—24no—
78C4×Dic11—24no—
79#2854—111nomaximal, Sylow
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—21no—
87C23×C11C2×D412yes—
88C23×C11C2×D412yes—
89C23×C11#4112yes—
90C23×C11C2411yescharacteristic
91C22×D11—21no—
92C22×D11—21no—
93C22×D11—22no—
94C22×D11—21no—
95C22×D11—22no—
96D4×C11—44no—
97C2×C4×C11—28no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11#4114yes—
107C22⋊D11—44no—
108C22⋊D11—44no—
109C2×Dic11—28no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—28no—
114C2×Dic11—22no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—22no—
118C2×Dic11—22no—
119C2×Dic11—21no—
120C2×Dic11C2×D412yes—
121C2×Dic11C2×D414yes—
122C2×Dic11C2×D412yes—
123C2×Dic11#4114yes—
124C2×#123—111no—
125C2×#123—111no—
126C2×#121—111no—
127C22×C42—111no—
128#390—112no—
129#389—112no—
130#388—112no—
131#388—112no—
132#386—111no—
133#386D1111yescharacteristic, complemented
134#380—111no—
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—24no—
138C22×C11—24no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11#12114yes—
145C22×C11C22×D411yescharacteristic
146C22×C11C22×D411yescharacteristic
147C22×C11C2×#4111yescharacteristic
148C22×C11C2×#4112yes—
149C22×C11C2×#4112yes—
150C2×D11—41no—
151C2×D11—41no—
152C2×D11—41no—
153C2×D11—42no—
154C2×D11—42no—
155C4×C11—24no—
156C4×C11—41no—
157C4×C11—42no—
158Dic11—24no—
159Dic11—22no—
160Dic11—41no—
161Dic11—42no—
162Dic11#12314yescomplemented
163C22×D4—111no—
164C22×D4—111no—
165C22×D4C2×D1111yescharacteristic
166C23×C4—111no—
167C23×C4—111no—
168C23×C4C2×D1111yescharacteristic
169#123—224no—
170#123—224no—
171#121—224no—
172C2×C4⋊C4—111no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—112no—
176C2×C22⋊C4—111no—
177C2×C22⋊C4—111no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—111no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4C2×D1111yescharacteristic
183C2×C22⋊C4C2×D1112yes—
184C2×C42—112no—
185C2×C42—112no—
186C2×C42—224no—
187#95—112no—
188#95—112no—
189#95C2×D1112yes—
190C2×C11—24no—
191C2×C11—81no—
192C2×C11C2×#12111yescharacteristic
193C2×C11C2×#12311yescharacteristic
194C2×C11#52511yescharacteristic
195C2×C11#52912yes—
196C2×C11#53212yes—
197D11—81no—
198C24—111no—
199C24C22×D1111yescharacteristic
200C24C22×D1111yescharacteristic
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—222no—
205C2×D4—224no—
206C2×D4—222no—
207C2×D4—222no—
208C2×D4—222no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—111no—
212C22×C4—114no—
213C22×C4—114no—
214C22×C4—111no—
215C22×C4—112no—
216C22×C4—112no—
217C22×C4—111no—
218C22×C4—224no—
219C22×C4—222no—
220C22×C4—222no—
221C22×C4C22×D1112yes—
222C22×C4C22×D1111yescharacteristic
223C22×C4C22×D1112yes—
224C4⋊C4—222no—
225C4⋊C4—224no—
226C4⋊C4—224no—
227C4⋊C4—224no—
228C22⋊C4—22no—
229C22⋊C4—24no—
230C22⋊C4—222no—
231C22⋊C4—224no—
232C22⋊C4—222no—
233C22⋊C4—224no—
234C22⋊C4—222no—
235C22⋊C4—224no—
236C42—224no—
237C42—224no—
238C11#285411yescharacteristic, complemented, Sylow
239C23—22no—
240C23—22no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—22no—
245C23—22no—
246C23—221no—
247C23—221no—
248C23—221no—
249C23—222no—
250C23—222no—
251C23#433912yes—
252C23D4×D1112yes—
253C23D4×D1112yes—
254C23C23×D1111yescharacteristic
255D4—44no—
256D4—444no—
257D4—444no—
258C2×C4—28no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—112no—
268C2×C4—114no—
269C2×C4—112no—
270C2×C4—114no—
271C2×C4—228no—
272C2×C4—228no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—222no—
276C2×C4—221no—
277C2×C4—222no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—222no—
281C2×C4—222no—
282C2×C4#434114yes—
283C22—24no—
284C22—22no—
285C22—24no—
286C22—22no—
287C22—41no—
288C22—42no—
289C22—41no—
290C22—42no—
291C22—41no—
292C22—441no—
293C22—442no—
294C22—441no—
295C22—442no—
296C22—441no—
297C22#6693714yes—
298C22C2×#433911yescharacteristic
299C22C2×D4×D1111yescharacteristic
300C22C2×D4×D1111yescharacteristic
301C22C2×#434112yes—
302C22#41×D1112yes—
303C4—24no—
304C4—41no—
305C4—42no—
306C4—114no—
307C4—224no—
308C4—222no—
309C4—441no—
310C4—442no—
311C2—24no—
312C2—81no—
313C2—881no—
314C2C2×#6693711yescharacteristic
315C2#1062306912yes—
316C2#1062311711yescharacteristic
317C2#1062312712yes—
318C2D11×#12311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC2×#66992C2
hypercenter#386D11
hypocenterC11#2854
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#66988C2semidirect
3. C22×C4×Dic11C2semidirect
4. C2×#66939C2semidirect
5. C11×#386C2semidirect
6. #10622826C2semidirect
7. #10622570C2semidirect
8. #10622564C2semidirect
9. #10622555C2semidirect
10. #10622282C2semidirect
11. #10622260C2semidirect
59. C22×Dic11D4semidirect
133. #386D11semidirect
162. Dic11#123semidirect
238. C11#2854semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C2×#669882
C22×C4×Dic112
C2×#669392
C11×#3862
#106228262
#106225702
#106225642
#106225552
#106222822
#106222602
#285411