Finite Group Databasebeta

← #13071977

Subgroups — #13071977

Order 1408.

840 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D11C211yesmaximal, characteristic, complemented
2C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D11C211yesmaximal, characteristic
4C2×#66977C211yesmaximal, characteristic, complemented
5#10622843C211yesmaximal, characteristic, complemented
6#10622602C212yesmaximal, complemented
7#10622600C211yesmaximal, characteristic, complemented
8#10622592C212yesmaximal, complemented
9#10622587C211yesmaximal, characteristic, complemented
10#10622569C212yesmaximal
11#10622560C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C2×Q8×D11—24no—
16C2×Q8×D11—24no—
17C2×Q8×D11—24no—
18C22×C4×D11C2212yes—
19C22×C4×D11C2211yescharacteristic
20C22×Dic22C2212yes—
21C22×Dic22C2211yescharacteristic
22C11×C22⋊Q8—24no—
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2212yes—
25C2×C11×C22⋊C4C2212yes—
26C2×C22⋊Dic11C2212yes—
27C2×C22⋊Dic11C2211yescharacteristic
28C4×C22⋊D11—24no—
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2212yes—
31C2×C4⋊Dic11C2211yescharacteristic
32#66977—24no—
33C2×Dic11⋊C4C2212yes—
34C2×Dic11⋊C4C2211yescharacteristic
35C2×C4×Dic11C2211yescharacteristic
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C11⋊#95C2212yes—
40C11⋊#95C2212yes—
41C24×C11C2311yescharacteristic
42C23×D11C2311yescharacteristic
43C2×Q8×C11—22no—
44C2×Q8×C11—22no—
45C2×Q8×C11D414yescomplemented
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11C2312yes—
50C22×C4×C11C2311yescharacteristic
51C22×C4×C11C2312yes—
52C22×C4×C11C2311yescharacteristic
53C2×C22⋊D11—22no—
54C2×C22⋊D11—22no—
55C2×C22⋊D11Q814yescomplemented
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2312yes—
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2312yes—
60C22×Dic11C2311yescharacteristic
61Q8×D11—232no—
62C2×C4×D11—24no—
63C2×C4×D11—24no—
64C2×C4×D11—22no—
65C2×C4×D11—24no—
66C2×C4×D11—22no—
67C2×C4×D11D414yes—
68C2×Dic22—24no—
69C2×Dic22—24no—
70C2×Dic22—22no—
71C2×Dic22—24no—
72C2×Dic22—22no—
73C2×Dic22D414yescomplemented
74C11×C4⋊C4—22no—
75C11×C4⋊C4—24no—
76C11×C22⋊C4—24no—
77C22⋊Dic11—24no—
78C22⋊Dic11—22no—
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—24no—
81C4⋊Dic11—22no—
82Dic11⋊C4—24no—
83Dic11⋊C4—22no—
84C4×Dic11—22no—
85#2409—111nomaximal, Sylow
86C23×C11—21no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11C2×Q812yescomplemented
93C23×C11C2411yescharacteristic
94C22×D11—21no—
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11C2×D412yes—
99C22×D11C2×Q812yes—
100C22×D11#4112yes—
101Q8×C11—28no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—44no—
111C2×C4×C11C2×D412yes—
112C2×C4×C11C2×D412yes—
113C2×C4×C11C2×D414yes—
114C2×C4×C11C2×D412yes—
115C22⋊D11—28no—
116C2×Dic11—21no—
117C2×Dic11—22no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—22no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—22no—
124C2×Dic11—22no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11—21no—
128C2×Dic11C2×D412yes—
129C2×Dic11C2×D414yes—
130C2×Dic11C2×Q812yescomplemented
131C4×D11—216no—
132C4×D11—28no—
133Dic22—216no—
134Dic22—28no—
135C23×Q8—111no—
136C2×C22⋊Q8—111no—
137C2×C22⋊Q8D1111yescharacteristic, complemented
138C2×C4×D4—111no—
139#395—112no—
140#393—112no—
141#391—111no—
142#391—111no—
143#386—112no—
144#385—112no—
145#380—111no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11C22×D411yescharacteristic
154C22×C11C22×D411yescharacteristic
155C22×C11C22×D411yescharacteristic
156C22×C11C22×Q811yescharacteristic
157C22×C11C2×#4111yescharacteristic
158C22×C112−1+411yescharacteristic
159C22×C112−1+411yescharacteristic
160C2×D11—22no—
161C2×D11—22no—
162C2×D11—22no—
163C2×D11—22no—
164C2×D11—22no—
165C2×D11—22no—
166C2×D11C22⋊Q814yescomplemented
167C4×C11—24no—
168C4×C11—41no—
169C4×C11—42no—
170C4×C11#12014yes—
171Dic11—22no—
172Dic11—24no—
173Dic11—22no—
174Dic11—41no—
175Dic11—42no—
176C22×Q8—111no—
177C22×Q8—112no—
178C22×Q8—224no—
179C22×Q8—224no—
180C22×Q8—224no—
181C22×Q8C2×D1111yescharacteristic
182C22×D4—111no—
183C23×C4—111no—
184C23×C4—112no—
185C23×C4C2×D1111yescharacteristic
186C22⋊Q8—24no—
187C22⋊Q8—224no—
188C4×D4—224no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4C2×D1111yescharacteristic
193C2×C4⋊C4C2×D1112yes—
194C2×C22⋊C4—111no—
195C2×C22⋊C4—112no—
196C2×C22⋊C4—111no—
197C2×C22⋊C4—112no—
198C2×C22⋊C4C2×D1112yes—
199C2×C42—111no—
200#95—112no—
201#95—112no—
202#95—112no—
203#95—112no—
204#95—112no—
205C2×C11—42no—
206C2×C11C2×#12011yescharacteristic
207C2×C11C2×C22⋊Q811yescharacteristic
208C2×C11#53611yescharacteristic
209C2×C11#54811yescharacteristic
210C2×C11#54811yescharacteristic
211C2×C11D4×Q811yescharacteristic
212C2×C11D4×Q811yescharacteristic
213D11—24no—
214C24—111no—
215C24C22×D1111yescharacteristic
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—114no—
219C2×Q8—224no—
220C2×Q8—224no—
221C2×Q8—2232no—
222C2×Q8—222no—
223C2×Q8—224no—
224C2×Q8—222no—
225C2×Q8C22⋊D1114yescomplemented
226C2×D4—114no—
227C2×D4—222no—
228C2×D4—222no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—112no—
235C22×C4—114no—
236C22×C4—111no—
237C22×C4—112no—
238C22×C4—224no—
239C22×C4—224no—
240C22×C4—222no—
241C22×C4—224no—
242C22×C4—222no—
243C22×C4C22×D1112yes—
244C22×C4C22×D1111yescharacteristic
245C22×C4C22×D1112yes—
246C22×C4C22×D1111yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—24no—
249C4⋊C4—222no—
250C4⋊C4—224no—
251C4⋊C4—222no—
252C22⋊C4—24no—
253C22⋊C4—222no—
254C22⋊C4—224no—
255C22⋊C4—222no—
256C22⋊C4—224no—
257C42—222no—
258C11#240911yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—112no—
266C23—112no—
267C23—112no—
268C23—221no—
269C23—221no—
270C23—221no—
271C23—221no—
272C23Q8×D1112yescomplemented
273C23C23×D1111yescharacteristic
274Q8—28no—
275Q8—2216no—
276Q8—228no—
277D4—228no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—44no—
287C2×C4—112no—
288C2×C4—114no—
289C2×C4—112no—
290C2×C4—2216no—
291C2×C4—221no—
292C2×C4—222no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—222no—
297C2×C4—228no—
298C2×C4—221no—
299C2×C4—222no—
300C2×C4—221no—
301C2×C4—222no—
302C2×C4—222no—
303C2×C4—221no—
304C2×C4D4×D1112yes—
305C2×C4D4×D1112yes—
306C2×C4C2×C22⋊D1114yes—
307C2×C4C2×C22⋊D1112yes—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—114no—
316C22—222no—
317C22—222no—
318C22—222no—
319C22—222no—
320C22—222no—
321C22—222no—
322C22C2×D4×D1111yescharacteristic
323C22C2×D4×D1111yescharacteristic
324C22C2×Q8×D1111yescharacteristic
325C22#6704011yescharacteristic
326C22#41×D1111yescharacteristic
327C22#6704311yescharacteristic
328C22C22×C22⋊D1111yescharacteristic
329C4—24no—
330C4—41no—
331C4—42no—
332C4—222no—
333C4—224no—
334C4—222no—
335C4—441no—
336C4—442no—
337C4#6699014yes—
338C2—42no—
339C2—224no—
340C2D11×C22⋊Q811yescharacteristic
341C2#1062315911yescharacteristic
342C2#1062316311yescharacteristic
343C2#1062316411yescharacteristic
344C2C2×#6699011yescharacteristic
345C2Q8×C22⋊D1111yescharacteristic
346C2#1062336211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC22×C22⋊D11C22
hypercenterC2×C22⋊Q8D11
hypocenterC11#2409
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D11C2semidirect
2. C2×C11×C22⋊Q8C2semidirect
4. C2×#66977C2semidirect
5. #10622843C2semidirect
6. #10622602C2semidirect
7. #10622600C2semidirect
8. #10622592C2semidirect
9. #10622587C2semidirect
11. #10622560C2semidirect
45. C2×Q8×C11D4semidirect
55. C2×C22⋊D11Q8semidirect
73. C2×Dic22D4semidirect
92. C23×C11C2×Q8semidirect
130. C2×Dic11C2×Q8semidirect
137. C2×C22⋊Q8D11semidirect
166. C2×D11C22⋊Q8semidirect
225. C2×Q8C22⋊D11semidirect
258. C11#2409semidirect
272. C23Q8×D11semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D112
C2×C11×C22⋊Q82
C2×C4×C22⋊D112
C2×#669772
#106228432
#106226022
#106226002
#106225922
#106225872
#106225692
#106225602
#240911