Finite Group Databasebeta

← #13082527

Subgroups — #13082527

Order 1408.

1104 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#41C211yesmaximal, characteristic, complemented
2#10623364C212yesmaximal, complemented
3#10623115C212yesmaximal, complemented
4#10623110C212yesmaximal, complemented
5#10623096C214yesmaximal, complemented
6#10623094C212yesmaximal, complemented
7#10623083C214yesmaximal, complemented
8#10623082C212yesmaximal, complemented
9#10623065C214yesmaximal, complemented
10#10623054C212yesmaximal, complemented
11#10623008C212yesmaximal, complemented
12#10623008C211yesmaximal, characteristic, complemented
13#10623001C212yesmaximal, complemented
14C2×#66922C211yesmaximal, characteristic, complemented
15C2×C11×#41C2211yescharacteristic
16C2×#4339C2212yes—
17C2×#4339C2214yes—
18C22×Dic22C2212yes—
19C4×Q8×C11C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic
22C4×D4×C11C2212yes—
23C4×D4×C11C2211yescharacteristic
24C4×D4×C11C2212yes—
25C11×#117C2211yescharacteristic
26C11×#117C2212yes—
27C2×C42×C11C2211yescharacteristic
28C2×C42×C11C2212yes—
29#66999C2214yes—
30#66992C2218yes—
31#66991C2214yes—
32#66983C2214yes—
33#66983C2212yes—
34#66983C2214yes—
35#66983C2212yes—
36#66979C2214yes—
37C2×C4⋊Dic11C2212yes—
38C2×C4⋊Dic11C2212yes—
39#66977C2214yes—
40#66977C2214yes—
41#66951C2218yes—
42#66949C2218yes—
43#66945C2214yes—
44C4⋊C4×D11C2214yes—
45#66938C2218yes—
46#66936C2218yes—
47(C22⋊D11)⋊C4C2218yes—
48#66928C2212yes—
49#66928C2214yes—
50#66927C2211yescharacteristic
51C4×D44C2214yes—
52C4×D44C2212yes—
53C4×D44C2212yes—
54C4×D44C2214yes—
55#66923C2214yes—
56#66922C2212yes—
57#66922C2212yes—
58#66922C2212yes—
59#66922C2212yes—
60#66922C2211yescharacteristic
61C4×Dic22C2214yes—
62C4×Dic22C2214yes—
63C11×#41—24no—
64C2×Q8×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C2×D4×C11C2312yes—
67C22×C4×C11C2312yes—
68C22×C4×C11C2312yes—
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2312yes—
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C2×C22⋊D11C2314yes—
74C2×C22⋊D11C2318yes—
75C22×Dic11C2314yes—
76#4339—28no—
77#4339—48no—
78C2×D44C2312yes—
79C2×D44C2312yes—
80C2×D44C2312yes—
81C2×C4×D11C2314yes—
82C2×C4×D11C2318yes—
83C2×Dic22—44no—
84C2×Dic22C2312yes—
85C2×Dic22C2314yes—
86C2×Dic22C2314yes—
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C4⋊C4C2312yes—
90C11×C4⋊C4C2312yes—
91C11×C22⋊C4C2312yes—
92C11×C22⋊C4C2312yes—
93C11×C22⋊C4C2312yes—
94C42×C11C2312yes—
95C42×C11C2312yes—
96C42×C11C2311yescharacteristic
97C42×C11C2311yescharacteristic
98C42×C11C2311yescharacteristic
99C42×C11C2311yescharacteristic
100C42×C11C2312yes—
101C22⋊Dic11C2318yes—
102(C2×D11)⋊C4C2318yes—
103(C2×D11)⋊C4C2314yes—
104(C2×D11)⋊C4C2314yes—
105(C2×D11)⋊C4C2318yes—
106C4⋊Dic11C2312yes—
107C4⋊Dic11C2314yes—
108C4⋊Dic11C2314yes—
109C4⋊Dic11C2314yes—
110C4⋊Dic11C2314yes—
111C4⋊Dic11C2312yes—
112Dic11⋊C4C2318yes—
113Dic11⋊C4C2318yes—
114C4×Dic11C2318yes—
115#3511—111nomaximal, Sylow
116C23×C11C2412yes—
117C23×C11C2411yescharacteristic
118C22×D11C2414yes—
119Q8×C11—22no—
120D4×C11—24no—
121D4×C11—22no—
122C2×C4×C11—24no—
123C2×C4×C11—22no—
124C2×C4×C11—24no—
125C2×C4×C11—22no—
126C2×C4×C11—24no—
127C2×C4×C11#4114yescomplemented
128C2×C4×C11C2412yes—
129C2×C4×C11C2412yes—
130C2×C4×C11C2412yes—
131C2×C4×C11C2411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C2×C4×C11C2411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C22⋊D11—28no—
138C22⋊D11—48no—
139C2×Dic11—44no—
140C2×Dic11C2414yes—
141C2×Dic11C2418yes—
142D44—24no—
143D44—24no—
144D44—24no—
145C4×D11—28no—
146C4×D11—48no—
147Dic22—24no—
148Dic22—28no—
149Dic22—44no—
150#556—112no—
151#555—112no—
152#554—112no—
153#553—114no—
154#548—114no—
155#547—112no—
156#542—114no—
157#537—112no—
158#533—112no—
159#532—111no—
160#532—112no—
161C2×C4⋊Q8—111no—
162#520—112no—
163C4×#41D1111yescharacteristic, complemented
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11C2×#4112yes—
170C22×C11C2511yescharacteristic
171C2×D11—24no—
172C2×D11—24no—
173C2×D11—24no—
174C4×C11—22no—
175C4×C11—21no—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—21no—
179C4×C11C2×#4112yes—
180C4×C11C2×#4112yes—
181C4×C11H(5,𝔽2)12yes—
182C4×C112−1+412yes—
183Dic11—24no—
184Dic11—28no—
185C2×#41—112no—
186C2×#41—114no—
187C2×#41C2×D1111yescharacteristic
188C22×Q8—112no—
189C4⋊Q8—112no—
190C4⋊Q8—112no—
191C4⋊Q8—112no—
192C4⋊Q8—112no—
193C4⋊Q8—111no—
194#127—111no—
195#126—118no—
196#125—114no—
197#124—118no—
198#124—112no—
199#124—114no—
200#123—118no—
201C22⋊Q8—114no—
202C22⋊Q8—114no—
203C22⋊Q8—114no—
204C22⋊Q8—118no—
205#121—114no—
206#121—118no—
207#121—114no—
208#121—112no—
209#121—112no—
210#121—114no—
211C4×Q8—114no—
212C4×Q8—114no—
213C4×Q8C2×D1111yescharacteristic
214C4×Q8C2×D1111yescharacteristic
215C4×D4—118no—
216C4×D4—114no—
217C4×D4—112no—
218C4×D4—114no—
219C4×D4—112no—
220C4×D4C2×D1111yescharacteristic
221C4×D4C2×D1112yes—
222C4×D4C2×D1112yes—
223C4×D4C2×D1111yescharacteristic
224#117—114no—
225#117—114no—
226#117C2×D1111yescharacteristic
227#117C2×D1112yes—
228C2×C4⋊C4—112no—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—114no—
231C2×C42C2×D1111yescharacteristic
232C2×C42C2×D1112yes—
233C2×C11—22no—
234C2×C11—42no—
235C2×C11C22×#4111yescharacteristic
236C2×C11C2×H(5,𝔽2)11yescharacteristic
237C2×C11C2×2−1+411yescharacteristic
238D11—44no—
239#41—24no—
240#41—228no—
241#41—448no—
242C2×Q8—112no—
243C2×Q8—114no—
244C2×Q8—114no—
245C2×Q8—444no—
246C2×Q8C22×D1111yescharacteristic
247C2×D4—114no—
248C2×D4—118no—
249C2×D4—112no—
250C2×D4—112no—
251C2×D4—112no—
252C2×D4C22×D1112yes—
253C2×D4C22×D1111yescharacteristic
254C22×C4—114no—
255C22×C4—114no—
256C22×C4—118no—
257C22×C4C22×D1111yescharacteristic
258C22×C4C22×D1112yes—
259C22×C4C22×D1112yes—
260C22×C4C22×D1111yescharacteristic
261C22×C4C22×D1112yes—
262C22×C4C22×D1111yescharacteristic
263C4⋊C4—114no—
264C4⋊C4—114no—
265C4⋊C4—114no—
266C4⋊C4—118no—
267C4⋊C4—114no—
268C4⋊C4—112no—
269C4⋊C4—112no—
270C4⋊C4—118no—
271C4⋊C4C22×D1111yescharacteristic
272C4⋊C4C22×D1111yescharacteristic
273C4⋊C4C22×D1112yes—
274C4⋊C4C22×D1112yes—
275C22⋊C4—118no—
276C22⋊C4—118no—
277C22⋊C4—118no—
278C22⋊C4—114no—
279C22⋊C4—114no—
280C22⋊C4C22×D1112yes—
281C22⋊C4C22×D1112yes—
282C22⋊C4C22×D1112yes—
283C42—118no—
284C42C22×D1111yescharacteristic
285C42C22×D1112yes—
286C42C22×D1111yescharacteristic
287C42C22×D1112yes—
288C42C22×D1111yescharacteristic
289C42C22×D1111yescharacteristic
290C42C22×D1112yes—
291C11#351111yescharacteristic, complemented, Sylow
292C23—114no—
293C23C23×D1112yes—
294C23C23×D1111yescharacteristic
295Q8—22no—
296Q8—224no—
297Q8—228no—
298Q8—444no—
299D4—24no—
300D4—22no—
301D4—228no—
302D4—224no—
303D4—224no—
304D4—224no—
305D4—448no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—114no—
312C2×C4—118no—
313C2×C4—228no—
314C2×C4—448no—
315C2×C4—444no—
316C2×C4#433914yescomplemented
317C2×C4C23×D1112yes—
318C2×C4C23×D1111yescharacteristic
319C2×C4C23×D1111yescharacteristic
320C2×C4C23×D1112yes—
321C2×C4C23×D1112yes—
322C2×C4C23×D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C2×C4C23×D1111yescharacteristic
325C2×C4C23×D1111yescharacteristic
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22—224no—
332C22—224no—
333C22—224no—
334C22C2×#433912yes—
335C22C24×D1111yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—22no—
340C4—21no—
341C4—224no—
342C4—228no—
343C4C2×#433912yes—
344C4C2×#433912yes—
345C4#6704212yes—
346C4#6704312yes—
347C2—22no—
348C2—42no—
349C2—444no—
350C2C22×#433911yescharacteristic
351C2C2×#6704211yescharacteristic
352C2C2×#6704311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC4×C11×#41C2
hypercenterC4×#41D11
hypocenterC11#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C11×#41C2semidirect
2. #10623364C2semidirect
3. #10623115C2semidirect
4. #10623110C2semidirect
5. #10623096C2semidirect
6. #10623094C2semidirect
7. #10623083C2semidirect
8. #10623082C2semidirect
9. #10623065C2semidirect
10. #10623054C2semidirect
11. #10623008C2semidirect
12. #10623008C2semidirect
13. #10623001C2semidirect
14. C2×#66922C2semidirect
127. C2×C4×C11#41semidirect
163. C4×#41D11semidirect
291. C11#3511semidirect
316. C2×C4#4339semidirect

Maximal subgroups

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

subgroupindex
C4×C11×#412
#106233642
#106231152
#106231102
#106230962
#106230942
#106230832
#106230822
#106230652
#106230542
#106230082
#106230012
C2×#669222
#351111