Finite Group Databasebeta

← #13082718

Subgroups — #13082718

Order 1408.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#548C211yesmaximal, characteristic, complemented
2#10623365C211yesmaximal, characteristic, complemented
3#10623358C211yesmaximal, characteristic, complemented
4#10623348C211yesmaximal, characteristic, complemented
5#10623343C211yesmaximal, characteristic, complemented
6#10623212C213yesmaximal, complemented
7#10623211C213yesmaximal, complemented
8#10623174C213yesmaximal, complemented
9#10623173C213yesmaximal, complemented
10#10623150C213yesmaximal, complemented
11#10623147C213yesmaximal, complemented
12C4×#4343C211yesmaximal, characteristic, complemented
13#10623100C211yesmaximal, characteristic, complemented
14#10623096C213yesmaximal, complemented
15#10623088C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C2×#4343C2211yescharacteristic
19C11×#124C2213yes—
20C11×C22⋊Q8C2213yes—
21C11×#121C2213yes—
22C4×Q8×C11C2211yescharacteristic
23C4×D4×C11C2213yes—
24#67000C2213yes—
25#66999C2213yes—
26Q8×Dic11C2211yescharacteristic
27Q8×Dic11C2211yescharacteristic
28Q8×Dic11C2213yes—
29Q8×Dic11C2213yes—
30Q8×Dic11C2211yescharacteristic
31#66993C2213yes—
32#66992C2216yes—
33#66991C2213yes—
34#66991C2213yes—
35#66989C2213yes—
36D4×Dic11C2213yes—
37D4×Dic11C2213yes—
38#66983C2213yes—
39#66983C2213yes—
40C4×C22⋊D11C2213yes—
41C4×C22⋊D11C2213yes—
42#66979C2213yes—
43#66979C2213yes—
44#66979C2213yes—
45C2×C4⋊Dic11C2213yes—
46#66951C2216yes—
47#66950C2213yes—
48#66946C2213yes—
49#66945C2213yes—
50#66943C2213yes—
51#66943C2213yes—
52#66941C2213yes—
53#66939C2216yes—
54#66938C2216yes—
55#66936C2213yes—
56#66936C2213yes—
57#66936C2216yes—
58(C22⋊D11)⋊C4C2216yes—
59#66932C2211yescharacteristic
60#66932C2213yes—
61#66930C2216yes—
62C4×D44C2213yes—
63C42×D11C2213yes—
64#66923C2213yes—
65C4×Dic22C2213yes—
66C11×#41—24no—
67C2×Q8×C11—24no—
68C2×Q8×C11C2313yes—
69C2×Q8×C11C2311yescharacteristic
70C2×D4×C11C2313yes—
71C2×D4×C11C2313yes—
72C22×C4×C11C2313yes—
73C22×C4×C11C2313yes—
74C2×C22⋊D11C2316yes—
75C2×C22⋊D11C2313yes—
76C2×C22⋊D11C2313yes—
77C22×Dic11C2316yes—
78#4343—24no—
79C2×D44C2313yes—
80C2×C4×D11C2313yes—
81C2×C4×D11C2313yes—
82C2×C4×D11C2313yes—
83C2×Dic22C2313yes—
84C11×C4⋊C4C2313yes—
85C11×C4⋊C4C2313yes—
86C11×C22⋊C4C2316yes—
87C11×C22⋊C4C2313yes—
88C11×C22⋊C4C2311yescharacteristic
89C42×C11C2313yes—
90C22⋊Dic11C2313yes—
91C22⋊Dic11C2313yes—
92C22⋊Dic11C2311yescharacteristic
93C22⋊Dic11C2311yescharacteristic
94C22⋊Dic11C2313yes—
95C22⋊Dic11C2313yes—
96(C2×D11)⋊C4C2316yes—
97(C2×D11)⋊C4C2316yes—
98(C2×D11)⋊C4C2313yes—
99(C2×D11)⋊C4C2313yes—
100C4⋊Dic11C2313yes—
101C4⋊Dic11C2313yes—
102C4⋊Dic11C2313yes—
103C4⋊Dic11C2313yes—
104C4⋊Dic11C2313yes—
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2313yes—
107C4⋊Dic11C2313yes—
108Dic11⋊C4C2311yescharacteristic
109Dic11⋊C4C2313yes—
110Dic11⋊C4C2316yes—
111Dic11⋊C4C2313yes—
112Dic11⋊C4C2311yescharacteristic
113C4×Dic11C2313yes—
114C4×Dic11C2313yes—
115C4×Dic11C2311yescharacteristic
116C4×Dic11C2313yes—
117C4×Dic11C2313yes—
118C4×Dic11C2316yes—
119#3524—111nomaximal, Sylow
120C23×C11C2411yescharacteristic
121C23×C11C2413yes—
122C22×D11C2413yes—
123Q8×C11—26no—
124Q8×C11#4114yes—
125D4×C11—26no—
126D4×C11—43no—
127C2×C4×C11—26no—
128C2×C4×C11—26no—
129C2×C4×C11C2413yes—
130C2×C4×C11C2411yescharacteristic
131C2×C4×C11C2413yes—
132C2×C4×C11C2411yescharacteristic
133C2×C4×C11C2413yes—
134C22⋊D11—46no—
135C22⋊D11—43no—
136C22⋊D11—43no—
137C2×Dic11—46no—
138C2×Dic11C2411yescharacteristic
139C2×Dic11C2413yes—
140C2×Dic11C2411yescharacteristic
141C2×Dic11C2413yes—
142C2×Dic11C2411yescharacteristic
143C2×Dic11C2411yescharacteristic
144C2×Dic11C2413yes—
145D44—26no—
146C4×D11—26no—
147C4×D11—43no—
148C4×D11—43no—
149Dic22—43no—
150#559—113no—
151#557—111no—
152#555—113no—
153#553—113no—
154#552—113no—
155#550—111no—
156#548—111no—
157#548D1111yescharacteristic, complemented
158#542—113no—
159#540—113no—
160#529—113no—
161#529—113no—
162#520—111no—
163#519—111no—
164C4×#41—111no—
165C22×C11—21no—
166C22×C11—23no—
167C22×C11—21no—
168C22×C11—23no—
169C22×C11—23no—
170C22×C11—21no—
171C22×C11C2511yescharacteristic
172C2×D11—23no—
173C2×D11—23no—
174C2×D11—23no—
175C4×C11—21no—
176C4×C11—23no—
177C4×C11—23no—
178C4×C11—21no—
179C4×C11C2×#4116yes—
180Dic11—21no—
181Dic11—21no—
182Dic11—23no—
183Dic11—21no—
184Dic11—23no—
185Dic11—23no—
186Dic11—21no—
187C2×#41—111no—
188C2×#41C2×D1111yescharacteristic
189C22×Q8C2×D1111yescharacteristic
190C4⋊Q8—113no—
191#127—113no—
192#126—116no—
193#126—111no—
194#126—113no—
195#125—113no—
196#125—113no—
197#125—113no—
198#124—113no—
199#124—113no—
200#124—116no—
201#124C2×D1113yes—
202#123—116no—
203#123—113no—
204#123—113no—
205#123—116no—
206C22⋊Q8—113no—
207C22⋊Q8—113no—
208C22⋊Q8C2×D1113yes—
209#121—113no—
210#121—113no—
211#121—116no—
212#121—113no—
213#121—113no—
214#121C2×D1113yes—
215C4×Q8—111no—
216C4×Q8—113no—
217C4×Q8—111no—
218C4×Q8—113no—
219C4×Q8—111no—
220C4×Q8—113no—
221C4×Q8C2×D1111yescharacteristic
222C4×D4—113no—
223C4×D4—113no—
224C4×D4—113no—
225C4×D4—113no—
226C4×D4—113no—
227C4×D4—116no—
228C4×D4—113no—
229C4×D4C2×D1113yes—
230#117—113no—
231#117—113no—
232#117—113no—
233#117—113no—
234#117—116no—
235C2×C4⋊C4—113no—
236C2×C42—113no—
237C2×C11—41no—
238C2×C11—43no—
239C2×C11C22×#4111yescharacteristic
240C2×C11#58511yescharacteristic
241C2×C11#58511yescharacteristic
242D11—43no—
243#41—24no—
244#41—224no—
245C2×Q8—24no—
246C2×Q8—113no—
247C2×Q8C22×D1113yes—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—113no—
250C2×D4—116no—
251C2×D4—113no—
252C2×D4—113no—
253C2×D4C22×D1113yes—
254C2×D4C22×D1113yes—
255C22×C4—116no—
256C22×C4—113no—
257C22×C4—113no—
258C22×C4—113no—
259C22×C4C22×D1113yes—
260C22×C4C22×D1113yes—
261C4⋊C4—113no—
262C4⋊C4—113no—
263C4⋊C4—113no—
264C4⋊C4—111no—
265C4⋊C4—113no—
266C4⋊C4—113no—
267C4⋊C4—113no—
268C4⋊C4—113no—
269C4⋊C4—116no—
270C4⋊C4—111no—
271C4⋊C4—113no—
272C4⋊C4—111no—
273C4⋊C4—113no—
274C4⋊C4C22×D1113yes—
275C4⋊C4C22×D1113yes—
276C22⋊C4—111no—
277C22⋊C4—113no—
278C22⋊C4—113no—
279C22⋊C4—113no—
280C22⋊C4—113no—
281C22⋊C4—111no—
282C22⋊C4—116no—
283C22⋊C4—113no—
284C22⋊C4—116no—
285C22⋊C4—113no—
286C22⋊C4C22×D1116yes—
287C22⋊C4C22×D1113yes—
288C22⋊C4C22×D1111yescharacteristic
289C42—111no—
290C42—113no—
291C42—113no—
292C42—116no—
293C42—113no—
294C42—113no—
295C42C22×D1113yes—
296C11#352411yescharacteristic, complemented, Sylow
297C23—113no—
298C23C23×D1111yescharacteristic
299C23C23×D1113yes—
300Q8—26no—
301Q8—443no—
302Q8#434114yes—
303D4—26no—
304D4—43no—
305D4—226no—
306D4—446no—
307D4—443no—
308D4—443no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—113no—
314C2×C4—111no—
315C2×C4—113no—
316C2×C4—111no—
317C2×C4—113no—
318C2×C4—226no—
319C2×C4—443no—
320C2×C4—443no—
321C2×C4—446no—
322C2×C4C23×D1113yes—
323C2×C4C23×D1111yescharacteristic
324C2×C4C23×D1113yes—
325C2×C4C23×D1111yescharacteristic
326C2×C4C23×D1113yes—
327C22—21no—
328C22—23no—
329C22—21no—
330C22—23no—
331C22—23no—
332C22—21no—
333C22—223no—
334C22—223no—
335C22—223no—
336C22C24×D1111yescharacteristic
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—221no—
342C4—221no—
343C4—223no—
344C4—221no—
345C4—223no—
346C4—223no—
347C4—221no—
348C4C2×#434116yes—
349C2—41no—
350C2—43no—
351C2—443no—
352C2C22×#434111yescharacteristic
353C2#1062345311yescharacteristic
354C2#1062345711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#548C2
hypercenter#548D11
hypocenterC11#3524
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C11×#548C2semidirect
2. #10623365C2semidirect
3. #10623358C2semidirect
4. #10623348C2semidirect
5. #10623343C2semidirect
6. #10623212C2semidirect
7. #10623211C2semidirect
8. #10623174C2semidirect
9. #10623173C2semidirect
10. #10623150C2semidirect
11. #10623147C2semidirect
12. C4×#4343C2semidirect
13. #10623100C2semidirect
14. #10623096C2semidirect
15. #10623088C2semidirect
157. #548D11semidirect
296. C11#3524semidirect

Maximal subgroups

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

subgroupindex
C11×#5482
#106233652
#106233582
#106233482
#106233432
#106232122
#106232112
#106231742
#106231732
#106231502
#106231472
C4×#43432
#106231002
#106230962
#106230882
#352411