Finite Group Databasebeta

← #13079321

Subgroups — #13079321

Order 1408.

366 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623109C211yesmaximal, characteristic, complemented
2#10623088C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622784C211yesmaximal, characteristic
5#10622780C211yesmaximal, characteristic, complemented
6#10622643C211yesmaximal, characteristic, complemented
7#10622631C211yesmaximal, characteristic, complemented
8#10622500C211yesmaximal, characteristic, complemented
9#10622489C211yesmaximal, characteristic, complemented
10#10622426C211yesmaximal, characteristic, complemented
11#10622410C211yesmaximal, characteristic, complemented
12#10622391C211yesmaximal, characteristic
13#10622378C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15D11×#97C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66999C2211yescharacteristic
20#66997C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22#66991C2211yescharacteristic
23#66989C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25C4×C22⋊D11—21no—
26#66979—21no—
27C2×Dic44C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66950C2211yescharacteristic
31#66950C2211yescharacteristic
32#66949—21no—
33#66943C2211yescharacteristic
34#66942—21no—
35#66941C2211yescharacteristic
36#66936—21no—
37#66932—21no—
38#66925—21no—
39C42×D11C2211yescharacteristic
40C4×Dic22—21no—
41C4×Dic22C2211yescharacteristic
42C4×Dic22C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66881C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53#66879C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C4×D11D411yescharacteristic
64C2×C4×D11D411yescharacteristic
65C2×C4×D11C2311yescharacteristic
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C11×SD16—22no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C42×C11—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81#4326—22no—
82#4324—22no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11D411yescharacteristic
101C4×Dic11D411yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105Dic44—22no—
106C8×D11—22no—
107C8×D11—22no—
108#3181—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113D4×C11—21no—
114D4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C22⋊D11—42no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C4×D11—22no—
131C4×D11—21no—
132C4×D11—21no—
133C4×D11—41no—
134Dic22—21no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22—42no—
139C8×C11—21no—
140C8×C11#4112yes—
141C11⋊C8—21no—
142C11⋊C8#4112yes—
143#533—111no—
144#529—111no—
145#501—111no—
146#497—111no—
147#491—111no—
148#489—111no—
149#467—111no—
150#467—111no—
151#465—111no—
152#465—111no—
153#441—111no—
154#441—111no—
155#440—111no—
156#440D1111yescharacteristic, complemented
157C2×#97—111no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11C22×D411yescharacteristic
162C2×D11—21no—
163C2×D11—21no—
164C2×D11#13712yes—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11C2×#4111yescharacteristic
171C4×C11C2×#4111yescharacteristic
172Dic11—21no—
173Dic11—21no—
174Dic11—21no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×Q16—111no—
180C2×Q16—111no—
181C2×SD16—111no—
182C2×SD16C2×D1111yescharacteristic
183C22×C8—111no—
184C22×C8—111no—
185C4⋊Q8—111no—
186C4⋊Q8—111no—
187#126—221no—
188#125—111no—
189#125—221no—
190#124—111no—
191#123—221no—
192C22⋊Q8—111no—
193C22⋊Q8—111no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196#121—111no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—221no—
200C4×Q8C2×D1111yescharacteristic
201C4×D4—221no—
202C4×D4C2×D1111yescharacteristic
203#117—221no—
204#117—221no—
205C2×C42—111no—
206#107—111no—
207#107C2×D1111yescharacteristic
208#106—111no—
209#106—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#103—111no—
215#103C2×D1111yescharacteristic
216#102—111no—
217#102C2×D1111yescharacteristic
218#97—111no—
219#97—111no—
220#97—111no—
221#97C2×D1111yescharacteristic
222C2×C11—81no—
223C2×C11#53211yescharacteristic
224C2×C11C2×#13711yescharacteristic
225C2×C11#57511yescharacteristic
226D11—22no—
227C2×Q8—111no—
228C2×Q8—111no—
229C2×Q8—221no—
230C2×Q8C22×D1111yescharacteristic
231C2×D4—221no—
232C2×D4C22×D1111yescharacteristic
233C22×C4—21no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237Q16—222no—
238Q16—222no—
239SD16—22no—
240SD16—222no—
241C2×C8—111no—
242C2×C8—111no—
243C2×C8—222no—
244C2×C8—222no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—21no—
270C42—111no—
271C42—111no—
272C42—111no—
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#318111yescharacteristic, complemented, Sylow
277C23—21no—
278C23—111no—
279Q8—21no—
280Q8—21no—
281Q8—221no—
282Q8—221no—
283Q8—221no—
284Q8—221no—
285Q8—442no—
286D4—21no—
287D4—21no—
288D4—442no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—222no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—441no—
304C2×C4D4×D1111yescharacteristic
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—112no—
309C8—221no—
310C8#433912yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—112no—
315C22—221no—
316C22—221no—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—221no—
324C4—221no—
325C4—221no—
326C4—441no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4C2×#433911yescharacteristic
331C4#41×D1111yescharacteristic
332C2—81no—
333C2—222no—
334C2#1062307911yescharacteristic
335C2#1062330411yescharacteristic
336C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#440D11
hypocenterC11#3181
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623109C2semidirect
3. C11×#440C2semidirect
5. #10622780C2semidirect
6. #10622643C2semidirect
7. #10622631C2semidirect
8. #10622500C2semidirect
9. #10622489C2semidirect
10. #10622426C2semidirect
11. #10622410C2semidirect
13. #10622378C2semidirect
14. #10622329C2semidirect
15. D11×#97C2semidirect
156. #440D11semidirect
276. C11#3181semidirect

Maximal subgroups

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

subgroupindex
#106231092
#106230882
C11×#4402
#106227842
#106227802
#106226432
#106226312
#106225002
#106224892
#106224262
#106224102
#106223912
#106223782
#106223292
D11×#972
#318111