Finite Group Databasebeta

← #13080992

Subgroups — #13080992

Order 1408.

354 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623226C211yesmaximal, characteristic
2#10623112C211yesmaximal, characteristic, complemented
3C11×#479C211yesmaximal, characteristic, complemented
4#10622677C211yesmaximal, characteristic, complemented
5C4×#4325C211yesmaximal, characteristic, complemented
6#10622495C211yesmaximal, characteristic, complemented
7#10622493C211yesmaximal, characteristic, complemented
8#10622479C211yesmaximal, characteristic, complemented
9D11×#106C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622447C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic, complemented
13#10622422C211yesmaximal, characteristic, complemented
14#10622420C211yesmaximal, characteristic, complemented
15#10622420C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#66999C2211yescharacteristic
19#66999C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21C2×C8×D11C2211yescharacteristic
22C2×C8×D11C2211yescharacteristic
23#66951—21no—
24#66948—21no—
25#66948C2211yescharacteristic
26#66948C2211yescharacteristic
27#66947—21no—
28#66947—21no—
29#66946—21no—
30#66945C2211yescharacteristic
31#66945C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66942—21no—
35#66929—21no—
36C4×D44C2211yescharacteristic
37C4×D44C2211yescharacteristic
38#66925—21no—
39#66923C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45#66899C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66873C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D44—21no—
61C2×D44—21no—
62C2×D44D411yescharacteristic
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11C2311yescharacteristic
68C2×C4×D11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79#4325—22no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4D411yescharacteristic
88(C2×D11)⋊C4D411yescharacteristic
89C4⋊Dic11D411yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C8×D11—22no—
104C8×D11—22no—
105#3337—111nomaximal, Sylow
106C22×D11—21no—
107C22×D11C2×D411yescharacteristic
108C22×D11C2×D411yescharacteristic
109Q8×C11—21no—
110Q8×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2411yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123D44—22no—
124D44—21no—
125D44—21no—
126D44—42no—
127D44—81no—
128C4×D11—21no—
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—42no—
133C4×D11—81no—
134C4×D11—81no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8#4112yes—
139#553—111no—
140#552—111no—
141#499—111no—
142#485—111no—
143#484—111no—
144#482—111no—
145#480—111no—
146#479D1111yescharacteristic, complemented
147#478—111no—
148#465—111no—
149#465—111no—
150C4×SD16—111no—
151C8×D4—111no—
152#427—111no—
153C2×#106—111no—
154C22×C11C22×D411yescharacteristic
155C2×D11—21no—
156C2×D11—21no—
157C2×D11—21no—
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11#13512yes—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11C2×#4111yescharacteristic
171C4×C112−1+411yescharacteristic
172Dic11—21no—
173Dic11—21no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16—111no—
178C22×C8—111no—
179C22×C8—111no—
180#126—221no—
181#126—221no—
182#125—111no—
183#125—221no—
184#125C2×D1111yescharacteristic
185#123—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189#121—111no—
190#121—111no—
191#121—221no—
192C4×Q8C2×D1111yescharacteristic
193C4×D4—111no—
194C4×D4—111no—
195C4×D4—221no—
196#117—111no—
197#117—111no—
198#117—221no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201#107—111no—
202#107—111no—
203#107—111no—
204#107C2×D1111yescharacteristic
205#106—111no—
206#106—111no—
207#106—111no—
208#106—111no—
209#106C2×D1111yescharacteristic
210C4⋊C8C2×D1111yescharacteristic
211#103—111no—
212#103C2×D1111yescharacteristic
213#103C2×D1111yescharacteristic
214#102—111no—
215#102—111no—
216#102—111no—
217C22⋊C8—111no—
218C22⋊C8—111no—
219C4×C8—111no—
220C2×C11#54711yescharacteristic
221C2×C11C2×#13511yescharacteristic
222C2×C11#57711yescharacteristic
223D11—22no—
224D11—41no—
225D11—81no—
226C2×Q8C22×D1111yescharacteristic
227C2×D4—111no—
228C2×D4—111no—
229C2×D4—221no—
230C2×D4—221no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236SD16—222no—
237C2×C8—111no—
238C2×C8—111no—
239C2×C8—222no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—111no—
247C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
257C4⋊C4C22×D1111yescharacteristic
258C4⋊C4C22×D1111yescharacteristic
259C22⋊C4—111no—
260C22⋊C4—111no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C42—21no—
269C42—221no—
270C42—221no—
271C42C22×D1111yescharacteristic
272C11#333711yescharacteristic, complemented, Sylow
273C23—111no—
274C23—111no—
275C23—221no—
276Q8—21no—
277Q8—21no—
278D4—222no—
279D4—221no—
280D4—221no—
281D4—442no—
282D4—881no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—111no—
288C2×C4—111no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—442no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4D4×D1111yescharacteristic
300C2×C4D4×D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—21no—
303C8—21no—
304C8—112no—
305C8—221no—
306C22—112no—
307C22—221no—
308C22—221no—
309C22—221no—
310C22—221no—
311C22—221no—
312C22—441no—
313C22—441no—
314C22—441no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—221no—
323C4—221no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4#6704011yescharacteristic
328C4#41×D1111yescharacteristic
329C2—222no—
330C2—441no—
331C2—881no—
332C2#1062316211yescharacteristic
333C2D11×#13511yescharacteristic
334C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radical#10623226C2
hypercenter#479D11
hypocenterC11#3337
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. #10623112C2semidirect
3. C11×#479C2semidirect
4. #10622677C2semidirect
5. C4×#4325C2semidirect
6. #10622495C2semidirect
7. #10622493C2semidirect
8. #10622479C2semidirect
9. D11×#106C2semidirect
10. #10622460C2semidirect
11. #10622447C2semidirect
12. #10622428C2semidirect
13. #10622422C2semidirect
14. #10622420C2semidirect
15. #10622420C2semidirect
146. #479D11semidirect
272. C11#3337semidirect

Maximal subgroups

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

subgroupindex
#106232262
#106231122
C11×#4792
#106226772
C4×#43252
#106224952
#106224932
#106224792
D11×#1062
#106224602
#106224472
#106224282
#106224222
#106224202
#333711