Finite Group Databasebeta

← #13081129

Subgroups — #13081129

Order 1408.

348 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#10623147C211yesmaximal, characteristic
2#10623060C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622654C211yesmaximal, characteristic, complemented
5#10622611C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622489C211yesmaximal, characteristic, complemented
8#10622474C211yesmaximal, characteristic, complemented
9#10622467C211yesmaximal, characteristic, complemented
10#10622393C211yesmaximal, characteristic, complemented
11#10622390C211yesmaximal, characteristic, complemented
12#10622379C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622343C211yesmaximal, characteristic, complemented
15#10622336C211yesmaximal, characteristic, complemented
16C11×#121C2211yescharacteristic
17C11×#117C2211yescharacteristic
18#66992—21no—
19#66991C2211yescharacteristic
20#66989—21no—
21D4×Dic11C2211yescharacteristic
22C2×#4324C2211yescharacteristic
23C4×C22⋊D11C2211yescharacteristic
24#66979C2211yescharacteristic
25#66977C2211yescharacteristic
26C22×C11⋊C8C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28#66950C2211yescharacteristic
29#66945C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31#66943C2211yescharacteristic
32#66941C2211yescharacteristic
33#66940C2211yescharacteristic
34#66938—21no—
35#66936—21no—
36#66932—21no—
37#66930—21no—
38#66925—21no—
39#66923—21no—
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66896C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66882C2211yescharacteristic
48#66881C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51#66879C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64C22×Dic11—21no—
65C2×C4×D11—21no—
66C2×C4×D11C2311yescharacteristic
67C2×Dic22—21no—
68C2×Dic22C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C42×C11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11D411yescharacteristic
82#4324—22no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4D411yescharacteristic
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105#3348—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11C2×D411yescharacteristic
108C22×D11C2×D411yescharacteristic
109D4×C11—21no—
110D4×C11—21no—
111D4×C11—81no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—41no—
120C22⋊D11—81no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—42no—
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—42no—
132Dic22—21no—
133Dic22—21no—
134Dic22—81no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8#4112yes—
139#555—111no—
140#552—111no—
141#501—111no—
142#485—111no—
143#485—111no—
144#482D1111yescharacteristic, complemented
145#481—111no—
146#478—111no—
147#475—111no—
148#468—111no—
149#465—111no—
150#440—111no—
151#435—111no—
152#428—111no—
153#427—111no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11C2×#4111yescharacteristic
169C4×C112−1+411yescharacteristic
170Dic11—21no—
171Dic11—21no—
172Dic11—21no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16—111no—
178C2×M16—111no—
179C22×C8—111no—
180C4⋊Q8—111no—
181#126—221no—
182#125—111no—
183#125—221no—
184#124—221no—
185#124—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189#121—111no—
190#121—221no—
191#121C2×D1111yescharacteristic
192C4×Q8—111no—
193C4×D4—111no—
194C4×D4—111no—
195#117—111no—
196#117—111no—
197#117—221no—
198#117—221no—
199#117C2×D1111yescharacteristic
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⋊C8—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#102—111no—
215#102C2×D1111yescharacteristic
216#102C2×D1111yescharacteristic
217C22⋊C8—111no—
218C22⋊C8C2×D1111yescharacteristic
219#97—111no—
220C2×C11—41no—
221C2×C11—81no—
222C2×C11#54711yescharacteristic
223C2×C11#57511yescharacteristic
224C2×C11#57711yescharacteristic
225D11—41no—
226C2×Q8—111no—
227C2×Q8—221no—
228C2×D4—21no—
229C2×D4—111no—
230C2×D4—221no—
231C2×D4C22×D1111yescharacteristic
232C22×C4—111no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4C22×D1111yescharacteristic
236SD16—222no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—111no—
260C22⋊C4—111no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C42—21no—
268C42—111no—
269C42—221no—
270C42—221no—
271C42—221no—
272C11#334811yescharacteristic, complemented, Sylow
273C23—21no—
274C23—111no—
275C23D4×D1111yescharacteristic
276Q8—221no—
277Q8—221no—
278Q8—881no—
279D4—21no—
280D4—21no—
281D4—81no—
282D4—441no—
283D4—881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—111no—
290C2×C4—111no—
291C2×C4—111no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4D4×D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—21no—
303C8—21no—
304C8—112no—
305C8—221no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—221no—
313C22—221no—
314C22—221no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—221no—
321C4—221no—
322C4—221no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4#41×D1111yescharacteristic
328C4#6704311yescharacteristic
329C2—41no—
330C2—81no—
331C2—441no—
332C2#1062318611yescharacteristic
333C2#1062329911yescharacteristic
334C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
prime radical#10623147C2
hypercenter#482D11
hypocenterC11#3348
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #10623060C2semidirect
3. C11×#482C2semidirect
4. #10622654C2semidirect
5. #10622611C2semidirect
6. #10622501C2semidirect
7. #10622489C2semidirect
8. #10622474C2semidirect
9. #10622467C2semidirect
10. #10622393C2semidirect
11. #10622390C2semidirect
12. #10622379C2semidirect
13. #10622370C2semidirect
14. #10622343C2semidirect
15. #10622336C2semidirect
144. #482D11semidirect
272. C11#3348semidirect

Maximal subgroups

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

subgroupindex
#106231472
#106230602
C11×#4822
#106226542
#106226112
#106225012
#106224892
#106224742
#106224672
#106223932
#106223902
#106223792
#106223702
#106223432
#106223362
#334811