Finite Group Databasebeta

← #13081097

Subgroups — #13081097

Order 1408.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623045C211yesmaximal, characteristic
2#10623042C211yesmaximal, characteristic, complemented
3C2×C11×#107C211yesmaximal, characteristic, complemented
4#10622727C211yesmaximal, characteristic, complemented
5#10622724C211yesmaximal, characteristic, complemented
6#10622583C211yesmaximal, characteristic, complemented
7#10622581C211yesmaximal, characteristic, complemented
8#10622503C211yesmaximal, characteristic, complemented
9#10622502C211yesmaximal, characteristic, complemented
10#10622501C211yesmaximal, characteristic, complemented
11#10622499C211yesmaximal, characteristic, complemented
12#10622495C211yesmaximal, characteristic, complemented
13#10622494C211yesmaximal, characteristic, complemented
14#10622490C211yesmaximal, characteristic, complemented
15#10622489C211yesmaximal, characteristic, complemented
16C22×C8×C11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19#66983—21no—
20#66983C2211yescharacteristic
21C4×C22⋊D11—21no—
22C4×C22⋊D11—21no—
23C4×C22⋊D11C2211yescharacteristic
24#66977—21no—
25#66977C2211yescharacteristic
26C2×#4314C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28#66951—21no—
29#66950C2211yescharacteristic
30#66949—21no—
31#66948C2211yescharacteristic
32#66947—21no—
33#66946C2211yescharacteristic
34#66945C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66943C2211yescharacteristic
37#66942—21no—
38#66941C2211yescharacteristic
39#66940C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66881C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51#66874C2211yescharacteristic
52#66874C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64C2×D44—21no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11C2311yescharacteristic
69C2×Dic22—21no—
70C2×Dic22C2311yescharacteristic
71C2×C8×C11—22no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C22⋊Dic11—21no—
81C22⋊Dic11D411yescharacteristic
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
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#4314—22no—
104#4313—22no—
105#3346—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C22×D11—21no—
108C22×D11C2×D411yescharacteristic
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—22no—
120C22⋊D11—42no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—21no—
128D44—21no—
129D44—81no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—81no—
133C4×D11—81no—
134Dic22—21no—
135Dic22—21no—
136Dic22—81no—
137C8×C11—21no—
138C8×C11#4112yes—
139C11⋊C8—21no—
140C11⋊C8—21no—
141#554—111no—
142#553—111no—
143#501—111no—
144#485—111no—
145#484—111no—
146#481—111no—
147#480—111no—
148#479—111no—
149#474—111no—
150#468—111no—
151#465—111no—
152#440—111no—
153#435—111no—
154#428—111no—
155C2×#107D1111yescharacteristic, complemented
156C22×C11—21no—
157C22×C11—21no—
158C22×C11#13712yes—
159C22×C11C22×D411yescharacteristic
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×SD16—111no—
180C2×M16—111no—
181C22×C8C2×D1111yescharacteristic
182C4⋊Q8—111no—
183#126—221no—
184#125—111no—
185#125—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189C22⋊Q8—221no—
190C22⋊Q8—221no—
191#121—111no—
192#121—111no—
193#121—221no—
194C4×Q8—111no—
195C4×D4—111no—
196C4×D4—111no—
197C4×D4—221no—
198C4×D4—221no—
199#117—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4C2×D1111yescharacteristic
202C2×C4⋊C4C2×D1111yescharacteristic
203#107—111no—
204#107—111no—
205#107C2×D1111yescharacteristic
206#107C2×D1111yescharacteristic
207#107C2×D1111yescharacteristic
208#107C2×D1111yescharacteristic
209#106—111no—
210#106—111no—
211#106—111no—
212C4⋊C8—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219C22⋊C8—111no—
220C22⋊C8—111no—
221#97—111no—
222C2×C11—22no—
223C2×C11#54711yescharacteristic
224C2×C11C2×#13711yescharacteristic
225C2×C11#57611yescharacteristic
226D11—41no—
227D11—81no—
228C2×Q8—111no—
229C2×Q8—221no—
230C2×D4—111no—
231C2×D4—111no—
232C2×D4—221no—
233C2×D4—221no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—111no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4C22×D1111yescharacteristic
240SD16—222no—
241M16—222no—
242C2×C8—22no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4C22×D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C22⋊C4—111no—
264C22⋊C4—111no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C42—111no—
272C42—221no—
273C42—221no—
274C11#334611yescharacteristic, complemented, Sylow
275C23—111no—
276C23—221no—
277C23D4×D1111yescharacteristic
278Q8—221no—
279Q8—221no—
280Q8—881no—
281D4—222no—
282D4—221no—
283D4—221no—
284D4—442no—
285D4—881no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4D4×D1111yescharacteristic
305C2×C4C23×D1111yescharacteristic
306C8—21no—
307C8—221no—
308C8—221no—
309C8#433912yes—
310C22—21no—
311C22—21no—
312C22—221no—
313C22—221no—
314C22—221no—
315C22—441no—
316C22—441no—
317C22—441no—
318C22#6697112yes—
319C22C2×D4×D1111yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—221no—
326C4—221no—
327C4—221no—
328C4—441no—
329C4—441no—
330C4—441no—
331C4C2×#433911yescharacteristic
332C4#6704011yescharacteristic
333C2—22no—
334C2—441no—
335C2—881no—
336C2#1062303811yescharacteristic
337C2#1062328811yescharacteristic
338C2C2×#6697111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#107C2
socleC22×C11C22×D4
prime radical#10623045C2
hypercenterC2×#107D11
hypocenterC11#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #10623042C2semidirect
3. C2×C11×#107C2semidirect
4. #10622727C2semidirect
5. #10622724C2semidirect
6. #10622583C2semidirect
7. #10622581C2semidirect
8. #10622503C2semidirect
9. #10622502C2semidirect
10. #10622501C2semidirect
11. #10622499C2semidirect
12. #10622495C2semidirect
13. #10622494C2semidirect
14. #10622490C2semidirect
15. #10622489C2semidirect
155. C2×#107D11semidirect
274. C11#3346semidirect

Maximal subgroups

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

subgroupindex
#106230452
#106230422
C2×C11×#1072
#106227272
#106227242
#106225832
#106225812
#106225032
#106225022
#106225012
#106224992
#106224952
#106224942
#106224902
#106224892
#334611