Finite Group Databasebeta

← #13081237

Subgroups — #13081237

Order 1408.

354 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#10623166C211yesmaximal, characteristic, complemented
2#10623147C211yesmaximal, characteristic
3C11×#468C211yesmaximal, characteristic, complemented
4#10622787C211yesmaximal, characteristic, complemented
5SD16×Dic11C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622734C211yesmaximal, characteristic, complemented
8#10622658C211yesmaximal, characteristic, complemented
9#10622646C211yesmaximal, characteristic, complemented
10#10622494C211yesmaximal, characteristic, complemented
11#10622487C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic, complemented
13#10622407C211yesmaximal, characteristic, complemented
14#10622387C211yesmaximal, characteristic, complemented
15#10622374C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×M16C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#121C2211yescharacteristic
20#66999C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22#66992—21no—
23#66991C2211yescharacteristic
24#66989—21no—
25D4×Dic11C2211yescharacteristic
26C4×C22⋊D11C2211yescharacteristic
27#66979C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30#66950—21no—
31#66945C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33#66942—21no—
34#66941C2211yescharacteristic
35#66941C2211yescharacteristic
36#66938—21no—
37(C22⋊D11)⋊C4—21no—
38#66931—21no—
39#66930—21no—
40C11×#107C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11D411yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C2×C4×D11—21no—
68C2×C4×D11C2311yescharacteristic
69C2×Dic22—21no—
70C2×Dic22—21no—
71C11×SD16—22no—
72C11×M16—22no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11D411yescharacteristic
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4D411yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105#3357—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11C2×D411yescharacteristic
108C22×D11C2×D411yescharacteristic
109Q8×C11—21no—
110Q8×C11—21no—
111D4×C11—21no—
112D4×C11—21no—
113D4×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—22no—
122C22⋊D11—81no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—42no—
128C2×Dic11—81no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—81no—
135Dic22—81no—
136Dic22—81no—
137C8×C11—21no—
138C8×C11#4112yes—
139C11⋊C8—21no—
140C11⋊C8—21no—
141#555—111no—
142#554—111no—
143#500—111no—
144#485—111no—
145#485—111no—
146#480—111no—
147#480—111no—
148#477—111no—
149#476—111no—
150#468—111no—
151#468D1111yescharacteristic, complemented
152C4×SD16—111no—
153#436—111no—
154#428—111no—
155#428—111no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11C22×D411yescharacteristic
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—21no—
166C4×C11—21no—
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—
177Dic11—41no—
178Dic11#13712yes—
179C2×SD16C2×D1111yescharacteristic
180C2×M16—111no—
181C2×M16C2×D1111yescharacteristic
182C4⋊Q8—111no—
183C4⋊Q8—111no—
184#125—221no—
185#124—221no—
186#124—221no—
187C22⋊Q8—111no—
188C22⋊Q8—221no—
189C22⋊Q8—221no—
190C22⋊Q8C2×D1111yescharacteristic
191#121—111no—
192#121—221no—
193#121C2×D1111yescharacteristic
194C4×Q8—111no—
195C4×D4—111no—
196C4×D4—111no—
197C4×D4—221no—
198#117—111no—
199#117—111no—
200#117—221no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203#107—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107C2×D1111yescharacteristic
209#106—111no—
210#106—111no—
211#106—111no—
212C4⋊C8—111no—
213#103—111no—
214#103—111no—
215#103C2×D1111yescharacteristic
216#102—111no—
217#102—111no—
218#102C2×D1111yescharacteristic
219C22⋊C8—111no—
220C22⋊C8—111no—
221C4×C8—111no—
222C2×C11—41no—
223C2×C11—81no—
224C2×C11#54711yescharacteristic
225C2×C11C2×#13711yescharacteristic
226C2×C11#57611yescharacteristic
227D11—41no—
228C2×Q8—221no—
229C2×Q8—221no—
230C2×Q8C22×D1111yescharacteristic
231C2×D4—21no—
232C2×D4—111no—
233C2×D4—221no—
234C2×D4C22×D1111yescharacteristic
235C22×C4—111no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4C22×D1111yescharacteristic
240SD16—22no—
241M16—22no—
242M16—222no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4C22×D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—111no—
264C22⋊C4—111no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C42—111no—
271C42—221no—
272C42—221no—
273C42—221no—
274C11#335711yescharacteristic, complemented, Sylow
275C23—21no—
276C23—111no—
277C23D4×D1111yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—881no—
281Q8—881no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—222no—
286D4—881no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—442no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4D4×D1111yescharacteristic
305C2×C4C23×D1111yescharacteristic
306C8—21no—
307C8—221no—
308C8—221no—
309C8#434112yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—221no—
317C22—221no—
318C22—221no—
319C22C2×D4×D1111yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—112no—
325C4—221no—
326C4—221no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4—441no—
331C4C2×#434111yescharacteristic
332C4#6704311yescharacteristic
333C2—41no—
334C2—81no—
335C2—441no—
336C2#1062314211yescharacteristic
337C2#1062330511yescharacteristic
338C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
prime radical#10623147C2
hypercenter#468D11
hypocenterC11#3357
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #10623166C2semidirect
3. C11×#468C2semidirect
4. #10622787C2semidirect
5. SD16×Dic11C2semidirect
6. #10622741C2semidirect
7. #10622734C2semidirect
8. #10622658C2semidirect
9. #10622646C2semidirect
10. #10622494C2semidirect
11. #10622487C2semidirect
12. #10622428C2semidirect
13. #10622407C2semidirect
14. #10622387C2semidirect
15. #10622374C2semidirect
151. #468D11semidirect
274. C11#3357semidirect

Maximal subgroups

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

subgroupindex
#106231662
#106231472
C11×#4682
#106227872
SD16×Dic112
#106227412
#106227342
#106226582
#106226462
#106224942
#106224872
#106224282
#106224072
#106223872
#106223742
#335711