Finite Group Databasebeta

← #13080627

Subgroups — #13080627

Order 1408.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623108C211yesmaximal, characteristic, complemented
2#10623089C211yesmaximal, characteristic, complemented
3C11×#440C211yesmaximal, characteristic, complemented
4#10622785C211yesmaximal, characteristic, complemented
5#10622785C211yesmaximal, characteristic, complemented
6#10622635C211yesmaximal, characteristic, complemented
7#10622628C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic, complemented
9#10622495C211yesmaximal, characteristic, complemented
10#10622417C211yesmaximal, characteristic, complemented
11#10622416C211yesmaximal, characteristic, complemented
12#10622395C211yesmaximal, characteristic, complemented
13#10622388C211yesmaximal, characteristic, complemented
14#10622326C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21#66991C2211yescharacteristic
22#66991C2211yescharacteristic
23C2×#4323C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25#66982—21no—
26C4×C22⋊D11—21no—
27C2×#4313C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29#66948—21no—
30#66948—21no—
31#66948C2211yescharacteristic
32#66948C2211yescharacteristic
33#66945C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35#66937—21no—
36#66932—21no—
37#66927—21no—
38#66927C2211yescharacteristic
39C4×D44—21no—
40C4×D44C2211yescharacteristic
41#66923C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#97C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53(C2×D11)⋊C8C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64#4343—22no—
65#4343—22no—
66#4343—41no—
67#4343—41no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44D411yescharacteristic
75C2×D44C2311yescharacteristic
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11C2311yescharacteristic
81C2×C4×D11C2311yescharacteristic
82C11×SD16—22no—
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C22⋊C4—21no—
89C42×C11—21no—
90C42×C11C2311yescharacteristic
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93#4323—41no—
94#4323—41no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4D411yescharacteristic
99(C2×D11)⋊C4D411yescharacteristic
100C4⋊Dic11D411yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4313—41no—
110C8×D11—41no—
111#3309—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11C2×D411yescharacteristic
116C22×D11C2×D411yescharacteristic
117Q8×C11—21no—
118Q8×C11#4112yes—
119D4×C11—21no—
120D4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—81no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—42no—
129C22⋊D11—81no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136D44—21no—
137D44—21no—
138D44—41no—
139D44—42no—
140D44—42no—
141D44—42no—
142D44—81no—
143D44—81no—
144D44—81no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—42no—
150C4×D11—42no—
151C4×D11—81no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#553—111no—
157#550—111no—
158#490—111no—
159#482—111no—
160#480—111no—
161#479—111no—
162#469—111no—
163#466—111no—
164#459—111no—
165#449—111no—
166#449—111no—
167#440D1111yescharacteristic, complemented
168#435—111no—
169#417—111no—
170#416—111no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C4×C11—22no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11C2×#4111yescharacteristic
193C4×C11H(5,𝔽2)11yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—41no—
197Dic11—41no—
198C2×#41—111no—
199C2×#41—111no—
200C2×SD16C2×D1111yescharacteristic
201C2×D8—111no—
202C2×D8—111no—
203C2×M16—111no—
204C22×C8—111no—
205#127—111no—
206#127—221no—
207#126—221no—
208#125—111no—
209#123—221no—
210#121—111no—
211#121—111no—
212#121—111no—
213#121—111no—
214#121—221no—
215#121—221no—
216#121—221no—
217C4×Q8C2×D1111yescharacteristic
218C4×D4—111no—
219C4×D4—221no—
220C4×D4—221no—
221C4×D4C2×D1111yescharacteristic
222#117—111no—
223C2×C4⋊C4—111no—
224#107—111no—
225#107C2×D1111yescharacteristic
226#106—111no—
227C4⋊C8—111no—
228#103—111no—
229#103—111no—
230#103C2×D1111yescharacteristic
231#102—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236#102—111no—
237#102C2×D1111yescharacteristic
238C22⋊C8—111no—
239C22⋊C8—111no—
240#97C2×D1111yescharacteristic
241C2×C11—81no—
242C2×C11#54611yescharacteristic
243C2×C11#57511yescharacteristic
244C2×C11#57611yescharacteristic
245D11—41no—
246D11—41no—
247D11—81no—
248D11—81no—
249#41—222no—
250#41—222no—
251#41—441no—
252#41—441no—
253C2×Q8C22×D1111yescharacteristic
254C2×D4—111no—
255C2×D4—111no—
256C2×D4—111no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4C22×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272SD16—22no—
273D8—441no—
274D8—441no—
275M16—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8—441no—
279C2×C8C22×D1111yescharacteristic
280C2×C8C22×D1111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—111no—
283C4⋊C4—111no—
284C4⋊C4—111no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4C22×D1111yescharacteristic
289C4⋊C4C22×D1111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—111no—
292C22⋊C4—111no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C42—21no—
299C42—221no—
300C42C22×D1111yescharacteristic
301C11#330911yescharacteristic, complemented, Sylow
302C23—21no—
303C23—111no—
304C23—111no—
305C23—221no—
306C23—221no—
307Q8—21no—
308Q8#433912yes—
309D4—21no—
310D4—21no—
311D4—221no—
312D4—221no—
313D4—221no—
314D4—221no—
315D4—441no—
316D4—442no—
317D4—442no—
318D4—442no—
319D4—442no—
320D4—881no—
321D4—881no—
322D4—881no—
323D4—881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—111no—
329C2×C4—111no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—881no—
339C2×C4D4×D1111yescharacteristic
340C2×C4D4×D1111yescharacteristic
341C2×C4C23×D1111yescharacteristic
342C8—21no—
343C8—21no—
344C8—221no—
345C8—221no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—221no—
350C22—221no—
351C22—221no—
352C22—221no—
353C22—221no—
354C22—221no—
355C22—441no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22C2×D4×D1111yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—221no—
368C4—221no—
369C4—441no—
370C4—441no—
371C4C2×#433911yescharacteristic
372C4#6704211yescharacteristic
373C2—81no—
374C2—441no—
375C2—441no—
376C2—881no—
377C2—881no—
378C2#1062308111yescharacteristic
379C2#1062330511yescharacteristic
380C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
hypercenter#440D11
hypocenterC11#3309
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. #10623108C2semidirect
2. #10623089C2semidirect
3. C11×#440C2semidirect
4. #10622785C2semidirect
5. #10622785C2semidirect
6. #10622635C2semidirect
7. #10622628C2semidirect
8. #10622498C2semidirect
9. #10622495C2semidirect
10. #10622417C2semidirect
11. #10622416C2semidirect
12. #10622395C2semidirect
13. #10622388C2semidirect
14. #10622326C2semidirect
15. #10622319C2semidirect
167. #440D11semidirect
301. C11#3309semidirect

Maximal subgroups

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

subgroupindex
#106231082
#106230892
C11×#4402
#106227852
#106226352
#106226282
#106224982
#106224952
#106224172
#106224162
#106223952
#106223882
#106223262
#106223192
#330911