Finite Group Databasebeta

← #13080807

Subgroups — #13080807

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623107C211yesmaximal, characteristic, complemented
2#10623094C211yesmaximal, characteristic, complemented
3C11×#440C211yesmaximal, characteristic, complemented
4#10622785C211yesmaximal, characteristic, complemented
5#10622783C211yesmaximal, characteristic, complemented
6#10622633C211yesmaximal, characteristic, complemented
7#10622629C211yesmaximal, characteristic, complemented
8#10622501C211yesmaximal, characteristic, complemented
9#10622498C211yesmaximal, characteristic, complemented
10#10622417C211yesmaximal, characteristic, complemented
11#10622415C211yesmaximal, characteristic, complemented
12#10622395C211yesmaximal, characteristic, complemented
13#10622391C211yesmaximal, characteristic, complemented
14#10622327C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21#66991C2211yescharacteristic
22#66991C2211yescharacteristic
23C2×#4324C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25#66983—21no—
26#66979—21no—
27C2×#4313C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29#66950—21no—
30#66950C2211yescharacteristic
31#66948—21no—
32#66948C2211yescharacteristic
33#66945C2211yescharacteristic
34#66945C2211yescharacteristic
35#66938—21no—
36#66938—21no—
37#66928—21no—
38#66928C2211yescharacteristic
39C4×D44—21no—
40C4×D44C2211yescharacteristic
41#66922C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#97C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
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—41no—
66Q8×D11—22no—
67Q8×D11—41no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44D411yescharacteristic
71C2×D44C2311yescharacteristic
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11C2311yescharacteristic
75C2×C4×D11C2311yescharacteristic
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22C2311yescharacteristic
79C11×SD16—22no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C42×C11—21no—
87C42×C11C2311yescharacteristic
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90#4324—41no—
91#4323—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4D411yescharacteristic
99(C2×D11)⋊C4D411yescharacteristic
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11D411yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105C4×Dic11—21no—
106C4×Dic11—21no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4313—41no—
110C8×D11—41no—
111#3321—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114C22×D11C2×D411yescharacteristic
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11#4112yes—
118D4×C11—21no—
119D4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—81no—
128C22⋊D11—81no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136D44—41no—
137D44—42no—
138D44—42no—
139C4×D11—21no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—21no—
143C4×D11—42no—
144C4×D11—42no—
145Dic22—21no—
146Dic22—21no—
147Dic22—42no—
148Dic22—81no—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#555—111no—
154#548—111no—
155#489—111no—
156#485—111no—
157#482—111no—
158#475—111no—
159#469—111no—
160#465—111no—
161#463—111no—
162#449—111no—
163#448—111no—
164#440D1111yescharacteristic, complemented
165#435—111no—
166#419—111no—
167#416—111no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11C22×D411yescharacteristic
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C4×C11—22no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11C2×#4111yescharacteristic
187C4×C11H(5,𝔽2)11yescharacteristic
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C22×Q8—111no—
195C2×SD16—111no—
196C2×SD16C2×D1111yescharacteristic
197C2×D8—111no—
198C2×M16—111no—
199C22×C8—111no—
200C4⋊Q8—111no—
201#124—111no—
202#124—221no—
203#124—221no—
204#124—221no—
205C22⋊Q8—111no—
206C22⋊Q8—221no—
207#121—111no—
208#121—111no—
209#121—111no—
210#121—221no—
211#121—221no—
212C4×Q8C2×D1111yescharacteristic
213C4×D4—111no—
214C4×D4—221no—
215C4×D4C2×D1111yescharacteristic
216#117—111no—
217#117—111no—
218#117—221no—
219#107C2×D1111yescharacteristic
220#106—111no—
221#106—111no—
222C4⋊C8—111no—
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#103C2×D1111yescharacteristic
229#102—111no—
230#102—111no—
231#102—111no—
232#102C2×D1111yescharacteristic
233C22⋊C8—111no—
234C22⋊C8—111no—
235#97C2×D1111yescharacteristic
236C2×C11—81no—
237C2×C11#54611yescharacteristic
238C2×C11#57511yescharacteristic
239C2×C11#57711yescharacteristic
240D11—41no—
241D11—41no—
242D11—81no—
243#41—222no—
244#41—441no—
245C2×Q8—111no—
246C2×Q8—221no—
247C2×Q8—221no—
248C2×Q8—222no—
249C2×Q8—441no—
250C2×Q8C22×D1111yescharacteristic
251C2×D4—111no—
252C2×D4—111no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4C22×D1111yescharacteristic
258C22×C4—21no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4—221no—
263SD16—22no—
264SD16—441no—
265D8—441no—
266M16—441no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—441no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4C22×D1111yescharacteristic
279C4⋊C4C22×D1111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—111no—
282C22⋊C4—111no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C42—21no—
292C42—221no—
293C42—221no—
294C42C22×D1111yescharacteristic
295C11#332111yescharacteristic, complemented, Sylow
296C23—21no—
297C23—111no—
298C23—111no—
299C23—221no—
300Q8—21no—
301Q8—221no—
302Q8—221no—
303Q8—442no—
304Q8—881no—
305Q8#433912yes—
306D4—21no—
307D4—21no—
308D4—221no—
309D4—221no—
310D4—441no—
311D4—442no—
312D4—442no—
313D4—881no—
314D4—881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4D4×D1111yescharacteristic
331C2×C4D4×D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—221no—
336C8—221no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—221no—
341C22—221no—
342C22—221no—
343C22—221no—
344C22—221no—
345C22—221no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—221no—
356C4—221no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4C2×#433911yescharacteristic
361C4#6704211yescharacteristic
362C2—81no—
363C2—441no—
364C2—441no—
365C2—881no—
366C2#1062308111yescharacteristic
367C2#1062330411yescharacteristic
368C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
hypercenter#440D11
hypocenterC11#3321
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. #10623107C2semidirect
2. #10623094C2semidirect
3. C11×#440C2semidirect
4. #10622785C2semidirect
5. #10622783C2semidirect
6. #10622633C2semidirect
7. #10622629C2semidirect
8. #10622501C2semidirect
9. #10622498C2semidirect
10. #10622417C2semidirect
11. #10622415C2semidirect
12. #10622395C2semidirect
13. #10622391C2semidirect
14. #10622327C2semidirect
15. #10622319C2semidirect
164. #440D11semidirect
295. C11#3321semidirect

Maximal subgroups

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

subgroupindex
#106231072
#106230942
C11×#4402
#106227852
#106227832
#106226332
#106226292
#106225012
#106224982
#106224172
#106224152
#106223952
#106223912
#106223272
#106223192
#332111