Finite Group Databasebeta

← #13080869

Subgroups — #13080869

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
1C11×#548C211yesmaximal, characteristic, complemented
2#10623096C211yesmaximal, characteristic, complemented
3#10622851C211yesmaximal, characteristic, complemented
4#10622845C211yesmaximal, characteristic, complemented
5#10622840C211yesmaximal, characteristic, complemented
6#10622838C211yesmaximal, characteristic, complemented
7#10622670C211yesmaximal, characteristic, complemented
8#10622669C211yesmaximal, characteristic, complemented
9#10622662C211yesmaximal, characteristic, complemented
10#10622656C211yesmaximal, characteristic, complemented
11#10622652C211yesmaximal, characteristic, complemented
12#10622648C211yesmaximal, characteristic, complemented
13C4×#4325C211yesmaximal, characteristic, complemented
14#10622635C211yesmaximal, characteristic, complemented
15#10622625C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C11×#124—21no—
19C11×#124C2211yescharacteristic
20C11×C22⋊Q8—21no—
21C11×C22⋊Q8C2211yescharacteristic
22C11×#121—21no—
23C11×#121C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×D4×C11—21no—
26C4×D4×C11C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29#66992—21no—
30C2×#4323C2211yescharacteristic
31#66983C2211yescharacteristic
32#66983C2211yescharacteristic
33#66979C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×#4318C2211yescharacteristic
36C2×#4318C2211yescharacteristic
37#66951—21no—
38#66936—21no—
39(C22⋊D11)⋊C4—21no—
40C4×D44C2211yescharacteristic
41#66923C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51C22⋊(C11⋊C8)C2211yescharacteristic
52C22⋊(C11⋊C8)C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11—21no—
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×Q8×C11C2311yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11D411yescharacteristic
69C2×D4×C11C2311yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C22×Dic11—21no—
77C2×D44C2311yescharacteristic
78C2×C4×D11—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4D411yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4D411yescharacteristic
88C11×C22⋊C4D411yescharacteristic
89C42×C11—21no—
90C42×C11C2311yescharacteristic
91C22⋊Dic11—21no—
92#4325—22no—
93#4325—41no—
94#4323—41no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3326—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C23×C11C2×D411yescharacteristic
115C22×D11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—42no—
120Q8×C11#4112yes—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—41no—
124D4×C11—42no—
125D4×C11—42no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2411yescharacteristic
140C22⋊D11—42no—
141C22⋊D11—81no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—81no—
146D44—21no—
147D44—21no—
148C4×D11—81no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#553—111no—
154#548D1111yescharacteristic, complemented
155#488—111no—
156#483—111no—
157#482—111no—
158#479—111no—
159#469—111no—
160#468—111no—
161#463—111no—
162#449—111no—
163#448—111no—
164C4×SD16—111no—
165#436—111no—
166#419—111no—
167#417—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—22no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11C2×#4111yescharacteristic
189C4×C11H(5,𝔽2)11yescharacteristic
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41C2×D1111yescharacteristic
194C22×Q8C2×D1111yescharacteristic
195C2×SD16—111no—
196C2×SD16—111no—
197C2×D8—111no—
198C2×M16—111no—
199C2×M16—111no—
200#126—221no—
201#125—111no—
202#124—21no—
203#124C2×D1111yescharacteristic
204#123—221no—
205C22⋊Q8—21no—
206C22⋊Q8C2×D1111yescharacteristic
207#121—21no—
208#121—111no—
209#121—111no—
210#121—221no—
211#121C2×D1111yescharacteristic
212C4×Q8C2×D1111yescharacteristic
213C4×D4—21no—
214C4×D4—111no—
215C4×D4—221no—
216C4×D4C2×D1111yescharacteristic
217#117—111no—
218C2×C4⋊C4—111no—
219#107—111no—
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#103—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233C22⋊C8—111no—
234C22⋊C8—111no—
235C4×C8—111no—
236C2×C11—41no—
237C2×C11—41no—
238C2×C11—81no—
239C2×C11#54611yescharacteristic
240C2×C11#57511yescharacteristic
241C2×C11#57711yescharacteristic
242D11—81no—
243#41—22no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8C22×D1111yescharacteristic
249C2×Q8C22×D1111yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—111no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4C22⋊D1111yescharacteristic
256C2×D4C22×D1111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4C22×D1111yescharacteristic
262C22×C4C22×D1111yescharacteristic
263SD16—222no—
264SD16—441no—
265D8—441no—
266M16—441no—
267M16—441no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—111no—
271C2×C8—111no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—111no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4C22⋊D1111yescharacteristic
281C4⋊C4C22×D1111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4C22⋊D1111yescharacteristic
291C22⋊C4C22⋊D1111yescharacteristic
292C42—21no—
293C42—221no—
294C42C22×D1111yescharacteristic
295C11#332611yescharacteristic, complemented, Sylow
296C23—21no—
297C23—221no—
298C23C2×C22⋊D1111yescharacteristic
299C23C2×C22⋊D1111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#434112yes—
305D4—21no—
306D4—21no—
307D4—41no—
308D4—42no—
309D4—42no—
310D4—221no—
311D4—221no—
312D4—442no—
313D4—881no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—881no—
327C2×C4—881no—
328C2×C4C2×C22⋊D1111yescharacteristic
329C2×C4C2×C22⋊D1111yescharacteristic
330C2×C4C2×C22⋊D1111yescharacteristic
331C2×C4C2×C22⋊D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—221no—
334C8—221no—
335C8—221no—
336C8—221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22C22×C22⋊D1111yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4C2×#434111yescharacteristic
361C4#6703711yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—881no—
366C2#1062333711yescharacteristic
367C2#1062335311yescharacteristic
368C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#548C2
socleC22×C11C22×D4
hypercenter#548D11
hypocenterC11#3326
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C11×#548C2semidirect
2. #10623096C2semidirect
3. #10622851C2semidirect
4. #10622845C2semidirect
5. #10622840C2semidirect
6. #10622838C2semidirect
7. #10622670C2semidirect
8. #10622669C2semidirect
9. #10622662C2semidirect
10. #10622656C2semidirect
11. #10622652C2semidirect
12. #10622648C2semidirect
13. C4×#4325C2semidirect
14. #10622635C2semidirect
15. #10622625C2semidirect
154. #548D11semidirect
295. C11#3326semidirect

Maximal subgroups

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

subgroupindex
C11×#5482
#106230962
#106228512
#106228452
#106228402
#106228382
#106226702
#106226692
#106226622
#106226562
#106226522
#106226482
C4×#43252
#106226352
#106226252
#332611