Finite Group Databasebeta

← #14909001

Subgroups — #14909001

Order 2816.

564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077527C211yesmaximal, characteristic, complemented
2#13070828C212yesmaximal, complemented
3#13070784C212yesmaximal, complemented
4#13070689C212yesmaximal, complemented
5#13070561C212yesmaximal, complemented
6#13070512C214yesmaximal, complemented
7#13070428C211yesmaximal, characteristic, complemented
8C11×#3184C211yesmaximal, characteristic, complemented
9C11×#532—21no—
10#10623279C2211yescharacteristic
11#10623276—21no—
12C11×#498C2211yescharacteristic, complemented
13C11×#493C2211yescharacteristic, complemented
14C11×#486—21no—
15C11×#469—21no—
16C11×#469C2212yes—
17C11×#442—21no—
18C11×#442C2212yescomplemented
19C4×C11×M16C2211yescharacteristic
20#10622760C2214yes—
21#10622738C2211yescharacteristic
22C2×#66869—21no—
23#10622330—21no—
24#10622330C2212yes—
25#10622313—21no—
26#10622313C2212yes—
27#10622201C2214yescomplemented
28#10622191C2212yes—
29#10622126C2214yes—
30#10622125C2214yescomplemented
31#10622104C2212yescomplemented
32#10622101C2212yescomplemented
33C2×C11×#41—41no—
34C2×#4339—21no—
35C2×C11×D8—21no—
36C2×C11×D8C2312yes—
37C2×C11×M16D411yescharacteristic
38C2×C11×M16C2311yescharacteristic
39C11×C4⋊Q8—21no—
40C11×#127—21no—
41C11×#124—41no—
42C11×#121—22no—
43C11×#121—41no—
44C4×D4×C11—22no—
45C4×D4×C11—41no—
46C2×C42×C11D411yescharacteristic
47C2×#4318—21no—
48#66962—22no—
49#66961—22no—
50#66960—42no—
51M16×D11—42no—
52#66957—21no—
53#66957C2312yes—
54#66954—22no—
55#66954—22no—
56C11×#106—21no—
57C11×#106C2312yes—
58C11×#102—22no—
59C11×#102—22no—
60C11×#97D411yescharacteristic
61C11×#97C2311yescharacteristic
62C4×C8×C11D411yescharacteristic
63C4×C8×C11C2311yescharacteristic
64#66891—24no—
65#66890—24no—
66#66883—21no—
67#66883C2312yes—
68#66876C2314yes—
69#66869—22no—
70#66869—22no—
71#33688—111nomaximal, Sylow
72C11×#41—84no—
73C2×Q8×C11—41no—
74C2×D4×C11—22no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—42no—
78C22×C4×C11—21no—
79C22×C4×C11—42no—
80C22×C4×C11C2×D411yescharacteristic
81C2×C22⋊D11—41no—
82#4339—22no—
83#4339—22no—
84#4339—41no—
85#4339—41no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C11×D8—24no—
90C11×D8—42no—
91C11×M16—22no—
92C11×M16—22no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C42×C11—21no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104#4318—22no—
105#4318—41no—
106C2×C11⋊C8—41no—
107Dic44—21no—
108Dic44#4112yescomplemented
109D88—21no—
110D88#4112yescomplemented
111#4314—22no—
112#4314—22no—
113#4313—42no—
114#4313—42no—
115C8×D11—42no—
116C8×D11—42no—
117C11⋊C16—24no—
118#3184D1111yescharacteristic, complemented
119#2956—111no—
120#2238—112no—
121#2230—112no—
122#2213—112no—
123#2190—112no—
124AGL(1,ℤ/16)—114no—
125#2165—111no—
126C23×C11—42no—
127C23×C11AGL(1,ℤ/8)11yescharacteristic
128C22×D11—41no—
129Q8×C11—82no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—82no—
133D4×C11—82no—
134D4×C11—84no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—84no—
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C22⋊D11—42no—
145C22⋊D11—42no—
146C2×Dic11—41no—
147D44—22no—
148D44—41no—
149C4×D11—42no—
150C4×D11—42no—
151Dic22—22no—
152Dic22—41no—
153C8×C11—21no—
154C8×C11—21no—
155C8×C11AGL(1,ℤ/8)12yes—
156C8×C11C2×#4112yes—
157C11⋊C8—42no—
158#575—111no—
159#568—221no—
160#532—21no—
161#509—114no—
162#498C2×D1111yescharacteristic, complemented
163#493C2×D1111yescharacteristic, complemented
164#486—21no—
165#469—21no—
166#469C2×D1112yes—
167#444—112no—
168#444—221no—
169#443—112no—
170#443—221no—
171#442—21no—
172#442C2×D1112yescomplemented
173#430—111no—
174C2×#104—221no—
175C4×M16C2×D1111yescharacteristic
176#365—114no—
177#364—112no—
178#361—114no—
179#360—114no—
180#349—112no—
181#347—112no—
182C22×C11—21no—
183C22×C11—41no—
184C22×C11—82no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
188C2×D11—42no—
189C2×D11—161no—
190C4×C11—22no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—82no—
194C4×C11#52511yescharacteristic
195C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
196Dic11—42no—
197C2×#41—41no—
198C2×#41—221no—
199#137—222no—
200AGL(1,ℤ/8)—222no—
201#135—112no—
202#135—221no—
203C2×D8—21no—
204C2×D8C22×D1112yes—
205#131—222no—
206#131—222no—
207#131—442no—
208C2×M16—221no—
209C2×M16—442no—
210C2×M16C22⋊D1111yescharacteristic
211C2×M16C22×D1111yescharacteristic
212C4⋊Q8—21no—
213#127—21no—
214#124—41no—
215#121—22no—
216#121—41no—
217C4×D4—22no—
218C4×D4—41no—
219C2×C42C22⋊D1111yescharacteristic
220SD32—224no—
221D16—224no—
222M32—114no—
223#108—112no—
224#108—221no—
225#106—21no—
226#106C22×D1112yes—
227#104—222no—
228#104—222no—
229#102—22no—
230#102—22no—
231#97C22⋊D1111yescharacteristic
232#97C22×D1111yescharacteristic
233C4×C8C22⋊D1111yescharacteristic
234C4×C8C22×D1111yescharacteristic
235C2×C11—21no—
236C2×C11—41no—
237C2×C11—162no—
238C2×C11#310911yescharacteristic
239D11—82no—
240#41—84no—
241#41—222no—
242#41—222no—
243#41—441no—
244#41—441no—
245C2×Q8—41no—
246C2×Q8—221no—
247C2×D4—22no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—221no—
252C2×D4—441no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—441no—
256C22×C4C2×C22⋊D1111yescharacteristic
257Q16—112no—
258Q16—221no—
259SD16—222no—
260SD16—222no—
261D8—24no—
262D8—42no—
263D8—112no—
264D8—221no—
265M16—22no—
266M16—22no—
267M16—222no—
268M16—442no—
269M16—441no—
270M16—442no—
271C2×C8—442no—
272C2×C8—441no—
273C2×C8—442no—
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C2×C22⋊D1111yescharacteristic
276C2×C8C2×C22⋊D1111yescharacteristic
277C2×C8C23×D1111yescharacteristic
278C4⋊C4—22no—
279C4⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C42—21no—
283C42C2×C22⋊D1111yescharacteristic
284C42C2×C22⋊D1111yescharacteristic
285C16—224no—
286C11#3368811yescharacteristic, complemented, Sylow
287C23—42no—
288C23—441no—
289C23#6698511yescharacteristic
290Q8—82no—
291Q8—222no—
292Q8—441no—
293D4—42no—
294D4—42no—
295D4—82no—
296D4—82no—
297D4—84no—
298D4—222no—
299D4—441no—
300D4—442no—
301D4—442no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—84no—
309C2×C4—442no—
310C2×C4—441no—
311C2×C4—442no—
312C2×C4#6698511yescharacteristic
313C2×C4C22×C22⋊D1111yescharacteristic
314C8—21no—
315C8—21no—
316C8—442no—
317C8#6700212yes—
318C8#41×D1112yes—
319C22—21no—
320C22—41no—
321C22—82no—
322C22—82no—
323C22—82no—
324C22—442no—
325C22—1761no—
326C22C2×#6698511yescharacteristic
327C4—22no—
328C4—21no—
329C4—41no—
330C4—82no—
331C4—442no—
332C4C2×#6700211yescharacteristic
333C4#1062335911yescharacteristic
334C2—21no—
335C2—41no—
336C2—162no—
337C2—882no—
338C2#1307870311yescharacteristic
subgroupG/H
centerC2#13078703
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3184C2
socleC2×C11#3109
hypercenter#3184D11
hypocenterC11#33688
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3184

Complements

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

NH ≅ G/Ntype
1. #13077527C2semidirect
2. #13070828C2semidirect
3. #13070784C2semidirect
4. #13070689C2semidirect
5. #13070561C2semidirect
6. #13070512C2semidirect
7. #13070428C2semidirect
8. C11×#3184C2semidirect
12. C11×#498C22semidirect
13. C11×#493C22semidirect
18. C11×#442C22semidirect
27. #10622201C22semidirect
30. #10622125C22semidirect
31. #10622104C22semidirect
32. #10622101C22semidirect
108. Dic44#41semidirect
110. D88#41semidirect
118. #3184D11semidirect
162. #498C2×D11semidirect
163. #493C2×D11semidirect
172. #442C2×D11semidirect
286. C11#33688semidirect

Maximal subgroups

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

subgroupindex
#130775272
#130708282
#130707842
#130706892
#130705612
#130705122
#130704282
C11×#31842
#3368811