Finite Group Databasebeta

← #14667016

Subgroups — #14667016

Order 2816.

318 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 63 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#13070811C211yesmaximal, characteristic, complemented
2#13070799C211yesmaximal, characteristic, complemented
3#13070056C211yesmaximal, characteristic, complemented
4#13066634C211yesmaximal, characteristic, complemented
5#13066631C211yesmaximal, characteristic, complemented
6#13066542C211yesmaximal, characteristic, complemented
7C11×#3203C211yesmaximal, characteristic
8C11×#537—21no—
9C11×#484—21no—
10C11×#480—21no—
11C11×#468—21no—
12C11×#467C2211yescharacteristic
13C11×#466C2211yescharacteristic
14C11×#452—21no—
15C11×#449—21no—
16C11×#408C2211yescharacteristic
17#10622845—21no—
18C2×#66882C2211yescharacteristic
19#10622202—21no—
20#10622200—21no—
21#10622192—21no—
22#10622190C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24C22⋊(C11⋊C16)C2211yescharacteristic
25#10622128—21no—
26#10622128—21no—
27C2×C11×#41—21no—
28C2×C11×#41D411yescharacteristic
29C2×C11×Q16D411yescharacteristic
30C2×C11×SD16—21no—
31C2×C11×D8D411yescharacteristic
32C2×C11×M16D411yescharacteristic
33C22×C8×C11C2311yescharacteristic
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—41no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—41no—
40C11×#121—41no—
41C11×#121—41no—
42C2×C11×C4⋊C4—21no—
43C2×C4⋊Dic11—21no—
44C2×#4318—21no—
45C11×#107—21no—
46C11×#107D411yescharacteristic
47C11×#107D411yescharacteristic
48C11×#103—21no—
49C11×#103—21no—
50C11×#102—21no—
51C11×#102—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54#66899—41no—
55#66896—41no—
56#66882—21no—
57#66882—21no—
58C2×C11⋊C16—21no—
59C2×C11⋊C16—21no—
60#12285—111nomaximal, Sylow
61C11×#41—41no—
62C11×#41—41no—
63C11×#41—81no—
64C11×#41—81no—
65C2×Q8×C11—21no—
66C2×Q8×C11D811yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11D811yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—41no—
78C11×Q16—41no—
79C11×SD16—81no—
80C11×D8—41no—
81C11×M16—41no—
82C2×C8×C11—21no—
83C2×C8×C11—41no—
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11C2×D411yescharacteristic
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97#4318—41no—
98#4318—41no—
99C2×C11⋊C8—41no—
100C11⋊C16—41no—
101C11⋊C16—41no—
102#3203D1111yescharacteristic
103#2235—111no—
104#2233—111no—
105#2078—111no—
106#1350—111no—
107#1349—111no—
108#1315—111no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11AGL(1,ℤ/8)11yescharacteristic
112Q8×C11—41no—
113Q8×C11—41no—
114Q8×C11—41no—
115D4×C11—41no—
116D4×C11—41no—
117D4×C11—41no—
118D4×C11—81no—
119D4×C11—82no—
120D4×C11—161no—
121D4×C11—161no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—82no—
131C2×C4×C11—161no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11C2×D811yescharacteristic
134C2×Dic11—81no—
135C2×Dic11—161no—
136C8×C11—21no—
137C8×C11—21no—
138C8×C11—41no—
139C11⋊C8—81no—
140#537—21no—
141#484—21no—
142#480—21no—
143#468—21no—
144#467C2×D1111yescharacteristic
145#466C2×D1111yescharacteristic
146#452—21no—
147#449—21no—
148C2×#107—111no—
149#417—221no—
150#408C2×D1111yescharacteristic
151#367—221no—
152#367—221no—
153#358—221no—
154#357—221no—
155C22⋊C16—111no—
156C22⋊C16—111no—
157#343—221no—
158#341—111no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11#44711yescharacteristic
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—81no—
172C4×C11—81no—
173C4×C11—81no—
174C4×C11#45511yescharacteristic
175C4×C11#45811yescharacteristic
176Dic11—161no—
177C2×#41—21no—
178C2×#41C22⋊D1111yescharacteristic
179C2×Q16C22⋊D1111yescharacteristic
180C2×SD16—21no—
181C2×D8C22⋊D1111yescharacteristic
182C2×M16—221no—
183C2×M16C22⋊D1111yescharacteristic
184C22×C8C22×D1111yescharacteristic
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187C22⋊Q8—41no—
188#121—21no—
189#121—21no—
190#121—41no—
191#121—41no—
192#121—41no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—221no—
195C2×C16—221no—
196C2×C16—221no—
197#107—21no—
198#107—221no—
199#107—221no—
200#107C22⋊D1111yescharacteristic
201#107C22⋊D1111yescharacteristic
202#103—21no—
203#103—21no—
204#103—441no—
205#102—21no—
206#102—21no—
207#102—441no—
208C22⋊C8—21no—
209C22⋊C8—21no—
210C2×C11—41no—
211C2×C11—81no—
212C2×C11—161no—
213C2×C11#160711yescharacteristic
214C2×C11#219311yescharacteristic
215C2×C11#219411yescharacteristic
216#41—41no—
217#41—41no—
218#41—81no—
219#41—81no—
220C2×Q8—21no—
221C2×Q8#432311yescharacteristic
222C2×D4—21no—
223C2×D4—21no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4—41no—
227C2×D4#432311yescharacteristic
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—441no—
232C22×C4C2×C22⋊D1111yescharacteristic
233Q16—41no—
234SD16—81no—
235D8—41no—
236M16—41no—
237M16—441no—
238M16—441no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—441no—
242C2×C8C2×C22⋊D1111yescharacteristic
243C2×C8C2×C22⋊D1111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C16—441no—
256C16—441no—
257C11#1228511yescharacteristic, complemented, Sylow
258C23—21no—
259C23—41no—
260C23#6698511yescharacteristic
261Q8—41no—
262Q8—41no—
263Q8—41no—
264D4—41no—
265D4—41no—
266D4—41no—
267D4—81no—
268D4—82no—
269D4—161no—
270D4—161no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—82no—
280C2×C4—161no—
281C2×C4—881no—
282C2×C4—1761no—
283C2×C4C2×#432311yescharacteristic
284C2×C4#6700611yescharacteristic
285C8—21no—
286C8—21no—
287C8—41no—
288C8—881no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22#1062283011yescharacteristic
299C4—21no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C4—1761no—
305C4#1062285511yescharacteristic
306C4#1062285611yescharacteristic
307C2—41no—
308C2—81no—
309C2—161no—
310C2#1306760211yescharacteristic
311C2#1307058011yescharacteristic
312C2#1307058711yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
Fitting, prime radicalC11×#3203C2
socleC22×C11#447
hypercenter#3203D11
hypocenterC11#12285
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408 ◁ #3203

Complements

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

NH ≅ G/Ntype
1. #13070811C2semidirect
2. #13070799C2semidirect
3. #13070056C2semidirect
4. #13066634C2semidirect
5. #13066631C2semidirect
6. #13066542C2semidirect
257. C11#12285semidirect

Maximal subgroups

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

subgroupindex
#130708112
#130707992
#130700562
#130666342
#130666312
#130665422
C11×#32032
#1228511