Finite Group Databasebeta

← #14667009

Subgroups — #14667009

Order 2816.

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

normal subgroups only

This group has 338 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#13070799C211yesmaximal, characteristic, complemented
2#13070794C211yesmaximal, characteristic, complemented
3#13070056C211yesmaximal, characteristic, complemented
4#13066631C211yesmaximal, characteristic, complemented
5#13066631C211yesmaximal, characteristic, complemented
6#13066542C211yesmaximal, characteristic, complemented
7C11×#3199C211yesmaximal, characteristic
8C11×#535—21no—
9C11×#482—21no—
10C11×#482—21no—
11C11×#469—21no—
12C11×#466C2211yescharacteristic
13C11×#466C2211yescharacteristic
14C11×#447—21no—
15C11×#447—21no—
16C11×#408C2211yescharacteristic
17#10622845—21no—
18C2×#66882C2211yescharacteristic, complemented
19#10622200—21no—
20#10622200—21no—
21#10622192—21no—
22#10622190C2211yescharacteristic, complemented
23C22⋊(C11⋊C16)C2211yescharacteristic, complemented
24C22⋊(C11⋊C16)C2211yescharacteristic, complemented
25#10622128—21no—
26#10622127—21no—
27C2×C11×#41D411yescharacteristic
28C22×D4×C11—21no—
29C2×C11×D8—21no—
30C2×C11×D8D411yescharacteristic
31C2×C11×D8D411yescharacteristic
32C2×C11×M16D411yescharacteristic
33C22×C8×C11C2311yescharacteristic
34C11×#127—41no—
35C11×#124—41no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#120—41no—
41C11×#120—41no—
42C11×#117—21no—
43C2×C4⋊Dic11—21no—
44C2×#4318—21no—
45C11×#107D411yescharacteristic
46C11×#107D411yescharacteristic
47C11×#106—21no—
48C11×#102—21no—
49C11×#102—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#12284—111nomaximal, Sylow
61C24×C11—41no—
62C11×#41—41no—
63C11×#41—41no—
64C2×Q8×C11D811yescharacteristic
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—81no—
74C2×D4×C11—81no—
75C2×D4×C11D811yescharacteristic
76C22×C4×C11—21no—
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—41no—
79C11×D8—41no—
80C11×D8—41no—
81C11×D8—81no—
82C11×M16—41no—
83C2×C8×C11—21no—
84C2×C8×C11—41no—
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97#4318—41no—
98#4318—41no—
99C2×C11⋊C8—41no—
100C11⋊C16—41no—
101C11⋊C16—41no—
102#3199D1111yescharacteristic
103#2233—111no—
104#2232—111no—
105#2078—111no—
106#1349—111no—
107#1349—111no—
108#1315—111no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—82no—
113C23×C11—161no—
114C23×C11—161no—
115C23×C11AGL(1,ℤ/8)11yescharacteristic
116Q8×C11—41no—
117D4×C11—41no—
118D4×C11—41no—
119D4×C11—41no—
120D4×C11—41no—
121D4×C11—41no—
122D4×C11—81no—
123D4×C11—82no—
124D4×C11—161no—
125D4×C11—161no—
126D4×C11—161no—
127D4×C11—161no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×Dic11—81no—
138C2×Dic11—161no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11—41no—
142C11⋊C8—81no—
143#535—21no—
144#482—21no—
145#482—21no—
146#469—21no—
147#466C2×D1111yescharacteristic
148#466C2×D1111yescharacteristic
149#447—21no—
150#447—21no—
151C2×#107—111no—
152#417—221no—
153#408C2×D1111yescharacteristic
154#367—221no—
155#366—221no—
156#357—221no—
157#357—221no—
158C22⋊C16—111no—
159C22⋊C16—111no—
160#343—221no—
161#341—111no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—81no—
169C22×C11—81no—
170C22×C11—81no—
171C22×C11—81no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11—164no—
175C22×C11#44711yescharacteristic
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11#45511yescharacteristic
181C4×C11#45811yescharacteristic
182Dic11—161no—
183C2×#41C22⋊D1111yescharacteristic
184C22×D4—21no—
185C2×D8—21no—
186C2×D8C22⋊D1111yescharacteristic
187C2×D8C22⋊D1111yescharacteristic
188C2×M16—221no—
189C2×M16C22⋊D1111yescharacteristic
190C22×C8C22×D1111yescharacteristic
191#127—41no—
192#124—41no—
193#121—21no—
194#121—21no—
195#121—21no—
196#121—21no—
197#120—41no—
198#120—41no—
199#117—21no—
200C2×C4⋊C4—221no—
201C2×C16—221no—
202C2×C16—221no—
203#107—221no—
204#107—221no—
205#107C22⋊D1111yescharacteristic
206#107C22⋊D1111yescharacteristic
207#106—21no—
208#103—441no—
209#102—21no—
210#102—21no—
211#102—21no—
212#102—21no—
213#102—441no—
214C22⋊C8—21no—
215C22⋊C8—21no—
216C2×C11—41no—
217C2×C11—81no—
218C2×C11—161no—
219C2×C11—161no—
220C2×C11#160711yescharacteristic
221C2×C11#219211yescharacteristic
222C2×C11#219411yescharacteristic
223C24—41no—
224#41—41no—
225#41—41no—
226C2×Q8#432311yescharacteristic
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4—81no—
236C2×D4—81no—
237C2×D4#432311yescharacteristic
238C22×C4—21no—
239C22×C4—441no—
240C22×C4C2×C22⋊D1111yescharacteristic
241D8—41no—
242D8—41no—
243D8—81no—
244M16—41no—
245M16—441no—
246M16—441no—
247C2×C8—21no—
248C2×C8—41no—
249C2×C8—441no—
250C2×C8C2×C22⋊D1111yescharacteristic
251C2×C8C2×C22⋊D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C42—41no—
262C16—441no—
263C16—441no—
264C11#1228411yescharacteristic, complemented, Sylow
265C23—21no—
266C23—41no—
267C23—41no—
268C23—82no—
269C23—161no—
270C23—161no—
271C23#6698511yescharacteristic
272Q8—41no—
273D4—41no—
274D4—41no—
275D4—41no—
276D4—41no—
277D4—41no—
278D4—81no—
279D4—82no—
280D4—161no—
281D4—161no—
282D4—161no—
283D4—161no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—881no—
292C2×C4—1761no—
293C2×C4C2×#432311yescharacteristic
294C2×C4#6700611yescharacteristic
295C8—21no—
296C8—21no—
297C8—41no—
298C8—881no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—164no—
312C22#1062283011yescharacteristic
313C4—21no—
314C4—41no—
315C4—81no—
316C4—81no—
317C4—1761no—
318C4#1062285511yescharacteristic
319C4#1062285611yescharacteristic
320C2—41no—
321C2—81no—
322C2—161no—
323C2—161no—
324C2#1306760211yescharacteristic
325C2#1307057311yescharacteristic
326C2#1307058711yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
Fitting, prime radicalC11×#3199C2
socleC22×C11#447
hypercenter#3199D11
hypocenterC11#12284
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408 ◁ #3199

Complements

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

NH ≅ G/Ntype
1. #13070799C2semidirect
2. #13070794C2semidirect
3. #13070056C2semidirect
4. #13066631C2semidirect
5. #13066631C2semidirect
6. #13066542C2semidirect
18. C2×#66882C22semidirect
22. #10622190C22semidirect
23. C22⋊(C11⋊C16)C22semidirect
24. C22⋊(C11⋊C16)C22semidirect
264. C11#12284semidirect

Maximal subgroups

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

subgroupindex
#130707992
#130707942
#130700562
#130666312
#130665422
C11×#31992
#1228411