Finite Group Databasebeta

← #14664729

Subgroups — #14664729

Order 2816.

336 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079181C211yesmaximal, characteristic
2#13070416C211yesmaximal, characteristic, complemented
3#13068742C211yesmaximal, characteristic, complemented
4#13066629C211yesmaximal, characteristic, complemented
5#13066627C211yesmaximal, characteristic, complemented
6#13066625C211yesmaximal, characteristic
7C11×#1347C211yesmaximal, characteristic
8#10623131—21no—
9C11×#466C2211yescharacteristic
10#10622768C411yescharacteristic, complemented
11D8×Dic11C411yescharacteristic, complemented
12#10622729C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14#10622654—21no—
15#10622589—21no—
16#10622491C411yescharacteristic, complemented
17#10622486C411yescharacteristic, complemented
18#10622381—21no—
19#10622371—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#340C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25#10622140—21no—
26Dic11⋊C16—21no—
27C2×C11×D8C2×C411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×#121—21no—
30C2×C11×C4⋊C4—21no—
31#66989—21no—
32#66988—41no—
33D4×Dic11—21no—
34D4×Dic11—41no—
35C2×#4324—21no—
36C2×C4⋊Dic11—21no—
37#66977—21no—
38C2×Dic11⋊C4—41no—
39C2×Dic11⋊C4—41no—
40C2×C4×Dic11D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42C2×Dic44C2×C411yescharacteristic
43#66943—21no—
44#66940—21no—
45#66932—41no—
46#66930—41no—
47C2×C11×C16—21no—
48C11×#107C2×C411yescharacteristic
49C11×#102—21no—
50#66896—21no—
51#66882C2×C411yescharacteristic
52#66880—21no—
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66874—21no—
59#66872—21no—
60#11860—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11D811yescharacteristic
68C22×Dic11D811yescharacteristic
69C2×Dic22—21no—
70C11×D8—41no—
71C2×C8×C11—41no—
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80C22⋊Dic11—41no—
81C22⋊Dic11—41no—
82#4324—42no—
83C4⋊Dic11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—82no—
91Dic11⋊C4—82no—
92C4×Dic11—41no—
93C4×Dic11C22⋊C411yescharacteristic
94C4×Dic11C22⋊C411yescharacteristic
95C4×Dic11SD1611yescharacteristic
96C4×Dic11SD1611yescharacteristic
97C2×C11⋊C8—41no—
98C2×C11⋊C8C22⋊C411yescharacteristic
99C2×C11⋊C8C22⋊C411yescharacteristic
100Dic44—41no—
101C11×C16—41no—
102C11⋊C16—41no—
103#3168—111no—
104#2163—111no—
105#1834—111no—
106#1348—111no—
107#1348—111no—
108#1347—111no—
109#1347D1111yescharacteristic
110C23×C11—41no—
111C23×C11C2×D811yescharacteristic
112D4×C11—41no—
113D4×C11—41no—
114D4×C11—81no—
115D4×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C2×SD1611yescharacteristic
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—82no—
130C2×Dic11—81no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C2×Dic11#10211yescharacteristic
134C2×Dic11#10211yescharacteristic
135C2×Dic11#10211yescharacteristic
136C2×Dic11#10211yescharacteristic
137Dic22—41no—
138Dic22—41no—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#529—221no—
144#499—111no—
145#495—111no—
146#488—221no—
147#467—111no—
148#466C2×D1111yescharacteristic
149#465—221no—
150C4×Q16—111no—
151C4×SD16—221no—
152C4×D8—111no—
153C2×C4×C8—111no—
154#384—221no—
155C4⋊C16—221no—
156C22⋊C16—111no—
157C22⋊C16C2×D1111yescharacteristic
158#346—221no—
159#340—111no—
160#340—221no—
161#340C2×D1111yescharacteristic
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—81no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11C2×#10211yescharacteristic
168C22×C11#50911yescharacteristic
169C22×C11#51011yescharacteristic
170C4×C11—21no—
171C4×C11—81no—
172C4×C11—161no—
173C4×C11#41011yescharacteristic
174C4×C11#42111yescharacteristic
175Dic11—21no—
176Dic11—21no—
177Dic11—21no—
178Dic11—81no—
179Dic11—81no—
180Dic11—161no—
181Dic11#36012yes—
182C2×Q16—111no—
183C2×SD16—221no—
184C2×D8C4×D1111yescharacteristic
185C22×C8—111no—
186C22×C8C22×D1111yescharacteristic
187#126—441no—
188#125—221no—
189#124—221no—
190#123—441no—
191C22⋊Q8—221no—
192#121—21no—
193C4×Q8—221no—
194C4×D4—221no—
195C4×D4—441no—
196#117—441no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—441no—
200C2×C4⋊C4—441no—
201C2×C42—111no—
202C2×C16—21no—
203C2×C16—221no—
204#107—111no—
205#107C4×D1111yescharacteristic
206#106—221no—
207#103—221no—
208#103—221no—
209#102—21no—
210#102—221no—
211C4×C8—111no—
212C4×C8—111no—
213C4×C8—111no—
214C4×C8—111no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11—161no—
218C2×C11#151711yescharacteristic
219C2×C11#213911yescharacteristic
220C2×C11C2×#36011yescharacteristic
221C2×Q8—221no—
222C2×D4—21no—
223C2×D4—41no—
224C22×C4—41no—
225C22×C4—111no—
226C22×C4—111no—
227C22×C4—441no—
228C22×C4—441no—
229C22×C4D4×D1111yescharacteristic
230Q16—441no—
231SD16—442no—
232D8—41no—
233C2×C8—41no—
234C2×C8—111no—
235C2×C8—111no—
236C2×C8—441no—
237C2×C8C2×C4×D1111yescharacteristic
238C2×C8D4×D1111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—221no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—882no—
250C4⋊C4—882no—
251C22⋊C4—41no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C22⋊C4—441no—
256C42—111no—
257C42—111no—
258C42—111no—
259C42—111no—
260C42—441no—
261C16—41no—
262C16—441no—
263C11#1186011yescharacteristic, complemented, Sylow
264C23—41no—
265C23D8×D1111yescharacteristic
266Q8—441no—
267Q8—441no—
268D4—41no—
269D4—41no—
270D4—81no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—111no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—222no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—882no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4C22⋊C4×D1111yescharacteristic
292C2×C4SD16×D1111yescharacteristic
293C8—21no—
294C8—21no—
295C8—221no—
296C8—221no—
297C22—21no—
298C22—21no—
299C22—81no—
300C22—81no—
301C22—81no—
302C22D11×#10211yescharacteristic
303C22#1062252411yescharacteristic
304C22#1062252811yescharacteristic
305C4—21no—
306C4—81no—
307C4—112no—
308C4—161no—
309C4—221no—
310C4—221no—
311C4—221no—
312C4—881no—
313C4—881no—
314C4—1761no—
315C4#1062235311yescharacteristic
316C4#1062243411yescharacteristic
317C2—21no—
318C2—21no—
319C2—161no—
320C2#1306717411yescharacteristic
321C2#1307032511yescharacteristic
322C2D11×#36011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1347C2
socleC22×C11C2×#102
prime radicalC11×#466C22
cosocleC22×C8×C11C23
hypercenter#1347D11
hypocenterC11#11860
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. #13070416C2semidirect
3. #13068742C2semidirect
4. #13066629C2semidirect
5. #13066627C2semidirect
10. #10622768C4semidirect
11. D8×Dic11C4semidirect
16. #10622491C4semidirect
17. #10622486C4semidirect
263. C11#11860semidirect

Maximal subgroups

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

subgroupindex
#130791812
#130704162
#130687422
#130666292
#130666272
#130666252
C11×#13472
#1186011