Finite Group Databasebeta

← #14664810

Subgroups — #14664810

Order 2816.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068604C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic
3#13066616C214yesmaximal, complemented
4C11×#2547C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×#124—21no—
7C2×C4×D4×C11C2211yescharacteristic
8C11×#397C412yescomplemented
9C11×#397C2212yes—
10C11×#391—21no—
11C11×#380—21no—
12C11×#380—21no—
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898—21no—
15#10622825—21no—
16C2×C22⋊(C11⋊C8)—21no—
17#10622166—21no—
18#10622164C2212yes—
19#10622163C2212yes—
20C22×Q8×C11—21no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C11×#124—42no—
27C11×#124—42no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C22⋊Dic11—22no—
41C2×C4⋊Dic11—41no—
42C22×C11⋊C8—41no—
43C11×#95—22no—
44C11×#95—22no—
45C11×#95C2×C412yes—
46#66898—42no—
47C11⋊#95—41no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—41no—
50#11878—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11D812yes—
59C2×D4×C11SD1612yes—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—42no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—44no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—42no—
87C22⋊Dic11—42no—
88C22⋊Dic11—42no—
89C4⋊Dic11—82no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—82no—
92#2547D1111yescharacteristic
93#1799—111no—
94#1459—111no—
95#1344—114no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11#10212yes—
105C23×C11C2×C22⋊C411yescharacteristic
106C23×C11C2×D811yescharacteristic
107C23×C11C2×SD1611yescharacteristic
108Q8×C11—84no—
109D4×C11—42no—
110D4×C11—42no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11#10212yes—
133C2×Dic11—82no—
134C2×Dic11—82no—
135C2×Dic11—82no—
136C11⋊C8—82no—
137C2×C4⋊Q8Dic1111yescharacteristic, complemented
138C2×#124—21no—
139C2×C4×D4C2×D1111yescharacteristic
140C2×#99—221no—
141C2×C22⋊C8—221no—
142#397Dic1112yescomplemented
143#397C2×D1112yes—
144#391—21no—
145#380—21no—
146#380—21no—
147#380—221no—
148C4×C4⋊C4Dic1111yescharacteristic, complemented
149#342—112no—
150#324—221no—
151#323—112no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—22no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—42no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—81no—
165C22×C11—81no—
166C22×C11C2×#9911yescharacteristic
167C22×C11C2×#10211yescharacteristic
168C22×C11#42111yescharacteristic
169C4×C11—21no—
170C4×C11—22no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—82no—
175C4×C11—82no—
176C4×C11#35412yes—
177Dic11—162no—
178C22×Q8—21no—
179C22×D4C22⋊D1111yescharacteristic
180C23×C4C22⋊D1111yescharacteristic
181C23×C4C22⋊D1111yescharacteristic
182C22×C8—441no—
183C4⋊Q8—41no—
184C4⋊Q8—41no—
185#124—42no—
186#124—42no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—441no—
192C2×C4⋊C4C2×Dic1112yes—
193C2×C4⋊C4C22⋊D1111yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4C2×Dic1111yescharacteristic
198C2×C22⋊C4C22×D1111yescharacteristic
199C2×C42—21no—
200C2×C42C2×Dic1111yescharacteristic
201#99—442no—
202C22⋊C8—222no—
203C22⋊C8—441no—
204#95—22no—
205#95—22no—
206#95—441no—
207#95C2×Dic1112yes—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—41no—
211C2×C11—42no—
212C2×C11—41no—
213C2×C11#151911yescharacteristic
214C2×C11#212311yescharacteristic
215C2×C11C2×#35411yescharacteristic
216C24C22⋊Dic1111yescharacteristic
217C24C2×C22⋊D1111yescharacteristic
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4#432312yes—
224C2×D4#432412yes—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—442no—
234C22×C4C22⋊Dic1111yescharacteristic
235C22×C4C22⋊Dic1111yescharacteristic
236C22×C4C22⋊Dic1111yescharacteristic
237C22×C4C22×Dic1111yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239C2×C8—442no—
240C2×C8—882no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—882no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—442no—
253C22⋊C4—442no—
254C42—21no—
255C42—21no—
256C42—42no—
257C11#1187811yescharacteristic, complemented, Sylow
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23#6689612yes—
267C23C2×#432311yescharacteristic
268C23C2×#432411yescharacteristic
269C23C2×C22⋊Dic1111yescharacteristic
270Q8—84no—
271D4—42no—
272D4—42no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—882no—
293C2×C4—882no—
294C2×C4—882no—
295C2×C4#6689612yes—
296C2×C4#6689811yescharacteristic
297C2×C4#6689811yescharacteristic
298C8—882no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—22no—
303C22—21no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—81no—
312C22—81no—
313C22C2×#6689611yescharacteristic
314C22C2×#6689811yescharacteristic
315C22#1062284911yescharacteristic
316C4—22no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—82no—
322C4—82no—
323C4—1762no—
324C4#1062217912yes—
325C2—21no—
326C2—21no—
327C2—41no—
328C2—42no—
329C2—41no—
330C2#1306718411yescharacteristic
331C2#1307027011yescharacteristic
332C2C2×#1062217911yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2547C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2547D11
hypocenterC11#11878
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
3. #13066616C2semidirect
5. C2×C11×C4⋊Q8C4semidirect
8. C11×#397C4semidirect
13. C4×C11×C4⋊C4C4semidirect
137. C2×C4⋊Q8Dic11semidirect
142. #397Dic11semidirect
148. C4×C4⋊C4Dic11semidirect
257. C11#11878semidirect

Maximal subgroups

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

subgroupindex
#130686042
#130669342
#130666162
C11×#25472
#1187811