Finite Group Databasebeta

← #14645331

Subgroups — #14645331

Order 2816.

774 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 167 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#13069411C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13067306C212yesmaximal, complemented
4#13067071C212yesmaximal, complemented
5C11×#3501C211yesmaximal, characteristic
6C11×#554—22no—
7C11×#554—24no—
8D4×Q8×C11—22no—
9C11×#544—21no—
10C11×#543C414yes—
11C11×#533C2212yes—
12C2×C11×C22⋊Q8—22no—
13C11×#518—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66897—21no—
16C2×C22⋊(C11⋊C8)—22no—
17#10622537C2212yes—
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20#10622185—22no—
21#10622184—22no—
22Q8⋊(C11⋊C8)—24no—
23#10622168—21no—
24C22×Q8×C11—22no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11D412yes—
27C11×C4⋊Q8—24no—
28C11×C4⋊Q8D412yes—
29C11×C4⋊Q8D412yes—
30C11×#125—24no—
31C11×#125—22no—
32C11×C22⋊Q8—24no—
33C11×C22⋊Q8—24no—
34C11×C22⋊Q8—28no—
35C11×C22⋊Q8—24no—
36C11×C22⋊Q8—22no—
37C11×C22⋊Q8—28no—
38C11×C22⋊Q8C2×C414yes—
39C4×Q8×C11—22no—
40C4×Q8×C11D414yes—
41C4×D4×C11—24no—
42C4×D4×C11—24no—
43C4×D4×C11—22no—
44C4×D4×C11—22no—
45C11×#117—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4C2×C412yes—
51C2×C42×C11C2311yescharacteristic
52C2×#4318—22no—
53C22×C11⋊C8—21no—
54C22×C11⋊C8—21no—
55#66897—42no—
56C22⋊(C11⋊C8)—44no—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—22no—
60C4×C11⋊C8—22no—
61#8355—111nomaximal, Sylow
62C24×C11C22⋊C412yes—
63C2×Q8×C11—24no—
64C2×Q8×C11—22no—
65C2×Q8×C11—82no—
66C2×Q8×C11—82no—
67C2×Q8×C11C22⋊C414yes—
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11SD1612yes—
71C2×D4×C11Q1612yes—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11C22⋊C412yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C11×C4⋊C4—24no—
83C11×C4⋊C4—28no—
84C11×C4⋊C4—24no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—24no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4C22⋊C414yes—
91C11×C22⋊C4—28no—
92C11×C22⋊C4—24no—
93C11×C22⋊C4—24no—
94C42×C11—24no—
95C42×C11C2×D412yes—
96C42×C11C2×D412yes—
97#4318—42no—
98#4318—42no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—42no—
105#3501D1111yescharacteristic
106#1954—111no—
107#1800—111no—
108#1550—112no—
109#1493—112no—
110C23×C11—22no—
111C23×C11—22no—
112C23×C11—42no—
113C23×C11—42no—
114C23×C11#10314yes—
115C23×C11C2×C22⋊C411yescharacteristic
116Q8×C11—44no—
117Q8×C11—42no—
118Q8×C11—42no—
119Q8×C11—84no—
120D4×C11—24no—
121D4×C11—24no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—82no—
132C2×C4×C11—84no—
133C2×C4×C11—84no—
134C2×C4×C11C2×C22⋊C412yes—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12012yes—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11C2×Q1611yescharacteristic
140C2×C4×C11#13712yes—
141C11⋊C8—42no—
142C11⋊C8—82no—
143C11⋊C8—81no—
144#554—22no—
145#554—24no—
146D4×Q8—22no—
147#544—21no—
148#543Dic1114yes—
149#533C2×D1112yes—
150C2×C22⋊Q8—22no—
151#518—21no—
152C2×C4×D4C2×D1111yescharacteristic
153#423—112no—
154C2×C4⋊C8—111no—
155C2×#100—221no—
156C2×C22⋊C8—222no—
157C2×C4×C8—111no—
158#343—221no—
159#333—222no—
160#332—222no—
161Q8⋊C8—224no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—24no—
165C22×C11—44no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—82no—
169C22×C11#37911yescharacteristic
170C22×C11C2×#10311yescharacteristic
171C22×C11#41911yescharacteristic
172C4×C11—21no—
173C4×C11—22no—
174C4×C11—42no—
175C4×C11—44no—
176C4×C11—44no—
177C4×C11#44812yes—
178C4×C11#45112yes—
179C4×C11#45311yescharacteristic
180C4×C11#45511yescharacteristic
181C22×Q8—22no—
182C22×D4C22⋊D1111yescharacteristic
183C23×C4C22⋊D1112yes—
184C2×M16—222no—
185C22×C8—221no—
186C22×C8—221no—
187C4⋊Q8—24no—
188C4⋊Q8C22⋊D1112yes—
189C4⋊Q8C22⋊D1112yes—
190#125—24no—
191#125—22no—
192C22⋊Q8—24no—
193C22⋊Q8—24no—
194C22⋊Q8—28no—
195C22⋊Q8—24no—
196C22⋊Q8—22no—
197C22⋊Q8—28no—
198C22⋊Q8C2×Dic1114yes—
199C4×Q8—22no—
200C4×Q8C22⋊D1114yes—
201C4×D4—24no—
202C4×D4—24no—
203C4×D4—22no—
204C4×D4—22no—
205#117—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4C22⋊D1111yescharacteristic
209C2×C22⋊C4—24no—
210C2×C22⋊C4C2×Dic1112yes—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—222no—
213C4⋊C8—222no—
214C4⋊C8—222no—
215#100—442no—
216C22⋊C8—444no—
217C4×C8—222no—
218C2×C11—21no—
219C2×C11—21no—
220C2×C11—44no—
221C2×C11#178711yescharacteristic
222C2×C11#179111yescharacteristic
223C2×C11#179211yescharacteristic
224C24C22⋊Dic1112yes—
225C2×Q8—24no—
226C2×Q8—22no—
227C2×Q8—82no—
228C2×Q8—82no—
229C2×Q8C22⋊Dic1114yes—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4#432512yes—
233C2×D4#432612yes—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4C22⋊Dic1112yes—
241C22×C4C22×Dic1111yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244M16—442no—
245M16—442no—
246C2×C8—222no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—442no—
250C2×C8—441no—
251C2×C8—442no—
252C4⋊C4—24no—
253C4⋊C4—28no—
254C4⋊C4—24no—
255C4⋊C4—22no—
256C4⋊C4—24no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4C22⋊Dic1114yes—
261C22⋊C4—28no—
262C22⋊C4—24no—
263C22⋊C4—24no—
264C42—24no—
265C42C2×C22⋊D1112yes—
266C42C2×C22⋊D1112yes—
267C11#835511yescharacteristic, complemented, Sylow
268C23—22no—
269C23—22no—
270C23—42no—
271C23—42no—
272C23#6689914yes—
273C23C2×C22⋊Dic1111yescharacteristic
274Q8—44no—
275Q8—42no—
276Q8—42no—
277Q8—84no—
278D4—24no—
279D4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4—84no—
291C2×C4—84no—
292C2×C4C2×#432511yescharacteristic
293C2×C4#6699512yes—
294C2×C4C2×#432611yescharacteristic
295C2×C4C2×C22⋊Dic1112yes—
296C2×C4#6700611yescharacteristic
297C2×C4#6700612yes—
298C2×C4#6700611yescharacteristic
299C8—442no—
300C8—882no—
301C8—881no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—44no—
306C22—42no—
307C22—42no—
308C22—82no—
309C22C2×#6689911yescharacteristic
310C22#1062283811yescharacteristic
311C22#1062286011yescharacteristic
312C4—22no—
313C4—21no—
314C4—44no—
315C4—42no—
316C4—44no—
317C4#1062284012yes—
318C4#1062284112yes—
319C4#1062285411yescharacteristic
320C4#1062285511yescharacteristic
321C2—21no—
322C2—21no—
323C2—44no—
324C2#1306855111yescharacteristic
325C2#1306856711yescharacteristic
326C2#1306857011yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3501C2
socleC22×C11#379
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#3501D11
hypocenterC11#8355
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
3. #13067306C2semidirect
4. #13067071C2semidirect
267. C11#8355semidirect

Maximal subgroups

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

subgroupindex
#130694112
#130686082
#130673062
#130670712
C11×#35012
#835511