Finite Group Databasebeta

← #14664085

Subgroups — #14664085

Order 2816.

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

normal subgroups only

This group has 452 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#13074429C211yesmaximal, characteristic
2C2×#10622168C211yesmaximal, characteristic
3#13066647C212yesmaximal, complemented
4#13066644C212yesmaximal, complemented
5C2×C11×#324C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C22×#4318—21no—
9C2×C11×C22⋊C8—21no—
10#10622825C411yescharacteristic
11#10622824—21no—
12#10622823—21no—
13#10622599C411yescharacteristic
14#10622599C2211yescharacteristic
15#10622597—21no—
16#10622597—21no—
17#10622592C411yescharacteristic
18#10622592C2211yescharacteristic
19C11×#324—21no—
20C11×#324C2212yes—
21#10622168—21no—
22#10622168C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C22×C8×C11—41no—
28C2×C11×C4⋊C4—41no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38#66977—41no—
39#66977—41no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×#4318—24no—
44C2×#4318—22no—
45C2×#4318—41no—
46C2×#4318—42no—
47C22×C11⋊C8—41no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58#11722—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—81no—
68C22×C4×C11—81no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11SD1612yes—
73C22×C4×C11Q1612yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C2×Dic22—41no—
82C2×Dic22—81no—
83C2×C8×C11—42no—
84C2×C8×C11—82no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C22⋊Dic11—41no—
90C22⋊Dic11—41no—
91C22⋊Dic11—42no—
92C4⋊Dic11—41no—
93C4⋊Dic11—81no—
94Dic11⋊C4—42no—
95Dic11⋊C4—81no—
96Dic11⋊C4—81no—
97#4318—24no—
98#4318—44no—
99#4318—42no—
100C2×C11⋊C8—44no—
101C2×C11⋊C8—42no—
102#2627—111no—
103C2×#343—111no—
104C2×#324D1111yescharacteristic
105#1354—112no—
106#1353—112no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11#9911yescharacteristic
110C23×C11#9911yescharacteristic
111C23×C11#10312yes—
112C23×C11#10412yes—
113C23×C11C2×C22⋊C411yescharacteristic
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11#10312yes—
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11C2×Q1611yescharacteristic
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148Dic22—82no—
149C8×C11—82no—
150C11⋊C8—44no—
151C22×M16—221no—
152C2×C22⋊Q8—111no—
153C22×C4⋊C4C2×D1111yescharacteristic
154C2×C22⋊C8—21no—
155#400—111no—
156#400—111no—
157#398—221no—
158#398—221no—
159#395—111no—
160#395—111no—
161#385—221no—
162#381—221no—
163#380—111no—
164#343—112no—
165#343—221no—
166#324—21no—
167#324C2×D1112yes—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11#32812yes—
177C22×C11#32812yes—
178C22×C11C2×#9911yescharacteristic
179C22×C11C2×#10311yescharacteristic
180C22×C11C2×#10411yescharacteristic
181C4×C11—22no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188Dic11—81no—
189Dic11—81no—
190Dic11—81no—
191Dic11—81no—
192C22×Q8—111no—
193C23×C4C4×D1111yescharacteristic
194C23×C4D4411yescharacteristic
195C23×C4C22⋊D1111yescharacteristic
196C2×M16—224no—
197C2×M16—222no—
198C2×M16—441no—
199C2×M16—442no—
200C22×C8—41no—
201C22×C8—441no—
202C22⋊Q8—441no—
203C22⋊Q8—441no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—41no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4C4×D1111yescharacteristic
212C2×C4⋊C4D4411yescharacteristic
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22×D1111yescharacteristic
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C22⋊C8—22no—
218C22⋊C8—41no—
219#95—111no—
220#95—111no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227C2×C11—21no—
228C2×C11—22no—
229C2×C11—22no—
230C2×C11—21no—
231C2×C11C2×#32811yescharacteristic
232C2×C11#212111yescharacteristic
233C2×C11#213311yescharacteristic
234C24(C2×D11)⋊C411yescharacteristic
235C2×Q8—441no—
236C2×Q8—881no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4#431412yes—
251C22×C4Dic4412yes—
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4C2×C4×D1111yescharacteristic
256C22×C4C2×D4411yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258M16—224no—
259M16—444no—
260M16—442no—
261C2×C8—42no—
262C2×C8—82no—
263C2×C8—442no—
264C2×C8—444no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—441no—
270C4⋊C4—442no—
271C4⋊C4—881no—
272C4⋊C4—881no—
273C4⋊C4—881no—
274C22⋊C4—441no—
275C22⋊C4—441no—
276C22⋊C4—442no—
277C11#1172211yescharacteristic, complemented, Sylow
278C23—41no—
279C23—41no—
280C23#6687011yescharacteristic
281C23#6687011yescharacteristic
282C23#6688012yes—
283C23#6688912yes—
284C23C2×(C2×D11)⋊C411yescharacteristic
285Q8—882no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—442no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4#6688012yes—
318C2×C4C2×#431411yescharacteristic
319C2×C4C2×Dic4411yescharacteristic
320C8—82no—
321C8—444no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22#1062210512yes—
331C22#1062210512yes—
332C22C2×#6687011yescharacteristic
333C22C2×#6688011yescharacteristic
334C22C2×#6688911yescharacteristic
335C4—21no—
336C4—22no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—881no—
343C4—881no—
344C4—881no—
345C4—881no—
346C2—21no—
347C2—22no—
348C2—22no—
349C2—21no—
350C2C2×#1062210511yescharacteristic
351C2#1307026011yescharacteristic
352C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC2×C11×#324C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenterC2×#324D11
hypocenterC11#11722
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #13066647C2semidirect
4. #13066644C2semidirect
277. C11#11722semidirect

Maximal subgroups

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

subgroupindex
#130744292
C2×#106221682
#130666472
#130666442
C2×C11×#3242
#1172211