Finite Group Databasebeta

← #14663339

Subgroups — #14663339

Order 2816.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#13066946C211yesmaximal, characteristic
2C2×#10622166C211yesmaximal, characteristic
3#13066560C212yesmaximal, complemented
4#13066550C212yesmaximal, complemented
5C11×#2503C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#400—21no—
9C11×#400—21no—
10C11×#391C411yescharacteristic
11C11×#391C2211yescharacteristic
12C11×#382C411yescharacteristic
13C11×#382C2211yescharacteristic
14C11×#381—21no—
15C11×#381—21no—
16C4×C11×C22⋊C4C411yescharacteristic
17#10622820—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622166—21no—
20#10622166—21no—
21#10622166C2212yes—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C11×C22⋊Q8—41no—
28C11×C22⋊Q8—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×#4318—41no—
42C22×C11⋊C8—41no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—41no—
55C22⋊(C11⋊C8)—41no—
56#11551—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C42×C11—22no—
91C42×C11—41no—
92#4318—82no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—42no—
95C2×C11⋊C8—82no—
96#2503D1111yescharacteristic
97#1463—111no—
98C2×#324—111no—
99#1324—112no—
100#1319—112no—
101C23×C11—22no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—41no—
105C23×C11#9911yescharacteristic
106C23×C11#9911yescharacteristic
107C23×C11C2×C22⋊C411yescharacteristic
108Q8×C11—82no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11#13112yes—
140C11⋊C8—82no—
141C11⋊C8—82no—
142C2×C22⋊Q8Dic1111yescharacteristic
143C22×C4⋊C4C2×D1111yescharacteristic
144#407—221no—
145C2×C22⋊C8—221no—
146#400—21no—
147#400—21no—
148#391Dic1111yescharacteristic
149#391C2×D1111yescharacteristic
150#382Dic1111yescharacteristic
151#382C2×D1111yescharacteristic
152#381—21no—
153#381—21no—
154C4×C22⋊C4Dic1111yescharacteristic
155#324—112no—
156#324—112no—
157#324—221no—
158#324—221no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11#35412yes—
169C22×C11#40811yescharacteristic
170C22×C11C2×#9911yescharacteristic
171C22×C11#41311yescharacteristic
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11—81no—
182C22×Q8C2×Dic1111yescharacteristic
183C23×C4C2×Dic1111yescharacteristic
184C23×C4C22⋊D1111yescharacteristic
185C23×C4C22⋊D1111yescharacteristic
186C2×M16—441no—
187C22×C8—441no—
188C22⋊Q8—41no—
189C22⋊Q8—41no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4C2×Dic1111yescharacteristic
194C2×C4⋊C4C2×Dic1111yescharacteristic
195C2×C4⋊C4C22⋊D1111yescharacteristic
196C2×C4⋊C4C22⋊D1111yescharacteristic
197C2×C4⋊C4C22×D1111yescharacteristic
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C42C2×Dic1111yescharacteristic
201C2×C42C2×Dic1111yescharacteristic
202C22⋊C8—222no—
203C22⋊C8—222no—
204C22⋊C8—441no—
205C22⋊C8—441no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11—22no—
218C2×C11—41no—
219C2×C11#146811yescharacteristic
220C2×C11C2×#35411yescharacteristic
221C2×C11#213311yescharacteristic
222C24C22⋊Dic1111yescharacteristic
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4C22⋊Dic1111yescharacteristic
241C22×C4C22⋊Dic1111yescharacteristic
242C22×C4C22⋊Dic1111yescharacteristic
243C22×C4C22×Dic1111yescharacteristic
244C22×C4C2×C22⋊D1111yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246M16—882no—
247C2×C8—442no—
248C2×C8—442no—
249C2×C8—882no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C42—22no—
260C42—41no—
261C11#1155111yescharacteristic, complemented, Sylow
262C23—21no—
263C23—21no—
264C23—22no—
265C23—41no—
266C23#6689811yescharacteristic
267C23#6689811yescharacteristic
268C23C2×C22⋊Dic1111yescharacteristic
269Q8—82no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4#6700112yes—
301C8—882no—
302C8—882no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22#1062217912yes—
313C22C2×#6689811yescharacteristic
314C22#1062284711yescharacteristic
315C22#1062285011yescharacteristic
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—81no—
323C4—81no—
324C4—81no—
325C4—81no—
326C2—21no—
327C2—21no—
328C2—22no—
329C2—41no—
330C2#1306696411yescharacteristic
331C2C2×#1062217911yescharacteristic
332C2#1307030511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2503C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2503D11
hypocenterC11#11551
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2503

Complements

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

NH ≅ G/Ntype
3. #13066560C2semidirect
4. #13066550C2semidirect
261. C11#11551semidirect

Maximal subgroups

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

subgroupindex
#130669462
C2×#106221662
#130665602
#130665502
C11×#25032
#1155111