Finite Group Databasebeta

← #14664686

Subgroups — #14664686

Order 2816.

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

normal subgroups only

This group has 396 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#13068696C211yesmaximal, characteristic
2C2×#10622166C211yesmaximal, characteristic
3#13066643C212yesmaximal, complemented
4#13066622C212yesmaximal, complemented
5C11×#2484C211yesmaximal, characteristic
6C2×C11×#117C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#400C411yescharacteristic
9C11×#400C2211yescharacteristic
10C11×#398C411yescharacteristic
11C11×#398C2211yescharacteristic
12C11×#387—21no—
13C11×#387—21no—
14C11×#385—21no—
15C11×#381—21no—
16C11×#381C411yescharacteristic
17#10622820—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622168—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C11×#117—41no—
27C11×#117—41no—
28C2×C11×C4⋊C4—21no—
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⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×#4318—22no—
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×#95C2×C411yescharacteristic
51C11×#95C2×C411yescharacteristic
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—41no—
54C22⋊(C11⋊C8)—41no—
55C22⋊(C11⋊C8)—41no—
56#11850—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—42no—
86C11×C22⋊C4—42no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—42no—
90#4318—42no—
91#4318—42no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—82no—
95#2484D1111yescharacteristic
96#1821—111no—
97C2×#324—111no—
98#1353—112no—
99#1346—112no—
100C23×C11—22no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11#9911yescharacteristic
105C23×C11#9911yescharacteristic
106C23×C11C2×C22⋊C411yescharacteristic
107C2×C4×C11—21no—
108C2×C4×C11—21no—
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—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
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—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—81no—
137C2×C4×C11#13512yes—
138C11⋊C8—82no—
139C11⋊C8—82no—
140C2×#117Dic1111yescharacteristic
141C22×C4⋊C4C2×D1111yescharacteristic
142#407—221no—
143C2×C22⋊C8—221no—
144#400Dic1111yescharacteristic
145#400C2×D1111yescharacteristic
146#398Dic1111yescharacteristic
147#398C2×D1111yescharacteristic
148#387—21no—
149#387—21no—
150#385—21no—
151#381—21no—
152#381Dic1111yescharacteristic
153#343—112no—
154#343—221no—
155#324—112no—
156#324—221no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—42no—
165C22×C11—42no—
166C22×C11#35212yes—
167C22×C11C2×#9911yescharacteristic
168C22×C11#41611yescharacteristic
169C22×C11#42111yescharacteristic
170C4×C11—22no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—81no—
177C4×C11—81no—
178C4×C11—81no—
179C4×C11—81no—
180C23×C4C2×Dic1111yescharacteristic
181C23×C4C22⋊D1111yescharacteristic
182C23×C4C22⋊D1111yescharacteristic
183C2×M16—222no—
184C22×C8—441no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4C2×Dic1111yescharacteristic
192C2×C4⋊C4C2×Dic1111yescharacteristic
193C2×C4⋊C4C2×Dic1111yescharacteristic
194C2×C4⋊C4C22⋊D1111yescharacteristic
195C2×C4⋊C4C22⋊D1111yescharacteristic
196C2×C4⋊C4C22×D1111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C42—21no—
200C22⋊C8—222no—
201C22⋊C8—441no—
202C22⋊C8—441no—
203C22⋊C8—441no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95C2×Dic1111yescharacteristic
212#95C2×Dic1111yescharacteristic
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—22no—
216C2×C11—41no—
217C2×C11#151611yescharacteristic
218C2×C11C2×#35211yescharacteristic
219C2×C11#213311yescharacteristic
220C24C22⋊Dic1111yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C22⋊Dic1111yescharacteristic
236C22×C4C22⋊Dic1111yescharacteristic
237C22×C4C22⋊Dic1111yescharacteristic
238C22×C4C22×Dic1111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—442no—
242M16—442no—
243C2×C8—442no—
244C2×C8—442no—
245C2×C8—882no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C42—42no—
258C11#1185011yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—22no—
262C23—41no—
263C23#6689811yescharacteristic
264C23#6689811yescharacteristic
265C23C2×C22⋊Dic1111yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4#6700312yes—
297C8—882no—
298C8—882no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22#1062217712yes—
309C22C2×#6689811yescharacteristic
310C22#1062284611yescharacteristic
311C22#1062284911yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2#1306717211yescharacteristic
327C2C2×#1062217711yescharacteristic
328C2#1307030511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2484C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2484D11
hypocenterC11#11850
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
3. #13066643C2semidirect
4. #13066622C2semidirect
258. C11#11850semidirect

Maximal subgroups

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

subgroupindex
#130686962
C2×#106221662
#130666432
#130666222
C11×#24842
#1185011