Finite Group Databasebeta

← #14664599

Subgroups — #14664599

Order 2816.

382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068612C211yesmaximal, characteristic, complemented
2#13066960C211yesmaximal, characteristic, complemented
3#13066646C212yesmaximal, complemented
4#13066619C212yesmaximal
5C11×#2632C211yesmaximal, characteristic
6C2×C11×#124C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#399—21no—
9C11×#395C411yescharacteristic
10C11×#395C2211yescharacteristic
11C11×#394C411yescharacteristic
12C11×#394C2211yescharacteristic
13C11×#393—21no—
14C11×#388—21no—
15C11×#388—21no—
16C11×#383C411yescharacteristic
17C2×#66900—21no—
18#10622539—21no—
19#10622537—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×Q8×C11D411yescharacteristic
25C22×D4×C11C2×C411yescharacteristic
26C11×#124—41no—
27C11×#124—41no—
28C4×Q8×C11—41no—
29C4×Q8×C11—41no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2×C411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×#4318—22no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95C2×C411yescharacteristic
50C11×#95C2×C411yescharacteristic
51#66900—42no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—41no—
54C4⋊(C11⋊C8)—41no—
55C4⋊(C11⋊C8)—41no—
56#66867—41no—
57#11833—111nomaximal, Sylow
58C24×C11—21no—
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11—81no—
65C2×D4×C11—41no—
66C2×D4×C11—81no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—81no—
81C11×C4⋊C4—81no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—81no—
89C11×C22⋊C4—81no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11—21no—
95C42×C11—21no—
96#4318—42no—
97#4318—42no—
98C2×C11⋊C8—42no—
99C2×C11⋊C8—42no—
100#2632D1111yescharacteristic
101#1801—111no—
102#1467—111no—
103#1354—112no—
104#1345—112no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11C2×C22⋊C411yescharacteristic
113Q8×C11—42no—
114Q8×C11—42no—
115Q8×C11—82no—
116D4×C11—82no—
117C2×C4×C11—21no—
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—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
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—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11#9911yescharacteristic
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C11⋊C8—82no—
146C11⋊C8—82no—
147C2×#124Dic1111yescharacteristic
148C2×C4×Q8C2×D1111yescharacteristic
149#432—221no—
150#423—221no—
151C2×#101—221no—
152#399—21no—
153#395Dic1111yescharacteristic
154#395C2×D1111yescharacteristic
155#394Dic1111yescharacteristic
156#394C2×D1111yescharacteristic
157#393—21no—
158#388—21no—
159#388—21no—
160#383Dic1111yescharacteristic
161#343—112no—
162#324—112no—
163#324—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11—81no—
169C22×C11—81no—
170C22×C11—81no—
171C22×C11—81no—
172C22×C11—81no—
173C22×C11C2×#9911yescharacteristic
174C22×C11#41711yescharacteristic
175C22×C11#42111yescharacteristic
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—81no—
188C22×Q8C2×Dic1111yescharacteristic
189C22×Q8C22⋊D1111yescharacteristic
190C22×D4C2×Dic1111yescharacteristic
191C2×M16—222no—
192#124—41no—
193#124—41no—
194C4×Q8—41no—
195C4×Q8—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×Dic1111yescharacteristic
199C2×C4⋊C4C22⋊D1111yescharacteristic
200C2×C4⋊C4C22×D1111yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42C2×Dic1111yescharacteristic
208C2×C42C22⋊D1111yescharacteristic
209C2×C42C22⋊D1111yescharacteristic
210C4⋊C8—441no—
211C4⋊C8—441no—
212C4⋊C8—441no—
213#101—442no—
214C22⋊C8—222no—
215#97—441no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C2×Dic1111yescharacteristic
221#95C2×Dic1111yescharacteristic
222C2×C11—21no—
223C2×C11—21no—
224C2×C11—161no—
225C2×C11#151311yescharacteristic
226C2×C11#212211yescharacteristic
227C2×C11#213311yescharacteristic
228C24—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—81no—
235C2×D4—41no—
236C2×D4—81no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C22⋊Dic1111yescharacteristic
241C22×C4C22⋊Dic1111yescharacteristic
242C22×C4C22⋊Dic1111yescharacteristic
243C22×C4C22⋊Dic1111yescharacteristic
244C22×C4C22×Dic1111yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247M16—442no—
248M16—442no—
249C2×C8—442no—
250C2×C8—442no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—81no—
263C22⋊C4—81no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C11#1183311yescharacteristic, complemented, Sylow
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊Dic1111yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—82no—
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#6689811yescharacteristic
308C2×C4#6689811yescharacteristic
309C2×C4#6700211yescharacteristic
310C2×C4#6700411yescharacteristic
311C8—882no—
312C8—882no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C2×#6689811yescharacteristic
323C22#1062284511yescharacteristic
324C22#1062284911yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C2—21no—
338C2—21no—
339C2—161no—
340C2#1306715911yescharacteristic
341C2#1307026611yescharacteristic
342C2#1307030511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2632C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2632D11
hypocenterC11#11833
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2632

Complements

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

NH ≅ G/Ntype
1. #13068612C2semidirect
2. #13066960C2semidirect
3. #13066646C2semidirect
270. C11#11833semidirect

Maximal subgroups

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

subgroupindex
#130686122
#130669602
#130666462
#130666192
C11×#26322
#1183311