Finite Group Databasebeta

← #14666994

Subgroups — #14666994

Order 2816.

344 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 63 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#13079387C211yesmaximal, characteristic
2#13070818C211yesmaximal, characteristic, complemented
3#13070045C211yesmaximal, characteristic
4#13066629C211yesmaximal, characteristic, complemented
5#13066628C211yesmaximal, characteristic, complemented
6#13066539C211yesmaximal, characteristic
7C11×#2236C211yesmaximal, characteristic, complemented
8D11×C22⋊Q8—21no—
9C11×#467C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11#10622799—21no—
12#10622729C2211yescharacteristic
13C2×(C2×D11)⋊C8C2211yescharacteristic
14#10622664—21no—
15#10622600—21no—
16#10622497—21no—
17#10622422—21no—
18#10622421—21no—
19C11×#366—21no—
20C11×#358—21no—
21C11×C22⋊C16C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25#10622130—21no—
26#10622127—21no—
27C2×Q8×D11—21no—
28C22×C4×D11D411yescharacteristic
29C2×C11×Q16D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C11×C22⋊Q8—21no—
32C2×C11×C4⋊C4—21no—
33#66999—21no—
34C2×#4326—21no—
35C2×(C2×D11)⋊C4—41no—
36C2×C4⋊Dic11—21no—
37#66977—21no—
38C22×C11⋊C8D411yescharacteristic
39C2×Dic44D411yescharacteristic
40#66950—21no—
41#66949—41no—
42C4⋊C4×D11—21no—
43C4⋊C4×D11—41no—
44C22⋊C4×D11—41no—
45#66931—41no—
46C2×C11×C16—21no—
47C11×#107—21no—
48C11×#107—21no—
49C11×#107D411yescharacteristic
50C11×#103—21no—
51#66899—21no—
52C11⋊#95—41no—
53(C2×D11)⋊C8—21no—
54(C2×D11)⋊C8—21no—
55#66882D411yescharacteristic
56#66880—21no—
57C2×C11⋊C16—21no—
58#66874—21no—
59#66871—21no—
60#12282—111nomaximal, Sylow
61C23×D11D811yescharacteristic
62C2×Q8×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—41no—
66C22×Dic11D811yescharacteristic
67Q8×D11—81no—
68Q8×D11—81no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—41no—
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×Dic22—21no—
76C2×Dic22—41no—
77C11×Q16—41no—
78C2×C8×C11—41no—
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C22⋊Dic11—41no—
87#4326—81no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—82no—
91C4⋊Dic11—21no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—41no—
100Dic44—41no—
101C11×C16—41no—
102C11⋊C16—41no—
103#3189—111no—
104#2236—111no—
105#2236D1111yescharacteristic, complemented
106#2076—111no—
107#1348—111no—
108#1348—111no—
109#1314—111no—
110C23×C11C2×D811yescharacteristic
111C22×D11—21no—
112C22×D11—21no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11Q3212yes—
116Q8×C11—41no—
117Q8×C11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×Dic11—21no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C4×D11—41no—
135C4×D11—41no—
136C4×D11—81no—
137C4×D11—82no—
138C4×D11—82no—
139Dic22—41no—
140Dic22—41no—
141Dic22—82no—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—41no—
145C2×C22⋊Q8—221no—
146#484—221no—
147#484—221no—
148#467—111no—
149#467—221no—
150#467C2×D1111yescharacteristic
151#451—221no—
152#451—221no—
153C2×#107C2×D1111yescharacteristic
154C2×C22⋊C8—111no—
155#380—221no—
156#366—21no—
157#366—221no—
158#358—21no—
159#358—221no—
160C22⋊C16—111no—
161C22⋊C16C2×D1111yescharacteristic
162#340—111no—
163#340—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#44711yescharacteristic
167C22×C11C2×Q3211yescharacteristic
168C22×C11#51011yescharacteristic
169C2×D11—22no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—42no—
173C2×D11—81no—
174C4×C11—21no—
175C4×C11—81no—
176C4×C11—81no—
177C4×C11—161no—
178C4×C11#45511yescharacteristic
179C4×C11#45811yescharacteristic
180Dic11—41no—
181Dic11—81no—
182Dic11—81no—
183Dic11—161no—
184C22×Q8—221no—
185C23×C4—111no—
186C2×Q16—111no—
187C2×Q16—221no—
188C2×Q16C22⋊D1111yescharacteristic
189C22×C8—111no—
190C22×C8C22×D1111yescharacteristic
191C22⋊Q8—21no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194C22⋊Q8—221no—
195C22⋊Q8—441no—
196C22⋊Q8—441no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—441no—
201C2×C22⋊C4—441no—
202C2×C22⋊C4—441no—
203C2×C16—21no—
204C2×C16—221no—
205#107—21no—
206#107—21no—
207#107—111no—
208#107—221no—
209#107C22⋊D1111yescharacteristic
210#103—21no—
211#103—221no—
212#103—221no—
213#103—221no—
214C22⋊C8—221no—
215C22⋊C8—221no—
216#95—441no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11#160711yescharacteristic
220C2×C11#218811yescharacteristic
221C2×C11#219011yescharacteristic
222D11—42no—
223C24—111no—
224C2×Q8—21no—
225C2×Q8—221no—
226C2×Q8—441no—
227C2×Q8—881no—
228C2×Q8—881no—
229C22×C4—41no—
230C22×C4—111no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4—441no—
234C22×C4—441no—
235C22×C4—441no—
236C22×C4—441no—
237C22×C4—441no—
238C22×C4D4×D1111yescharacteristic
239Q16—41no—
240Q16—441no—
241Q16—881no—
242C2×C8—41no—
243C2×C8—221no—
244C2×C8—441no—
245C2×C8D4×D1111yescharacteristic
246C2×C8C2×C22⋊D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—221no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C22⋊C4—41no—
259C22⋊C4—441no—
260C22⋊C4—441no—
261C22⋊C4—441no—
262C22⋊C4—882no—
263C16—41no—
264C16—441no—
265C11#1228211yescharacteristic, complemented, Sylow
266C23—112no—
267C23—221no—
268C23—221no—
269C23—441no—
270C23—441no—
271C23D8×D1111yescharacteristic
272Q8—41no—
273Q8—41no—
274Q8—441no—
275Q8—441no—
276Q8—882no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—221no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—881no—
291C2×C4—882no—
292C2×C4—882no—
293C2×C4—881no—
294C2×C4—881no—
295C2×C4—881no—
296C2×C4#6696411yescharacteristic
297C2×C4#6699011yescharacteristic
298C8—21no—
299C8—21no—
300C8—441no—
301C22—21no—
302C22—21no—
303C22—222no—
304C22—442no—
305C22—441no—
306C22—441no—
307C22—881no—
308C22D11×Q3211yescharacteristic
309C22#1062253111yescharacteristic
310C22#1062276911yescharacteristic
311C4—21no—
312C4—81no—
313C4—81no—
314C4—161no—
315C4—441no—
316C4—881no—
317C4—881no—
318C4—1761no—
319C4#1062266611yescharacteristic
320C4#1062281511yescharacteristic
321C2—21no—
322C2—21no—
323C2—442no—
324C2#1306760011yescharacteristic
325C2#1307054811yescharacteristic
326C2#1307056011yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2236C2
socleC22×C11#447
prime radicalC23×D11D8
hypercenter#2236D11
hypocenterC11#12282
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
2. #13070818C2semidirect
4. #13066629C2semidirect
5. #13066628C2semidirect
7. C11×#2236C2semidirect
105. #2236D11semidirect
265. C11#12282semidirect

Maximal subgroups

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

subgroupindex
#130793872
#130708182
#130700452
#130666292
#130666282
#130665392
C11×#22362
#1228211