Finite Group Databasebeta

← #14670883

Subgroups — #14670883

Order 2816.

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

normal subgroups only

This group has 460 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
1C22×#66893C211yesmaximal, characteristic
2#13077483C211yesmaximal, characteristic
3C2×#10622155C211yesmaximal, characteristic
4#13069532C211yesmaximal, characteristic
5#13066711C211yesmaximal, characteristic
6#13066706C211yesmaximal, characteristic
7C11×#2141C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9C22×Dic44C2211yescharacteristic
10#10623047—21no—
11C2×C11×M32C2211yescharacteristic
12C11×#427C2211yescharacteristic
13C2×#66900—21no—
14#10622838—21no—
15C2×#66893—22no—
16C2×#66893—22no—
17C2×#66893C414yescomplemented
18C2×#66883C2211yescharacteristic
19#10622714C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622617—21no—
22#10622486—22no—
23#10622466—22no—
24C11×#358—22no—
25#10622155—22no—
26C22×Q8×C11—21no—
27C22×Dic22—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16—21no—
33C2×C11×Q16C2×C412yes—
34C22×C8×C11C2311yescharacteristic
35C11×#117—21no—
36#66979D411yescharacteristic
37C2×#4318—21no—
38C2×#4318D411yescharacteristic
39C2×Dic44—21no—
40C2×Dic44—21no—
41C2×Dic44—21no—
42C2×Dic44C2×C412yes—
43C2×Dic44D412yes—
44C2×Dic44D412yes—
45#66940—24no—
46#66930—42no—
47C4×Dic22—42no—
48C11×M32—21no—
49C11×M32—21no—
50C2×C11×C16—21no—
51C11×#107D412yes—
52C11×#106—21no—
53#66900—42no—
54#66899—42no—
55#66893—28no—
56#66883—21no—
57#66883—21no—
58#66879—21no—
59C8×Dic11—21no—
60C2×C11⋊C16—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16C2×C412yes—
63#66874—24no—
64#13020—111nomaximal, Sylow
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—41no—
74C2×Dic22—22no—
75C2×Dic22—22no—
76C2×Dic22—22no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C11×Q16—22no—
81C11×Q16—22no—
82C11×Q16—41no—
83C11×Q16—41no—
84C2×C8×C11C22×C411yescharacteristic
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11#4111yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C11×C4⋊C4—22no—
91C11×C22⋊C4—41no—
92C42×C11—41no—
93C22⋊Dic11—21no—
94C4⋊Dic11D812yes—
95Dic11⋊C4—44no—
96C4×Dic11—21no—
97C4×Dic11—44no—
98#4318—21no—
99#4318—21no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—41no—
104Dic44—22no—
105Dic44—22no—
106Dic44—22no—
107Dic44C22⋊C414yes—
108C11×C16—41no—
109C11⋊C16—22no—
110C22×Q32—111no—
111#2950—111no—
112C2×#362—111no—
113#2141D1111yescharacteristic
114#1979—111no—
115#1382—111no—
116#1379—111no—
117C23×C11AGL(1,ℤ/8)11yescharacteristic
118Q8×C11—42no—
119Q8×C11—42no—
120Q8×C11—81no—
121Q8×C11—81no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11C2×D811yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136Dic22—24no—
137Dic22—42no—
138Dic22—42no—
139Dic22—42no—
140C8×C11C2×C22⋊C411yescharacteristic
141C8×C11C4×D411yescharacteristic
142C8×C11#12111yescharacteristic
143C8×C11#12311yescharacteristic
144C11⋊C8—41no—
145C11⋊C8—81no—
146C22×Q16—111no—
147C22×Q16C2×D1111yescharacteristic
148#519—221no—
149C2×Q32—114no—
150C2×Q32—222no—
151C2×Q32—222no—
152C2×M32C2×D1111yescharacteristic
153C22×C16—111no—
154#441—222no—
155C4×Q16—222no—
156C2×#108—111no—
157#427C2×D1111yescharacteristic
158#419—221no—
159#419—221no—
160C2×#101—221no—
161#405—111no—
162#362—222no—
163#358—22no—
164C22×C11—22no—
165C22×C11#44211yescharacteristic
166C22×C11#44711yescharacteristic
167C22×C11#46311yescharacteristic
168C4×C11—82no—
169C4×C11—82no—
170C4×C11#38611yescharacteristic
171C4×C11C4×D811yescharacteristic
172C4×C11#44911yescharacteristic
173C4×C11#45911yescharacteristic
174Dic11—44no—
175Dic11—42no—
176C22×Q8—21no—
177C22×Q8—221no—
178C2×Q16—21no—
179C2×Q16—21no—
180C2×Q16—21no—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16—112no—
184C2×Q16—112no—
185C2×Q16—112no—
186C2×Q16—221no—
187C2×Q16—221no—
188C2×Q16—221no—
189C2×Q16C4×D1112yes—
190C2×M16—111no—
191C2×M16—221no—
192C22×C8C22×D1111yescharacteristic
193C4×Q8—224no—
194C4×Q8—442no—
195#117—21no—
196#117—111no—
197#117—442no—
198Q32—228no—
199M32—21no—
200M32—21no—
201C2×C16—21no—
202C2×C16—112no—
203C2×C16—221no—
204C2×C16—221no—
205#108—221no—
206#108—221no—
207#107C22⋊D1112yes—
208#106—21no—
209#103—224no—
210#103—442no—
211#101—442no—
212#97—221no—
213C4×C8—221no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#187911yescharacteristic
217C2×C11#219512yes—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—222no—
225C2×Q8—222no—
226C2×Q8—222no—
227C2×Q8—441no—
228C2×Q8—441no—
229C2×Q8—441no—
230C22×C4—41no—
231C22×C4—441no—
232C22×C4D4×D1111yescharacteristic
233Q16—22no—
234Q16—22no—
235Q16—41no—
236Q16—41no—
237Q16—114no—
238Q16—222no—
239Q16—222no—
240Q16—222no—
241M16—221no—
242M16—221no—
243M16—441no—
244M16—441no—
245C2×C8—221no—
246C2×C8—441no—
247C2×C8C2×C4×D1111yescharacteristic
248C2×C8#433911yescharacteristic
249C2×C8D4×D1111yescharacteristic
250C2×C8D4×D1111yescharacteristic
251C2×C8#434111yescharacteristic
252C2×C8C2×C22⋊D1111yescharacteristic
253C4⋊C4—22no—
254C4⋊C4—112no—
255C4⋊C4—444no—
256C22⋊C4—41no—
257C22⋊C4—221no—
258C42—41no—
259C42—221no—
260C42—444no—
261C16—41no—
262C16—222no—
263C11#1302011yescharacteristic, complemented, Sylow
264C23#6696411yescharacteristic
265Q8—42no—
266Q8—42no—
267Q8—81no—
268Q8—81no—
269Q8—224no—
270Q8—442no—
271Q8—442no—
272Q8—442no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—222no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4(C22⋊D11)⋊C411yescharacteristic
282C2×C4#6693711yescharacteristic
283C2×C4D8×D1111yescharacteristic
284C2×C4#6696711yescharacteristic
285C2×C4#6696911yescharacteristic
286C2×C4#6699011yescharacteristic
287C8—441no—
288C8—881no—
289C8C22⋊C4×D1111yescharacteristic
290C8#6693611yescharacteristic
291C8C4×C22⋊D1111yescharacteristic
292C8#6699111yescharacteristic
293C22—22no—
294C22#1062239811yescharacteristic
295C22#1062240011yescharacteristic
296C22#1062276911yescharacteristic
297C4—82no—
298C4—82no—
299C4—444no—
300C4—442no—
301C4#1062236911yescharacteristic
302C4#1062239911yescharacteristic
303C4#1062256911yescharacteristic
304C4#1062278511yescharacteristic
305C2—21no—
306C2—21no—
307C2#1306896111yescharacteristic
308C2#1307059112yes—
subgroupG/H
centerC22#10622769
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2141C2
socleC22×C11#447
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC22×C8×C11C23
hypercenter#2141D11
hypocenterC11#13020
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2141

Complements

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

NH ≅ G/Ntype
17. C2×#66893C4semidirect
263. C11#13020semidirect

Maximal subgroups

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

subgroupindex
C22×#668932
#130774832
C2×#106221552
#130695322
#130667112
#130667062
C11×#21412
#1302011