Finite Group Databasebeta

← #14670871

Subgroups — #14670871

Order 2816.

480 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 109 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×#66864C211yesmaximal, characteristic
2#13077485C211yesmaximal, characteristic, complemented
3C2×#10622155C211yesmaximal, characteristic, complemented
4#13070333C211yesmaximal, characteristic
5#13069526C211yesmaximal, characteristic
6#13066712C211yesmaximal, characteristic, complemented
7C11×#1379C211yesmaximal, characteristic, complemented
8C22×Dic44C2211yescharacteristic
9C22×D88C2211yescharacteristic
10#10623047—21no—
11C2×C11×M32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C11×#405C2211yescharacteristic
14C2×#66887—21no—
15#10622733—21no—
16C2×#66883C2211yescharacteristic
17#10622719C2211yescharacteristic
18#10622614—21no—
19C2×#66864—22no—
20C2×#66864—22no—
21C2×#66864C414yescomplemented
22#10622329—22no—
23C4×Dic44—22no—
24#10622155—22no—
25#10622147—22no—
26C22×D44—21no—
27C22×Dic22—21no—
28C2×C11×M16D411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C11×#117D411yescharacteristic
31#66979—21no—
32C2×#4318—21no—
33C2×Dic44—21no—
34C2×Dic44—21no—
35C2×Dic44—21no—
36C2×Dic44C2×C412yes—
37C2×Dic44D412yes—
38C2×Dic44D412yes—
39C2×D88—21no—
40C2×D88—21no—
41C2×D88—21no—
42C2×D88—21no—
43C2×D88—21no—
44C2×D88C2×C412yes—
45#66940—42no—
46#66930—42no—
47C4×Dic22—24no—
48C11×M32—21no—
49C11×M32—21no—
50C2×C11×C16—21no—
51C2×C11×C16—21no—
52C2×C11×C16—21no—
53C2×C11×C16C2×C412yes—
54C11×#97—21no—
55C4×C8×C11—21no—
56#66887—42no—
57#66883—21no—
58#66883—21no—
59#66882D412yes—
60#66881—21no—
61#66880—24no—
62#66873—42no—
63#66864—28no—
64#13018—111nomaximal, Sylow
65C23×D11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—41no—
68C2×D44—22no—
69C2×D44—41no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—41no—
74C2×Dic22—22no—
75C2×Dic22—22no—
76C2×Dic22—22no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C11×M16—21no—
81C11×M16—21no—
82C2×C8×C11—21no—
83C2×C8×C11C22×C411yescharacteristic
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11#4111yescharacteristic
88C2×C8×C11#4111yescharacteristic
89C11×C4⋊C4D812yes—
90C11×C22⋊C4—21no—
91C42×C11—21no—
92C22⋊Dic11—41no—
93C4⋊Dic11—22no—
94Dic11⋊C4—44no—
95C4×Dic11—44no—
96C4×Dic11—41no—
97#4318—41no—
98#4318—41no—
99C2×C11⋊C8—41no—
100Dic44—22no—
101Dic44—22no—
102Dic44—22no—
103Dic44C22⋊C414yes—
104D88—22no—
105D88—22no—
106D88—41no—
107D88—41no—
108C11×C16—22no—
109C11×C16—41no—
110C22×SD32—111no—
111#2950—111no—
112C2×#362—111no—
113#2140—111no—
114#1978—111no—
115#1382—111no—
116#1379D1111yescharacteristic, complemented
117C23×C11AGL(1,ℤ/8)11yescharacteristic
118C22×D11—42no—
119C22×D11—81no—
120C22×D11—81no—
121C22×D11—162no—
122C2×C4×C11—22no—
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11C2×D811yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133D44—42no—
134D44—42no—
135D44—81no—
136D44—81no—
137Dic22—24no—
138Dic22—42no—
139Dic22—42no—
140Dic22—42no—
141C8×C11—41no—
142C8×C11C2×C22⋊C411yescharacteristic
143C8×C11C4×D411yescharacteristic
144C8×C11#12111yescharacteristic
145C8×C11#12311yescharacteristic
146C11⋊C8—81no—
147C22×Q16—111no—
148C22×D8—111no—
149#519—221no—
150C2×SD32—114no—
151C2×SD32—222no—
152C2×SD32—222no—
153C2×M32C2×D1111yescharacteristic
154C22×C16C2×D1111yescharacteristic
155#441—222no—
156C4×Q16—222no—
157C2×#108—111no—
158#427—111no—
159#419—221no—
160#418—221no—
161C2×#100—221no—
162#405C2×D1111yescharacteristic
163#362—222no—
164#357—222no—
165C22×C11—22no—
166C22×C11#44211yescharacteristic
167C22×C11#44711yescharacteristic
168C22×C11#46311yescharacteristic
169C2×D11—82no—
170C2×D11—162no—
171C2×D11—162no—
172C2×D11—162no—
173C4×C11—42no—
174C4×C11#38611yescharacteristic
175C4×C11C4×D811yescharacteristic
176C4×C11#44911yescharacteristic
177C4×C11#45911yescharacteristic
178Dic11—44no—
179Dic11—82no—
180C22×Q8—221no—
181C22×D4—221no—
182C2×Q16—112no—
183C2×Q16—112no—
184C2×Q16—112no—
185C2×Q16—221no—
186C2×Q16—221no—
187C2×Q16—221no—
188C2×D8—112no—
189C2×D8—221no—
190C2×D8—221no—
191C2×D8—221no—
192C2×D8—221no—
193C2×D8—221no—
194C2×M16—221no—
195C2×M16D4411yescharacteristic
196C22×C8C22×D1111yescharacteristic
197C4×Q8—224no—
198C4×Q8—442no—
199#117—221no—
200#117—442no—
201#117D4411yescharacteristic
202SD32—228no—
203M32—21no—
204M32—21no—
205C2×C16—21no—
206C2×C16—21no—
207C2×C16—21no—
208C2×C16C4×D1112yes—
209#108—221no—
210#108—221no—
211#107—112no—
212#106—221no—
213#103—224no—
214#102—442no—
215#100—442no—
216#97—21no—
217C4×C8—21no—
218C2×C11—21no—
219C2×C11—21no—
220C2×C11#187911yescharacteristic
221C2×C11#219312yes—
222D11—162no—
223C24—441no—
224C2×Q8—222no—
225C2×Q8—222no—
226C2×Q8—222no—
227C2×Q8—441no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×D4—222no—
231C2×D4—441no—
232C2×D4—441no—
233C2×D4—441no—
234C2×D4—441no—
235C2×D4—441no—
236C22×C4—441no—
237C22×C4C2×D4411yescharacteristic
238Q16—114no—
239Q16—222no—
240Q16—222no—
241Q16—222no—
242D8—222no—
243D8—222no—
244D8—441no—
245D8—441no—
246M16—21no—
247M16—21no—
248M16—441no—
249M16—441no—
250C2×C8—21no—
251C2×C8—441no—
252C2×C8C2×C4×D1111yescharacteristic
253C2×C8#433911yescharacteristic
254C2×C8D4×D1111yescharacteristic
255C2×C8D4×D1111yescharacteristic
256C2×C8D4×D1111yescharacteristic
257C2×C8#434311yescharacteristic
258C4⋊C4—222no—
259C4⋊C4—444no—
260C4⋊C4D8812yes—
261C22⋊C4—21no—
262C22⋊C4—441no—
263C42—21no—
264C42—444no—
265C42—441no—
266C16—22no—
267C16—41no—
268C11#1301811yescharacteristic, complemented, Sylow
269C23—442no—
270C23—881no—
271C23—881no—
272C23—1762no—
273C23#6696111yescharacteristic
274Q8—224no—
275Q8—442no—
276Q8—442no—
277Q8—442no—
278D4—442no—
279D4—442no—
280D4—881no—
281D4—881no—
282C2×C4—22no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4C4×D4411yescharacteristic
288C2×C4#6693511yescharacteristic
289C2×C4#6694811yescharacteristic
290C2×C4C2×D8811yescharacteristic
291C2×C4#6695711yescharacteristic
292C2×C4#6696111yescharacteristic
293C8—41no—
294C8—881no—
295C8C22⋊C4×D1111yescharacteristic
296C8#6693711yescharacteristic
297C8#6694611yescharacteristic
298C8#6694711yescharacteristic
299C22—22no—
300C22—882no—
301C22—1762no—
302C22—1762no—
303C22—1762no—
304C22#1062232411yescharacteristic
305C22#1062234511yescharacteristic
306C22#1062245711yescharacteristic
307C4—42no—
308C4—444no—
309C4—882no—
310C4#1062227811yescharacteristic
311C4C4×D8811yescharacteristic
312C4#1062234711yescharacteristic
313C4#1062245611yescharacteristic
314C2—21no—
315C2—21no—
316C2—1762no—
317C2#1306896311yescharacteristic
318C2#1307058212yes—
subgroupG/H
centerC22#10622345
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1379C2
socleC22×C11#447
prime radicalC22×D88C22
cosocleC22×C8×C11C23
hypercenter#1379D11
hypocenterC11#13018
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405 ◁ #1379

Complements

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

NH ≅ G/Ntype
2. #13077485C2semidirect
3. C2×#10622155C2semidirect
6. #13066712C2semidirect
7. C11×#1379C2semidirect
21. C2×#66864C4semidirect
116. #1379D11semidirect
268. C11#13018semidirect

Maximal subgroups

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

subgroupindex
C22×#668642
#130774852
C2×#106221552
#130703332
#130695262
#130667122
C11×#13792
#1301811