Finite Group Databasebeta

← #14670885

Subgroups — #14670885

Order 2816.

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

normal subgroups only

This group has 460 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×Dic88C211yesmaximal, characteristic
2#13077485C211yesmaximal, characteristic
3C2×#10622155C211yesmaximal, characteristic
4#13070337C211yesmaximal, characteristic
5#13069531C211yesmaximal, characteristic
6#13066712C211yesmaximal, characteristic
7C11×#1379C211yesmaximal, characteristic
8C22×Dic44C2211yescharacteristic
9C22×Dic44C2211yescharacteristic
10#10623047—21no—
11C2×C11×M32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C11×#405C2211yescharacteristic
14C2×#66888—21no—
15#10622733—21no—
16C2×#66883C2211yescharacteristic
17#10622719C2211yescharacteristic
18#10622617—21no—
19C2×Dic88—22no—
20C2×Dic88—22no—
21C2×Dic88C414yescomplemented
22#10622329—22no—
23C4×Dic44—22no—
24#10622155—22no—
25#10622141—22no—
26C22×Dic22—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×Dic44—21no—
37C2×Dic44—21no—
38C2×Dic44—21no—
39C2×Dic44—21no—
40C2×Dic44—21no—
41C2×Dic44C2×C412yes—
42C2×Dic44C2×C412yes—
43C2×Dic44D412yes—
44C2×Dic44D412yes—
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#66888—42no—
57#66883—21no—
58#66883—21no—
59#66882D412yes—
60#66881—21no—
61#66880—24no—
62#66874—42no—
63Dic88—28no—
64#13020—111nomaximal, Sylow
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—41no—
67C22×Dic11—41no—
68C2×Dic22—22no—
69C2×Dic22—22no—
70C2×Dic22—22no—
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22—41no—
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—
103Dic44—22no—
104Dic44—22no—
105Dic44—41no—
106Dic44—41no—
107Dic44C22⋊C414yes—
108C11×C16—22no—
109C11×C16—41no—
110C22×Q32—111no—
111#2950—111no—
112C2×#362—111no—
113#2141—111no—
114#1979—111no—
115#1382—111no—
116#1379D1111yescharacteristic
117C23×C11AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C11—22no—
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11C2×D811yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—81no—
131C2×Dic11—81no—
132Dic22—24no—
133Dic22—42no—
134Dic22—42no—
135Dic22—42no—
136Dic22—42no—
137Dic22—42no—
138Dic22—81no—
139Dic22—81no—
140C8×C11—41no—
141C8×C11C2×C22⋊C411yescharacteristic
142C8×C11C4×D411yescharacteristic
143C8×C11#12111yescharacteristic
144C8×C11#12311yescharacteristic
145C11⋊C8—81no—
146C22×Q16—111no—
147C22×Q16—111no—
148#519—221no—
149C2×Q32—114no—
150C2×Q32—222no—
151C2×Q32—222no—
152C2×M32C2×D1111yescharacteristic
153C22×C16C2×D1111yescharacteristic
154#441—222no—
155C4×Q16—222no—
156C2×#108—111no—
157#427—111no—
158#419—221no—
159#419—221no—
160C2×#101—221no—
161#405C2×D1111yescharacteristic
162#362—222no—
163#358—222no—
164C22×C11—22no—
165C22×C11#44211yescharacteristic
166C22×C11#44711yescharacteristic
167C22×C11#46311yescharacteristic
168C4×C11—42no—
169C4×C11#38611yescharacteristic
170C4×C11C4×D811yescharacteristic
171C4×C11#44911yescharacteristic
172C4×C11#45911yescharacteristic
173Dic11—44no—
174Dic11—82no—
175Dic11—82no—
176C22×Q8—221no—
177C22×Q8—221no—
178C2×Q16—112no—
179C2×Q16—112no—
180C2×Q16—112no—
181C2×Q16—112no—
182C2×Q16—221no—
183C2×Q16—221no—
184C2×Q16—221no—
185C2×Q16—221no—
186C2×Q16—221no—
187C2×Q16—221no—
188C2×Q16—221no—
189C2×Q16—221no—
190C2×M16—221no—
191C2×M16D4411yescharacteristic
192C22×C8C22×D1111yescharacteristic
193C4×Q8—224no—
194C4×Q8—442no—
195#117—221no—
196#117—442no—
197#117D4411yescharacteristic
198Q32—228no—
199M32—21no—
200M32—21no—
201C2×C16—21no—
202C2×C16—21no—
203C2×C16—21no—
204C2×C16C4×D1112yes—
205#108—221no—
206#108—221no—
207#107—112no—
208#106—221no—
209#103—224no—
210#103—442no—
211#101—442no—
212#97—21no—
213C4×C8—21no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#187911yescharacteristic
217C2×C11#219512yes—
218C2×Q8—222no—
219C2×Q8—222no—
220C2×Q8—222no—
221C2×Q8—222no—
222C2×Q8—441no—
223C2×Q8—441no—
224C2×Q8—441no—
225C2×Q8—441no—
226C2×Q8—441no—
227C2×Q8—441no—
228C2×Q8—441no—
229C2×Q8—441no—
230C22×C4—441no—
231C22×C4—441no—
232C22×C4C2×D4411yescharacteristic
233Q16—114no—
234Q16—222no—
235Q16—222no—
236Q16—222no—
237Q16—222no—
238Q16—222no—
239Q16—441no—
240Q16—441no—
241M16—21no—
242M16—21no—
243M16—441no—
244M16—441no—
245C2×C8—21no—
246C2×C8—441no—
247C2×C8C2×C4×D1111yescharacteristic
248C2×C8#433911yescharacteristic
249C2×C8D4×D1111yescharacteristic
250C2×C8D4×D1111yescharacteristic
251C2×C8D4×D1111yescharacteristic
252C2×C8#434311yescharacteristic
253C4⋊C4—222no—
254C4⋊C4—444no—
255C4⋊C4D8812yes—
256C22⋊C4—21no—
257C22⋊C4—441no—
258C42—21no—
259C42—444no—
260C42—441no—
261C16—22no—
262C16—41no—
263C11#1302011yescharacteristic, complemented, Sylow
264C23#6696111yescharacteristic
265Q8—224no—
266Q8—442no—
267Q8—442no—
268Q8—442no—
269Q8—442no—
270Q8—442no—
271Q8—881no—
272Q8—881no—
273C2×C4—22no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4—881no—
280C2×C4—881no—
281C2×C4C4×D4411yescharacteristic
282C2×C4#6693511yescharacteristic
283C2×C4#6694811yescharacteristic
284C2×C4C2×D8811yescharacteristic
285C2×C4#6695711yescharacteristic
286C2×C4#6696111yescharacteristic
287C8—41no—
288C8—881no—
289C8C22⋊C4×D1111yescharacteristic
290C8#6693711yescharacteristic
291C8#6694611yescharacteristic
292C8#6694711yescharacteristic
293C22—22no—
294C22#1062232411yescharacteristic
295C22#1062234511yescharacteristic
296C22#1062245711yescharacteristic
297C4—42no—
298C4—444no—
299C4—882no—
300C4—882no—
301C4#1062227811yescharacteristic
302C4C4×D8811yescharacteristic
303C4#1062234711yescharacteristic
304C4#1062245611yescharacteristic
305C2—21no—
306C2—21no—
307C2#1306896311yescharacteristic
308C2#1307059612yes—
subgroupG/H
centerC22#10622345
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1379C2
socleC22×C11#447
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC22×C8×C11C23
hypercenter#1379D11
hypocenterC11#13020
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
21. C2×Dic88C4semidirect
263. C11#13020semidirect

Maximal subgroups

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

subgroupindex
C22×Dic882
#130774852
C2×#106221552
#130703372
#130695312
#130667122
C11×#13792
#1302011