Finite Group Databasebeta

← #14672098

Subgroups — #14672098

Order 2816.

472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073601C211yesmaximal, characteristic
2C2×#10622116C214yesmaximal
3C4×#66900C211yesmaximal, characteristic
4C11×#1801C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66997C2212yes—
7C2×#66922C411yescharacteristic
8C11×#423—21no—
9C2×C11×#101C2212yes—
10C2×#66900C2212yes—
11#10622596—21no—
12#10622596—21no—
13#10622587C412yes—
14C4×C4⋊Dic11C411yescharacteristic
15#10622541—21no—
16#10622541—21no—
17C4×#4318—21no—
18C11×#343—21no—
19#10622168—21no—
20#10622116—28no—
21C22×Q8×C11C2311yescharacteristic
22C22×Dic22C2×C412yes—
23C2×C11×M16—22no—
24C4×Q8×C11—41no—
25C4×Q8×C11—41no—
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32#66997—24no—
33#66997—24no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—22no—
38C2×Dic11⋊C4—22no—
39C2×C4×Dic11C2×C412yes—
40C2×#4318—22no—
41#66922—41no—
42#66922—41no—
43C11×C4⋊C8—41no—
44C11×C4⋊C8—41no—
45C11×#101—24no—
46#66900—22no—
47#66900D414yes—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—21no—
51#66867—41no—
52C4×C11⋊C8—41no—
53#13227—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×Q8×C11—41no—
56C2×Q8×C11C2×D412yes—
57C2×Q8×C11#4112yes—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—22no—
66C22×Dic11—22no—
67C2×Dic22—24no—
68C2×Dic22—42no—
69C2×Dic22—42no—
70C11×M16—42no—
71C11×M16—42no—
72C2×C8×C11—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C4⋊Dic11—24no—
83C4⋊Dic11—42no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86Dic11⋊C4—44no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89C4×Dic11—24no—
90#4318—24no—
91#4318—42no—
92C2×C11⋊C8—42no—
93#2546—111no—
94C2×#356—114no—
95#1801D1111yescharacteristic
96C4×#101—111no—
97C23×C11C2×C22⋊C411yescharacteristic
98Q8×C11—42no—
99Q8×C11—42no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11#9911yescharacteristic
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11C4×D412yes—
116C2×C4×C11#12112yes—
117C2×C4×C11#12411yescharacteristic
118C2×C4×C11#12711yescharacteristic
119C2×Dic11—24no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125Dic22—84no—
126C8×C11—82no—
127C11⋊C8—44no—
128C2×C4⋊Q8—112no—
129C2×C4⋊Q8—111no—
130C2×C4×Q8C2×D1111yescharacteristic
131#423—21no—
132C2×#101—112no—
133C2×#101C2×D1112yes—
134C4×M16—221no—
135#398—221no—
136#398—221no—
137#391—112no—
138#389—221no—
139#389—221no—
140C4×C4⋊C4—111no—
141#356—228no—
142#343—21no—
143#343—221no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11#39011yescharacteristic
147C22×C11C2×#9911yescharacteristic
148C22×C11#41011yescharacteristic
149C4×C11—21no—
150C4×C11—22no—
151C4×C11—22no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11#35612yescomplemented
158Dic11—44no—
159Dic11—82no—
160C22×Q8—112no—
161C22×Q8C22×D1111yescharacteristic
162C2×M16—22no—
163C2×M16—222no—
164C4⋊Q8—224no—
165C4⋊Q8—224no—
166C4⋊Q8—441no—
167C4⋊Q8—441no—
168C4×Q8—41no—
169C4×Q8—41no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—222no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4C4×D1111yescharacteristic
176C2×C4⋊C4D4411yescharacteristic
177C2×C4⋊C4C22⋊D1111yescharacteristic
178C2×C42—112no—
179C2×C42C4×D1111yescharacteristic
180C2×C42D4411yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C4⋊C8—41no—
183C4⋊C8—41no—
184#101—24no—
185#101—114no—
186#101—222no—
187#97—441no—
188C4×C8—441no—
189#95—221no—
190#95—222no—
191#95—222no—
192C2×C11—21no—
193C2×C11—21no—
194C2×C11#196411yescharacteristic
195C2×C11C2×#35611yescharacteristic
196C2×C11#213511yescharacteristic
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—224no—
200C2×Q8—442no—
201C2×Q8—442no—
202C2×Q8D4×D1112yes—
203C2×Q8#434312yes—
204C22×C4—222no—
205C22×C4—222no—
206C22×C4(C2×D11)⋊C411yescharacteristic
207C22×C4(C2×D11)⋊C411yescharacteristic
208C22×C4(C2×D11)⋊C411yescharacteristic
209C22×C4(C2×D11)⋊C411yescharacteristic
210C22×C4C2×C4×D1111yescharacteristic
211C22×C4C2×D4411yescharacteristic
212C22×C4C2×C22⋊D1111yescharacteristic
213M16—42no—
214M16—42no—
215M16—224no—
216M16—442no—
217C2×C8—42no—
218C2×C8—442no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—224no—
223C4⋊C4—442no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—444no—
227C4⋊C4—442no—
228C4⋊C4—442no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—224no—
236C11#1322711yescharacteristic, complemented, Sylow
237C23C2×(C2×D11)⋊C411yescharacteristic
238Q8—42no—
239Q8—42no—
240Q8—884no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—224no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4—442no—
260C2×C4#6687011yescharacteristic
261C2×C4#6687011yescharacteristic
262C2×C4#6694612yes—
263C2×C4#6694812yes—
264C2×C4#6699311yescharacteristic
265C2×C4#6700011yescharacteristic
266C8—82no—
267C8—444no—
268C22—21no—
269C22—21no—
270C22C2×#6687011yescharacteristic
271C22#1062260111yescharacteristic
272C22#1062261911yescharacteristic
273C4—21no—
274C4—22no—
275C4—22no—
276C4—21no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—444no—
282C4—882no—
283C4#1062211612yescomplemented
284C2—21no—
285C2—21no—
286C2#1306945111yescharacteristic
287C2C2×#1062211611yescharacteristic
288C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1801C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC22×Q8×C11C23
hypercenter#1801D11
hypocenterC11#13227
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
157. C4×C11#356semidirect
236. C11#13227semidirect
283. C4#10622116semidirect

Maximal subgroups

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

subgroupindex
#130736012
C2×#106221162
C4×#669002
C11×#18012
#1322711