Finite Group Databasebeta

← #14670596

Subgroups — #14670596

Order 2816.

472 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 95 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#13071790C211yesmaximal, characteristic
2C2×#10622180C211yesmaximal, characteristic
3#13068831C212yesmaximal, complemented
4#13066742C212yesmaximal, complemented
5C11×#1888C211yesmaximal, characteristic
6C2×C11×#124C2211yescharacteristic
7C11×#519C2211yescharacteristic
8C11×#418—21no—
9C2×C11×#101C2211yescharacteristic
10#10622843C2212yes—
11C2×#66900C2212yes—
12#10622833—21no—
13#10622608—22no—
14#10622564—22no—
15#10622563—22no—
16#10622549—21no—
17C11×#339—21no—
18#10622180C414yescomplemented
19#10622170—22no—
20C22×Q8×C11C2311yescharacteristic
21C22×D4×C11D411yescharacteristic
22C23×Dic11—21no—
23C2×C11×M16—21no—
24C11×#124—22no—
25C11×#124C2×C412yes—
26C11×#124Q812yes—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C11×#117—21no—
30C11×#117—22no—
31C2×C11×C22⋊C4—22no—
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D412yes—
38C2×C4×Dic11D412yes—
39C2×#4318—22no—
40C11×#102—41no—
41C11×#102—41no—
42C11×#101—22no—
43#66900—22no—
44#66900C2×C414yescomplemented
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48#66872—42no—
49#66871—42no—
50#12970—111nomaximal, Sylow
51C24×C11—21no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11C22×C411yescharacteristic
55C2×Q8×C11C2×Q811yescharacteristic
56C2×Q8×C11#4112yes—
57C2×D4×C11—21no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11C4⋊C412yes—
61C22×C4×C11—21no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C22×Dic11—82no—
67C22×Dic11—81no—
68C11×M16—41no—
69C11×M16—41no—
70C2×C8×C11—41no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C22⋊C4—24no—
76C11×C22⋊C4—24no—
77C11×C22⋊C4—41no—
78C42×C11—21no—
79C42×C11—42no—
80C42×C11—41no—
81C42×C11C4⋊C412yes—
82C22⋊Dic11—82no—
83C22⋊Dic11—81no—
84C4⋊Dic11—42no—
85C4⋊Dic11—81no—
86C4⋊Dic11—81no—
87C4×Dic11—42no—
88#4318—24no—
89#4318—42no—
90C2×C11⋊C8—42no—
91#2379—111no—
92C2×#355—111no—
93#1888D1111yescharacteristic
94#1857—112no—
95#1394—112no—
96C23×C11—22no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11#12011yescharacteristic
102Q8×C11—41no—
103Q8×C11—41no—
104Q8×C11—42no—
105D4×C11—42no—
106D4×C11—81no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11C2×C4⋊C411yescharacteristic
117C2×C4×C11C4×D412yes—
118C2×C4×C11C22⋊Q812yes—
119C2×C4×C11#12311yescharacteristic
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—84no—
127C8×C11—81no—
128C11⋊C8—44no—
129C2×#124C2×D1111yescharacteristic
130#519C2×D1111yescharacteristic
131#428—222no—
132#418—21no—
133C2×#101—112no—
134C2×#101C2×D1111yescharacteristic
135#391—112no—
136#388—222no—
137#386—221no—
138#385—222no—
139#382—221no—
140#355—114no—
141#339—21no—
142#339—222no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—44no—
146C22×C11—42no—
147C22×C11—82no—
148C22×C11—81no—
149C22×C11—81no—
150C22×C11#38511yescharacteristic
151C22×C11B(4,𝔽2)11yescharacteristic
152C22×C11#45811yescharacteristic
153C4×C11—21no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—42no—
158C4×C11—81no—
159C4×C11—81no—
160Dic11—82no—
161Dic11—82no—
162C22×Q8C22×D1111yescharacteristic
163C22×D4C22⋊D1111yescharacteristic
164C23×C4—221no—
165C2×M16—21no—
166C2×M16—222no—
167#124—22no—
168#124Dic2212yes—
169#124C4×D1112yes—
170C4×Q8—41no—
171C4×Q8—41no—
172#117—22no—
173#117—21no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—221no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—222no—
179C2×C22⋊C4—221no—
180C2×C42—112no—
181C2×C42C22⋊D1111yescharacteristic
182#107—442no—
183#106—442no—
184#102—41no—
185#102—41no—
186#101—22no—
187#101—114no—
188#101—222no—
189#95—222no—
190#95—222no—
191#95—222no—
192C2×C11—21no—
193C2×C11—21no—
194C2×C11—82no—
195C2×C11#186711yescharacteristic
196C2×C11#220211yescharacteristic
197C2×C11#220311yescharacteristic
198C24—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8C2×Dic2211yescharacteristic
202C2×Q8C2×C4×D1111yescharacteristic
203C2×Q8#434112yes—
204C2×D4—21no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4Dic11⋊C412yes—
208C22×C4—21no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4—882no—
212C22×C4—881no—
213C22×C4D4×D1112yes—
214C22×C4C2×C22⋊D1111yescharacteristic
215M16—41no—
216M16—41no—
217M16—224no—
218M16—442no—
219C2×C8—41no—
220C2×C8—442no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—442no—
226C4⋊C4—881no—
227C4⋊C4—881no—
228C22⋊C4—24no—
229C22⋊C4—24no—
230C22⋊C4—41no—
231C22⋊C4—882no—
232C22⋊C4—881no—
233C42—21no—
234C42—42no—
235C42—41no—
236C42—442no—
237C42Dic11⋊C412yes—
238C11#1297011yescharacteristic, complemented, Sylow
239C23—22no—
240C23—42no—
241C23—42no—
242C23—41no—
243C23—41no—
244C23#6699011yescharacteristic
245Q8—41no—
246Q8—41no—
247Q8—42no—
248D4—42no—
249D4—81no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—442no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—884no—
266C2×C4#6693112yes—
267C2×C4(C22⋊D11)⋊C412yes—
268C2×C4C2×Dic11⋊C411yescharacteristic
269C2×C4#6698811yescharacteristic
270C8—81no—
271C8—444no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22—42no—
276C22—82no—
277C22—81no—
278C22—81no—
279C22#1062255911yescharacteristic
280C22#1062264511yescharacteristic
281C22#1062266611yescharacteristic
282C4—21no—
283C4—22no—
284C4—22no—
285C4—21no—
286C4—42no—
287C4—81no—
288C4—81no—
289C4—882no—
290C4—882no—
291C2—21no—
292C2—21no—
293C2—82no—
294C2#1306889611yescharacteristic
295C2#1307063211yescharacteristic
296C2#1307063611yescharacteristic
subgroupG/H
centerC22#10622645
commutatorC2×Q8×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1888C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
cosocleC22×Q8×C11C23
hypercenter#1888D11
hypocenterC11#12970
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1888

Complements

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

NH ≅ G/Ntype
3. #13068831C2semidirect
4. #13066742C2semidirect
18. #10622180C4semidirect
44. #66900C2×C4semidirect
238. C11#12970semidirect

Maximal subgroups

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

subgroupindex
#130717902
C2×#106221802
#130688312
#130667422
C11×#18882
#1297011