Finite Group Databasebeta

← #14655613

Subgroups — #14655613

Order 2816.

492 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079760C211yesmaximal, characteristic
2#13079162C211yesmaximal, characteristic
3C2×#10622706C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic
7C11×#1966C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#101—22no—
13C4×C11×M16C2211yescharacteristic
14#10622734—22no—
15#10622707—22no—
16#10622706—22no—
17#10622706—21no—
18#10622706—22no—
19#10622692—21no—
20#10622584—22no—
21C2×#66874—22no—
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622315—22no—
25#10622295—21no—
26#10622293—21no—
27#10622124—22no—
28#10622122—22no—
29C22×Q8×C11—21no—
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C2×C11×M16D412yes—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D412yes—
39C2×C42×C11C2311yescharacteristic
40#66979—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43#66977—21no—
44#66977—21no—
45C22×C11⋊C8—21no—
46#66923—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922D412yes—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×#101—44no—
58C11×#97—21no—
59C4×C8×C11—21no—
60C22⋊(C11⋊C8)—21no—
61#66882—24no—
62#66881—24no—
63#66874—28no—
64#66874—24no—
65#66872—24no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10159—111nomaximal, Sylow
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—41no—
80C2×Dic22—21no—
81C2×Dic22—22no—
82C2×Dic22—21no—
83C2×Dic22—44no—
84C2×Dic22—41no—
85C11×M16—22no—
86C11×M16—42no—
87C11×M16SD1614yes—
88C2×C8×C11—22no—
89C2×C8×C11—41no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C22⋊Dic11—41no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—22no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—41no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—42no—
113#3229—111no—
114#3165—111no—
115C2×#487—111no—
116#1966D1111yescharacteristic
117#1549—111no—
118#1493—111no—
119#1278—111no—
120C23×C11#12111yescharacteristic
121Q8×C11—82no—
122Q8×C11—81no—
123Q8×C11—81no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—42no—
127C2×C4×C11—44no—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12711yescharacteristic
134C2×C4×C11C2×SD1612yes—
135C2×C4×C11#13712yes—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—42no—
139C2×Dic11—82no—
140Dic22—44no—
141Dic22—42no—
142Dic22—42no—
143Dic22—82no—
144C8×C11—24no—
145C8×C11—81no—
146C11⋊C8—42no—
147C11⋊C8—42no—
148#533—111no—
149C2×C4⋊Q8—111no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151#501—222no—
152#500—221no—
153#498—221no—
154#498—221no—
155#487—222no—
156#487—222no—
157#487—221no—
158#483—222no—
159#475—222no—
160#431—111no—
161#428—222no—
162#423C2×D1111yescharacteristic
163C2×#103—222no—
164C2×#101—22no—
165C4×M16C2×D1111yescharacteristic
166C2×C4×C8—111no—
167#332—222no—
168Q8⋊C8—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#39211yescharacteristic
172C22×C11#46112yes—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—82no—
176C4×C11#44812yes—
177C4×C11#45412yes—
178C4×C11#47312yes—
179C4×C11#49211yescharacteristic
180C4×C11#49711yescharacteristic
181Dic11—82no—
182Dic11—81no—
183Dic11—81no—
184C22×Q8—21no—
185C22×Q8—221no—
186C2×M16—21no—
187C2×M16C22⋊D1112yes—
188C22×C8—221no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—112no—
194C4⋊Q8—111no—
195C4⋊Q8—111no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199#125—221no—
200C22⋊Q8—221no—
201C22⋊Q8—221no—
202C4×Q8—221no—
203C4×Q8—221no—
204#117—221no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4D4412yes—
209C2×C42C22×D1111yescharacteristic
210#107—224no—
211#106—224no—
212#106—224no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—112no—
216#103—228no—
217#103—224no—
218#101—44no—
219C22⋊C8—221no—
220#97—21no—
221C4×C8—21no—
222C4×C8—112no—
223C4×C8—221no—
224C4×C8—221no—
225C2×C11—22no—
226C2×C11#200311yescharacteristic
227C2×C11#201311yescharacteristic
228C2×C11#202011yescharacteristic
229C2×Q8—42no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—42no—
233C2×Q8—221no—
234C2×Q8—222no—
235C2×Q8—221no—
236C2×Q8—444no—
237C2×Q8—441no—
238C22×C4—22no—
239C22×C4—441no—
240C22×C4C2×D4411yescharacteristic
241C22×C4#433911yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243M16—22no—
244M16—42no—
245M16#432414yes—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—222no—
249C2×C8—222no—
250C2×C8—442no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—221no—
256C4⋊C4—222no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—222no—
260C4⋊C4—221no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C22⋊C4—441no—
266C42—441no—
267C42D4×D1111yescharacteristic
268C42D4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C42D4×D1111yescharacteristic
271C11#1015911yescharacteristic, complemented, Sylow
272C23#6698311yescharacteristic
273Q8—82no—
274Q8—81no—
275Q8—81no—
276Q8—444no—
277Q8—442no—
278Q8—442no—
279Q8—882no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—442no—
287C2×C4—882no—
288C2×C4#6693511yescharacteristic
289C2×C4#6693511yescharacteristic
290C2×C4#6693711yescharacteristic
291C2×C4#6693711yescharacteristic
292C2×C4C2×#432412yes—
293C2×C4#6699011yescharacteristic
294C2×C4#6699311yescharacteristic
295C2×C4#6700412yes—
296C8—24no—
297C8—81no—
298C8—442no—
299C8—442no—
300C22—21no—
301C22—21no—
302C22#1062257311yescharacteristic
303C22#1062263212yes—
304C4—21no—
305C4—21no—
306C4—82no—
307C4—882no—
308C4—881no—
309C4—881no—
310C4#1062236612yes—
311C4#1062236812yes—
312C4#1062265312yes—
313C4#1062267311yescharacteristic
314C4#1062268911yescharacteristic
315C2—22no—
316C2#1306964011yescharacteristic
317C2#1306969811yescharacteristic
318C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1966C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1966D11
hypocenterC11#10159
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
271. C11#10159semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130791622
C2×#106227062
#130673022
#130670702
#130664542
C11×#19662
#1015911