Finite Group Databasebeta

← #14655656

Subgroups — #14655656

Order 2816.

476 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079764C211yesmaximal, characteristic
2#13079163C211yesmaximal, characteristic
3C2×#10622295C211yesmaximal, characteristic
4#13069604C211yesmaximal, characteristic
5#13067298C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic
7C11×#1493C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66882—22no—
14#10622694—21no—
15#10622692—21no—
16#10622691—21no—
17#10622691—21no—
18#10622678—22no—
19#10622657—22no—
20#10622634—22no—
21#10622608—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622295—22no—
25#10622295—22no—
26C11×Q8⋊C8—22no—
27#10622192—22no—
28#10622119—22no—
29C22×Dic22—21no—
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×#125—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C11×#117—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D412yes—
46C2×#4318D412yes—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C4×C8×C11—21no—
58C4×C8×C11D412yes—
59#66899—24no—
60C22⋊(C11⋊C8)—21no—
61#66882—28no—
62#66872—24no—
63#66871—24no—
64#66871—24no—
65C4⋊(C11⋊C8)D412yes—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69#10165—111nomaximal, Sylow
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×Dic11—22no—
76C22×Dic11—41no—
77C2×Dic22—22no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—82no—
82C2×Dic22—82no—
83C11×M16—42no—
84C2×C8×C11—24no—
85C2×C8×C11—22no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C4⋊Dic11—22no—
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11—22no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107#4318—22no—
108#4318Q1614yes—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111#3230—111no—
112#3165—111no—
113C2×#500—111no—
114#1997—111no—
115#1548—111no—
116#1493D1111yescharacteristic
117#1278—111no—
118C23×C11#12111yescharacteristic
119Q8×C11—42no—
120Q8×C11—42no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12711yescharacteristic
131C2×C4×C11C2×Q1612yes—
132C2×C4×C11#13712yes—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—82no—
136C2×Dic11—82no—
137Dic22—82no—
138Dic22—82no—
139Dic22—82no—
140Dic22—82no—
141C8×C11—24no—
142C8×C11—81no—
143C11⋊C8—24no—
144C11⋊C8—42no—
145#533C2×D1111yescharacteristic
146C2×C4⋊Q8—111no—
147C2×C4⋊Q8—111no—
148#501—222no—
149#500—222no—
150#500—221no—
151#500—221no—
152#500—222no—
153#498—221no—
154#487—221no—
155#484—222no—
156#477—222no—
157#431—111no—
158#428—222no—
159C2×#107—222no—
160#423C2×D1111yescharacteristic
161C4×M16—111no—
162C2×C4×C8C2×D1111yescharacteristic
163#343—222no—
164#333—222no—
165Q8⋊C8—22no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39211yescharacteristic
169C22×C11#46212yes—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—81no—
173C4×C11—81no—
174C4×C11#45112yes—
175C4×C11#45612yes—
176C4×C11#47212yes—
177C4×C11#49411yescharacteristic
178C4×C11#49711yescharacteristic
179Dic11—82no—
180Dic11—82no—
181C22×Q8—221no—
182C22×Q8—221no—
183C2×M16—21no—
184C2×M16—112no—
185C22×C8—21no—
186C4⋊Q8—112no—
187C4⋊Q8—221no—
188C4⋊Q8—221no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8D4411yescharacteristic
195C4⋊Q8D4411yescharacteristic
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201#117—21no—
202C2×C4⋊C4—112no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C42C22×D1111yescharacteristic
207#107—224no—
208#107—224no—
209#107—228no—
210#106—224no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—112no—
214#103—224no—
215C22⋊C8—221no—
216#97—221no—
217C4×C8—21no—
218C4×C8—221no—
219C4×C8—221no—
220C4×C8C22⋊D1112yes—
221C2×C11—22no—
222C2×C11#200511yescharacteristic
223C2×C11#201611yescharacteristic
224C2×C11#201811yescharacteristic
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—222no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—882no—
232C2×Q8—882no—
233C22×C4—222no—
234C22×C4—441no—
235C22×C4#433911yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C22×C4D4×D1111yescharacteristic
238M16—42no—
239M16—114no—
240M16—222no—
241C2×C8—24no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—222no—
245C2×C8—222no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—222no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—222no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—41no—
261C42—41no—
262C42C2×D4411yescharacteristic
263C42D4×D1111yescharacteristic
264C42D4×D1111yescharacteristic
265C42C2×C22⋊D1111yescharacteristic
266C11#1016511yescharacteristic, complemented, Sylow
267C23#6693711yescharacteristic
268Q8—42no—
269Q8—42no—
270Q8—882no—
271Q8—882no—
272Q8—882no—
273Q8—882no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—882no—
281C2×C4—882no—
282C2×C4#6693511yescharacteristic
283C2×C4#6693511yescharacteristic
284C2×C4#6693711yescharacteristic
285C2×C4#6696812yes—
286C2×C4Q16×D1112yes—
287C2×C4#6698311yescharacteristic
288C2×C4#6699011yescharacteristic
289C2×C4#6699311yescharacteristic
290C8—24no—
291C8—81no—
292C8—224no—
293C8—442no—
294C22—21no—
295C22—21no—
296C22#1062240612yes—
297C22#1062257311yescharacteristic
298C4—21no—
299C4—21no—
300C4—81no—
301C4—81no—
302C4—882no—
303C4—882no—
304C4#1062242112yes—
305C4#1062243912yes—
306C4#1062275512yes—
307C4#1062278011yescharacteristic
308C4#1062279411yescharacteristic
309C2—22no—
310C2#1306965111yescharacteristic
311C2#1306971711yescharacteristic
312C2#1306972511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1493C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1493D11
hypocenterC11#10165
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
266. C11#10165semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130791632
C2×#106222952
#130696042
#130672982
#130664532
C11×#14932
#1016511