Finite Group Databasebeta

← #14658094

Subgroups — #14658094

Order 2816.

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

normal subgroups only

This group has 364 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#13078996C211yesmaximal, characteristic
2#13069392C211yesmaximal, characteristic
3#13067304C211yesmaximal, characteristic
4#13067288C211yesmaximal, characteristic
5#13067018C211yesmaximal, characteristic
6#13066466C211yesmaximal, characteristic
7C2×C11×#332C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12#10622838—21no—
13#10622838—21no—
14C2×#66883—21no—
15#10622695—22no—
16#10622694—21no—
17#10622694—21no—
18#10622538C2211yescharacteristic
19#10622537C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21C11×#332—22no—
22#10622190—21no—
23#10622185—22no—
24#10622122—22no—
25#10622120—21no—
26#10622119—21no—
27C22×Q8×C11—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8D412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37#66979—21no—
38#66977—21no—
39#66977—21no—
40C2×#4318—21no—
41C2×#4318D411yescharacteristic
42C2×#4318D411yescharacteristic
43#66923—21no—
44#66922D411yescharacteristic
45#66922D411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8D412yes—
52#66899—22no—
53#66899—22no—
54#66899—22no—
55#66899—22no—
56C22⋊(C11⋊C8)—21no—
57#66883—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61#66867—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10554—111nomaximal, Sylow
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—81no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C22⋊Dic11—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—41no—
98#4318—21no—
99#4318—21no—
100#4318—21no—
101#4318—21no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#3139—111no—
109#1950—111no—
110#1550—111no—
111#1546—111no—
112C2×#332D1111yescharacteristic
113#1481—111no—
114#1283—111no—
115C23×C11#12411yescharacteristic
116Q8×C11—42no—
117Q8×C11—42no—
118Q8×C11—81no—
119Q8×C11—81no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×Dic11—41no—
137C2×Dic11—41no—
138Dic22—41no—
139Dic22—41no—
140Dic22—81no—
141C8×C11—42no—
142C8×C11—81no—
143C11⋊C8—41no—
144C11⋊C8—41no—
145C11⋊C8—81no—
146C11⋊C8—81no—
147#533—111no—
148C2×C4⋊Q8C2×D1111yescharacteristic
149#491—222no—
150#487—221no—
151#487—221no—
152#431—111no—
153C2×#108—221no—
154#423—111no—
155C2×C4⋊C8C2×D1111yescharacteristic
156C2×C4⋊C8C2×D1111yescharacteristic
157#419—221no—
158#419—221no—
159C4×M16—111no—
160#341—221no—
161#333—221no—
162#332—22no—
163#332—221no—
164#332—222no—
165Q8⋊C8—222no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39411yescharacteristic
169C22×C11#48811yescharacteristic
170C22×C11#48911yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—82no—
175C4×C11#44911yescharacteristic
176C4×C11#45211yescharacteristic
177C4×C11#46311yescharacteristic
178C4×C11#46411yescharacteristic
179C4×C11#47111yescharacteristic
180C4×C11#47311yescharacteristic
181Dic11—81no—
182Dic11—81no—
183C22×Q8—21no—
184C2×M16—111no—
185C2×M16—111no—
186C2×M16—221no—
187C22×C8—21no—
188C22×C8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—111no—
193C4⋊Q8—111no—
194C4⋊Q8D4412yes—
195#125—221no—
196C22⋊Q8—221no—
197C22⋊Q8—221no—
198C4×Q8—221no—
199C4×Q8—221no—
200#117—221no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C42C22×D1111yescharacteristic
204#108—442no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8C22⋊D1112yes—
212#103—222no—
213#103—222no—
214#103—222no—
215#103—222no—
216C22⋊C8—221no—
217#97—221no—
218C4×C8—221no—
219C4×C8—221no—
220C2×C11—21no—
221C2×C11—21no—
222C2×C11#204211yescharacteristic
223C2×C11#204911yescharacteristic
224C2×C11#205211yescharacteristic
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—221no—
232C2×Q8—221no—
233C22×C4—41no—
234C22×C4#433911yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C22×C4#434111yescharacteristic
237M16—221no—
238M16—221no—
239M16—221no—
240M16—221no—
241M16—441no—
242M16—441no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—81no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—441no—
251C2×C8—441no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C22⋊C4—441no—
263C42—441no—
264C42C2×D4411yescharacteristic
265C42D4×D1111yescharacteristic
266C42#434111yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C11#1055411yescharacteristic, complemented, Sylow
269C23#6693811yescharacteristic
270Q8—42no—
271Q8—42no—
272Q8—81no—
273Q8—81no—
274Q8—441no—
275Q8—441no—
276Q8—881no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4#6693511yescharacteristic
286C2×C4#6693611yescharacteristic
287C2×C4#6693911yescharacteristic
288C2×C4#6696411yescharacteristic
289C2×C4#6696511yescharacteristic
290C2×C4#6696811yescharacteristic
291C2×C4#6696911yescharacteristic
292C2×C4#6698311yescharacteristic
293C2×C4#6699111yescharacteristic
294C2×C4#6699211yescharacteristic
295C8—42no—
296C8—81no—
297C8—441no—
298C8—441no—
299C8—881no—
300C8—881no—
301C22—21no—
302C22—21no—
303C22#1062237811yescharacteristic
304C22#1062238111yescharacteristic
305C22#1062257411yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—82no—
310C4—881no—
311C4—881no—
312C4#1062239411yescharacteristic
313C4#1062239611yescharacteristic
314C4#1062276611yescharacteristic
315C4#1062277911yescharacteristic
316C4#1062279011yescharacteristic
317C4#1062280511yescharacteristic
318C2—21no—
319C2—21no—
320C2#1306985611yescharacteristic
321C2#1306989511yescharacteristic
322C2#1306991611yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenterC2×#332D11
hypocenterC11#10554
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
268. C11#10554semidirect

Maximal subgroups

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

subgroupindex
#130789962
#130693922
#130673042
#130672882
#130670182
#130664662
C2×C11×#3322
#1055411