Finite Group Databasebeta

← #14658091

Subgroups — #14658091

Order 2816.

364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078998C211yesmaximal, characteristic
2#13069389C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic
4C2×#10622124C211yesmaximal, characteristic
5#13067019C211yesmaximal, characteristic
6#13066466C211yesmaximal, characteristic
7C11×#1550C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66886—21no—
13#10622706—21no—
14#10622706—21no—
15#10622682—22no—
16#10622617—21no—
17#10622617—21no—
18#10622538C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21C11×#333—21no—
22C11×#332—21no—
23#10622196—21no—
24Q8⋊(C11⋊C8)—22no—
25#10622124—22no—
26#10622120—22no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8D411yescharacteristic
31C11×C4⋊Q8D411yescharacteristic
32C11×#125—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C11×#117—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×#4318D411yescharacteristic
42C2×#4318D411yescharacteristic
43C22×C11⋊C8—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922D412yes—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C22⋊(C11⋊C8)—21no—
53#66886—42no—
54#66874—22no—
55#66874—22no—
56#66874—22no—
57#66874—22no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61#66867—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10554—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×Dic11—41no—
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C11×M16—41no—
78C11×M16—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—81no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98#4318—21no—
99#4318—21no—
100#4318—21no—
101#4318—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#3139—111no—
109#1950—111no—
110#1550D1111yescharacteristic
111#1546—111no—
112C2×#332—111no—
113#1481—111no—
114#1283—111no—
115C23×C11#12411yescharacteristic
116Q8×C11—41no—
117Q8×C11—41no—
118Q8×C11—81no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×Dic11—42no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137Dic22—42no—
138Dic22—42no—
139Dic22—81no—
140Dic22—81no—
141C8×C11—81no—
142C8×C11—81no—
143C11⋊C8—41no—
144C11⋊C8—41no—
145C11⋊C8—42no—
146C11⋊C8—81no—
147#533C2×D1111yescharacteristic
148C2×C4⋊Q8—111no—
149#491—222no—
150#487—221no—
151#487—221no—
152#431—111no—
153C2×#108—221no—
154#423C2×D1111yescharacteristic
155C2×C4⋊C8—111no—
156C2×C4⋊C8C2×D1111yescharacteristic
157#419—221no—
158#419—221no—
159C4×M16—111no—
160#341—221no—
161#333—21no—
162#332—21no—
163#332—222no—
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—81no—
175C4×C11—81no—
176C4×C11#44911yescharacteristic
177C4×C11#45211yescharacteristic
178C4×C11#46311yescharacteristic
179C4×C11#46411yescharacteristic
180C4×C11#47111yescharacteristic
181C4×C11#47311yescharacteristic
182Dic11—82no—
183C22×Q8—221no—
184C2×M16—21no—
185C2×M16—111no—
186C2×M16—111no—
187C22×C8—21no—
188C22×C8—221no—
189C4⋊Q8—112no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193C4⋊Q8C22⋊D1111yescharacteristic
194C4⋊Q8C22⋊D1111yescharacteristic
195#125—21no—
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200#117—21no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42C22×D1111yescharacteristic
204#108—442no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—112no—
210C4⋊C8—221no—
211C4⋊C8—221no—
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—21no—
226C2×Q8—21no—
227C2×Q8—222no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C22×C4—441no—
234C22×C4#433911yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C22×C4#434111yescharacteristic
237M16—41no—
238M16—41no—
239M16—221no—
240M16—221no—
241M16—221no—
242M16—221no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—81no—
246C2×C8—222no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—441no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C22⋊C4—41no—
263C42—41no—
264C42#433911yescharacteristic
265C42D4×D1111yescharacteristic
266C42D4×D1111yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C11#1055411yescharacteristic, complemented, Sylow
269C23#6693811yescharacteristic
270Q8—41no—
271Q8—41no—
272Q8—81no—
273Q8—442no—
274Q8—442no—
275Q8—881no—
276Q8—881no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—442no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4#6693611yescharacteristic
286C2×C4#6693711yescharacteristic
287C2×C4#6693711yescharacteristic
288C2×C4#6696711yescharacteristic
289C2×C4#6696911yescharacteristic
290C2×C4#6697111yescharacteristic
291C2×C4#6697211yescharacteristic
292C2×C4#6698211yescharacteristic
293C2×C4#6699011yescharacteristic
294C2×C4#6699211yescharacteristic
295C8—81no—
296C8—81no—
297C8—441no—
298C8—441no—
299C8—442no—
300C8—881no—
301C22—21no—
302C22—21no—
303C22#1062240811yescharacteristic
304C22#1062241311yescharacteristic
305C22#1062257211yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—882no—
312C4#1062241111yescharacteristic
313C4#1062243211yescharacteristic
314C4#1062278511yescharacteristic
315C4#1062280011yescharacteristic
316C4#1062281311yescharacteristic
317C4#1062281711yescharacteristic
318C2—21no—
319C2—21no—
320C2#1306985311yescharacteristic
321C2#1306989611yescharacteristic
322C2#1306991311yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1550C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenter#1550D11
hypocenterC11#10554
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

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
#130789982
#130693892
#130672892
C2×#106221242
#130670192
#130664662
C11×#15502
#1055411