Finite Group Databasebeta

← #14658090

Subgroups — #14658090

Order 2816.

364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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#13069391C211yesmaximal, characteristic
2#13067306C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic
5#13067019C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic
7C11×#3139C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#491—22no—
11C11×#487—21no—
12C11×#487—21no—
13C11×#419—21no—
14C11×#419—21no—
15C4×C11×M16C2211yescharacteristic
16C2×#66886—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622196—21no—
22#10622185—22no—
23#10622185—21no—
24#10622185—22no—
25#10622184—21no—
26Q8⋊(C11⋊C8)—22no—
27C22×Q8×C11—21no—
28C2×C11×M16D411yescharacteristic
29C2×C11×M16D411yescharacteristic
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C11×#117—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4318—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C11×#103—22no—
49C11×#103—22no—
50C11×#103—22no—
51C11×#103—22no—
52C11×#97—21no—
53C4×C8×C11—21no—
54C22⋊(C11⋊C8)—21no—
55#66886—42no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63C4×C11⋊C8—21no—
64#10554—111nomaximal, Sylow
65C2×Q8×C11—22no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C11×M16—21no—
78C11×M16—21no—
79C11×M16—21no—
80C11×M16—21no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
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×C11#4111yescharacteristic
99#4318—41no—
100#4318—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—81no—
108#3139D1111yescharacteristic
109#1950—111no—
110#1550—111no—
111#1546—111no—
112C2×#332—111no—
113#1481—111no—
114#1283—111no—
115C23×C11#12411yescharacteristic
116Q8×C11—42no—
117Q8×C11—42no—
118Q8×C11—41no—
119Q8×C11—41no—
120Q8×C11—81no—
121Q8×C11—81no—
122Q8×C11—81no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C8×C11—41no—
142C8×C11—41no—
143C11⋊C8—42no—
144C11⋊C8—81no—
145C11⋊C8—81no—
146C11⋊C8—81no—
147#533C2×D1111yescharacteristic
148C2×C4⋊Q8C2×D1111yescharacteristic
149#491—22no—
150#487—21no—
151#487—21no—
152#431—111no—
153C2×#108—221no—
154#423—111no—
155C2×C4⋊C8—111no—
156C2×C4⋊C8—111no—
157#419—21no—
158#419—21no—
159C4×M16C2×D1111yescharacteristic
160#341—221no—
161#333—221no—
162#332—222no—
163#332—222no—
164#332—221no—
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—82no—
177C4×C11#44911yescharacteristic
178C4×C11#45211yescharacteristic
179C4×C11#46311yescharacteristic
180C4×C11#46411yescharacteristic
181C4×C11#47111yescharacteristic
182C4×C11#47311yescharacteristic
183C22×Q8—21no—
184C2×M16—221no—
185C2×M16C22⋊D1111yescharacteristic
186C2×M16C22⋊D1111yescharacteristic
187C22×C8—221no—
188C22×C8—221no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8C22⋊D1112yes—
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—21no—
202C2×C4⋊C4—21no—
203C2×C42C22×D1111yescharacteristic
204#108—442no—
205C4⋊C8—112no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#103—22no—
213#103—22no—
214#103—22no—
215#103—22no—
216C22⋊C8—221no—
217#97—21no—
218C4×C8—21no—
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—22no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C22×C4—41no—
234C22×C4#434111yescharacteristic
235C22×C4#434111yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237M16—21no—
238M16—21no—
239M16—21no—
240M16—21no—
241M16—441no—
242M16—441no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—222no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—881no—
252C4⋊C4—22no—
253C4⋊C4—21no—
254C4⋊C4—22no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C22⋊C4—41no—
263C42—41no—
264C42D4×D1111yescharacteristic
265C42#434111yescharacteristic
266C42C2×C22⋊D1111yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C11#1055411yescharacteristic, complemented, Sylow
269C23#6698911yescharacteristic
270Q8—41no—
271Q8—41no—
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276Q8—81no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4#6698811yescharacteristic
286C2×C4#6698811yescharacteristic
287C2×C4#6699111yescharacteristic
288C2×C4#6699211yescharacteristic
289C2×C4#6699211yescharacteristic
290C2×C4#6700211yescharacteristic
291C2×C4#6700311yescharacteristic
292C2×C4#6700311yescharacteristic
293C2×C4#6700411yescharacteristic
294C2×C4#6700611yescharacteristic
295C8—41no—
296C8—41no—
297C8—442no—
298C8—881no—
299C8—881no—
300C8—881no—
301C22—21no—
302C22—21no—
303C22#1062266811yescharacteristic
304C22#1062266911yescharacteristic
305C22#1062283511yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—82no—
310C4—81no—
311C4—81no—
312C4#1062266711yescharacteristic
313C4#1062267011yescharacteristic
314C4#1062281611yescharacteristic
315C4#1062281711yescharacteristic
316C4#1062285111yescharacteristic
317C4#1062285211yescharacteristic
318C2—21no—
319C2—21no—
320C2#1306985211yescharacteristic
321C2#1306989311yescharacteristic
322C2#1306991211yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3139C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenter#3139D11
hypocenterC11#10554
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

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
#130693912
#130673062
#130672882
C2×#106221852
#130670192
#130664672
C11×#31392
#1055411