Finite Group Databasebeta

← #14655386

Subgroups — #14655386

Order 2816.

420 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079818C211yesmaximal, characteristic
2#13079169C211yesmaximal, characteristic
3#13067089C211yesmaximal, characteristic
4#13067037C211yesmaximal, characteristic
5#13066973C211yesmaximal, characteristic
6#13066489C211yesmaximal, characteristic
7C11×#3237C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#533C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#501—21no—
12C11×#491—21no—
13C11×#485—22no—
14C11×#477—21no—
15C11×#475—21no—
16C11×#432C2211yescharacteristic
17#10622695—21no—
18#10622693—21no—
19#10622693—21no—
20#10622693—21no—
21#10622677—22no—
22#10622657—21no—
23#10622656—21no—
24#10622635—22no—
25#10622608—21no—
26#10622608—21no—
27#10622539C2211yescharacteristic
28#10622538C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622107—22no—
33C11×C4⋊Q8D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C11×#117—21no—
48C11×#117—21no—
49C2×C42×C11C2311yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C2×#4318—21no—
55#66923—21no—
56#66923—21no—
57#66923—21no—
58#66923—21no—
59C11×#107—22no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×#103—22no—
63C11×#103—22no—
64C11×C22⋊C8D412yes—
65C11×#97—21no—
66#66899—22no—
67#66899—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66872—22no—
71#66872—22no—
72#66872—22no—
73#66871—22no—
74#66871—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78#66867—21no—
79#66867—21no—
80C4×C11⋊C8—21no—
81C4×C11⋊C8D412yes—
82#10127—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×C8×C11—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121#4318—24no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#3237D1111yescharacteristic
126#3236—111no—
127#3166—111no—
128#1497—111no—
129#1485—111no—
130#1470—111no—
131#1291—111no—
132C23×C11#12111yescharacteristic
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—42no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C2×Dic11—42no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—81no—
154C8×C11—42no—
155C11⋊C8—24no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158#533C2×D1111yescharacteristic
159#533C2×D1111yescharacteristic
160C2×#125—111no—
161#501—21no—
162#501—221no—
163#501—221no—
164#501—221no—
165#499—222no—
166#491—21no—
167#491—221no—
168#485—22no—
169#484—221no—
170#483—221no—
171#479—222no—
172#477—21no—
173#475—21no—
174#432—111no—
175#432C2×D1111yescharacteristic
176#431—111no—
177#428—221no—
178#428—221no—
179C4×M16—111no—
180Q8⋊C8—222no—
181Q8⋊C8—222no—
182#324—222no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11#39211yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11#45612yes—
197Dic11—81no—
198Dic11—81no—
199C2×M16—221no—
200C4⋊Q8C22⋊D1111yescharacteristic
201C4⋊Q8C22⋊D1111yescharacteristic
202C4⋊Q8C22⋊D1111yescharacteristic
203C4⋊Q8C22⋊D1111yescharacteristic
204#125—21no—
205#125—21no—
206#125—221no—
207#125—221no—
208#125—221no—
209#125—221no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218#117—21no—
219#117—21no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C42C22×D1111yescharacteristic
225#107—22no—
226#107—222no—
227#107—222no—
228#107—222no—
229#106—22no—
230#106—222no—
231#106—222no—
232#106—222no—
233C4⋊C8—21no—
234C4⋊C8—112no—
235C4⋊C8—221no—
236#103—22no—
237#103—22no—
238#103—222no—
239#103—222no—
240C22⋊C8—221no—
241C22⋊C8—221no—
242C22⋊C8C22⋊D1112yes—
243#97—21no—
244#97—221no—
245#97—221no—
246C4×C8—112no—
247C4×C8—221no—
248C2×C11—41no—
249C2×C11#200511yescharacteristic
250C2×C11#200911yescharacteristic
251C2×C11#201711yescharacteristic
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4D4×D1111yescharacteristic
259C22×C4#434111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261M16—224no—
262C2×C8—22no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—441no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42—41no—
289C42—41no—
290C42D4×D1111yescharacteristic
291C42D4×D1111yescharacteristic
292C42C2×C22⋊D1111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C11#1012711yescharacteristic, complemented, Sylow
295C23#6699111yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—42no—
299Q8—42no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—442no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—881no—
311C2×C4#6699011yescharacteristic
312C2×C4#6699011yescharacteristic
313C2×C4#6699211yescharacteristic
314C2×C4#6699211yescharacteristic
315C2×C4#6699311yescharacteristic
316C2×C4#6700611yescharacteristic
317C8—42no—
318C8—224no—
319C8—442no—
320C8—881no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22#1062283611yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—881no—
335C4—881no—
336C4#1062281812yes—
337C2—41no—
338C2#1306964911yescharacteristic
339C2#1306967611yescharacteristic
340C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3237C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3237D11
hypocenterC11#10127
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3237

Complements

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

NH ≅ G/Ntype
294. C11#10127semidirect

Maximal subgroups

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

subgroupindex
#130798182
#130791692
#130670892
#130670372
#130669732
#130664892
C11×#32372
#1012711