Finite Group Databasebeta

← #14655553

Subgroups — #14655553

Order 2816.

544 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079760C211yesmaximal, characteristic, complemented
2#13078990C211yesmaximal, characteristic
3#13069461C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic
5#13067072C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#486—22no—
12C11×#486—22no—
13C2×C11×#102—22no—
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66900—22no—
16#10622828—22no—
17#10622707—22no—
18#10622706—21no—
19#10622692—21no—
20#10622684—22no—
21#10622683—21no—
22#10622683—21no—
23#10622584—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27#10622182—22no—
28#10622094—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127D412yes—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D412yes—
44C2×C42×C11C2311yescharacteristic
45#66979—21no—
46#66977—21no—
47#66977—21no—
48C2×#4318—21no—
49C2×#4318D412yes—
50#66923—21no—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×#102—28no—
56C4×C8×C11—21no—
57C4×C8×C11D412yes—
58#66900—44no—
59#66896—24no—
60#66896—24no—
61C22⋊(C11⋊C8)—21no—
62#66874—24no—
63#66872—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#10151—111nomaximal, Sylow
71C24×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—42no—
75C2×Q8×C11—42no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—44no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—82no—
86C22×C4×C11—22no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×C8×C11—22no—
93C2×C8×C11—42no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—41no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—41no—
110#4318—22no—
111#4318—22no—
112#4318—42no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116#3229—111no—
117#3138—111no—
118C2×#486D1111yescharacteristic
119#1966—111no—
120#1545—111no—
121#1493—111no—
122#1278—111no—
123C23×C11—42no—
124C23×C11—82no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11#12111yescharacteristic
128Q8×C11—82no—
129Q8×C11—81no—
130Q8×C11—81no—
131D4×C11—44no—
132D4×C11—44no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—42no—
141C2×C4×C11—44no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11#13512yes—
149C2×C4×C11AGL(1,ℤ/8)12yes—
150C2×Dic11—41no—
151C2×Dic11—41no—
152Dic22—42no—
153Dic22—42no—
154C8×C11—42no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158#533—111no—
159C2×C4⋊Q8C2×D1111yescharacteristic
160C2×#127C2×D1111yescharacteristic
161#498—221no—
162#490—222no—
163#487—221no—
164#486—22no—
165#486—22no—
166#486—221no—
167#486—221no—
168#483—222no—
169#475—222no—
170#431—111no—
171#423—111no—
172#418—222no—
173C2×#102—22no—
174C2×#101—222no—
175C4×M16—111no—
176C2×C4×C8C2×D1111yescharacteristic
177#331—222no—
178Q8⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—164no—
185C22×C11#39211yescharacteristic
186C22×C11#46312yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11#44912yes—
191C4×C11#45412yes—
192C4×C11#47112yes—
193C4×C11#49511yescharacteristic
194C4×C11#49611yescharacteristic
195Dic11—81no—
196Dic11—81no—
197C22×Q8—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C2×M16—112no—
202C2×M16—221no—
203C22×C8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—111no—
209C4⋊Q8—111no—
210#127—21no—
211#127—21no—
212#127—21no—
213#127C22⋊D1112yes—
214#125—221no—
215C22⋊Q8—221no—
216C22⋊Q8—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219#117—221no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C22⋊D1112yes—
222C2×C42C22×D1111yescharacteristic
223#106—224no—
224C4⋊C8—112no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227#103—224no—
228#102—28no—
229#102—224no—
230#102—224no—
231#101—444no—
232C22⋊C8—221no—
233#97—221no—
234C4×C8—21no—
235C4×C8—221no—
236C4×C8—221no—
237C4×C8C22⋊D1112yes—
238C2×C11—22no—
239C2×C11—162no—
240C2×C11#200311yescharacteristic
241C2×C11#201211yescharacteristic
242C2×C11#201911yescharacteristic
243C24—41no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—221no—
249C2×Q8—221no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—44no—
254C2×D4—42no—
255C2×D4—42no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—82no—
260C22×C4—22no—
261C22×C4D4×D1111yescharacteristic
262C22×C4#434111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264M16—222no—
265M16—222no—
266M16—442no—
267C2×C8—22no—
268C2×C8—42no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—441no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C22⋊C4—441no—
283C42—441no—
284C42D4×D1111yescharacteristic
285C42D4×D1111yescharacteristic
286C42C2×C22⋊D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C11#1015111yescharacteristic, complemented, Sylow
289C23—42no—
290C23—82no—
291C23—82no—
292C23—82no—
293C23#6699211yescharacteristic
294Q8—81no—
295Q8—81no—
296Q8—82no—
297Q8—442no—
298Q8—442no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—81no—
303D4—81no—
304D4—82no—
305D4—82no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4#6696412yes—
313C2×C4#6696512yes—
314C2×C4#6699011yescharacteristic
315C2×C4#6699011yescharacteristic
316C2×C4#6699111yescharacteristic
317C2×C4#6699211yescharacteristic
318C2×C4#6699311yescharacteristic
319C2×C4#6700611yescharacteristic
320C8—42no—
321C8—442no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22#1062276612yes—
331C22#1062283611yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—881no—
336C4—881no—
337C4#1062267512yes—
338C4#1062276711yescharacteristic
339C4#1062276811yescharacteristic
340C4#1062277112yes—
341C4#1062279012yes—
342C2—22no—
343C2—162no—
344C2#1306963811yescharacteristic
345C2#1306969111yescharacteristic
346C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenterC2×#486D11
hypocenterC11#10151
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13079760C2semidirect
3. #13069461C2semidirect
5. #13067072C2semidirect
6. #13066453C2semidirect
288. C11#10151semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130789902
#130694612
#130672842
#130670722
#130664532
C2×C11×#4862
#1015111