Finite Group Databasebeta

← #14655406

Subgroups — #14655406

Order 2816.

520 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079806C211yesmaximal, characteristic, complemented
2#13079534C211yesmaximal, characteristic
3#13067330C211yesmaximal, characteristic, complemented
4#13067226C211yesmaximal, characteristic, complemented
5#13066972C211yesmaximal, characteristic, complemented
6#13066515C211yesmaximal, characteristic, complemented
7C2×C11×#490C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#490—22no—
12C11×#490—22no—
13C2×C11×#102—21no—
14C2×C11×#102—21no—
15C2×C11×#97C2211yescharacteristic
16#10622830—22no—
17#10622686—21no—
18#10622685—22no—
19#10622683—21no—
20#10622680—21no—
21#10622679—22no—
22#10622678—21no—
23#10622581—21no—
24#10622580—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622182—22no—
29#10622166—22no—
30#10622102—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C2×#4339—21no—
35C22×C8×C11—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127D412yes—
40C11×#125—21no—
41C11×#125—21no—
42C11×#125—21no—
43C11×#125—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×#4323—24no—
50#66983—21no—
51#66983—21no—
52#66928—21no—
53#66927D411yescharacteristic
54C4×D44—21no—
55C4×D44—21no—
56#66922D411yescharacteristic
57C11×#102—24no—
58C11×#102—24no—
59C11×#97—21no—
60C11×#97D412yes—
61#66896—24no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)D412yes—
65#66873—22no—
66#66873—22no—
67#66872—22no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75#10130—111nomaximal, Sylow
76C24×C11—41no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—82no—
85C2×D4×C11—82no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—41no—
92#4339—82no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×C4×D11—41no—
97C2×Dic22—21no—
98C2×C8×C11—22no—
99C2×C8×C11—42no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112#4323—84no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3234—111no—
121#3205—111no—
122C2×#490D1111yescharacteristic, complemented
123#1555—111no—
124#1530—111no—
125#1470—111no—
126#1302—111no—
127C23×C11—42no—
128C23×C11—82no—
129C23×C11—82no—
130C23×C11—82no—
131C23×C11#12111yescharacteristic
132C22×D11—41no—
133D4×C11—44no—
134D4×C11—44no—
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—82no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—81no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C22⋊D11—82no—
153C2×Dic11—41no—
154D44—42no—
155D44—42no—
156D44—81no—
157C4×D11—82no—
158Dic22—81no—
159C8×C11—42no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163#532—111no—
164C2×#127C2×D1111yescharacteristic
165C2×#125C2×D1111yescharacteristic
166#501—221no—
167#493—221no—
168#490—22no—
169#490—22no—
170#490—221no—
171#486—221no—
172#481—221no—
173#480—221no—
174#478—222no—
175#459—222no—
176#447—222no—
177#432—111no—
178#432—111no—
179#431—111no—
180C2×#102—21no—
181C2×#102—21no—
182C2×#97C2×D1111yescharacteristic
183#331—222no—
184#329—222no—
185#324—222no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—164no—
192C22×C11#39211yescharacteristic
193C22×C11#47212yes—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—81no—
203C4×C11—81no—
204C4×C11#45412yes—
205Dic11—81no—
206C2×#41—221no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C2×D8—224no—
211C22×C8—21no—
212C4⋊Q8—111no—
213#127—21no—
214#127—21no—
215#127—21no—
216#127—111no—
217#127C22⋊D1112yes—
218#125—21no—
219#125—21no—
220#125—21no—
221#125—21no—
222#124—221no—
223#121—221no—
224#121—221no—
225C4×D4—221no—
226C4×D4—221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C22⋊D1111yescharacteristic
230C2×C4⋊C4C22⋊D1111yescharacteristic
231C2×C42C22×D1111yescharacteristic
232#107—222no—
233#106—222no—
234C4⋊C8—112no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237#102—24no—
238#102—24no—
239#102—222no—
240#102—222no—
241#102—224no—
242C22⋊C8—112no—
243C22⋊C8—221no—
244C22⋊C8—221no—
245#97—21no—
246#97—221no—
247#97—221no—
248#97C22⋊D1112yes—
249C4×C8—221no—
250C2×C11—22no—
251C2×C11—162no—
252C2×C11#200311yescharacteristic
253C2×C11#200811yescharacteristic
254C2×C11#201811yescharacteristic
255D11—161no—
256C24—41no—
257#41—882no—
258C2×Q8—221no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—44no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—82no—
267C2×D4—82no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—441no—
275C22×C4D4×D1111yescharacteristic
276C22×C4#434111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278D8—884no—
279C2×C8—22no—
280C2×C8—42no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—441no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C42D4×D1111yescharacteristic
297C42D4×D1111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C42C2×C22⋊D1111yescharacteristic
300C11#1013011yescharacteristic, complemented, Sylow
301C23—42no—
302C23—82no—
303C23—82no—
304C23—82no—
305C23—441no—
306C23#6699211yescharacteristic
307Q8—881no—
308D4—44no—
309D4—44no—
310D4—82no—
311D4—82no—
312D4—82no—
313D4—82no—
314D4—442no—
315D4—442no—
316D4—881no—
317D4—882no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—441no—
326C2×C4—882no—
327C2×C4#6699011yescharacteristic
328C2×C4#6699011yescharacteristic
329C2×C4#6699111yescharacteristic
330C2×C4#6699211yescharacteristic
331C2×C4#6699311yescharacteristic
332C2×C4#6700611yescharacteristic
333C8—42no—
334C8—442no—
335C8—442no—
336C8—881no—
337C22—21no—
338C22—21no—
339C22—82no—
340C22—82no—
341C22—82no—
342C22—164no—
343C22—881no—
344C22—881no—
345C22—881no—
346C22#1062281212yes—
347C22#1062283611yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—81no—
354C4—81no—
355C4—881no—
356C4#1062267512yes—
357C2—22no—
358C2—162no—
359C2—1761no—
360C2#1306963811yescharacteristic
361C2#1306966711yescharacteristic
362C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#490C2
socleC22×C11#392
prime radical#13079534C2
hypercenterC2×#490D11
hypocenterC11#10130
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. #13079806C2semidirect
3. #13067330C2semidirect
4. #13067226C2semidirect
5. #13066972C2semidirect
6. #13066515C2semidirect
7. C2×C11×#490C2semidirect
122. C2×#490D11semidirect
300. C11#10130semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130795342
#130673302
#130672262
#130669722
#130665152
C2×C11×#4902
#1013011