Finite Group Databasebeta

← #14655920

Subgroups — #14655920

Order 2816.

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

normal subgroups only

This group has 490 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#13079764C211yesmaximal, characteristic
2#13079163C211yesmaximal, characteristic
3#13069561C211yesmaximal, characteristic
4#13069538C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic
6#13066466C211yesmaximal, characteristic
7C11×#3249C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#533C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#477—21no—
12C11×#477—21no—
13C11×#467—22no—
14C11×#462—21no—
15C11×#462—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×#66880—22no—
18#10622694—21no—
19#10622692—21no—
20#10622691—21no—
21#10622691—21no—
22#10622678—22no—
23#10622657—22no—
24#10622634—22no—
25#10622608—22no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622538C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622176—22no—
30#10622170—22no—
31C22×Dic22—21no—
32C2×C11×Q16—22no—
33C22×C8×C11D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C11×#117—21no—
49C11×#117—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4×Dic11—21no—
55C2×#4318D412yes—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60C11×#107—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×#103—22no—
64C11×#103—22no—
65#66899—24no—
66C11⋊#95—21no—
67C22⋊(C11⋊C8)D412yes—
68#66880—44no—
69#66872—24no—
70#66871—24no—
71#66871—24no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10203—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—41no—
85C22×Dic11—41no—
86C2×Dic22—22no—
87C2×Dic22—42no—
88C2×Dic22—42no—
89C2×Dic22—41no—
90C11×Q16—82no—
91C2×C8×C11—22no—
92C2×C8×C11—42no—
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×C11#4111yescharacteristic
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4×Dic11—42no—
120#4318—22no—
121#4318Q1614yescomplemented
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124#3249D1111yescharacteristic
125#3230—111no—
126#3165—111no—
127#1986—111no—
128#1981—111no—
129#1503—111no—
130#1283—111no—
131C23×C11#12711yescharacteristic
132Q8×C11—42no—
133Q8×C11—41no—
134Q8×C11—41no—
135Q8×C11—41no—
136Q8×C11—41no—
137Q8×C11—81no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11C2×Q1612yes—
152C2×C4×C11#13712yes—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—82no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158Dic22—44no—
159Dic22—81no—
160Dic22—81no—
161C8×C11—42no—
162C11⋊C8—24no—
163C11⋊C8—42no—
164#533C2×D1111yescharacteristic
165#533C2×D1111yescharacteristic
166C2×C4⋊Q8—111no—
167#501—222no—
168#500—221no—
169#500—221no—
170#498—221no—
171#487—221no—
172#484—222no—
173#477—21no—
174#477—21no—
175#477—222no—
176#467—22no—
177#462—21no—
178#462—21no—
179#431—111no—
180#428—222no—
181C2×C4⋊C8C2×D1111yescharacteristic
182C2×#103—222no—
183C4×M16—111no—
184C4×C4⋊C4—111no—
185#339—222no—
186#328—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11#39211yescharacteristic
190C22×C11#49411yescharacteristic
191C22×C11#49711yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11#45112yes—
200C4×C11#45311yescharacteristic
201C4×C11#45411yescharacteristic
202C4×C11#46212yes—
203Dic11—82no—
204Dic11—82no—
205C22×Q8—221no—
206C2×Q16—22no—
207C2×M16—112no—
208C22×C8C22⋊D1112yes—
209C4⋊Q8—112no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8C22⋊D1111yescharacteristic
214C4⋊Q8C22⋊D1111yescharacteristic
215C4⋊Q8C22⋊D1111yescharacteristic
216C4⋊Q8C22⋊D1111yescharacteristic
217#125—21no—
218#125—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227#117—21no—
228#117—21no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C42—221no—
233C2×C42C22×D1111yescharacteristic
234#107—22no—
235#107—224no—
236#107—224no—
237#106—224no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—221no—
241#103—22no—
242#103—22no—
243#103—224no—
244#103—444no—
245C22⋊C8—112no—
246#97—221no—
247C4×C8—221no—
248C4×C8—221no—
249#95—221no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#200611yescharacteristic
253C2×C11#200911yescharacteristic
254C2×C11#201611yescharacteristic
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—222no—
260C2×Q8—442no—
261C2×Q8—442no—
262C2×Q8—441no—
263C22×C4—441no—
264C22×C4—441no—
265C22×C4D4×D1111yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268Q16—82no—
269M16—114no—
270M16—222no—
271C2×C8—22no—
272C2×C8—42no—
273C2×C8—222no—
274C2×C8—222no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—222no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42—41no—
296C42—41no—
297C42—442no—
298C42D4×D1111yescharacteristic
299C42#434111yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C11#1020311yescharacteristic, complemented, Sylow
303C23#6699311yescharacteristic
304Q8—42no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308Q8—41no—
309Q8—81no—
310Q8—444no—
311Q8—881no—
312Q8—881no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—882no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4Q16×D1112yes—
326C2×C4#6697112yes—
327C2×C4#6699011yescharacteristic
328C2×C4#6699011yescharacteristic
329C2×C4#6699111yescharacteristic
330C2×C4#6699211yescharacteristic
331C2×C4#6699211yescharacteristic
332C2×C4#6700611yescharacteristic
333C8—42no—
334C8—224no—
335C8—442no—
336C22—21no—
337C22—21no—
338C22#1062279411yescharacteristic
339C22#1062280311yescharacteristic
340C22#1062283611yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—882no—
349C4—882no—
350C4#1062279512yes—
351C4#1062279912yes—
352C4#1062285411yescharacteristic
353C4#1062285811yescharacteristic
354C2—21no—
355C2—21no—
356C2#1306965811yescharacteristic
357C2#1306967311yescharacteristic
358C2#1306971411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3249C2
socleC22×C11#392
prime radicalC23×C11#127
hypercenter#3249D11
hypocenterC11#10203
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
121. #4318Q16semidirect
302. C11#10203semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130791632
#130695612
#130695382
#130671152
#130664662
C11×#32492
#1020311