Finite Group Databasebeta

← #14651496

Subgroups — #14651496

Order 2816.

512 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 93 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#13073101C211yesmaximal, characteristic
2#13071217C211yesmaximal, characteristic
3#13068694C211yesmaximal, characteristic
4#13067150C211yesmaximal, characteristic
5#13067148C211yesmaximal, characteristic
6#13066469C211yesmaximal, characteristic
7C11×#1284C211yesmaximal, characteristic
8C22×C4⋊Dic11C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622824C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622556—21no—
16#10622556—21no—
17#10622555—21no—
18C22⋊C4×Dic11—21no—
19#10622549C412yescomplemented
20#10622542C412yescomplemented
21#10622272—22no—
22#10622267—22no—
23#10622266—22no—
24#10622192—22no—
25#10622105—22no—
26#10622090—22no—
27C23×C4×C11C2311yescharacteristic
28C23×Dic11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×Dic22C2×C411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C42×C11C2×C412yes—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C412yes—
43C2×C4⋊Dic11D412yes—
44#66977—21no—
45#66977—21no—
46#66977—21no—
47#66977—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—22no—
50C2×C4×Dic11—22no—
51C2×#4318—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95D412yes—
57C11⋊#95—22no—
58C11⋊#95—22no—
59C11⋊#95—21no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#9460—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—42no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—22no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C22×Dic11C22⋊C412yes—
88C22×Dic11C22⋊C412yes—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—42no—
92C11×M16—42no—
93C2×C8×C11—41no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C42×C11—42no—
97C22⋊Dic11—42no—
98C22⋊Dic11—41no—
99C22⋊Dic11—41no—
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—82no—
109C4×Dic11—82no—
110#4318—42no—
111C2×C11⋊C8—41no—
112#2503—111no—
113#2313—111no—
114#1821—111no—
115#1511—111no—
116#1511—111no—
117#1284—111no—
118#1284D1111yescharacteristic
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—41no—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11#12011yescharacteristic
124C23×C11#12311yescharacteristic
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156Dic22—81no—
157Dic22—81no—
158C8×C11—81no—
159C11⋊C8—81no—
160C2×C22⋊Q8—111no—
161C22×C4⋊C4—111no—
162#407—111no—
163#407C2×D1111yescharacteristic
164#400—222no—
165#391—112no—
166#387—222no—
167#387—222no—
168#382—112no—
169#381—111no—
170#381—221no—
171#381—221no—
172#381C2×D1111yescharacteristic
173#380—221no—
174C4×C22⋊C4—221no—
175C4×C22⋊C4C2×D1111yescharacteristic
176#343—222no—
177#328—222no—
178#328—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—44no—
187C22×C11#38611yescharacteristic
188C22×C11#41012yes—
189C22×C11#45512yes—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—82no—
195C4×C11—82no—
196Dic11—42no—
197Dic11—42no—
198Dic11—82no—
199Dic11—81no—
200Dic11—81no—
201C22×Q8—111no—
202C23×C4—111no—
203C23×C4—111no—
204C23×C4C22×D1111yescharacteristic
205C2×M16—21no—
206C2×M16—221no—
207C22⋊Q8—221no—
208C22⋊Q8—221no—
209C22⋊Q8—221no—
210C22⋊Q8—221no—
211C2×C4⋊C4—112no—
212C2×C4⋊C4—112no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—222no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C42—222no—
225C2×C42C4×D1112yes—
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—221no—
229C22⋊C8—221no—
230#95—21no—
231#95—21no—
232#95—112no—
233#95—222no—
234#95—222no—
235#95—222no—
236#95—222no—
237#95—222no—
238#95—222no—
239#95—221no—
240#95D4412yes—
241C2×C11—22no—
242C2×C11—22no—
243C2×C11—41no—
244C2×C11#188511yescharacteristic
245C2×C11#189911yescharacteristic
246C2×C11#191211yescharacteristic
247C24D4×D1111yescharacteristic
248C2×Q8—221no—
249C2×Q8—221no—
250C2×Q8—442no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—42no—
254C22×C4—112no—
255C22×C4—112no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—222no—
263C22×C4—442no—
264C22×C4—442no—
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4C2×D4411yescharacteristic
267C22×C4#433911yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4#434311yescharacteristic
271M16—42no—
272M16—442no—
273C2×C8—41no—
274C2×C8—441no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—882no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—442no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C42—42no—
290C42—882no—
291C11#946011yescharacteristic, complemented, Sylow
292C23—22no—
293C23—22no—
294C23—41no—
295C23C22⋊C4×D1111yescharacteristic
296C23#6693511yescharacteristic
297C23#6694711yescharacteristic
298Q8—881no—
299Q8—881no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4C4×D4411yescharacteristic
328C2×C4#6693711yescharacteristic
329C2×C4#6694611yescharacteristic
330C2×C4#6694811yescharacteristic
331C8—81no—
332C8—881no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—44no—
341C22#1062227811yescharacteristic
342C22#1062235312yes—
343C22#1062243812yes—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—82no—
350C4—442no—
351C4—442no—
352C4—882no—
353C4—881no—
354C4—881no—
355C2—22no—
356C2—22no—
357C2—41no—
358C2#1306900311yescharacteristic
359C2#1306907311yescharacteristic
360C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9460
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
19. #10622549C4semidirect
20. #10622542C4semidirect
291. C11#9460semidirect

Maximal subgroups

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

subgroupindex
#130731012
#130712172
#130686942
#130671502
#130671482
#130664692
C11×#12842
#946011