Finite Group Databasebeta

← #14651501

Subgroups — #14651501

Order 2816.

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

normal subgroups only

This group has 528 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#13073094C211yesmaximal, 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#10622563—21no—
16#10622563—21no—
17#10622555—21no—
18C22⋊C4×Dic11—21no—
19#10622548C412yescomplemented
20#10622542C412yescomplemented
21#10622274—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⋊Dic11—22no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4⋊Dic11C2×C412yes—
45C2×C4⋊Dic11D412yes—
46#66977—21no—
47#66977—21no—
48#66977—21no—
49#66977—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—22no—
52C2×C4×Dic11—22no—
53C2×#4318—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95D412yes—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—21no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#9461—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—81no—
86C22×Dic11—81no—
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—24no—
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—
106C4⋊Dic11—82no—
107C4⋊Dic11—82no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110Dic11⋊C4—82no—
111C4×Dic11—82no—
112#4318—42no—
113C2×C11⋊C8—41no—
114#2502—111no—
115#2313—111no—
116#1821—111no—
117#1511—111no—
118#1511—111no—
119#1284—111no—
120#1284D1111yescharacteristic
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—41no—
124C23×C11C2×C22⋊C411yescharacteristic
125C23×C11#12011yescharacteristic
126C23×C11#12311yescharacteristic
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—24no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158Dic22—81no—
159Dic22—81no—
160C8×C11—81no—
161C11⋊C8—81no—
162C2×C22⋊Q8—111no—
163C22×C4⋊C4—111no—
164#407—111no—
165#407C2×D1111yescharacteristic
166#398—222no—
167#391—112no—
168#387—222no—
169#387—222no—
170#385—221no—
171#385—221no—
172#384—112no—
173#381—111no—
174#381C2×D1111yescharacteristic
175#380—221no—
176C4×C22⋊C4—221no—
177C4×C22⋊C4C2×D1111yescharacteristic
178#343—222no—
179#328—222no—
180#328—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—44no—
189C22×C11#38611yescharacteristic
190C22×C11#41012yes—
191C22×C11#45612yes—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—44no—
197C4×C11—82no—
198Dic11—42no—
199Dic11—42no—
200Dic11—82no—
201Dic11—81no—
202Dic11—81no—
203C22×Q8—111no—
204C23×C4—111no—
205C23×C4—111no—
206C23×C4C22×D1111yescharacteristic
207C2×M16—21no—
208C2×M16—221no—
209C22⋊Q8—221no—
210C22⋊Q8—221no—
211C22⋊Q8—221no—
212C22⋊Q8—221no—
213C2×C4⋊C4—112no—
214C2×C4⋊C4—112no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4—222no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C42—222no—
229C2×C42C4×D1112yes—
230C22⋊C8—21no—
231C22⋊C8—21no—
232C22⋊C8—221no—
233C22⋊C8—221no—
234#95—21no—
235#95—21no—
236#95—112no—
237#95—222no—
238#95—222no—
239#95—222no—
240#95—222no—
241#95—221no—
242#95D4412yes—
243C2×C11—22no—
244C2×C11—22no—
245C2×C11—41no—
246C2×C11#188611yescharacteristic
247C2×C11#189911yescharacteristic
248C2×C11#191111yescharacteristic
249C24D4×D1111yescharacteristic
250C2×Q8—221no—
251C2×Q8—221no—
252C2×Q8—442no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—42no—
256C22×C4—112no—
257C22×C4—112no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—222no—
265C22×C4—881no—
266C22×C4—881no—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4C2×D4411yescharacteristic
269C22×C4#433911yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272C22×C4#434311yescharacteristic
273M16—42no—
274M16—442no—
275C2×C8—41no—
276C2×C8—441no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—882no—
286C4⋊C4—882no—
287C4⋊C4—882no—
288C22⋊C4—24no—
289C22⋊C4—42no—
290C22⋊C4—442no—
291C22⋊C4—441no—
292C22⋊C4—441no—
293C42—42no—
294C42—882no—
295C11#946111yescharacteristic, complemented, Sylow
296C23—22no—
297C23—22no—
298C23—41no—
299C23C22⋊C4×D1111yescharacteristic
300C23#6693511yescharacteristic
301C23#6694711yescharacteristic
302Q8—881no—
303Q8—881no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4C4×D4411yescharacteristic
332C2×C4#6693711yescharacteristic
333C2×C4#6694611yescharacteristic
334C2×C4#6694811yescharacteristic
335C8—81no—
336C8—881no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—44no—
345C22#1062227811yescharacteristic
346C22#1062235312yes—
347C22#1062243912yes—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—44no—
353C4—82no—
354C4—442no—
355C4—442no—
356C4—882no—
357C4—881no—
358C4—881no—
359C2—22no—
360C2—22no—
361C2—41no—
362C2#1306900811yescharacteristic
363C2#1306907311yescharacteristic
364C2#1306914711yescharacteristic
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#9461
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. #10622548C4semidirect
20. #10622542C4semidirect
295. C11#9461semidirect

Maximal subgroups

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

subgroupindex
#130730942
#130712172
#130686942
#130671502
#130671482
#130664692
C11×#12842
#946111