Finite Group Databasebeta

← #14656849

Subgroups — #14656849

Order 2816.

400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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#13076888C211yesmaximal, characteristic
2#13069589C211yesmaximal, characteristic
3#13069588C211yesmaximal, characteristic
4#13069436C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66880—21no—
13C2×#66880—21no—
14#10622599—21no—
15#10622592—21no—
16#10622549C2211yescharacteristic
17#10622549C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19#10622273—21no—
20#10622273—21no—
21#10622269—21no—
22#10622269—21no—
23#10622189—21no—
24#10622189—21no—
25#10622167—21no—
26#10622167—21no—
27C22×Dic22—21no—
28C22×Dic22—21no—
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C22×C11⋊C8—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922Q812yescomplemented
48C11×#97—21no—
49C11×#97—21no—
50C11×#97—21no—
51C11×#97—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62#66880—42no—
63#66880—42no—
64#66867—21no—
65#66867—21no—
66#10359—111nomaximal, Sylow
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—41no—
77C2×Dic22—22no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—81no—
84C2×Dic22—81no—
85C2×Dic22—81no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C42×C11C2×Q811yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—81no—
107Dic11⋊C4—81no—
108Dic11⋊C4—81no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#2844—111no—
113#1993—111no—
114#1993—111no—
115#1960—111no—
116#1295—111no—
117#1295—111no—
118#1295D1111yescharacteristic
119C23×C11#12011yescharacteristic
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11C22⋊Q811yescharacteristic
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11#12411yescharacteristic
136C2×C4×C11#12411yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×Dic11—42no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153Dic22—42no—
154Dic22—42no—
155Dic22—81no—
156Dic22—81no—
157Dic22—84no—
158C8×C11—42no—
159C8×C11—42no—
160C11⋊C8—42no—
161C2×C4⋊Q8—111no—
162C2×#103—221no—
163C2×#103—221no—
164C2×#97—111no—
165C2×#97C2×D1111yescharacteristic
166C2×#97C2×D1111yescharacteristic
167#400—221no—
168#400—221no—
169#400—221no—
170#395—221no—
171#395—221no—
172#395—221no—
173#382—111no—
174#382—111no—
175#382C2×D1111yescharacteristic
176#340—221no—
177#340—221no—
178#340—221no—
179#340—221no—
180C22×C11#39311yescharacteristic
181C22×C11#45311yescharacteristic
182C22×C11#45411yescharacteristic
183C22×C11#45511yescharacteristic
184C22×C11#45511yescharacteristic
185C22×C11#45611yescharacteristic
186C22×C11#45611yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—81no—
194C4×C11—81no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199Dic11—82no—
200C22×Q8—221no—
201C22×Q8—221no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—221no—
205C4⋊Q8—112no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4D4411yescharacteristic
219C2×C4⋊C4D4411yescharacteristic
220C2×C42C22×D1111yescharacteristic
221#103—442no—
222#103—442no—
223#97—21no—
224#97—21no—
225#97—21no—
226#97—21no—
227#97—221no—
228#97—221no—
229#95—21no—
230#95—21no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239C2×C11#165911yescharacteristic
240C2×C11#166011yescharacteristic
241C2×C11#166411yescharacteristic
242C2×C11#166411yescharacteristic
243C2×C11#202711yescharacteristic
244C2×C11#202811yescharacteristic
245C2×C11#202811yescharacteristic
246C2×Q8—222no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×Q8—881no—
253C2×Q8—881no—
254C2×Q8—881no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—441no—
262C22×C4C2×D4411yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—222no—
272C2×C8—441no—
273C2×C8—441no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—881no—
285C4⋊C4—881no—
286C4⋊C4—881no—
287C42#433911yescharacteristic
288C42#433911yescharacteristic
289C42#434111yescharacteristic
290C42Q8×D1111yescharacteristic
291C11#1035911yescharacteristic, complemented, Sylow
292C23#6693511yescharacteristic
293Q8—442no—
294Q8—442no—
295Q8—881no—
296Q8—881no—
297Q8—884no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—442no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4#6692811yescharacteristic
326C2×C4#6693811yescharacteristic
327C2×C4#6693811yescharacteristic
328C2×C4#6694911yescharacteristic
329C2×C4#6694911yescharacteristic
330C2×C4#6695011yescharacteristic
331C8—42no—
332C8—42no—
333C8—442no—
334C22#1062228611yescharacteristic
335C22#1062235911yescharacteristic
336C22#1062236511yescharacteristic
337C22#1062243511yescharacteristic
338C22#1062243811yescharacteristic
339C22#1062243911yescharacteristic
340C22#1062244011yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—81no—
349C4—881no—
350C4—881no—
351C4—881no—
352C4—881no—
353C4—882no—
354C2#1306792411yescharacteristic
355C2#1306792911yescharacteristic
356C2#1306795211yescharacteristic
357C2#1306795311yescharacteristic
358C2#1306977111yescharacteristic
359C2#1306977611yescharacteristic
360C2#1306977811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
hypercenter#1295D11
hypocenterC11#10359
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
47. #66922Q8semidirect
291. C11#10359semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130695892
#130695882
#130694362
#130664982
C11×#12952
#1035911