Finite Group Databasebeta

← #14648148

Subgroups — #14648148

Order 2816.

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

normal subgroups only

This group has 428 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#13071801C211yesmaximal, characteristic
2#13069585C211yesmaximal, characteristic
3#13068785C211yesmaximal, characteristic
4#13068784C211yesmaximal, characteristic
5C2×#10622103C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic
8C2×#66923C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66882—21no—
13C2×#66881—21no—
14#10622591—21no—
15#10622585—21no—
16C2×#66872—21no—
17C2×#66871—21no—
18#10622549C2211yescharacteristic
19#10622548C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622268—21no—
22#10622267—21no—
23#10622266—21no—
24#10622260—21no—
25#10622189—21no—
26#10622189—21no—
27#10622103C414yescomplemented
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8—21no—
47#66923—21no—
48#66923—21no—
49#66923C2×C412yes—
50#66923Q812yes—
51C11×#97—21no—
52C11×#97—21no—
53C11×#97—21no—
54C11×#97C2×C412yes—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63#66882—42no—
64#66881—42no—
65#66872—42no—
66#66871—42no—
67#66867—21no—
68#66867C2×C412yes—
69#8913—111nomaximal, Sylow
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—41no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×Q811yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—42no—
101C4⋊Dic11C4⋊C412yes—
102C4⋊Dic11C4⋊C412yes—
103Dic11⋊C4—22no—
104Dic11⋊C4—22no—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4—81no—
108Dic11⋊C4—81no—
109C4×Dic11—81no—
110C4×Dic11—81no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114#2382—111no—
115#1992—111no—
116#1847—111no—
117#1847—111no—
118C2×#330—111no—
119#1295—111no—
120#1295D1111yescharacteristic
121C23×C11#12011yescharacteristic
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11C2×C4⋊C411yescharacteristic
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C22⋊Q811yescharacteristic
138C2×C4×C11C22⋊Q811yescharacteristic
139C2×C4×C11#12311yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—22no—
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—41no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C8×C11—24no—
156C8×C11—42no—
157C11⋊C8—24no—
158C2×#125—111no—
159C2×#107—221no—
160C2×#107—221no—
161C2×#106—221no—
162C2×#106—221no—
163C2×#97—111no—
164C2×#97C2×D1111yescharacteristic
165C2×#97C2×D1111yescharacteristic
166#389—221no—
167#389—221no—
168#387—221no—
169#387—221no—
170#387—221no—
171#387—221no—
172#384—111no—
173#382—111no—
174#382C2×D1111yescharacteristic
175#340—221no—
176#340—221no—
177#330—114no—
178C22×C11#38511yescharacteristic
179C22×C11#45311yescharacteristic
180C22×C11#45311yescharacteristic
181C22×C11#45411yescharacteristic
182C22×C11#45611yescharacteristic
183C22×C11#45611yescharacteristic
184C22×C11#45611yescharacteristic
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—81no—
192C4×C11—81no—
193Dic11—42no—
194Dic11—42no—
195Dic11—81no—
196Dic11—81no—
197Dic11—161no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—221no—
201#125—112no—
202#125—112no—
203#125—221no—
204#125—221no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4D4411yescharacteristic
217C2×C4⋊C4D4411yescharacteristic
218C2×C42—221no—
219C2×C42—221no—
220C2×C42C22×D1111yescharacteristic
221#107—442no—
222#107—442no—
223#106—442no—
224#106—442no—
225#97—21no—
226#97—21no—
227#97—21no—
228#97—112no—
229#97—221no—
230#97C4×D1112yes—
231#95—21no—
232#95—21no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239C2×C11#165611yescharacteristic
240C2×C11#166011yescharacteristic
241C2×C11#166011yescharacteristic
242C2×C11#166311yescharacteristic
243C2×C11#185711yescharacteristic
244C2×C11#185911yescharacteristic
245C2×C11#185911yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—441no—
253C22×C4C2×D4411yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8—222no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—112no—
268C4⋊C4—112no—
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—442no—
282C4⋊C4—881no—
283C4⋊C4—881no—
284C42—881no—
285C42—881no—
286C42C2×C4×D1111yescharacteristic
287C42#433911yescharacteristic
288C42#434111yescharacteristic
289C42Q8×D1111yescharacteristic
290C11#891311yescharacteristic, complemented, Sylow
291C23#6693511yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4C4×D4411yescharacteristic
320C2×C4(C22⋊D11)⋊C411yescharacteristic
321C2×C4#6693611yescharacteristic
322C2×C4C4⋊C4×D1111yescharacteristic
323C2×C4#6694911yescharacteristic
324C2×C4#6695011yescharacteristic
325C8—24no—
326C8—42no—
327C8—224no—
328C22#1062228111yescharacteristic
329C22#1062236011yescharacteristic
330C22#1062236511yescharacteristic
331C22#1062243511yescharacteristic
332C22#1062243911yescharacteristic
333C22#1062243911yescharacteristic
334C22#1062244011yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—81no—
342C4—81no—
343C4—442no—
344C4—442no—
345C4—881no—
346C4—881no—
347C4—1761no—
348C2#1306791011yescharacteristic
349C2#1306792811yescharacteristic
350C2#1306792911yescharacteristic
351C2#1306794611yescharacteristic
352C2#1306883211yescharacteristic
353C2#1306884311yescharacteristic
354C2#1306884511yescharacteristic
subgroupG/H
centerC23#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#8913
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
27. #10622103C4semidirect
290. C11#8913semidirect

Maximal subgroups

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

subgroupindex
#130718012
#130695852
#130687852
#130687842
C2×#106221032
#130664982
C11×#12952
#891311