Finite Group Databasebeta

← #14657265

Subgroups — #14657265

Order 2816.

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

normal subgroups only

This group has 386 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#13076683C211yesmaximal, characteristic
2#13069584C211yesmaximal, characteristic
3#13068751C211yesmaximal, characteristic
4C2×#10622181C211yesmaximal, characteristic
5C2×#10622103C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic
7C11×#1992C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622599—21no—
13#10622597—21no—
14#10622597—21no—
15#10622596—21no—
16#10622595—21no—
17#10622593—21no—
18#10622549C2211yescharacteristic
19C2×#66867C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21C11×#340—21no—
22C11×#340—21no—
23#10622181—22no—
24#10622167—21no—
25#10622167—21no—
26#10622167—21no—
27#10622167—21no—
28#10622103—22no—
29C22×C8×C11—21no—
30C11×#125—21no—
31C11×#125—21no—
32C11×#125—21no—
33C11×#125—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52#66923—21no—
53#66923—21no—
54#66923—21no—
55#66923—21no—
56C11×#97—21no—
57C11×#97—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66#66867—21no—
67#66867—21no—
68#66867—21no—
69#66867D412yes—
70#10428—111nomaximal, Sylow
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—81no—
110Dic11⋊C4—81no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117#2822—111no—
118#1992—111no—
119#1992D1111yescharacteristic
120#1836—111no—
121C2×#330—111no—
122C2×#330—111no—
123#1295—111no—
124C23×C11#12011yescharacteristic
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C8×C11—42no—
159C11⋊C8—42no—
160C11⋊C8—42no—
161C2×#125—111no—
162C2×#125C2×D1111yescharacteristic
163C2×#97—111no—
164C2×#97—111no—
165C2×#97C2×D1111yescharacteristic
166#400—221no—
167#400—221no—
168#398—221no—
169#398—221no—
170#398—221no—
171#398—221no—
172#384C2×D1111yescharacteristic
173#382—111no—
174#340—21no—
175#340—21no—
176#340—221no—
177#340—221no—
178#340—221no—
179#340—221no—
180#330—222no—
181#330—222no—
182C22×C11#39411yescharacteristic
183C22×C11#45411yescharacteristic
184C22×C11#45411yescharacteristic
185C22×C11#45411yescharacteristic
186C22×C11#45511yescharacteristic
187C22×C11#45611yescharacteristic
188C22×C11#45611yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—161no—
198Dic11—81no—
199Dic11—81no—
200Dic11—81no—
201Dic11—81no—
202C22×C8—21no—
203C22×C8—221no—
204C22×C8—221no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#125—221no—
210#125—221no—
211#125—221no—
212#125—221no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4C22⋊D1111yescharacteristic
227C2×C4⋊C4C22⋊D1111yescharacteristic
228C2×C42C22×D1111yescharacteristic
229#97—21no—
230#97—21no—
231#97—112no—
232#97—221no—
233#97—221no—
234#97—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243C2×C11#165811yescharacteristic
244C2×C11#166311yescharacteristic
245C2×C11#166411yescharacteristic
246C2×C11#166411yescharacteristic
247C2×C11#203811yescharacteristic
248C2×C11#203811yescharacteristic
249C2×C11#204011yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—441no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—441no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—881no—
291C4⋊C4—881no—
292C42#433911yescharacteristic
293C42#433911yescharacteristic
294C42D4×D1111yescharacteristic
295C42#434111yescharacteristic
296C11#1042811yescharacteristic, complemented, Sylow
297C23#6699011yescharacteristic
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—81no—
311C2×C4—81no—
312C2×C4—81no—
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—441no—
324C2×C4—441no—
325C2×C4#6693611yescharacteristic
326C2×C4#6693711yescharacteristic
327C2×C4#6693711yescharacteristic
328C2×C4#6693811yescharacteristic
329C2×C4#6698211yescharacteristic
330C2×C4#6699211yescharacteristic
331C8—42no—
332C8—442no—
333C8—442no—
334C22#1062257211yescharacteristic
335C22#1062267511yescharacteristic
336C22#1062270811yescharacteristic
337C22#1062281411yescharacteristic
338C22#1062281411yescharacteristic
339C22#1062281511yescharacteristic
340C22#1062281811yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—81no—
349C4—161no—
350C4—881no—
351C4—881no—
352C4—881no—
353C4—881no—
354C2#1306791711yescharacteristic
355C2#1306794311yescharacteristic
356C2#1306794711yescharacteristic
357C2#1306794811yescharacteristic
358C2#1306983111yescharacteristic
359C2#1306983311yescharacteristic
360C2#1306984311yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1992C2
socle, prime radicalC23×C11#120
hypercenter#1992D11
hypocenterC11#10428
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
296. C11#10428semidirect

Maximal subgroups

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

subgroupindex
#130766832
#130695842
#130687512
C2×#106221812
C2×#106221032
#130664982
C11×#19922
#1042811