Finite Group Databasebeta

← #14651446

Subgroups — #14651446

Order 2816.

424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077700C211yesmaximal, characteristic
2#13073807C211yesmaximal, characteristic
3#13067242C211yesmaximal, characteristic
4#13067242C211yesmaximal, characteristic
5#13066959C211yesmaximal, characteristic
6#13066472C211yesmaximal, characteristic
7C11×#1285C211yesmaximal, characteristic
8C2×#66923C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622596—21no—
14#10622596—21no—
15#10622549C411yescharacteristic
16#10622548C411yescharacteristic
17#10622542C411yescharacteristic
18#10622542C411yescharacteristic
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622441—22no—
22#10622332—21no—
23#10622331—21no—
24#10622314—22no—
25#10622266—21no—
26#10622266—21no—
27#10622107—21no—
28#10622107—21no—
29#10622103—22no—
30#10622103—22no—
31C22×Dic22C2×C411yescharacteristic
32C2×C11×C4⋊C4—21no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4D411yescharacteristic
44C2×Dic11⋊C4D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47#66923—21no—
48#66923—21no—
49#66923—21no—
50#66923—21no—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#97D412yes—
61C11×#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66879—22no—
71Dic11⋊C8—22no—
72Dic11⋊C8—22no—
73C8×Dic11—22no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76#66867—21no—
77#66867D412yes—
78#9450—111nomaximal, Sylow
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C2×Dic22—22no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C11×C4⋊C4—42no—
97C42×C11—41no—
98C42×C11—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—42no—
110C4⋊Dic11—42no—
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4—21no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#2983—111no—
126#2565—111no—
127#1534—111no—
128#1534—111no—
129#1467—111no—
130#1285—111no—
131#1285D1111yescharacteristic
132C23×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11#10112yes—
164Dic22—42no—
165Dic22—42no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×#125—111no—
171C2×C4×Q8—111no—
172#446—222no—
173#446—222no—
174#432—111no—
175#432—111no—
176#432—221no—
177#432C2×D1111yescharacteristic
178#432C2×D1111yescharacteristic
179#431—221no—
180#398—221no—
181#398—221no—
182#391—111no—
183#391—111no—
184#387—221no—
185#387—221no—
186#384—111no—
187#382—111no—
188C4×C4⋊C4C2×D1111yescharacteristic
189#330—222no—
190#330—222no—
191#324—221no—
192#324—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#38611yescharacteristic
196C22×C11C2×#10111yescharacteristic
197C22×C11#41311yescharacteristic
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—42no—
205C4×C11—81no—
206Dic11—22no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210Dic11—81no—
211Dic11—81no—
212C22×Q8—111no—
213#125—221no—
214#125—221no—
215#125—221no—
216#125—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219C4×Q8—221no—
220C4×Q8—221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C42—111no—
232C2×C42—111no—
233C2×C42C4×D1111yescharacteristic
234C2×C42C4×D1111yescharacteristic
235C2×C42C22×D1111yescharacteristic
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—222no—
239C4⋊C8—222no—
240C4⋊C8—221no—
241C4⋊C8—221no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—221no—
245C22⋊C8—221no—
246#97—21no—
247#97—112no—
248#97—222no—
249#97—221no—
250#97D4412yes—
251C4×C8—222no—
252#95—21no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95—221no—
257#95—221no—
258#95—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11#188411yescharacteristic
262C2×C11#190111yescharacteristic
263C2×C11#191211yescharacteristic
264C2×Q8—222no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×Q8—441no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—222no—
282C2×C8—441no—
283C4⋊C4—42no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C42—41no—
301C42—41no—
302C42—221no—
303C42—221no—
304C42—221no—
305C42—221no—
306C42C2×D4411yescharacteristic
307C42#433911yescharacteristic
308C42D4×D1111yescharacteristic
309C42#434311yescharacteristic
310C11#945011yescharacteristic, complemented, Sylow
311C23C22⋊C4×D1111yescharacteristic
312Q8—442no—
313Q8—442no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—112no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—442no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4C4×D4411yescharacteristic
340C2×C4#6693511yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6694611yescharacteristic
343C2×C4#6694711yescharacteristic
344C2×C4#6694811yescharacteristic
345C8—42no—
346C8—81no—
347C8—442no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22#1062227811yescharacteristic
352C22#1062235811yescharacteristic
353C22D11×#10111yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—81no—
362C4—222no—
363C4—441no—
364C4—441no—
365C4—441no—
366C4—881no—
367C4—881no—
368C2—21no—
369C2—21no—
370C2#1306899811yescharacteristic
371C2#1306908311yescharacteristic
372C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1285D11
hypocenterC11#9450
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
310. C11#9450semidirect

Maximal subgroups

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

subgroupindex
#130777002
#130738072
#130672422
#130669592
#130664722
C11×#12852
#945011