Finite Group Databasebeta

← #14655089

Subgroups — #14655089

Order 2816.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#10622695C211yesmaximal, characteristic
2#13076683C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic
4C2×#10622181C211yesmaximal, characteristic
5C2×#10622103C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic
7C2×C11×#501C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#501—22no—
12C11×#501—22no—
13C2×C11×#107—21no—
14C2×C11×#106—21no—
15C2×C11×#97C2211yescharacteristic
16C2×#66899—21no—
17C2×#66899—21no—
18#10622695—22no—
19#10622695—22no—
20#10622599—21no—
21#10622597—22no—
22#10622596—21no—
23#10622595—21no—
24#10622593—21no—
25#10622549C2211yescharacteristic
26C2×#66867C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622181—22no—
29#10622167—22no—
30#10622103—22no—
31C22×Q8×C11—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D412yes—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D412yes—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—22no—
54C22×C11⋊C8—21no—
55C22×C11⋊C8—21no—
56#66923—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60C11×#107—24no—
61C11×#106—24no—
62C11×#97—21no—
63C11×#97D412yes—
64#66899—24no—
65#66899—24no—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71#66867—21no—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75#10084—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—44no—
78C2×Q8×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C2×C8×C11—24no—
89C2×C8×C11—22no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—42no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115Dic11⋊C4—82no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×#501D1111yescharacteristic
122C2×#491—111no—
123#2822—111no—
124#1993—111no—
125C2×#330—111no—
126C2×#330—111no—
127#1295—111no—
128C23×C11#12011yescharacteristic
129Q8×C11—44no—
130Q8×C11—82no—
131C2×C4×C11—22no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—82no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C8×C11—24no—
157C11⋊C8—42no—
158C11⋊C8—42no—
159C2×C4⋊Q8C2×D1111yescharacteristic
160C2×#125—111no—
161C2×#125C2×D1111yescharacteristic
162#501—22no—
163#501—22no—
164#491—222no—
165#491—222no—
166C2×#107—21no—
167C2×#106—21no—
168C2×#103—221no—
169C2×#103—221no—
170C2×#97—111no—
171C2×#97—111no—
172C2×#97C2×D1111yescharacteristic
173#400—221no—
174#400—221no—
175#398—221no—
176#398—222no—
177#398—221no—
178#382—111no—
179#340—222no—
180#330—222no—
181#330—222no—
182C22×C11#39211yescharacteristic
183C22×C11#45412yes—
184C22×C11#45511yescharacteristic
185C22×C11#45611yescharacteristic
186C22×C11#45612yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—81no—
194C4×C11—82no—
195C4×C11—81no—
196Dic11—82no—
197Dic11—81no—
198Dic11—81no—
199C22×Q8—21no—
200C22×C8—21no—
201C22×C8—221no—
202C22×C8—221no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8C22⋊D1112yes—
207#125—21no—
208#125—21no—
209#125—21no—
210#125—21no—
211#125—221no—
212#125—221no—
213#125—221no—
214#125—221no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—112no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—222no—
225C2×C4⋊C4C22⋊D1111yescharacteristic
226C2×C4⋊C4C22⋊D1111yescharacteristic
227C2×C42C22×D1111yescharacteristic
228#107—24no—
229#106—24no—
230#103—224no—
231#103—224no—
232#97—21no—
233#97—112no—
234#97—221no—
235#97—221no—
236#97—221no—
237#97C22⋊D1112yes—
238#95—222no—
239#95—222no—
240#95—222no—
241#95—221no—
242#95—221no—
243C2×C11#166312yes—
244C2×C11#166412yes—
245C2×C11#200311yescharacteristic
246C2×C11#200511yescharacteristic
247C2×C11#200711yescharacteristic
248C2×Q8—22no—
249C2×Q8—44no—
250C2×Q8—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—222no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260C2×C8—24no—
261C2×C8—22no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8—442no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—442no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—882no—
289C42D4×D1111yescharacteristic
290C42#434111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C42C2×C22⋊D1111yescharacteristic
293C11#1008411yescharacteristic, complemented, Sylow
294C23#6699011yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4#6699011yescharacteristic
317C2×C4#6699111yescharacteristic
318C2×C4#6699211yescharacteristic
319C2×C4#6699211yescharacteristic
320C2×C4#6699311yescharacteristic
321C2×C4#6700611yescharacteristic
322C8—24no—
323C8—442no—
324C8—442no—
325C22#1062270812yes—
326C22#1062281412yes—
327C22#1062281511yescharacteristic
328C22#1062281811yescharacteristic
329C22#1062283611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—82no—
338C4—81no—
339C4—881no—
340C4—881no—
341C4—882no—
342C2#1306794312yes—
343C2#1306794812yes—
344C2#1306963511yescharacteristic
345C2#1306965211yescharacteristic
346C2#1306966111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#501C2
socle, prime radicalC23×C11#120
hypercenterC2×#501D11
hypocenterC11#10084
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
293. C11#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#106226952
#130766832
#130695902
C2×#106221812
C2×#106221032
#130664982
C2×C11×#5012
#1008411