Finite Group Databasebeta

← #14666952

Subgroups — #14666952

Order 2816.

372 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076783C211yesmaximal, characteristic
2#13067590C211yesmaximal, characteristic, complemented
3#13067556C211yesmaximal, characteristic
4#13066645C211yesmaximal, characteristic, complemented
5#13066618C211yesmaximal, characteristic
6#13066550C211yesmaximal, characteristic, complemented
7C11×#2028C211yesmaximal, characteristic, complemented
8C11×#544C2211yescharacteristic
9C11×#419—21no—
10C11×#391C2211yescharacteristic
11#10622844—21no—
12#10622663—21no—
13#10622659—21no—
14#10622604C2211yescharacteristic
15#10622592C2211yescharacteristic
16#10622553—21no—
17#10622288—21no—
18#10622286—21no—
19#10622285—21no—
20#10622271—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23#10622176—21no—
24#10622176—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C11×C4⋊Q8—41no—
32C11×#125—41no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×#117—21no—
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×#4326—41no—
39C2×#4325—41no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C11×#103—41no—
49C11×#103—41no—
50C11×#95—21no—
51C11×#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66873—41no—
62#12275—111nomaximal, Sylow
63C23×D11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
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—
78C2×D44—41no—
79C2×D44—81no—
80C2×Dic22—41no—
81C2×Dic22—81no—
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11—41no—
94C42×C11—41no—
95#4326—82no—
96#4325—82no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—81no—
100(C2×D11)⋊C4—81no—
101(C2×D11)⋊C4—81no—
102(C2×D11)⋊C4—81no—
103(C2×D11)⋊C4—81no—
104Dic11⋊C4—81no—
105Dic11⋊C4—81no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2832—111no—
109#2028D1111yescharacteristic, complemented
110#1605—111no—
111#1599—111no—
112#1354—111no—
113#1345—111no—
114#1319—111no—
115C23×C11#12011yescharacteristic
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123Q8×C11—42no—
124Q8×C11—81no—
125Q8×C11—81no—
126Q8×C11—81no—
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—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13711yescharacteristic
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—
152D44—42no—
153D44—81no—
154Dic22—42no—
155Dic22—81no—
156C8×C11—81no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159#544C2×D1111yescharacteristic
160#451—221no—
161#450—221no—
162#419—21no—
163#400—221no—
164#397—221no—
165#395—111no—
166#394—111no—
167#394—221no—
168#393—221no—
169#393—221no—
170#391C2×D1111yescharacteristic
171#388—221no—
172#343C2×D1111yescharacteristic
173#339—21no—
174#328—221no—
175#328—221no—
176#324—111no—
177#324—111no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#45211yescharacteristic
181C22×C11#45511yescharacteristic
182C22×C11B(4,𝔽2)11yescharacteristic
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198Dic11—81no—
199Dic11—81no—
200Dic11—81no—
201C22×Q8—111no—
202C22×Q8C22⋊D1111yescharacteristic
203C22×D4—111no—
204C2×Q16—441no—
205C2×SD16—441no—
206C2×M16—21no—
207C4⋊Q8—41no—
208#125—41no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#117—21no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4C22×D1111yescharacteristic
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C42C22⋊D1111yescharacteristic
222#103—41no—
223#103—41no—
224#103—441no—
225#102—441no—
226C22⋊C8—221no—
227C22⋊C8—221no—
228#95—21no—
229#95—21no—
230#95—111no—
231#95—111no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11#160611yescharacteristic
239C2×C11#219911yescharacteristic
240C2×C11#220311yescharacteristic
241D11—161no—
242C24—221no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—441no—
250C2×Q8—881no—
251C2×D4—441no—
252C2×D4—881no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261Q16—882no—
262SD16—882no—
263M16—41no—
264M16—41no—
265C2×C8—41no—
266C2×C8—441no—
267C2×C8—441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—881no—
276C4⋊C4—881no—
277C22⋊C4—41no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C22⋊C4—881no—
281C22⋊C4—881no—
282C22⋊C4—881no—
283C22⋊C4—881no—
284C22⋊C4—881no—
285C42—41no—
286C42—41no—
287C11#1227511yescharacteristic, complemented, Sylow
288C23—441no—
289C23—441no—
290C23—441no—
291C23—441no—
292C23—441no—
293C23—441no—
294C23—441no—
295C23#6699011yescharacteristic
296Q8—42no—
297Q8—81no—
298Q8—81no—
299Q8—81no—
300Q8—442no—
301Q8—881no—
302D4—442no—
303D4—881no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4#6699511yescharacteristic
328C2×C4#6700311yescharacteristic
329C8—81no—
330C8—881no—
331C8—881no—
332C22—21no—
333C22—21no—
334C22—881no—
335C22—881no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22—881no—
340C22—881no—
341C22#1062264511yescharacteristic
342C22#1062266011yescharacteristic
343C22#1062267411yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—881no—
353C4—881no—
354C4—881no—
355C2—21no—
356C2—21no—
357C2—1761no—
358C2#1306759411yescharacteristic
359C2#1307061611yescharacteristic
360C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2028C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D44D4
hypercenter#2028D11
hypocenterC11#12275
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2028

Complements

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

NH ≅ G/Ntype
2. #13067590C2semidirect
4. #13066645C2semidirect
6. #13066550C2semidirect
7. C11×#2028C2semidirect
109. #2028D11semidirect
287. C11#12275semidirect

Maximal subgroups

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

subgroupindex
#130767832
#130675902
#130675562
#130666452
#130666182
#130665502
C11×#20282
#1227511