Finite Group Databasebeta

← #14666708

Subgroups — #14666708

Order 2816.

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

normal subgroups only

This group has 368 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#13076449C211yesmaximal, characteristic
2#13069958C211yesmaximal, characteristic, complemented
3#13067658C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic
6#13066561C211yesmaximal, characteristic, complemented
7C11×#1599C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#450—21no—
10C11×#394C2211yescharacteristic
11#10622835—21no—
12#10622657—21no—
13#10622608—21no—
14#10622599C2211yescharacteristic
15#10622589C2211yescharacteristic
16#10622564—21no—
17#10622561—21no—
18#10622557—21no—
19#10622557—21no—
20#10622265—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C2×C11×SD16—41no—
29C11×C4⋊Q8—41no—
30C11×#125—41no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×#117—21no—
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C11×#102—41no—
50C11×C22⋊C8—21no—
51C11×#95D411yescharacteristic
52#66899—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66872—41no—
60#66871—41no—
61#66871—41no—
62#12238—111nomaximal, Sylow
63C24×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×D4×C11—41no—
67C2×D4×C11—81no—
68C22×C4×C11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C11×SD16—82no—
77C2×C8×C11—41no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—81no—
89C42×C11—41no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C22⋊Dic11—81no—
93C22⋊Dic11—81no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96Dic11⋊C4—42no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—81no—
102#4318—22no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2795—111no—
107#2060—111no—
108#1617—111no—
109#1599D1111yescharacteristic
110#1353—111no—
111#1345—111no—
112#1325—111no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11#12011yescharacteristic
121Q8×C11—81no—
122Q8×C11—81no—
123D4×C11—42no—
124D4×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—22no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C8×C11—81no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153#544C2×D1111yescharacteristic
154#484—221no—
155#450—21no—
156#428—221no—
157#400—111no—
158#396—221no—
159#394—221no—
160#394C2×D1111yescharacteristic
161#388—221no—
162#388—221no—
163#388—221no—
164#387—221no—
165#384—111no—
166#343—111no—
167#339—221no—
168#328—21no—
169#328—221no—
170#324—111no—
171#324C2×D1111yescharacteristic
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—81no—
175C22×C11—81no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11#45211yescharacteristic
182C22×C11#45611yescharacteristic
183C22×C11B(4,𝔽2)11yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11—81no—
191Dic11—42no—
192Dic11—81no—
193Dic11—81no—
194Dic11—81no—
195C22×D4C22⋊D1111yescharacteristic
196C2×SD16—41no—
197C2×M16—221no—
198C4⋊Q8—41no—
199#125—41no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202#117—21no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C22×D1111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C42—111no—
216C2×C42—221no—
217#107—441no—
218#107—441no—
219#106—441no—
220#103—441no—
221#102—41no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224#95—111no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95C22⋊D1111yescharacteristic
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—161no—
233C2×C11#160311yescharacteristic
234C2×C11#220011yescharacteristic
235C2×C11#220411yescharacteristic
236C24—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×D4—41no—
240C2×D4—81no—
241C22×C4—21no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4D4×D1111yescharacteristic
247C22×C4D4×D1111yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249SD16—82no—
250M16—222no—
251M16—441no—
252C2×C8—41no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—442no—
265C4⋊C4—881no—
266C4⋊C4—881no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—81no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C22⋊C4—881no—
274C22⋊C4—881no—
275C42—41no—
276C42—221no—
277C42—221no—
278C42—881no—
279C11#1223811yescharacteristic, complemented, Sylow
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23#6699011yescharacteristic
288Q8—81no—
289Q8—81no—
290D4—42no—
291D4—81no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—222no—
304C2×C4—441no—
305C2×C4—441no—
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#6696811yescharacteristic
316C2×C4#6696911yescharacteristic
317C8—81no—
318C8—442no—
319C8—881no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#1062264511yescharacteristic
330C22#1062278611yescharacteristic
331C22#1062281811yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—442no—
340C4—881no—
341C4—881no—
342C4—881no—
343C2—21no—
344C2—21no—
345C2—161no—
346C2#1306757611yescharacteristic
347C2#1307062111yescharacteristic
348C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1599C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
hypercenter#1599D11
hypocenterC11#12238
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1599

Complements

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

NH ≅ G/Ntype
2. #13069958C2semidirect
3. #13067658C2semidirect
4. #13066644C2semidirect
6. #13066561C2semidirect
279. C11#12238semidirect

Maximal subgroups

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

subgroupindex
#130764492
#130699582
#130676582
#130666442
#130666192
#130665612
C11×#15992
#1223811