Finite Group Databasebeta

← #14666136

Subgroups — #14666136

Order 2816.

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

normal subgroups only

This group has 380 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#13076416C211yesmaximal, characteristic, complemented
2#13069837C211yesmaximal, characteristic
3#13067585C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066561C211yesmaximal, characteristic, complemented
7C11×#1610C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C11×#480—21no—
10C11×#398C2211yescharacteristic
11C2×#66901—21no—
12#10622845—21no—
13#10622653—21no—
14#10622598—21no—
15#10622596—21no—
16#10622592C2211yescharacteristic
17#10622591—21no—
18#10622589C2211yescharacteristic
19#10622269—21no—
20#10622265—21no—
21#10622260—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Dic22D411yescharacteristic
29C11×C22⋊Q8—41no—
30C11×#121—21no—
31C11×#121—21no—
32C11×#121—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×#4324—41no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C11×#107—41no—
48C11×#102—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95D411yescharacteristic
52#66901—42no—
53#66899—41no—
54#66896—41no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66874—41no—
63#12146—111nomaximal, Sylow
64C11×#41—41no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—41no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C2×Dic22—41no—
84C2×Dic22—81no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94#4324—82no—
95C4⋊Dic11—41no—
96C4⋊Dic11—81no—
97C4⋊Dic11—81no—
98Dic11⋊C4—24no—
99Dic11⋊C4—81no—
100Dic11⋊C4—81no—
101Dic11⋊C4—81no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—81no—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2792—111no—
110#2039—111no—
111#1610D1111yescharacteristic
112#1604—111no—
113#1354—111no—
114#1346—111no—
115#1325—111no—
116C23×C11—41no—
117C23×C11#12011yescharacteristic
118Q8×C11—41no—
119Q8×C11—41no—
120D4×C11—41no—
121D4×C11—41no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
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—81no—
140C2×C4×C11—81no—
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—41no—
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—
155Dic22—42no—
156Dic22—81no—
157C8×C11—81no—
158C11⋊C8—81no—
159C11⋊C8—81no—
160#537C2×D1111yescharacteristic
161#480—21no—
162#448—221no—
163C2×#104—221no—
164#417—221no—
165#398—221no—
166#398C2×D1111yescharacteristic
167#395—111no—
168#395—221no—
169#389—221no—
170#389—221no—
171#387—221no—
172#387—221no—
173#384—111no—
174#343—111no—
175#327—21no—
176#327—221no—
177#324—111no—
178#324C2×D1111yescharacteristic
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11#44911yescharacteristic
185C22×C11#45411yescharacteristic
186C22×C11B(4,𝔽2)11yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—81no—
193C4×C11—81no—
194Dic11—42no—
195Dic11—42no—
196Dic11—81no—
197Dic11—81no—
198C2×#41—21no—
199C22×Q8—111no—
200C2×SD16—441no—
201C2×M16—221no—
202C22⋊Q8—41no—
203#121—21no—
204#121—21no—
205#121—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C4⋊C4C22×D1111yescharacteristic
216C2×C42—111no—
217C2×C42—221no—
218#107—41no—
219#104—442no—
220#103—441no—
221#103—441no—
222#102—41no—
223#102—441no—
224C22⋊C8—21no—
225C22⋊C8—221no—
226#95—21no—
227#95—111no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95C22⋊D1111yescharacteristic
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—161no—
237C2×C11#159711yescharacteristic
238C2×C11#220011yescharacteristic
239C2×C11#220511yescharacteristic
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—441no—
246C2×Q8—881no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261SD16—882no—
262M16—441no—
263M16—441no—
264C2×C8—41no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—224no—
274C4⋊C4—441no—
275C4⋊C4—881no—
276C4⋊C4—881no—
277C4⋊C4—881no—
278C4⋊C4—881no—
279C4⋊C4—881no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—221no—
283C42—221no—
284C42—881no—
285C11#1214611yescharacteristic, complemented, Sylow
286C23—41no—
287C23#6699011yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—442no—
291Q8—881no—
292D4—41no—
293D4—41no—
294D4—81no—
295D4—81no—
296D4—81no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—222no—
314C2×C4—222no—
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#6696411yescharacteristic
326C2×C4#6696511yescharacteristic
327C8—81no—
328C8—881no—
329C8—881no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1062264511yescharacteristic
336C22#1062277111yescharacteristic
337C22#1062281411yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—442no—
346C4—442no—
347C4—881no—
348C4—881no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2#1306754211yescharacteristic
353C2#1307062011yescharacteristic
354C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1610C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1610D11
hypocenterC11#12146
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #13076416C2semidirect
4. #13066647C2semidirect
5. #13066622C2semidirect
6. #13066561C2semidirect
285. C11#12146semidirect

Maximal subgroups

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

subgroupindex
#130764162
#130698372
#130675852
#130666472
#130666222
#130665612
C11×#16102
#1214611