Finite Group Databasebeta

← #14666793

Subgroups — #14666793

Order 2816.

342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076682C211yesmaximal, characteristic
2#13069963C211yesmaximal, characteristic
3#13067624C211yesmaximal, characteristic
4#13066623C211yesmaximal, characteristic
5#13066622C211yesmaximal, characteristic
6#13066559C211yesmaximal, characteristic
7C11×#1611C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C2×#66942—21no—
10C11×#483—21no—
11C11×#398C2211yescharacteristic
12#10622656—21no—
13#10622608—21no—
14#10622597—21no—
15#10622597—21no—
16#10622596C2211yescharacteristic
17#10622590C2211yescharacteristic
18#10622273—21no—
19#10622271—21no—
20#10622270—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C11×C4⋊Q8—41no—
28C11×#125—41no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—21no—
31C11×#117—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45#66942—42no—
46#66942—42no—
47C11×#106—41no—
48C11×#103—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95D411yescharacteristic
52#66899—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66872—41no—
62#66872—41no—
63#66871—41no—
64#12251—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C22×C4×C11—21no—
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—
76C2×C8×C11—41no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—81no—
98C4×Dic11—21no—
99C4×Dic11SD1612yes—
100#4318—22no—
101#4318—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2822—111no—
105#2061—111no—
106#1611—111no—
107#1611D1111yescharacteristic
108#1346—111no—
109#1346—111no—
110#1324—111no—
111C23×C11#12011yescharacteristic
112Q8×C11—81no—
113Q8×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×Dic11—22no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—42no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C8×C11—81no—
142C11⋊C8—42no—
143C11⋊C8—81no—
144#544C2×D1111yescharacteristic
145C2×#125—221no—
146#483—21no—
147#483—221no—
148#428—221no—
149#400—221no—
150#400—221no—
151#398—111no—
152#398—221no—
153#398—221no—
154#398—221no—
155#398C2×D1111yescharacteristic
156#382—111no—
157#343—111no—
158#339—221no—
159#328—21no—
160#328—221no—
161#324—111no—
162#324C2×D1111yescharacteristic
163C22×C11—21no—
164C22×C11—21no—
165C22×C11#45011yescharacteristic
166C22×C11#45611yescharacteristic
167C22×C11B(4,𝔽2)11yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—81no—
173C4×C11—81no—
174C4×C11—81no—
175C4×C11—81no—
176Dic11—42no—
177Dic11—81no—
178Dic11—81no—
179Dic11—81no—
180C2×M16—221no—
181C4⋊Q8—41no—
182#125—41no—
183#125—442no—
184#125—442no—
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187#117—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4C22⋊D1111yescharacteristic
198C2×C4⋊C4C22×D1111yescharacteristic
199C2×C42—111no—
200#107—441no—
201#106—41no—
202#106—441no—
203#106—441no—
204#103—41no—
205#103—441no—
206C22⋊C8—21no—
207C22⋊C8—221no—
208#95—21no—
209#95—111no—
210#95—221no—
211#95—221no—
212#95—221no—
213#95—221no—
214#95—221no—
215#95—221no—
216#95C22⋊D1111yescharacteristic
217C2×C11—21no—
218C2×C11—21no—
219C2×C11#160411yescharacteristic
220C2×C11#220111yescharacteristic
221C2×C11#220311yescharacteristic
222C2×Q8—21no—
223C2×Q8—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4D4×D1111yescharacteristic
231C22×C4D4×D1111yescharacteristic
232C22×C4C2×C22⋊D1111yescharacteristic
233M16—222no—
234M16—441no—
235C2×C8—41no—
236C2×C8—441no—
237C2×C8—441no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—442no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—881no—
257C22⋊C4—41no—
258C42—41no—
259C42—112no—
260C42—221no—
261C11#1225111yescharacteristic, complemented, Sylow
262C23#6699011yescharacteristic
263Q8—81no—
264Q8—81no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—222no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—442no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4SD16×D1111yescharacteristic
291C2×C4#6696711yescharacteristic
292C8—81no—
293C8—442no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22#1062264511yescharacteristic
298C22#1062278211yescharacteristic
299C22#1062281811yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—81no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—442no—
309C4—881no—
310C4—881no—
311C4—881no—
312C2—21no—
313C2—21no—
314C2#1306758311yescharacteristic
315C2#1307062711yescharacteristic
316C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1611C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1611D11
hypocenterC11#12251
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

Complements

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

NH ≅ G/Ntype
261. C11#12251semidirect

Maximal subgroups

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

subgroupindex
#130766822
#130699632
#130676242
#130666232
#130666222
#130665592
C11×#16112
#1225111