Finite Group Databasebeta

← #14666786

Subgroups — #14666786

Order 2816.

386 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 59 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#13076690C211yesmaximal, characteristic
2#13069961C211yesmaximal, characteristic, complemented
3#13067626C211yesmaximal, characteristic, complemented
4#13067558C211yesmaximal, characteristic
5#13066623C211yesmaximal, characteristic, complemented
6#13066620C211yesmaximal, characteristic
7C11×#1325C211yesmaximal, characteristic, complemented
8#10623031C2211yescharacteristic
9C2×#66929—21no—
10C11×#384C2211yescharacteristic
11#10622607—21no—
12#10622607—21no—
13#10622607—21no—
14#10622604—21no—
15#10622604C2211yescharacteristic
16#10622596—21no—
17#10622596C2211yescharacteristic
18#10622577—21no—
19#10622344—21no—
20#10622334—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622168C2211yescharacteristic
24#10622161—21no—
25#10622105—21no—
26#10622105—21no—
27C22×D44D411yescharacteristic
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39#66979—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42#66977—21no—
43#66977—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×#4318—21no—
48C2×#4314—41no—
49#66943—41no—
50#66941—41no—
51#66929—42no—
52#66929—42no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C11⋊#95D411yescharacteristic
59#66885—41no—
60#66881—41no—
61#66880—41no—
62#66872—41no—
63#66871—41no—
64#12249—111nomaximal, Sylow
65C23×D11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×D44—41no—
75C2×D44—81no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—81no—
83C11×C4⋊C4—81no—
84C42×C11—21no—
85C42×C11SD1612yescomplemented
86C22⋊Dic11—41no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—81no—
92(C2×D11)⋊C4—81no—
93(C2×D11)⋊C4—81no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—41no—
99C4⋊Dic11—81no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—41no—
107#4318—22no—
108#4318—41no—
109C2×C11⋊C8—41no—
110#4314—82no—
111#2823—111no—
112#2060—111no—
113#1611—111no—
114#1599—111no—
115#1346—111no—
116#1345—111no—
117#1325D1111yescharacteristic, complemented
118C23×C11#12011yescharacteristic
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
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×C11C2×SD1611yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
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—
150C2×Dic11—41no—
151D44—42no—
152D44—81no—
153Dic22—81no—
154Dic22—81no—
155C8×C11—81no—
156C8×C11—81no—
157C11⋊C8—42no—
158#544—111no—
159C2×#126—221no—
160#483—221no—
161#450—221no—
162#428—221no—
163#398—111no—
164#398—221no—
165#396—221no—
166#396—221no—
167#396—221no—
168#394—111no—
169#394—221no—
170#384C2×D1111yescharacteristic
171#343—111no—
172#339—221no—
173#328—221no—
174#328—221no—
175#324C2×D1111yescharacteristic
176#324C2×D1111yescharacteristic
177C22×C11—21no—
178C22×C11—21no—
179C22×C11#45011yescharacteristic
180C22×C11#45611yescharacteristic
181C22×C11B(4,𝔽2)11yescharacteristic
182C2×D11—81no—
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—42no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199Dic11—81no—
200C22×D4—111no—
201C2×SD16—441no—
202C2×M16—221no—
203C4⋊Q8—441no—
204#126—442no—
205#126—442no—
206#125—441no—
207C22⋊Q8—221no—
208C22⋊Q8—221no—
209#117—221no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4D4411yescharacteristic
218C2×C4⋊C4C22×D1111yescharacteristic
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C42D4411yescharacteristic
226#107—441no—
227#106—441no—
228#106—441no—
229#103—441no—
230#102—441no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233#95—111no—
234#95—111no—
235#95—221no—
236#95—221no—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11#160411yescharacteristic
240C2×C11#220011yescharacteristic
241C2×C11#220311yescharacteristic
242D11—161no—
243C24—221no—
244C2×Q8—221no—
245C2×Q8—221no—
246C2×D4—441no—
247C2×D4—881no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4C2×D4411yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256SD16—882no—
257M16—222no—
258M16—441no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—441no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—441no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—881no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C22⋊C4—881no—
284C22⋊C4—881no—
285C22⋊C4—881no—
286C42—21no—
287C42—441no—
288C42#431412yescomplemented
289C11#1224911yescharacteristic, complemented, Sylow
290C23—441no—
291C23—441no—
292C23—441no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23#6693511yescharacteristic
298Q8—881no—
299Q8—881no—
300D4—442no—
301D4—881no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—441no—
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×C4C2×#431411yescharacteristic
326C2×C4#6696111yescharacteristic
327C8—81no—
328C8—81no—
329C8—442no—
330C22—21no—
331C22—21no—
332C22—881no—
333C22—881no—
334C22—881no—
335C22—881no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22#1062234411yescharacteristic
340C22#1062235411yescharacteristic
341C22#1062236511yescharacteristic
342C4—21no—
343C4—21no—
344C4—42no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—881no—
349C4—881no—
350C4—881no—
351C4—881no—
352C4—881no—
353C2—21no—
354C2—21no—
355C2—1761no—
356C2#1306758711yescharacteristic
357C2#1307062611yescharacteristic
358C2#1307063811yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D44D4
hypercenter#1325D11
hypocenterC11#12249
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #13069961C2semidirect
3. #13067626C2semidirect
5. #13066623C2semidirect
7. C11×#1325C2semidirect
85. C42×C11SD16semidirect
117. #1325D11semidirect
288. C42#4314semidirect
289. C11#12249semidirect

Maximal subgroups

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

subgroupindex
#130766902
#130699612
#130676262
#130675582
#130666232
#130666202
C11×#13252
#1224911