Finite Group Databasebeta

← #14673151

Subgroups — #14673151

Order 2816.

540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#10622764C211yesmaximal, characteristic
2C2×#10622133C211yesmaximal, characteristic, complemented
3#13070333C211yesmaximal, characteristic, complemented
4#13070332C211yesmaximal, characteristic, complemented
5#13069362C211yesmaximal, characteristic, complemented
6#13066697C211yesmaximal, characteristic, complemented
7C2×C11×#361C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66993—21no—
10C22×#4323—21no—
11C22×D88C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C2×C11×#108C2211yescharacteristic
14#10622764—22no—
15#10622764—22no—
16#10622732—21no—
17#10622719C2211yescharacteristic
18C2×C8×Dic11C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C11×#361—22no—
21#10622200—22no—
22#10622193—21no—
23#10622147—22no—
24#10622133—22no—
25C22×D4×C11—21no—
26C22×C22⋊D11—42no—
27C22×D44—21no—
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8D412yes—
34C2×C11×M16—21no—
35C22×C8×C11C2311yescharacteristic
36#66993—24no—
37#66993—42no—
38C2×#4323—24no—
39C2×#4323—42no—
40C2×#4323—42no—
41#66979—21no—
42C2×C4×Dic11D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44C2×D88—21no—
45C2×D88—21no—
46C2×D88—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88D412yes—
50C11×M32—21no—
51C11×M32—21no—
52C2×C11×C16—21no—
53C11×#108—21no—
54C11×#108—21no—
55#66882D412yescomplemented
56#66881—21no—
57Dic11⋊C8—42no—
58C8×Dic11—21no—
59C8×Dic11—21no—
60#66876—21no—
61#66876—21no—
62C2×C11⋊C16—21no—
63#13413—111nomaximal, Sylow
64C24×C11—41no—
65C23×D11—41no—
66C2×D4×C11—22no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—48no—
74C2×C22⋊D11—88no—
75C22×Dic11—21no—
76C2×D44—22no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C11×D8—22no—
83C11×D8—22no—
84C11×D8—41no—
85C11×D8—41no—
86C11×M16—41no—
87C11×M16—41no—
88C2×C8×C11—41no—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C2×C8×C11#4111yescharacteristic
95C22⋊Dic11—41no—
96#4323—48no—
97C4⋊Dic11—22no—
98C4×Dic11—21no—
99C4×Dic11—41no—
100C4×Dic11SD1612yes—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8D812yes—
104D88—22no—
105D88—22no—
106D88—41no—
107D88—41no—
108C11×C16—41no—
109C11⋊C16—41no—
110C2×#493—111no—
111C2×#361—111no—
112C2×#361D1111yescharacteristic, complemented
113#2140—111no—
114#2140—111no—
115#1945—111no—
116#1376—111no—
117C23×C11—42no—
118C23×C11—84no—
119C23×C11—81no—
120C23×C11—81no—
121C23×C11AGL(1,ℤ/8)11yescharacteristic
122C22×D11—42no—
123C22×D11—84no—
124C22×D11—81no—
125C22×D11—81no—
126D4×C11—42no—
127D4×C11—42no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12411yescharacteristic
133C2×C4×C11C2×D811yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C22⋊D11—816no—
137C2×Dic11—24no—
138C2×Dic11—22no—
139C2×Dic11—42no—
140D44—42no—
141D44—42no—
142D44—81no—
143D44—81no—
144C8×C11—81no—
145C8×C11#12111yescharacteristic
146C8×C11#12111yescharacteristic
147C8×C11#12311yescharacteristic
148C8×C11#12311yescharacteristic
149C11⋊C8—22no—
150C22×D8—111no—
151C22×D8—221no—
152C22×D8C2×D1111yescharacteristic
153C2×#127—221no—
154C2×M32—111no—
155C2×M32C2×D1111yescharacteristic
156#493—222no—
157#493—222no—
158C2×#108C2×D1111yescharacteristic
159#427—111no—
160#424—221no—
161C2×C4×C8—111no—
162#361—22no—
163#361—222no—
164#357—222no—
165#357—222no—
166#339—221no—
167C22×C11—22no—
168C22×C11—84no—
169C22×C11—82no—
170C22×C11—162no—
171C22×C11—162no—
172C22×C11#45011yescharacteristic
173C22×C11#45911yescharacteristic
174C22×C11#49011yescharacteristic
175C2×D11—84no—
176C2×D11—82no—
177C2×D11—162no—
178C2×D11—162no—
179C4×C11#39411yescharacteristic
180C4×C11#44711yescharacteristic
181C4×C11#46011yescharacteristic
182C4×C11#48611yescharacteristic
183Dic11—24no—
184Dic11—82no—
185C22×D4—21no—
186C22×D4—221no—
187C22×D4—442no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8—21no—
193C2×D8—112no—
194C2×D8—224no—
195C2×D8—221no—
196C2×D8—221no—
197C2×D8—221no—
198C2×D8—221no—
199C2×D8—221no—
200C2×D8—442no—
201C2×D8—442no—
202C2×D8C22⋊D1112yes—
203C2×M16—21no—
204C22×C8—111no—
205C22×C8C22×D1111yescharacteristic
206#127—224no—
207#127—442no—
208#117—221no—
209C2×C42—111no—
210M32—21no—
211M32—21no—
212M32—221no—
213M32—221no—
214C2×C16—21no—
215C2×C16—221no—
216#108—21no—
217#108—21no—
218#107—112no—
219#106—221no—
220C4⋊C8—442no—
221C4×C8—221no—
222C4×C8—221no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11—162no—
226C2×C11#204111yescharacteristic
227C2×C11#221312yes—
228D11—162no—
229C24—41no—
230C24—441no—
231C2×D4—22no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—222no—
238C2×D4—448no—
239C2×D4—441no—
240C2×D4—441no—
241C2×D4—441no—
242C2×D4—441no—
243C2×D4—441no—
244C2×D4—888no—
245C22×C4—221no—
246C22×C4D4×D1111yescharacteristic
247D8—22no—
248D8—22no—
249D8—41no—
250D8—41no—
251D8—222no—
252D8—222no—
253D8—448no—
254D8—441no—
255D8—441no—
256M16—41no—
257M16—41no—
258C2×C8—41no—
259C2×C8—112no—
260C2×C8—221no—
261C2×C8—221no—
262C2×C8#433911yescharacteristic
263C2×C8#433911yescharacteristic
264C2×C8D4×D1111yescharacteristic
265C2×C8D4×D1111yescharacteristic
266C2×C8#434111yescharacteristic
267C2×C8C2×C22⋊D1111yescharacteristic
268C4⋊C4—222no—
269C22⋊C4—441no—
270C42—112no—
271C42—221no—
272C42—441no—
273C16—41no—
274C16—441no—
275C11#1341311yescharacteristic, complemented, Sylow
276C23—42no—
277C23—84no—
278C23—81no—
279C23—81no—
280C23—442no—
281C23—884no—
282C23—881no—
283C23—881no—
284C23#6696711yescharacteristic
285D4—42no—
286D4—42no—
287D4—81no—
288D4—81no—
289D4—442no—
290D4—442no—
291D4—8816no—
292D4—881no—
293D4—881no—
294C2×C4—224no—
295C2×C4—222no—
296C2×C4—442no—
297C2×C4#6693711yescharacteristic
298C2×C4#6693811yescharacteristic
299C2×C4D8×D1111yescharacteristic
300C2×C4#6696411yescharacteristic
301C2×C4SD16×D1111yescharacteristic
302C2×C4#6699011yescharacteristic
303C8—81no—
304C8—222no—
305C8#6693611yescharacteristic
306C8#6693711yescharacteristic
307C8#6698211yescharacteristic
308C8#6699211yescharacteristic
309C22—22no—
310C22—84no—
311C22—82no—
312C22—162no—
313C22—162no—
314C22—884no—
315C22—882no—
316C22—1762no—
317C22—1762no—
318C22#1062237711yescharacteristic
319C22#1062239911yescharacteristic
320C22#1062278211yescharacteristic
321C4—224no—
322C4—882no—
323C4#1062237311yescharacteristic
324C4#1062237511yescharacteristic
325C4#1062257211yescharacteristic
326C4#1062276911yescharacteristic
327C2—21no—
328C2—21no—
329C2—162no—
330C2—1762no—
331C2#1306984811yescharacteristic
332C2#1307069112yes—
subgroupG/H
centerC22#10622399
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#361C2
socleC22×C11#459
prime radicalC2×#10622764C2
hypercenterC2×#361D11
hypocenterC11#13413
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C2×#10622133C2semidirect
3. #13070333C2semidirect
4. #13070332C2semidirect
5. #13069362C2semidirect
6. #13066697C2semidirect
7. C2×C11×#361C2semidirect
55. #66882D4semidirect
112. C2×#361D11semidirect
275. C11#13413semidirect

Maximal subgroups

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

subgroupindex
C2×#106227642
C2×#106221332
#130703332
#130703322
#130693622
#130666972
C2×C11×#3612
#1341311