Finite Group Databasebeta

← #14673152

Subgroups — #14673152

Order 2816.

540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10622154C211yesmaximal, characteristic, complemented
3C2×#10622201C211yesmaximal, characteristic, complemented
4#13070331C211yesmaximal, characteristic, complemented
5#13069365C211yesmaximal, characteristic, complemented
6#13066697C211yesmaximal, characteristic, complemented
7C11×#2140C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66993—21no—
10C22×#4323—21no—
11C22×D88C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C11×#427C2211yescharacteristic
14#10622764—22no—
15#10622764—22no—
16C2×#66883C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C2×#66876C2211yescharacteristic
19#10622612—21no—
20C11×#357—22no—
21#10622201—22no—
22#10622170—21no—
23#10622154—22no—
24#10622129—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—
34C22×C8×C11C2311yescharacteristic
35C11×#117—21no—
36#66993—24no—
37#66993—42no—
38C2×#4323—24no—
39C2×#4323—42no—
40C2×#4323—42no—
41C2×C4×Dic11D411yescharacteristic
42C2×#4318—21no—
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×#107D412yescomplemented
54C11×#106—21no—
55#66883—21no—
56#66883—21no—
57C8×Dic11—21no—
58C8×Dic11—21no—
59#66876—21no—
60#66876—21no—
61C2×C11⋊C16—21no—
62C4⋊(C11⋊C8)—42no—
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—
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C2×C8×C11#4111yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C11×C4⋊C4—22no—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95#4323—48no—
96C4×Dic11—21no—
97C4×Dic11SD1612yes—
98#4318—41no—
99#4318—41no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8D812yes—
104D88—22no—
105D88—22no—
106D88—41no—
107D88—41no—
108C11×C16—41no—
109C11⋊C16—41no—
110C2×#493—111no—
111C2×#361—111no—
112C2×#361—111no—
113#2140—111no—
114#2140D1111yescharacteristic, complemented
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—42no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C22⋊D11—816no—
138C2×Dic11—24no—
139C2×Dic11—22no—
140D44—42no—
141D44—42no—
142D44—81no—
143D44—81no—
144C8×C11#12111yescharacteristic
145C8×C11#12111yescharacteristic
146C8×C11#12311yescharacteristic
147C8×C11#12311yescharacteristic
148C11⋊C8—22no—
149C11⋊C8—81no—
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×#108—111no—
159#427C2×D1111yescharacteristic
160#424—221no—
161C2×C4×C8—111no—
162#361—222no—
163#361—222no—
164#357—22no—
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—82no—
180C4×C11#39411yescharacteristic
181C4×C11#44711yescharacteristic
182C4×C11#46011yescharacteristic
183C4×C11#48611yescharacteristic
184Dic11—24no—
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×D8D4412yes—
203C2×M16—221no—
204C22×C8—111no—
205C22×C8C22×D1111yescharacteristic
206#127—224no—
207#127—442no—
208#117—21no—
209C2×C42—111no—
210M32—21no—
211M32—21no—
212M32—221no—
213M32—221no—
214C2×C16—21no—
215C2×C16—221no—
216#108—221no—
217#108—221no—
218#107C22⋊D1112yescomplemented
219#106—21no—
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—441no—
257M16—441no—
258C2×C8—112no—
259C2×C8—221no—
260C2×C8—221no—
261C2×C8—441no—
262C2×C8C2×D4411yescharacteristic
263C2×C8#433911yescharacteristic
264C2×C8D4×D1111yescharacteristic
265C2×C8#434111yescharacteristic
266C2×C8#434111yescharacteristic
267C2×C8C2×C22⋊D1111yescharacteristic
268C4⋊C4—22no—
269C22⋊C4—41no—
270C42—41no—
271C42—112no—
272C42—221no—
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#6696411yescharacteristic
285D4—42no—
286D4—42no—
287D4—81no—
288D4—81no—
289D4—442no—
290D4—442no—
291D4—8816no—
292D4—881no—
293D4—881no—
294C2×C4—42no—
295C2×C4—224no—
296C2×C4—222no—
297C2×C4#6693511yescharacteristic
298C2×C4#6693811yescharacteristic
299C2×C4D8×D1111yescharacteristic
300C2×C4SD16×D1111yescharacteristic
301C2×C4#6696711yescharacteristic
302C2×C4#6699211yescharacteristic
303C8—222no—
304C8—881no—
305C8#6693611yescharacteristic
306C8#6693911yescharacteristic
307C8#6698311yescharacteristic
308C8#6699111yescharacteristic
309C22—22no—
310C22—84no—
311C22—82no—
312C22—162no—
313C22—162no—
314C22—884no—
315C22—882no—
316C22—1762no—
317C22—1762no—
318C22#1062237711yescharacteristic
319C22#1062238911yescharacteristic
320C22#1062276311yescharacteristic
321C4—82no—
322C4—224no—
323C4#1062237311yescharacteristic
324C4#1062238611yescharacteristic
325C4#1062257411yescharacteristic
326C4#1062277611yescharacteristic
327C2—21no—
328C2—21no—
329C2—162no—
330C2—1762no—
331C2#1306984911yescharacteristic
332C2#1307069012yes—
subgroupG/H
centerC22#10622763
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2140C2
socleC22×C11#459
prime radicalC2×#10622764C2
hypercenter#2140D11
hypocenterC11#13413
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2140

Complements

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

NH ≅ G/Ntype
2. C2×#10622154C2semidirect
3. C2×#10622201C2semidirect
4. #13070331C2semidirect
5. #13069365C2semidirect
6. #13066697C2semidirect
7. C11×#2140C2semidirect
53. C11×#107D4semidirect
114. #2140D11semidirect
218. #107C22⋊D11semidirect
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×#106221542
C2×#106222012
#130703312
#130693652
#130666972
C11×#21402
#1341311