Finite Group Databasebeta

← #14670863

Subgroups — #14670863

Order 2816.

516 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C22×#66890C211yesmaximal, characteristic
2#13077468C211yesmaximal, characteristic, complemented
3#13070333C211yesmaximal, characteristic, complemented
4#13069524C211yesmaximal, characteristic, complemented
5#13066713C211yesmaximal, characteristic, complemented
6#13066706C211yesmaximal, characteristic, complemented
7C2×C11×#361C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9#10623329—21no—
10C22×D88C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13#10622828—21no—
14#10622765—22no—
15D8×Dic11—22no—
16C2×#66890—22no—
17C2×#66890—22no—
18C2×#66890C414yescomplemented
19#10622744—21no—
20C2×#66887—21no—
21#10622719C2211yescharacteristic
22#10622714C2211yescharacteristic
23C22×C11⋊C16C2211yescharacteristic
24C11×#361—22no—
25#10622147—22no—
26C22×D4×C11—21no—
27C22×D44—21no—
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8C2×C412yes—
32C2×C11×D8D412yes—
33C2×C11×D8D412yes—
34C2×C11×M16—21no—
35C22×C8×C11C2311yescharacteristic
36C2×C22⋊Dic11—42no—
37D4×Dic11—24no—
38D4×Dic11—42no—
39#66979—21no—
40#66979D411yescharacteristic
41C2×#4318D411yescharacteristic
42C2×D88—21no—
43C2×D88—21no—
44C2×D88—21no—
45C2×D88—21no—
46C2×D88—21no—
47C2×D88C2×C412yescomplemented
48C11×M32—21no—
49C11×M32—21no—
50C2×C11×C16—21no—
51C11×#108—21no—
52C11×#108—21no—
53#66896—24no—
54#66890—28no—
55#66887—42no—
56#66885—42no—
57#66882D412yes—
58#66881—21no—
59#66879—21no—
60C8×Dic11—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16—21no—
63C2×C11⋊C16C2×C412yescomplemented
64#13017—111nomaximal, Sylow
65C24×C11—41no—
66C23×D11—41no—
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—44no—
75C2×D44—22no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C11×D8—22no—
82C11×D8—22no—
83C11×D8—22no—
84C11×D8C22⋊C414yes—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C2×C8×C11C22×C411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C22⋊Dic11—21no—
95C22⋊Dic11—44no—
96C22⋊Dic11—41no—
97C4⋊Dic11—22no—
98C4⋊Dic11D812yes—
99C4×Dic11—21no—
100C4×Dic11—41no—
101#4318—21no—
102#4318—21no—
103C2×C11⋊C8—21no—
104D88—22no—
105D88—22no—
106D88—41no—
107D88—41no—
108C11×C16—41no—
109C11⋊C16—22no—
110C22×D16—111no—
111#2948—111no—
112C2×#361D1111yescharacteristic, complemented
113#2140—111no—
114#1978—111no—
115#1382—111no—
116#1379—111no—
117C23×C11—42no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—162no—
121C23×C11AGL(1,ℤ/8)11yescharacteristic
122C22×D11—42no—
123C22×D11—81no—
124C22×D11—81no—
125C22×D11—162no—
126D4×C11—24no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—42no—
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11C2×D811yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×Dic11—22no—
137C2×Dic11—42no—
138C2×Dic11—164no—
139D44—42no—
140D44—42no—
141D44—81no—
142D44—81no—
143C8×C11—81no—
144C8×C11C2×C22⋊C411yescharacteristic
145C8×C11C4×D411yescharacteristic
146C8×C11#12111yescharacteristic
147C8×C11#12311yescharacteristic
148C11⋊C8—41no—
149C22×D8—111no—
150C22×D8C2×D1111yescharacteristic
151#518—221no—
152C2×D16—114no—
153C2×D16—222no—
154C2×D16—222no—
155C2×M32C2×D1111yescharacteristic
156C22×C16—111no—
157#442—222no—
158C4×D8—222no—
159C2×#108C2×D1111yescharacteristic
160#427—111no—
161#418—221no—
162#418—221no—
163C2×#100—221no—
164#405—111no—
165#361—22no—
166#357—222no—
167C22×C11—22no—
168C22×C11—44no—
169C22×C11—84no—
170C22×C11—162no—
171C22×C11—162no—
172C22×C11#44211yescharacteristic
173C22×C11#44711yescharacteristic
174C22×C11#46311yescharacteristic
175C2×D11—82no—
176C2×D11—162no—
177C2×D11—162no—
178C2×D11—162no—
179C4×C11#38611yescharacteristic
180C4×C11C4×D811yescharacteristic
181C4×C11#44911yescharacteristic
182C4×C11#45911yescharacteristic
183Dic11—42no—
184Dic11—82no—
185C22×D4—21no—
186C22×D4—221no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8—112no—
191C2×D8—221no—
192C2×D8—221no—
193C2×D8—221no—
194C2×D8—221no—
195C2×D8—221no—
196C2×D8C4×D1112yes—
197C2×D8D4412yes—
198C2×D8C22⋊D1112yes—
199C2×M16—21no—
200C2×M16—111no—
201C22×C8C22×D1111yescharacteristic
202C4×D4—224no—
203C4×D4—442no—
204#117—111no—
205#117—221no—
206C2×C22⋊C4—442no—
207D16—228no—
208M32—21no—
209M32—21no—
210C2×C16—21no—
211C2×C16—112no—
212C2×C16—221no—
213C2×C16—221no—
214#108—21no—
215#108—21no—
216#107—112no—
217#106—221no—
218#102—224no—
219#102—442no—
220#100—442no—
221#97—221no—
222C4×C8—221no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11—84no—
226C2×C11#187911yescharacteristic
227C2×C11#219212yes—
228D11—162no—
229C24—41no—
230C24—441no—
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—222no—
238C2×D4—441no—
239C2×D4—441no—
240C2×D4—441no—
241C2×D4—441no—
242C2×D4—441no—
243C22×C4—444no—
244C22×C4D4×D1111yescharacteristic
245D8—22no—
246D8—22no—
247D8—22no—
248D8—222no—
249D8—222no—
250D8—441no—
251D8—441no—
252D8(C2×D11)⋊C414yes—
253M16—41no—
254M16—41no—
255M16—221no—
256M16—221no—
257C2×C8—41no—
258C2×C8—221no—
259C2×C8C2×C4×D1111yescharacteristic
260C2×C8C2×D4411yescharacteristic
261C2×C8D4×D1111yescharacteristic
262C2×C8#434111yescharacteristic
263C2×C8#434111yescharacteristic
264C2×C8C2×C22⋊D1111yescharacteristic
265C4⋊C4—112no—
266C4⋊C4—222no—
267C22⋊C4—221no—
268C22⋊C4—444no—
269C22⋊C4—441no—
270C42—221no—
271C42—441no—
272C16—41no—
273C16—222no—
274C11#1301711yescharacteristic, complemented, Sylow
275C23—42no—
276C23—42no—
277C23—42no—
278C23—162no—
279C23—442no—
280C23—881no—
281C23—881no—
282C23—1762no—
283C23#6696711yescharacteristic
284D4—24no—
285D4—42no—
286D4—42no—
287D4—42no—
288D4—442no—
289D4—442no—
290D4—881no—
291D4—881no—
292C2×C4—222no—
293C2×C4—442no—
294C2×C4—1764no—
295C2×C4(C22⋊D11)⋊C411yescharacteristic
296C2×C4#6693511yescharacteristic
297C2×C4D8×D1111yescharacteristic
298C2×C4#6696411yescharacteristic
299C2×C4#6696911yescharacteristic
300C2×C4#6699211yescharacteristic
301C8—81no—
302C8—441no—
303C8(C22⋊D11)⋊C411yescharacteristic
304C8#6693911yescharacteristic
305C8C2×(C2×D11)⋊C411yescharacteristic
306C8#6699211yescharacteristic
307C22—22no—
308C22—44no—
309C22—84no—
310C22—162no—
311C22—162no—
312C22—882no—
313C22—1762no—
314C22—1762no—
315C22—1762no—
316C22#1062238611yescharacteristic
317C22#1062239811yescharacteristic
318C22#1062277811yescharacteristic
319C4—442no—
320C4—882no—
321C4#1062236911yescharacteristic
322C4#1062239411yescharacteristic
323C4#1062257111yescharacteristic
324C4#1062276311yescharacteristic
325C2—21no—
326C2—21no—
327C2—84no—
328C2—1762no—
329C2#1306896211yescharacteristic
330C2#1307057612yes—
subgroupG/H
centerC22#10622386
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#361C2
socleC22×C11#447
prime radicalC22×#66890C2
cosocleC22×C8×C11C23
hypercenterC2×#361D11
hypocenterC11#13017
LCSG ▷ C2×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. #13077468C2semidirect
3. #13070333C2semidirect
4. #13069524C2semidirect
5. #13066713C2semidirect
6. #13066706C2semidirect
7. C2×C11×#361C2semidirect
18. C2×#66890C4semidirect
47. C2×D88C2×C4semidirect
63. C2×C11⋊C16C2×C4semidirect
112. C2×#361D11semidirect
274. C11#13017semidirect

Maximal subgroups

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

subgroupindex
C22×#668902
#130774682
#130703332
#130695242
#130667132
#130667062
C2×C11×#3612
#1301711