Finite Group Databasebeta

← #14650529

Subgroups — #14650529

Order 2816.

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

normal subgroups only

This group has 488 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
1#13078415C211yesmaximal, characteristic
2#13077639C211yesmaximal, characteristic
3#13068627C211yesmaximal, characteristic
4#13067181C211yesmaximal, characteristic, complemented
5#13067018C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622744—21no—
14#10622734—21no—
15C2×#66885—21no—
16#10622549C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622460—22no—
19#10622459C412yescomplemented
20#10622455C412yescomplemented
21#10622447—22no—
22D11×C22⋊C8—22no—
23C8×D44—22no—
24#10622189—21no—
25#10622122—22no—
26#10622105—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C2×C11×M16—21no—
30C22×C8×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×(C2×D11)⋊C4—21no—
33#66979—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D411yescharacteristic
36#66977—21no—
37#66977—21no—
38C2×C8×D11—24no—
39C4×D44—21no—
40C4×D44—21no—
41C4×D44C2×C412yes—
42C4×D44D412yes—
43#66923—21no—
44#66922C2×C411yescharacteristic
45#66922C2×C411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8C2×C412yes—
53C11×C22⋊C8D412yes—
54C4×C8×C11—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C22⋊(C11⋊C8)—21no—
58#66885—22no—
59#66885—22no—
60#66885—42no—
61(C2×D11)⋊C8—24no—
62#66882—22no—
63#66881—22no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8D412yes—
66#9303—111nomaximal, Sylow
67C23×D11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—41no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44C22⋊C412yes—
77C2×D44SD1612yes—
78C2×D44Q1612yes—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—82no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C11×M16—41no—
85C11×M16—41no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C42×C11C22×C411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95C22⋊Dic11—41no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11C22⋊C412yes—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109C2×C11⋊C8—22no—
110C8×D11—84no—
111#3077—111no—
112#2972—111no—
113#1804—111no—
114#1518—111no—
115#1481—111no—
116#1301D1111yescharacteristic, complemented
117#1286—111no—
118C23×C11#12111yescharacteristic
119C22×D11—22no—
120C22×D11—22no—
121C22×D11—22no—
122C22×D11—81no—
123C22×D11—81no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11C2×SD1611yescharacteristic
133C2×C4×C11C2×Q1611yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143D44—22no—
144D44—22no—
145D44—22no—
146D44#10314yes—
147C4×D11—44no—
148C4×D11—82no—
149Dic22—42no—
150Dic22—81no—
151C8×C11—42no—
152C8×C11—42no—
153C8×C11—81no—
154C11⋊C8—42no—
155#533—111no—
156C2×C4×D4—111no—
157#478—222no—
158#476—112no—
159#474—112no—
160C8×D4—222no—
161C8×D4—222no—
162#431—111no—
163#431C2×D1111yescharacteristic
164#428—221no—
165#423C2×D1111yescharacteristic
166C2×C4⋊C8C2×D1111yescharacteristic
167#418—221no—
168C2×#102—221no—
169C2×C22⋊C8—222no—
170#382—111no—
171#340—221no—
172#328—222no—
173Q8⋊C8—222no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11#38611yescharacteristic
177C22×C11#46511yescharacteristic
178C22×C11#46711yescharacteristic
179C2×D11—24no—
180C2×D11—42no—
181C2×D11—42no—
182C2×D11—82no—
183C2×D11—82no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11C2×#10311yescharacteristic
189C4×C11#41611yescharacteristic
190C4×C11#46511yescharacteristic
191C4×C11#46711yescharacteristic
192Dic11—42no—
193Dic11—81no—
194Dic11—81no—
195Dic11—161no—
196C22×D4—111no—
197C23×C4—221no—
198C2×M16—21no—
199C22×C8—21no—
200C22×C8—224no—
201C4⋊Q8—111no—
202C4⋊Q8—111no—
203#125—221no—
204C22⋊Q8—221no—
205C22⋊Q8—221no—
206C4×Q8—221no—
207C4×Q8—221no—
208C4×D4—112no—
209C4×D4—112no—
210C4×D4—221no—
211C4×D4—221no—
212#117—221no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C42C22×D1111yescharacteristic
217#107—222no—
218#106—222no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—221no—
224C4⋊C8C4×D1112yes—
225#102—222no—
226#102—222no—
227#102—442no—
228C22⋊C8—224no—
229C22⋊C8—221no—
230C22⋊C8D4412yes—
231C4×C8—21no—
232C4×C8—112no—
233#95—221no—
234#95—221no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11#188111yescharacteristic
238C2×C11#189211yescharacteristic
239C2×C11#190411yescharacteristic
240D11—44no—
241C24—221no—
242C2×Q8—221no—
243C2×Q8—221no—
244C2×D4—112no—
245C2×D4—112no—
246C2×D4—112no—
247C2×D4—221no—
248C2×D4—221no—
249C2×D4—221no—
250C22×C4—221no—
251C22×C4—222no—
252C22×C4—222no—
253C22×C4—441no—
254C22×C4—882no—
255C22×C4C2×D4411yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4#434311yescharacteristic
258M16—41no—
259M16—41no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—222no—
266C2×C8—884no—
267C4⋊C4—112no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—222no—
278C22⋊C4—222no—
279C22⋊C4—441no—
280C42—441no—
281C42C2×C4×D1111yescharacteristic
282C42#433911yescharacteristic
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C11#930311yescharacteristic, complemented, Sylow
286C23—222no—
287C23—222no—
288C23—222no—
289C23—881no—
290C23—881no—
291C23#6694811yescharacteristic
292Q8—442no—
293Q8—881no—
294D4—114no—
295D4—222no—
296D4—222no—
297D4—222no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—222no—
301C2×C4—444no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—882no—
305C2×C4—881no—
306C2×C4—881no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4C4×D4411yescharacteristic
310C2×C4C22⋊C4×D1111yescharacteristic
311C2×C4#6693511yescharacteristic
312C2×C4#6693711yescharacteristic
313C2×C4#6694611yescharacteristic
314C2×C4#6694711yescharacteristic
315C2×C4#6696511yescharacteristic
316C2×C4SD16×D1111yescharacteristic
317C2×C4#6696911yescharacteristic
318C2×C4Q16×D1111yescharacteristic
319C8—42no—
320C8—42no—
321C8—81no—
322C8—442no—
323C22—21no—
324C22—21no—
325C22—224no—
326C22—442no—
327C22—442no—
328C22—882no—
329C22—882no—
330C22#1062227811yescharacteristic
331C22#1062247711yescharacteristic
332C22#1062250011yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—442no—
338C4—881no—
339C4—881no—
340C4—1761no—
341C4#1062238511yescharacteristic
342C4#1062239111yescharacteristic
343C4D11×#10311yescharacteristic
344C4#1062242611yescharacteristic
345C2—21no—
346C2—21no—
347C2—444no—
348C2#1306897911yescharacteristic
349C2#1306903811yescharacteristic
350C2#1306910211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1301D11
hypocenterC11#9303
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
4. #13067181C2semidirect
5. #13067018C2semidirect
6. #13066476C2semidirect
7. C11×#1301C2semidirect
19. #10622459C4semidirect
20. #10622455C4semidirect
116. #1301D11semidirect
285. C11#9303semidirect

Maximal subgroups

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

subgroupindex
#130784152
#130776392
#130686272
#130671812
#130670182
#130664762
C11×#13012
#930311