Finite Group Databasebeta

← #14652124

Subgroups — #14652124

Order 2816.

398 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069578C211yesmaximal, characteristic
2#13069374C211yesmaximal, characteristic
3C4⋊C4×C11⋊C8C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic
7C11×#1981C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×#103—21no—
11C2×C11×#103—21no—
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66871—21no—
14#10622548C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4×C11⋊C8—21no—
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622185C414yescomplemented
20#10622167—21no—
21#10622167—21no—
22#10622167—21no—
23#10622162—21no—
24C22×Q8×C11—21no—
25C22×C8×C11—21no—
26C11×C4⋊Q8—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8C2×C412yes—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C22×C11⋊C8—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×#103—42no—
46C11×#103—42no—
47C11×#95—21no—
48#66871—42no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)C2×C412yes—
52C4⋊(C11⋊C8)C2×C412yes—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—42no—
56#9566—111nomaximal, Sylow
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×Dic11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4D812yes—
80C11×C4⋊C4SD1612yes—
81C42×C11—41no—
82C42×C11—41no—
83C42×C11C22×C411yescharacteristic
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—81no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8Q1612yes—
104#1990—111no—
105#1981D1111yescharacteristic
106#1947—111no—
107C8×C4⋊C4—111no—
108C2×#332—111no—
109#1296—111no—
110#1277—111no—
111C23×C11#12111yescharacteristic
112Q8×C11—42no—
113Q8×C11—42no—
114Q8×C11—81no—
115Q8×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11#11711yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11#12411yescharacteristic
132C2×C4×C11#12611yescharacteristic
133C2×C4×C11C2×D811yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11C2×Q1611yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×Dic11—81no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144C8×C11—81no—
145C11⋊C8—22no—
146C11⋊C8—42no—
147C11⋊C8—42no—
148C11⋊C8—41no—
149C2×C4⋊Q8C2×D1111yescharacteristic
150C2×#107—221no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8C2×D1111yescharacteristic
154C2×#103—21no—
155C2×#103—21no—
156C2×C4×C8—111no—
157C2×C4×C8—221no—
158#384—111no—
159C4×C4⋊C4C2×D1111yescharacteristic
160#340—221no—
161#340—221no—
162#340—221no—
163#336—221no—
164#332—114no—
165C22×C11#38811yescharacteristic
166C22×C11#46211yescharacteristic
167C22×C11#46311yescharacteristic
168C22×C11#46511yescharacteristic
169C22×C11#46611yescharacteristic
170C22×C11#47111yescharacteristic
171C22×C11#47311yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—42no—
175C4×C11—42no—
176C4×C11—82no—
177C4×C11C4×D811yescharacteristic
178C4×C11C4×SD1611yescharacteristic
179C4×C11C4×Q1611yescharacteristic
180C4×C11#44011yescharacteristic
181C4×C11#48411yescharacteristic
182C4×C11#48511yescharacteristic
183C4×C11#48611yescharacteristic
184C4×C11#48811yescharacteristic
185Dic11—161no—
186C22×Q8—21no—
187C22×C8—21no—
188C22×C8—111no—
189C22×C8—111no—
190C22×C8—221no—
191C22×C8—221no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8C4×D1112yes—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4C22⋊D1111yescharacteristic
202C2×C4⋊C4C22⋊D1111yescharacteristic
203C2×C42—21no—
204C2×C42C22×D1111yescharacteristic
205#107—442no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—112no—
209C4⋊C8—112no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#103—42no—
213#103—42no—
214C4×C8—221no—
215C4×C8—221no—
216C4×C8—442no—
217#95—21no—
218C2×C11#167211yescharacteristic
219C2×C11#167411yescharacteristic
220C2×C11#167911yescharacteristic
221C2×C11#168111yescharacteristic
222C2×C11#192811yescharacteristic
223C2×C11#193011yescharacteristic
224C2×C11#193411yescharacteristic
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—441no—
235C22×C4D4×D1111yescharacteristic
236C22×C4#434111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—112no—
242C2×C8—221no—
243C2×C8—221no—
244C2×C8—222no—
245C2×C8—221no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—222no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—441no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—881no—
264C4⋊C4#432312yes—
265C4⋊C4#432412yes—
266C42—41no—
267C42—41no—
268C42C2×C4×D1111yescharacteristic
269C42#433911yescharacteristic
270C42#434111yescharacteristic
271C42#434111yescharacteristic
272C11#956611yescharacteristic, complemented, Sylow
273C23#6699211yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4#6693011yescharacteristic
293C2×C4#6693211yescharacteristic
294C2×C4(C22⋊D11)⋊C411yescharacteristic
295C2×C4#6693611yescharacteristic
296C2×C4#6696711yescharacteristic
297C2×C4#6696911yescharacteristic
298C2×C4Q16×D1111yescharacteristic
299C2×C4#6697111yescharacteristic
300C2×C4C4×C22⋊D1111yescharacteristic
301C2×C4C2×#432311yescharacteristic
302C2×C4C2×#432411yescharacteristic
303C2×C4#6698911yescharacteristic
304C2×C4#6700311yescharacteristic
305C2×C4#6700311yescharacteristic
306C8—81no—
307C8—222no—
308C8—442no—
309C8—441no—
310C8—442no—
311C22#1062255811yescharacteristic
312C22#1062265111yescharacteristic
313C22#1062265411yescharacteristic
314C22#1062277811yescharacteristic
315C22#1062279511yescharacteristic
316C22#1062281611yescharacteristic
317C22#1062281711yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—42no—
322C4—82no—
323C4—1761no—
324C4#1062240311yescharacteristic
325C4#1062242211yescharacteristic
326C4#1062242811yescharacteristic
327C4#1062243011yescharacteristic
328C4C4×#432311yescharacteristic
329C4C4×#432411yescharacteristic
330C4#1062266911yescharacteristic
331C4#1062268311yescharacteristic
332C2#1306799611yescharacteristic
333C2#1306800811yescharacteristic
334C2#1306804111yescharacteristic
335C2#1306805511yescharacteristic
336C2#1306926011yescharacteristic
337C2#1306927411yescharacteristic
338C2#1306930211yescharacteristic
subgroupG/H
centerC23#66992
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1981C2
socle, prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1981D11
hypocenterC11#9566
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
19. #10622185C4semidirect
272. C11#9566semidirect

Maximal subgroups

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

subgroupindex
#130695782
#130693742
C4⋊C4×C11⋊C82
C2×#106221852
#130665002
#130664502
C11×#19812
#956611