Finite Group Databasebeta

← #14652115

Subgroups — #14652115

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#13069577C211yesmaximal, characteristic
2#13069538C211yesmaximal, characteristic
3#13069380C211yesmaximal, characteristic
4C8×C4⋊Dic11C211yesmaximal, characteristic
5C2×#10622120C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66881—21no—
13C2×#66880—21no—
14C2×#66880—21no—
15C2×C8×Dic11—21no—
16#10622548C2211yescharacteristic
17C4×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19#10622189—21no—
20#10622189—21no—
21#10622189—21no—
22#10622188—21no—
23#10622120C414yescomplemented
24C22×Dic22—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4×Dic11—21no—
38C22×C11⋊C8—21no—
39#66922—21no—
40#66922—21no—
41#66922—21no—
42#66922C2×C412yes—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8C2×C412yes—
47C4×C8×C11—21no—
48C4×C8×C11—21no—
49C11⋊#95—21no—
50#66881—42no—
51#66880—42no—
52#66880—42no—
53C8×Dic11—42no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)C2×C412yes—
56#9565—111nomaximal, Sylow
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×Dic11—21no—
61C22×Dic11—21no—
62C22×Dic11—41no—
63C22×Dic11—41no—
64C2×Dic22—22no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×Dic22—41no—
70C2×C8×C11—22no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11SD1612yes—
82C42×C11C22×C411yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86C4⋊Dic11—22no—
87C4⋊Dic11—22no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—81no—
97C4⋊Dic11D812yes—
98C4⋊Dic11SD1612yes—
99C4×Dic11—41no—
100C4×Dic11—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#1990—111no—
105#1981—111no—
106#1948—111no—
107C8×C4⋊C4—111no—
108C2×#332—111no—
109#1296—111no—
110#1277D1111yescharacteristic
111C23×C11#12111yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11#11711yescharacteristic
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11C4×D411yescharacteristic
117C2×C4×C11#12311yescharacteristic
118C2×C4×C11#12411yescharacteristic
119C2×C4×C11#12611yescharacteristic
120C2×C4×C11C2×D811yescharacteristic
121C2×C4×C11C2×SD1611yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140Dic22—42no—
141Dic22—42no—
142Dic22—81no—
143Dic22—81no—
144C8×C11—22no—
145C8×C11—42no—
146C8×C11—41no—
147C8×C11—81no—
148C11⋊C8—42no—
149C2×C4⋊Q8—111no—
150C2×#106—221no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8C2×D1111yescharacteristic
153C2×C4⋊C8C2×D1111yescharacteristic
154C2×#103—221no—
155C2×#103—221no—
156C2×C4×C8—221no—
157C2×C4×C8C2×D1111yescharacteristic
158#384—111no—
159C4×C4⋊C4—111no—
160#340—221no—
161#340—221no—
162#340—221no—
163#336—221no—
164#332—114no—
165C22×C11#38811yescharacteristic
166C22×C11#46111yescharacteristic
167C22×C11#46411yescharacteristic
168C22×C11#46511yescharacteristic
169C22×C11#46611yescharacteristic
170C22×C11#47111yescharacteristic
171C22×C11#47311yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11C4×D811yescharacteristic
175C4×C11C4×SD1611yescharacteristic
176C4×C11C4×SD1611yescharacteristic
177C4×C11#44111yescharacteristic
178C4×C11#48311yescharacteristic
179C4×C11#48511yescharacteristic
180C4×C11#48611yescharacteristic
181C4×C11#48811yescharacteristic
182Dic11—42no—
183Dic11—42no—
184Dic11—82no—
185Dic11—161no—
186C22×Q8—221no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—221no—
190C22×C8D4411yescharacteristic
191C22×C8D4411yescharacteristic
192C4⋊Q8—112no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42—221no—
204C2×C42C22×D1111yescharacteristic
205#106—442no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—112no—
210C4⋊C8—221no—
211C4⋊C8C4×D1112yes—
212#103—442no—
213#103—442no—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—442no—
217#95—221no—
218C2×C11#167111yescharacteristic
219C2×C11#167311yescharacteristic
220C2×C11#168011yescharacteristic
221C2×C11#168211yescharacteristic
222C2×C11#192711yescharacteristic
223C2×C11#193011yescharacteristic
224C2×C11#193411yescharacteristic
225C2×Q8—222no—
226C2×Q8—441no—
227C2×Q8—441no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4—441no—
234C22×C4—441no—
235C22×C4C2×D4411yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C22×C4#434311yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—222no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8#431412yes—
253C4⋊C4—112no—
254C4⋊C4—112no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—222no—
258C4⋊C4—222no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—881no—
266C42—441no—
267C42—441no—
268C42C2×C4×D1111yescharacteristic
269C42#433911yescharacteristic
270C42#434111yescharacteristic
271C42#434111yescharacteristic
272C11#956511yescharacteristic, complemented, Sylow
273C23#6694811yescharacteristic
274Q8—442no—
275Q8—442no—
276Q8—881no—
277Q8—881no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—222no—
281C2×C4—222no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—442no—
287C2×C4—881no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4C4×D4411yescharacteristic
293C2×C4(C22⋊D11)⋊C411yescharacteristic
294C2×C4#6693811yescharacteristic
295C2×C4#6693911yescharacteristic
296C2×C4#6694511yescharacteristic
297C2×C4#6695111yescharacteristic
298C2×C4C2×#431411yescharacteristic
299C2×C4#6695711yescharacteristic
300C2×C4#6696211yescharacteristic
301C2×C4#6696211yescharacteristic
302C2×C4D8×D1111yescharacteristic
303C2×C4SD16×D1111yescharacteristic
304C2×C4#6696911yescharacteristic
305C2×C4#6697211yescharacteristic
306C8—22no—
307C8—41no—
308C8—42no—
309C8—81no—
310C8—442no—
311C22#1062228311yescharacteristic
312C22#1062245411yescharacteristic
313C22#1062245811yescharacteristic
314C22#1062247711yescharacteristic
315C22#1062249611yescharacteristic
316C22#1062250911yescharacteristic
317C22#1062251111yescharacteristic
318C4—21no—
319C4—21no—
320C4—442no—
321C4—442no—
322C4—882no—
323C4—1761no—
324C4C4×#431411yescharacteristic
325C4#1062232911yescharacteristic
326C4#1062233411yescharacteristic
327C4#1062233611yescharacteristic
328C4#1062236911yescharacteristic
329C4#1062237311yescharacteristic
330C4#1062240111yescharacteristic
331C4#1062241311yescharacteristic
332C2#1306799211yescharacteristic
333C2#1306800611yescharacteristic
334C2#1306804711yescharacteristic
335C2#1306806111yescharacteristic
336C2#1306925111yescharacteristic
337C2#1306927211yescharacteristic
338C2#1306930011yescharacteristic
subgroupG/H
centerC23#66948
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socle, prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1277D11
hypocenterC11#9565
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
23. #10622120C4semidirect
272. C11#9565semidirect

Maximal subgroups

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

subgroupindex
#130695772
#130695382
#130693802
C8×C4⋊Dic112
C2×#106221202
#130665002
C11×#12772
#956511