Finite Group Databasebeta

← #14652012

Subgroups — #14652012

Order 2816.

378 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66897C211yesmaximal, characteristic
2#13067369C211yesmaximal, characteristic, complemented
3C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
4#13066897C211yesmaximal, characteristic, complemented
5#13066465C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1478C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×#66897C411yescharacteristic
12C2×#66897C411yescharacteristic
13C2×C4⋊(C11⋊C8)C2211yescharacteristic
14C4×#4318C2211yescharacteristic
15C4×#4318C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17C11×D4⋊C8—21no—
18C11×D4⋊C8—21no—
19D4⋊(C11⋊C8)—21no—
20D4⋊(C11⋊C8)—21no—
21#10622168C411yescharacteristic
22#10622168C411yescharacteristic
23#10622118—21no—
24#10622117—21no—
25#10622092—21no—
26C8×C11⋊C8—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11—21no—
29C4×D4×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×#4318C2×C411yescharacteristic
37C2×#4318C2×C411yescharacteristic
38C2×#4318C2×C411yescharacteristic
39C2×#4318C2×C411yescharacteristic
40C22×C11⋊C8—21no—
41C22×C11⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×C4⋊C8D411yescharacteristic
45C11×C22⋊C8—21no—
46C11×C22⋊C8—21no—
47C4×C8×C11—21no—
48C4×C8×C11—21no—
49#66897—22no—
50#66897C814yescomplemented
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53#66867—21no—
54#66867—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58C4×C11⋊C8D411yescharacteristic
59C4×C11⋊C8D411yescharacteristic
60#9550—111nomaximal, Sylow
61C24×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11C2×C812yes—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—81no—
72C22×C4×C11—81no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87#4318—21no—
88#4318—21no—
89#4318—21no—
90#4318—21no—
91#4318—21no—
92#4318C2×C812yes—
93#4318C2×C812yes—
94#4318M1612yes—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—81no—
104C4×#100—111no—
105#1565—111no—
106#1478D1111yescharacteristic
107C2×D4⋊C8—111no—
108C8×M16—111no—
109#1283—111no—
110#1278—111no—
111C23×C11—22no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—81no—
115C23×C11—81no—
116C23×C11#11711yescharacteristic
117D4×C11—22no—
118D4×C11—22no—
119D4×C11—41no—
120D4×C11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—82no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12611yescharacteristic
135C2×C4×C11C22×C811yescharacteristic
136C2×C4×C11C2×M1611yescharacteristic
137C2×C4×C11#13111yescharacteristic
138C2×C4×C11#13111yescharacteristic
139C8×C11—41no—
140C8×C11—41no—
141C8×C11—81no—
142C11⋊C8—22no—
143C11⋊C8—22no—
144C11⋊C8—22no—
145C11⋊C8—22no—
146C11⋊C8—41no—
147C11⋊C8—41no—
148C11⋊C8—81no—
149C2×C4×D4C2×D1111yescharacteristic
150#431C2×D1111yescharacteristic
151#431C2×D1111yescharacteristic
152C2×C4⋊C8—111no—
153C2×#100—111no—
154C2×#100—111no—
155C4×M16—111no—
156C4×M16—111no—
157C2×C4×C8—111no—
158#343—111no—
159#343—111no—
160#335—221no—
161#334—221no—
162D4⋊C8—21no—
163D4⋊C8—21no—
164D4⋊C8—221no—
165D4⋊C8—221no—
166#322—221no—
167C82—221no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—42no—
171C22×C11—82no—
172C22×C11—82no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11#38811yescharacteristic
176C22×C11#43111yescharacteristic
177C22×C11#43311yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—81no—
182C4×C11C8×D411yescharacteristic
183C4×C11C8×D411yescharacteristic
184C4×C11#43511yescharacteristic
185C4×C11#43611yescharacteristic
186C4×C11#47111yescharacteristic
187C4×C11#47211yescharacteristic
188C22×D4C4×D1111yescharacteristic
189C23×C4—21no—
190C2×M16—111no—
191C2×M16—111no—
192C2×M16—111no—
193C2×M16—111no—
194C22×C8—221no—
195C22×C8—221no—
196C4×D4—21no—
197C4×D4—21no—
198C4×D4—21no—
199C4×D4—21no—
200C2×C4⋊C4C4×D1111yescharacteristic
201C2×C22⋊C4—21no—
202C2×C42C22×D1111yescharacteristic
203C4⋊C8—21no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8C22⋊D1111yescharacteristic
207C4⋊C8C22⋊D1111yescharacteristic
208#100—114no—
209#100—222no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212#97—221no—
213#97—221no—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—111no—
217C4×C8—111no—
218C4×C8—221no—
219C4×C8—221no—
220C4×C8—221no—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11—82no—
224C2×C11#192311yescharacteristic
225C2×C11#193111yescharacteristic
226C2×C11#193211yescharacteristic
227C24—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4C8×D1112yes—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4C2×C4×D1111yescharacteristic
240C22×C4#434111yescharacteristic
241C22×C4#434111yescharacteristic
242M16—112no—
243M16—112no—
244M16—112no—
245M16—221no—
246M16—221no—
247M16—221no—
248M16—221no—
249M16—221no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—41no—
253C2×C8—221no—
254C2×C8—221no—
255C2×C8—221no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—442no—
260C2×C8—441no—
261C2×C8—881no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42#433911yescharacteristic
267C42D4×D1111yescharacteristic
268C42#434111yescharacteristic
269C42C2×C22⋊D1111yescharacteristic
270C11#955011yescharacteristic, complemented, Sylow
271C23—22no—
272C23—41no—
273C23—41no—
274C23—81no—
275C23—81no—
276C23#6693011yescharacteristic
277D4—22no—
278D4—22no—
279D4—41no—
280D4—41no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4#6693211yescharacteristic
290C2×C4(C22⋊D11)⋊C411yescharacteristic
291C2×C4#6693611yescharacteristic
292C2×C4C2×C8×D1111yescharacteristic
293C2×C4#6695411yescharacteristic
294C2×C4M16×D1111yescharacteristic
295C2×C4#6696011yescharacteristic
296C2×C4C4×C22⋊D1111yescharacteristic
297C2×C4#6698911yescharacteristic
298C2×C4#6699211yescharacteristic
299C8—41no—
300C8—41no—
301C8—81no—
302C8—222no—
303C8—222no—
304C8—222no—
305C8—222no—
306C8—441no—
307C8—441no—
308C8—881no—
309C22—21no—
310C22—21no—
311C22—42no—
312C22—82no—
313C22—82no—
314C22—81no—
315C22—81no—
316C22#1062233111yescharacteristic
317C22#1062233311yescharacteristic
318C22#1062255811yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—81no—
323C4(C22⋊D11)⋊C811yescharacteristic
324C4#1062234111yescharacteristic
325C4C8×C22⋊D1111yescharacteristic
326C4#1062274111yescharacteristic
327C4#1062281211yescharacteristic
328C4#1062281311yescharacteristic
329C2—21no—
330C2—21no—
331C2—82no—
332C2#1306922511yescharacteristic
333C2#1306928111yescharacteristic
334C2#1306928811yescharacteristic
subgroupG/H
centerC2×C4#66992
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1478C2
socleC22×C11#388
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1478D11
hypocenterC11#9550
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #13067369C2semidirect
4. #13066897C2semidirect
5. #13066465C2semidirect
6. #13066452C2semidirect
50. #66897C8semidirect
270. C11#9550semidirect

Maximal subgroups

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

subgroupindex
C4×#668972
#130673692
C2×D4⋊(C11⋊C8)2
#130668972
#130664652
#130664522
C11×#14782
#955011