Finite Group Databasebeta

← #14644739

Subgroups — #14644739

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068469C211yesmaximal, characteristic, complemented
2C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C2×#10622182C212yesmaximal
4#13066499C212yesmaximal, complemented
5C4×C11×#127C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11—21no—
9C2×C4×D4×C11C412yes—
10C11×#390—21no—
11C11×#390—21no—
12C11×#390C412yes—
13C11×#384C2211yescharacteristic
14C43×C11C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2212yes—
16C2×C4⋊(C11⋊C8)C2212yes—
17C2×#66867—21no—
18C2×C4×C11⋊C8—21no—
19#10622182C418yescomplemented
20#10622162—21no—
21#10622162—21no—
22C22×D4×C11—21no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C412yes—
25C23×C4×C11—22no—
26C11×#127—22no—
27C11×#127C2×C414yes—
28C4×D4×C11—44no—
29C4×D4×C11—44no—
30C4×D4×C11—42no—
31C4×D4×C11—42no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C22×C11⋊C8—22no—
46C22×C11⋊C8—22no—
47C4⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)C2×C414yescomplemented
50C4⋊(C11⋊C8)C2×C414yescomplemented
51#66867—42no—
52C4×C11⋊C8—42no—
53#8234—111nomaximal, Sylow
54C24×C11—22no—
55C2×D4×C11—22no—
56C2×D4×C11—24no—
57C2×D4×C11—24no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11C4214yes—
67C22×C4×C11—22no—
68C22×C4×C11—44no—
69C22×C4×C11—44no—
70C22×C4×C11—44no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C11×C4⋊C4—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—42no—
82C11×C22⋊C4—44no—
83C11×C22⋊C4—44no—
84C11×C22⋊C4—44no—
85C42×C11—22no—
86C42×C11—22no—
87C42×C11—21no—
88C42×C11—22no—
89C42×C11—21no—
90C42×C11—41no—
91C42×C11D812yes—
92C42×C11SD1612yes—
93C42×C11C22×C412yes—
94C42×C11#4112yes—
95C2×C11⋊C8—24no—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101C4×#127D1111yescharacteristic
102#1767—111no—
103C4×C4⋊C8—111no—
104C2×#331—112no—
105#1296—112no—
106C23×C11—24no—
107C23×C11—42no—
108C23×C11—42no—
109C23×C11—42no—
110C23×C11—42no—
111C23×C11—42no—
112C23×C11—42no—
113C23×C11C2×C22⋊C411yescharacteristic
114D4×C11—44no—
115D4×C11—44no—
116D4×C11—44no—
117D4×C11—44no—
118D4×C11—44no—
119D4×C11—44no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—88no—
135C2×C4×C11#10012yes—
136C2×C4×C11#10212yes—
137C2×C4×C11#10212yes—
138C2×C4×C11C2×C4211yescharacteristic
139C2×C4×C11#11711yescharacteristic
140C2×C4×C11C4×D412yes—
141C2×C4×C11C4×D412yes—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11#13512yes—
145C2×C4×C11AGL(1,ℤ/8)12yes—
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C11⋊C8—44no—
149C11⋊C8—44no—
150C2×#127C2×D1111yescharacteristic
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4Dic1112yes—
154C2×C4⋊C8—112no—
155C2×C4⋊C8—112no—
156C2×#97—221no—
157C2×C4×C8—221no—
158#390—21no—
159#390—21no—
160#390Dic1112yes—
161#384C2×D1111yescharacteristic
162C43C2×D1111yescharacteristic
163#336—221no—
164#336—221no—
165#331—118no—
166C22×C11—44no—
167C22×C11—44no—
168C22×C11—44no—
169C22×C11—82no—
170C22×C11—82no—
171C22×C11—82no—
172C22×C11—82no—
173C22×C11C4×C22⋊C411yescharacteristic
174C22×C11C2×#10011yescharacteristic
175C22×C11#41311yescharacteristic
176C22×C11C2×#10211yescharacteristic
177C22×C11#41611yescharacteristic
178C22×C11#41711yescharacteristic
179C22×C11#41811yescharacteristic
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—82no—
187C4×C11C4×D812yes—
188C4×C11C4×SD1612yes—
189C4×C11#44012yes—
190C4×C11#44212yes—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4C2×Dic1112yes—
194C23×C4—22no—
195C22×C8—222no—
196C22×C8—222no—
197#127—22no—
198#127C4×D1114yes—
199C4×D4—44no—
200C4×D4—44no—
201C4×D4—42no—
202C4×D4—42no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic1112yes—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—22no—
209C2×C42C2×Dic1111yescharacteristic
210C2×C42C2×Dic1111yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212C2×C42C22⋊D1111yescharacteristic
213C2×C42C22⋊D1111yescharacteristic
214C2×C42C22⋊D1111yescharacteristic
215C2×C42C22×D1111yescharacteristic
216C4⋊C8—114no—
217C4⋊C8—114no—
218C4⋊C8—222no—
219C4⋊C8—222no—
220#97—442no—
221C4×C8—442no—
222C2×C11—84no—
223C2×C11#154511yescharacteristic
224C2×C11#154711yescharacteristic
225C2×C11#155111yescharacteristic
226C2×C11#155311yescharacteristic
227C2×C11C4×#10011yescharacteristic
228C2×C11C4×#10211yescharacteristic
229C2×C11#176211yescharacteristic
230C24—22no—
231C2×D4—22no—
232C2×D4—24no—
233C2×D4—24no—
234C2×D4—42no—
235C2×D4—42no—
236C2×D4—41no—
237C2×D4—42no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—42no—
241C2×D4—41no—
242C2×D4C4×Dic1114yes—
243C22×C4—22no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4—44no—
247C22×C4C22⋊Dic1111yescharacteristic
248C22×C4C22⋊Dic1111yescharacteristic
249C22×C4C22⋊Dic1111yescharacteristic
250C22×C4C22⋊Dic1111yescharacteristic
251C22×C4C22×Dic1111yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254C2×C8—224no—
255C2×C8—224no—
256C2×C8—442no—
257C2×C8—442no—
258C2×C8—442no—
259C2×C8—442no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C22⋊C4—44no—
265C22⋊C4—44no—
266C22⋊C4—44no—
267C42—22no—
268C42—22no—
269C42—21no—
270C42—22no—
271C42—21no—
272C42—41no—
273C42#432312yes—
274C42#432412yes—
275C42C2×C4×D1112yes—
276C42#433912yes—
277C11#823411yescharacteristic, complemented, Sylow
278C23—24no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—42no—
284C23—42no—
285C23C2×C22⋊Dic1111yescharacteristic
286D4—44no—
287D4—44no—
288D4—44no—
289D4—44no—
290D4—44no—
291D4—44no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—88no—
307C2×C4#6689612yes—
308C2×C4#6689612yes—
309C2×C4#6689712yes—
310C2×C4C2×C4×Dic1111yescharacteristic
311C2×C4#6697911yescharacteristic
312C2×C4C4×C22⋊D1112yes—
313C2×C4C4×C22⋊D1112yes—
314C2×C4C2×#432311yescharacteristic
315C2×C4#6698512yes—
316C2×C4C2×#432411yescharacteristic
317C2×C4#6700211yescharacteristic
318C2×C4#6700312yes—
319C2×C4#6700411yescharacteristic
320C8—444no—
321C8—444no—
322C22—44no—
323C22—44no—
324C22—44no—
325C22—82no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22C4×C22⋊Dic1111yescharacteristic
330C22C2×#6689611yescharacteristic
331C22#1062282811yescharacteristic
332C22C2×#6689711yescharacteristic
333C22#1062284511yescharacteristic
334C22#1062284611yescharacteristic
335C22#1062285011yescharacteristic
336C4—22no—
337C4—22no—
338C4—22no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—82no—
343C4C4×#432312yes—
344C4#1062262712yes—
345C4C4×#432412yes—
346C4#1062263112yes—
347C2—84no—
348C2#1306728411yescharacteristic
349C2#1306729311yescharacteristic
350C2#1306731111yescharacteristic
351C2#1306732111yescharacteristic
352C2C4×#6689711yescharacteristic
353C2C4×#6689611yescharacteristic
354C2#1306844111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC4×C11×#127C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenterC4×#127D11
hypocenterC11#8234
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. #13068469C2semidirect
2. C4×C4⋊(C11⋊C8)C2semidirect
4. #13066499C2semidirect
19. #10622182C4semidirect
49. C4⋊(C11⋊C8)C2×C4semidirect
50. C4⋊(C11⋊C8)C2×C4semidirect
277. C11#8234semidirect

Maximal subgroups

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

subgroupindex
#130684692
C4×C4⋊(C11⋊C8)2
C2×#106221822
#130664992
C4×C11×#1272
#823411