Finite Group Databasebeta

← #14647142

Subgroups — #14647142

Order 2816.

496 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066457C212yesmaximal, complemented
4#13066457C212yesmaximal, complemented
5C11×#2283C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C11×#383—21no—
8C11×#382C411yescharacteristic
9C11×#382C411yescharacteristic
10C11×#381—21no—
11C11×#380C411yescharacteristic
12C11×#380C411yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15C4×C11×C22⋊C4—21no—
16C11×#376—21no—
17C2×C22⋊(C11⋊C8)—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)C2212yes—
20C2×C4×C11⋊C8C2212yes—
21#10622162—21no—
22#10622162—21no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C42×C11—24no—
33C2×C42×C11—21no—
34C2×C42×C11—21no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C22×C11⋊C8—22no—
40C22×C11⋊C8—22no—
41C11×#95—21no—
42C11×#95—21no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C22⋊(C11⋊C8)—24no—
50C22⋊(C11⋊C8)—42no—
51C4⋊(C11⋊C8)—24no—
52C4×C11⋊C8—24no—
53#8711—111nomaximal, Sylow
54C24×C11C22⋊C411yescharacteristic
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—42no—
81C42×C11—22no—
82C42×C11—22no—
83C42×C11—22no—
84C42×C11—42no—
85C42×C11—41no—
86C42×C11—41no—
87C42×C11#4114yes—
88C2×C11⋊C8—24no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94#2283D1111yescharacteristic
95#1797—111no—
96C4×C22⋊C8—111no—
97#1279—112no—
98#1279—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11#10412yes—
106C23×C11C2×C22⋊C411yescharacteristic
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11#11712yes—
135C2×C4×C11#12312yes—
136C2×C4×C11#12312yes—
137C2×C4×C11#13112yes—
138C2×C4×C11#13112yes—
139C2×C4×C11#13512yes—
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C11⋊C8—44no—
143C11⋊C8—82no—
144C22×C42C2×D1111yescharacteristic
145C2×C4⋊C8—112no—
146C2×C22⋊C8—221no—
147C2×C22⋊C8—221no—
148C2×C4×C8—112no—
149#383—21no—
150#382Dic1111yescharacteristic
151#382Dic1111yescharacteristic
152#381—21no—
153#380Dic1111yescharacteristic
154#380Dic1111yescharacteristic
155C4×C4⋊C4C2×D1111yescharacteristic
156C4×C4⋊C4C2×D1111yescharacteristic
157C4×C22⋊C4—21no—
158#376—21no—
159#336—221no—
160#336—221no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11#38111yescharacteristic
169C22×C11#40811yescharacteristic
170C22×C11#40811yescharacteristic
171C22×C11#41611yescharacteristic
172C22×C11#41711yescharacteristic
173C22×C11C2×#10411yescharacteristic
174C22×C11#42111yescharacteristic
175C4×C11—22no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11—81no—
182C4×C11—81no—
183C4×C11#43314yes—
184C4×C11#48212yes—
185C4×C11#48512yes—
186C23×C4C2×Dic1111yescharacteristic
187C23×C4C22⋊D1111yescharacteristic
188C23×C4C22⋊D1111yescharacteristic
189C22×C8—222no—
190C22×C8—222no—
191C2×C4⋊C4C2×Dic1111yescharacteristic
192C2×C4⋊C4C2×Dic1111yescharacteristic
193C2×C4⋊C4C2×Dic1111yescharacteristic
194C2×C4⋊C4C2×Dic1111yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C42—24no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42C2×Dic1111yescharacteristic
201C2×C42C22⋊D1111yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C2×C42C22×D1111yescharacteristic
204C4⋊C8—224no—
205C22⋊C8—224no—
206C22⋊C8—442no—
207C4×C8—224no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216C2×C11—42no—
217C2×C11#148211yescharacteristic
218C2×C11#148311yescharacteristic
219C2×C11#149411yescharacteristic
220C2×C11#149511yescharacteristic
221C2×C11#181811yescharacteristic
222C2×C11#182511yescharacteristic
223C2×C11#182611yescharacteristic
224C24C22⋊Dic1111yescharacteristic
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4C22⋊Dic1111yescharacteristic
240C22×C4C22⋊Dic1111yescharacteristic
241C22×C4C22⋊Dic1111yescharacteristic
242C22×C4C22×Dic1111yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244C22×C4C2×C22⋊D1111yescharacteristic
245C2×C8—224no—
246C2×C8—442no—
247C2×C8—442no—
248C2×C8—442no—
249C2×C8—442no—
250C2×C8—442no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C42—22no—
258C42—22no—
259C42—22no—
260C42—41no—
261C42—42no—
262C42—41no—
263C42#433914yes—
264C11#871111yescharacteristic, complemented, Sylow
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23#6690112yes—
272C23C2×C22⋊Dic1111yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4#6697912yes—
301C2×C4#6698212yes—
302C2×C4#6698212yes—
303C2×C4#6700112yes—
304C2×C4#6700112yes—
305C2×C4#6700211yescharacteristic
306C2×C4#6700312yes—
307C2×C4#6700411yescharacteristic
308C8—444no—
309C8—882no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1062282411yescharacteristic
318C22#1062284511yescharacteristic
319C22#1062284611yescharacteristic
320C22#1062284711yescharacteristic
321C22#1062284711yescharacteristic
322C22C2×#6690111yescharacteristic
323C22#1062284911yescharacteristic
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—81no—
332C4#1062260912yes—
333C4#1062261314yes—
334C4#1062261612yes—
335C2—42no—
336C2#1306702411yescharacteristic
337C2#1306702911yescharacteristic
338C2#1306707611yescharacteristic
339C2#1306708111yescharacteristic
340C2#1306868711yescharacteristic
341C2#1306871111yescharacteristic
342C2#1306871511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2283C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2283D11
hypocenterC11#8711
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
3. #13066457C2semidirect
4. #13066457C2semidirect
264. C11#8711semidirect

Maximal subgroups

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

subgroupindex
#130685962
C4×C22⋊(C11⋊C8)2
#130664572
C11×#22832
#871111