Finite Group Databasebeta

← #14658234

Subgroups — #14658234

Order 2816.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069379C211yesmaximal, characteristic
2#13069374C211yesmaximal, characteristic
3#13068743C211yesmaximal, characteristic
4#13066499C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic
6#13066457C211yesmaximal, characteristic
7C11×#2571C211yesmaximal, characteristic
8C11×#400—22no—
9C11×#389—21no—
10C11×#389—21no—
11C11×#384C2211yescharacteristic
12C11×#382—21no—
13C11×#382—21no—
14C4×C11×C4⋊C4C2211yescharacteristic
15C4×C11×C4⋊C4C2211yescharacteristic
16C2×#66872—21no—
17C2×#66871—21no—
18#10622548C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622167—22no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D412yes—
33C2×C42×C11—21no—
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⋊C8—21no—
42C11×#95—22no—
43C11×#95—22no—
44C11×#95—22no—
45C11×#95—21no—
46C11×#95—21no—
47#66872—42no—
48#66871—42no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)Q812yes—
52C4⋊(C11⋊C8)Q812yes—
53C4×C11⋊C8—21no—
54C4×C11⋊C8Q812yes—
55#10578—111nomaximal, Sylow
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—41no—
65C11×C4⋊C4—21no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—82no—
79C42×C11—41no—
80C42×C11—41no—
81C42×C11—41no—
82C42×C11—41no—
83C42×C11C2×Q811yescharacteristic
84C42×C11C2×Q811yescharacteristic
85C42×C11C2×Q811yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—42no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101#2571D1111yescharacteristic
102#1948—111no—
103#1947—111no—
104#1834—111no—
105#1296—111no—
106#1279—111no—
107#1279—111no—
108C23×C11#12011yescharacteristic
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11C4⋊Q811yescharacteristic
130C2×C4×C11C4⋊Q811yescharacteristic
131C2×C4×C11C4⋊Q811yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—81no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143C11⋊C8—42no—
144C11⋊C8—42no—
145C11⋊C8—42no—
146C2×#107—221no—
147C2×#106—221no—
148C2×C4⋊C8—111no—
149C2×C4⋊C8—111no—
150C2×C4×C8—111no—
151#400—22no—
152#389—21no—
153#389—21no—
154#384—111no—
155#384C2×D1111yescharacteristic
156#382—21no—
157#382—21no—
158C4×C4⋊C4C2×D1111yescharacteristic
159C4×C4⋊C4C2×D1111yescharacteristic
160#340—222no—
161#340—221no—
162#340—221no—
163C22×C11#39511yescharacteristic
164C22×C11#44911yescharacteristic
165C22×C11#44911yescharacteristic
166C22×C11#45211yescharacteristic
167C22×C11#45211yescharacteristic
168C22×C11#45411yescharacteristic
169C22×C11#45511yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—81no—
173C4×C11—81no—
174C4×C11—82no—
175C4×C11—81no—
176C4×C11—81no—
177C4×C11#47811yescharacteristic
178C4×C11#47811yescharacteristic
179C4×C11#47911yescharacteristic
180C4×C11#47911yescharacteristic
181C4×C11#49911yescharacteristic
182C4×C11#49911yescharacteristic
183C4×C11#50111yescharacteristic
184C4×C11#50111yescharacteristic
185Dic11—161no—
186C22×C8—221no—
187C22×C8—221no—
188C22×C8—221no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4C22⋊D1111yescharacteristic
196C2×C4⋊C4C22⋊D1111yescharacteristic
197C2×C4⋊C4C22⋊D1111yescharacteristic
198C2×C4⋊C4C22⋊D1111yescharacteristic
199C2×C4⋊C4C22⋊D1112yes—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42C22×D1111yescharacteristic
203#107—442no—
204#106—442no—
205C4⋊C8—112no—
206C4⋊C8—112no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4×C8—112no—
210C4×C8—221no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—21no—
215#95—21no—
216C2×C11#162811yescharacteristic
217C2×C11#163811yescharacteristic
218C2×C11#164011yescharacteristic
219C2×C11#164611yescharacteristic
220C2×C11#205911yescharacteristic
221C2×C11#205911yescharacteristic
222C2×C11#206111yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—441no—
229C22×C4C2×C22⋊D1111yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—222no—
233C2×C8—222no—
234C2×C8—222no—
235C2×C8—441no—
236C2×C8—441no—
237C2×C8—441no—
238C2×C8—441no—
239C2×C8—441no—
240C2×C8—441no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—82no—
255C4⋊C4—442no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C42—41no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42Q8×D1111yescharacteristic
265C42Q8×D1111yescharacteristic
266C42Q8×D1111yescharacteristic
267C42#434311yescharacteristic
268C11#1057811yescharacteristic, complemented, Sylow
269C23#6700611yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—881no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4#6699711yescharacteristic
291C2×C4#6699711yescharacteristic
292C2×C4#6699711yescharacteristic
293C2×C4#6699911yescharacteristic
294C2×C4#6699911yescharacteristic
295C2×C4#6699911yescharacteristic
296C2×C4#6700211yescharacteristic
297C2×C4#6700211yescharacteristic
298C2×C4#6700311yescharacteristic
299C2×C4#6700311yescharacteristic
300C2×C4#6700311yescharacteristic
301C2×C4#6700311yescharacteristic
302C2×C4#6700411yescharacteristic
303C2×C4#6700411yescharacteristic
304C8—442no—
305C8—442no—
306C8—442no—
307C22#1062284211yescharacteristic
308C22#1062285111yescharacteristic
309C22#1062285111yescharacteristic
310C22#1062285211yescharacteristic
311C22#1062285211yescharacteristic
312C22#1062285511yescharacteristic
313C22#1062285811yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—82no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—1761no—
322C4#1062267611yescharacteristic
323C4#1062267611yescharacteristic
324C4#1062267711yescharacteristic
325C4#1062267711yescharacteristic
326C4#1062267811yescharacteristic
327C4#1062267811yescharacteristic
328C4#1062267911yescharacteristic
329C4#1062267911yescharacteristic
330C2#1306772611yescharacteristic
331C2#1306778811yescharacteristic
332C2#1306780211yescharacteristic
333C2#1306784411yescharacteristic
334C2#1306995111yescharacteristic
335C2#1306995111yescharacteristic
336C2#1306996311yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2571C2
socle, prime radicalC23×C11#120
hypercenter#2571D11
hypocenterC11#10578
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
268. C11#10578semidirect

Maximal subgroups

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

subgroupindex
#130693792
#130693742
#130687432
#130664992
#130664572
C11×#25712
#1057811