Finite Group Databasebeta

← #14658262

Subgroups — #14658262

Order 2816.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069379C211yesmaximal, characteristic
2#13069379C211yesmaximal, characteristic
3#13068743C211yesmaximal, characteristic
4#13066499C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic
6#13066457C211yesmaximal, characteristic
7C11×#2552C211yesmaximal, characteristic
8C2×C11×#125—21no—
9C11×#398—22no—
10C11×#389—21no—
11C11×#389—21no—
12C11×#384—21no—
13C11×#384C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15C4×C11×C4⋊C4C2211yescharacteristic
16C2×#66872—21no—
17C2×#66872—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—
25C11×#125—42no—
26C11×#125—42no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D412yes—
37C2×C42×C11—21no—
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C22×C11⋊C8—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C11×#95—22no—
47C11×#95—21no—
48C11×#95—21no—
49#66872—42no—
50#66872—42no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)Q812yes—
54C4⋊(C11⋊C8)Q812yes—
55C4×C11⋊C8—21no—
56C4×C11⋊C8Q812yes—
57#10582—111nomaximal, Sylow
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—41no—
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—44no—
74C11×C4⋊C4—44no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—82no—
81C11×C4⋊C4SD1612yes—
82C11×C4⋊C4SD1612yes—
83C42×C11—41no—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11—41no—
87C42×C11C2×Q811yescharacteristic
88C42×C11C2×Q811yescharacteristic
89C42×C11C2×Q811yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—42no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2552D1111yescharacteristic
106#1948—111no—
107#1948—111no—
108#1834—111no—
109#1296—111no—
110#1279—111no—
111#1279—111no—
112C23×C11#12011yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11C22⋊Q811yescharacteristic
132C2×C4×C11C22⋊Q811yescharacteristic
133C2×C4×C11C4⋊Q811yescharacteristic
134C2×C4×C11C4⋊Q811yescharacteristic
135C2×C4×C11C4⋊Q811yescharacteristic
136C2×C4×C11C2×SD1611yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C11⋊C8—42no—
148C11⋊C8—42no—
149C11⋊C8—42no—
150C2×#125—21no—
151C2×#106—221no—
152C2×#106—221no—
153C2×C4⋊C8—111no—
154C2×C4⋊C8—111no—
155C2×C4×C8—111no—
156#398—22no—
157#389—21no—
158#389—21no—
159#384—21no—
160#384—111no—
161#384C2×D1111yescharacteristic
162C4×C4⋊C4C2×D1111yescharacteristic
163C4×C4⋊C4C2×D1111yescharacteristic
164#340—222no—
165#340—221no—
166#340—221no—
167C22×C11#39511yescharacteristic
168C22×C11#44811yescharacteristic
169C22×C11#44911yescharacteristic
170C22×C11#45011yescharacteristic
171C22×C11#45211yescharacteristic
172C22×C11#45411yescharacteristic
173C22×C11#45511yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—42no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—82no—
181C4×C11#47511yescharacteristic
182C4×C11#47611yescharacteristic
183C4×C11#47811yescharacteristic
184C4×C11#47911yescharacteristic
185C4×C11#49811yescharacteristic
186C4×C11#49911yescharacteristic
187C4×C11#50111yescharacteristic
188C4×C11#50111yescharacteristic
189Dic11—161no—
190C22×C8—221no—
191C22×C8—221no—
192C22×C8—221no—
193#125—42no—
194#125—42no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C4⋊C4C22⋊D1111yescharacteristic
205C2×C4⋊C4C22⋊D1111yescharacteristic
206C2×C4⋊C4C22⋊D1111yescharacteristic
207C2×C4⋊C4C22⋊D1112yes—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42C22×D1111yescharacteristic
211#106—442no—
212#106—442no—
213C4⋊C8—112no—
214C4⋊C8—112no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4×C8—112no—
218C4×C8—221no—
219#95—22no—
220#95—21no—
221#95—21no—
222C2×C11#162611yescharacteristic
223C2×C11#163511yescharacteristic
224C2×C11#164211yescharacteristic
225C2×C11#164311yescharacteristic
226C2×C11#205811yescharacteristic
227C2×C11#205911yescharacteristic
228C2×C11#206111yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—441no—
235C22×C4C2×C22⋊D1111yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238C2×C8—222no—
239C2×C8—222no—
240C2×C8—222no—
241C2×C8—441no—
242C2×C8—441no—
243C2×C8—441no—
244C2×C8—441no—
245C2×C8—441no—
246C2×C8—441no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—42no—
254C4⋊C4—44no—
255C4⋊C4—44no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—82no—
261C4⋊C4—442no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4#432412yes—
267C4⋊C4#432512yes—
268C42—41no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42Q8×D1111yescharacteristic
273C42Q8×D1111yescharacteristic
274C42Q8×D1111yescharacteristic
275C42#434311yescharacteristic
276C11#1058211yescharacteristic, complemented, Sylow
277C23#6700611yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4#6698511yescharacteristic
299C2×C4C2×#432411yescharacteristic
300C2×C4C2×#432511yescharacteristic
301C2×C4#6699511yescharacteristic
302C2×C4#6699711yescharacteristic
303C2×C4#6699711yescharacteristic
304C2×C4#6699711yescharacteristic
305C2×C4#6699911yescharacteristic
306C2×C4#6699911yescharacteristic
307C2×C4#6699911yescharacteristic
308C2×C4#6700211yescharacteristic
309C2×C4#6700311yescharacteristic
310C2×C4#6700311yescharacteristic
311C2×C4#6700411yescharacteristic
312C8—442no—
313C8—442no—
314C8—442no—
315C22#1062283111yescharacteristic
316C22#1062284011yescharacteristic
317C22#1062284211yescharacteristic
318C22#1062285111yescharacteristic
319C22#1062285211yescharacteristic
320C22#1062285511yescharacteristic
321C22#1062285811yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—81no—
327C4—82no—
328C4—81no—
329C4—1761no—
330C4#1062267611yescharacteristic
331C4#1062267711yescharacteristic
332C4#1062267811yescharacteristic
333C4#1062267911yescharacteristic
334C4#1062269211yescharacteristic
335C4#1062269311yescharacteristic
336C4#1062269711yescharacteristic
337C4#1062270711yescharacteristic
338C2#1306771211yescharacteristic
339C2#1306776711yescharacteristic
340C2#1306781611yescharacteristic
341C2#1306782311yescharacteristic
342C2#1306994611yescharacteristic
343C2#1306995111yescharacteristic
344C2#1306996311yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2552C2
socle, prime radicalC23×C11#120
hypercenter#2552D11
hypocenterC11#10582
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2552

Complements

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

NH ≅ G/Ntype
276. C11#10582semidirect

Maximal subgroups

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

subgroupindex
#130693792
#130687432
#130664992
#130664572
C11×#25522
#1058211