Finite Group Databasebeta

← #14658254

Subgroups — #14658254

Order 2816.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073651C211yesmaximal, characteristic
2#13069379C211yesmaximal, characteristic
3#13069375C211yesmaximal, characteristic
4#13068773C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×#66923—21no—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12C2×#66882—21no—
13C2×#66881—22no—
14#10622589—21no—
15#10622586—21no—
16C2×#66872—21no—
17#10622548C2211yescharacteristic
18#10622548C2211yescharacteristic
19C4×C4⋊Dic11C2211yescharacteristic
20#10622541—21no—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22#10622270—22no—
23#10622189—21no—
24#10622167—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D412yes—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—22no—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44#66923—42no—
45#66923—42no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8Q812yes—
48C4×C8×C11—21no—
49C4×C8×C11Q812yes—
50C11×#95—21no—
51C11⋊#95—22no—
52C11⋊#95—21no—
53#66882—42no—
54#66881—44no—
55#66872—42no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)Q812yes—
58#10580—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—22no—
67C22×Dic11—41no—
68C2×C8×C11—22no—
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C42×C11—41no—
79C42×C11—41no—
80C42×C11C2×Q811yescharacteristic
81C42×C11C2×Q811yescharacteristic
82C42×C11C2×Q811yescharacteristic
83C42×C11#4111yescharacteristic
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11SD1612yes—
97C4⋊Dic11SD1612yes—
98Dic11⋊C4—44no—
99Dic11⋊C4—44no—
100Dic11⋊C4—82no—
101C4×Dic11—41no—
102C4×Dic11—41no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2552—111no—
107#1948—111no—
108#1947—111no—
109#1844—111no—
110#1296—111no—
111#1279—111no—
112#1279D1111yescharacteristic
113C23×C11#12011yescharacteristic
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11C4⋊Q811yescharacteristic
126C2×C4×C11C4⋊Q811yescharacteristic
127C2×C4×C11C4⋊Q811yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11C2×SD1611yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C8×C11—24no—
149C8×C11—42no—
150C11⋊C8—42no—
151C2×#125—221no—
152C2×#107—221no—
153C2×#106—222no—
154C2×#106—221no—
155C2×C4⋊C8—111no—
156C2×C4⋊C8C2×D1111yescharacteristic
157C2×C4×C8C2×D1111yescharacteristic
158#398—222no—
159#389—221no—
160#389—221no—
161#384—111no—
162#384—111no—
163#384—221no—
164C4×C4⋊C4—111no—
165C4×C4⋊C4C2×D1111yescharacteristic
166#340—221no—
167#340—221no—
168C22×C11#39511yescharacteristic
169C22×C11#44811yescharacteristic
170C22×C11#44911yescharacteristic
171C22×C11#45011yescharacteristic
172C22×C11#45211yescharacteristic
173C22×C11#45311yescharacteristic
174C22×C11#45611yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—81no—
178C4×C11—81no—
179C4×C11#47511yescharacteristic
180C4×C11#47611yescharacteristic
181C4×C11#47811yescharacteristic
182C4×C11#47911yescharacteristic
183C4×C11#49811yescharacteristic
184C4×C11#49911yescharacteristic
185C4×C11#50111yescharacteristic
186C4×C11#50111yescharacteristic
187Dic11—42no—
188Dic11—42no—
189Dic11—82no—
190Dic11—161no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—221no—
194#125—442no—
195#125—442no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—112no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—222no—
207C2×C4⋊C4D4411yescharacteristic
208C2×C4⋊C4D4411yescharacteristic
209C2×C42—21no—
210C2×C42—221no—
211C2×C42C22×D1111yescharacteristic
212#107—442no—
213#106—442no—
214#106—444no—
215C4⋊C8—21no—
216C4⋊C8—112no—
217C4⋊C8—221no—
218C4⋊C8Dic2212yes—
219C4×C8—21no—
220C4×C8Dic2212yes—
221#95—21no—
222#95—222no—
223#95—221no—
224C2×C11#162211yescharacteristic
225C2×C11#163111yescharacteristic
226C2×C11#165311yescharacteristic
227C2×C11#165411yescharacteristic
228C2×C11#205811yescharacteristic
229C2×C11#205911yescharacteristic
230C2×C11#206011yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—222no—
236C22×C4—441no—
237C22×C4C2×D4411yescharacteristic
238C22×C4D4×D1111yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—222no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—112no—
254C4⋊C4—112no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—442no—
258C4⋊C4—442no—
259C4⋊C4—444no—
260C4⋊C4—444no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—882no—
270C42—41no—
271C42—41no—
272C42—441no—
273C42—441no—
274C42C2×Dic2211yescharacteristic
275C42C2×Dic2211yescharacteristic
276C42#434111yescharacteristic
277C42Q8×D1111yescharacteristic
278C11#1058011yescharacteristic, complemented, Sylow
279C23#6693511yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4#6692211yescharacteristic
301C2×C4#6693111yescharacteristic
302C2×C4#6693111yescharacteristic
303C2×C4#6694111yescharacteristic
304C2×C4#6694111yescharacteristic
305C2×C4#6695011yescharacteristic
306C2×C4#6695711yescharacteristic
307C2×C4#6695711yescharacteristic
308C2×C4#6696111yescharacteristic
309C2×C4#6696211yescharacteristic
310C2×C4#6696411yescharacteristic
311C2×C4SD16×D1111yescharacteristic
312C2×C4SD16×D1111yescharacteristic
313C2×C4#6697111yescharacteristic
314C8—24no—
315C8—42no—
316C8—442no—
317C22#1062226911yescharacteristic
318C22#1062234611yescharacteristic
319C22#1062234711yescharacteristic
320C22#1062238911yescharacteristic
321C22#1062241911yescharacteristic
322C22#1062243511yescharacteristic
323C22#1062243911yescharacteristic
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—442no—
329C4—442no—
330C4—882no—
331C4—1761no—
332C4#1062229611yescharacteristic
333C4#1062231511yescharacteristic
334C4#1062237411yescharacteristic
335C4#1062240411yescharacteristic
336C4#1062244211yescharacteristic
337C4#1062246011yescharacteristic
338C4#1062246811yescharacteristic
339C4#1062248911yescharacteristic
340C2#1306769111yescharacteristic
341C2#1306774611yescharacteristic
342C2#1306789611yescharacteristic
343C2#1306790211yescharacteristic
344C2#1306994811yescharacteristic
345C2#1306995511yescharacteristic
346C2#1306996011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socle, prime radicalC23×C11#120
hypercenter#1279D11
hypocenterC11#10580
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
278. C11#10580semidirect

Maximal subgroups

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

subgroupindex
#130736512
#130693792
#130693752
#130687732
#130665002
#130664562
C11×#12792
#1058011