Finite Group Databasebeta

← #14658235

Subgroups — #14658235

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#13073858C211yesmaximal, characteristic
2#13069377C211yesmaximal, characteristic
3#13069372C211yesmaximal, characteristic
4#13066499C211yesmaximal, characteristic
5#13066456C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic
7C11×#1834C211yesmaximal, characteristic
8C2×C4×C8×C11C2211yescharacteristic
9C11×#384C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622599—22no—
12#10622598—21no—
13#10622598—21no—
14#10622590—21no—
15#10622590—21no—
16C2×#66872—21no—
17C2×#66871—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19C4×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C11×#340—22no—
23#10622167—21no—
24#10622167—21no—
25C22×C8×C11—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D412yes—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11D411yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4×Dic11—21no—
39C2×C4×Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8—21no—
42C4×C8×C11—21no—
43C4×C8×C11Q812yes—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49#66872—42no—
50#66871—42no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)Q812yes—
54C4⋊(C11⋊C8)Q812yes—
55#10578—111nomaximal, Sylow
56C22×C4×C11—22no—
57C22×C4×C11—41no—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C2×C8×C11—22no—
66C2×C8×C11—41no—
67C2×C8×C11—41no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C42×C11C2×Q811yescharacteristic
79C42×C11C2×Q811yescharacteristic
80C42×C11C2×Q811yescharacteristic
81C42×C11#4111yescharacteristic
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—82no—
91C4×Dic11—41no—
92C4×Dic11—41no—
93C4×Dic11—41no—
94C4×Dic11—41no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101#2571—111no—
102#1948—111no—
103#1947—111no—
104#1834D1111yescharacteristic
105#1296—111no—
106#1279—111no—
107#1279—111no—
108C23×C11#12011yescharacteristic
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11C22⋊Q811yescharacteristic
118C2×C4×C11C22⋊Q811yescharacteristic
119C2×C4×C11C22⋊Q811yescharacteristic
120C2×C4×C11C4⋊Q811yescharacteristic
121C2×C4×C11C4⋊Q811yescharacteristic
122C2×C4×C11C4⋊Q811yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C8×C11—42no—
144C11⋊C8—42no—
145C11⋊C8—42no—
146C2×#107—221no—
147C2×#106—221no—
148C2×C4⋊C8—111no—
149C2×C4⋊C8—111no—
150C2×C4×C8C2×D1111yescharacteristic
151#400—222no—
152#389—221no—
153#389—221no—
154#384C2×D1111yescharacteristic
155#384C2×D1111yescharacteristic
156#382—221no—
157#382—221no—
158C4×C4⋊C4—111no—
159C4×C4⋊C4—111no—
160#340—22no—
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—82no—
173C4×C11—161no—
174C4×C11#47811yescharacteristic
175C4×C11#47811yescharacteristic
176C4×C11#47911yescharacteristic
177C4×C11#47911yescharacteristic
178C4×C11#49911yescharacteristic
179C4×C11#49911yescharacteristic
180C4×C11#50111yescharacteristic
181C4×C11#50111yescharacteristic
182Dic11—81no—
183Dic11—81no—
184Dic11—81no—
185Dic11—81no—
186C22×C8—21no—
187C22×C8—221no—
188C22×C8—221no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4C22⋊D1112yes—
200C2×C42—221no—
201C2×C42—221no—
202C2×C42C22×D1111yescharacteristic
203#107—442no—
204#106—442no—
205C4⋊C8—112no—
206C4⋊C8—112no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4×C8—21no—
210C4×C8Dic2212yes—
211#95—222no—
212#95—222no—
213#95—222no—
214#95—221no—
215#95—221no—
216C2×C11#162811yescharacteristic
217C2×C11#163811yescharacteristic
218C2×C11#164011yescharacteristic
219C2×C11#164611yescharacteristic
220C2×C11#205911yescharacteristic
221C2×C11#205911yescharacteristic
222C2×C11#206111yescharacteristic
223C22×C4—22no—
224C22×C4—41no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4D4×D1111yescharacteristic
230C22×C4D4×D1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—22no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—222no—
236C2×C8—222no—
237C2×C8—441no—
238C2×C8—441no—
239C2×C8—441no—
240C2×C8—441no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—882no—
260C42—441no—
261C42—441no—
262C42—441no—
263C42—441no—
264C42C2×Dic2211yescharacteristic
265C42#433911yescharacteristic
266C42Q8×D1111yescharacteristic
267C42Q8×D1111yescharacteristic
268C11#1057811yescharacteristic, complemented, Sylow
269C23#6699011yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4#6694111yescharacteristic
291C2×C4#6694111yescharacteristic
292C2×C4#6694911yescharacteristic
293C2×C4#6694911yescharacteristic
294C2×C4#6696411yescharacteristic
295C2×C4#6696511yescharacteristic
296C2×C4#6696711yescharacteristic
297C2×C4#6696811yescharacteristic
298C2×C4#6696911yescharacteristic
299C2×C4#6696911yescharacteristic
300C2×C4#6697111yescharacteristic
301C2×C4#6697211yescharacteristic
302C2×C4#6697711yescharacteristic
303C2×C4#6699711yescharacteristic
304C8—42no—
305C8—442no—
306C8—442no—
307C22#1062259211yescharacteristic
308C22#1062267411yescharacteristic
309C22#1062267511yescharacteristic
310C22#1062277111yescharacteristic
311C22#1062278511yescharacteristic
312C22#1062278611yescharacteristic
313C22#1062280011yescharacteristic
314C4—21no—
315C4—21no—
316C4—82no—
317C4—161no—
318C4—881no—
319C4—881no—
320C4—881no—
321C4—881no—
322C4#1062246911yescharacteristic
323C4#1062247011yescharacteristic
324C4#1062247111yescharacteristic
325C4#1062248411yescharacteristic
326C4#1062248911yescharacteristic
327C4#1062249011yescharacteristic
328C4#1062249111yescharacteristic
329C4#1062250411yescharacteristic
330C2#1306772311yescharacteristic
331C2#1306778511yescharacteristic
332C2#1306779911yescharacteristic
333C2#1306784111yescharacteristic
334C2#1306995211yescharacteristic
335C2#1306995611yescharacteristic
336C2#1306996611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1834C2
socle, prime radicalC23×C11#120
hypercenter#1834D11
hypocenterC11#10578
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

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
#130738582
#130693772
#130693722
#130664992
#130664562
C11×#18342
#1057811