Finite Group Databasebeta

← #14658232

Subgroups — #14658232

Order 2816.

406 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073855C211yesmaximal, characteristic
2#13069372C211yesmaximal, characteristic
3#13068772C211yesmaximal, characteristic
4#13066500C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic
6#13066455C211yesmaximal, characteristic
7C11×#1947C211yesmaximal, characteristic
8C2×C11×#107—21no—
9C2×C11×C4⋊C8C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622590—21no—
13#10622586—21no—
14C2×#66872—22no—
15C2×#66871—21no—
16#10622549—21no—
17#10622548C2211yescharacteristic
18C4×C4⋊Dic11C2211yescharacteristic
19#10622541—21no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622273—22no—
23C11×#340—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⋊C4D411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C42×C11—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D412yes—
38C2×Dic11⋊C4—22no—
39C2×C4×Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8—21no—
42C11×#107—42no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8Q812yes—
45C11×#95—21no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—21no—
50#66872—44no—
51#66871—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)Q812yes—
54C4×C11⋊C8—21no—
55C4×C11⋊C8Q812yes—
56#10577—111nomaximal, Sylow
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—22no—
66C2×C8×C11—22no—
67C2×C8×C11—41no—
68C2×C8×C11—41no—
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—
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—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—42no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93Dic11⋊C4—82no—
94C4×Dic11—41no—
95C4×Dic11—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102#2571—111no—
103#1947—111no—
104#1947D1111yescharacteristic
105#1844—111no—
106#1296—111no—
107#1279—111no—
108#1279—111no—
109C23×C11#12011yescharacteristic
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C4⋊Q811yescharacteristic
125C2×C4×C11C4⋊Q811yescharacteristic
126C2×C4×C11C4⋊Q811yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—41no—
144C8×C11—42no—
145C11⋊C8—24no—
146C11⋊C8—42no—
147C2×#107—21no—
148C2×#107—221no—
149C2×#106—222no—
150C2×C4⋊C8—111no—
151C2×C4⋊C8C2×D1111yescharacteristic
152C2×C4×C8—111no—
153#400—222no—
154#389—221no—
155#389—221no—
156#384—111no—
157#384C2×D1111yescharacteristic
158#382—221no—
159#382—221no—
160C4×C4⋊C4—111no—
161C4×C4⋊C4C2×D1111yescharacteristic
162#340—21no—
163#340—221no—
164C22×C11#39511yescharacteristic
165C22×C11#44911yescharacteristic
166C22×C11#44911yescharacteristic
167C22×C11#45211yescharacteristic
168C22×C11#45211yescharacteristic
169C22×C11#45311yescharacteristic
170C22×C11#45611yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—81no—
174C4×C11—81no—
175C4×C11—161no—
176C4×C11#47811yescharacteristic
177C4×C11#47811yescharacteristic
178C4×C11#47911yescharacteristic
179C4×C11#47911yescharacteristic
180C4×C11#49911yescharacteristic
181C4×C11#49911yescharacteristic
182C4×C11#50111yescharacteristic
183C4×C11#50111yescharacteristic
184Dic11—81no—
185Dic11—82no—
186Dic11—81no—
187C22×C8—21no—
188C22×C8—221no—
189C22×C8—221no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—112no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4C22⋊D1111yescharacteristic
200C2×C4⋊C4C22⋊D1111yescharacteristic
201C2×C42—21no—
202C2×C42—221no—
203C2×C42C22×D1111yescharacteristic
204#107—42no—
205#107—442no—
206#106—444no—
207C4⋊C8—21no—
208C4⋊C8—112no—
209C4⋊C8—221no—
210C4⋊C8Dic2212yes—
211C4×C8—112no—
212C4×C8—221no—
213#95—21no—
214#95—222no—
215#95—222no—
216#95—222no—
217#95—221no—
218C2×C11#162411yescharacteristic
219C2×C11#163011yescharacteristic
220C2×C11#165211yescharacteristic
221C2×C11#165211yescharacteristic
222C2×C11#205911yescharacteristic
223C2×C11#205911yescharacteristic
224C2×C11#206011yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—222no—
231C22×C4D4×D1111yescharacteristic
232C22×C4D4×D1111yescharacteristic
233C22×C4C2×C22⋊D1111yescharacteristic
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—222no—
238C2×C8—222no—
239C2×C8—222no—
240C2×C8—222no—
241C2×C8—441no—
242C2×C8—441no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—442no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—882no—
262C42—41no—
263C42—41no—
264C42—441no—
265C42—441no—
266C42C2×Dic2211yescharacteristic
267C42#433911yescharacteristic
268C42Q8×D1111yescharacteristic
269C42Q8×D1111yescharacteristic
270C11#1057711yescharacteristic, complemented, Sylow
271C23#6699011yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—442no—
292C2×C4#6694111yescharacteristic
293C2×C4#6694111yescharacteristic
294C2×C4#6694911yescharacteristic
295C2×C4#6694911yescharacteristic
296C2×C4#6696411yescharacteristic
297C2×C4#6696511yescharacteristic
298C2×C4#6697111yescharacteristic
299C2×C4#6697211yescharacteristic
300C2×C4#6697711yescharacteristic
301C2×C4#6698511yescharacteristic
302C2×C4#6699511yescharacteristic
303C2×C4#6699711yescharacteristic
304C2×C4#6700311yescharacteristic
305C2×C4#6700311yescharacteristic
306C8—42no—
307C8—224no—
308C8—442no—
309C22#1062259211yescharacteristic
310C22#1062265011yescharacteristic
311C22#1062266011yescharacteristic
312C22#1062277111yescharacteristic
313C22#1062280011yescharacteristic
314C22#1062281111yescharacteristic
315C22#1062281811yescharacteristic
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—161no—
321C4—881no—
322C4—881no—
323C4—882no—
324C4#1062248911yescharacteristic
325C4#1062249011yescharacteristic
326C4#1062249111yescharacteristic
327C4#1062250411yescharacteristic
328C4#1062262211yescharacteristic
329C4#1062263511yescharacteristic
330C4#1062267711yescharacteristic
331C4#1062269311yescharacteristic
332C2#1306769811yescharacteristic
333C2#1306773611yescharacteristic
334C2#1306788411yescharacteristic
335C2#1306788511yescharacteristic
336C2#1306995211yescharacteristic
337C2#1306995411yescharacteristic
338C2#1306995911yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1947C2
socle, prime radicalC23×C11#120
hypercenter#1947D11
hypocenterC11#10577
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
270. C11#10577semidirect

Maximal subgroups

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

subgroupindex
#130738552
#130693722
#130687722
#130665002
#130664572
#130664552
C11×#19472
#1057711