Finite Group Databasebeta

← #14658536

Subgroups — #14658536

Order 2816.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069552C211yesmaximal, characteristic
2#13068744C211yesmaximal, characteristic
3#13068622C211yesmaximal, characteristic
4#13068622C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66880—21no—
13C2×#66880—21no—
14#10622548C2211yescharacteristic
15#10622548C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17#10622189—21no—
18#10622189—21no—
19#10622189—21no—
20#10622189—21no—
21#10622188—21no—
22#10622188—21no—
23C22×Dic22D411yescharacteristic
24C22×C8×C11—21no—
25C22×C8×C11—21no—
26C22×C8×C11D411yescharacteristic
27C22×C8×C11D411yescharacteristic
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×C4×Dic11—21no—
38C22×C11⋊C8—21no—
39C4×Dic22—21no—
40C4×Dic22—21no—
41C4×Dic22—21no—
42C4×Dic22—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C4×C8×C11—21no—
48C4×C8×C11—21no—
49#66880—42no—
50#66880—42no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53#10626—111nomaximal, Sylow
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11#4111yescharacteristic
57C22×Dic11—21no—
58C22×Dic11—21no—
59C22×Dic11—41no—
60C22×Dic11—41no—
61C2×Dic22—21no—
62C2×Dic22—21no—
63C2×Dic22—21no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22SD1612yes—
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C42×C11#4111yescharacteristic
80C42×C11#4111yescharacteristic
81C42×C11#4111yescharacteristic
82C42×C11#4111yescharacteristic
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—81no—
94C4⋊Dic11—81no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102#1984—111no—
103#1834—111no—
104#1803—111no—
105#1803—111no—
106#1296—111no—
107#1296—111no—
108#1277D1111yescharacteristic
109C23×C11#12111yescharacteristic
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11#12311yescharacteristic
113C2×C4×C11#12311yescharacteristic
114C2×C4×C11#12311yescharacteristic
115C2×C4×C11#12411yescharacteristic
116C2×C4×C11#12611yescharacteristic
117C2×C4×C11#12611yescharacteristic
118C2×C4×C11C2×SD1611yescharacteristic
119C2×C4×C11#13511yescharacteristic
120C2×C4×C11#13511yescharacteristic
121C2×C4×C11#13511yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C11#13711yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—22no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138Dic22—22no—
139Dic22—22no—
140Dic22—41no—
141Dic22—41no—
142C8×C11—41no—
143C8×C11—41no—
144C8×C11—81no—
145C8×C11—81no—
146C11⋊C8—81no—
147C2×C4×Q8—111no—
148C2×C4⋊C8—111no—
149C2×C4⋊C8C2×D1111yescharacteristic
150C2×C4⋊C8C2×D1111yescharacteristic
151C2×#103—221no—
152C2×#103—221no—
153C2×C4×C8C2×D1111yescharacteristic
154#384—111no—
155#384—111no—
156#340—221no—
157#340—221no—
158#340—221no—
159#340—221no—
160#336—221no—
161#336—221no—
162C22×C11#39711yescharacteristic
163C22×C11#46411yescharacteristic
164C22×C11#46411yescharacteristic
165C22×C11#46511yescharacteristic
166C22×C11#46811yescharacteristic
167C22×C11#47211yescharacteristic
168C22×C11#47311yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11#48111yescharacteristic
172C4×C11#48211yescharacteristic
173C4×C11#48311yescharacteristic
174C4×C11#48511yescharacteristic
175C4×C11#48511yescharacteristic
176C4×C11#48511yescharacteristic
177C4×C11#48811yescharacteristic
178C4×C11#49111yescharacteristic
179Dic11—42no—
180Dic11—81no—
181Dic11—161no—
182Dic11—161no—
183C22×Q8—111no—
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—221no—
187C22×C8D4411yescharacteristic
188C22×C8D4411yescharacteristic
189C4×Q8—221no—
190C4×Q8—221no—
191C4×Q8—221no—
192C4×Q8—221no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C42—221no—
202C2×C42C22×D1111yescharacteristic
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209#103—442no—
210#103—442no—
211C4×C8—21no—
212C4×C8—21no—
213C2×C11#167811yescharacteristic
214C2×C11#168011yescharacteristic
215C2×C11#169811yescharacteristic
216C2×C11#170011yescharacteristic
217C2×C11#207411yescharacteristic
218C2×C11#207711yescharacteristic
219C2×C11#207811yescharacteristic
220C2×Q8—112no—
221C2×Q8—221no—
222C2×Q8—221no—
223C2×Q8—221no—
224C2×Q8—221no—
225C2×Q8—221no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—441no—
229C22×C4—441no—
230C22×C4C2×D4411yescharacteristic
231C22×C4D4×D1111yescharacteristic
232C22×C4#434311yescharacteristic
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—441no—
246C2×C8—441no—
247C2×C8—441no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—441no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—881no—
261C4⋊C4—881no—
262C42—441no—
263C42—441no—
264C42#433911yescharacteristic
265C42#433911yescharacteristic
266C42#434111yescharacteristic
267C42#434111yescharacteristic
268C11#1062611yescharacteristic, complemented, Sylow
269C23#6694811yescharacteristic
270Q8—222no—
271Q8—222no—
272Q8—441no—
273Q8—441no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—222no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—881no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4#6692811yescharacteristic
289C2×C4#6693611yescharacteristic
290C2×C4#6693611yescharacteristic
291C2×C4#6693911yescharacteristic
292C2×C4#6695111yescharacteristic
293C2×C4#6695111yescharacteristic
294C2×C4#6695711yescharacteristic
295C2×C4#6695711yescharacteristic
296C2×C4#6696211yescharacteristic
297C2×C4#6696211yescharacteristic
298C2×C4#6696411yescharacteristic
299C2×C4SD16×D1111yescharacteristic
300C2×C4#6696911yescharacteristic
301C2×C4#6697111yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—81no—
306C8—881no—
307C22#1062228711yescharacteristic
308C22#1062245811yescharacteristic
309C22#1062245811yescharacteristic
310C22#1062247711yescharacteristic
311C22#1062249911yescharacteristic
312C22#1062250911yescharacteristic
313C22#1062251011yescharacteristic
314C4—21no—
315C4—21no—
316C4—442no—
317C4—881no—
318C4—1761no—
319C4—1761no—
320C4#1062231011yescharacteristic
321C4#1062231611yescharacteristic
322C4#1062233611yescharacteristic
323C4#1062233611yescharacteristic
324C4#1062239011yescharacteristic
325C4#1062239211yescharacteristic
326C4#1062241811yescharacteristic
327C4#1062242811yescharacteristic
328C2#1306803311yescharacteristic
329C2#1306804711yescharacteristic
330C2#1306815711yescharacteristic
331C2#1306817111yescharacteristic
332C2#1307003611yescharacteristic
333C2#1307005111yescharacteristic
334C2#1307005811yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socle, prime radicalC23×C11#121
hypercenter#1277D11
hypocenterC11#10626
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
268. C11#10626semidirect

Maximal subgroups

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

subgroupindex
#130695522
#130687442
#130686222
#130665002
C11×#12772
#1062611