Finite Group Databasebeta

← #14658502

Subgroups — #14658502

Order 2816.

366 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#13069552C211yesmaximal, characteristic
2#13068773C211yesmaximal, 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×#66881—21no—
13C2×#66881—21no—
14C2×#66880—21no—
15C2×#66880—21no—
16#10622548C2211yescharacteristic
17#10622548C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
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#66881—42no—
50#66881—42no—
51#66880—42no—
52#66880—42no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55#10620—111nomaximal, Sylow
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11#4111yescharacteristic
59C22×Dic11—21no—
60C22×Dic11—21no—
61C22×Dic11—41no—
62C22×Dic11—41no—
63C2×Dic22—21no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22SD1612yes—
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—
79C2×C8×C11SD1612yes—
80C2×C8×C11Q1612yes—
81C42×C11#4111yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—81no—
96C4⋊Dic11—81no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—41no—
100C4×Dic11—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#1984—111no—
105#1844—111no—
106#1803—111no—
107#1803—111no—
108#1296—111no—
109#1296—111no—
110#1277D1111yescharacteristic
111C23×C11#12111yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11#12311yescharacteristic
115C2×C4×C11#12311yescharacteristic
116C2×C4×C11#12311yescharacteristic
117C2×C4×C11#12411yescharacteristic
118C2×C4×C11#12611yescharacteristic
119C2×C4×C11#12611yescharacteristic
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11C2×SD1611yescharacteristic
122C2×C4×C11C2×Q1611yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—22no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140Dic22—22no—
141Dic22—22no—
142Dic22—41no—
143Dic22—41no—
144C8×C11—22no—
145C8×C11—22no—
146C8×C11—81no—
147C8×C11—81no—
148C11⋊C8—81no—
149C2×C4×Q8—111no—
150C2×#106—221no—
151C2×#106—221no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8C2×D1111yescharacteristic
154C2×C4⋊C8C2×D1111yescharacteristic
155C2×#103—221no—
156C2×#103—221no—
157C2×C4×C8C2×D1111yescharacteristic
158#384—111no—
159#384—111no—
160#340—221no—
161#340—221no—
162#336—221no—
163#336—221no—
164C22×C11#39711yescharacteristic
165C22×C11#46011yescharacteristic
166C22×C11#46211yescharacteristic
167C22×C11#46511yescharacteristic
168C22×C11#46811yescharacteristic
169C22×C11#47111yescharacteristic
170C22×C11#47111yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11#48111yescharacteristic
174C4×C11#48211yescharacteristic
175C4×C11#48311yescharacteristic
176C4×C11#48311yescharacteristic
177C4×C11#48411yescharacteristic
178C4×C11#48511yescharacteristic
179C4×C11#48711yescharacteristic
180C4×C11#48911yescharacteristic
181Dic11—42no—
182Dic11—81no—
183Dic11—161no—
184Dic11—161no—
185C22×Q8—111no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—221no—
189C22×C8D4411yescharacteristic
190C22×C8D4411yescharacteristic
191C4×Q8—221no—
192C4×Q8—221no—
193C4×Q8—221no—
194C4×Q8—221no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42—221no—
204C2×C42C22×D1111yescharacteristic
205#106—442no—
206#106—442no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213#103—442no—
214#103—442no—
215C4×C8—21no—
216C4×C8—21no—
217C2×C11#166611yescharacteristic
218C2×C11#167211yescharacteristic
219C2×C11#168611yescharacteristic
220C2×C11#169211yescharacteristic
221C2×C11#207211yescharacteristic
222C2×C11#207711yescharacteristic
223C2×C11#207911yescharacteristic
224C2×Q8—112no—
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—221no—
229C2×Q8—221no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—441no—
233C22×C4—441no—
234C22×C4C2×D4411yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C22×C4#434311yescharacteristic
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8#431412yes—
251C2×C8Dic4412yes—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—881no—
265C4⋊C4—881no—
266C42—441no—
267C42—441no—
268C42#433911yescharacteristic
269C42#433911yescharacteristic
270C42#434111yescharacteristic
271C42#434111yescharacteristic
272C11#1062011yescharacteristic, complemented, Sylow
273C23#6694811yescharacteristic
274Q8—222no—
275Q8—222no—
276Q8—441no—
277Q8—441no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—222no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4#6692811yescharacteristic
293C2×C4#6693611yescharacteristic
294C2×C4#6693611yescharacteristic
295C2×C4#6693911yescharacteristic
296C2×C4#6695111yescharacteristic
297C2×C4#6695111yescharacteristic
298C2×C4C2×#431411yescharacteristic
299C2×C4C2×Dic4411yescharacteristic
300C2×C4#6696111yescharacteristic
301C2×C4#6696211yescharacteristic
302C2×C4#6696411yescharacteristic
303C2×C4SD16×D1111yescharacteristic
304C2×C4#6696911yescharacteristic
305C2×C4#6697111yescharacteristic
306C8—22no—
307C8—22no—
308C8—81no—
309C8—81no—
310C8—881no—
311C22#1062228711yescharacteristic
312C22#1062246111yescharacteristic
313C22#1062246211yescharacteristic
314C22#1062247711yescharacteristic
315C22#1062249911yescharacteristic
316C22#1062251111yescharacteristic
317C22#1062251111yescharacteristic
318C4—21no—
319C4—21no—
320C4—442no—
321C4—881no—
322C4—1761no—
323C4—1761no—
324C4#1062229411yescharacteristic
325C4#1062232711yescharacteristic
326C4#1062233411yescharacteristic
327C4#1062233511yescharacteristic
328C4#1062239011yescharacteristic
329C4#1062239211yescharacteristic
330C4#1062241811yescharacteristic
331C4#1062242811yescharacteristic
332C2#1306796511yescharacteristic
333C2#1306799911yescharacteristic
334C2#1306808911yescharacteristic
335C2#1306812311yescharacteristic
336C2#1307002611yescharacteristic
337C2#1307005111yescharacteristic
338C2#1307006311yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socle, prime radicalC23×C11#121
hypercenter#1277D11
hypocenterC11#10620
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
272. C11#10620semidirect

Maximal subgroups

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

subgroupindex
#130695522
#130687732
#130686222
#130665002
C11×#12772
#1062011