Finite Group Databasebeta

← #14658500

Subgroups — #14658500

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#13068773C211yesmaximal, characteristic
2#13068621C211yesmaximal, characteristic
3#13068621C211yesmaximal, characteristic
4#13066500C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066451C211yesmaximal, characteristic
7C11×#1984C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66899—21no—
12C2×#66899—21no—
13C2×#66881—21no—
14C2×#66881—21no—
15#10622548C2211yescharacteristic
16#10622548C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C11×#336—21no—
20C11×#336—21no—
21#10622167—21no—
22#10622167—21no—
23C22×Q8×C11D411yescharacteristic
24C22×C8×C11—21no—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C4×Q8×C11—21no—
28C4×Q8×C11—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C4×C8×C11—21no—
46C4×C8×C11—21no—
47#66899—42no—
48#66899—42no—
49#66881—42no—
50#66881—42no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55#10620—111nomaximal, Sylow
56C2×Q8×C11—21no—
57C2×Q8×C11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11SD1612yes—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×Dic11—41no—
68C22×Dic11—41no—
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×C11SD1612yes—
77C2×C8×C11Q1612yes—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C42×C11—41no—
83C42×C11—41no—
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
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⋊Dic11—81no—
97C4⋊Dic11—81no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#1984D1111yescharacteristic
105#1844—111no—
106#1803—111no—
107#1803—111no—
108#1296—111no—
109#1296—111no—
110#1277—111no—
111C23×C11#12111yescharacteristic
112Q8×C11—22no—
113Q8×C11—22no—
114Q8×C11—41no—
115Q8×C11—41no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11#12311yescharacteristic
126C2×C4×C11#12311yescharacteristic
127C2×C4×C11#12411yescharacteristic
128C2×C4×C11#12611yescharacteristic
129C2×C4×C11#12611yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11C2×SD1611yescharacteristic
132C2×C4×C11C2×Q1611yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—81no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144C8×C11—22no—
145C8×C11—22no—
146C8×C11—81no—
147C11⋊C8—81no—
148C11⋊C8—81no—
149C2×C4×Q8C2×D1111yescharacteristic
150C2×#106—221no—
151C2×#106—221no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8—111no—
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—21no—
163#336—21no—
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—42no—
174C4×C11—81no—
175C4×C11#48111yescharacteristic
176C4×C11#48211yescharacteristic
177C4×C11#48311yescharacteristic
178C4×C11#48311yescharacteristic
179C4×C11#48411yescharacteristic
180C4×C11#48511yescharacteristic
181C4×C11#48711yescharacteristic
182C4×C11#48911yescharacteristic
183Dic11—161no—
184Dic11—161no—
185C22×Q8D4411yescharacteristic
186C22×C8—21no—
187C22×C8—221no—
188C22×C8—221no—
189C22×C8C22⋊D1111yescharacteristic
190C22×C8C22⋊D1111yescharacteristic
191C4×Q8—21no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195C2×C4⋊C4—21no—
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⋊C4D4411yescharacteristic
203C2×C42—21no—
204C2×C42C22×D1111yescharacteristic
205#106—442no—
206#106—442no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—221no—
210C4⋊C8—221no—
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—21no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8#431412yes—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—441no—
233C22×C4—441no—
234C22×C4C2×D4411yescharacteristic
235C22×C4#433911yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—441no—
245C2×C8—441no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8#432512yes—
251C2×C8#432612yes—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
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—41no—
267C42—41no—
268C42#434111yescharacteristic
269C42#434111yescharacteristic
270C42#434111yescharacteristic
271C42#434111yescharacteristic
272C11#1062011yescharacteristic, complemented, Sylow
273C23#6698311yescharacteristic
274Q8—22no—
275Q8—22no—
276Q8—41no—
277Q8—41no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4#6693211yescharacteristic
293C2×C4#6693211yescharacteristic
294C2×C4#6693911yescharacteristic
295C2×C4#6693911yescharacteristic
296C2×C4C2×#431411yescharacteristic
297C2×C4#6695711yescharacteristic
298C2×C4#6696111yescharacteristic
299C2×C4#6696211yescharacteristic
300C2×C4#6698811yescharacteristic
301C2×C4#6698911yescharacteristic
302C2×C4C2×#432511yescharacteristic
303C2×C4C2×#432611yescharacteristic
304C2×C4#6700211yescharacteristic
305C2×C4#6700411yescharacteristic
306C8—22no—
307C8—22no—
308C8—81no—
309C8—881no—
310C8—881no—
311C22#1062256611yescharacteristic
312C22#1062264011yescharacteristic
313C22#1062264411yescharacteristic
314C22#1062272711yescharacteristic
315C22#1062274711yescharacteristic
316C22#1062275411yescharacteristic
317C22#1062275411yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—81no—
322C4—1761no—
323C4—1761no—
324C4#1062233411yescharacteristic
325C4#1062233611yescharacteristic
326C4#1062234811yescharacteristic
327C4#1062235011yescharacteristic
328C4#1062265611yescharacteristic
329C4#1062265711yescharacteristic
330C4#1062266811yescharacteristic
331C4#1062269411yescharacteristic
332C2#1306796411yescharacteristic
333C2#1306799811yescharacteristic
334C2#1306808811yescharacteristic
335C2#1306812211yescharacteristic
336C2#1307002411yescharacteristic
337C2#1307004911yescharacteristic
338C2#1307006111yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1984C2
socle, prime radicalC23×C11#121
hypercenter#1984D11
hypocenterC11#10620
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

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
#130687732
#130686212
#130665002
#130664512
C11×#19842
#1062011