Finite Group Databasebeta

← #14652172

Subgroups — #14652172

Order 2816.

386 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#13069578C211yesmaximal, characteristic
2#13069540C211yesmaximal, characteristic
3#13069380C211yesmaximal, characteristic
4#13068486C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic
7C2×C11×#332C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×#66899—21no—
12C2×#66899—21no—
13C2×#66881—21no—
14C2×#66879—21no—
15#10622548C2211yescharacteristic
16C4×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C11×#332C414yescomplemented
20#10622189—21no—
21#10622188—21no—
22#10622167—21no—
23#10622167—21no—
24C22×Q8×C11—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8C2×C412yes—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4×Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8C2×C412yes—
46C11×C4⋊C8C2×C412yes—
47#66899—42no—
48#66899—42no—
49C11⋊#95—21no—
50#66881—42no—
51#66879—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56#9573—111nomaximal, Sylow
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—41no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C42×C11C22×C411yescharacteristic
81C42×C11#4111yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—81no—
93C4×Dic11—41no—
94C4×Dic11—41no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8SD1612yes—
104#1990—111no—
105#1981—111no—
106#1948—111no—
107#1770—111no—
108C2×#332D1111yescharacteristic
109#1296—111no—
110#1277—111no—
111C23×C11#12111yescharacteristic
112Q8×C11—42no—
113Q8×C11—42no—
114Q8×C11—81no—
115Q8×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11#11711yescharacteristic
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11#12411yescharacteristic
126C2×C4×C11#12611yescharacteristic
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144C8×C11—42no—
145C8×C11—42no—
146C11⋊C8—22no—
147C11⋊C8—41no—
148C11⋊C8—81no—
149C2×C4⋊Q8C2×D1111yescharacteristic
150C2×#106—221no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8C2×D1111yescharacteristic
153C2×C4⋊C8C2×D1111yescharacteristic
154C2×#103—221no—
155C2×#103—221no—
156C2×#97—221no—
157C2×C4×C8—111no—
158#384—111no—
159C4×C4⋊C4—111no—
160#340—221no—
161#340—221no—
162#340—221no—
163#336—221no—
164#332Dic1114yescomplemented
165C22×C11#38811yescharacteristic
166C22×C11#46111yescharacteristic
167C22×C11#46411yescharacteristic
168C22×C11#46811yescharacteristic
169C22×C11#46911yescharacteristic
170C22×C11#47111yescharacteristic
171C22×C11#47311yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—82no—
175C4×C11C4×SD1611yescharacteristic
176C4×C11#44011yescharacteristic
177C4×C11#44111yescharacteristic
178C4×C11#44211yescharacteristic
179C4×C11#48311yescharacteristic
180C4×C11#48511yescharacteristic
181C4×C11#48911yescharacteristic
182C4×C11#49011yescharacteristic
183Dic11—81no—
184Dic11—81no—
185Dic11—161no—
186C22×Q8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—111no—
190C22×C8—111no—
191C22×C8—221no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8C2×Dic1112yes—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42—221no—
204C2×C42C22×D1111yescharacteristic
205#106—442no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8C2×Dic1112yes—
211C4⋊C8C2×Dic1112yes—
212#103—442no—
213#103—442no—
214#97—442no—
215C4×C8—221no—
216C4×C8—221no—
217#95—221no—
218C2×C11#169111yescharacteristic
219C2×C11#169311yescharacteristic
220C2×C11#170011yescharacteristic
221C2×C11#170211yescharacteristic
222C2×C11#192711yescharacteristic
223C2×C11#193011yescharacteristic
224C2×C11#193611yescharacteristic
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—41no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—441no—
235C22×C4#433911yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—112no—
245C2×C8—221no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—441no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—881no—
266C42—441no—
267C42—441no—
268C42#433911yescharacteristic
269C42#434111yescharacteristic
270C42#434111yescharacteristic
271C42C22×Dic1111yescharacteristic
272C11#957311yescharacteristic, complemented, Sylow
273C23#6693711yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4#6693211yescharacteristic
293C2×C4#6693611yescharacteristic
294C2×C4#6693811yescharacteristic
295C2×C4#6696411yescharacteristic
296C2×C4#6696411yescharacteristic
297C2×C4SD16×D1111yescharacteristic
298C2×C4#6696711yescharacteristic
299C2×C4#6696811yescharacteristic
300C2×C4#6696911yescharacteristic
301C2×C4#6697111yescharacteristic
302C2×C4#6697111yescharacteristic
303C2×C4#6697911yescharacteristic
304C2×C4D4×Dic1111yescharacteristic
305C2×C4D4×Dic1111yescharacteristic
306C8—42no—
307C8—42no—
308C8—222no—
309C8—441no—
310C8—881no—
311C22#1062236711yescharacteristic
312C22#1062236811yescharacteristic
313C22#1062239311yescharacteristic
314C22#1062239511yescharacteristic
315C22#1062241111yescharacteristic
316C22#1062243111yescharacteristic
317C22#1062256411yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—881no—
322C4—881no—
323C4—1761no—
324C4#1062237711yescharacteristic
325C4#1062237811yescharacteristic
326C4#1062241811yescharacteristic
327C4#1062242811yescharacteristic
328C4#1062276511yescharacteristic
329C4SD16×Dic1111yescharacteristic
330C4#1062277711yescharacteristic
331C4#1062279711yescharacteristic
332C2#1306811411yescharacteristic
333C2#1306812811yescharacteristic
334C2#1306817311yescharacteristic
335C2#1306818711yescharacteristic
336C2#1306925211yescharacteristic
337C2#1306927311yescharacteristic
338C2#1306931511yescharacteristic
subgroupG/H
centerC23#66937
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socle, prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9573
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
19. C11×#332C4semidirect
164. #332Dic11semidirect
272. C11#9573semidirect

Maximal subgroups

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

subgroupindex
#130695782
#130695402
#130693802
#130684862
#130665002
#130664502
C2×C11×#3322
#957311