Finite Group Databasebeta

← #14658358

Subgroups — #14658358

Order 2816.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069565C211yesmaximal, characteristic
2#13069377C211yesmaximal, characteristic
3#13069334C211yesmaximal, characteristic
4C2×#10622095C211yesmaximal, characteristic
5C2×#10622184C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic
7C11×#1990C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C2×Dic11⋊C8—21no—
12C2×#66872—21no—
13C4×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C11×#340—21no—
18C11×#340—21no—
19#10622188—21no—
20#10622184—22no—
21#10622167—21no—
22#10622167—21no—
23#10622167—21no—
24#10622095—22no—
25C22×Q8×C11—21no—
26C22×C8×C11D411yescharacteristic
27C22×C8×C11D411yescharacteristic
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8Q812yes—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4×Dic11—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44C4×C8×C11—21no—
45C4×C8×C11—21no—
46C11⋊#95—21no—
47Dic11⋊C8—42no—
48#66872—42no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)D412yes—
55#10597—111nomaximal, Sylow
56C2×Q8×C11—22no—
57C2×Q8×C11—41no—
58C2×Q8×C11—81no—
59C2×Q8×C11—81no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11SD1612yes—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—81no—
82C42×C11C2×D411yescharacteristic
83C42×C11C2×Q811yescharacteristic
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11SD1612yes—
90C4×Dic11—41no—
91C4×Dic11—41no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101#1990D1111yescharacteristic
102#1987—111no—
103#1948—111no—
104#1939—111no—
105C2×#334—111no—
106C2×#333—111no—
107#1296—111no—
108C23×C11#12111yescharacteristic
109Q8×C11—82no—
110Q8×C11—82no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—42no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11#12611yescharacteristic
125C2×C4×C11C2×SD1611yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C8×C11—22no—
140C8×C11—41no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143C11⋊C8—81no—
144C2×C4⋊Q8C2×D1111yescharacteristic
145C2×#106—221no—
146C2×C4⋊C8—111no—
147C2×C4⋊C8—111no—
148C2×C4⋊C8—111no—
149C2×C4⋊C8—221no—
150C2×C4×C8C2×D1111yescharacteristic
151#384C2×D1111yescharacteristic
152C4×C4⋊C4—111no—
153#340—21no—
154#340—21no—
155#340—221no—
156#340—221no—
157#340—221no—
158#336—221no—
159#334—222no—
160#333—222no—
161C22×C11#39611yescharacteristic
162C22×C11#46111yescharacteristic
163C22×C11#46411yescharacteristic
164C22×C11#46511yescharacteristic
165C22×C11#47011yescharacteristic
166C22×C11#47111yescharacteristic
167C22×C11#47211yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—82no—
171C4×C11—161no—
172C4×C11#46111yescharacteristic
173C4×C11#46411yescharacteristic
174C4×C11#46511yescharacteristic
175C4×C11#47011yescharacteristic
176C4×C11#47511yescharacteristic
177C4×C11#47511yescharacteristic
178C4×C11#47911yescharacteristic
179C4×C11#47911yescharacteristic
180Dic11—42no—
181Dic11—81no—
182C22×Q8—21no—
183C22×C8—221no—
184C22×C8—221no—
185C22×C8—221no—
186C22×C8C22⋊D1111yescharacteristic
187C22×C8C22⋊D1111yescharacteristic
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8Dic2212yes—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C42—221no—
200C2×C42C22×D1111yescharacteristic
201#106—442no—
202C4⋊C8—112no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208C4⋊C8—442no—
209C4×C8—21no—
210C4×C8—21no—
211#95—221no—
212C2×C11#167111yescharacteristic
213C2×C11#167811yescharacteristic
214C2×C11#169511yescharacteristic
215C2×C11#170411yescharacteristic
216C2×C11#206311yescharacteristic
217C2×C11#206611yescharacteristic
218C2×C11#206611yescharacteristic
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—81no—
222C2×Q8—81no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4D4×D1111yescharacteristic
228C22×C4#434111yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—222no—
236C2×C8—441no—
237C2×C8—441no—
238C2×C8—441no—
239C2×C8—441no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8—441no—
243C2×C8—441no—
244C2×C8#432512yes—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—112no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C42—441no—
259C42—441no—
260C42C2×Dic2211yescharacteristic
261C42#433911yescharacteristic
262C42D4×D1111yescharacteristic
263C42#434111yescharacteristic
264C11#1059711yescharacteristic, complemented, Sylow
265C23#6699111yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—222no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4#6693111yescharacteristic
283C2×C4#6693111yescharacteristic
284C2×C4#6693211yescharacteristic
285C2×C4#6693711yescharacteristic
286C2×C4SD16×D1111yescharacteristic
287C2×C4#6696911yescharacteristic
288C2×C4#6697111yescharacteristic
289C2×C4#6697111yescharacteristic
290C2×C4#6697711yescharacteristic
291C2×C4#6699211yescharacteristic
292C2×C4C2×#432511yescharacteristic
293C2×C4#6699511yescharacteristic
294C2×C4#6700311yescharacteristic
295C2×C4#6700411yescharacteristic
296C8—22no—
297C8—41no—
298C8—442no—
299C8—881no—
300C8—881no—
301C22#1062256111yescharacteristic
302C22#1062266711yescharacteristic
303C22#1062269611yescharacteristic
304C22#1062277311yescharacteristic
305C22#1062278411yescharacteristic
306C22#1062279011yescharacteristic
307C22#1062280211yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—161no—
312C4—442no—
313C4—881no—
314C4#1062240411yescharacteristic
315C4#1062241111yescharacteristic
316C4#1062241211yescharacteristic
317C4#1062243111yescharacteristic
318C4#1062263311yescharacteristic
319C4#1062263511yescharacteristic
320C4#1062266111yescharacteristic
321C4#1062266511yescharacteristic
322C2#1306798811yescharacteristic
323C2#1306802911yescharacteristic
324C2#1306813611yescharacteristic
325C2#1306819511yescharacteristic
326C2#1306997411yescharacteristic
327C2#1306999511yescharacteristic
328C2#1306999711yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socle, prime radicalC23×C11#121
hypercenter#1990D11
hypocenterC11#10597
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
264. C11#10597semidirect

Maximal subgroups

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

subgroupindex
#130695652
#130693772
#130693342
C2×#106220952
C2×#106221842
#130664992
C11×#19902
#1059711