Finite Group Databasebeta

← #14658357

Subgroups — #14658357

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#13069576C211yesmaximal, characteristic
2#13069564C211yesmaximal, characteristic
3#13069335C211yesmaximal, characteristic
4C2×#10622118C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic
7C11×#1948C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C11×#106—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C11⋊C8)—21no—
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17C11×#340—21no—
18#10622167—21no—
19#10622167—21no—
20#10622167—21no—
21#10622167—21no—
22#10622162—21no—
23#10622119—22no—
24#10622118—22no—
25C22×Dic22—21no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C22×C11⋊C8—21no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8D411yescharacteristic
39C22×C11⋊C8D411yescharacteristic
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922Q812yes—
44C11×#106—42no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×#95—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—42no—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55#10597—111nomaximal, Sylow
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—41no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C22×Dic11—41no—
63C2×Dic22—22no—
64C2×Dic22—41no—
65C2×Dic22—81no—
66C2×Dic22—81no—
67C2×C8×C11—22no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—81no—
78C11×C4⋊C4SD1612yes—
79C42×C11—41no—
80C42×C11—41no—
81C42×C11C2×D411yescharacteristic
82C42×C11C2×Q811yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85C4⋊Dic11—22no—
86C4⋊Dic11—22no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—21no—
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⋊C8SD1612yes—
101#1990—111no—
102#1987—111no—
103#1948D1111yescharacteristic
104#1939—111no—
105C2×#334—111no—
106C2×#333—111no—
107#1296—111no—
108C23×C11#12111yescharacteristic
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11#12611yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×Dic11—42no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137Dic22—82no—
138Dic22—82no—
139C8×C11—42no—
140C11⋊C8—22no—
141C11⋊C8—41no—
142C11⋊C8—81no—
143C11⋊C8—81no—
144C2×C4⋊Q8—111no—
145C2×#106—21no—
146C2×C4⋊C8—111no—
147C2×C4⋊C8—111no—
148C2×C4⋊C8—221no—
149C2×C4⋊C8C2×D1111yescharacteristic
150C2×C4×C8—111no—
151#384C2×D1111yescharacteristic
152C4×C4⋊C4C2×D1111yescharacteristic
153#340—21no—
154#340—221no—
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—42no—
171C4×C11—81no—
172C4×C11—161no—
173C4×C11#46111yescharacteristic
174C4×C11#46411yescharacteristic
175C4×C11#46511yescharacteristic
176C4×C11#47011yescharacteristic
177C4×C11#47511yescharacteristic
178C4×C11#47511yescharacteristic
179C4×C11#47911yescharacteristic
180C4×C11#47911yescharacteristic
181Dic11—82no—
182C22×Q8—221no—
183C22×C8—21no—
184C22×C8—111no—
185C22×C8—111no—
186C22×C8—221no—
187C22×C8—221no—
188C4⋊Q8—112no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4C22⋊D1111yescharacteristic
198C2×C4⋊C4C22⋊D1111yescharacteristic
199C2×C42—21no—
200C2×C42C22×D1111yescharacteristic
201#106—42no—
202C4⋊C8—21no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—442no—
208C4⋊C8D4412yes—
209C4×C8—221no—
210C4×C8—221no—
211#95—21no—
212C2×C11#167111yescharacteristic
213C2×C11#167811yescharacteristic
214C2×C11#169511yescharacteristic
215C2×C11#170411yescharacteristic
216C2×C11#206311yescharacteristic
217C2×C11#206611yescharacteristic
218C2×C11#206611yescharacteristic
219C2×Q8—222no—
220C2×Q8—441no—
221C2×Q8—881no—
222C2×Q8—881no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—441no—
227C22×C4D4×D1111yescharacteristic
228C22×C4#434111yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—112no—
234C2×C8—221no—
235C2×C8—221no—
236C2×C8—221no—
237C2×C8—221no—
238C2×C8—221no—
239C2×C8—441no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8—441no—
243C2×C8—441no—
244C2×C8—441no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—81no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4#432412yes—
258C42—41no—
259C42—41no—
260C42C2×D4411yescharacteristic
261C42#433911yescharacteristic
262C42Q8×D1111yescharacteristic
263C42#434311yescharacteristic
264C11#1059711yescharacteristic, complemented, Sylow
265C23#6699211yescharacteristic
266Q8—882no—
267Q8—882no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—442no—
280C2×C4—881no—
281C2×C4—881no—
282C2×C4#6694811yescharacteristic
283C2×C4#6694911yescharacteristic
284C2×C4#6695011yescharacteristic
285C2×C4#6695111yescharacteristic
286C2×C4SD16×D1111yescharacteristic
287C2×C4#6696811yescharacteristic
288C2×C4#6696811yescharacteristic
289C2×C4#6696911yescharacteristic
290C2×C4#6698311yescharacteristic
291C2×C4C2×#432411yescharacteristic
292C2×C4#6699511yescharacteristic
293C2×C4#6699911yescharacteristic
294C2×C4#6700311yescharacteristic
295C2×C4#6700411yescharacteristic
296C8—42no—
297C8—222no—
298C8—441no—
299C8—881no—
300C8—881no—
301C22#1062260711yescharacteristic
302C22#1062265411yescharacteristic
303C22#1062266511yescharacteristic
304C22#1062277511yescharacteristic
305C22#1062277911yescharacteristic
306C22#1062281211yescharacteristic
307C22#1062281611yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—161no—
313C4—882no—
314C4#1062246711yescharacteristic
315C4#1062247011yescharacteristic
316C4#1062247711yescharacteristic
317C4#1062248111yescharacteristic
318C4#1062263211yescharacteristic
319C4#1062264111yescharacteristic
320C4#1062267611yescharacteristic
321C4#1062270711yescharacteristic
322C2#1306798911yescharacteristic
323C2#1306803011yescharacteristic
324C2#1306813711yescharacteristic
325C2#1306819611yescharacteristic
326C2#1306997311yescharacteristic
327C2#1306999211yescharacteristic
328C2#1306999411yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1948C2
socle, prime radicalC23×C11#121
hypercenter#1948D11
hypocenterC11#10597
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

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
#130695762
#130695642
#130693352
C2×#106221182
C2×#106221192
#130664992
C11×#19482
#1059711