Finite Group Databasebeta

← #14653523

Subgroups — #14653523

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622307C211yesmaximal, characteristic
2#13069576C211yesmaximal, characteristic, complemented
3#13069421C211yesmaximal, characteristic
4#13069421C211yesmaximal, characteristic
5#13069417C211yesmaximal, characteristic, complemented
6C2×C8×C11⋊C8C211yesmaximal, characteristic, complemented
7C11×#1834C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C11×#384C2211yescharacteristic
13C2×#66885—22no—
14C2×#66874—22no—
15C2×#66873—22no—
16C2×#66873—22no—
17C2×C4×C11⋊C8C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622307—22no—
20#10622307C414yescomplemented
21C11×#340—22no—
22#10622167—22no—
23C8×C11⋊C8—22no—
24C22×D44—21no—
25C22×D44—21no—
26C22×D44—21no—
27C22×Dic22—21no—
28C22×C8×C11D412yes—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C22×C11⋊C8D412yes—
39C22×C11⋊C8D412yes—
40#66927—21no—
41#66927—21no—
42#66927—21no—
43#66927C2×C412yes—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922C2×C412yes—
48C4×C8×C11C2×C412yes—
49C4×C8×C11D412yes—
50#66885—28no—
51#66874—44no—
52#66873—44no—
53#66873—44no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58#9822—111nomaximal, Sylow
59C23×D11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—41no—
66C2×D44—22no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—41no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—42no—
73C2×D44—42no—
74C2×D44—42no—
75C2×D44—42no—
76C2×D44—42no—
77C2×D44—42no—
78C2×Dic22—22no—
79C2×Dic22—41no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11C22⋊C414yes—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—42no—
91C42×C11C22×C411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94C42×C11#4111yescharacteristic
95C4⋊Dic11—22no—
96C4⋊Dic11—22no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8D814yes—
104C2×C11⋊C8SD1614yes—
105C2×#486—111no—
106#1990—111no—
107#1957—111no—
108#1957—111no—
109#1956—111no—
110#1834D1111yescharacteristic, complemented
111C2×C82—111no—
112C23×C11#12711yescharacteristic
113C22×D11—42no—
114C22×D11—81no—
115C22×D11—81no—
116C22×D11—81no—
117C22×D11—81no—
118C22×D11—81no—
119C22×D11—81no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12411yescharacteristic
132C2×C4×C11C2×D812yes—
133C2×C4×C11C2×SD1612yes—
134C2×C4×C11#13512yes—
135C2×C4×C11#13512yes—
136C2×C4×C11#13512yes—
137C2×C4×C11#13512yes—
138C2×Dic11—42no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141D44—44no—
142D44—44no—
143D44—44no—
144D44—82no—
145D44—82no—
146D44—82no—
147Dic22—44no—
148Dic22—82no—
149C8×C11—24no—
150C11⋊C8—24no—
151C11⋊C8—24no—
152C2×C4⋊Q8—111no—
153C2×#127—111no—
154#486—114no—
155#486—222no—
156C2×#103—222no—
157C2×#102—222no—
158C2×#102—222no—
159C2×#102—222no—
160C2×C4×C8—111no—
161C2×C4×C8—111no—
162C2×C4×C8C2×D1111yescharacteristic
163#384C2×D1111yescharacteristic
164#384C2×D1111yescharacteristic
165#340—22no—
166#340—222no—
167C82—222no—
168C22×C11#39011yescharacteristic
169C22×C11#49211yescharacteristic
170C22×C11#49311yescharacteristic
171C22×C11#49511yescharacteristic
172C22×C11#49511yescharacteristic
173C22×C11#49511yescharacteristic
174C22×C11#49511yescharacteristic
175C2×D11—82no—
176C2×D11—82no—
177C2×D11—82no—
178C2×D11—161no—
179C2×D11—161no—
180C2×D11—161no—
181C2×D11—161no—
182C4×C11—161no—
183C4×C11—161no—
184C4×C11#41612yes—
185C4×C11C4×D812yes—
186C4×C11C4×SD1612yes—
187C4×C11#46512yes—
188C4×C11#46612yes—
189C4×C11#48812yes—
190Dic11—82no—
191C22×Q8—221no—
192C22×D4—221no—
193C22×D4—221no—
194C22×D4—221no—
195C22×C8—112no—
196C22×C8—112no—
197C22×C8C22⋊D1112yes—
198C4⋊Q8—112no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202#127—112no—
203#127—221no—
204#127—221no—
205#127—221no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C42C22×D1111yescharacteristic
215#103—444no—
216#102—228no—
217#102—444no—
218#102—444no—
219C4×C8—221no—
220C4×C8—221no—
221C4×C8—221no—
222C4×C8—221no—
223C4×C8C4×D1112yes—
224C4×C8D4412yes—
225C2×C11#170611yescharacteristic
226C2×C11#170811yescharacteristic
227C2×C11#170911yescharacteristic
228C2×C11#171111yescharacteristic
229C2×C11#195811yescharacteristic
230C2×C11#196811yescharacteristic
231C2×C11#197011yescharacteristic
232D11—162no—
233C24—441no—
234C2×Q8—222no—
235C2×Q8—441no—
236C2×Q8—442no—
237C2×Q8—442no—
238C2×D4—222no—
239C2×D4—222no—
240C2×D4—222no—
241C2×D4—441no—
242C2×D4—441no—
243C2×D4—442no—
244C2×D4—442no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4—441no—
248C2×D4—442no—
249C2×D4—442no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—441no—
253C22×C4D4×D1111yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—114no—
259C2×C8—114no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8(C2×D11)⋊C414yes—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C42C2×C4×D1111yescharacteristic
276C42C2×D4411yescharacteristic
277C42#434311yescharacteristic
278C42#434311yescharacteristic
279C11#982211yescharacteristic, complemented, Sylow
280C23—442no—
281C23—881no—
282C23—881no—
283C23—881no—
284C23—881no—
285C23—881no—
286C23—881no—
287C23#6699311yescharacteristic
288Q8—444no—
289Q8—882no—
290D4—444no—
291D4—444no—
292D4—444no—
293D4—882no—
294D4—882no—
295D4—882no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—442no—
303C2×C4—881no—
304C2×C4—881no—
305C2×C4#6694611yescharacteristic
306C2×C4#6694611yescharacteristic
307C2×C4#6694811yescharacteristic
308C2×C4#6694811yescharacteristic
309C2×C4D8×D1112yes—
310C2×C4SD16×D1112yes—
311C2×C4#6696912yes—
312C2×C4#6697212yes—
313C2×C4C2×(C2×D11)⋊C411yescharacteristic
314C2×C4#6700011yescharacteristic
315C2×C4#6700312yes—
316C2×C4#6700312yes—
317C8—24no—
318C8—224no—
319C8—224no—
320C22—882no—
321C22—882no—
322C22—882no—
323C22—1761no—
324C22—1761no—
325C22—1761no—
326C22—1761no—
327C22#1062260111yescharacteristic
328C22#1062267211yescharacteristic
329C22#1062267211yescharacteristic
330C22#1062276411yescharacteristic
331C22#1062278111yescharacteristic
332C22#1062278811yescharacteristic
333C22#1062280411yescharacteristic
334C4—161no—
335C4—161no—
336C4—882no—
337C4#1062246512yes—
338C4#1062247712yes—
339C4#1062248512yes—
340C4#1062249612yes—
341C4#1062261512yes—
342C4#1062268112yes—
343C2—1762no—
344C2#1306820711yescharacteristic
345C2#1306821911yescharacteristic
346C2#1306822011yescharacteristic
347C2#1306822911yescharacteristic
348C2#1306942511yescharacteristic
349C2#1306946811yescharacteristic
350C2#1306948011yescharacteristic
subgroupG/H
centerC23#66993
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1834C2
socleC23×C11#127
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1834D11
hypocenterC11#9822
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #13069576C2semidirect
5. #13069417C2semidirect
6. C2×C8×C11⋊C8C2semidirect
7. C11×#1834C2semidirect
20. #10622307C4semidirect
110. #1834D11semidirect
279. C11#9822semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
#130695762
#130694212
#130694172
C2×C8×C11⋊C82
C11×#18342
#982211