Finite Group Databasebeta

← #14653576

Subgroups — #14653576

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2#13069422C211yesmaximal, characteristic
3#13069421C211yesmaximal, characteristic
4#13069419C211yesmaximal, characteristic, complemented
5#13068775C211yesmaximal, characteristic, complemented
6C2×#10622092C211yesmaximal, characteristic, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66899—22no—
13C2×#66885—22no—
14#10622701—22no—
15#10622701C414yescomplemented
16C2×#66873—22no—
17C2×#66873—22no—
18C2×#66871—22no—
19#10622548C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22C11×#340—22no—
23#10622092—22no—
24C22×Q8×C11—21no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44—21no—
28C22×C8×C11D412yes—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8C2×C412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C22×C11⋊C8D412yes—
43C22×C11⋊C8D412yes—
44#66927—21no—
45#66927—21no—
46#66927—21no—
47#66927C2×C412yes—
48C4×C8×C11—21no—
49C4×C8×C11—21no—
50#66899—44no—
51#66885—44no—
52#66873—28no—
53#66873—44no—
54#66871—44no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8C2×C412yes—
58C4×C11⋊C8D412yes—
59#9830—111nomaximal, Sylow
60C23×D11—41no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×Q8×C11—42no—
64C2×Q8×C11—42no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—41no—
71C2×D44—22no—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—42no—
78C2×D44—42no—
79C2×D44—42no—
80C2×D44—42no—
81C2×D44—42no—
82C2×D44—42no—
83C2×C8×C11—22no—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—42no—
93C42×C11C22×C411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C4⋊Dic11—42no—
98C4⋊Dic11—42no—
99C4⋊Dic11—42no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8C22⋊C414yes—
105C2×C11⋊C8D814yes—
106C2×#486—111no—
107#1990D1111yescharacteristic, complemented
108#1957—111no—
109#1957—111no—
110#1956—111no—
111#1845—111no—
112C2×#322—111no—
113C23×C11#12711yescharacteristic
114C22×D11—42no—
115C22×D11—81no—
116C22×D11—81no—
117C22×D11—81no—
118C22×D11—81no—
119C22×D11—81no—
120C22×D11—81no—
121Q8×C11—44no—
122Q8×C11—82no—
123C2×C4×C11—42no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11C2×C22⋊C411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11C2×D812yes—
136C2×C4×C11#13512yes—
137C2×C4×C11AGL(1,ℤ/8)12yes—
138C2×C4×C11AGL(1,ℤ/8)12yes—
139C2×C4×C11#13712yes—
140C2×C4×C11#13712yes—
141C2×Dic11—81no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144D44—44no—
145D44—44no—
146D44—44no—
147D44—82no—
148D44—82no—
149D44—82no—
150C8×C11—42no—
151C11⋊C8—24no—
152C11⋊C8—24no—
153C2×C4⋊Q8C2×D1111yescharacteristic
154C2×#127—111no—
155#486—114no—
156#486—222no—
157C2×#107—222no—
158C2×#103—222no—
159C2×#102—222no—
160C2×#102—222no—
161C2×#102—222no—
162C2×C4×C8—111no—
163C2×C4×C8—111no—
164C2×C4×C8C2×D1111yescharacteristic
165#384—111no—
166#384C2×D1111yescharacteristic
167#340—22no—
168#322—222no—
169C22×C11#39011yescharacteristic
170C22×C11#49311yescharacteristic
171C22×C11#49511yescharacteristic
172C22×C11#49611yescharacteristic
173C22×C11#49611yescharacteristic
174C22×C11#49711yescharacteristic
175C22×C11#49711yescharacteristic
176C2×D11—82no—
177C2×D11—82no—
178C2×D11—82no—
179C2×D11—161no—
180C2×D11—161no—
181C2×D11—161no—
182C2×D11—161no—
183C4×C11—82no—
184C4×C11—161no—
185C4×C11#41712yes—
186C4×C11C4×D812yes—
187C4×C11#44012yes—
188C4×C11#46612yes—
189C4×C11#46812yes—
190C4×C11#48912yes—
191Dic11—161no—
192C22×Q8—21no—
193C22×D4—221no—
194C22×D4—221no—
195C22×D4—221no—
196C22×C8—112no—
197C22×C8—112no—
198C22×C8C22⋊D1112yes—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8C4×D1112yes—
203#127—112no—
204#127—221no—
205#127—221no—
206#127—221no—
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×C4⋊C4—221no—
215C2×C42C22×D1111yescharacteristic
216#107—444no—
217#103—444no—
218#102—228no—
219#102—444no—
220#102—444no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—112no—
224C4×C8—112no—
225C4×C8—221no—
226C4×C8—221no—
227C2×C11#171911yescharacteristic
228C2×C11#172011yescharacteristic
229C2×C11#172111yescharacteristic
230C2×C11#172211yescharacteristic
231C2×C11#195911yescharacteristic
232C2×C11#197011yescharacteristic
233C2×C11#197311yescharacteristic
234D11—162no—
235C24—441no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×D4—222no—
241C2×D4—222no—
242C2×D4—222no—
243C2×D4—441no—
244C2×D4—441no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4—442no—
248C2×D4—442no—
249C2×D4—441no—
250C2×D4—442no—
251C2×D4—442no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—441no—
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—114no—
262C2×C8—114no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—222no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C42C2×C4×D1111yescharacteristic
278C42#433911yescharacteristic
279C42D4×D1111yescharacteristic
280C42#434111yescharacteristic
281C11#983011yescharacteristic, complemented, Sylow
282C23—442no—
283C23—881no—
284C23—881no—
285C23—881no—
286C23—881no—
287C23—881no—
288C23—881no—
289C23#6699311yescharacteristic
290Q8—44no—
291Q8—82no—
292D4—444no—
293D4—444no—
294D4—444no—
295D4—882no—
296D4—882no—
297D4—882no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—881no—
305C2×C4—881no—
306C2×C4—881no—
307C2×C4C22⋊C4×D1111yescharacteristic
308C2×C4(C22⋊D11)⋊C411yescharacteristic
309C2×C4#6693711yescharacteristic
310C2×C4#6693811yescharacteristic
311C2×C4D8×D1112yes—
312C2×C4#6696712yes—
313C2×C4#6696912yes—
314C2×C4#6697112yes—
315C2×C4C4×C22⋊D1111yescharacteristic
316C2×C4#6699211yescharacteristic
317C2×C4#6699512yes—
318C2×C4#6700212yes—
319C8—42no—
320C8—224no—
321C8—224no—
322C22—882no—
323C22—882no—
324C22—882no—
325C22—1761no—
326C22—1761no—
327C22—1761no—
328C22—1761no—
329C22#1062257011yescharacteristic
330C22#1062267111yescharacteristic
331C22#1062269911yescharacteristic
332C22#1062276411yescharacteristic
333C22#1062278111yescharacteristic
334C22#1062278911yescharacteristic
335C22#1062280311yescharacteristic
336C4—82no—
337C4—161no—
338C4—1761no—
339C4#1062236912yes—
340C4#1062238812yes—
341C4#1062240812yes—
342C4#1062241612yes—
343C4#1062263912yes—
344C4#1062266212yes—
345C2—1762no—
346C2#1306827111yescharacteristic
347C2#1306827411yescharacteristic
348C2#1306828411yescharacteristic
349C2#1306828611yescharacteristic
350C2#1306942911yescharacteristic
351C2#1306947911yescharacteristic
352C2#1306950011yescharacteristic
subgroupG/H
centerC23#66993
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socleC23×C11#127
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1990D11
hypocenterC11#9830
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13069419C2semidirect
5. #13068775C2semidirect
6. C2×#10622092C2semidirect
7. C11×#1990C2semidirect
15. #10622701C4semidirect
107. #1990D11semidirect
281. C11#9830semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
#130694222
#130694212
#130694192
#130687752
C2×#106220922
C11×#19902
#983011