Finite Group Databasebeta

← #14909072

Subgroups — #14909072

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079129C211yesmaximal, characteristic, complemented
2#13079041C211yesmaximal, characteristic
3#13070850C211yesmaximal, characteristic, complemented
4#13070848C211yesmaximal, characteristic, complemented
5#13070847C211yesmaximal, characteristic, complemented
6#13070842C212yesmaximal, complemented
7#13070838C212yesmaximal, complemented
8#13070322C212yesmaximal, complemented
9#13070320C212yesmaximal, complemented
10C4×C16×D11C211yesmaximal, characteristic, complemented
11C11×#2242C211yesmaximal, characteristic, complemented
12C2×#66972C2211yescharacteristic
13C2×#66969—21no—
14C2×#66965C2211yescharacteristic
15#10623219—21no—
16#10623199—21no—
17C11×#499C2211yescharacteristic
18C11×#495C2211yescharacteristic
19#10622794C2211yescharacteristic
20#10622788—21no—
21#10622764C2211yescharacteristic
22#10622677—21no—
23#10622672—21no—
24C2×C16×D11C2212yes—
25#10622493C2212yes—
26#10622487C2212yes—
27#10622473—21no—
28#10622468—21no—
29#10622309C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622296C2211yescharacteristic
32C11×#358C2212yes—
33C11×#357C2212yes—
34C4×C11×C16C2211yescharacteristic
35#10622202C2212yes—
36#10622200C2212yes—
37#10622147C2212yes—
38#10622141C2212yes—
39C16×Dic11C2212yes—
40#10622130C2212yes—
41#10622129C2212yes—
42C4×C11⋊C16C2211yescharacteristic
43C2×#4343—21no—
44C2×#4341—21no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C11×#125—21no—
49C11×#124—21no—
50#66997—21no—
51C2×#4326—21no—
52C2×#4325—21no—
53#66993—21no—
54C2×#4324—21no—
55C2×#4323—21no—
56#66972—24no—
57#66969—44no—
58#66965—24no—
59C2×Dic44C2311yescharacteristic
60C2×D88C2311yescharacteristic
61C2×#4314—21no—
62C2×C8×D11D411yescharacteristic
63C2×C8×D11C2311yescharacteristic
64#66949—42no—
65#66945—22no—
66#66941—22no—
67#66940—42no—
68#66937—42no—
69(C22⋊D11)⋊C4—42no—
70#66928—21no—
71C42×D11D411yescharacteristic
72#66923—21no—
73C2×C11×C16C2312yes—
74C11×#107C2312yes—
75C11×#106—21no—
76C4×C8×C11C2311yescharacteristic
77#66882C2312yes—
78#66881—21no—
79C8×Dic11D411yescharacteristic
80C8×Dic11C2311yescharacteristic
81C2×C11⋊C16C2312yes—
82#66872—22no—
83#66871—22no—
84C4×C11⋊C8D411yescharacteristic
85C16×D11—24no—
86#33697—111nomaximal, Sylow
87C2×Q8×C11—21no—
88C2×D4×C11—21no—
89C2×C22⋊D11—42no—
90C2×C22⋊D11—41no—
91C22×Dic11—41no—
92#4343—42no—
93#4343—42no—
94#4341—42no—
95#4341—42no—
96C2×D44—21no—
97C2×D44—41no—
98C2×C4×D11—41no—
99C2×C4×D11D812yes—
100C2×C4×D11C2×D411yescharacteristic
101C2×Dic22—21no—
102C2×Dic22—42no—
103C11×Q16—22no—
104C11×SD16—42no—
105C11×D8—22no—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2411yescharacteristic
108C11×C4⋊C4—22no—
109C11×C4⋊C4—42no—
110C11×C22⋊C4—42no—
111C42×C11C2×D411yescharacteristic
112#4326—42no—
113#4325—42no—
114#4324—42no—
115#4323—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—42no—
118C4⋊Dic11—22no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122C4×Dic11—42no—
123C4×Dic11D812yes—
124C4×Dic11C2×D411yescharacteristic
125C2×C11⋊C8C2×D411yescharacteristic
126C2×C11⋊C8C2×D411yescharacteristic
127Dic44—22no—
128D88—22no—
129#4314—42no—
130C8×D11SD1614yes—
131C8×D11#4114yes—
132C11×C16—22no—
133C11⋊C16—22no—
134#3160—111no—
135#3147—111no—
136#2242—111no—
137#2242—111no—
138#2242—111no—
139#2242D1111yescharacteristic, complemented
140#2241—112no—
141#2240—112no—
142#2138—112no—
143#2138—112no—
144C2×C4×C16—111no—
145C23×C11—41no—
146C22×D11—41no—
147C22×D11C2×D811yescharacteristic
148Q8×C11—41no—
149Q8×C11—41no—
150D4×C11—41no—
151D4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11C2×D812yes—
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—82no—
157C22⋊D11—84no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—82no—
161C2×Dic11C2×D811yescharacteristic
162C2×Dic11C2×D812yes—
163D44—41no—
164D44—41no—
165D44—82no—
166C4×D11—24no—
167C4×D11—82no—
168C4×D11#12412yes—
169C4×D11C2×SD1612yes—
170Dic22—41no—
171Dic22—41no—
172Dic22—84no—
173C8×C11C2×SD1612yes—
174C8×C11C2×#4112yes—
175C11⋊C8#12412yes—
176C11⋊C8C2×SD1612yes—
177C2×#135—111no—
178C2×#135—111no—
179C2×#135—221no—
180#533—221no—
181#532—221no—
182C22×C16—112no—
183#500—112no—
184#499—111no—
185#499—221no—
186#499C2×D1111yescharacteristic
187#498—221no—
188#495—111no—
189#495—221no—
190#495C2×D1111yescharacteristic
191#494—111no—
192#493—111no—
193#492—221no—
194#427—112no—
195#427—221no—
196C2×C4×C8—111no—
197#358—112no—
198#358—112no—
199#358—112no—
200#358C2×D1112yes—
201#357—112no—
202#357—112no—
203#357—112no—
204#357C2×D1112yes—
205C4×C16—112no—
206C4×C16—111no—
207C4×C16C2×D1111yescharacteristic
208C22×C11—81no—
209C22×C11—82no—
210C22×C11C22×D811yescharacteristic
211C2×D11—22no—
212C2×D11—81no—
213C2×D11—82no—
214C2×D11#48612yes—
215C4×C11—22no—
216C4×C11—81no—
217C4×C11—82no—
218C4×C11C2×#12411yescharacteristic
219C4×C11C22×SD1611yescharacteristic
220Dic11—81no—
221Dic11—82no—
222Dic11#48612yes—
223Dic11#50814yes—
224C2×#41—221no—
225C2×#41—221no—
226#135—224no—
227#135—224no—
228#135—444no—
229C2×Q16—111no—
230C2×Q16—221no—
231C2×Q16C22×D1111yescharacteristic
232C2×SD16—21no—
233C2×SD16—221no—
234C2×SD16—221no—
235C2×SD16—221no—
236C2×D8—111no—
237C2×D8—221no—
238C2×D8C22×D1111yescharacteristic
239C22×C8—111no—
240C22×C8—111no—
241C4⋊Q8—222no—
242C4⋊Q8—221no—
243#127—221no—
244#125—21no—
245#125—221no—
246#124—21no—
247#124—221no—
248C22⋊Q8—442no—
249#121—442no—
250C4×Q8—442no—
251C4×D4—442no—
252#117—222no—
253C2×C42—111no—
254C2×C16—112no—
255C2×C16—224no—
256C2×C16C22×D1112yes—
257#107—112no—
258#107—222no—
259#107C22×D1112yes—
260#106—21no—
261#106—222no—
262#106—221no—
263C4×C8—111no—
264C4×C8—111no—
265C4×C8—111no—
266C4×C8C22×D1111yescharacteristic
267C2×C11—161no—
268C2×C11C2×#48611yescharacteristic
269C2×C11C2×#50812yes—
270D11—22no—
271D11—161no—
272#41—442no—
273#41—442no—
274#41—442no—
275#41—442no—
276C2×Q8—21no—
277C2×Q8—221no—
278C2×Q8—442no—
279C2×D4—21no—
280C2×D4—221no—
281C2×D4—441no—
282C2×D4—442no—
283C2×D4—441no—
284C22×C4—111no—
285C22×C4—112no—
286C22×C4—441no—
287C22×C4—441no—
288Q16—22no—
289Q16—222no—
290Q16—442no—
291SD16—42no—
292SD16—442no—
293SD16—442no—
294SD16—442no—
295D8—22no—
296D8—222no—
297D8—442no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—114no—
301C2×C8—114no—
302C2×C8D4×D1111yescharacteristic
303C2×C8C23×D1111yescharacteristic
304C4⋊C4—22no—
305C4⋊C4—42no—
306C4⋊C4—222no—
307C4⋊C4—442no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C22⋊C4—42no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C42—112no—
314C42—111no—
315C42—442no—
316C42D4×D1111yescharacteristic
317C16—22no—
318C16—222no—
319C11#3369711yescharacteristic, complemented, Sylow
320C23—41no—
321C23—111no—
322C23—441no—
323Q8—41no—
324Q8—41no—
325Q8—441no—
326Q8—441no—
327Q8—884no—
328D4—41no—
329D4—41no—
330D4—441no—
331D4—441no—
332D4—882no—
333D4—884no—
334D4—882no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—111no—
338C2×C4—112no—
339C2×C4—112no—
340C2×C4—112no—
341C2×C4—224no—
342C2×C4—442no—
343C2×C4—441no—
344C2×C4—882no—
345C2×C4—882no—
346C2×C4D8×D1112yes—
347C2×C4C2×D4×D1111yescharacteristic
348C8—112no—
349C8—112no—
350C8SD16×D1112yes—
351C8#41×D1112yes—
352C22—82no—
353C22—81no—
354C22—112no—
355C22—222no—
356C22—882no—
357C22—881no—
358C22C2×D8×D1111yescharacteristic
359C4—22no—
360C4—82no—
361C4—81no—
362C4—114no—
363C4—112no—
364C4—882no—
365C4—881no—
366C4D11×#12411yescharacteristic
367C4C2×SD16×D1111yescharacteristic
368C2—161no—
369C2—222no—
370C2—1761no—
371C2D11×#48611yescharacteristic
372C2D11×#50812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2242C2
socleC22×C11C22×D8
prime radical#13079041C2
hypercenter#2242D11
hypocenterC11#33697
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #13079129C2semidirect
3. #13070850C2semidirect
4. #13070848C2semidirect
5. #13070847C2semidirect
6. #13070842C2semidirect
7. #13070838C2semidirect
8. #13070322C2semidirect
9. #13070320C2semidirect
10. C4×C16×D11C2semidirect
11. C11×#2242C2semidirect
139. #2242D11semidirect
319. C11#33697semidirect

Maximal subgroups

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

subgroupindex
#130791292
#130790412
#130708502
#130708482
#130708472
#130708422
#130708382
#130703222
#130703202
C4×C16×D112
C11×#22422
#3369711