Finite Group Databasebeta

← #25259459

Subgroups — #25259459

Order 11008.

2410 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137776C212yesmaximal, complemented
2#19137772C212yesmaximal, complemented
3#19137707C214yesmaximal, complemented
4#19137524C218yesmaximal, complemented
5#19137362C218yesmaximal, complemented
6#19137187C214yesmaximal, complemented
7#19136993C212yesmaximal, complemented
8C2×C43×#532C211yesmaximal, characteristic
9C2×#13063284C2214yes—
10C22×C4⋊Dic43C2214yes—
11#14582806C2218yes—
12#14582802C2218yes—
13#14582792C22116yes—
14#14582785C22116yes—
15#14582779C2218yes—
16#14582779C22116yes—
17#14582779C2218yes—
18#14582767C2214yes—
19#14582765C2214yes—
20#14582762C2214yes—
21#14582759C2214yes—
22#14582759C2218yes—
23C4×C4⋊Dic43C2214yes—
24C22⋊C4×Dic43C22116yes—
25C4×C22⋊Dic43C2214yes—
26#14582745C2214yes—
27C22×#41×C43C2212yes—
28C43×#532C4116yescomplemented
29C2×C4⋊Q8×C43C2211yescharacteristic
30C2×#127×C43C2211yescharacteristic
31C2×#124×C43C2212yes—
32C2×#121×C43C2214yes—
33C2×C4×D4×C43C2214yes—
34C22×C42×C43C2211yescharacteristic
35C23×Dic43C2318yes—
36#13063284—48no—
37C2×C4⋊Dic43—48no—
38C2×C4⋊Dic43C2318yes—
39C2×C4⋊Dic43C2318yes—
40C2×C22⋊Dic43C2318yes—
41C2×C22⋊Dic43C23116yes—
42C2×C22⋊Dic43C2318yes—
43C2×C4×Dic43C2318yes—
44C2×C4×Dic43C2318yes—
45C43⋊#95C23116yes—
46C43⋊#95C2318yes—
47C43⋊#95C2318yes—
48C43⋊#95C2318yes—
49C43⋊#95C2318yes—
50C2×#41×C43—44no—
51C2×#41×C43—44no—
52C2×#41×C43C2×C4116yescomplemented
53C22×Q8×C43C2312yes—
54C22×D4×C43C2314yes—
55C22×D4×C43C2314yes—
56C22×D4×C43C2312yes—
57C23×C4×C43C2311yescharacteristic
58C23×C4×C43C2314yes—
59C23×C4×C43C2312yes—
60C4⋊Q8×C43C2×C418yescomplemented
61#127×C43C2×C418yes—
62#124×C43C2×C4116yescomplemented
63#121×C43C2×C4132yescomplemented
64C4×D4×C43C2×C4132yescomplemented
65C2×C4⋊C4×C43C2314yes—
66C2×C22⋊C4×C43C2318yes—
67C2×C42×C43C2×C418yescomplemented
68C2×C42×C43C2312yes—
69C2×C42×C43C2311yescharacteristic
70C2×C42×C43C2311yescharacteristic
71C24×C43C2414yes—
72C24×C43C2411yescharacteristic
73#41×C43—432no—
74C2×Q8×C43—42no—
75C2×Q8×C43—42no—
76C2×Q8×C43C22×C418yes—
77C2×D4×C43—44no—
78C2×D4×C43—44no—
79C2×D4×C43—42no—
80C2×D4×C43—44no—
81C2×D4×C43—42no—
82C2×D4×C43—44no—
83C2×D4×C43C22×C4116yes—
84C2×D4×C43C22×C4116yes—
85C2×D4×C43C22×C418yes—
86C22×C4×C43—24no—
87C22×C4×C43—28no—
88C22×C4×C43—28no—
89C22×C4×C43—44no—
90C22×C4×C43C22×C414yes—
91C22×C4×C43C22×C4116yes—
92C22×C4×C43C22×C418yes—
93C22×C4×C43C2412yes—
94C22×C4×C43C2412yes—
95C22×C4×C43C2411yescharacteristic
96C22×C4×C43C2414yes—
97C22×C4×C43C2411yescharacteristic
98C22×Dic43—48no—
99C22×Dic43—416no—
100C22×Dic43C24116yes—
101C4⋊C4×C43C22×C4116yes—
102C22⋊C4×C43C22×C4132yes—
103C42×C43C22×C418yes—
104C42×C43C22×C414yes—
105C42×C43C22×C414yes—
106C22⋊Dic43—48no—
107C22⋊Dic43—416no—
108C22⋊Dic43—48no—
109C4⋊Dic43—216no—
110C4⋊Dic43—48no—
111C4×Dic43—48no—
112C4×Dic43—48no—
113C23×C43—24no—
114C23×C43—24no—
115C23×C43—22no—
116C23×C43—24no—
117C23×C43—28no—
118C23×C43—28no—
119C23×C43C23×C418yes—
120C23×C43C23×C412yes—
121C23×C43C2511yescharacteristic
122Q8×C43—48no—
123D4×C43—416no—
124D4×C43—48no—
125D4×C43—416no—
126C2×C4×C43—24no—
127C2×C4×C43—24no—
128C2×C4×C43—22no—
129C2×C4×C43—24no—
130C2×C4×C43—24no—
131C2×C4×C43—232no—
132C2×C4×C43—28no—
133C2×C4×C43—48no—
134C2×C4×C43C23×C414yes—
135C2×C4×C43C23×C414yes—
136C2×C4×C43C23×C412yes—
137C2×C4×C43C23×C418yes—
138C2×C4×C43C23×C412yes—
139C2×C4×C43H(5,𝔽2)14yes—
140C2×Dic43—216no—
141C2×Dic43—216no—
142C2×Dic43—216no—
143C2×Dic43—816no—
144#34369—431nomaximal, Sylow
145C22×C43—28no—
146C22×C43—22no—
147C22×C43—24no—
148C22×C43—216no—
149C22×C43—48no—
150C22×C43—44no—
151C22×C43—44no—
152C22×C43—44no—
153C22×C43C24×C411yescharacteristic
154C22×C43C2×H(5,𝔽2)12yes—
155C22×C43#58514yes—
156C4×C43—22no—
157C4×C43—28no—
158C4×C43—24no—
159C4×C43—24no—
160C4×C43#51814yes—
161Dic43—416no—
162C2×#532D4311yescharacteristic
163#2381—432no—
164#2380—432no—
165#2372—434no—
166#2352—438no—
167#2333—438no—
168#2311—434no—
169#2283—432no—
170C2×C43—48no—
171C2×C43—42no—
172C2×C43C2×#51811yescharacteristic
173C2×C43#342812yes—
174C2×C43#355114yes—
175C22×#41C2×D4312yes—
176#532Dic43116yescomplemented
177C2×C4⋊Q8C2×D4311yescharacteristic
178C2×#127C2×D4311yescharacteristic
179C2×#124C2×D4312yes—
180C2×#121C2×D4314yes—
181C2×C4×D4C2×D4314yes—
182C2×#117—434no—
183C22×C4⋊C4—434no—
184C22×C42C2×D4311yescharacteristic
185#391—438no—
186#390—438no—
187#388—4316no—
188#387—4316no—
189#386—438no—
190#386—438no—
191#386—4316no—
192#383—434no—
193#382—434no—
194#381—434no—
195#380—434no—
196#380—438no—
197C4×C4⋊C4—434no—
198C4×C22⋊C4—434no—
199C4×C22⋊C4—4316no—
200#376—434no—
201C43#3436911yescharacteristic, complemented, Sylow
202C2×#41—44no—
203C2×#41—44no—
204C2×#41C2×Dic43116yescomplemented
205C22×Q8C22×D4312yes—
206C22×D4C22×D4314yes—
207C22×D4C22×D4314yes—
208C22×D4C22×D4312yes—
209C23×C4—438no—
210C23×C4C22×D4314yes—
211C23×C4C22×D4311yescharacteristic
212C23×C4C22×D4312yes—
213C4⋊Q8C2×Dic4318yescomplemented
214#127C2×Dic4318yes—
215#124C2×Dic43116yescomplemented
216#121C2×Dic43132yescomplemented
217C4×D4C2×Dic43132yescomplemented
218#117—1728no—
219C2×C4⋊C4—438no—
220C2×C4⋊C4—438no—
221C2×C4⋊C4—1728no—
222C2×C4⋊C4C22×D4314yes—
223C2×C22⋊C4—438no—
224C2×C22⋊C4—438no—
225C2×C22⋊C4—4316no—
226C2×C22⋊C4C22×D4318yes—
227C2×C42—438no—
228C2×C42—438no—
229C2×C42C2×Dic4318yescomplemented
230C2×C42C22×D4312yes—
231C2×C42C22×D4311yescharacteristic
232C2×C42C22×D4311yescharacteristic
233#95—438no—
234#95—438no—
235#95—4316no—
236#95—438no—
237#95—438no—
238C24C23×D4311yescharacteristic
239C24C23×D4314yes—
240#41—432no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8C22×Dic4318yes—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—44no—
249C2×D4—44no—
250C2×D4C22×Dic43116yes—
251C2×D4C22×Dic43116yes—
252C2×D4C22×Dic4318yes—
253C22×C4—28no—
254C22×C4—28no—
255C22×C4—24no—
256C22×C4—44no—
257C22×C4—4316no—
258C22×C4—1728no—
259C22×C4—17216no—
260C22×C4C22×Dic4314yes—
261C22×C4C22×Dic43116yes—
262C22×C4C22×Dic4318yes—
263C22×C4C23×D4312yes—
264C22×C4C23×D4311yescharacteristic
265C22×C4C23×D4312yes—
266C22×C4C23×D4314yes—
267C22×C4C23×D4311yescharacteristic
268C4⋊C4—8616no—
269C4⋊C4—1728no—
270C4⋊C4C22×Dic43116yes—
271C22⋊C4—1728no—
272C22⋊C4—17216no—
273C22⋊C4—1728no—
274C22⋊C4C22×Dic43132yes—
275C42—1728no—
276C42—1728no—
277C42C22×Dic4318yes—
278C42C22×Dic4314yes—
279C42C22×Dic4314yes—
280C23—24no—
281C23—24no—
282C23—22no—
283C23—24no—
284C23—28no—
285C23—28no—
286C23C23×Dic4318yes—
287C23C23×Dic4312yes—
288C23C24×D4311yescharacteristic
289Q8—48no—
290D4—48no—
291D4—416no—
292D4—416no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—28no—
299C2×C4—232no—
300C2×C4—48no—
301C2×C4—8616no—
302C2×C4—8616no—
303C2×C4—8616no—
304C2×C4—34416no—
305C2×C4C23×Dic4314yes—
306C2×C4C23×Dic4314yes—
307C2×C4C23×Dic4312yes—
308C2×C4C23×Dic4318yes—
309C2×C4C23×Dic4312yes—
310C2×C4#1306337014yes—
311C22—22no—
312C22—28no—
313C22—24no—
314C22—216no—
315C22—44no—
316C22—48no—
317C22—44no—
318C22—44no—
319C22C24×Dic4311yescharacteristic
320C22C2×#1306337012yes—
321C22#1458373514yes—
322C4—22no—
323C4—28no—
324C4—24no—
325C4—24no—
326C4—17216no—
327C4#1458337414yes—
328C2—42no—
329C2—48no—
330C2C2×#1458337411yescharacteristic
331C2#1914779812yes—
332C2#1914902214yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
Fitting, prime radicalC2×C43×#532C2
socle, cosocleC23×C43C25
hypercenterC2×#532D43
hypocenterC43#34369
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #19137776C2semidirect
2. #19137772C2semidirect
3. #19137707C2semidirect
4. #19137524C2semidirect
5. #19137362C2semidirect
6. #19137187C2semidirect
7. #19136993C2semidirect
28. C43×#532C4semidirect
52. C2×#41×C43C2×C4semidirect
60. C4⋊Q8×C43C2×C4semidirect
62. #124×C43C2×C4semidirect
63. #121×C43C2×C4semidirect
64. C4×D4×C43C2×C4semidirect
67. C2×C42×C43C2×C4semidirect
176. #532Dic43semidirect
201. C43#34369semidirect
204. C2×#41C2×Dic43semidirect
213. C4⋊Q8C2×Dic43semidirect
215. #124C2×Dic43semidirect
216. #121C2×Dic43semidirect
217. C4×D4C2×Dic43semidirect
229. C2×C42C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191377762
#191377722
#191377072
#191375242
#191373622
#191371872
#191369932
C2×C43×#5322
#3436943