Finite Group Databasebeta

← #25072861

Subgroups — #25072861

Order 11008.

1004 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583629C211yesmaximal, characteristic, complemented
2#19145052C211yesmaximal, characteristic
3#19144718C212yesmaximal
4#19133736C214yesmaximal, complemented
5#19133674C214yesmaximal, complemented
6#19133041C212yesmaximal, complemented
7C43×#1558C211yesmaximal, characteristic, complemented
8C2×#13063356—22no—
9#14583629—24no—
10#14583629—22no—
11#14583629C2214yes—
12#14583449C2211yescharacteristic
13C2×#13063324—22no—
14C2×#13063323—22no—
15C2×C4×Dic86C2212yes—
16C2×#13063290—22no—
17#14583291—22no—
18#14583278C2212yes—
19#14583273C2212yes—
20#14583213—22no—
21#14583195C2214yes—
22#14583100C2214yes—
23#14583040—22no—
24#14583001—24no—
25C4×#10621877C2211yescharacteristic
26#14582629C2218yes—
27C2×C4⋊Q8×C43C2211yescharacteristic
28C43×#432C2212yes—
29C43×#333C2214yes—
30C2×#10621898—21no—
31C22×Dic86—22no—
32C22×Dic86D412yes—
33#13063356—48no—
34C2×#10621885—24no—
35C2×#10621873—24no—
36C2×#10621884—24no—
37C2×#10621877—21no—
38#13063325C2311yescharacteristic
39#13063324—28no—
40#13063324—28no—
41#13063323—28no—
42#13063323—28no—
43#13063322C2311yescharacteristic
44#13063313—21no—
45#13063299—22no—
46C4×Dic86—22no—
47C4×Dic86—22no—
48C4×Dic86D414yes—
49C4×Dic86C2314yes—
50#13063290—28no—
51#13063290—28no—
52C4×D172—22no—
53C2×C4⋊Dic43D412yes—
54C2×Dic43⋊C4—24no—
55C2×Dic43⋊C4—22no—
56C2×C4×Dic43—22no—
57C2×C4×Dic43—22no—
58#13063259—24no—
59#13063250—24no—
60#13063247—24no—
61#13063236—21no—
62C4×C43⋊C8C2312yes—
63C22×Q8×C43D412yes—
64C4⋊Q8×C43—22no—
65C4⋊Q8×C43D412yes—
66C4⋊Q8×C43C2312yes—
67C2×C4⋊C4×C43—22no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43C2314yes—
70C22⋊C8×C43—22no—
71#97×C43—22no—
72C2×Q8×C43—22no—
73C2×Q8×C43—44no—
74C2×Q8×C43C2×D414yes—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D412yes—
78C2×C22⋊D43—41no—
79C22×Dic43—22no—
80C22×Dic43—22no—
81#10621898—44no—
82C2×D172—22no—
83C2×D172—21no—
84C2×C4×D43—41no—
85C2×Dic86—22no—
86C2×Dic86—28no—
87C2×Dic86—21no—
88C2×Dic86—28no—
89C2×Dic86—84no—
90C2×Dic86C2×D414yes—
91C2×C8×C43—24no—
92C4⋊C4×C43—24no—
93C4⋊C4×C43—24no—
94C42×C43C2×D411yescharacteristic
95C42×C43C2×D412yes—
96C42×C43C2411yescharacteristic
97#10621885—48no—
98#10621884—48no—
99(C2×D43)⋊C4—42no—
100C4⋊Dic43—22no—
101C4⋊Dic43—22no—
102C4⋊Dic43C2×D414yes—
103Dic43⋊C4—216no—
104Dic43⋊C4—24no—
105Dic43⋊C4—24no—
106C4×Dic43—28no—
107C4×Dic43—24no—
108C4×Dic43—24no—
109#10621877—24no—
110C2×C43⋊C8—22no—
111#10621873—48no—
112C23×C43#12011yescharacteristic
113C22×D43—41no—
114Q8×C43—44no—
115Q8×C43—82no—
116C2×C4×C43—22no—
117C2×C4×C43—24no—
118C2×C4×C43—24no—
119C2×C4×C43—44no—
120C2×C4×C43#12012yes—
121C2×C4×C43#12011yescharacteristic
122C2×C4×C43C22×D412yes—
123C2×C4×C43C22×D411yescharacteristic
124C22⋊D43—82no—
125C2×Dic43—28no—
126C2×Dic43—24no—
127C2×Dic43—24no—
128C2×Dic43—44no—
129C2×Dic43—41no—
130D172—42no—
131D172—44no—
132C4×D43—82no—
133Dic86—28no—
134Dic86—24no—
135Dic86—42no—
136Dic86—88no—
137Dic86#13718yescomplemented
138C8×C43—44no—
139C43⋊C8—24no—
140#18546—431nomaximal, Sylow
141C22×C43—22no—
142C22×C43#45312yes—
143C22×C43C2×#12011yescharacteristic
144C2×D43—82no—
145C2×D43—81no—
146C4×C43—22no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—44no—
150C4×C43C2×#13714yes—
151Dic43—28no—
152Dic43—44no—
153Dic43—81no—
154C2×Q82—431no—
155#3152—431no—
156#3112—432no—
157#1633—434no—
158#1623—434no—
159#1558D4311yescharacteristic, complemented
160#1491—432no—
161C2×C43—22no—
162C2×C43#300412yes—
163C2×C43C2×#45311yescharacteristic
164D43—161no—
165C2×#137—862no—
166Q82—434no—
167Q82—864no—
168Q82—862no—
169#532—431no—
170C2×C4⋊Q8—862no—
171C2×C4⋊Q8—862no—
172C2×C4⋊Q8C2×D4311yescharacteristic
173C2×C4×Q8—432no—
174C2×C4×Q8—862no—
175#497—862no—
176#494—432no—
177#492—432no—
178#480—862no—
179#477—434no—
180#460—434no—
181#448—862no—
182#440—864no—
183#432C2×D4312yes—
184C4×M16—431no—
185#333C2×D4314yes—
186Q8⋊C8—438no—
187C43#1854611yescharacteristic, complemented, Sylow
188C2×#41—861no—
189C22×Q8—432no—
190C22×Q8—862no—
191C22×Q8D17212yes—
192#137—1728no—
193C2×Q16—864no—
194C2×SD16—864no—
195C2×SD16—864no—
196C2×M16—861no—
197C4⋊Q8—22no—
198C4⋊Q8—431no—
199C4⋊Q8—868no—
200C4⋊Q8—868no—
201C4⋊Q8—868no—
202C4⋊Q8—868no—
203C4⋊Q8D17212yes—
204C4⋊Q8C22×D4312yes—
205#127—431no—
206#124—861no—
207#121—862no—
208C4×Q8—434no—
209C4×Q8—434no—
210C4×Q8—868no—
211C4×Q8—868no—
212C4×Q8—862no—
213C4×Q8—862no—
214C4×D4—862no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—432no—
217C2×C4⋊C4—864no—
218C2×C4⋊C4—862no—
219C2×C42—862no—
220C2×C42—862no—
221C2×C42C22×D4311yescharacteristic
222#107—864no—
223C4⋊C8C22×D4314yes—
224#103—864no—
225#102—864no—
226C22⋊C8—22no—
227#97—22no—
228#97—861no—
229C4×C8—432no—
230#41—1724no—
231C2×Q8—22no—
232C2×Q8—44no—
233C2×Q8—434no—
234C2×Q8—868no—
235C2×Q8—868no—
236C2×Q8—862no—
237C2×Q8—861no—
238C2×Q8—3444no—
239C2×Q8C2×D17214yes—
240C2×D4—862no—
241C2×D4—861no—
242C2×D4—1721no—
243C22×C4—22no—
244C22×C4—862no—
245C22×C4—862no—
246C22×C4—1721no—
247C22×C4C2×D17211yescharacteristic
248C22×C4D4×D4312yes—
249Q16—1728no—
250SD16—1728no—
251SD16—1728no—
252M16—864no—
253C2×C8—24no—
254C2×C8—862no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—434no—
258C4⋊C4—8616no—
259C4⋊C4—862no—
260C4⋊C4—864no—
261C4⋊C4—864no—
262C4⋊C4—862no—
263C22⋊C4—1722no—
264C42—868no—
265C42—864no—
266C42—864no—
267C42C2×D17211yescharacteristic
268C42D4×D4312yes—
269C42C23×D4311yescharacteristic
270C23—1721no—
271C23#1306329511yescharacteristic
272Q8—44no—
273Q8—82no—
274Q8—438no—
275Q8—868no—
276Q8—864no—
277Q8—3448no—
278Q8—1722no—
279D4—3442no—
280D4—1722no—
281D4—1724no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—44no—
286C2×C4—868no—
287C2×C4—864no—
288C2×C4—864no—
289C2×C4—3442no—
290C2×C4—1721no—
291C2×C4—1724no—
292C2×C4#1306329512yes—
293C2×C4#1306329511yescharacteristic
294C2×C4C2×D4×D4312yes—
295C2×C4C22×D17211yescharacteristic
296C8—44no—
297C8—864no—
298C22—22no—
299C22—3442no—
300C22—3441no—
301C22#1458306912yes—
302C22C2×#1306329511yescharacteristic
303C4—22no—
304C4—21no—
305C4—21no—
306C4—44no—
307C4—868no—
308C4—3441no—
309C4—1724no—
310C4#137×D4314yes—
311C2—22no—
312C2—6881no—
313C2#1914383112yes—
314C2C2×#1458306911yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1558C2
socleC22×C43C2×#120
prime radical#14583449C22
hypercenter#1558D43
hypocenterC43#18546
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
1. C2×#14583629C2semidirect
4. #19133736C2semidirect
5. #19133674C2semidirect
6. #19133041C2semidirect
7. C43×#1558C2semidirect
137. Dic86#137semidirect
159. #1558D43semidirect
187. C43#18546semidirect

Maximal subgroups

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

subgroupindex
C2×#145836292
#191450522
#191447182
#191337362
#191336742
#191330412
C43×#15582
#1854643