Finite Group Databasebeta

← #25012097

Subgroups — #25012097

Order 11008.

1182 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14582692C214yesmaximal, complemented
2#19134513C212yesmaximal, complemented
3C2×C43×#535C211yesmaximal, characteristic
4C2×#13063240—22no—
5C2×#13063240C2214yescomplemented
6#14582762—22no—
7#14582692—28no—
8C22×#41×C43C2211yescharacteristic
9C23×D4×C43C411yescharacteristic, complemented
10C43×#535—28no—
11C2×#127×C43C2212yes—
12C2×#124×C43C412yescomplemented
13C2×#121×C43—22no—
14C2×#120×C43—22no—
15C2×#117×C43C411yescharacteristic, complemented
16C2×C22⋊Dic43—24no—
17#13063240—28no—
18#13063240—44no—
19C43⋊#95—44no—
20C25×C43—21no—
21C2×#41×C43—24no—
22C2×#41×C43—42no—
23C2×#41×C43—42no—
24C22×Q8×C43C2×C411yescharacteristic
25C22×D4×C43—24no—
26C22×D4×C43—24no—
27C22×D4×C43—21no—
28C22×D4×C43—42no—
29C22×D4×C43—42no—
30C22×D4×C43C2×C412yes—
31C22×D4×C43D412yes—
32C22×D4×C43C2311yescharacteristic
33C23×C4×C43C2×C411yescharacteristic
34C23×C4×C43D412yes—
35#127×C43—24no—
36#127×C43D418yes—
37#124×C43—24no—
38#124×C43—24no—
39#121×C43—216no—
40#120×C43—216no—
41#117×C43—24no—
42C2×C4⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—24no—
45C2×C42×C43C2×C412yes—
46C24×C43—24no—
47C24×C43—22no—
48C24×C43—42no—
49C24×C43—42no—
50C24×C43—84no—
51C24×C43C22⋊C411yescharacteristic
52C24×C43C2×D412yes—
53#41×C43—416no—
54C2×Q8×C43—22no—
55C2×Q8×C43—41no—
56C2×Q8×C43—41no—
57C2×D4×C43—24no—
58C2×D4×C43—22no—
59C2×D4×C43—24no—
60C2×D4×C43—24no—
61C2×D4×C43—216no—
62C2×D4×C43—42no—
63C2×D4×C43—41no—
64C2×D4×C43—41no—
65C2×D4×C43—416no—
66C2×D4×C43—42no—
67C2×D4×C43—42no—
68C2×D4×C43—42no—
69C2×D4×C43—42no—
70C2×D4×C43—88no—
71C2×D4×C43C22⋊C414yes—
72C2×D4×C43C2×D414yes—
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—24no—
76C22×C4×C43—22no—
77C22×C4×C43—22no—
78C22×C4×C43—24no—
79C22×C4×C43—42no—
80C22×C4×C43C22⋊C412yes—
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22×C411yescharacteristic
83C22×Dic43—44no—
84C4⋊C4×C43—24no—
85C22⋊C4×C43—24no—
86C22⋊C4×C43—216no—
87C42×C43—22no—
88C42×C43C22⋊C414yes—
89C22⋊Dic43—44no—
90C22⋊Dic43—44no—
91C23×C43—21no—
92C23×C43—22no—
93C23×C43—21no—
94C23×C43—22no—
95C23×C43—24no—
96C23×C43—42no—
97C23×C43—44no—
98C23×C43—48no—
99C23×C43—48no—
100C23×C43—42no—
101C23×C43—42no—
102C23×C43—88no—
103C23×C43—88no—
104C23×C43—88no—
105C23×C43#9912yes—
106C23×C43C2×C22⋊C411yescharacteristic
107C23×C43#12014yes—
108Q8×C43—44no—
109D4×C43—44no—
110D4×C43—44no—
111D4×C43—48no—
112D4×C43—44no—
113D4×C43—48no—
114D4×C43—816no—
115C2×C4×C43—28no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—24no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—48no—
125C2×C4×C43—44no—
126C2×C4×C43#9912yes—
127C2×C4×C43C2×C22⋊C412yes—
128C2×Dic43—84no—
129C2×Dic43—88no—
130#12697—431nomaximal, Sylow
131C22×C43—22no—
132C22×C43—22no—
133C22×C43—24no—
134C22×C43—42no—
135C22×C43—44no—
136C22×C43—42no—
137C22×C43—48no—
138C22×C43—42no—
139C22×C43—44no—
140C22×C43—44no—
141C22×C43—82no—
142C22×C43—84no—
143C22×C43—816no—
144C22×C43—84no—
145C22×C43#37911yescharacteristic
146C22×C43C2×#9911yescharacteristic
147C22×C43C2×#9911yescharacteristic
148C4×C43—22no—
149C4×C43—22no—
150C4×C43—44no—
151C4×C43—42no—
152Dic43—164no—
153C2×#535D4311yescharacteristic
154C2×#353—434no—
155#1782—432no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43—44no—
159C2×C43—42no—
160C2×C43—84no—
161C2×C43#178111yescharacteristic
162C2×C43#212812yes—
163C22×#41C2×D4311yescharacteristic
164C23×D4Dic4311yescharacteristic, complemented
165#535—28no—
166C2×#127C2×D4312yes—
167C2×#124Dic4312yescomplemented
168C2×#121—22no—
169C2×#120—22no—
170C2×#117Dic4311yescharacteristic, complemented
171C2×#99—434no—
172C2×#99—862no—
173#381—862no—
174#353—868no—
175C43#1269711yescharacteristic, complemented, Sylow
176C25—21no—
177C2×#41—24no—
178C2×#41—42no—
179C2×#41—42no—
180C22×Q8C2×Dic4311yescharacteristic
181C22×D4—24no—
182C22×D4—24no—
183C22×D4—21no—
184C22×D4—42no—
185C22×D4—42no—
186C22×D4C2×Dic4312yes—
187C22×D4C22⋊D4312yes—
188C22×D4C22×D4311yescharacteristic
189C23×C4C2×Dic4311yescharacteristic
190C23×C4C22⋊D4312yes—
191#127—24no—
192#127C22⋊D4318yes—
193#124—24no—
194#124—24no—
195#121—216no—
196#120—216no—
197#117—24no—
198C2×C4⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4—864no—
202C2×C42C2×Dic4312yes—
203#99—868no—
204#99—1724no—
205#95—1724no—
206C24—24no—
207C24—22no—
208C24—42no—
209C24—42no—
210C24—84no—
211C24C22⋊Dic4311yescharacteristic
212C24C2×C22⋊D4312yes—
213#41—416no—
214C2×Q8—22no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×D4—24no—
218C2×D4—24no—
219C2×D4—24no—
220C2×D4—216no—
221C2×D4—22no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—42no—
227C2×D4—416no—
228C2×D4—42no—
229C2×D4—42no—
230C2×D4—88no—
231C2×D4C22⋊Dic4314yes—
232C2×D4C2×C22⋊D4314yes—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—42no—
240C22×C4—1724no—
241C22×C4C22⋊Dic4312yes—
242C22×C4C22⋊Dic4311yescharacteristic
243C22×C4C22×Dic4311yescharacteristic
244C4⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—216no—
247C22⋊C4—1724no—
248C22⋊C4—1724no—
249C42—22no—
250C42C22⋊Dic4314yes—
251C23—22no—
252C23—21no—
253C23—21no—
254C23—22no—
255C23—24no—
256C23—42no—
257C23—44no—
258C23—48no—
259C23—48no—
260C23—42no—
261C23—42no—
262C23—88no—
263C23—88no—
264C23—88no—
265C23#1306324012yes—
266C23C2×C22⋊Dic4311yescharacteristic
267C23#1306329414yes—
268Q8—44no—
269D4—44no—
270D4—44no—
271D4—48no—
272D4—44no—
273D4—48no—
274D4—816no—
275C2×C4—28no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—48no—
285C2×C4—44no—
286C2×C4—3444no—
287C2×C4—3448no—
288C2×C4#1306324012yes—
289C2×C4C2×C22⋊Dic4312yes—
290C22—22no—
291C22—22no—
292C22—24no—
293C22—44no—
294C22—42no—
295C22—42no—
296C22—48no—
297C22—44no—
298C22—42no—
299C22—44no—
300C22—82no—
301C22—84no—
302C22—816no—
303C22—84no—
304C22#1458275511yescharacteristic
305C22C2×#1306324011yescharacteristic
306C22C2×#1306324011yescharacteristic
307C4—22no—
308C4—22no—
309C4—44no—
310C4—42no—
311C4—6884no—
312C2—21no—
313C2—21no—
314C2—44no—
315C2—42no—
316C2—84no—
317C2#1913451011yescharacteristic
318C2#1913626712yes—
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
Fitting, prime radicalC2×C43×#535C2
socleC22×C43C2×#99
cosocleC22×D4×C43C23
hypercenterC2×#535D43
hypocenterC43#12697
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#14582692C2semidirect
2. #19134513C2semidirect
5. C2×#13063240C22semidirect
9. C23×D4×C43C4semidirect
12. C2×#124×C43C4semidirect
15. C2×#117×C43C4semidirect
164. C23×D4Dic43semidirect
167. C2×#124Dic43semidirect
170. C2×#117Dic43semidirect
175. C43#12697semidirect

Maximal subgroups

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

subgroupindex
C2×#145826922
#191345132
C2×C43×#5352
#1269743