Finite Group Databasebeta

← #25005961

Subgroups — #25005961

Order 11008.

662 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#19132929C212yesmaximal, complemented
2#19132525C212yesmaximal, complemented
3#19132523C212yesmaximal
4C43×#2280C211yesmaximal, characteristic
5#14582956—22no—
6#14582625—22no—
7#14582623C2214yes—
8C24×C4×C43C411yescharacteristic
9C2×#117×C43C411yescharacteristic
10C2×#117×C43C2211yescharacteristic
11C43×#381C411yescharacteristic
12C43×#381C2211yescharacteristic
13C43×#380—22no—
14C43×#379C411yescharacteristic
15C43×#379C2211yescharacteristic
16C4×C22⋊C4×C43—22no—
17C4⋊(C43⋊C8)—42no—
18C22⋊(C43⋊C8)—24no—
19#13063236—42no—
20C25×C43C2×C411yescharacteristic
21C23×C4×C43—22no—
22C23×C4×C43—21no—
23C23×C4×C43—21no—
24C23×C4×C43—22no—
25C23×C4×C43—42no—
26C23×C4×C43—42no—
27C23×C4×C43C2×C411yescharacteristic
28C23×C4×C43C2×C411yescharacteristic
29#117×C43—42no—
30#117×C43—42no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43D412yes—
33C2×C22⋊C4×C43—22no—
34C2×C22⋊C4×C43—22no—
35C2×C22⋊C4×C43C2×C411yescharacteristic
36C2×C22⋊C4×C43C2×C411yescharacteristic
37C2×C22⋊C4×C43C2×C411yescharacteristic
38C2×C22⋊C4×C43C2311yescharacteristic
39C2×C42×C43—21no—
40C2×C42×C43D412yes—
41#95×C43—22no—
42#95×C43—22no—
43C24×C43—21no—
44C24×C43—21no—
45C24×C43—41no—
46C24×C43—41no—
47C24×C43—44no—
48C24×C43M1612yes—
49C24×C43C22×C411yescharacteristic
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—24no—
53C22×C4×C43—24no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43—48no—
63C22×C4×C43—48no—
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43—42no—
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C412yes—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43M1612yes—
72C22×C4×C43C2×D412yes—
73C4⋊C4×C43—42no—
74C4⋊C4×C43—42no—
75C22⋊C4×C43—41no—
76C22⋊C4×C43—41no—
77C22⋊C4×C43—41no—
78C22⋊C4×C43—41no—
79C22⋊C4×C43—44no—
80C22⋊C4×C43—44no—
81C42×C43—22no—
82C42×C43—22no—
83C42×C43—42no—
84C2×C43⋊C8—44no—
85C23×C43—24no—
86C23×C43—22no—
87C23×C43—21no—
88C23×C43—21no—
89C23×C43—42no—
90C23×C43—44no—
91C23×C43—42no—
92C23×C43—42no—
93C23×C43—42no—
94C23×C43—44no—
95C23×C43—44no—
96C23×C43—48no—
97C23×C43—44no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43C2×C22⋊C411yescharacteristic
101C23×C43C2×M1611yescharacteristic
102C23×C43C2×M1611yescharacteristic
103C2×C4×C43—24no—
104C2×C4×C43—24no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—22no—
112C2×C4×C43—48no—
113C2×C4×C43—48no—
114C2×C4×C43—42no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43#9912yes—
125C2×C4×C43#10012yes—
126C43⋊C8—84no—
127#11501—431nomaximal, Sylow
128C22×C43—22no—
129C22×C43—24no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—41no—
133C22×C43—41no—
134C22×C43—44no—
135C22×C43—42no—
136C22×C43—42no—
137C22×C43—44no—
138C22×C43—44no—
139C22×C43—48no—
140C22×C43—44no—
141C22×C43—42no—
142C22×C43—42no—
143C22×C43#40711yescharacteristic
144C22×C43C2×#9911yescharacteristic
145C22×C43C2×#10011yescharacteristic
146C4×C43—22no—
147C4×C43—22no—
148C4×C43—42no—
149C4×C43—42no—
150C4×C43—42no—
151C4×C43—81no—
152C4×C43—81no—
153#2280D4311yescharacteristic
154#1464—432no—
155#1317—432no—
156#1316—432no—
157C2×C43—21no—
158C2×C43—21no—
159C2×C43—44no—
160C2×C43—41no—
161C2×C43—41no—
162C2×C43#146211yescharacteristic
163C2×C43#212012yes—
164C24×C4Dic4311yescharacteristic
165C2×#117Dic4311yescharacteristic
166C2×#117C2×D4311yescharacteristic
167#432—862no—
168#381Dic4311yescharacteristic
169#381C2×D4311yescharacteristic
170#380—22no—
171#379Dic4311yescharacteristic
172#379C2×D4311yescharacteristic
173C4×C22⋊C4—22no—
174#324—862no—
175#323—434no—
176C43#1150111yescharacteristic, complemented, Sylow
177C25C2×Dic4311yescharacteristic
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—42no—
183C23×C4—42no—
184C23×C4C2×Dic4311yescharacteristic
185C23×C4C2×Dic4311yescharacteristic
186#117—42no—
187#117—42no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C22⋊D4312yes—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4C2×Dic4311yescharacteristic
193C2×C22⋊C4C2×Dic4311yescharacteristic
194C2×C22⋊C4C2×Dic4311yescharacteristic
195C2×C22⋊C4C22×D4311yescharacteristic
196C2×C42—21no—
197C2×C42C22⋊D4312yes—
198C4⋊C8—1722no—
199C22⋊C8—864no—
200#97—1722no—
201#95—22no—
202#95—22no—
203C24—21no—
204C24—21no—
205C24—41no—
206C24—41no—
207C24—44no—
208C24#1062187712yes—
209C24C22×Dic4311yescharacteristic
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—48no—
221C22×C4—48no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4#1062187712yes—
229C22×C4C22⋊Dic4311yescharacteristic
230C22×C4C22⋊Dic4312yes—
231C22×C4C22⋊Dic4311yescharacteristic
232C22×C4C2×C22⋊D4312yes—
233C2×C8—1724no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—44no—
239C22⋊C4—44no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C42—22no—
243C42—22no—
244C42—42no—
245C23—24no—
246C23—22no—
247C23—21no—
248C23—21no—
249C23—42no—
250C23—44no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—44no—
255C23—44no—
256C23—48no—
257C23—44no—
258C23—41no—
259C23—41no—
260C23C2×C22⋊Dic4311yescharacteristic
261C23C2×#1062187711yescharacteristic
262C23C2×#1062187711yescharacteristic
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—48no—
273C2×C4—48no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4#1306324012yes—
285C2×C4#1306324212yes—
286C8—3444no—
287C22—22no—
288C22—24no—
289C22—21no—
290C22—21no—
291C22—41no—
292C22—41no—
293C22—44no—
294C22—42no—
295C22—42no—
296C22—44no—
297C22—44no—
298C22—48no—
299C22—44no—
300C22—42no—
301C22—42no—
302C22#1458286311yescharacteristic
303C22C2×#1306324011yescharacteristic
304C22C2×#1306324211yescharacteristic
305C4—22no—
306C4—22no—
307C4—42no—
308C4—42no—
309C4—42no—
310C4—81no—
311C4—81no—
312C2—21no—
313C2—21no—
314C2—44no—
315C2—41no—
316C2—41no—
317C2#1913292211yescharacteristic
318C2#1913623612yes—
subgroupG/H
centerC22C2×#13063240
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2280C2
socleC22×C43C2×#99
prime radicalC25×C43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#2280D43
hypocenterC43#11501
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. #19132929C2semidirect
2. #19132525C2semidirect
176. C43#11501semidirect

Maximal subgroups

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

subgroupindex
#191329292
#191325252
#191325232
C43×#22802
#1150143