Finite Group Databasebeta

← #25015285

Subgroups — #25015285

Order 11008.

420 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 111 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#19134591C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic
3#19132722C214yesmaximal
4C43×#2567C211yesmaximal, characteristic
5#14582923—21no—
6C2×#13063244C2212yes—
7C2×#13063244C2212yes—
8C4×#10621877—21no—
9#14582668—21no—
10#14582668—21no—
11C2×C4⋊Q8×C43C411yescharacteristic
12C2×C4×Q8×C43C2211yescharacteristic
13C43×#395—21no—
14C43×#395—21no—
15C43×#391C2212yes—
16C43×#389—21no—
17C43×#389—21no—
18C43×#384C412yes—
19C4×C4⋊C4×C43C411yescharacteristic
20C2×#10621877—22no—
21C2×#10621877—22no—
22C4⋊(C43⋊C8)—41no—
23C4⋊(C43⋊C8)—41no—
24#13063244—22no—
25#13063244—24no—
26#13063244Q814yescomplemented
27#13063236—41no—
28C4×C43⋊C8—41no—
29C22×Q8×C43—21no—
30C22×Q8×C43C2311yescharacteristic
31C4⋊Q8×C43—41no—
32C4⋊Q8×C43—41no—
33C4×Q8×C43—41no—
34C4×Q8×C43—41no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43—22no—
39C2×C4⋊C4×C43C2×C412yes—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43C2×C412yes—
45C2×C42×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47#95×C43—21no—
48#95×C43—22no—
49#95×C43—22no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43—42no—
53C2×Q8×C43—82no—
54C2×Q8×C43C2×Q812yes—
55C2×Q8×C43#4112yes—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C4⋊C4×C43—24no—
66C4⋊C4×C43—41no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—42no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C4⋊C4×C43—82no—
73C4⋊C4×C43—82no—
74C42×C43—21no—
75C42×C43—21no—
76C42×C43—21no—
77C42×C43—21no—
78C42×C43—21no—
79C42×C43—21no—
80C42×C43—42no—
81#10621877—24no—
82#10621877—42no—
83#10621877—42no—
84#10621877—42no—
85C2×C43⋊C8—42no—
86C2×C43⋊C8—42no—
87C23×C43C2×C22⋊C411yescharacteristic
88Q8×C43—42no—
89Q8×C43—42no—
90Q8×C43—84no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—24no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43#9911yescharacteristic
111C2×C4×C43#9911yescharacteristic
112C2×C4×C43C4×Q812yes—
113C2×C4×C43C22⋊Q812yes—
114C2×C4×C43#12411yescharacteristic
115C2×C4×C43C4⋊Q811yescharacteristic
116C43⋊C8—44no—
117C43⋊C8—82no—
118#13302—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43#39111yescharacteristic
122C22×C43C2×#9911yescharacteristic
123C22×C43#41011yescharacteristic
124C4×C43—21no—
125C4×C43—22no—
126C4×C43—21no—
127C4×C43—22no—
128C4×C43—21no—
129C4×C43—44no—
130C4×C43—41no—
131C4×C43—41no—
132C4×C43—41no—
133C4×C43—82no—
134C4×C43#35612yes—
135#2567D4311yescharacteristic
136#1801—431no—
137C4×#101—431no—
138#1394—434no—
139C2×C43—21no—
140C2×C43—21no—
141C2×C43#199611yescharacteristic
142C2×C43C2×#35611yescharacteristic
143C2×C43#213411yescharacteristic
144C2×C4⋊Q8Dic4311yescharacteristic
145C2×C4×Q8C2×D4311yescharacteristic
146#423—861no—
147C2×#101—432no—
148C2×#101—432no—
149C4×M16—861no—
150#395—21no—
151#395—21no—
152#391C2×D4312yes—
153#389—21no—
154#389—21no—
155#384Dic4312yes—
156C4×C4⋊C4Dic4311yescharacteristic
157#343—861no—
158#343—861no—
159C43#1330211yescharacteristic, complemented, Sylow
160C22×Q8—21no—
161C22×Q8C22×D4311yescharacteristic
162C2×M16—862no—
163C2×M16—862no—
164C4⋊Q8—41no—
165C4⋊Q8—41no—
166C4×Q8—41no—
167C4×Q8—41no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4C2×Dic4312yes—
173C2×C4⋊C4C2×Dic4311yescharacteristic
174C2×C4⋊C4C22⋊D4311yescharacteristic
175C2×C4⋊C4C22⋊D4311yescharacteristic
176C2×C42C2×Dic4311yescharacteristic
177C2×C42C2×Dic4312yes—
178C2×C42C22⋊D4311yescharacteristic
179C2×C42C22⋊D4311yescharacteristic
180C4⋊C8—1721no—
181C4⋊C8—1721no—
182#101—434no—
183#101—862no—
184#101—864no—
185#97—1721no—
186C4×C8—1721no—
187#95—21no—
188#95—22no—
189#95—22no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—82no—
194C2×Q8Q8×D4312yes—
195C2×Q8#1062190212yes—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4C22⋊Dic4311yescharacteristic
199C22×C4C22⋊Dic4311yescharacteristic
200C22×C4C22⋊Dic4311yescharacteristic
201C22×C4C22⋊Dic4311yescharacteristic
202C22×C4C22×Dic4311yescharacteristic
203C22×C4C2×C22⋊D4311yescharacteristic
204C22×C4C2×C22⋊D4311yescharacteristic
205M16—864no—
206M16—1722no—
207M16—1722no—
208M16—1722no—
209C2×C8—1722no—
210C2×C8—1722no—
211C4⋊C4—24no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—82no—
219C4⋊C4—82no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C23C2×C22⋊Dic4311yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4#1306324011yescharacteristic
251C2×C4#1306324011yescharacteristic
252C2×C4Q8×Dic4312yes—
253C2×C4#1306330112yes—
254C2×C4#1306331411yescharacteristic
255C2×C4#1306332311yescharacteristic
256C8—3442no—
257C8—1724no—
258C22—21no—
259C22—21no—
260C22#1458280611yescharacteristic
261C22C2×#1306324011yescharacteristic
262C22#1458287311yescharacteristic
263C4—21no—
264C4—21no—
265C4—22no—
266C4—22no—
267C4—21no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4#1458269812yes—
274C2—21no—
275C2—21no—
276C2#1913558111yescharacteristic
277C2C2×#1458269811yescharacteristic
278C2#1913628711yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#2567C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC22×Q8×C43C23
hypercenter#2567D43
hypocenterC43#13302
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
26. #13063244Q8semidirect
159. C43#13302semidirect

Maximal subgroups

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

subgroupindex
#191345912
C4×#130632442
#191327222
C43×#25672
#1330243