Finite Group Databasebeta

← #24994299

Subgroups — #24994299

Order 11008.

432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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#19143680C211yesmaximal, characteristic
2#19139807C211yesmaximal, characteristic
3#19133311C212yesmaximal
4#19132450C212yesmaximal
5C43×#1467C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7#14583030—24no—
8#14582956—21no—
9#14582956C2212yes—
10#14582952—21no—
11#14582838—21no—
12#14582838—21no—
13#14582806C412yes—
14#14582805—21no—
15#14582805—21no—
16#14582764C412yes—
17C4×C4⋊Dic43C2211yescharacteristic
18#14582644—24no—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#432C2212yes—
21C43×#324—21no—
22C43×#324—21no—
23C22×Dic86—21no—
24#13063325—22no—
25#13063325—22no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43C2×C412yes—
29C2×C4×Dic43C2×C412yes—
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—22no—
32C4⋊(C43⋊C8)D414yes—
33C22⋊(C43⋊C8)—22no—
34#13063236—22no—
35#13063236—22no—
36C4×C43⋊C8—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C43⋊#95—21no—
42C22×Q8×C43C2×C411yescharacteristic
43C4×Q8×C43—22no—
44C4×Q8×C43—22no—
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C2×C42×C43C2311yescharacteristic
51C4⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53#97×C43—22no—
54C2×Q8×C43—22no—
55C2×Q8×C43—22no—
56C2×Q8×C43—41no—
57C22×C4×C43C22⋊C411yescharacteristic
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×Dic43—22no—
65C22×Dic43—22no—
66C2×Dic86—44no—
67C2×Dic86—41no—
68C2×Dic86—41no—
69C2×C8×C43—42no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
73C42×C43—21no—
74C42×C43—21no—
75C42×C43—21no—
76C42×C43—21no—
77C42×C43C2×D412yes—
78C42×C43#4112yes—
79C4⋊Dic43—24no—
80C4⋊Dic43—42no—
81C4⋊Dic43—42no—
82C4×Dic43—42no—
83C2×C43⋊C8—24no—
84C23×C43C2×C22⋊C411yescharacteristic
85Q8×C43—44no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43#10112yes—
100C2×C4×C43C4×D412yes—
101C2×C4×C43#12011yescharacteristic
102C2×C4×C43#12112yes—
103C2×C4×C43#12311yescharacteristic
104C2×Dic43—42no—
105C2×Dic43—44no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109Dic86—82no—
110Dic86—82no—
111C8×C43—82no—
112C43⋊C8—44no—
113#9456—431nomaximal, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43#38611yescharacteristic
117C22×C43C2×#10111yescharacteristic
118C22×C43#41311yescharacteristic
119C4×C43—21no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—22no—
123C4×C43—41no—
124C4×C43—41no—
125C4×C43—41no—
126C4×C43#45412yes—
127Dic43—82no—
128Dic43—82no—
129#2983—431no—
130#2568—431no—
131#1556—432no—
132#1467D4311yescharacteristic
133#1285—432no—
134C2×C43—21no—
135C2×C43—21no—
136C2×C43#188811yescharacteristic
137C2×C43#190111yescharacteristic
138C2×C43#190911yescharacteristic
139C2×C4⋊Q8—431no—
140C2×C4×Q8C2×D4311yescharacteristic
141#446—864no—
142#432—432no—
143#432—861no—
144#432C2×D4312yes—
145#431—861no—
146#400—861no—
147#400—861no—
148#391—432no—
149#391—861no—
150#391—861no—
151#382—432no—
152C4×C4⋊C4—431no—
153#332—864no—
154#324—21no—
155#324—21no—
156C43#945611yescharacteristic, complemented, Sylow
157C22×Q8—861no—
158C22×Q8C4×D4311yescharacteristic
159C4⋊Q8—862no—
160C4⋊Q8—862no—
161C4×Q8—22no—
162C4×Q8—22no—
163C2×C4⋊C4—432no—
164C2×C4⋊C4—861no—
165C2×C4⋊C4—861no—
166C2×C4⋊C4C4×D4311yescharacteristic
167C2×C4⋊C4C22⋊D4311yescharacteristic
168C2×C4⋊C4C22⋊D4311yescharacteristic
169C2×C42—432no—
170C2×C42D17211yescharacteristic
171C2×C42D17211yescharacteristic
172C2×C42C22×D4311yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—434no—
175C4⋊C8—862no—
176C4⋊C8—862no—
177C22⋊C8—22no—
178C22⋊C8—862no—
179#97—22no—
180#97—862no—
181#97—862no—
182C4×C8—862no—
183#95—862no—
184#95—862no—
185#95—862no—
186#95—862no—
187#95—861no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—1724no—
192C2×Q8—1721no—
193C2×Q8—1721no—
194C22×C4—862no—
195C22×C4—862no—
196C22×C4(C2×D43)⋊C411yescharacteristic
197C22×C4(C2×D43)⋊C411yescharacteristic
198C22×C4(C2×D43)⋊C411yescharacteristic
199C22×C4(C2×D43)⋊C411yescharacteristic
200C22×C4C2×C4×D4311yescharacteristic
201C22×C4C2×D17211yescharacteristic
202C22×C4C2×C22⋊D4311yescharacteristic
203C2×C8—42no—
204C2×C8—864no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—864no—
209C4⋊C4—1722no—
210C4⋊C4—1722no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—1722no—
216C42D4×D4312yes—
217C42#1062190012yes—
218C23C2×(C2×D43)⋊C411yescharacteristic
219Q8—44no—
220Q8—3442no—
221Q8—3442no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—1722no—
236C2×C4—1724no—
237C2×C4—1722no—
238C2×C4—1722no—
239C2×C4—1722no—
240C2×C4#1306324312yes—
241C2×C4(C22⋊D43)⋊C412yes—
242C2×C4#1306329511yescharacteristic
243C2×C4#1306329712yes—
244C2×C4#1306330911yescharacteristic
245C8—82no—
246C8—1724no—
247C22—21no—
248C22—21no—
249C22#1458277611yescharacteristic
250C22C2×#1306324311yescharacteristic
251C22#1458288111yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—3442no—
260C4—3442no—
261C4#1458307412yes—
262C2—21no—
263C2—21no—
264C2#1913499611yescharacteristic
265C2#1913506111yescharacteristic
266C2#1913511511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1467C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1467D43
hypocenterC43#9456
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
156. C43#9456semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191398072
#191333112
#191324502
C43×#14672
#945643