Finite Group Databasebeta

← #25007193

Subgroups — #25007193

Order 11008.

414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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#19139580C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic
3#19132602C214yesmaximal
4C43×#1467C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6C2×#13063323—21no—
7C2×#13063244—21no—
8C4×#10621877—21no—
9#14582829C412yes—
10#14582829C2212yes—
11#14582804—21no—
12#14582797—21no—
13#14582797—21no—
14C4×C4⋊Dic43C411yescharacteristic
15#14582668C2212yes—
16C2×C4×Q8×C43C2211yescharacteristic
17C43×#432—21no—
18C43×#324—21no—
19C43×#324C2212yes—
20C22×Dic86—21no—
21C2×#10621877—22no—
22#13063325—41no—
23#13063325—41no—
24#13063323—44no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C412yes—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—22no—
30C2×C4×Dic43—21no—
31#13063244—24no—
32#13063236—41no—
33C4×C43⋊C8—41no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95C2×C412yes—
37C22×Q8×C43D411yescharacteristic
38C4×Q8×C43—41no—
39C4×Q8×C43—41no—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C4⋊C8×C43—41no—
47C22⋊C8×C43—22no—
48#97×C43—41no—
49C2×Q8×C43—22no—
50C2×Q8×C43—22no—
51C2×Q8×C43—41no—
52C22×C4×C43C22⋊C411yescharacteristic
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22⋊C411yescharacteristic
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×Dic43—22no—
60C22×Dic43—22no—
61C2×Dic86—42no—
62C2×Dic86—42no—
63C2×Dic86—42no—
64C2×C8×C43—42no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C4⋊C4×C43—41no—
68C42×C43—21no—
69C42×C43—21no—
70C42×C43—21no—
71C42×C43—21no—
72C42×C43—21no—
73C42×C43—21no—
74C4⋊Dic43—24no—
75C4⋊Dic43—41no—
76C4⋊Dic43—41no—
77C4⋊Dic43—42no—
78Dic43⋊C4—44no—
79Dic43⋊C4—44no—
80C4×Dic43—42no—
81#10621877—24no—
82#10621877—42no—
83C2×C43⋊C8—42no—
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—21no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43#9911yescharacteristic
101C2×C4×C43#9911yescharacteristic
102C2×C4×C43#10412yes—
103C2×C4×C43AGL(1,ℤ/8)12yes—
104C2×Dic43—24no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—42no—
110Dic86—84no—
111C8×C43—82no—
112C43⋊C8—44no—
113#11782—431nomaximal, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43C2×#9911yescharacteristic
117C22×C43#41811yescharacteristic
118C22×C43C2×#10411yescharacteristic
119C4×C43—21no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—41no—
123C4×C43—41no—
124C4×C43—41no—
125C4×C43—41no—
126C4×C43#35612yes—
127Dic43—44no—
128Dic43—82no—
129#2546—431no—
130C4×#101—431no—
131#1467D4311yescharacteristic
132#1346—434no—
133C2×C43—21no—
134C2×C43—21no—
135C2×C43#150711yescharacteristic
136C2×C43#212311yescharacteristic
137C2×C43C2×#35611yescharacteristic
138C2×C4⋊Q8—431no—
139C2×C4⋊Q8—861no—
140C2×C4×Q8C2×D4311yescharacteristic
141#432—21no—
142C2×#101—861no—
143C4×M16—861no—
144#398—432no—
145#398—432no—
146#391—861no—
147#389—861no—
148#389—861no—
149C4×C4⋊C4—431no—
150#343—432no—
151#324—21no—
152#324C2×D4312yes—
153C43#1178211yescharacteristic, complemented, Sylow
154C22×Q8—861no—
155C22×Q8D17211yescharacteristic
156C2×M16—862no—
157C4⋊Q8—1721no—
158C4⋊Q8—1721no—
159C4⋊Q8—1724no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—432no—
163C2×C4⋊C4—861no—
164C2×C4⋊C4—862no—
165C2×C4⋊C4—861no—
166C2×C4⋊C4—862no—
167C2×C4⋊C4C4×D4311yescharacteristic
168C2×C4⋊C4C22⋊D4311yescharacteristic
169C2×C4⋊C4C22×D4311yescharacteristic
170C2×C42—861no—
171C2×C42C4×D4311yescharacteristic
172C2×C42D17211yescharacteristic
173C2×C42C22⋊D4311yescharacteristic
174C4⋊C8—41no—
175#101—864no—
176C22⋊C8—22no—
177#97—41no—
178#97—1721no—
179C4×C8—1721no—
180#95—432no—
181#95—862no—
182#95—862no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—41no—
186C2×Q8—1722no—
187C2×Q8—1722no—
188C2×Q8—1722no—
189C22×C4—862no—
190C22×C4—862no—
191C22×C4(C2×D43)⋊C411yescharacteristic
192C22×C4(C2×D43)⋊C411yescharacteristic
193C22×C4(C2×D43)⋊C411yescharacteristic
194C22×C4(C2×D43)⋊C411yescharacteristic
195C22×C4C2×C4×D4311yescharacteristic
196C22×C4C2×D17211yescharacteristic
197C22×C4C2×C22⋊D4311yescharacteristic
198M16—864no—
199M16—1722no—
200C2×C8—42no—
201C2×C8—1722no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—864no—
206C4⋊C4—1722no—
207C4⋊C4—1724no—
208C4⋊C4—1721no—
209C4⋊C4—1721no—
210C4⋊C4—1724no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—1722no—
218C23C2×(C2×D43)⋊C411yescharacteristic
219Q8—44no—
220Q8—3444no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
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—864no—
236C2×C4—1722no—
237C2×C4—1722no—
238C2×C4—1722no—
239C2×C4—1722no—
240C2×C4—1722no—
241C2×C4#1306323911yescharacteristic
242C2×C4#1306323911yescharacteristic
243C2×C4#1306325112yes—
244C2×C4#1306335312yes—
245C8—82no—
246C8—1724no—
247C22—21no—
248C22—21no—
249C22C2×#1306323911yescharacteristic
250C22#1458290511yescharacteristic
251C22C2×#1306325111yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—41no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—3442no—
260C4—1724no—
261C4#1458269712yes—
262C2—21no—
263C2—21no—
264C2#1913311211yescharacteristic
265C2#1913624811yescharacteristic
266C2C2×#1458269711yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1467C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1467D43
hypocenterC43#11782
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
153. C43#11782semidirect

Maximal subgroups

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

subgroupindex
#191395802
C4×#130632442
#191326022
C43×#14672
#1178243