Finite Group Databasebeta

← #25007765

Subgroups — #25007765

Order 11008.

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

normal subgroups only

This group has 388 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#19139800C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic
3#19132626C214yesmaximal
4C43×#1461C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6#14582923—21no—
7C2×#13063244—21no—
8#14582819C412yes—
9#14582819C2212yes—
10#14582806—21no—
11#14582797—21no—
12#14582797—21no—
13#14582768—21no—
14C4×C4⋊Dic43C411yescharacteristic
15#14582668C2212yes—
16C2×C4×Q8×C43C2211yescharacteristic
17C43×#431—21no—
18C43×#324—21no—
19C43×#324C2212yes—
20C22×Dic86C2×C412yes—
21C2×#10621877—22no—
22#13063325—41no—
23#13063325—41no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—21no—
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×C4×Dic43—21no—
30C4⋊(C43⋊C8)—41no—
31C4⋊(C43⋊C8)—41no—
32#13063244—42no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95C2×C412yes—
36C22×Q8×C43D411yescharacteristic
37C4×Q8×C43—41no—
38C4×Q8×C43—41no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43D411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C4⋊C8×C43—41no—
46C22⋊C8×C43—22no—
47C4×C8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43SD1612yes—
51C2×Q8×C43Q1612yes—
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—82no—
63C2×C8×C43—42no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C42×C43—21no—
68C42×C43—21no—
69C42×C43—21no—
70C42×C43—21no—
71C42×C43—21no—
72C42×C43—21no—
73C4⋊Dic43—24no—
74C4⋊Dic43—42no—
75C4⋊Dic43—41no—
76C4⋊Dic43—41no—
77Dic43⋊C4—82no—
78Dic43⋊C4—82no—
79C4×Dic43—42no—
80#10621877—42no—
81#10621877—42no—
82C2×C43⋊C8—42no—
83C23×C43C2×C22⋊C411yescharacteristic
84Q8×C43—42no—
85Q8×C43—42no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
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#9911yescharacteristic
100C2×C4×C43#9911yescharacteristic
101C2×C4×C43#10312yes—
102C2×C4×C43#10312yes—
103C2×C4×C43C2×SD1611yescharacteristic
104C2×C4×C43C2×Q1611yescharacteristic
105C2×Dic43—24no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111Dic86—84no—
112C8×C43—82no—
113C43⋊C8—82no—
114#11908—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43C2×#9911yescharacteristic
118C22×C43C2×#10311yescharacteristic
119C22×C43#42111yescharacteristic
120C4×C43—21no—
121C4×C43—21no—
122C4×C43—22no—
123C4×C43—22no—
124C4×C43—21no—
125C4×C43—41no—
126C4×C43—41no—
127C4×C43—41no—
128C4×C43#35612yes—
129Dic43—44no—
130Dic43—82no—
131#2567—431no—
132#1801—431no—
133#1461D4311yescharacteristic
134#1354—434no—
135C2×C43—21no—
136C2×C43—21no—
137C2×C43#152011yescharacteristic
138C2×C43#212211yescharacteristic
139C2×C43C2×#35611yescharacteristic
140C2×C4⋊Q8—431no—
141C2×C4×Q8C2×D4311yescharacteristic
142#431—21no—
143#423—861no—
144C2×#101—861no—
145#395—432no—
146#395—432no—
147#391—861no—
148#389—861no—
149#389—861no—
150#384—861no—
151C4×C4⋊C4—431no—
152#343—432no—
153#324—21no—
154#324C2×D4312yes—
155C43#1190811yescharacteristic, complemented, Sylow
156C22×Q8—432no—
157C22×Q8D17211yescharacteristic
158C2×M16—862no—
159C4⋊Q8—1721no—
160C4⋊Q8—1721no—
161C4×Q8—41no—
162C4×Q8—41no—
163C2×C4⋊C4—861no—
164C2×C4⋊C4—862no—
165C2×C4⋊C4—862no—
166C2×C4⋊C4—861no—
167C2×C4⋊C4—861no—
168C2×C4⋊C4C4×D4311yescharacteristic
169C2×C4⋊C4C22⋊D4311yescharacteristic
170C2×C4⋊C4C22×D4311yescharacteristic
171C2×C42—861no—
172C2×C42C4×D4311yescharacteristic
173C2×C42D17211yescharacteristic
174C2×C42C22⋊D4311yescharacteristic
175C4⋊C8—41no—
176C4⋊C8—1721no—
177C4⋊C8—1721no—
178#101—1722no—
179C22⋊C8—22no—
180C4×C8—41no—
181#95—432no—
182#95—862no—
183#95—862no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—3442no—
187C2×Q8—1722no—
188C2×Q8#1062187312yes—
189C2×Q8Dic17212yes—
190C22×C4—862no—
191C22×C4—862no—
192C22×C4(C2×D43)⋊C411yescharacteristic
193C22×C4(C2×D43)⋊C411yescharacteristic
194C22×C4(C2×D43)⋊C411yescharacteristic
195C22×C4(C2×D43)⋊C411yescharacteristic
196C22×C4C2×C4×D4311yescharacteristic
197C22×C4C2×D17211yescharacteristic
198C22×C4C2×C22⋊D4311yescharacteristic
199M16—1722no—
200M16—1722no—
201C2×C8—42no—
202C2×C8—1722no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—864no—
207C4⋊C4—3442no—
208C4⋊C4—3442no—
209C4⋊C4—1722no—
210C4⋊C4—1721no—
211C4⋊C4—1721no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—1722no—
219C23C2×(C2×D43)⋊C411yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—3444no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—864no—
237C2×C4—1722no—
238C2×C4—1722no—
239C2×C4—1722no—
240C2×C4—1722no—
241C2×C4—1722no—
242C2×C4#1306323911yescharacteristic
243C2×C4#1306323911yescharacteristic
244C2×C4#1306325012yes—
245C2×C4#1306325012yes—
246C2×C4C2×#1062187311yescharacteristic
247C2×C4C2×Dic17211yescharacteristic
248C8—82no—
249C8—3442no—
250C22—21no—
251C22—21no—
252C22C2×#1306323911yescharacteristic
253C22C2×#1306325011yescharacteristic
254C22#1458291511yescharacteristic
255C4—21no—
256C4—21no—
257C4—22no—
258C4—22no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—3442no—
264C4—1724no—
265C4#1458269712yes—
266C2—21no—
267C2—21no—
268C2#1913316811yescharacteristic
269C2#1913624411yescharacteristic
270C2C2×#1458269711yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1461C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1461D43
hypocenterC43#11908
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
155. C43#11908semidirect

Maximal subgroups

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

subgroupindex
#191398002
#191345912
#191326262
C43×#14612
#1190843