Finite Group Databasebeta

← #25007759

Subgroups — #25007759

Order 11008.

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

normal subgroups only

This group has 372 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#19139807C211yesmaximal, characteristic
2#19132919C211yesmaximal, characteristic
3#19132621C214yesmaximal
4C43×#1801C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6#14582952—21no—
7#14582838C412yes—
8#14582838C2212yes—
9#14582806—21no—
10#14582805—21no—
11#14582805—21no—
12#14582764—21no—
13C4×C4⋊Dic43C411yescharacteristic
14#14582625—21no—
15#14582625C2212yes—
16C2×C4×Q8×C43C2211yescharacteristic
17C43×#423—21no—
18C2×#101×C43—21no—
19C43×#343C2212yes—
20C22×Dic86—21no—
21#13063325—41no—
22#13063325—41no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43C2×C412yes—
26C2×C4×Dic43—21no—
27C4⋊(C43⋊C8)—41no—
28C22⋊(C43⋊C8)—22no—
29C4×C43⋊C8—41no—
30C43⋊#95—22no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95C2×C412yes—
35C22×Q8×C43D411yescharacteristic
36C2×M16×C43—22no—
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—
46C4⋊C8×C43—41no—
47#101×C43—42no—
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—44no—
62C2×Dic86—41no—
63C2×Dic86—41no—
64M16×C43—42no—
65M16×C43—42no—
66C2×C8×C43—42no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C42×C43—21no—
71C42×C43—21no—
72C42×C43—21no—
73C42×C43—21no—
74C42×C43—21no—
75C42×C43—21no—
76C4⋊Dic43—42no—
77C4⋊Dic43—42no—
78C4⋊Dic43—42no—
79C4×Dic43—42no—
80C2×C43⋊C8—42no—
81C23×C43C2×C22⋊C411yescharacteristic
82Q8×C43—42no—
83Q8×C43—42no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
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—41no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43#9911yescharacteristic
98C2×C4×C43#9911yescharacteristic
99C2×C4×C43#10312yes—
100C2×C4×C43#10312yes—
101C2×C4×C43C2×SD1611yescharacteristic
102C2×C4×C43C2×Q1611yescharacteristic
103C2×Dic43—42no—
104C2×Dic43—44no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108Dic86—82no—
109Dic86—82no—
110C8×C43—82no—
111C43⋊C8—82no—
112#11907—431nomaximal, Sylow
113C22×C43—21no—
114C22×C43—21no—
115C22×C43C2×#9911yescharacteristic
116C22×C43C2×#10311yescharacteristic
117C22×C43#42111yescharacteristic
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—21no—
123C4×C43—41no—
124C4×C43—41no—
125C4×C43—41no—
126C4×C43#35512yes—
127Dic43—82no—
128Dic43—82no—
129#2568—431no—
130#1801D4311yescharacteristic
131#1461—431no—
132#1353—434no—
133C2×C43—21no—
134C2×C43—21no—
135C2×C43#152011yescharacteristic
136C2×C43#212311yescharacteristic
137C2×C43C2×#35511yescharacteristic
138C2×C4⋊Q8—431no—
139C2×C4×Q8C2×D4311yescharacteristic
140#431—861no—
141#423—21no—
142C2×#101—21no—
143#400—432no—
144#400—432no—
145#391—861no—
146#391—861no—
147#391—861no—
148#382—861no—
149C4×C4⋊C4—431no—
150#343C2×D4312yes—
151#324—432no—
152#324—861no—
153C43#1190711yescharacteristic, complemented, Sylow
154C22×Q8—861no—
155C22×Q8C22⋊D4311yescharacteristic
156C2×M16—22no—
157C4⋊Q8—1721no—
158C4⋊Q8—1721no—
159C4×Q8—41no—
160C4×Q8—41no—
161C2×C4⋊C4—432no—
162C2×C4⋊C4—861no—
163C2×C4⋊C4—861no—
164C2×C4⋊C4C4×D4311yescharacteristic
165C2×C4⋊C4D17211yescharacteristic
166C2×C4⋊C4C22×D4311yescharacteristic
167C2×C42—861no—
168C2×C42C4×D4311yescharacteristic
169C2×C42D17211yescharacteristic
170C2×C42C22⋊D4311yescharacteristic
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—1721no—
174#101—42no—
175C22⋊C8—862no—
176C4×C8—1721no—
177#95—432no—
178#95—862no—
179#95—862no—
180#95—862no—
181#95—862no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—1724no—
185C2×Q8—1721no—
186C2×Q8—1721no—
187C2×Q8#1062188312yes—
188C2×Q8#1062188512yes—
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—42no—
199M16—42no—
200C2×C8—42no—
201C2×C8—1722no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—1722no—
206C4⋊C4—1722no—
207C4⋊C4—1722no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—1722no—
215C23C2×(C2×D43)⋊C411yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—3442no—
219Q8—3442no—
220C2×C4—21no—
221C2×C4—21no—
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—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—1722no—
234C2×C4—1724no—
235C2×C4—1722no—
236C2×C4—1722no—
237C2×C4—1722no—
238C2×C4#1306323911yescharacteristic
239C2×C4#1306323911yescharacteristic
240C2×C4#1306324812yes—
241C2×C4#1306324812yes—
242C2×C4C2×#1062188311yescharacteristic
243C2×C4C2×#1062188511yescharacteristic
244C8—82no—
245C8—3442no—
246C22—21no—
247C22—21no—
248C22C2×#1306323911yescharacteristic
249C22C2×#1306324811yescharacteristic
250C22#1458291711yescharacteristic
251C4—21no—
252C4—21no—
253C4—22no—
254C4—22no—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—3442no—
260C4—3442no—
261C4#1458269512yes—
262C2—21no—
263C2—21no—
264C2#1913316611yescharacteristic
265C2#1913625011yescharacteristic
266C2C2×#1458269511yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1801C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1801D43
hypocenterC43#11907
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
153. C43#11907semidirect

Maximal subgroups

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

subgroupindex
#191398072
#191329192
#191326212
C43×#18012
#1190743