Finite Group Databasebeta

← #24983813

Subgroups — #24983813

Order 11008.

324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 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#19132916C211yesmaximal, characteristic
2#19132913C211yesmaximal, characteristic
3C43×#1870C211yesmaximal, characteristic
4#14582952—21no—
5C2×C22⋊(C43⋊C8)—21no—
6#14582625C412yes—
7#14582623—21no—
8#14582623—21no—
9#14582623C412yes—
10C22×M16×C43C411yescharacteristic
11C2×C4×D4×C43C2211yescharacteristic
12C2×C22⋊C8×C43—21no—
13C2×C22⋊C8×C43C411yescharacteristic
14C43×#336—21no—
15C22×C43⋊C8—41no—
16C4⋊(C43⋊C8)—41no—
17C22⋊(C43⋊C8)—22no—
18C22⋊(C43⋊C8)—22no—
19C22⋊(C43⋊C8)—41no—
20C4×C43⋊C8—41no—
21C22×D4×C43Q811yescharacteristic
22C23×C4×C43C2×C411yescharacteristic
23C23×C4×C43D411yescharacteristic
24C2×M16×C43—42no—
25C2×M16×C43—41no—
26C22×C8×C43—21no—
27C22×C8×C43—21no—
28C4×D4×C43—41no—
29C4×D4×C43—41no—
30C2×C4⋊C4×C43C2×C411yescharacteristic
31C2×C22⋊C4×C43C2×C411yescharacteristic
32C2×C22⋊C4×C43D411yescharacteristic
33C2×C42×C43D411yescharacteristic
34C22⋊C8×C43—42no—
35C22⋊C8×C43—41no—
36C24×C43C4⋊C411yescharacteristic
37C24×C43C4⋊C411yescharacteristic
38C2×D4×C43—22no—
39C2×D4×C43—22no—
40C2×D4×C43—41no—
41C22×C4×C43—21no—
42C22×C4×C43—21no—
43C22×C4×C43—21no—
44C22×C4×C43—21no—
45C22×C4×C43—41no—
46C22×C4×C43—41no—
47C22×C4×C43—41no—
48C22×C4×C43—41no—
49C22×C4×C43C4211yescharacteristic
50C22×C4×C43C22⋊C411yescharacteristic
51C22×C4×C43C22⋊C411yescharacteristic
52C22×C4×C43C22⋊C411yescharacteristic
53C22×C4×C43C4⋊C411yescharacteristic
54M16×C43—42no—
55M16×C43—42no—
56C2×C8×C43—22no—
57C2×C8×C43—41no—
58C2×C8×C43—41no—
59C2×C8×C43—41no—
60C2×C8×C43—41no—
61C2×C8×C43—41no—
62C4⋊C4×C43—41no—
63C22⋊C4×C43—41no—
64C22⋊C4×C43—41no—
65C42×C43—21no—
66C42×C43—21no—
67C2×C43⋊C8—42no—
68C2×C43⋊C8—42no—
69C2×C43⋊C8—81no—
70C2×C43⋊C8—81no—
71C23×C43—21no—
72C23×C43—21no—
73C23×C43—21no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43—41no—
77C23×C43—41no—
78C23×C43—41no—
79C23×C43—41no—
80C23×C43#9511yescharacteristic
81C23×C43#10812yes—
82D4×C43—44no—
83C2×C4×C43—21no—
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—42no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—81no—
99C2×C4×C43#9911yescharacteristic
100C2×C4×C43#9911yescharacteristic
101C2×C4×C43#10812yes—
102C8×C43—42no—
103C8×C43—81no—
104C43⋊C8—82no—
105C43⋊C8—82no—
106#7285—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—22no—
110C22×C43—42no—
111C22×C43—41no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43—41no—
115C22×C43—41no—
116C22×C43—81no—
117C22×C43—81no—
118C22×C43—81no—
119C22×C43#34111yescharacteristic
120C22×C43#34111yescharacteristic
121C22×C43#34211yescharacteristic
122C4×C43—22no—
123C4×C43—21no—
124C4×C43—41no—
125C4×C43—41no—
126C4×C43—41no—
127C4×C43AΣL(1,𝔽16)11yescharacteristic
128C4×C43#35211yescharacteristic
129#1870D4311yescharacteristic
130#1460—431no—
131#1459—431no—
132C2×C43—21no—
133C2×C43—21no—
134C2×C43—42no—
135C2×C43—81no—
136C2×C43#129811yescharacteristic
137C2×C43#139011yescharacteristic
138C2×C43#139511yescharacteristic
139C22×M16Dic4311yescharacteristic
140C2×C4×D4C2×D4311yescharacteristic
141#431—861no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—861no—
144C2×C22⋊C8Dic4311yescharacteristic
145#336—21no—
146#324—432no—
147#323—432no—
148#323—861no—
149#323—861no—
150C43#728511yescharacteristic, complemented, Sylow
151C22×D4Dic8611yescharacteristic
152C23×C4C2×Dic4311yescharacteristic
153C23×C4C22⋊D4311yescharacteristic
154C2×M16—42no—
155C2×M16—41no—
156C22×C8—21no—
157C22×C8—21no—
158C22×C8—1721no—
159C4×D4—41no—
160C4×D4—41no—
161C2×C4⋊C4C4×D4311yescharacteristic
162C2×C22⋊C4C4×D4311yescharacteristic
163C2×C22⋊C4D17211yescharacteristic
164C2×C42C22⋊D4311yescharacteristic
165C4⋊C8—1721no—
166C22⋊C8—42no—
167C22⋊C8—41no—
168C22⋊C8—862no—
169C22⋊C8—862no—
170C22⋊C8—1721no—
171C4×C8—1721no—
172C24Dic43⋊C411yescharacteristic
173C24C4⋊Dic4311yescharacteristic
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—41no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4C4×Dic4311yescharacteristic
186C22×C4Dic43⋊C411yescharacteristic
187C22×C4(C2×D43)⋊C411yescharacteristic
188C22×C4(C2×D43)⋊C411yescharacteristic
189C22×C4C22⋊Dic4311yescharacteristic
190M16—42no—
191M16—42no—
192C2×C8—22no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—3441no—
199C2×C8—3441no—
200C2×C8—1722no—
201C2×C8—1722no—
202C4⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C42—21no—
206C42—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23C43⋊#9511yescharacteristic
217C23#1306326012yes—
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4#1306324011yescharacteristic
236C2×C4#1306324011yescharacteristic
237C2×C4#1306326012yes—
238C8—42no—
239C8—81no—
240C8—3442no—
241C8—3442no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22#1458266311yescharacteristic
255C22#1458266311yescharacteristic
256C22#1458266611yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4#1458268611yescharacteristic
263C4#1458268911yescharacteristic
264C2—21no—
265C2—21no—
266C2—42no—
267C2—81no—
268C2#1913248211yescharacteristic
269C2#1913271311yescharacteristic
270C2#1913272411yescharacteristic
subgroupG/H
centerC2×C4#13063240
commutatorC22×C4×C43C42
FrattiniC2×C4×D4C2×D43
FittingC43×#1870C2
socleC22×C43#342
prime radicalC22×D4×C43Q8
cosocleC2×C4×D4×C43C22
hypercenter#1870D43
hypocenterC43#7285
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
150. C43#7285semidirect

Maximal subgroups

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

subgroupindex
#191329162
#191329132
C43×#18702
#728543