Finite Group Databasebeta

← #24990616

Subgroups — #24990616

Order 11008.

420 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 127 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#19143159C211yesmaximal, characteristic
2#19133369C212yesmaximal, complemented
3#19132909C211yesmaximal, characteristic
4#19132492C212yesmaximal, complemented
5C43×#1798C211yesmaximal, characteristic
6C22×#10621877—21no—
7#14582952C2212yes—
8#14582926—24no—
9#14582923—21no—
10#14582923C2212yes—
11#14582651—24no—
12#14582625C412yes—
13#14582623C412yes—
14C2×#117×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×C4⋊C8×C43C2211yescharacteristic
17C2×C22⋊C8×C43—21no—
18C43×#336—21no—
19C2×#10621877—22no—
20C2×#10621877—22no—
21C2×#10621877—42no—
22C2×#10621877—42no—
23C22×C43⋊C8—22no—
24C4⋊(C43⋊C8)—24no—
25C4⋊(C43⋊C8)—22no—
26C4⋊(C43⋊C8)—22no—
27C4⋊(C43⋊C8)D414yes—
28C22⋊(C43⋊C8)C2×C414yes—
29C4×C43⋊C8—22no—
30C23×C4×C43D411yescharacteristic
31C22×C8×C43—21no—
32C22×C8×C43—21no—
33#117×C43—22no—
34#117×C43—22no—
35C2×C4⋊C4×C43C2×C411yescharacteristic
36C2×C4⋊C4×C43Q811yescharacteristic
37C2×C22⋊C4×C43C2×C411yescharacteristic
38C2×C22⋊C4×C43Q811yescharacteristic
39C2×C42×C43D411yescharacteristic
40C2×C42×C43C2311yescharacteristic
41C4⋊C8×C43—22no—
42C4⋊C8×C43—22no—
43C22⋊C8×C43—42no—
44C24×C43C4⋊C411yescharacteristic
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C4⋊C411yescharacteristic
50C22×C4×C43C4⋊C411yescharacteristic
51C22×C4×C43C4⋊C411yescharacteristic
52C22×C4×C43D812yes—
53C22×C4×C43Q1612yes—
54C22×C4×C43C22×C411yescharacteristic
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43C2×Q811yescharacteristic
57C2×C8×C43—41no—
58C2×C8×C43—41no—
59C2×C8×C43—41no—
60C2×C8×C43—41no—
61C2×C8×C43—41no—
62C2×C8×C43—41no—
63C4⋊C4×C43—22no—
64C4⋊C4×C43—22no—
65C22⋊C4×C43—22no—
66C22⋊C4×C43—22no—
67C42×C43—21no—
68C42×C43—21no—
69C42×C43C2×D412yes—
70C42×C43#4112yes—
71#10621877—44no—
72#10621877—42no—
73#10621877—42no—
74C2×C43⋊C8—24no—
75C2×C43⋊C8—24no—
76C2×C43⋊C8—44no—
77C23×C43—21no—
78C23×C43—21no—
79C23×C43—41no—
80C23×C43—41no—
81C23×C43#10712yes—
82C23×C43C2×C4⋊C411yescharacteristic
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43#10712yes—
96C2×C4×C43C4×D412yes—
97C2×C4×C43#12011yescharacteristic
98C2×C4×C43C22⋊Q812yes—
99C2×C4×C43#12311yescharacteristic
100C2×C4×C43C2×D811yescharacteristic
101C2×C4×C43C2×Q1611yescharacteristic
102C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C43#13711yescharacteristic
104C8×C43—81no—
105C8×C43—81no—
106C43⋊C8—44no—
107C43⋊C8—44no—
108#8861—431nomaximal, Sylow
109C22×C43—21no—
110C22×C43—21no—
111C22×C43—22no—
112C22×C43—42no—
113C22×C43—41no—
114C22×C43—41no—
115C22×C43—81no—
116C22×C43#38511yescharacteristic
117C22×C43C2×#10711yescharacteristic
118C22×C43#42811yescharacteristic
119C4×C43—22no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—41no—
123C4×C43—41no—
124C4×C43#44711yescharacteristic
125C4×C43#45111yescharacteristic
126C4×C43#48011yescharacteristic
127C4×C43#48411yescharacteristic
128#2905—431no—
129#1798D4311yescharacteristic
130#1571—432no—
131#1458—431no—
132#1301—432no—
133C2×C43—21no—
134C2×C43—21no—
135C2×C43—42no—
136C2×C43#185211yescharacteristic
137C2×C43#185811yescharacteristic
138C2×C43#186811yescharacteristic
139C22×M16—861no—
140C2×#117C2×D4311yescharacteristic
141#431—432no—
142#424—864no—
143#423—432no—
144#423—861no—
145C2×C4⋊C8C2×D4311yescharacteristic
146C2×C4⋊C8C2×D4311yescharacteristic
147C2×C22⋊C8—21no—
148#336—21no—
149#335—864no—
150#324—432no—
151#323—432no—
152C43#886111yescharacteristic, complemented, Sylow
153C23×C4C22⋊D4311yescharacteristic
154C2×M16—862no—
155C2×M16—862no—
156C2×M16—1722no—
157C2×M16—1722no—
158C22×C8—21no—
159C22×C8—21no—
160C22×C8—862no—
161#117—22no—
162#117—22no—
163C2×C4⋊C4Dic8611yescharacteristic
164C2×C4⋊C4C4×D4311yescharacteristic
165C2×C22⋊C4Dic8611yescharacteristic
166C2×C22⋊C4C4×D4311yescharacteristic
167C2×C42C22⋊D4311yescharacteristic
168C2×C42C22×D4311yescharacteristic
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—434no—
172C4⋊C8—864no—
173C4⋊C8—862no—
174C4⋊C8—862no—
175C22⋊C8—42no—
176C22⋊C8—434no—
177C4×C8—862no—
178C24Dic43⋊C411yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4Dic43⋊C411yescharacteristic
184C22×C4Dic43⋊C411yescharacteristic
185C22×C4Dic43⋊C411yescharacteristic
186C22×C4#1062188212yes—
187C22×C4#1062188512yes—
188C22×C4C2×Dic8611yescharacteristic
189C22×C4C2×C4×D4311yescharacteristic
190C22×C4C2×C22⋊D4311yescharacteristic
191M16—1724no—
192M16—1722no—
193M16—1722no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—864no—
201C2×C8—864no—
202C2×C8—1724no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C42—21no—
208C42—21no—
209C42D4×D4312yes—
210C42#1062190012yes—
211C23—21no—
212C23—21no—
213C23—41no—
214C23—41no—
215C23#1306325812yes—
216C23C2×Dic43⋊C411yescharacteristic
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4#1306325812yes—
230C2×C4(C22⋊D43)⋊C412yes—
231C2×C4#1306329311yescharacteristic
232C2×C4#1306330212yes—
233C2×C4#1306330611yescharacteristic
234C2×C4C2×#1062188211yescharacteristic
235C2×C4C2×#1062188511yescharacteristic
236C2×C4#1306335011yescharacteristic
237C2×C4#1306335511yescharacteristic
238C8—81no—
239C8—81no—
240C8—1724no—
241C8—1724no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—81no—
249C22#1458277111yescharacteristic
250C22C2×#1306325811yescharacteristic
251C22#1458294211yescharacteristic
252C4—22no—
253C4—22no—
254C4—22no—
255C4—41no—
256C4—41no—
257C4#1458303211yescharacteristic
258C4#1458305411yescharacteristic
259C4#1458321011yescharacteristic
260C4#1458323211yescharacteristic
261C2—21no—
262C2—21no—
263C2—42no—
264C2#1913478211yescharacteristic
265C2#1913481411yescharacteristic
266C2#1913488011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1798C2
socleC22×C43#385
prime radicalC24×C43C4⋊C4
cosocleC2×C42×C43C23
hypercenter#1798D43
hypocenterC43#8861
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #19133369C2semidirect
4. #19132492C2semidirect
152. C43#8861semidirect

Maximal subgroups

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

subgroupindex
#191431592
#191333692
#191329092
#191324922
C43×#17982
#886143