Finite Group Databasebeta

← #25016933

Subgroups — #25016933

Order 11008.

398 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#14582698C212yesmaximal, complemented
2#19132764C212yesmaximal, complemented
3#19132762C212yesmaximal, complemented
4C43×#3152C211yesmaximal, characteristic
5C2×#13063244—22no—
6#14582698—22no—
7#14582698C2214yes—
8C2×#137×C43—22no—
9C43×#532C411yescharacteristic
10C2×C4⋊Q8×C43C2211yescharacteristic
11C43×#497—22no—
12C43×#494C411yescharacteristic
13C43×#494C2211yescharacteristic
14C43×#492C411yescharacteristic
15C43×#492C2211yescharacteristic
16C4×M16×C43C411yescharacteristic
17C2×#10621877—42no—
18#13063244—24no—
19#13063244—42no—
20C2×#41×C43—21no—
21C22×Q8×C43D412yes—
22#137×C43—44no—
23#137×C43—44no—
24C2×Q16×C43—22no—
25C2×Q16×C43—22no—
26C2×SD16×C43—22no—
27C2×SD16×C43—22no—
28C2×M16×C43—21no—
29C4⋊Q8×C43—41no—
30C4⋊Q8×C43C2×C411yescharacteristic
31C4⋊Q8×C43C2×C411yescharacteristic
32C4⋊Q8×C43D412yes—
33C4⋊Q8×C43C2311yescharacteristic
34#127×C43C2×C411yescharacteristic
35#124×C43—21no—
36#121×C43—41no—
37C4×D4×C43—41no—
38C2×C4⋊C4×C43—41no—
39C2×C42×C43C2×C411yescharacteristic
40#97×C43—21no—
41C4×C8×C43C2×C411yescharacteristic
42C4×C8×C43C2×C411yescharacteristic
43#41×C43—42no—
44#41×C43—42no—
45C2×Q8×C43—22no—
46C2×Q8×C43—21no—
47C2×Q8×C43—42no—
48C2×Q8×C43—42no—
49C2×Q8×C43C22⋊C412yes—
50C2×Q8×C43C2×D412yes—
51C2×D4×C43—21no—
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C22×C4×C43—21no—
55C22×C4×C43—22no—
56C22×C4×C43—41no—
57C22×C4×C43C22⋊C411yescharacteristic
58Q16×C43—44no—
59Q16×C43—44no—
60SD16×C43—44no—
61SD16×C43—44no—
62M16×C43—24no—
63C2×C8×C43—21no—
64C2×C8×C43—21no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—42no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C22⋊C4×C43—42no—
70C42×C43—21no—
71C42×C43C22⋊C411yescharacteristic
72C42×C43C22×C411yescharacteristic
73#10621877—44no—
74#10621877—82no—
75C2×C43⋊C8—82no—
76C23×C43—41no—
77C23×C43#9911yescharacteristic
78Q8×C43—42no—
79Q8×C43—42no—
80Q8×C43—42no—
81Q8×C43—82no—
82D4×C43—42no—
83D4×C43—82no—
84D4×C43—82no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—41no—
94C2×C4×C43—81no—
95C2×C4×C43—81no—
96C2×C4×C43#9911yescharacteristic
97C2×C4×C43C2×C22⋊C411yescharacteristic
98C8×C43—22no—
99C8×C43—22no—
100C43⋊C8—84no—
101#13590—431nomaximal, Sylow
102C22×C43—41no—
103C22×C43—82no—
104C22×C43—81no—
105C22×C43#35312yes—
106C22×C43C2×#9911yescharacteristic
107C4×C43—22no—
108C4×C43—21no—
109C4×C43—21no—
110C4×C43—41no—
111C4×C43—42no—
112C4×C43—42no—
113C4×C43—81no—
114#3152D4311yescharacteristic
115C2×#356—432no—
116#1411—432no—
117#1410—432no—
118C2×C43—21no—
119C2×C43—22no—
120C2×C43—161no—
121C2×C43C2×#35311yescharacteristic
122C2×#137—22no—
123#532Dic4311yescharacteristic
124C2×C4⋊Q8C2×D4311yescharacteristic
125#497—22no—
126#494Dic4311yescharacteristic
127#494C2×D4311yescharacteristic
128#492Dic4311yescharacteristic
129#492C2×D4311yescharacteristic
130C2×#101—862no—
131C4×M16Dic4311yescharacteristic
132#356—434no—
133#356—862no—
134C43#1359011yescharacteristic, complemented, Sylow
135C2×#41—21no—
136C22×Q8C22⋊D4312yes—
137#137—44no—
138#137—44no—
139C2×Q16—22no—
140C2×Q16—22no—
141C2×SD16—22no—
142C2×SD16—22no—
143C2×M16—21no—
144C2×M16—1722no—
145C4⋊Q8—41no—
146C4⋊Q8C2×Dic4311yescharacteristic
147C4⋊Q8C2×Dic4311yescharacteristic
148C4⋊Q8C22⋊D4312yes—
149C4⋊Q8C22×D4311yescharacteristic
150#127C2×Dic4311yescharacteristic
151#124—21no—
152#121—41no—
153C4×D4—41no—
154C2×C4⋊C4—41no—
155C2×C42C2×Dic4311yescharacteristic
156#101—864no—
157#101—1722no—
158#97—21no—
159C4×C8C2×Dic4311yescharacteristic
160C4×C8C2×Dic4311yescharacteristic
161#41—42no—
162#41—42no—
163C2×Q8—22no—
164C2×Q8—21no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8C22⋊Dic4312yes—
168C2×Q8C2×C22⋊D4312yes—
169C2×D4—21no—
170C2×D4—41no—
171C2×D4—41no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4C22⋊Dic4311yescharacteristic
176Q16—44no—
177Q16—44no—
178SD16—44no—
179SD16—44no—
180M16—24no—
181M16—3442no—
182M16—1724no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—3442no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—41no—
190C22⋊C4—42no—
191C42—21no—
192C42C22⋊Dic4311yescharacteristic
193C42C22×Dic4311yescharacteristic
194C23—41no—
195C23#1306324011yescharacteristic
196Q8—42no—
197Q8—42no—
198Q8—42no—
199Q8—82no—
200D4—42no—
201D4—82no—
202D4—82no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4#1306324011yescharacteristic
215C2×C4C2×C22⋊Dic4311yescharacteristic
216C8—22no—
217C8—22no—
218C8—3444no—
219C22—41no—
220C22—82no—
221C22—81no—
222C22#1458269212yes—
223C22C2×#1306324011yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—42no—
230C4—81no—
231C2—21no—
232C2—22no—
233C2—161no—
234C2C2×#1458269211yescharacteristic
subgroupG/H
centerC2C2×#14582692
commutatorC42×C43C22×C4
FrattiniC4⋊Q8C22×D43
FittingC43×#3152C2
socleC2×C43C2×#353
prime radicalC43×#532C4
cosocleC4⋊Q8×C43C23
hypercenter#3152D43
hypocenterC43#13590
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ #3152

Complements

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

NH ≅ G/Ntype
1. C2×#14582698C2semidirect
2. #19132764C2semidirect
3. #19132762C2semidirect
134. C43#13590semidirect

Maximal subgroups

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

subgroupindex
C2×#145826982
#191327642
#191327622
C43×#31522
#1359043