Finite Group Databasebeta

← #46825978

Subgroups — #46825978

Order 34432.

232 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D269⋊#99C211yesmaximal, characteristic
2#31771557C211yesmaximal, characteristic
3#99×D269C211yesmaximal, characteristic
4C2×C4⋊#11761640C411yescharacteristic, complemented
5C2×C22⋊#11761640—21no—
6C2×C22⋊#11761640—21no—
7C2×C22⋊#11761640—21no—
8C2×C4×#11761640C411yescharacteristic, complemented
9#22575512C412yescomplemented
10#22575511—21no—
11C2×D4×D269C2211yescharacteristic
12C22⋊C4×D269—21no—
13#22575368C411yescharacteristic, complemented
14#22575367—21no—
15#99×C269C411yescharacteristic, complemented
16C22×#11761640—21no—
17C22×#11761640—21no—
18C22×#11761640—41no—
19C4⋊#11761640—41no—
20C22⋊#11761640—22no—
21C22⋊#11761640—41no—
22C22⋊#11761640—42no—
23C22⋊#11761640—42no—
24C4×#11761640—41no—
25C23×D269D411yescharacteristic
26C23×D269D411yescharacteristic
27C2×D1076C2×C411yescharacteristic
28C2×C22⋊D269D411yescharacteristic
29C2×C22⋊D269Q811yescharacteristic
30D4×D269—41no—
31D4×D269—41no—
32C2×C4×D269—41no—
33C2×C4×D269C2×C411yescharacteristic
34C22⋊Dic269—21no—
35#16864379—41no—
36C2×D4×C269C2×C411yescharacteristic
37C22⋊C4×C269—21no—
38C2×#11761640—22no—
39C2×#11761640—41no—
40C2×#11761640—41no—
41C2×#11761640—42no—
42C2×#11761640—41no—
43C2×#11761640—41no—
44C2×#11761640—41no—
45C2×#11761640—81no—
46C2×#11761640—81no—
47C22×D269—21no—
48C22×D269—21no—
49C22×D269—21no—
50C22×D269—21no—
51C22×D269—41no—
52C22×D269—41no—
53C22×D269—41no—
54C22×D269—41no—
55C22×D269C22⋊C411yescharacteristic
56C22×D269C22⋊C411yescharacteristic
57C22×D269C4⋊C411yescharacteristic
58D1076—41no—
59C22⋊D269—41no—
60C22⋊D269—41no—
61C2×Dic269—41no—
62C2×Dic269C4⋊C411yescharacteristic
63C4×D269—21no—
64C4×D269—21no—
65C4×D269—81no—
66C4×D269—81no—
67C23×C269C22⋊C411yescharacteristic
68C23×C269C4⋊C411yescharacteristic
69D4×C269—41no—
70C2×C4×C269—41no—
71C2×C4×C269C4211yescharacteristic
72C22×C269—21no—
73C22×C269—21no—
74C22×C269—41no—
75C22×C269—41no—
76C22×C269#9511yescharacteristic
77C2×D269—21no—
78C2×D269—21no—
79C2×D269—21no—
80C2×D269—21no—
81C2×D269—41no—
82C2×D269—41no—
83C2×D269—41no—
84C2×D269—41no—
85C2×D269—41no—
86C2×D269—41no—
87C2×D269—81no—
88C2×D269—81no—
89C2×D269#9911yescharacteristic
90C2×D269#9911yescharacteristic
91#11761640—42no—
92#11761640—82no—
93#11761640—81no—
94C4×C269—21no—
95C4×C269—81no—
96Dic269—21no—
97Dic269—81no—
98C2×C269—21no—
99C2×C269—41no—
100C2×C269—41no—
101C2×C269#34211yescharacteristic
102D269—21no—
103D269—41no—
104D269—41no—
105D269#35311yescharacteristic
106D269#35411yescharacteristic
107C269#139311yescharacteristic, complemented, Sylow
108#1393—2691nomaximal, Sylow
109C2×#99—2691no—
110C2×#99—2691no—
111#390—2691no—
112C22×D4—2691no—
113C2×C4⋊C4—2691no—
114C2×C22⋊C4—5381no—
115C2×C22⋊C4—5381no—
116C2×C22⋊C4—5381no—
117C2×C22⋊C4—5381no—
118C2×C42—2691no—
119#99—2692no—
120#99—2691no—
121#99—5381no—
122#99—5381no—
123#99#1176164011yescharacteristic, complemented
124C24—2691no—
125C24—2691no—
126C2×D4—2691no—
127C2×D4—2691no—
128C2×D4—2691no—
129C2×D4—10761no—
130C2×D4—10761no—
131C2×D4C2×#1176164011yescharacteristic
132C22×C4—2691no—
133C22×C4—5381no—
134C22×C4—5381no—
135C22×C4—10761no—
136C22×C4—10761no—
137C4⋊C4—10761no—
138C22⋊C4—21no—
139C22⋊C4—5382no—
140C22⋊C4—5381no—
141C22⋊C4—10761no—
142C22⋊C4—10762no—
143C22⋊C4—10762no—
144C22⋊C4—10761no—
145C42—10761no—
146C23—2691no—
147C23—2691no—
148C23—2691no—
149C23—5381no—
150C23—5381no—
151C23—5381no—
152C23—5381no—
153C23—10761no—
154C23—10761no—
155C23—10761no—
156C23—10761no—
157C23C22⋊#1176164011yescharacteristic
158C23C4⋊#1176164011yescharacteristic
159D4—41no—
160D4—10761no—
161D4—10761no—
162D4—10761no—
163C2×C4—41no—
164C2×C4—2691no—
165C2×C4—5381no—
166C2×C4—5381no—
167C2×C4—5382no—
168C2×C4—10761no—
169C2×C4—10761no—
170C2×C4—10761no—
171C2×C4—10761no—
172C2×C4—10762no—
173C2×C4—10761no—
174C2×C4—10761no—
175C2×C4—21521no—
176C2×C4—21521no—
177C2×C4—21521no—
178C2×C4—21521no—
179C2×C4C4×#1176164011yescharacteristic
180C22—21no—
181C22—21no—
182C22—41no—
183C22—41no—
184C22—2691no—
185C22—2691no—
186C22—5381no—
187C22—5381no—
188C22—5381no—
189C22—5381no—
190C22—10761no—
191C22—10761no—
192C22—10761no—
193C22—10761no—
194C22—10761no—
195C22—10761no—
196C22—21521no—
197C22—21521no—
198C22(C2×#11761640)⋊C411yescharacteristic
199C4—21no—
200C4—81no—
201C4—5381no—
202C4—10762no—
203C4—21521no—
204C4—21521no—
205C4—21522no—
206C2—21no—
207C2—41no—
208C2—41no—
209C2—2691no—
210C2—2691no—
211C2—5381no—
212C2—10761no—
213C2—10761no—
214C2#3177148211yescharacteristic
subgroupG/H
centerC2#31771482
commutatorC2×C4×C269C42
FrattiniC2×D4C2×#11761640
Fitting#99×C269C4
socleC2×C269#342
prime radical, cosocleC2×D4×D269C22
hypercenter#99#11761640
hypocenterC269#1393
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊#11761640C4semidirect
8. C2×C4×#11761640C4semidirect
9. #22575512C4semidirect
13. #22575368C4semidirect
15. #99×C269C4semidirect
107. C269#1393semidirect
123. #99#11761640semidirect

Maximal subgroups

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

subgroupindex
D269⋊#992
#317715572
#99×D2692
#1393269