Finite Group Databasebeta

← #2126×C233 #44448158

Subgroups — #2126×C233 #44448158

Order 29824.

258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 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#532×C233C211yesmaximal, characteristic
2#410×C233C212yesmaximal, complemented
3#354×C233C212yesmaximal, complemented
4#353×C233C212yesmaximal, complemented
5C2×#41×C233C411yescharacteristic, complemented
6C2×#41×C233C2211yescharacteristic
7C4⋊Q8×C233C411yescharacteristic, complemented
8#127×C233C2211yescharacteristic
9#124×C233C411yescharacteristic, complemented
10#124×C233C2211yescharacteristic
11#121×C233—22no—
12C4×D4×C233—22no—
13#117×C233—22no—
14C2×C42×C233C411yescharacteristic, complemented
15#99×C233—22no—
16#99×C233C2214yes—
17#41×C233—41no—
18#41×C233—41no—
19#41×C233—41no—
20#41×C233—41no—
21C2×Q8×C233C2×C411yescharacteristic
22C2×Q8×C233C2×C411yescharacteristic
23C2×D4×C233—21no—
24C2×D4×C233—22no—
25C2×D4×C233C2×C411yescharacteristic
26C2×D4×C233D412yes—
27C2×D4×C233C2311yescharacteristic
28C22×C4×C233—21no—
29C22×C4×C233—21no—
30C22×C4×C233C2×C411yescharacteristic
31C22×C4×C233D412yes—
32C4⋊C4×C233—22no—
33C4⋊C4×C233—42no—
34C22⋊C4×C233—22no—
35C22⋊C4×C233—22no—
36C22⋊C4×C233—24no—
37C42×C233—21no—
38C42×C233—42no—
39C42×C233C2×C411yescharacteristic
40C42×C233C2×C411yescharacteristic
41C23×C233—21no—
42C23×C233C22⋊C411yescharacteristic
43C23×C233C2×D412yes—
44Q8×C233—41no—
45Q8×C233—41no—
46D4×C233—42no—
47D4×C233—41no—
48D4×C233—41no—
49D4×C233—44no—
50D4×C233—42no—
51C2×C4×C233—21no—
52C2×C4×C233—22no—
53C2×C4×C233—21no—
54C2×C4×C233—22no—
55C2×C4×C233—21no—
56C2×C4×C233—21no—
57C2×C4×C233—21no—
58C2×C4×C233—42no—
59C2×C4×C233—41no—
60C2×C4×C233—41no—
61C2×C4×C233—44no—
62C2×C4×C233C22⋊C412yes—
63C2×C4×C233C22⋊C411yescharacteristic
64C2×C4×C233C22×C411yescharacteristic
65C22×C233—22no—
66C22×C233—21no—
67C22×C233—41no—
68C22×C233—42no—
69C22×C233—42no—
70C22×C233—41no—
71C22×C233C2×C22⋊C411yescharacteristic
72C4×C233—22no—
73C4×C233—22no—
74C4×C233—21no—
75C4×C233—41no—
76C4×C233—41no—
77C4×C233—84no—
78C4×C233#9911yescharacteristic
79C4×C233#9911yescharacteristic
80C2×C233—21no—
81C2×C233—42no—
82C2×C233—41no—
83C2×C233—81no—
84C2×C233C2×#9911yescharacteristic
85C233#212611yescharacteristic, direct product factor, Sylow
86#2126C23311yesmaximal, characteristic, direct product factor, Sylow
87#532C2×C23311yescharacteristic
88#410C2×C23312yescomplemented
89#354C2×C23312yescomplemented
90#353C2×C23312yescomplemented
91C2×#41C4×C23311yescharacteristic, complemented
92C2×#41C22×C23311yescharacteristic
93C4⋊Q8C4×C23311yescharacteristic, complemented
94#127C22×C23311yescharacteristic
95#124C4×C23311yescharacteristic, complemented
96#124C22×C23311yescharacteristic
97#121—22no—
98C4×D4—22no—
99#117—22no—
100C2×C42C4×C23311yescharacteristic, complemented
101#99—22no—
102#99C22×C23314yes—
103#41—41no—
104#41—41no—
105#41—41no—
106#41—41no—
107C2×Q8C2×C4×C23311yescharacteristic
108C2×Q8C2×C4×C23311yescharacteristic
109C2×D4—21no—
110C2×D4—22no—
111C2×D4C2×C4×C23311yescharacteristic
112C2×D4D4×C23312yes—
113C2×D4C23×C23311yescharacteristic
114C22×C4—21no—
115C22×C4—21no—
116C22×C4C2×C4×C23311yescharacteristic
117C22×C4D4×C23312yes—
118C4⋊C4—22no—
119C4⋊C4—42no—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—24no—
123C42—21no—
124C42—42no—
125C42C2×C4×C23311yescharacteristic
126C42C2×C4×C23311yescharacteristic
127C23—21no—
128C23C22⋊C4×C23311yescharacteristic
129C23C2×D4×C23312yes—
130Q8—41no—
131Q8—41no—
132D4—42no—
133D4—41no—
134D4—41no—
135D4—44no—
136D4—42no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—44no—
148C2×C4C22⋊C4×C23312yes—
149C2×C4C22⋊C4×C23311yescharacteristic
150C2×C4C22×C4×C23311yescharacteristic
151C22—22no—
152C22—21no—
153C22—41no—
154C22—42no—
155C22—42no—
156C22—41no—
157C22C2×C22⋊C4×C23311yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—41no—
162C4—41no—
163C4—84no—
164C4#99×C23311yescharacteristic
165C4#99×C23311yescharacteristic
166C2—21no—
167C2—42no—
168C2—41no—
169C2—81no—
170C2C2×#99×C23311yescharacteristic
subgroupG/H
centerC4×C233#99
commutatorC2×C4C22×C4×C233
Frattini, cosocleC2×D4C23×C233
socleC2×C233C2×#99
prime radical#532×C233C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C233 ◁ C2×C4×C233 ◁ C2×#41×C233 ◁ G

Complements

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

NH ≅ G/Ntype
2. #410×C233C2semidirect
3. #354×C233C2semidirect
4. #353×C233C2semidirect
5. C2×#41×C233C4semidirect
7. C4⋊Q8×C233C4semidirect
9. #124×C233C4semidirect
14. C2×C42×C233C4semidirect
85. C233#2126direct (N × H)
86. #2126C233direct (N × H)
88. #410C2×C233semidirect
89. #354C2×C233semidirect
90. #353C2×C233semidirect
91. C2×#41C4×C233semidirect
93. C4⋊Q8C4×C233semidirect
95. #124C4×C233semidirect
100. C2×C42C4×C233semidirect

Maximal subgroups

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

subgroupindex
#532×C2332
#410×C2332
#354×C2332
#353×C2332
#2126233