Finite Group Databasebeta

← #1502×C241 #44503169

Subgroups — #1502×C241 #44503169

Order 30848.

284 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 108 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×C241C211yesmaximal, characteristic
2#431×C241C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×C241C211yesmaximal, characteristic, complemented
4#327×C241C214yesmaximal, complemented
5C2×#41×C241—21no—
6C4⋊Q8×C241C411yescharacteristic, complemented
7#127×C241C411yescharacteristic, complemented
8#124×C241—21no—
9#121×C241—21no—
10#121×C241C2212yes—
11C4×D4×C241—21no—
12C4×D4×C241C412yescomplemented
13C2×C4⋊C4×C241—21no—
14C2×C42×C241—21no—
15C2×C42×C241C2211yescharacteristic
16C4⋊C8×C241—21no—
17C22⋊C8×C241C2212yes—
18C4×C8×C241—21no—
19#95×C241C2212yes—
20#41×C241—42no—
21#41×C241—42no—
22C2×Q8×C241—21no—
23C2×D4×C241—22no—
24C2×D4×C241—21no—
25C2×D4×C241—21no—
26C2×D4×C241C2×C412yes—
27C22×C4×C241—22no—
28C22×C4×C241—22no—
29C22×C4×C241D411yescharacteristic
30C22×C4×C241D411yescharacteristic
31C22×C4×C241C2311yescharacteristic
32C2×C8×C241—22no—
33C4⋊C4×C241—24no—
34C4⋊C4×C241—21no—
35C4⋊C4×C241C2×C412yes—
36C22⋊C4×C241—22no—
37C22⋊C4×C241—22no—
38C42×C241—42no—
39C42×C241C2×C411yescharacteristic
40C42×C241C2×C411yescharacteristic
41C42×C241D411yescharacteristic
42C42×C241D411yescharacteristic
43C23×C241—22no—
44C23×C241C2×D411yescharacteristic
45Q8×C241—42no—
46D4×C241—42no—
47D4×C241—42no—
48D4×C241—42no—
49D4×C241—42no—
50D4×C241—42no—
51C2×C4×C241—22no—
52C2×C4×C241—24no—
53C2×C4×C241—22no—
54C2×C4×C241—41no—
55C2×C4×C241—42no—
56C2×C4×C241—42no—
57C2×C4×C241—44no—
58C2×C4×C241C22⋊C411yescharacteristic
59C2×C4×C241C22⋊C411yescharacteristic
60C2×C4×C241C22⋊C411yescharacteristic
61C2×C4×C241C22⋊C411yescharacteristic
62C2×C4×C241D812yes—
63C2×C4×C241SD1612yes—
64C2×C4×C241C22×C411yescharacteristic
65C2×C4×C241C2×D411yescharacteristic
66C8×C241—42no—
67C22×C241—21no—
68C22×C241—21no—
69C22×C241—42no—
70C22×C241—42no—
71C22×C241—42no—
72C22×C241C2×C22⋊C411yescharacteristic
73C22×C241C2×D811yescharacteristic
74C22×C241C2×SD1611yescharacteristic
75C4×C241—21no—
76C4×C241—21no—
77C4×C241—21no—
78C4×C241—44no—
79C4×C241—42no—
80C4×C241#10212yes—
81C4×C241#10212yes—
82C4×C241#10412yes—
83C2×C241—21no—
84C2×C241—21no—
85C2×C241—82no—
86C2×C241#41011yescharacteristic
87C2×C241C2×#10211yescharacteristic
88C2×C241C2×#10411yescharacteristic
89C241#150211yescharacteristic, direct product factor, Sylow
90#1502C24111yesmaximal, characteristic, direct product factor, Sylow
91#532C2×C24111yescharacteristic
92#431C2×C24111yescharacteristic, complemented
93C4×C4⋊C4C2×C24111yescharacteristic, complemented
94#327C2×C24114yescomplemented
95C2×#41—21no—
96C4⋊Q8C4×C24111yescharacteristic, complemented
97#127C4×C24111yescharacteristic, complemented
98#124—21no—
99#121—21no—
100#121C22×C24112yes—
101C4×D4—21no—
102C4×D4C4×C24112yescomplemented
103C2×C4⋊C4—21no—
104C2×C42—21no—
105C2×C42C22×C24111yescharacteristic
106C4⋊C8—21no—
107C22⋊C8C22×C24112yes—
108C4×C8—21no—
109#95C22×C24112yes—
110#41—42no—
111#41—42no—
112C2×Q8—21no—
113C2×D4—22no—
114C2×D4—21no—
115C2×D4—21no—
116C2×D4C2×C4×C24112yes—
117C22×C4—22no—
118C22×C4—22no—
119C22×C4D4×C24111yescharacteristic
120C22×C4D4×C24111yescharacteristic
121C22×C4C23×C24111yescharacteristic
122C2×C8—22no—
123C4⋊C4—24no—
124C4⋊C4—21no—
125C4⋊C4C2×C4×C24112yes—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C42—42no—
129C42C2×C4×C24111yescharacteristic
130C42C2×C4×C24111yescharacteristic
131C42D4×C24111yescharacteristic
132C42D4×C24111yescharacteristic
133C23—22no—
134C23C2×D4×C24111yescharacteristic
135Q8—42no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—42no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—44no—
148C2×C4C22⋊C4×C24111yescharacteristic
149C2×C4C22⋊C4×C24111yescharacteristic
150C2×C4C22⋊C4×C24111yescharacteristic
151C2×C4C22⋊C4×C24111yescharacteristic
152C2×C4D8×C24112yes—
153C2×C4SD16×C24112yes—
154C2×C4C22×C4×C24111yescharacteristic
155C2×C4C2×D4×C24111yescharacteristic
156C8—42no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22C2×C22⋊C4×C24111yescharacteristic
163C22C2×D8×C24111yescharacteristic
164C22C2×SD16×C24111yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—44no—
169C4—42no—
170C4#102×C24112yes—
171C4#102×C24112yes—
172C4#104×C24112yes—
173C2—21no—
174C2—21no—
175C2—82no—
176C2#410×C24111yescharacteristic
177C2C2×#102×C24111yescharacteristic
178C2C2×#104×C24111yescharacteristic
subgroupG/H
centerC2×C4×C241C22⋊C4
commutatorC2×C4C22×C4×C241
Frattini, cosocleC22×C4C23×C241
socleC22×C241C2×C22⋊C4
prime radical#532×C241C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C241 ◁ C2×C42×C241 ◁ G

Complements

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

NH ≅ G/Ntype
2. #431×C241C2semidirect
3. C4×C4⋊C4×C241C2semidirect
4. #327×C241C2semidirect
6. C4⋊Q8×C241C4semidirect
7. #127×C241C4semidirect
12. C4×D4×C241C4semidirect
89. C241#1502direct (N × H)
90. #1502C241direct (N × H)
92. #431C2×C241semidirect
93. C4×C4⋊C4C2×C241semidirect
94. #327C2×C241semidirect
96. C4⋊Q8C4×C241semidirect
97. #127C4×C241semidirect
102. C4×D4C4×C241semidirect

Maximal subgroups

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

subgroupindex
#532×C2412
#431×C2412
C4×C4⋊C4×C2412
#327×C2412
#1502241