Finite Group Databasebeta

← #44506149

Subgroups — #44506149

Order 30848.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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#29508268C211yesmaximal, characteristic
2#29507773C211yesmaximal, characteristic, complemented
3#29507769C211yesmaximal, characteristic, complemented
4#29507463C211yesmaximal, characteristic, complemented
5#29507460C211yesmaximal, characteristic, complemented
6#29507460C211yesmaximal, characteristic, complemented
7#332×C241C211yesmaximal, characteristic, complemented
8C2×#16838771—21no—
9#21440639C2211yescharacteristic
10#21440631—21no—
11#21440617—21no—
12#21440617C412yes—
13#21440604—21no—
14#21440604C412yes—
15C42×D241C2211yescharacteristic
16C4⋊#14515349C2211yescharacteristic
17C4⋊#14515349C2211yescharacteristic
18#21440554—21no—
19#21440554—21no—
20#21440552—21no—
21C8×Dic241—21no—
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25#16838771—42no—
26#16838771—42no—
27C2×D964—22no—
28C2×D964—21no—
29C2×D964—21no—
30C2×D964C2×C412yes—
31C2×C4×D241—22no—
32C2×C4×D241C2×C411yescharacteristic
33C2×C4×D241D411yescharacteristic
34C2×C4×D241D411yescharacteristic
35C2×#14515349—21no—
36C2×#14515349—21no—
37#16838747—22no—
38#16838747—22no—
39C4×Dic241C2×C411yescharacteristic
40C4×Dic241D411yescharacteristic
41C4×Dic241D411yescharacteristic
42C2×Q8×C241—21no—
43C2×C8×C241—21no—
44C2×C8×C241—21no—
45C4⋊C4×C241—21no—
46C4⋊C4×C241C2×C412yes—
47C42×C241C2311yescharacteristic
48C22×D241—22no—
49C22×D241C22⋊C411yescharacteristic
50D964—42no—
51D964—44no—
52D964—41no—
53D964—41no—
54D964—41no—
55D964—41no—
56C2×Dic241C22⋊C411yescharacteristic
57C2×Dic241C22⋊C411yescharacteristic
58C2×Dic241C22⋊C411yescharacteristic
59C4×D241—21no—
60C4×D241—21no—
61C4×D241—21no—
62C4×D241—21no—
63C4×D241—41no—
64C4×D241—44no—
65#14515349—41no—
66#14515349—41no—
67Q8×C241—41no—
68Q8×C241—41no—
69C2×C4×C241—22no—
70C2×C4×C241C22×C411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C8×C241—41no—
74C8×C241—41no—
75C22×C241C2×C22⋊C411yescharacteristic
76C2×D241—21no—
77C2×D241—21no—
78C2×D241—21no—
79C2×D241—42no—
80C2×D241—42no—
81C2×D241—42no—
82C4×C241—21no—
83C4×C241—42no—
84C4×C241#13511yescharacteristic
85C4×C241#13511yescharacteristic
86C4×C241AGL(1,ℤ/8)11yescharacteristic
87C4×C241AGL(1,ℤ/8)11yescharacteristic
88Dic241—21no—
89Dic241—21no—
90Dic241—21no—
91C2×C241#41311yescharacteristic
92C2×C241#41611yescharacteristic
93C2×C241#41811yescharacteristic
94D241—41no—
95D241—82no—
96C241#155311yescharacteristic, complemented, Sylow
97#1553—2411nomaximal, Sylow
98#532—2411no—
99#432—2411no—
100#431—2411no—
101#332—2411no—
102#332D24111yescharacteristic, complemented
103#331—2411no—
104#331—2411no—
105C2×#41—4821no—
106C4⋊Q8C2×D24111yescharacteristic
107#127—2411no—
108#124—4821no—
109#121—4821no—
110#121—2412no—
111C4×D4—4821no—
112C4×D4—2412no—
113C2×C42—2411no—
114C4⋊C8—2411no—
115C4⋊C8—2411no—
116C4⋊C8C2×D24111yescharacteristic
117C4⋊C8C2×D24111yescharacteristic
118C22⋊C8—4821no—
119C22⋊C8—4821no—
120#97—4821no—
121C4×C8—4821no—
122#41—9642no—
123#41—9642no—
124C2×Q8—21no—
125C2×D4—4822no—
126C2×D4—4821no—
127C2×D4—4821no—
128C2×D4—2412no—
129C22×C4—4822no—
130C22×C4—2411no—
131C22×C4—2411no—
132C22×C4—2411no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—4821no—
136C2×C8—4821no—
137C4⋊C4—21no—
138C4⋊C4C4×D24112yes—
139C22⋊C4—4822no—
140C22⋊C4—4822no—
141C42—2411no—
142C42—2411no—
143C42—2411no—
144C42C22×D24111yescharacteristic
145C23—4822no—
146C23—2411no—
147Q8—41no—
148Q8—41no—
149D4—9642no—
150D4—9644no—
151D4—9641no—
152D4—9641no—
153D4—9641no—
154D4—9641no—
155C2×C4—22no—
156C2×C4—9641no—
157C2×C4—9644no—
158C2×C4—4821no—
159C2×C4—4821no—
160C2×C4—4821no—
161C2×C4—4821no—
162C2×C4—2411no—
163C2×C4—2411no—
164C2×C4—2411no—
165C2×C4C2×C4×D24111yescharacteristic
166C2×C4D4×D24111yescharacteristic
167C2×C4D4×D24111yescharacteristic
168C8—41no—
169C8—41no—
170C8—9641no—
171C8—9641no—
172C22—9642no—
173C22—9642no—
174C22—9642no—
175C22—4821no—
176C22—4821no—
177C22—4821no—
178C22C22⋊C4×D24111yescharacteristic
179C4—21no—
180C4—42no—
181C4—4821no—
182C4—4821no—
183C4—4821no—
184C4#2144066311yescharacteristic
185C4#2144066511yescharacteristic
186C4#2144066611yescharacteristic
187C4#2144066911yescharacteristic
188C2—19282no—
189C2—9641no—
190C2#2950770011yescharacteristic
191C2#2950771211yescharacteristic
192C2#2950772011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC42C22×D241
Fitting#332×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508268C2
cosocleC42×C241C23
hypercenter#332D241
hypocenterC241#1553
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #29507773C2semidirect
3. #29507769C2semidirect
4. #29507463C2semidirect
5. #29507460C2semidirect
6. #29507460C2semidirect
7. #332×C241C2semidirect
96. C241#1553semidirect
102. #332D241semidirect

Maximal subgroups

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

subgroupindex
#295082682
#295077732
#295077692
#295074632
#295074602
#332×C2412
#1553241