Finite Group Databasebeta

← #44507371

Subgroups — #44507371

Order 30848.

584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#16838770C211yesmaximal, characteristic
2C2×#21440560C212yesmaximal, complemented
3C2×#21440558C212yesmaximal, complemented
4#29507681C211yesmaximal, characteristic, complemented
5#407×C241C211yesmaximal, characteristic, complemented
6C2×#16838770—24no—
7C2×#16838770—24no—
8C2×#16838770—22no—
9C2×#16838770—22no—
10C22×Dic482C2211yescharacteristic
11C22×D964C2211yescharacteristic
12C22×C22⋊D241C412yes—
13C22×C4×D241C412yes—
14C2×#16838754C2212yes—
15#21440560—24no—
16#21440558—24no—
17C22⋊#14515349—22no—
18C23×C4×C241C2211yescharacteristic
19C2×M16×C241C2212yes—
20C22⋊C8×C241—22no—
21C23×D241C2×C412yes—
22#16838770—216no—
23#16838770—216no—
24C2×Dic482—22no—
25C2×Dic482—21no—
26C2×Dic482—21no—
27C2×Dic482D414yes—
28C2×D964—22no—
29C2×D964—21no—
30C2×D964—21no—
31C2×D964D414yes—
32C2×C22⋊D241—24no—
33C2×C22⋊D241—24no—
34C2×C22⋊D241—24no—
35C22×Dic241C2×C412yes—
36C2×C4×D241—24no—
37C2×C4×D241—24no—
38C2×C4×D241—24no—
39#16838754—22no—
40#16838754—22no—
41C2×#14515349—22no—
42C24×C241C2×C411yescharacteristic
43C22×C4×C241—22no—
44C22×C4×C241—22no—
45C22×C4×C241C2×C411yescharacteristic
46C22×C4×C241D412yes—
47C22×C4×C241D412yes—
48C22×C4×C241C2311yescharacteristic
49M16×C241—22no—
50M16×C241—22no—
51C2×C8×C241—22no—
52C22×D241—22no—
53C22×D241—22no—
54C22×D241—44no—
55C22×D241C22⋊C414yes—
56Dic482—24no—
57Dic482—24no—
58D964—24no—
59D964—24no—
60C22⋊D241—216no—
61C2×Dic241—22no—
62C2×Dic241—22no—
63C2×Dic241C22⋊C414yes—
64C4×D241—216no—
65#14515349—42no—
66C23×C241—21no—
67C23×C241—21no—
68C23×C241—42no—
69C23×C241C22⋊C412yes—
70C23×C241C22×C411yescharacteristic
71C2×C4×C241—21no—
72C2×C4×C241—21no—
73C2×C4×C241—24no—
74C2×C4×C241—24no—
75C2×C4×C241C22⋊C412yes—
76C2×C4×C241C2×D412yes—
77C2×C4×C241C2×D412yes—
78C2×C4×C241C2×D411yescharacteristic
79C2×C4×C241C2×D411yescharacteristic
80C8×C241—42no—
81C22×C241—22no—
82C22×C241—22no—
83C22×C241—24no—
84C22×C241—42no—
85C22×C241—42no—
86C22×C241C2×C22⋊C411yescharacteristic
87C22×C241C2×C22⋊C411yescharacteristic
88C22×C241C2×C22⋊C411yescharacteristic
89C2×D241—24no—
90C2×D241—44no—
91C2×D241—44no—
92C2×D241—44no—
93C4×C241—22no—
94C4×C241#12012yes—
95C4×C241#12012yes—
96Dic241—24no—
97C2×C241—21no—
98C2×C241—21no—
99C2×C241—42no—
100C2×C241#37911yescharacteristic
101C2×C241#41312yes—
102D241—44no—
103C241#178511yescharacteristic, complemented, Sylow
104#1785—2411nomaximal, Sylow
105C22×#41—2411no—
106C2×#101—2412no—
107C2×#100—2412no—
108#407—2411no—
109#407D24111yescharacteristic, complemented
110C2×#41—4824no—
111C2×#41—4824no—
112C2×#41—4822no—
113C2×#41—4822no—
114C22×Q8—2411no—
115C22×D4—2412no—
116C22×D4—2411no—
117C23×C4—2412no—
118C23×C4C2×D24111yescharacteristic
119C2×M16—2412no—
120C2×M16C2×D24112yes—
121#101—4824no—
122#100—4824no—
123C22⋊C8—22no—
124C22⋊C8—4822no—
125C24—2412no—
126C24C4×D24111yescharacteristic
127#41—48216no—
128#41—48216no—
129C2×Q8—4822no—
130C2×Q8—4821no—
131C2×Q8—4821no—
132C2×Q8—2414no—
133C2×D4—4824no—
134C2×D4—4824no—
135C2×D4—4824no—
136C2×D4—4822no—
137C2×D4—4821no—
138C2×D4—4821no—
139C2×D4—2414no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—4824no—
143C22×C4—4824no—
144C22×C4—4824no—
145C22×C4—2412no—
146C22×C4C4×D24111yescharacteristic
147C22×C4C22⋊D24112yes—
148C22×C4D96412yes—
149C22×C4C22×D24111yescharacteristic
150M16—22no—
151M16—22no—
152M16—4822no—
153M16—4822no—
154C2×C8—22no—
155C2×C8—4822no—
156C23—21no—
157C23—21no—
158C23—42no—
159C23—9644no—
160C23—4822no—
161C23—4822no—
162C23—2414no—
163C23#1683874712yes—
164C23C2×C4×D24111yescharacteristic
165Q8—4824no—
166Q8—4824no—
167D4—48216no—
168D4—4824no—
169D4—4824no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—48216no—
175C2×C4—4822no—
176C2×C4—4822no—
177C2×C4—2414no—
178C2×C4#1683874712yes—
179C2×C4D4×D24112yes—
180C2×C4D4×D24112yes—
181C2×C4C2×C22⋊D24111yescharacteristic
182C2×C4C2×D96411yescharacteristic
183C8—42no—
184C8—9642no—
185C22—22no—
186C22—24no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—9644no—
191C22—9644no—
192C22—9644no—
193C22—4824no—
194C22C22⋊C4×D24111yescharacteristic
195C22C22⋊C4×D24111yescharacteristic
196C22C2×#1683874711yescharacteristic
197C4—22no—
198C4—4824no—
199C4#2144061012yes—
200C4#2144061212yes—
201C2—21no—
202C2—21no—
203C2—42no—
204C2—9644no—
205C2#2950757211yescharacteristic
206C2#2950769912yes—
subgroupG/H
centerC22C2×#16838747
commutatorC23×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#407×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC22×#16838770C2
cosocleC22×C4×C241C23
hypercenter#407D241
hypocenterC241#1785
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#21440560C2semidirect
3. C2×#21440558C2semidirect
4. #29507681C2semidirect
5. #407×C241C2semidirect
103. C241#1785semidirect
109. #407D241semidirect

Maximal subgroups

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

subgroupindex
C22×#168387702
C2×#214405602
C2×#214405582
#295076812
#407×C2412
#1785241