Finite Group Databasebeta

← #44507547

Subgroups — #44507547

Order 30848.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#29508185C211yesmaximal, characteristic
2#29507699C211yesmaximal, characteristic
3#29507690C211yesmaximal, characteristic
4#29507478C211yesmaximal, characteristic, complemented
5#29507476C211yesmaximal, characteristic, complemented
6#29507473C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C2×#16838754C2211yescharacteristic
10#21440607—21no—
11#21440604—21no—
12#21440602—22no—
13#21440601C2211yescharacteristic
14#21440599C412yescomplemented
15C2×C4×Dic241C2211yescharacteristic
16C42×D241C412yescomplemented
17#21440560—21no—
18#21440558—21no—
19#21440556—22no—
20C2×M16×C241C2211yescharacteristic
21#117×C241C2211yescharacteristic
22#117×C241C2211yescharacteristic
23#16838770—21no—
24#16838770—21no—
25#16838770—21no—
26#16838770—21no—
27C2×Dic482D411yescharacteristic
28C2×D964D411yescharacteristic
29C2×C22⋊D241D412yes—
30C22×Dic241—21no—
31C2×C4×D241—22no—
32C2×C4×D241C2×C412yes—
33#16838754—21no—
34#16838754—21no—
35C2×#14515349—21no—
36C4⋊Dic241—21no—
37#16838749—22no—
38C22⋊Dic241—21no—
39#16838747—22no—
40C4×Dic241—22no—
41C4×Dic241—21no—
42C4×Dic241—21no—
43C4×Dic241C2×C411yescharacteristic
44C4×Dic241C2×C411yescharacteristic
45C22×C4×C241C2311yescharacteristic
46M16×C241—21no—
47M16×C241—21no—
48C2×C8×C241—21no—
49C4⋊C4×C241—21no—
50C4⋊C4×C241—21no—
51C22⋊C4×C241—21no—
52C22⋊C4×C241—21no—
53C42×C241—21no—
54C42×C241C2×C412yes—
55C22×D241C22⋊C412yes—
56Dic482—21no—
57Dic482—21no—
58D964—21no—
59D964—21no—
60C22⋊D241—22no—
61C22⋊D241—22no—
62C2×Dic241—21no—
63C2×Dic241—21no—
64C2×Dic241—42no—
65C2×Dic241—41no—
66C2×Dic241C22⋊C412yes—
67C4×D241—22no—
68C4×D241—22no—
69C4×D241—44no—
70#14515349—41no—
71C23×C241C2×D411yescharacteristic
72C2×C4×C241—22no—
73C2×C4×C241—41no—
74C2×C4×C241C22×C411yescharacteristic
75C2×C4×C241C2×D411yescharacteristic
76C2×C4×C241#4111yescharacteristic
77C2×C4×C241#4111yescharacteristic
78C2×C4×C241#4111yescharacteristic
79C2×C4×C241#4111yescharacteristic
80C8×C241—41no—
81C22×C241—41no—
82C22×C241C2×C22⋊C411yescharacteristic
83C22×C241#12311yescharacteristic
84C22×C241#12311yescharacteristic
85C2×D241—22no—
86C2×D241—42no—
87C4×C241—42no—
88C4×C241—81no—
89C4×C241#11711yescharacteristic
90C4×C241#11711yescharacteristic
91C4×C241#12311yescharacteristic
92C4×C241#12311yescharacteristic
93Dic241—22no—
94Dic241—22no—
95Dic241—41no—
96Dic241—81no—
97C2×C241—21no—
98C2×C241—21no—
99C2×C241—21no—
100C2×C241#38111yescharacteristic
101D241—42no—
102C241#182711yescharacteristic, complemented, Sylow
103#1827—2411nomaximal, Sylow
104C4×#41—2411no—
105#413—2411no—
106#410—2411no—
107#339—2411no—
108#339—2411no—
109H(3,ℤ/4)—2411no—
110H(3,ℤ/4)D24111yescharacteristic, complemented
111C2×#41—2411no—
112C2×M16—2411no—
113C2×M16C2×D24111yescharacteristic
114C4×Q8—4821no—
115C4×D4—4822no—
116C4×D4—4821no—
117#117—2411no—
118#117—2412no—
119#117C2×D24111yescharacteristic
120#117C2×D24111yescharacteristic
121C2×C42—2411no—
122C2×C42—2412no—
123#101—4821no—
124#100—4821no—
125#99—4822no—
126#41—4821no—
127#41—4821no—
128#41—4821no—
129#41—4821no—
130C2×Q8—2411no—
131C2×D4—2412no—
132C2×D4—2411no—
133C22×C4—4822no—
134C22×C4—4821no—
135C22×C4—2412no—
136C22×C4C22×D24111yescharacteristic
137M16—21no—
138M16—21no—
139M16—4821no—
140M16—4821no—
141C2×C8—21no—
142C2×C8—4821no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—4822no—
146C4⋊C4—4821no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—4822no—
150C22⋊C4—4821no—
151C42—21no—
152C42—4822no—
153C42—4821no—
154C42—4821no—
155C42—2411no—
156C42—2411no—
157C42C4×D24112yes—
158C23—2412no—
159C23D4×D24111yescharacteristic
160Q8—4821no—
161Q8—4821no—
162D4—4822no—
163D4—4822no—
164D4—4821no—
165D4—4821no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—9644no—
169C2×C4—9641no—
170C2×C4—9642no—
171C2×C4—4821no—
172C2×C4—4821no—
173C2×C4—4822no—
174C2×C4—4822no—
175C2×C4—2412no—
176C2×C4C2×C4×D24111yescharacteristic
177C2×C4D4×D24111yescharacteristic
178C2×C4#1683876911yescharacteristic
179C2×C4#1683877011yescharacteristic
180C2×C4#1683877011yescharacteristic
181C2×C4#1683877111yescharacteristic
182C8—41no—
183C8—9641no—
184C22—41no—
185C22—9642no—
186C22—4822no—
187C22C22⋊C4×D24111yescharacteristic
188C22#2144062411yescharacteristic
189C22#2144062711yescharacteristic
190C4—42no—
191C4—81no—
192C4—19281no—
193C4—9641no—
194C4—4822no—
195C4—4822no—
196C4#2144059911yescharacteristic
197C4#2144060011yescharacteristic
198C4#2144062411yescharacteristic
199C4#2144062711yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—9642no—
204C2#2950757911yescharacteristic
subgroupG/H
centerC4#21440599
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
FittingH(3,ℤ/4)×C241C2
socleC2×C241#381
prime radicalC2×#16838770C22
cosocleC22×C4×C241C23
hypercenterH(3,ℤ/4)D241
hypocenterC241#1827
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #29507478C2semidirect
5. #29507476C2semidirect
6. #29507473C2semidirect
7. H(3,ℤ/4)×C241C2semidirect
14. #21440599C4semidirect
16. C42×D241C4semidirect
102. C241#1827semidirect
110. H(3,ℤ/4)D241semidirect

Maximal subgroups

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

subgroupindex
#295081852
#295076992
#295076902
#295074782
#295074762
#295074732
H(3,ℤ/4)×C2412
#1827241