Finite Group Databasebeta

← #44507546

Subgroups — #44507546

Order 30848.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic241C211yesmaximal, characteristic
2#29507701C211yesmaximal, characteristic
3#29507476C212yesmaximal, complemented
4#29507473C212yesmaximal, complemented
5#410×C241C211yesmaximal, characteristic
6C2×#16838754C2212yes—
7Q8×Dic241—21no—
8D4×Dic241—22no—
9D4×Dic241—21no—
10#21440601C412yescomplemented
11#21440601C2211yescharacteristic
12C2×C4×Dic241C412yescomplemented
13C2×C4×Dic241C2211yescharacteristic
14#21440561—21no—
15#21440559—21no—
16C2×#41×C241C2211yescharacteristic
17#117×C241C2212yes—
18#99×C241—22no—
19C22×Dic241—22no—
20C22×Dic241—21no—
21#16838754—22no—
22#16838754—22no—
23C2×#14515349—22no—
24C4⋊Dic241—22no—
25C4⋊Dic241—21no—
26C22⋊Dic241—22no—
27C22⋊Dic241—21no—
28C4×Dic241—22no—
29C4×Dic241—21no—
30C4×Dic241C2×C411yescharacteristic
31C4×Dic241C2×C412yes—
32C4×Dic241C2×C411yescharacteristic
33#41×C241—22no—
34#41×C241—22no—
35C2×Q8×C241D411yescharacteristic
36C2×D4×C241D412yes—
37C2×D4×C241D411yescharacteristic
38C22×C4×C241C2×C412yes—
39C22×C4×C241C2311yescharacteristic
40C4⋊C4×C241—22no—
41C22⋊C4×C241—22no—
42C42×C241—22no—
43C2×Dic241—21no—
44C2×Dic241—22no—
45C2×Dic241—21no—
46C2×Dic241—42no—
47C2×Dic241—44no—
48#14515349—42no—
49C23×C241C22⋊C412yes—
50C23×C241C2×D411yescharacteristic
51Q8×C241—22no—
52D4×C241—24no—
53D4×C241—22no—
54C2×C4×C241—22no—
55C2×C4×C241—22no—
56C2×C4×C241—42no—
57C2×C4×C241C22⋊C412yes—
58C2×C4×C241C22×C411yescharacteristic
59C2×C4×C241C2×D411yescharacteristic
60C2×C4×C241#4112yes—
61C2×C4×C241#4112yes—
62C22×C241—22no—
63C22×C241—41no—
64C22×C241—42no—
65C22×C241C2×C22⋊C411yescharacteristic
66C22×C241#12312yes—
67C4×C241—22no—
68C4×C241—82no—
69C4×C241#11711yescharacteristic
70C4×C241#11711yescharacteristic
71C4×C241#12312yes—
72Dic241—22no—
73Dic241—42no—
74Dic241—41no—
75C2×C241—21no—
76C2×C241—22no—
77C2×C241—42no—
78C2×C241#38111yescharacteristic
79C241#182711yescharacteristic, complemented, Sylow
80#1827—2411nomaximal, Sylow
81C4×#41—2411no—
82#413—2411no—
83#410D24111yescharacteristic
84#339—2412no—
85H(3,ℤ/4)—2412no—
86C2×#41C2×D24111yescharacteristic
87C2×M16—2412no—
88C4×Q8—4821no—
89C4×D4—4822no—
90C4×D4—4821no—
91#117—2412no—
92#117—2411no—
93#117C2×D24112yes—
94C2×C42—2412no—
95C2×C42—2411no—
96#101—4821no—
97#100—4821no—
98#99—22no—
99#41—22no—
100#41—22no—
101C2×Q8D96411yescharacteristic
102C2×D4C22⋊D24112yes—
103C2×D4D96411yescharacteristic
104C22×C4—4822no—
105C22×C4—4821no—
106C22×C4C4×D24112yes—
107C22×C4C22×D24111yescharacteristic
108M16—4822no—
109M16—4822no—
110C2×C8—4822no—
111C4⋊C4—22no—
112C4⋊C4—4822no—
113C4⋊C4—4821no—
114C22⋊C4—22no—
115C22⋊C4—4822no—
116C22⋊C4—4821no—
117C42—22no—
118C42—4822no—
119C42—4821no—
120C42—2411no—
121C42—2412no—
122C42—2411no—
123C23#1683874712yes—
124C23C2×C22⋊D24111yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—9642no—
132C2×C4—9644no—
133C2×C4—4822no—
134C2×C4—4821no—
135C2×C4—4821no—
136C2×C4#1683874712yes—
137C2×C4C2×C4×D24111yescharacteristic
138C2×C4C2×D96411yescharacteristic
139C2×C4#1683876912yes—
140C2×C4#1683876912yes—
141C8—9642no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×#1683874711yescharacteristic
146C22#2144062312yes—
147C4—22no—
148C4—82no—
149C4—9641no—
150C4—9642no—
151C4—4822no—
152C4#2144059811yescharacteristic
153C4#2144059811yescharacteristic
154C4#2144062612yes—
155C2—22no—
156C2—21no—
157C2—42no—
158C2#2950757811yescharacteristic
subgroupG/H
centerC4#21440598
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#410×C241C2
socleC2×C241#381
prime radicalC2×#41×C241C22
cosocleC22×C4×C241C23
hypercenter#410D241
hypocenterC241#1827
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #29507476C2semidirect
4. #29507473C2semidirect
10. #21440601C4semidirect
12. C2×C4×Dic241C4semidirect
79. C241#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic2412
#295077012
#295074762
#295074732
#410×C2412
#1827241