Finite Group Databasebeta

← #44508489

Subgroups — #44508489

Order 30848.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#21440670C212yesmaximal, complemented
2#29508298C211yesmaximal, characteristic, complemented
3C2×#21440568C212yesmaximal, complemented
4#29507618C211yesmaximal, characteristic, complemented
5#343×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2212yes—
7C22×D964C2211yescharacteristic
8#21440670—24no—
9#21440670—24no—
10C2×#16838759—22no—
11C2×D1928—22no—
12#21440622—22no—
13#21440617—22no—
14#21440616—22no—
15C2×#16838747—22no—
16C2×C4×Dic241C2211yescharacteristic
17#21440568—24no—
18C2×M16×C241C2212yes—
19C2×C4⋊C4×C241C2211yescharacteristic
20C23×D241—21no—
21#16838770—22no—
22#16838770—22no—
23#16838770—22no—
24#16838770—22no—
25C2×Dic482D412yes—
26C2×D964—22no—
27C2×D964—22no—
28C2×D964—22no—
29C2×D964—21no—
30C2×D964D412yes—
31C2×D964D412yescomplemented
32C2×C22⋊D241—22no—
33C22×Dic241—21no—
34C2×C4×D241—22no—
35#16838759—28no—
36D1928—28no—
37C4⋊Dic241—22no—
38#16838747—24no—
39#16838747—44no—
40C4×Dic241—22no—
41C22×C4×C241D412yes—
42C22×C4×C241C2311yescharacteristic
43M16×C241—22no—
44M16×C241D414yescomplemented
45C2×C8×C241—22no—
46C4⋊C4×C241—22no—
47C22×D241—22no—
48C22×D241—22no—
49C22×D241—42no—
50C22×D241—42no—
51C22×D241—41no—
52C22×D241—41no—
53Dic482—22no—
54Dic482—22no—
55D964—22no—
56D964—24no—
57D964—22no—
58D964—42no—
59D964—82no—
60C22⋊D241—42no—
61C22⋊D241—42no—
62C2×Dic241—22no—
63C2×Dic241—22no—
64C2×Dic241—41no—
65C2×Dic241—41no—
66C4×D241—42no—
67C4×D241—42no—
68C23×C241C2×D411yescharacteristic
69C2×C4×C241—22no—
70C2×C4×C241—42no—
71C2×C4×C241C2×D411yescharacteristic
72C2×C4×C241C2×D412yes—
73C2×C4×C241C2×D412yes—
74C2×C4×C241#4111yescharacteristic
75C8×C241—24no—
76C22×C241—21no—
77C22×C241—21no—
78C22×C241#12011yescharacteristic
79C22×C241#12111yescharacteristic
80C22×C241#12711yescharacteristic
81C2×D241—44no—
82C2×D241—42no—
83C2×D241—42no—
84C2×D241—42no—
85C2×D241—42no—
86C2×D241—82no—
87C2×D241—81no—
88C2×D241—81no—
89C4×C241—42no—
90C4×C241#12012yes—
91C4×C241#12112yes—
92Dic241—42no—
93Dic241—42no—
94C2×C241—21no—
95C2×C241—21no—
96C2×C241#39211yescharacteristic
97C2×C241#45311yescharacteristic
98C2×C241#45411yescharacteristic
99D241—82no—
100D241—82no—
101C241#200611yescharacteristic, complemented, Sylow
102#2006—2411nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2412no—
104#537—2411no—
105C2×#104—2412no—
106#390—2411no—
107#343D24111yescharacteristic, complemented
108C2×#41—2412no—
109C22×D4—2411no—
110AGL(1,ℤ/8)—4824no—
111AGL(1,ℤ/8)—4824no—
112C2×SD16—4822no—
113C2×D8—4822no—
114C2×M16C2×D24112yes—
115C22⋊Q8—4822no—
116#121—4822no—
117#121—4822no—
118C2×C4⋊C4C2×D24111yescharacteristic
119C2×C22⋊C4—4822no—
120C2×C42—2411no—
121#104—4824no—
122C24—4821no—
123#41—4822no—
124#41—4822no—
125#41—4822no—
126#41—4822no—
127C2×Q8—2412no—
128C2×D4—4822no—
129C2×D4—4822no—
130C2×D4—4822no—
131C2×D4—4822no—
132C2×D4—4821no—
133C2×D4—2412no—
134C2×D4—2412no—
135C22×C4—4821no—
136C22×C4—4822no—
137C22×C4D96412yes—
138C22×C4C22×D24111yescharacteristic
139SD16—4828no—
140D8—4828no—
141M16—22no—
142M16D96414yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—4822no—
146C22⋊C4—9644no—
147C22⋊C4—4824no—
148C42—4822no—
149C23—9642no—
150C23—9642no—
151C23—9641no—
152C23—9641no—
153C23—4822no—
154C23—4822no—
155C23C2×D96411yescharacteristic
156Q8—4822no—
157Q8—4822no—
158D4—19282no—
159D4—9642no—
160D4—9642no—
161D4—9642no—
162D4—4822no—
163D4—4824no—
164D4—4822no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—9641no—
168C2×C4—9641no—
169C2×C4—9642no—
170C2×C4—9642no—
171C2×C4—4822no—
172C2×C4—4822no—
173C2×C4D4×D24111yescharacteristic
174C2×C4D4×D24112yes—
175C2×C4C2×D96412yes—
176C2×C4#1683877111yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—19282no—
181C22—19281no—
182C22—19281no—
183C22—9644no—
184C22—9642no—
185C22—9642no—
186C22—9642no—
187C22—9642no—
188C22#2144061211yescharacteristic
189C22#2144061711yescharacteristic
190C22#2144063911yescharacteristic
191C4—42no—
192C4—9642no—
193C4—9642no—
194C4#2144061212yes—
195C4#2144061712yes—
196C2—21no—
197C2—21no—
198C2—19282no—
199C2—19282no—
200C2#2950762711yescharacteristic
201C2#2950788711yescharacteristic
202C2#2950789211yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#343×C241C2
socleC22×C241#120
hypercenter#343D241
hypocenterC241#2006
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#21440670C2semidirect
2. #29508298C2semidirect
3. C2×#21440568C2semidirect
4. #29507618C2semidirect
5. #343×C241C2semidirect
31. C2×D964D4semidirect
44. M16×C241D4semidirect
101. C241#2006semidirect
107. #343D241semidirect
142. M16D964semidirect

Maximal subgroups

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

subgroupindex
C2×#214406702
#295082982
C2×#214405682
#295076182
#343×C2412
#2006241