Finite Group Databasebeta

← #44508487

Subgroups — #44508487

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×#21440667C212yesmaximal, complemented
2C2×#21440569C212yesmaximal, complemented
3#29507618C211yesmaximal, characteristic, complemented
4#29507486C211yesmaximal, characteristic, complemented
5#537×C241C211yesmaximal, characteristic, complemented
6C22×D964C2211yescharacteristic
7#21440667—24no—
8#21440667—24no—
9C2×#16838757—22no—
10C2×#16838755—22no—
11C2×#16838754C2212yes—
12C2×#16838747—22no—
13C2×C4×Dic241C2211yescharacteristic
14#21440569—24no—
15C2×#41×C241C2212yes—
16C22⋊Q8×C241—22no—
17#121×C241—22no—
18#121×C241—22no—
19C2×C4⋊C4×C241C2211yescharacteristic
20C23×D241—21no—
21C2×D964—22no—
22C2×D964—22no—
23C2×D964—21no—
24C2×D964D412yescomplemented
25C22×Dic241—21no—
26#16838757—28no—
27#16838755—28no—
28#16838754—22no—
29#16838754D414yescomplemented
30C2×#14515349—22no—
31#16838747—44no—
32C4×Dic241—22no—
33#41×C241—22no—
34#41×C241—22no—
35#41×C241—22no—
36#41×C241—22no—
37C2×Q8×C241D412yes—
38C2×D4×C241—22no—
39C2×D4×C241—22no—
40C2×D4×C241D412yes—
41C22×C4×C241—22no—
42C22×C4×C241D412yes—
43C22×C4×C241C2311yescharacteristic
44C4⋊C4×C241—22no—
45C4⋊C4×C241—22no—
46C22⋊C4×C241—24no—
47C22×D241—22no—
48C22×D241—42no—
49C22×D241—42no—
50C22×D241—41no—
51C22×D241—41no—
52D964—24no—
53D964—42no—
54C2×Dic241—22no—
55C2×Dic241—41no—
56C2×Dic241—41no—
57#14515349—24no—
58C23×C241—22no—
59C23×C241C2×D411yescharacteristic
60Q8×C241—22no—
61Q8×C241—22no—
62D4×C241—22no—
63D4×C241—22no—
64D4×C241—42no—
65D4×C241—42no—
66D4×C241—82no—
67C2×C4×C241—22no—
68C2×C4×C241—22no—
69C2×C4×C241—42no—
70C2×C4×C241—42no—
71C2×C4×C241—42no—
72C2×C4×C241C2×D411yescharacteristic
73C2×C4×C241C2×D412yes—
74C2×C4×C241C2×D412yes—
75C2×C4×C241#4111yescharacteristic
76C22×C241—21no—
77C22×C241—21no—
78C22×C241—42no—
79C22×C241—42no—
80C22×C241—42no—
81C22×C241#12011yescharacteristic
82C22×C241#12111yescharacteristic
83C22×C241#12711yescharacteristic
84C2×D241—44no—
85C2×D241—42no—
86C2×D241—82no—
87C2×D241—81no—
88C2×D241—81no—
89C4×C241—42no—
90C4×C241—42no—
91C4×C241#12012yes—
92C4×C241#12112yes—
93Dic241—42no—
94C2×C241—21no—
95C2×C241—21no—
96C2×C241—82no—
97C2×C241#39211yescharacteristic
98C2×C241#45311yescharacteristic
99C2×C241#45411yescharacteristic
100D241—82no—
101C241#200611yescharacteristic, complemented, Sylow
102#2006—2411nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2412no—
104#537D24111yescharacteristic, complemented
105C2×#104—2412no—
106#390—2411no—
107#343—2411no—
108C2×#41C2×D24112yes—
109C22×D4—2411no—
110AGL(1,ℤ/8)—4824no—
111AGL(1,ℤ/8)—4824no—
112C2×SD16—4822no—
113C2×D8—4822no—
114C2×M16—2412no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D24111yescharacteristic
119C2×C22⋊C4—4822no—
120C2×C42—2411no—
121#104—4824no—
122C24—4821no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D24112yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—4822no—
131C2×D4—4822no—
132C2×D4—4821no—
133C2×D4—2412no—
134C2×D4C22⋊D24112yes—
135C22×C4—22no—
136C22×C4—4821no—
137C22×C4C22⋊D24112yes—
138C22×C4C22×D24111yescharacteristic
139SD16—4828no—
140D8—4828no—
141M16—4822no—
142M16—2414no—
143C2×C8—4822no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—9644no—
148C42—4822no—
149C23—22no—
150C23—9642no—
151C23—9642no—
152C23—9641no—
153C23—9641no—
154C23—4822no—
155C23C2×C22⋊D24111yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—9642no—
164D4—4824no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—9641no—
171C2×C4—9641no—
172C2×C4—4822no—
173C2×C4D4×D24111yescharacteristic
174C2×C4D4×D24112yes—
175C2×C4C2×C22⋊D24112yes—
176C2×C4#1683876911yescharacteristic
177C8—4824no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—19282no—
184C22—19281no—
185C22—19281no—
186C22—9644no—
187C22—9642no—
188C22#2144061111yescharacteristic
189C22#2144061311yescharacteristic
190C22#2144063811yescharacteristic
191C4—42no—
192C4—42no—
193C4—9642no—
194C4#2144061012yes—
195C4#2144061412yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—19282no—
200C2#2950762511yescharacteristic
201C2#2950788511yescharacteristic
202C2#2950789011yescharacteristic
subgroupG/H
centerC22#21440611
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#537×C241C2
socleC22×C241#120
hypercenter#537D241
hypocenterC241#2006
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#21440667C2semidirect
2. C2×#21440569C2semidirect
3. #29507618C2semidirect
4. #29507486C2semidirect
5. #537×C241C2semidirect
24. C2×D964D4semidirect
29. #16838754D4semidirect
101. C241#2006semidirect
104. #537D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406672
C2×#214405692
#295076182
#295074862
#537×C2412
#2006241