Finite Group Databasebeta

← #44508509

Subgroups — #44508509

Order 30848.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#29508224C212yesmaximal, complemented
2#29507734C212yesmaximal, complemented
3#29507680C211yesmaximal, characteristic, complemented
4#29507474C211yesmaximal, characteristic, complemented
5#575×C241C211yesmaximal, characteristic, complemented
6C22×C4×D241C2211yescharacteristic
7C2×#16838754C2211yescharacteristic
8#21440623—22no—
9#21440618—22no—
10#21440613—22no—
11#21440610—22no—
12C4×C22⋊D241—24no—
13#21440601C2212yes—
14#21440569—24no—
15#21440554—22no—
16C2×#41×C241C2212yes—
17#137×C241—22no—
18AGL(1,ℤ/8)×C241—22no—
19#135×C241—22no—
20C2×M16×C241C2211yescharacteristic
21C23×D241D411yescharacteristic
22C2×C22⋊D241—24no—
23C22×Dic241D411yescharacteristic
24C2×C4×D241—21no—
25C2×C4×D241—22no—
26C2×C4×D241—22no—
27C2×C4×D241—21no—
28#16838754—22no—
29C2×#14515349—21no—
30C4⋊Dic241—22no—
31#16838749—24no—
32C22⋊Dic241—24no—
33C22⋊Dic241—22no—
34#16838747—24no—
35C4×Dic241D414yescomplemented
36#41×C241—22no—
37#41×C241—22no—
38#41×C241—22no—
39#41×C241—22no—
40C2×Q8×C241D412yescomplemented
41C2×D4×C241—22no—
42C2×D4×C241D412yescomplemented
43C22×C4×C241—22no—
44C22×C4×C241C2311yescharacteristic
45Q16×C241—22no—
46SD16×C241—24no—
47D8×C241—22no—
48M16×C241—22no—
49C2×C8×C241D412yescomplemented
50C22×D241—22no—
51C22×D241—21no—
52C22×D241—42no—
53C22⋊D241—48no—
54C2×Dic241—24no—
55C2×Dic241—22no—
56C2×Dic241—21no—
57C4×D241—41no—
58C4×D241—42no—
59C4×D241—41no—
60#14515349—41no—
61C23×C241—22no—
62C23×C241C2×D411yescharacteristic
63Q8×C241—22no—
64Q8×C241—22no—
65D4×C241—22no—
66D4×C241—22no—
67D4×C241—42no—
68D4×C241—42no—
69C2×C4×C241—22no—
70C2×C4×C241—42no—
71C2×C4×C241—42no—
72C2×C4×C241C2×D412yes—
73C2×C4×C241C2×D412yes—
74C2×C4×C241C2×D411yescharacteristic
75C2×C4×C241#4111yescharacteristic
76C8×C241—22no—
77C22×C241—41no—
78C22×C241—44no—
79C22×C241—42no—
80C22×C241#12012yes—
81C22×C241#12111yescharacteristic
82C2×D241—24no—
83C2×D241—22no—
84C2×D241—42no—
85C2×D241—41no—
86C2×D241—41no—
87C4×C241—42no—
88C4×C241#12011yescharacteristic
89C4×C241#12112yes—
90C4×C241#12711yescharacteristic
91Dic241—44no—
92Dic241—41no—
93C2×C241—22no—
94C2×C241—21no—
95C2×C241—82no—
96C2×C241#39211yescharacteristic
97D241—42no—
98C241#201011yescharacteristic, complemented, Sylow
99#2010—2411nomaximal, Sylow
100#575D24111yescharacteristic, complemented
101#525—2412no—
102#421—2412no—
103#407—2411no—
104H(3,ℤ/4)—2411no—
105C2×#41C2×D24112yes—
106C23×C4—2411no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—2411no—
111C2×M16C2×D24111yescharacteristic
112#123—4822no—
113C22⋊Q8—4822no—
114#121—4822no—
115#120—4822no—
116C4×D4—4824no—
117#117—2412no—
118#104—4824no—
119C22⋊C8—4822no—
120C24—2411no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D24112yescomplemented
126C2×D4—22no—
127C2×D4—4824no—
128C2×D4C22⋊D24112yescomplemented
129C22×C4—22no—
130C22×C4—4822no—
131C22×C4—4821no—
132C22×C4—4822no—
133C22×C4—4821no—
134C22×C4—2411no—
135C22×C4C22×D24111yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—4822no—
141C2×C8—4821no—
142C2×C8C22⋊D24112yescomplemented
143C4⋊C4—4824no—
144C4⋊C4—4822no—
145C22⋊C4—4824no—
146C22⋊C4—4824no—
147C22⋊C4—4822no—
148C42—2414no—
149C23—22no—
150C23—9642no—
151C23—4822no—
152C23—4821no—
153C23D4×D24111yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—9648no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—9641no—
165C2×C4—9642no—
166C2×C4—9641no—
167C2×C4—4824no—
168C2×C4—4822no—
169C2×C4—4821no—
170C2×C4D4×D24112yes—
171C2×C4C2×C22⋊D24112yes—
172C2×C4C2×C22⋊D24111yescharacteristic
173C2×C4#1683876911yescharacteristic
174C8—22no—
175C8—9641no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—9642no—
180C22—9641no—
181C22—9641no—
182C22—4824no—
183C22—4822no—
184C22#2144061012yes—
185C22#2144061311yescharacteristic
186C4—42no—
187C4—9644no—
188C4—9641no—
189C4#2144061111yescharacteristic
190C4#2144061412yes—
191C4#2144063811yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—9642no—
196C2#2950762511yescharacteristic
subgroupG/H
centerC4#21440638
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#575×C241C2
socleC2×C241#392
hypercenter#575D241
hypocenterC241#2010
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #29508224C2semidirect
2. #29507734C2semidirect
3. #29507680C2semidirect
4. #29507474C2semidirect
5. #575×C241C2semidirect
35. C4×Dic241D4semidirect
40. C2×Q8×C241D4semidirect
42. C2×D4×C241D4semidirect
49. C2×C8×C241D4semidirect
98. C241#2010semidirect
100. #575D241semidirect
125. C2×Q8C22⋊D241semidirect
128. C2×D4C22⋊D241semidirect
142. C2×C8C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295082242
#295077342
#295076802
#295074742
#575×C2412
#2010241