Finite Group Databasebeta

← #44506514

Subgroups — #44506514

Order 30848.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#29508428C211yesmaximal, characteristic, complemented
2#29507914C211yesmaximal, characteristic, complemented
3#29507909C211yesmaximal, characteristic
4#29507466C211yesmaximal, characteristic, complemented
5#29507449C211yesmaximal, characteristic, complemented
6#29507446C211yesmaximal, characteristic, complemented
7#492×C241C211yesmaximal, characteristic, complemented
8C2×#16838758—21no—
9C2×#16838755—21no—
10#21440633—21no—
11#21440622—21no—
12#21440618—22no—
13C4×Dic482C2211yescharacteristic
14C4×D964C2211yescharacteristic
15#21440604—21no—
16C4⋊C4×D241—21no—
17C4⋊#14515349C2211yescharacteristic
18C4⋊#14515349C2211yescharacteristic
19#21440563—21no—
20#21440563—21no—
21C2×SD16×C241—22no—
22C4⋊Q8×C241C2211yescharacteristic
23#127×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25C2×Dic482D411yescharacteristic
26C2×D964D411yescharacteristic
27C2×C4×D241—22no—
28C2×C4×D241—21no—
29#16838758—42no—
30#16838755—42no—
31C2×#14515349—21no—
32C2×#14515349—21no—
33C4⋊Dic241—22no—
34C4⋊Dic241D411yescharacteristic
35C4⋊Dic241D411yescharacteristic
36#16838749—22no—
37#16838749—21no—
38#16838747—22no—
39#16838747—21no—
40C4×Dic241—21no—
41C2×Q8×C241D412yes—
42C2×D4×C241—21no—
43C2×D4×C241—21no—
44C2×D4×C241—21no—
45SD16×C241—44no—
46C2×C8×C241—21no—
47C4⋊C4×C241—21no—
48C4⋊C4×C241—21no—
49C42×C241C2311yescharacteristic
50C22×D241—21no—
51Dic482—21no—
52Dic482—21no—
53D964—21no—
54D964SD1612yescomplemented
55C2×Dic241—21no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C4×D241—41no—
59C4×D241—41no—
60C4×D241—82no—
61#14515349—41no—
62#14515349—41no—
63C23×C241—41no—
64Q8×C241—42no—
65D4×C241—42no—
66D4×C241—41no—
67D4×C241—41no—
68D4×C241—41no—
69D4×C241—41no—
70C2×C4×C241—22no—
71C2×C4×C241C2×D411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C2×C4×C241C2×D411yescharacteristic
74C8×C241—22no—
75C22×C241—81no—
76C22×C241—81no—
77C22×C241—81no—
78C22×C241#12011yescharacteristic
79C2×D241—22no—
80C2×D241—41no—
81C2×D241—41no—
82C4×C241—21no—
83C4×C241—42no—
84C4×C241C2×SD1611yescharacteristic
85C4×C241#13511yescharacteristic
86C4×C241AGL(1,ℤ/8)11yescharacteristic
87C4×C241#13711yescharacteristic
88Dic241—41no—
89Dic241—41no—
90Dic241—41no—
91C2×C241—161no—
92C2×C241#44811yescharacteristic
93C2×C241#44911yescharacteristic
94C2×C241#45311yescharacteristic
95D241—42no—
96C241#162211yescharacteristic, complemented, Sylow
97#1622—2411nomaximal, Sylow
98#554—2411no—
99#492D24111yescharacteristic, complemented
100#460—2411no—
101#459—2411no—
102#333—2411no—
103Q8⋊C8—2411no—
104D4⋊C8—2411no—
105C2×SD16—22no—
106C2×SD16—4821no—
107C2×D8—4821no—
108C4⋊Q8C2×D24111yescharacteristic
109#127C2×D24111yescharacteristic
110#125—4821no—
111C22⋊Q8—4821no—
112C22⋊Q8—4822no—
113C4×Q8—2411no—
114C4×D4—4821no—
115C4×D4—2411no—
116C2×C4⋊C4—4821no—
117C4⋊C8—2411no—
118C4⋊C8—2411no—
119#102—4821no—
120#102—4821no—
121C4×C8C2×D24111yescharacteristic
122C2×Q8—2411no—
123C2×Q8C22⋊D24112yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2411no—
128C22×C4—4822no—
129C22×C4—4821no—
130SD16—44no—
131SD16—9642no—
132D8—9642no—
133C2×C8—21no—
134C2×C8—4821no—
135C2×C8—4821no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—4822no—
139C4⋊C4—4822no—
140C4⋊C4—4821no—
141C4⋊C4—2411no—
142C4⋊C4—2411no—
143C22⋊C4—4822no—
144C22⋊C4—4821no—
145C42—4821no—
146C42C22×D24111yescharacteristic
147C23—41no—
148C23—4821no—
149Q8—42no—
150Q8—4821no—
151Q8—4821no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—4821no—
158D4—2412no—
159C2×C4—22no—
160C2×C4—19282no—
161C2×C4—9641no—
162C2×C4—9641no—
163C2×C4—4821no—
164C2×C4—4821no—
165C2×C4—4821no—
166C2×C4D4×D24111yescharacteristic
167C2×C4D4×D24111yescharacteristic
168C2×C4C2×C22⋊D24111yescharacteristic
169C8—22no—
170C8—9641no—
171C8—9641no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—9641no—
176C22—9641no—
177C22—4822no—
178C22#2144061011yescharacteristic
179C4—21no—
180C4—42no—
181C4—9641no—
182C4—9641no—
183C4—9641no—
184C4SD16×D24111yescharacteristic
185C4#2144066311yescharacteristic
186C4#2144066911yescharacteristic
187C4#2144067111yescharacteristic
188C2—161no—
189C2—9642no—
190C2#2950785411yescharacteristic
191C2#2950786111yescharacteristic
192C2#2950788411yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#492×C241C2
socleC22×C241#120
prime radical#29507909C2
hypercenter#492D241
hypocenterC241#1622
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #29508428C2semidirect
2. #29507914C2semidirect
4. #29507466C2semidirect
5. #29507449C2semidirect
6. #29507446C2semidirect
7. #492×C241C2semidirect
54. D964SD16semidirect
96. C241#1622semidirect
99. #492D241semidirect

Maximal subgroups

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

subgroupindex
#295084282
#295079142
#295079092
#295074662
#295074492
#295074462
#492×C2412
#1622241