Finite Group Databasebeta

← #44507399

Subgroups — #44507399

Order 30848.

620 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 125 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×#21440569C212yesmaximal, complemented
2#29507718C212yesmaximal, complemented
3C2×#21440559C211yesmaximal, characteristic, complemented
4#29507620C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C241C211yesmaximal, characteristic
6C2×#16838754C2212yescomplemented
7C2×C4⋊Dic241C2211yescharacteristic, complemented
8C2×C22⋊Dic241—22no—
9C2×C4×Dic241C2211yescharacteristic, complemented
10#21440569—24no—
11#21440566—22no—
12#21440563—22no—
13#21440559—22no—
14H(5,𝔽2)×C241—24no—
15H(5,𝔽2)×C241—22no—
16H(5,𝔽2)×C241C414yescomplemented
17C2×#41×C241—22no—
18C2×#41×C241C2212yes—
19C22×D4×C241—22no—
20C22×D4×C241—22no—
21C22×D4×C241C2211yescharacteristic
22C22×Dic241—21no—
23C22×Dic241—21no—
24#16838754—22no—
25#16838754—22no—
26C2×#14515349—22no—
27C4⋊Dic241—22no—
28C22⋊Dic241—44no—
29C4×Dic241—22no—
30C24×C241—22no—
31C24×C241D412yes—
32#41×C241—28no—
33#41×C241—28no—
34#41×C241—22no—
35#41×C241—22no—
36#41×C241C2×C414yes—
37#41×C241D414yes—
38C2×Q8×C241D412yes—
39C2×D4×C241—24no—
40C2×D4×C241—28no—
41C2×D4×C241—28no—
42C2×D4×C241—28no—
43C2×D4×C241—22no—
44C2×D4×C241—28no—
45C2×D4×C241—22no—
46C2×D4×C241—22no—
47C2×D4×C241C2×C412yes—
48C2×D4×C241D412yes—
49C2×D4×C241D412yes—
50C22×C4×C241—22no—
51C22×C4×C241—22no—
52C22×C4×C241C2311yescharacteristic
53C2×Dic241—22no—
54C2×Dic241—41no—
55C2×Dic241—41no—
56C2×Dic241—42no—
57C2×Dic241—41no—
58#14515349—42no—
59C23×C241—28no—
60C23×C241—22no—
61C23×C241—22no—
62C23×C241—22no—
63C23×C241—42no—
64C23×C241—42no—
65C23×C241—82no—
66C23×C241—82no—
67C23×C241C22⋊C414yes—
68C23×C241C2×D411yescharacteristic
69Q8×C241—22no—
70Q8×C241C22⋊C414yescomplemented
71D4×C241—216no—
72D4×C241—24no—
73D4×C241—24no—
74D4×C241—24no—
75D4×C241—24no—
76D4×C241—22no—
77D4×C241C22⋊C414yescomplemented
78C2×C4×C241—28no—
79C2×C4×C241—22no—
80C2×C4×C241—24no—
81C2×C4×C241—24no—
82C2×C4×C241C22×C411yescharacteristic
83C2×C4×C241C2×D412yes—
84C2×C4×C241C2×D412yes—
85C2×C4×C241C2×D411yescharacteristic
86C22×C241—21no—
87C22×C241—21no—
88C22×C241—24no—
89C22×C241—24no—
90C22×C241—44no—
91C22×C241—42no—
92C22×C241—42no—
93C22×C241—42no—
94C22×C241—42no—
95C22×C241—82no—
96C22×C241—88no—
97C22×C241C2×C22⋊C411yescharacteristic
98C22×C241#12011yescharacteristic
99C22×C241#12011yescharacteristic
100C4×C241—24no—
101C4×C241C2×C22⋊C412yes—
102C4×C241#12012yes—
103Dic241—42no—
104Dic241—81no—
105C2×C241—21no—
106C2×C241—21no—
107C2×C241—44no—
108C2×C241—44no—
109C2×C241#37911yescharacteristic
110C2×C241#45311yescharacteristic
111C2×C241#45511yescharacteristic
112C241#179211yescharacteristic, complemented, Sylow
113#1792—2411nomaximal, Sylow
114C2×H(5,𝔽2)D24111yescharacteristic
115C2×#104—2412no—
116#417—2412no—
117C2×#100—2411no—
118#390—2411no—
119H(5,𝔽2)—24no—
120H(5,𝔽2)—22no—
121H(5,𝔽2)Dic24114yescomplemented
122C2×#41—22no—
123C2×#41C2×D24112yes—
124C22×D4—22no—
125C22×D4—22no—
126C22×D4C2×D24111yescharacteristic
127C2×M16—2412no—
128C2×C4⋊C4—2411no—
129C2×C22⋊C4—4822no—
130C2×C42—2411no—
131#104—4824no—
132#103—4822no—
133#102—4822no—
134#100—4822no—
135C24—22no—
136C24C22⋊D24112yes—
137#41—28no—
138#41—28no—
139#41—22no—
140#41—22no—
141#41C2×Dic24114yes—
142#41C22⋊D24114yes—
143C2×Q8C22⋊D24112yes—
144C2×D4—24no—
145C2×D4—28no—
146C2×D4—28no—
147C2×D4—28no—
148C2×D4—22no—
149C2×D4—28no—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4C2×Dic24112yes—
153C2×D4C22⋊D24112yes—
154C2×D4C22⋊D24112yes—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—4821no—
158C22×C4—4821no—
159C22×C4C22×D24111yescharacteristic
160M16—4822no—
161M16—4822no—
162C2×C8—4822no—
163C4⋊C4—4822no—
164C22⋊C4—9644no—
165C42—4822no—
166C23—28no—
167C23—22no—
168C23—22no—
169C23—22no—
170C23—42no—
171C23—42no—
172C23—82no—
173C23—82no—
174C23C22⋊Dic24114yes—
175C23C2×C22⋊D24111yescharacteristic
176Q8—22no—
177Q8C22⋊Dic24114yescomplemented
178D4—216no—
179D4—24no—
180D4—24no—
181D4—24no—
182D4—24no—
183D4—22no—
184D4C22⋊Dic24114yescomplemented
185C2×C4—28no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—9642no—
190C2×C4—9641no—
191C2×C4—9641no—
192C2×C4—9641no—
193C2×C4—4822no—
194C2×C4C22×Dic24111yescharacteristic
195C2×C4C2×C22⋊D24112yes—
196C2×C4C2×C22⋊D24112yes—
197C2×C4C2×C22⋊D24111yescharacteristic
198C8—9642no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—24no—
203C22—44no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—82no—
209C22—88no—
210C22C2×C22⋊Dic24111yescharacteristic
211C22#2144061111yescharacteristic
212C22#2144061111yescharacteristic
213C4—24no—
214C4—19281no—
215C4—9642no—
216C4C2×C22⋊Dic24112yes—
217C4#2144061112yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—44no—
222C2#2950757311yescharacteristic
223C2#2950788511yescharacteristic
224C2#2950789511yescharacteristic
subgroupG/H
centerC22#21440611
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting, prime radicalC2×H(5,𝔽2)×C241C2
socleC22×C241#120
cosocleC22×C4×C241C23
hypercenterC2×H(5,𝔽2)D241
hypocenterC241#1792
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#21440569C2semidirect
2. #29507718C2semidirect
3. C2×#21440559C2semidirect
4. #29507620C2semidirect
6. C2×#16838754C22semidirect
7. C2×C4⋊Dic241C22semidirect
9. C2×C4×Dic241C22semidirect
16. H(5,𝔽2)×C241C4semidirect
70. Q8×C241C22⋊C4semidirect
77. D4×C241C22⋊C4semidirect
112. C241#1792semidirect
121. H(5,𝔽2)Dic241semidirect
177. Q8C22⋊Dic241semidirect
184. D4C22⋊Dic241semidirect

Maximal subgroups

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

subgroupindex
C2×#214405692
#295077182
C2×#214405592
#295076202
C2×H(5,𝔽2)×C2412
#1792241