Finite Group Databasebeta

← #44506560

Subgroups — #44506560

Order 30848.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D964C211yesmaximal, characteristic
2#29508091C211yesmaximal, characteristic, complemented
3#29508004C211yesmaximal, characteristic, complemented
4#29507460C211yesmaximal, characteristic, complemented
5D4⋊#14515349C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic, complemented
7#476×C241C211yesmaximal, characteristic, complemented
8C22×D964—21no—
9C2×D4×D241—21no—
10C2×#16838757—22no—
11#21440639C2211yescharacteristic
12#21440617—21no—
13#21440616—21no—
14#21440612—22no—
15C4×D964C2211yescharacteristic
16#21440573—21no—
17C4⋊#14515349C2211yescharacteristic, complemented
18#21440562—21no—
19C4×#14515349C2211yescharacteristic, complemented
20C4⋊Q8×C241C2211yescharacteristic, complemented
21C4×D4×C241C2211yescharacteristic
22#106×C241—21no—
23C4⋊C8×C241C2211yescharacteristic, complemented
24#102×C241—21no—
25C23×D241—22no—
26C2×D964—22no—
27C2×D964—21no—
28C2×D964—21no—
29C2×D964—42no—
30C2×D964—42no—
31C2×D964D411yescharacteristic
32C2×D964D412yes—
33C2×C22⋊D241—22no—
34D4×D241—42no—
35D4×D241—42no—
36C2×C4×D241—21no—
37#16838757—44no—
38C2×#14515349—21no—
39C2×#14515349—21no—
40C4⋊Dic241D411yescharacteristic
41#16838747—22no—
42#16838747—21no—
43C2×Q8×C241—21no—
44C2×D4×C241D411yescharacteristic
45C22×C4×C241—21no—
46C2×C8×C241—21no—
47C4⋊C4×C241—21no—
48C4⋊C4×C241—21no—
49C4⋊C4×C241D411yescharacteristic
50C22⋊C4×C241—21no—
51C42×C241C2311yescharacteristic
52C22×D241—21no—
53C22×D241—22no—
54C22×D241—44no—
55C22×D241—44no—
56C22×D241—82no—
57D964—21no—
58D964—42no—
59D964—44no—
60D964—41no—
61D964—41no—
62D964—41no—
63D964—41no—
64D964SD1612yescomplemented
65C22⋊D241—44no—
66C2×Dic241—21no—
67C4×D241—41no—
68C4×D241—41no—
69#14515349—22no—
70#14515349—41no—
71C23×C241—21no—
72Q8×C241—42no—
73D4×C241—21no—
74D4×C241SD1612yescomplemented
75C2×C4×C241—21no—
76C2×C4×C241—41no—
77C2×C4×C241—41no—
78C2×C4×C241—41no—
79C2×C4×C241C2×D411yescharacteristic
80C2×C4×C241C2×D411yescharacteristic
81C2×C4×C241C2×D411yescharacteristic
82C8×C241—41no—
83C22×C241—22no—
84C22×C241—41no—
85C22×C241—41no—
86C22×C241#12011yescharacteristic
87C2×D241—22no—
88C2×D241—41no—
89C2×D241—41no—
90C2×D241—42no—
91C2×D241—42no—
92C2×D241—42no—
93C2×D241—88no—
94C4×C241—21no—
95C4×C241—41no—
96C4×C241—81no—
97C4×C241C2×SD1611yescharacteristic
98C4×C241C2×SD1611yescharacteristic
99C4×C241AGL(1,ℤ/8)11yescharacteristic
100C4×C241AGL(1,ℤ/8)11yescharacteristic
101Dic241—41no—
102C2×C241—42no—
103C2×C241#45011yescharacteristic
104C2×C241#45011yescharacteristic
105C2×C241#45311yescharacteristic
106D241—42no—
107D241—82no—
108C241#162911yescharacteristic, complemented, Sylow
109#1629—2411nomaximal, Sylow
110D42—2411no—
111#492—2411no—
112#476—2411no—
113#476D24111yescharacteristic, complemented
114#331—2411no—
115D4⋊C8—2411no—
116D4⋊C8—2411no—
117C22×D4—4821no—
118C22×D4—4821no—
119C2×SD16—4822no—
120C4⋊Q8C2×D24111yescharacteristic, complemented
121#127—2411no—
122#121—4821no—
123#121—4821no—
124#120—4822no—
125C4×D4—2411no—
126C4×D4C2×D24111yescharacteristic
127#106—21no—
128#106—4821no—
129C4⋊C8—2411no—
130C4⋊C8C2×D24111yescharacteristic, complemented
131#102—21no—
132#102—4821no—
133C4×C8—2411no—
134C24—4822no—
135C2×Q8—21no—
136C2×D4—9642no—
137C2×D4—9642no—
138C2×D4—9642no—
139C2×D4—9642no—
140C2×D4—4822no—
141C2×D4—4822no—
142C2×D4—4821no—
143C2×D4—4821no—
144C2×D4—2412no—
145C2×D4—2411no—
146C2×D4C22⋊D24111yescharacteristic
147C22×C4—21no—
148C22×C4—4821no—
149SD16—9644no—
150C2×C8—21no—
151C2×C8—4821no—
152C2×C8—4821no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—2411no—
156C4⋊C4C22⋊D24111yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—4822no—
159C22⋊C4—4821no—
160C42C22×D24111yescharacteristic
161C23—21no—
162C23—19282no—
163C23—9644no—
164C23—9644no—
165C23—4822no—
166C23—4821no—
167Q8—42no—
168D4—21no—
169D4—9642no—
170D4—9644no—
171D4—9644no—
172D4—9641no—
173D4—9641no—
174D4—9641no—
175D4—9641no—
176D4—4821no—
177D4—2412no—
178D4#1683875712yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—9641no—
184C2×C4—9641no—
185C2×C4—4821no—
186C2×C4D4×D24111yescharacteristic
187C2×C4D4×D24111yescharacteristic
188C2×C4C2×C22⋊D24111yescharacteristic
189C8—41no—
190C8—9641no—
191C8—4822no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—19288no—
196C22—9642no—
197C22—9642no—
198C22—9642no—
199C22—9641no—
200C22—9641no—
201C22—4822no—
202C22#2144061011yescharacteristic
203C4—21no—
204C4—41no—
205C4—81no—
206C4—9641no—
207C4SD16×D24111yescharacteristic
208C4C2×#1683875711yescharacteristic
209C4#2144066711yescharacteristic
210C4#2144066911yescharacteristic
211C2—42no—
212C2—19282no—
213C2—9642no—
214C2#2950786611yescharacteristic
215C2#2950786711yescharacteristic
216C2#2950788311yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#476×C241C2
socleC22×C241#120
prime radicalD4×D964C2
hypercenter#476D241
hypocenterC241#1629
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #29508091C2semidirect
3. #29508004C2semidirect
4. #29507460C2semidirect
5. D4⋊#14515349C2semidirect
6. #29507444C2semidirect
7. #476×C241C2semidirect
17. C4⋊#14515349C22semidirect
19. C4×#14515349C22semidirect
20. C4⋊Q8×C241C22semidirect
23. C4⋊C8×C241C22semidirect
64. D964SD16semidirect
74. D4×C241SD16semidirect
108. C241#1629semidirect
113. #476D241semidirect
120. C4⋊Q8C2×D241semidirect
130. C4⋊C8C2×D241semidirect
178. D4#16838757semidirect

Maximal subgroups

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

subgroupindex
D4×D9642
#295080912
#295080042
#295074602
D4⋊#145153492
#295074442
#476×C2412
#1629241