Finite Group Databasebeta

← #44506626

Subgroups — #44506626

Order 30848.

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

normal subgroups only

This group has 308 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#29508064C211yesmaximal, characteristic, complemented
3#29507998C211yesmaximal, characteristic, complemented
4#29507922C211yesmaximal, characteristic, complemented
5#29507460C211yesmaximal, characteristic, complemented
6#29507446C211yesmaximal, characteristic, complemented
7D4⋊C8×C241C211yesmaximal, characteristic, complemented
8C22×D964—21no—
9C2×D4×D241—21no—
10C2×#16838758—21no—
11#21440642C2211yescharacteristic, complemented
12#21440639C2211yescharacteristic
13#21440617—21no—
14#21440616—21no—
15#21440612—22no—
16C4×D964C2211yescharacteristic
17#21440576—21no—
18C4⋊#14515349C2211yescharacteristic, complemented
19#21440565—21no—
20#21440564—21no—
21#21440564—22no—
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic, complemented
24C4×C8×C241C2211yescharacteristic, complemented
25C23×D241—22no—
26C2×Dic482—21no—
27C2×D964—22no—
28C2×D964—21no—
29C2×D964—21no—
30C2×D964—42no—
31C2×D964—42no—
32C2×D964D411yescharacteristic
33C2×D964D412yes—
34C2×C22⋊D241—22no—
35D4×D241—42no—
36D4×D241—42no—
37C2×C4×D241—21no—
38#16838758—42no—
39C2×#14515349—21no—
40C4⋊Dic241—21no—
41C4⋊Dic241—21no—
42C4⋊Dic241D411yescharacteristic
43#16838747—22no—
44#16838747—21no—
45C2×D4×C241D411yescharacteristic
46C22×C4×C241—21no—
47C2×C8×C241—21no—
48C2×C8×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—
57Dic482—41no—
58Dic482—41no—
59D964—21no—
60D964—42no—
61D964—44no—
62D964—41no—
63D964—41no—
64D964—41no—
65D964—41no—
66D964SD1612yescomplemented
67C22⋊D241—44no—
68C2×Dic241—21no—
69C2×Dic241—41no—
70C4×D241—41no—
71C4×D241—41no—
72#14515349—41no—
73C23×C241—21no—
74D4×C241—21no—
75D4×C241D812yes—
76C2×C4×C241—21no—
77C2×C4×C241—41no—
78C2×C4×C241—41no—
79C2×C4×C241C2×D411yescharacteristic
80C2×C4×C241C2×D411yescharacteristic
81C2×C4×C241C2×D411yescharacteristic
82C8×C241—41no—
83C8×C241—41no—
84C22×C241—22no—
85C22×C241—41no—
86C22×C241—41no—
87C22×C241#12011yescharacteristic
88C2×D241—22no—
89C2×D241—41no—
90C2×D241—41no—
91C2×D241—42no—
92C2×D241—42no—
93C2×D241—42no—
94C2×D241—88no—
95C4×C241—21no—
96C4×C241—41no—
97C4×C241C2×D811yescharacteristic
98C4×C241C2×SD1611yescharacteristic
99C4×C241AGL(1,ℤ/8)11yescharacteristic
100C4×C241AGL(1,ℤ/8)11yescharacteristic
101Dic241—41no—
102Dic241—81no—
103C2×C241—42no—
104C2×C241#44711yescharacteristic
105C2×C241#45011yescharacteristic
106C2×C241#45511yescharacteristic
107D241—42no—
108D241—82no—
109C241#163911yescharacteristic, complemented, Sylow
110#1639—2411nomaximal, Sylow
111D42—2411no—
112#486—2411no—
113#474—2411no—
114#461—2411no—
115#331—2411no—
116D4⋊C8—2411no—
117D4⋊C8D24111yescharacteristic, complemented
118C22×D4—4821no—
119C22×D4—4821no—
120C2×SD16—4821no—
121C4⋊Q8—2411no—
122#127—2411no—
123#121—4821no—
124#121—4821no—
125#120—4822no—
126C4×D4—2411no—
127C4×D4C2×D24111yescharacteristic
128#107—4821no—
129C4⋊C8—2411no—
130C4⋊C8C2×D24111yescharacteristic, complemented
131#103—4821no—
132#102—4821no—
133#102—4822no—
134C4×C8C2×D24111yescharacteristic, complemented
135C24—4822no—
136C2×Q8—4821no—
137C2×D4—9642no—
138C2×D4—9642no—
139C2×D4—9642no—
140C2×D4—9642no—
141C2×D4—4822no—
142C2×D4—4822no—
143C2×D4—4821no—
144C2×D4—4821no—
145C2×D4—2412no—
146C2×D4—2411no—
147C2×D4D96411yescharacteristic
148C22×C4—21no—
149C22×C4—4821no—
150SD16—9642no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—4821no—
154C4⋊C4—4821no—
155C4⋊C4—4821no—
156C4⋊C4—2411no—
157C4⋊C4D96411yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—4822no—
160C22⋊C4—4821no—
161C42C22×D24111yescharacteristic
162C23—21no—
163C23—19282no—
164C23—9644no—
165C23—9644no—
166C23—4822no—
167C23—4821no—
168Q8—9641no—
169Q8—9641no—
170D4—21no—
171D4—9642no—
172D4—9644no—
173D4—9644no—
174D4—9641no—
175D4—9641no—
176D4—9641no—
177D4—9641no—
178D4—4821no—
179D4—2412no—
180D4D192812yes—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—9641no—
185C2×C4—9641no—
186C2×C4—9641no—
187C2×C4—4821no—
188C2×C4D4×D24111yescharacteristic
189C2×C4D4×D24111yescharacteristic
190C2×C4C2×D96411yescharacteristic
191C8—41no—
192C8—41no—
193C8—9641no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—19288no—
198C22—9642no—
199C22—9642no—
200C22—9642no—
201C22—9641no—
202C22—9641no—
203C22—4822no—
204C22#2144061211yescharacteristic
205C4—21no—
206C4—41no—
207C4—19281no—
208C4—9641no—
209C4C2×D192811yescharacteristic
210C4SD16×D24111yescharacteristic
211C4#2144066611yescharacteristic
212C4#2144067011yescharacteristic
213C2—42no—
214C2—19282no—
215C2—9642no—
216C2#2950785311yescharacteristic
217C2#2950786911yescharacteristic
218C2#2950789611yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingD4⋊C8×C241C2
socleC22×C241#120
prime radicalD4×D964C2
hypercenterD4⋊C8D241
hypocenterC241#1639
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #29508064C2semidirect
3. #29507998C2semidirect
4. #29507922C2semidirect
5. #29507460C2semidirect
6. #29507446C2semidirect
7. D4⋊C8×C241C2semidirect
11. #21440642C22semidirect
18. C4⋊#14515349C22semidirect
23. C4⋊C8×C241C22semidirect
24. C4×C8×C241C22semidirect
66. D964SD16semidirect
109. C241#1639semidirect
117. D4⋊C8D241semidirect
130. C4⋊C8C2×D241semidirect
134. C4×C8C2×D241semidirect

Maximal subgroups

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

subgroupindex
D4×D9642
#295080642
#295079982
#295079222
#295074602
#295074462
D4⋊C8×C2412
#1639241