Finite Group Databasebeta

← #44505852

Subgroups — #44505852

Order 30848.

212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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#29508254C211yesmaximal, characteristic
2#29507769C211yesmaximal, characteristic, complemented
3#29507768C211yesmaximal, characteristic, complemented
4Q8⋊#14515349C211yesmaximal, characteristic, complemented
5#29507446C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic, complemented
7Q8⋊C8×C241C211yesmaximal, characteristic, complemented
8#21440637—21no—
9#21440633C411yescharacteristic
10#21440631C411yescharacteristic
11#21440627—21no—
12#21440618C411yescharacteristic
13#21440617C411yescharacteristic
14C4×D964—21no—
15C4×D964C2211yescharacteristic
16#21440599—21no—
17C42×D241C2211yescharacteristic
18C4⋊#14515349C2211yescharacteristic
19#21440571—21no—
20#21440554—21no—
21#21440554—21no—
22C4×#14515349C2211yescharacteristic
23C8×Dic241—21no—
24C4×Q8×C241C2211yescharacteristic
25C4⋊C8×C241C2211yescharacteristic
26C4×C8×C241C2211yescharacteristic
27C2×D964—21no—
28C2×D964C2×C411yescharacteristic
29C2×C4×D241—21no—
30C2×C4×D241C2×C411yescharacteristic
31C2×C4×D241D411yescharacteristic
32C2×C4×D241D411yescharacteristic
33C2×#14515349—21no—
34C2×#14515349—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241C2×C411yescharacteristic
37#16838749—21no—
38#16838749—21no—
39#16838747—21no—
40#16838747—21no—
41#16838747—21no—
42#16838747—21no—
43#16838747—21no—
44C4×Dic241C2×C411yescharacteristic
45C4×Dic241D411yescharacteristic
46C4×Dic241D411yescharacteristic
47C2×Q8×C241C2×C411yescharacteristic
48C2×C8×C241—21no—
49C2×C8×C241—21no—
50C4⋊C4×C241—21no—
51C4⋊C4×C241C2×C411yescharacteristic
52C42×C241—21no—
53C42×C241C2311yescharacteristic
54C22×D241—21no—
55C22×D241C22⋊C411yescharacteristic
56D964—21no—
57D964—21no—
58D964—42no—
59C2×Dic241—21no—
60C2×Dic241C22⋊C411yescharacteristic
61C2×Dic241C22⋊C411yescharacteristic
62C2×Dic241C22⋊C411yescharacteristic
63C4×D241—21no—
64C4×D241—21no—
65C4×D241—21no—
66C4×D241—21no—
67C4×D241—41no—
68C4×D241—41no—
69C4×D241—41no—
70#14515349—41no—
71#14515349—41no—
72Q8×C241—21no—
73Q8×C241—21no—
74C2×C4×C241—21no—
75C2×C4×C241—21no—
76C2×C4×C241C22×C411yescharacteristic
77C2×C4×C241C2×D411yescharacteristic
78C2×C4×C241C2×D411yescharacteristic
79C8×C241—41no—
80C8×C241—41no—
81C22×C241C2×C22⋊C411yescharacteristic
82C2×D241—21no—
83C2×D241—21no—
84C2×D241—21no—
85C2×D241—41no—
86C2×D241—41no—
87C2×D241—41no—
88C4×C241—21no—
89C4×C241—41no—
90C4×C241—41no—
91C4×C241#13111yescharacteristic
92C4×C241#13111yescharacteristic
93C4×C241#13511yescharacteristic
94C4×C241#13511yescharacteristic
95Dic241—21no—
96Dic241—21no—
97Dic241—21no—
98Dic241—41no—
99C2×C241#40811yescharacteristic
100C2×C241#41611yescharacteristic
101C2×C241#42111yescharacteristic
102D241—41no—
103D241—81no—
104C241#148211yescharacteristic, complemented, Sylow
105#1482—2411nomaximal, Sylow
106#529—2411no—
107#431—2411no—
108#431—2411no—
109Q8⋊C8—2411no—
110Q8⋊C8D24111yescharacteristic, complemented
111D4⋊C8—2411no—
112D4⋊C8—2411no—
113#126—4821no—
114#125—2411no—
115#124—2411no—
116#123—4821no—
117C22⋊Q8—2411no—
118#121—2411no—
119C4×Q8C2×D24111yescharacteristic
120C4×D4—4821no—
121C4×D4—2411no—
122#117—4821no—
123C2×C42—2411no—
124C4⋊C8—4821no—
125C4⋊C8—2411no—
126C4⋊C8C2×D24111yescharacteristic
127C22⋊C8—4821no—
128C22⋊C8—4821no—
129C4×C8—4821no—
130C4×C8—2411no—
131C4×C8C2×D24111yescharacteristic
132C2×Q8C4×D24111yescharacteristic
133C2×D4—4821no—
134C2×D4—2411no—
135C22×C4—4821no—
136C22×C4—2411no—
137C22×C4—2411no—
138C22×C4—2411no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—4821no—
142C2×C8—4821no—
143C4⋊C4—21no—
144C4⋊C4—4821no—
145C4⋊C4—4821no—
146C4⋊C4—4821no—
147C4⋊C4—2411no—
148C4⋊C4C4×D24111yescharacteristic
149C22⋊C4—4821no—
150C22⋊C4—4821no—
151C22⋊C4—4821no—
152C22⋊C4—4821no—
153C22⋊C4—4821no—
154C42—21no—
155C42—2411no—
156C42—2411no—
157C42—2411no—
158C42C22×D24111yescharacteristic
159C23—4821no—
160C23—2411no—
161Q8—21no—
162Q8—21no—
163D4—9642no—
164D4—4821no—
165D4—4821no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—9641no—
169C2×C4—9641no—
170C2×C4—9641no—
171C2×C4—4821no—
172C2×C4—4821no—
173C2×C4—4821no—
174C2×C4—4821no—
175C2×C4—4821no—
176C2×C4—2411no—
177C2×C4—2411no—
178C2×C4—2411no—
179C2×C4C2×C4×D24111yescharacteristic
180C2×C4D4×D24111yescharacteristic
181C2×C4D4×D24111yescharacteristic
182C8—41no—
183C8—41no—
184C8—9641no—
185C8—9641no—
186C22—9641no—
187C22—9641no—
188C22—9641no—
189C22—4821no—
190C22—4821no—
191C22—4821no—
192C22C22⋊C4×D24111yescharacteristic
193C4—21no—
194C4—41no—
195C4—41no—
196C4—9641no—
197C4—4821no—
198C4—4821no—
199C4—4821no—
200C4#2144064811yescharacteristic
201C4#2144065011yescharacteristic
202C4#2144066311yescharacteristic
203C4#2144066511yescharacteristic
204C2—19281no—
205C2—9641no—
206C2#2950768211yescharacteristic
207C2#2950771211yescharacteristic
208C2#2950773211yescharacteristic
subgroupG/H
centerC2×C4D4×D241
commutatorC2×C4×C241C22×C4
FrattiniC42C22×D241
FittingQ8⋊C8×C241C2
socleC22×C241C2×C22⋊C4
prime radical#21440617C4
cosocleC42×C241C23
hypercenterQ8⋊C8D241
hypocenterC241#1482
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #29507769C2semidirect
3. #29507768C2semidirect
4. Q8⋊#14515349C2semidirect
5. #29507446C2semidirect
6. #29507444C2semidirect
7. Q8⋊C8×C241C2semidirect
104. C241#1482semidirect
110. Q8⋊C8D241semidirect

Maximal subgroups

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

subgroupindex
#295082542
#295077692
#295077682
Q8⋊#145153492
#295074462
#295074442
Q8⋊C8×C2412
#1482241