Finite Group Databasebeta

← #44505909

Subgroups — #44505909

Order 30848.

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

normal subgroups only

This group has 216 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#29507768C211yesmaximal, characteristic, complemented
3#29507739C211yesmaximal, characteristic, complemented
4Q8⋊#14515349C211yesmaximal, characteristic, complemented
5#29507446C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic, complemented
7Q8⋊C8×C241C211yesmaximal, characteristic, complemented
8C2×#16838753—21no—
9#21440637—21no—
10#21440633C411yescharacteristic
11#21440631C411yescharacteristic
12#21440627—21no—
13#21440618C411yescharacteristic
14#21440617C411yescharacteristic
15C4×D964—21no—
16C4×D964C2211yescharacteristic
17#21440599—21no—
18C42×D241C2211yescharacteristic
19C4⋊#14515349C2211yescharacteristic
20#21440571—21no—
21#21440571—21no—
22#21440554—21no—
23C4×#14515349C2211yescharacteristic
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
33#16838753—42no—
34C2×#14515349—21no—
35C2×#14515349—21no—
36C4⋊Dic241—21no—
37C4⋊Dic241C2×C411yescharacteristic
38#16838749—21no—
39#16838749—21no—
40#16838747—21no—
41#16838747—21no—
42#16838747—21no—
43#16838747—21no—
44#16838747—21no—
45C4×Dic241C2×C411yescharacteristic
46C4×Dic241D411yescharacteristic
47C4×Dic241D411yescharacteristic
48C2×Q8×C241C2×C411yescharacteristic
49C2×C8×C241—21no—
50C2×C8×C241—21no—
51C4⋊C4×C241—21no—
52C4⋊C4×C241C2×C411yescharacteristic
53C42×C241—21no—
54C42×C241C2311yescharacteristic
55C22×D241—21no—
56C22×D241C22⋊C411yescharacteristic
57D964—21no—
58D964—21no—
59D964—42no—
60C2×Dic241—21no—
61C2×Dic241C22⋊C411yescharacteristic
62C2×Dic241C22⋊C411yescharacteristic
63C2×Dic241C22⋊C411yescharacteristic
64C4×D241—21no—
65C4×D241—21no—
66C4×D241—21no—
67C4×D241—21no—
68C4×D241—41no—
69C4×D241—41no—
70C4×D241—41no—
71#14515349—41no—
72#14515349—41no—
73Q8×C241—21no—
74Q8×C241—21no—
75C2×C4×C241—21no—
76C2×C4×C241—21no—
77C2×C4×C241C22×C411yescharacteristic
78C2×C4×C241C2×D411yescharacteristic
79C2×C4×C241C2×D411yescharacteristic
80C8×C241—41no—
81C8×C241—41no—
82C22×C241C2×C22⋊C411yescharacteristic
83C2×D241—21no—
84C2×D241—21no—
85C2×D241—21no—
86C2×D241—41no—
87C2×D241—41no—
88C2×D241—41no—
89C4×C241—21no—
90C4×C241—41no—
91C4×C241—41no—
92C4×C241#13111yescharacteristic
93C4×C241#13111yescharacteristic
94C4×C241AGL(1,ℤ/8)11yescharacteristic
95C4×C241#13711yescharacteristic
96Dic241—21no—
97Dic241—21no—
98Dic241—21no—
99Dic241—41no—
100C2×C241#40811yescharacteristic
101C2×C241#41711yescharacteristic
102C2×C241#42111yescharacteristic
103D241—41no—
104D241—81no—
105C241#149511yescharacteristic, complemented, Sylow
106#1495—2411nomaximal, Sylow
107#529—2411no—
108#431—2411no—
109#423—2411no—
110Q8⋊C8—2411no—
111Q8⋊C8D24111yescharacteristic, complemented
112D4⋊C8—2411no—
113D4⋊C8—2411no—
114C2×M16—4821no—
115#126—4821no—
116#125—2411no—
117#124—2411no—
118#123—4821no—
119C22⋊Q8—2411no—
120#121—2411no—
121C4×Q8C2×D24111yescharacteristic
122C4×D4—4821no—
123C4×D4—2411no—
124#117—4821no—
125C2×C42—2411no—
126C4⋊C8—4821no—
127C4⋊C8—4821no—
128C4⋊C8—2411no—
129C4⋊C8C2×D24111yescharacteristic
130C22⋊C8—4821no—
131C4×C8—2411no—
132C4×C8C2×D24111yescharacteristic
133C2×Q8C4×D24111yescharacteristic
134C2×D4—4821no—
135C2×D4—2411no—
136C22×C4—4821no—
137C22×C4—2411no—
138C22×C4—2411no—
139C22×C4—2411no—
140M16—9642no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—4821no—
144C2×C8—4821no—
145C4⋊C4—21no—
146C4⋊C4—4821no—
147C4⋊C4—4821no—
148C4⋊C4—4821no—
149C4⋊C4—2411no—
150C4⋊C4C4×D24111yescharacteristic
151C22⋊C4—4821no—
152C22⋊C4—4821no—
153C22⋊C4—4821no—
154C22⋊C4—4821no—
155C22⋊C4—4821no—
156C42—21no—
157C42—2411no—
158C42—2411no—
159C42—2411no—
160C42C22×D24111yescharacteristic
161C23—4821no—
162C23—2411no—
163Q8—21no—
164Q8—21no—
165D4—9642no—
166D4—4821no—
167D4—4821no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—9641no—
171C2×C4—9641no—
172C2×C4—9641no—
173C2×C4—4821no—
174C2×C4—4821no—
175C2×C4—4821no—
176C2×C4—4821no—
177C2×C4—4821no—
178C2×C4—2411no—
179C2×C4—2411no—
180C2×C4—2411no—
181C2×C4C2×C4×D24111yescharacteristic
182C2×C4D4×D24111yescharacteristic
183C2×C4D4×D24111yescharacteristic
184C8—41no—
185C8—41no—
186C8—9641no—
187C8—9641no—
188C22—9641no—
189C22—9641no—
190C22—9641no—
191C22—4821no—
192C22—4821no—
193C22—4821no—
194C22C22⋊C4×D24111yescharacteristic
195C4—21no—
196C4—41no—
197C4—41no—
198C4—9641no—
199C4—4821no—
200C4—4821no—
201C4—4821no—
202C4#2144064811yescharacteristic
203C4#2144065011yescharacteristic
204C4#2144066911yescharacteristic
205C4#2144067411yescharacteristic
206C2—19281no—
207C2—9641no—
208C2#2950768211yescharacteristic
209C2#2950771711yescharacteristic
210C2#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#1495
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. #29507768C2semidirect
3. #29507739C2semidirect
4. Q8⋊#14515349C2semidirect
5. #29507446C2semidirect
6. #29507444C2semidirect
7. Q8⋊C8×C241C2semidirect
105. C241#1495semidirect
111. Q8⋊C8D241semidirect

Maximal subgroups

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

subgroupindex
#295082542
#295077682
#295077392
Q8⋊#145153492
#295074462
#295074442
Q8⋊C8×C2412
#1495241