Finite Group Databasebeta

← #44505982

Subgroups — #44505982

Order 30848.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#29508253C211yesmaximal, characteristic
2#29507771C211yesmaximal, characteristic, complemented
3#29507581C211yesmaximal, characteristic, complemented
4#29507454C211yesmaximal, characteristic, complemented
5#29507452C211yesmaximal, characteristic
6#29507450C211yesmaximal, characteristic
7#328×C241C211yesmaximal, characteristic, complemented
8#21440637—21no—
9#21440633C411yescharacteristic, complemented
10#21440631C411yescharacteristic, complemented
11#21440626—21no—
12#21440616C2211yescharacteristic
13Q8×Dic241C411yescharacteristic, complemented
14#21440604C411yescharacteristic, complemented
15#21440602—21no—
16#21440600—21no—
17C2×#16838749—21no—
18C2×C4×Dic241C2211yescharacteristic
19#21440571—21no—
20C22⋊#14515349C2211yescharacteristic
21#21440552—21no—
22#21440549—21no—
23#21440549C2211yescharacteristic
24C22⋊Q8×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27C2×D964C2×C411yescharacteristic
28C2×C22⋊D241—21no—
29C22×Dic241—21no—
30C22×Dic241D411yescharacteristic
31C22×Dic241D411yescharacteristic
32C2×C4×D241—21no—
33C2×#14515349—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241C2×C411yescharacteristic
37#16838749—21no—
38#16838749—42no—
39#16838747—21no—
40#16838747—21no—
41#16838747—21no—
42#16838747—21no—
43C4×Dic241—21no—
44C4×Dic241C2×C411yescharacteristic
45C4×Dic241C2×C411yescharacteristic
46C4×Dic241D411yescharacteristic
47C4×Dic241D411yescharacteristic
48C2×Q8×C241C2×C411yescharacteristic
49C22×C4×C241—21no—
50C22×C4×C241C2311yescharacteristic
51C2×C8×C241—21no—
52C4⋊C4×C241—21no—
53C4⋊C4×C241C2×C411yescharacteristic
54C22⋊C4×C241—21no—
55C22×D241—21no—
56D964—41no—
57C22⋊D241—41no—
58C22⋊D241—41no—
59C2×Dic241—21no—
60C2×Dic241—21no—
61C2×Dic241—21no—
62C2×Dic241—41no—
63C2×Dic241—41no—
64C2×Dic241—41no—
65C2×Dic241—41no—
66C2×Dic241C22⋊C411yescharacteristic
67C2×Dic241C22⋊C411yescharacteristic
68C2×Dic241C22⋊C411yescharacteristic
69C2×Dic241C22⋊C411yescharacteristic
70C4×D241—42no—
71#14515349—41no—
72C23×C241C2×D411yescharacteristic
73Q8×C241—41no—
74C2×C4×C241—21no—
75C2×C4×C241—21no—
76C2×C4×C241—41no—
77C2×C4×C241—41no—
78C2×C4×C241—41no—
79C2×C4×C241—41no—
80C2×C4×C241C22×C411yescharacteristic
81C2×C4×C241C2×D411yescharacteristic
82C8×C241—41no—
83C22×C241—21no—
84C22×C241—21no—
85C22×C241C2×C22⋊C411yescharacteristic
86C22×C241AGL(1,ℤ/8)11yescharacteristic
87C22×C241#13711yescharacteristic
88C2×D241—41no—
89C2×D241—41no—
90C2×D241—41no—
91C4×C241—21no—
92C4×C241—21no—
93C4×C241—41no—
94C4×C241—41no—
95C4×C241—81no—
96Dic241—21no—
97Dic241—21no—
98Dic241—21no—
99Dic241—21no—
100Dic241—41no—
101Dic241—81no—
102C2×C241—21no—
103C2×C241—21no—
104C2×C241#41011yescharacteristic
105C2×C241#41711yescharacteristic
106C2×C241#42111yescharacteristic
107D241—81no—
108C241#151211yescharacteristic, complemented, Sylow
109#1512—2411nomaximal, Sylow
110#529—2411no—
111#432—2411no—
112#382—2411no—
113#328—2411no—
114#328D24111yescharacteristic, complemented
115#327—2411no—
116#327—2411no—
117#126—4821no—
118#125—2411no—
119#124—2411no—
120#123—4821no—
121C22⋊Q8C2×D24111yescharacteristic
122#121—2411no—
123C4×Q8—2411no—
124C4×D4—4821no—
125C4×D4—2411no—
126#117—4821no—
127C2×C4⋊C4—4821no—
128C2×C42—2411no—
129C4⋊C8—4821no—
130C22⋊C8—2411no—
131C22⋊C8C2×D24111yescharacteristic
132#97—4821no—
133#95—4821no—
134#95—2411no—
135#95C2×D24111yescharacteristic
136C2×Q8C4×D24111yescharacteristic
137C2×D4—4821no—
138C2×D4—2411no—
139C22×C4—21no—
140C22×C4—4821no—
141C22×C4—4821no—
142C22×C4—2411no—
143C22×C4—2411no—
144C22×C4C22×D24111yescharacteristic
145C2×C8—21no—
146C2×C8—4821no—
147C4⋊C4—21no—
148C4⋊C4—9642no—
149C4⋊C4—4821no—
150C4⋊C4—4821no—
151C4⋊C4—4821no—
152C4⋊C4—2411no—
153C4⋊C4C4×D24111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—4821no—
156C22⋊C4—4821no—
157C22⋊C4—4821no—
158C22⋊C4—4821no—
159C42—4821no—
160C42—2411no—
161C42—2411no—
162C42—2411no—
163C42—2411no—
164C23—4821no—
165C23D4×D24111yescharacteristic
166Q8—41no—
167D4—9641no—
168D4—9641no—
169D4—9641no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—9642no—
177C2×C4—9641no—
178C2×C4—9641no—
179C2×C4—9641no—
180C2×C4—9641no—
181C2×C4—4821no—
182C2×C4—4821no—
183C2×C4—4821no—
184C2×C4—2411no—
185C2×C4—2411no—
186C2×C4—2411no—
187C2×C4—2411no—
188C2×C4C2×C4×D24111yescharacteristic
189C2×C4D4×D24111yescharacteristic
190C8—41no—
191C8—9641no—
192C22—21no—
193C22—21no—
194C22—9641no—
195C22—9641no—
196C22—9641no—
197C22C22⋊C4×D24111yescharacteristic
198C22#2144066911yescharacteristic
199C22#2144067411yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—81no—
205C4—19281no—
206C4—9641no—
207C4—4821no—
208C4—4821no—
209C4—4821no—
210C4—4821no—
211C2—21no—
212C2—21no—
213C2—19281no—
214C2#2950768911yescharacteristic
215C2#2950771711yescharacteristic
216C2#2950773211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#328×C241C2
socleC22×C241C2×C22⋊C4
prime radical#21440616C22
cosocleC22×C4×C241C23
hypercenter#328D241
hypocenterC241#1512
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #29507771C2semidirect
3. #29507581C2semidirect
4. #29507454C2semidirect
7. #328×C241C2semidirect
9. #21440633C4semidirect
10. #21440631C4semidirect
13. Q8×Dic241C4semidirect
14. #21440604C4semidirect
108. C241#1512semidirect
114. #328D241semidirect

Maximal subgroups

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

subgroupindex
#295082532
#295077712
#295075812
#295074542
#295074522
#295074502
#328×C2412
#1512241