Finite Group Databasebeta

← #44509116

Subgroups — #44509116

Order 30848.

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

normal subgroups only

This group has 270 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#29508281C211yesmaximal, characteristic
2#29507691C211yesmaximal, characteristic, complemented
3#29507509C214yesmaximal, complemented
4#410×C241C211yesmaximal, characteristic, complemented
5C22×D964C411yescharacteristic, complemented
6#21440638C2212yes—
7#21440631C412yescomplemented
8#21440616—21no—
9#21440616—21no—
10#21440610—21no—
11#21440610—21no—
12#21440601—21no—
13#21440601C411yescharacteristic, complemented
14#21440557—21no—
15#21440557C2212yescomplemented
16C2×#41×C241C2211yescharacteristic
17#117×C241—21no—
18#99×C241—21no—
19#99×C241C2212yescomplemented
20C23×D241—21no—
21C2×D964—21no—
22C2×D964—41no—
23C2×D964—41no—
24C2×D964C2×C412yes—
25C2×C22⋊D241—22no—
26C2×C22⋊D241—22no—
27C4⋊Dic241—21no—
28C4⋊Dic241—41no—
29C22⋊Dic241—21no—
30C22⋊Dic241—22no—
31#16838747—22no—
32#16838747—22no—
33C4×Dic241—41no—
34C4×Dic241C2×C412yes—
35#41×C241—41no—
36#41×C241—41no—
37C2×Q8×C241C2×C411yescharacteristic
38C2×D4×C241D411yescharacteristic
39C2×D4×C241D411yescharacteristic
40C2×D4×C241C2311yescharacteristic
41C22×C4×C241C2×C411yescharacteristic
42C22×C4×C241D411yescharacteristic
43C22×C4×C241D411yescharacteristic
44C4⋊C4×C241—41no—
45C22⋊C4×C241—22no—
46C42×C241—41no—
47C22×D241—22no—
48C22×D241—42no—
49C22×D241—82no—
50D964—42no—
51D964—41no—
52D964—41no—
53C22⋊D241—82no—
54C22⋊D241—82no—
55C2×Dic241—22no—
56C2×Dic241—42no—
57C23×C241C22⋊C411yescharacteristic
58C23×C241C2×D411yescharacteristic
59C23×C241C2×D411yescharacteristic
60Q8×C241—41no—
61D4×C241—41no—
62D4×C241—41no—
63D4×C241—41no—
64C2×C4×C241—21no—
65C2×C4×C241—21no—
66C2×C4×C241—21no—
67C2×C4×C241—21no—
68C2×C4×C241—21no—
69C2×C4×C241—21no—
70C2×C4×C241—42no—
71C2×C4×C241C22⋊C411yescharacteristic
72C2×C4×C241C22⋊C411yescharacteristic
73C2×C4×C241C22⋊C411yescharacteristic
74C2×C4×C241C22×C411yescharacteristic
75C22×C241—21no—
76C22×C241—21no—
77C22×C241—21no—
78C22×C241—41no—
79C22×C241—41no—
80C22×C241—41no—
81C22×C241C2×C22⋊C411yescharacteristic
82C2×D241—42no—
83C2×D241—42no—
84C2×D241—42no—
85C2×D241—84no—
86C4×C241—21no—
87C4×C241—21no—
88C4×C241—21no—
89C4×C241—82no—
90C4×C241#9911yescharacteristic
91C4×C241#9911yescharacteristic
92Dic241—42no—
93Dic241—82no—
94C2×C241—21no—
95C2×C241—41no—
96C2×C241—41no—
97C2×C241—41no—
98C2×C241C2×#9911yescharacteristic
99D241—82no—
100C241#212811yescharacteristic, complemented, Sylow
101#2128—2411nomaximal, Sylow
102#535—2411no—
103#410—2411no—
104#410D24111yescharacteristic, complemented
105#353—2414no—
106C2×#41C2×D24111yescharacteristic
107C22×D4—2411no—
108#127—2412no—
109#124—2412no—
110#121—4821no—
111#121—4821no—
112#120—4821no—
113#120—4821no—
114#117—21no—
115#117—4821no—
116#117—2411no—
117#99—21no—
118#99—4821no—
119#99—2412no—
120#99C2×D24112yescomplemented
121C24—4821no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D24111yescharacteristic
125C2×D4—9641no—
126C2×D4—9641no—
127C2×D4—4822no—
128C2×D4—4822no—
129C2×D4—4821no—
130C2×D4—2412no—
131C2×D4C22⋊D24111yescharacteristic
132C2×D4D96411yescharacteristic
133C2×D4C22×D24111yescharacteristic
134C22×C4C4×D24111yescharacteristic
135C22×C4C22⋊D24111yescharacteristic
136C22×C4D96411yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—9641no—
139C4⋊C4—4821no—
140C22⋊C4—22no—
141C22⋊C4—4822no—
142C22⋊C4—4821no—
143C22⋊C4—4822no—
144C22⋊C4—4822no—
145C42—41no—
146C42—9641no—
147C42—2412no—
148C23—19282no—
149C23—9642no—
150C23—4822no—
151C23#1683874711yescharacteristic
152C23C2×C22⋊D24111yescharacteristic
153C23C2×D96411yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—19282no—
159D4—19282no—
160D4—9642no—
161D4—9641no—
162D4—9641no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—9642no—
171C2×C4—4822no—
172C2×C4#1683874711yescharacteristic
173C2×C4#1683874711yescharacteristic
174C2×C4#1683874711yescharacteristic
175C2×C4C2×C4×D24111yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—19284no—
183C22—9642no—
184C22—9642no—
185C22—9642no—
186C22C2×#1683874711yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—19282no—
192C4—9642no—
193C4#2144055611yescharacteristic
194C4#2144055611yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—19282no—
200C2C2×#2144055611yescharacteristic
subgroupG/H
centerC2C2×#21440556
commutatorC2×C4×C241C22×C4
FrattiniC2×D4C22×D241
Fitting#410×C241C2
socleC2×C241C2×#99
prime radical#29508281C2
cosocleC2×D4×C241C23
hypercenter#410D241
hypocenterC241#2128
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #29507691C2semidirect
3. #29507509C2semidirect
4. #410×C241C2semidirect
5. C22×D964C4semidirect
7. #21440631C4semidirect
13. #21440601C4semidirect
15. #21440557C22semidirect
19. #99×C241C22semidirect
100. C241#2128semidirect
104. #410D241semidirect
120. #99C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295082812
#295076912
#295075092
#410×C2412
#2128241