Finite Group Databasebeta

← #44509136

Subgroups — #44509136

Order 30848.

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

normal subgroups only

This group has 262 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#29507701C211yesmaximal, characteristic, complemented
3#29507513C214yesmaximal, complemented
4#413×C241C211yesmaximal, characteristic, complemented
5C22×D964C411yescharacteristic
6C2×#16838754—21no—
7#21440638C412yes—
8#21440631C2212yes—
9#21440616—21no—
10#21440616—21no—
11#21440610—21no—
12#21440610—21no—
13#21440601C411yescharacteristic
14#21440561C2212yescomplemented
15#21440559—21no—
16C2×#41×C241C2211yescharacteristic
17C2×M16×C241—21no—
18#101×C241C2212yescomplemented
19#100×C241—21no—
20C23×D241—21no—
21C2×D964—21no—
22C2×D964—41no—
23C2×D964—41no—
24C2×D964C2×C412yes—
25C2×C22⋊D241—22no—
26C2×C22⋊D241—22no—
27#16838754—22no—
28#16838754—41no—
29C2×#14515349—41no—
30C4⋊Dic241—21no—
31C22⋊Dic241—21no—
32#16838747—22no—
33#16838747—22no—
34C4×Dic241C2×C412yes—
35#41×C241—41no—
36#41×C241—41no—
37C2×Q8×C241C2311yescharacteristic
38C2×D4×C241C2×C411yescharacteristic
39C2×D4×C241D411yescharacteristic
40C2×D4×C241D411yescharacteristic
41C22×C4×C241C2×C411yescharacteristic
42C22×C4×C241D411yescharacteristic
43C22×C4×C241D411yescharacteristic
44M16×C241—22no—
45M16×C241—41no—
46C2×C8×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—
56#14515349—42no—
57C23×C241C22⋊C411yescharacteristic
58C23×C241C22⋊C411yescharacteristic
59C23×C241C22⋊C411yescharacteristic
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×C241C22⋊C411yescharacteristic
71C2×C4×C241C22×C411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C2×C4×C241C2×D411yescharacteristic
74C8×C241—42no—
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#9911yescharacteristic
90C4×C241#9911yescharacteristic
91Dic241—42no—
92C2×C241—21no—
93C2×C241—41no—
94C2×C241—41no—
95C2×C241—41no—
96C2×C241C2×#9911yescharacteristic
97D241—82no—
98C241#213411yescharacteristic, complemented, Sylow
99#2134—2411nomaximal, Sylow
100#535—2411no—
101#413—2411no—
102#413D24111yescharacteristic, complemented
103#355—2414no—
104C2×#41C2×D24111yescharacteristic
105C22×D4—2411no—
106C2×M16—21no—
107C2×M16—4821no—
108#127—2412no—
109#124—2412no—
110#121—4821no—
111#121—4821no—
112#120—4821no—
113#120—4821no—
114#117—2411no—
115#101—2412no—
116#101C2×D24112yescomplemented
117#100—21no—
118#100—4821no—
119C24—4821no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D24111yescharacteristic
123C2×D4—9641no—
124C2×D4—9641no—
125C2×D4—4822no—
126C2×D4—4822no—
127C2×D4—4821no—
128C2×D4—2412no—
129C2×D4C4×D24111yescharacteristic
130C2×D4C22⋊D24111yescharacteristic
131C2×D4D96411yescharacteristic
132C22×C4C4×D24111yescharacteristic
133C22×C4C22⋊D24111yescharacteristic
134C22×C4D96411yescharacteristic
135M16—22no—
136M16—41no—
137M16—9641no—
138M16—4822no—
139C2×C8—41no—
140C2×C8—9641no—
141C4⋊C4—4821no—
142C22⋊C4—4821no—
143C22⋊C4—4822no—
144C22⋊C4—4822no—
145C42—2412no—
146C23—19282no—
147C23—9642no—
148C23—4822no—
149C23#1683874711yescharacteristic
150C23#1683874711yescharacteristic
151C23#1683874711yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—19282no—
157D4—19282no—
158D4—9642no—
159D4—9641no—
160D4—9641no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—4822no—
168C2×C4#1683874711yescharacteristic
169C2×C4C2×C4×D24111yescharacteristic
170C2×C4C2×C22⋊D24111yescharacteristic
171C2×C4C2×D96411yescharacteristic
172C8—42no—
173C8—9642no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—19284no—
181C22—9642no—
182C22—9642no—
183C22—9642no—
184C22C2×#1683874711yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—9642no—
189C4#2144055611yescharacteristic
190C4#2144055611yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—19282no—
196C2C2×#2144055611yescharacteristic
subgroupG/H
centerC2C2×#21440556
commutatorC2×C4×C241C22×C4
FrattiniC2×Q8C22×D241
Fitting#413×C241C2
socleC2×C241C2×#99
prime radical#29508281C2
cosocleC2×Q8×C241C23
hypercenter#413D241
hypocenterC241#2134
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #29507701C2semidirect
3. #29507513C2semidirect
4. #413×C241C2semidirect
14. #21440561C22semidirect
18. #101×C241C22semidirect
98. C241#2134semidirect
102. #413D241semidirect
116. #101C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295082812
#295077012
#295075132
#413×C2412
#2134241