Finite Group Databasebeta

← #44507395

Subgroups — #44507395

Order 30848.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#29508553C211yesmaximal, characteristic
2#29507701C211yesmaximal, characteristic, complemented
3#29507699C212yesmaximal, complemented
4#29507683C212yesmaximal, complemented
5#408×C241C211yesmaximal, characteristic, complemented
6#21440690—21no—
7#21440689—22no—
8#21440688—22no—
9#21440687—21no—
10#21440687C414yes—
11C2×#16838770—22no—
12C2×#16838770C2212yes—
13#41×D241—24no—
14C2×#16838754C2212yescomplemented
15#21440561—21no—
16#21440560—22no—
17#21440559—21no—
18#21440558—22no—
19#21440554—24no—
20C2×#41×C241C2211yescharacteristic
21C2×M16×C241C2211yescharacteristic, complemented
22C22×C8×C241C2211yescharacteristic, complemented
23C22⋊C8×C241—22no—
24#16838771—24no—
25#16838770—24no—
26#16838770—24no—
27#16838770—24no—
28#16838770—22no—
29#16838770—22no—
30#16838770—22no—
31#16838770—22no—
32#16838769—24no—
33#16838769—28no—
34C2×Dic482—22no—
35C2×Dic482D412yes—
36Q8×D241—24no—
37C2×D964—22no—
38C2×D964D412yes—
39C2×C22⋊D241—24no—
40C2×C22⋊D241C2×C414yes—
41D4×D241—24no—
42D4×D241—28no—
43C2×C4×D241—24no—
44C2×C4×D241D414yes—
45#16838754—22no—
46#16838754—22no—
47C2×#14515349—22no—
48#41×C241—22no—
49#41×C241—22no—
50C2×Q8×C241D411yescharacteristic
51C2×D4×C241C2×C412yes—
52C2×D4×C241D411yescharacteristic
53C22×C4×C241D412yes—
54C22×C4×C241C2311yescharacteristic
55M16×C241—22no—
56C2×C8×C241—22no—
57C2×C8×C241—21no—
58C2×C8×C241—21no—
59C22×D241—24no—
60C22×D241C22⋊C414yes—
61Dic482—24no—
62Dic482—22no—
63Dic482—22no—
64D964—24no—
65D964—22no—
66D964—22no—
67C22⋊D241—28no—
68C22⋊D241—24no—
69C22⋊D241—24no—
70C2×Dic241—24no—
71C2×Dic241C22⋊C414yes—
72C4×D241—28no—
73C4×D241—24no—
74C4×D241—24no—
75#14515349—42no—
76C23×C241C22⋊C412yes—
77C23×C241C22×C411yescharacteristic
78Q8×C241—22no—
79D4×C241—24no—
80D4×C241—22no—
81C2×C4×C241—22no—
82C2×C4×C241—22no—
83C2×C4×C241C22⋊C412yes—
84C2×C4×C241C2×D412yes—
85C2×C4×C241C2×D412yes—
86C2×C4×C241C2×D411yescharacteristic
87C2×C4×C241C2×D411yescharacteristic
88C8×C241—41no—
89C8×C241—41no—
90C22×C241—22no—
91C22×C241—41no—
92C22×C241—42no—
93C22×C241C2×C22⋊C412yes—
94C22×C241C2×C22⋊C411yescharacteristic
95C2×D241—24no—
96C2×D241—44no—
97C2×D241—84no—
98C4×C241—22no—
99C4×C241#12011yescharacteristic
100C4×C241#12011yescharacteristic
101C4×C241#12012yes—
102Dic241—24no—
103C2×C241—22no—
104C2×C241—21no—
105C2×C241—42no—
106C2×C241#37911yescharacteristic
107D241—44no—
108C241#179111yescharacteristic, complemented, Sylow
109#1791—2411nomaximal, Sylow
110#585—2411no—
111#413—2411no—
112#413—2412no—
113#408—2412no—
114#408D24111yescharacteristic, complemented
1152−1+4—4822no—
1162−1+4—4821no—
117H(5,𝔽2)—4822no—
118H(5,𝔽2)—4821no—
119H(5,𝔽2)—2414no—
120C2×#41—4824no—
121C2×#41—4822no—
122C2×#41—2412no—
123C2×#41C2×D24111yescharacteristic
124C2×M16—2412no—
125C2×M16C2×D24111yescharacteristic, complemented
126C22×C8C2×D24111yescharacteristic, complemented
127#101—4822no—
128#101—4821no—
129#100—4822no—
130#100—4821no—
131C22⋊C8—22no—
132C22⋊C8—4824no—
133#41—22no—
134#41—22no—
135#41—4824no—
136#41—4824no—
137#41—4824no—
138#41—4824no—
139#41—4828no—
140#41—4824no—
141#41—4822no—
142#41—4822no—
143#41—4822no—
144#41—4822no—
145C2×Q8—4822no—
146C2×Q8—4824no—
147C2×Q8—2412no—
148C2×Q8D96411yescharacteristic
149C2×D4—4822no—
150C2×D4—4824no—
151C2×D4—4828no—
152C2×D4—4824no—
153C2×D4—2414no—
154C2×D4—2412no—
155C2×D4C4×D24112yes—
156C2×D4D96411yescharacteristic
157C22×C4—4824no—
158C22×C4—2414no—
159C22×C4C22⋊D24112yes—
160C22×C4C22×D24111yescharacteristic
161M16—22no—
162M16—4822no—
163M16—4822no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—4822no—
168C23—4824no—
169C23—2414no—
170C23#1683874712yes—
171C23C2×C4×D24111yescharacteristic
172Q8—22no—
173Q8—4824no—
174Q8—4822no—
175Q8—4822no—
176D4—24no—
177D4—22no—
178D4—4824no—
179D4—4828no—
180D4—4824no—
181D4—4824no—
182D4—4822no—
183D4—4822no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—4828no—
187C2×C4—4824no—
188C2×C4—4824no—
189C2×C4—4824no—
190C2×C4—2414no—
191C2×C4#1683874712yes—
192C2×C4D4×D24112yes—
193C2×C4D4×D24112yes—
194C2×C4C2×C22⋊D24111yescharacteristic
195C2×C4C2×D96411yescharacteristic
196C8—41no—
197C8—41no—
198C8—9642no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—19284no—
203C22—9644no—
204C22—4824no—
205C22C22⋊C4×D24112yes—
206C22C2×#1683874711yescharacteristic
207C4—22no—
208C4—4824no—
209C4#2144061011yescharacteristic
210C4#2144061011yescharacteristic
211C4#2144061212yes—
212C2—21no—
213C2—22no—
214C2—42no—
215C2—9644no—
216C2#2950757211yescharacteristic
subgroupG/H
centerC4#21440610
commutatorC23×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#408×C241C2
socleC2×C241#379
prime radical#29508553C2
cosocleC22×C4×C241C23
hypercenter#408D241
hypocenterC241#1791
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #29507701C2semidirect
3. #29507699C2semidirect
4. #29507683C2semidirect
5. #408×C241C2semidirect
14. C2×#16838754C22semidirect
21. C2×M16×C241C22semidirect
22. C22×C8×C241C22semidirect
108. C241#1791semidirect
114. #408D241semidirect
125. C2×M16C2×D241semidirect
126. C22×C8C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295085532
#295077012
#295076992
#295076832
#408×C2412
#1791241