Finite Group Databasebeta

← #46782710

Subgroups — #46782710

Order 33664.

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#30682774C211yesmaximal, characteristic
2#30681954C212yesmaximal, complemented
3#30681935C212yesmaximal, complemented
4#30681912C211yesmaximal, characteristic, complemented
5#408×C263C211yesmaximal, characteristic, complemented
6#22554518C412yescomplemented
7#22554517—22no—
8#22554516—22no—
9#22554515—22no—
10#22554515C412yescomplemented
11C2×#16862376—22no—
12C2×#16862376C2212yes—
13#41×D263—24no—
14#22554429C2212yescomplemented
15#22554396—24no—
16#22554395—22no—
17#22554392—22no—
18#22554385—22no—
19C2×#41×C263C2211yescharacteristic
20C2×M16×C263C2211yescharacteristic, complemented
21C22×C8×C263C2211yescharacteristic, complemented
22C22⋊C8×C263—22no—
23#16862377—24no—
24#16862376—24no—
25#16862376—24no—
26#16862376—24no—
27#16862376—22no—
28#16862376—22no—
29#16862376C2×C414yes—
30#16862376D414yes—
31#16862375—28no—
32#16862375—24no—
33C2×Dic526—22no—
34C2×Dic526D412yes—
35Q8×D263—24no—
36C2×D1052—22no—
37C2×D1052D412yes—
38C2×C22⋊D263—24no—
39C2×C22⋊D263—22no—
40D4×D263—28no—
41D4×D263—24no—
42C2×C4×D263—24no—
43C2×C4×D263—22no—
44C4⋊Dic263—22no—
45C22⋊Dic263—22no—
46C4×Dic263—22no—
47#41×C263—22no—
48#41×C263—22no—
49C2×Q8×C263C2×C411yescharacteristic
50C2×D4×C263C2×C411yescharacteristic
51C2×D4×C263D412yes—
52C22×C4×C263D412yes—
53C22×C4×C263C2311yescharacteristic
54M16×C263—22no—
55C2×C8×C263—22no—
56C2×C8×C263—21no—
57C2×C8×C263—21no—
58C22×D263—24no—
59C22×D263—22no—
60Dic526—24no—
61Dic526—22no—
62Dic526C22⋊C414yes—
63D1052—24no—
64D1052—22no—
65D1052C22⋊C414yes—
66C22⋊D263—28no—
67C22⋊D263—24no—
68C22⋊D263—24no—
69C2×Dic263—24no—
70C2×Dic263—22no—
71C2×Dic263—42no—
72C4×D263—28no—
73C4×D263—24no—
74C4×D263—24no—
75C23×C263C22⋊C412yes—
76C23×C263C2×D411yescharacteristic
77Q8×C263—22no—
78D4×C263—24no—
79D4×C263—22no—
80C2×C4×C263—22no—
81C2×C4×C263—22no—
82C2×C4×C263C22⋊C412yes—
83C2×C4×C263C22×C411yescharacteristic
84C2×C4×C263C2×D412yes—
85C2×C4×C263C2×D412yes—
86C2×C4×C263C2×D411yescharacteristic
87C8×C263—41no—
88C8×C263—41no—
89C22×C263—22no—
90C22×C263—41no—
91C22×C263—42no—
92C22×C263C2×C22⋊C411yescharacteristic
93C22×C263#12012yes—
94C2×D263—24no—
95C2×D263—82no—
96C2×D263—84no—
97C4×C263—22no—
98C4×C263C2×C22⋊C412yes—
99C4×C263#12011yescharacteristic
100C4×C263#12011yescharacteristic
101Dic263—24no—
102Dic263—82no—
103C2×C263—22no—
104C2×C263—21no—
105C2×C263—42no—
106C2×C263#37911yescharacteristic
107D263—44no—
108C263#179411yescharacteristic, complemented, Sylow
109#1794—2631nomaximal, Sylow
110#585—2631no—
111#421—2632no—
112#416—2632no—
113#410—2631no—
114#408D26311yescharacteristic, complemented
1152−1+4—2632no—
1162−1+4—5262no—
117H(5,𝔽2)—2632no—
118H(5,𝔽2)—5262no—
119H(5,𝔽2)—5262no—
120C2×#41—2632no—
121C2×#41—5264no—
122C2×#41—5262no—
123C2×#41C2×D26311yescharacteristic
124C2×M16C2×D26311yescharacteristic, complemented
125C22×C8C2×D26311yescharacteristic, complemented
126#117—2632no—
127#104—5264no—
128#103—5262no—
129#102—5262no—
130#99—5262no—
131C22⋊C8—22no—
132#41—22no—
133#41—22no—
134#41—2634no—
135#41—2634no—
136#41—5264no—
137#41—5264no—
138#41—5264no—
139#41—5268no—
140#41—5264no—
141#41—5264no—
142#41—5262no—
143#41—5262no—
144C2×Q8—2632no—
145C2×Q8—5262no—
146C2×Q8—5264no—
147C2×Q8C4×D26311yescharacteristic
148C2×D4—2632no—
149C2×D4—5262no—
150C2×D4—5264no—
151C2×D4—5268no—
152C2×D4—5264no—
153C2×D4—5262no—
154C2×D4C4×D26311yescharacteristic
155C2×D4D105212yes—
156C22×C4—5264no—
157C22×C4—5262no—
158C22×C4C22⋊D26312yes—
159C22×C4C22×D26311yescharacteristic
160M16—22no—
161C2×C8—22no—
162C2×C8—21no—
163C2×C8—21no—
164C4⋊C4—5262no—
165C22⋊C4—5262no—
166C42—5262no—
167C23—5264no—
168C23—5262no—
169C23(C2×D263)⋊C412yes—
170C23C2×D105211yescharacteristic
171Q8—22no—
172Q8—2634no—
173Q8—5264no—
174Q8—5262no—
175D4—24no—
176D4—22no—
177D4—2634no—
178D4—5264no—
179D4—5268no—
180D4—5264no—
181D4—5264no—
182D4—5262no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—5268no—
186C2×C4—5264no—
187C2×C4—5262no—
188C2×C4—5264no—
189C2×C4—5264no—
190C2×C4—10522no—
191C2×C4(C2×D263)⋊C412yes—
192C2×C4C2×C4×D26311yescharacteristic
193C2×C4D4×D26312yes—
194C2×C4D4×D26312yes—
195C2×C4C2×C22⋊D26311yescharacteristic
196C8—41no—
197C8—41no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—5264no—
202C22—21042no—
203C22—21044no—
204C22C2×(C2×D263)⋊C411yescharacteristic
205C22#2255444012yes—
206C4—22no—
207C4—5264no—
208C4—21042no—
209C4C22⋊C4×D26312yes—
210C4#2255443811yescharacteristic
211C4#2255443811yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—10524no—
216C2#3068179311yescharacteristic
subgroupG/H
centerC4#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#408×C263C2
socleC2×C263#379
prime radical#30682774C2
cosocleC22×C4×C263C23
hypercenter#408D263
hypocenterC263#1794
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #30681954C2semidirect
3. #30681935C2semidirect
4. #30681912C2semidirect
5. #408×C263C2semidirect
6. #22554518C4semidirect
10. #22554515C4semidirect
14. #22554429C22semidirect
20. C2×M16×C263C22semidirect
21. C22×C8×C263C22semidirect
108. C263#1794semidirect
114. #408D263semidirect
124. C2×M16C2×D263semidirect
125. C22×C8C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306827742
#306819542
#306819352
#306819122
#408×C2632
#1794263