Finite Group Databasebeta

← #46782697

Subgroups — #46782697

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#30681922C211yesmaximal, characteristic, complemented
3#30681920C212yesmaximal, complemented
4#30681904C212yesmaximal, complemented
5#408×C263C211yesmaximal, characteristic, complemented
6#22554518—21no—
7#22554517—22no—
8#22554516—22no—
9#22554515—21no—
10#22554515C414yes—
11C2×#16862376—22no—
12C2×#16862376C2212yes—
13#41×D263—24no—
14C2×#16862360C2212yescomplemented
15#22554389—21no—
16#22554388—22no—
17#22554387—21no—
18#22554386—22no—
19(C2×D263)⋊C8—24no—
20C2×#41×C263C2211yescharacteristic
21C2×M16×C263C2211yescharacteristic, complemented
22C22×C8×C263C2211yescharacteristic, complemented
23C22⋊C8×C263—22no—
24#16862377—24no—
25#16862376—24no—
26#16862376—24no—
27#16862376—24no—
28#16862376—22no—
29#16862376—22no—
30#16862376—22no—
31#16862376—22no—
32#16862375—24no—
33#16862375—28no—
34C2×Dic526—22no—
35C2×Dic526D412yes—
36Q8×D263—24no—
37C2×D1052—22no—
38C2×D1052D412yes—
39C2×C22⋊D263—24no—
40C2×C22⋊D263C2×C414yes—
41D4×D263—24no—
42D4×D263—28no—
43C2×C4×D263—24no—
44C2×C4×D263D414yes—
45#16862360—22no—
46#16862360—22no—
47C2×C263⋊C8—22no—
48#41×C263—22no—
49#41×C263—22no—
50C2×Q8×C263D411yescharacteristic
51C2×D4×C263C2×C412yes—
52C2×D4×C263D411yescharacteristic
53C22×C4×C263D412yes—
54C22×C4×C263C2311yescharacteristic
55M16×C263—22no—
56C2×C8×C263—22no—
57C2×C8×C263—21no—
58C2×C8×C263—21no—
59C22×D263—24no—
60C22×D263C22⋊C414yes—
61Dic526—24no—
62Dic526—22no—
63Dic526—22no—
64D1052—24no—
65D1052—22no—
66D1052—22no—
67C22⋊D263—28no—
68C22⋊D263—24no—
69C22⋊D263—24no—
70C2×Dic263—24no—
71C2×Dic263C22⋊C414yes—
72C4×D263—28no—
73C4×D263—24no—
74C4×D263—24no—
75C263⋊C8—42no—
76C23×C263C22⋊C412yes—
77C23×C263C22×C411yescharacteristic
78Q8×C263—22no—
79D4×C263—24no—
80D4×C263—22no—
81C2×C4×C263—22no—
82C2×C4×C263—22no—
83C2×C4×C263C22⋊C412yes—
84C2×C4×C263C2×D412yes—
85C2×C4×C263C2×D412yes—
86C2×C4×C263C2×D411yescharacteristic
87C2×C4×C263C2×D411yescharacteristic
88C8×C263—41no—
89C8×C263—41no—
90C22×C263—22no—
91C22×C263—41no—
92C22×C263—42no—
93C22×C263C2×C22⋊C412yes—
94C22×C263C2×C22⋊C411yescharacteristic
95C2×D263—24no—
96C2×D263—44no—
97C2×D263—84no—
98C4×C263—22no—
99C4×C263#12011yescharacteristic
100C4×C263#12011yescharacteristic
101C4×C263#12012yes—
102Dic263—24no—
103C2×C263—22no—
104C2×C263—21no—
105C2×C263—42no—
106C2×C263#37911yescharacteristic
107D263—44no—
108C263#179111yescharacteristic, complemented, Sylow
109#1791—2631nomaximal, Sylow
110#585—2631no—
111#413—2631no—
112#413—2632no—
113#408—2632no—
114#408D26311yescharacteristic, complemented
1152−1+4—5262no—
1162−1+4—5261no—
117H(5,𝔽2)—2634no—
118H(5,𝔽2)—5262no—
119H(5,𝔽2)—5261no—
120C2×#41—2632no—
121C2×#41—5264no—
122C2×#41—5262no—
123C2×#41C2×D26311yescharacteristic
124C2×M16—2632no—
125C2×M16C2×D26311yescharacteristic, complemented
126C22×C8C2×D26311yescharacteristic, complemented
127#101—5262no—
128#101—5261no—
129#100—5262no—
130#100—5261no—
131C22⋊C8—22no—
132C22⋊C8—5264no—
133#41—22no—
134#41—22no—
135#41—5264no—
136#41—5264no—
137#41—5268no—
138#41—5264no—
139#41—5264no—
140#41—5264no—
141#41—5262no—
142#41—5262no—
143#41—5262no—
144#41—5262no—
145C2×Q8—2632no—
146C2×Q8—5262no—
147C2×Q8—5264no—
148C2×Q8D105211yescharacteristic
149C2×D4—2634no—
150C2×D4—2632no—
151C2×D4—5262no—
152C2×D4—5268no—
153C2×D4—5264no—
154C2×D4—5264no—
155C2×D4C4×D26312yes—
156C2×D4D105211yescharacteristic
157C22×C4—2634no—
158C22×C4—5264no—
159C22×C4C22⋊D26312yes—
160C22×C4C22×D26311yescharacteristic
161M16—22no—
162M16—5262no—
163M16—5262no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—5262no—
168C23—2634no—
169C23—5264no—
170C23(C2×D263)⋊C412yes—
171C23C2×C4×D26311yescharacteristic
172Q8—22no—
173Q8—5264no—
174Q8—5262no—
175Q8—5262no—
176D4—24no—
177D4—22no—
178D4—5264no—
179D4—5268no—
180D4—5264no—
181D4—5264no—
182D4—5262no—
183D4—5262no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—2634no—
187C2×C4—5268no—
188C2×C4—5264no—
189C2×C4—5264no—
190C2×C4—5264no—
191C2×C4(C2×D263)⋊C412yes—
192C2×C4D4×D26312yes—
193C2×C4D4×D26312yes—
194C2×C4C2×C22⋊D26311yescharacteristic
195C2×C4C2×D105211yescharacteristic
196C8—41no—
197C8—41no—
198C8—10522no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—5264no—
203C22—10524no—
204C22—21044no—
205C22C22⋊C4×D26312yes—
206C22C2×(C2×D263)⋊C411yescharacteristic
207C4—22no—
208C4—5264no—
209C4#2255443811yescharacteristic
210C4#2255443811yescharacteristic
211C4#2255444012yes—
212C2—21no—
213C2—22no—
214C2—42no—
215C2—10524no—
216C2#3068179311yescharacteristic
subgroupG/H
centerC4#22554438
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#408×C263C2
socleC2×C263#379
prime radical#30682774C2
cosocleC22×C4×C263C23
hypercenter#408D263
hypocenterC263#1791
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #30681922C2semidirect
3. #30681920C2semidirect
4. #30681904C2semidirect
5. #408×C263C2semidirect
14. C2×#16862360C22semidirect
21. C2×M16×C263C22semidirect
22. C22×C8×C263C22semidirect
108. C263#1791semidirect
114. #408D263semidirect
125. C2×M16C2×D263semidirect
126. C22×C8C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306827742
#306819222
#306819202
#306819042
#408×C2632
#1791263