Finite Group Databasebeta

← #46782720

Subgroups — #46782720

Order 33664.

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

normal subgroups only

This group has 536 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
1C2×#22554517C211yesmaximal, characteristic
2#30681956C212yesmaximal, complemented
3#30681946C212yesmaximal, complemented
4#30681922C211yesmaximal, characteristic, complemented
5#410×C263C211yesmaximal, characteristic, complemented
6#22554517—24no—
7#22554517—24no—
8C2×#16862376C412yescomplemented
9C2×#16862376C2211yescharacteristic
10C2×#16862375—22no—
11C2×#16862375—21no—
12C22×Dic526C412yescomplemented
13C22×Dic526C2211yescharacteristic
14C2×Q8×D263—21no—
15C2×#16862360C2212yes—
16#22554398—24no—
17#22554393—24no—
18#22554389—21no—
19#22554387—21no—
20C2×#41×C263C2211yescharacteristic
21#117×C263C2212yes—
22#99×C263—22no—
23#16862376—24no—
24#16862376—24no—
25#16862376—22no—
26#16862376D414yes—
27#16862375—216no—
28#16862375—28no—
29C2×Dic526—24no—
30C2×Dic526—24no—
31C2×Dic526—22no—
32C2×Dic526—21no—
33C2×Dic526—22no—
34C2×Dic526C2×C411yescharacteristic
35C2×Dic526C2×C412yes—
36C2×Dic526D414yes—
37Q8×D263—28no—
38C2×D1052C2×C411yescharacteristic
39C2×C22⋊D263—22no—
40C2×C22⋊D263—21no—
41C22×Dic263—22no—
42C22×Dic263—21no—
43C2×C4×D263—22no—
44C2×C4×D263—21no—
45#16862360—22no—
46#16862360—22no—
47C2×C263⋊C8—22no—
48#41×C263—22no—
49#41×C263—22no—
50C2×Q8×C263D411yescharacteristic
51C2×D4×C263D412yes—
52C2×D4×C263D411yescharacteristic
53C22×C4×C263C2×C412yes—
54C22×C4×C263C2311yescharacteristic
55C4⋊C4×C263—22no—
56C22⋊C4×C263—22no—
57C42×C263—22no—
58C22×D263—21no—
59Dic526—28no—
60Dic526—21no—
61Dic526—22no—
62Dic526—24no—
63Dic526C22⋊C412yes—
64Dic526C22⋊C414yes—
65D1052—21no—
66D1052C22⋊C412yes—
67C22⋊D263—28no—
68C22⋊D263—24no—
69C2×Dic263—28no—
70C2×Dic263—22no—
71C2×Dic263—21no—
72C2×Dic263—24no—
73C4×D263—28no—
74C4×D263—24no—
75C263⋊C8—42no—
76C23×C263C22⋊C412yes—
77C23×C263C2×D411yescharacteristic
78Q8×C263—22no—
79D4×C263—24no—
80D4×C263—22no—
81C2×C4×C263—22no—
82C2×C4×C263—22no—
83C2×C4×C263—42no—
84C2×C4×C263C22⋊C412yes—
85C2×C4×C263C22×C411yescharacteristic
86C2×C4×C263C2×D412yes—
87C2×C4×C263C2×D412yes—
88C2×C4×C263C2×D411yescharacteristic
89C22×C263—22no—
90C22×C263—41no—
91C22×C263—42no—
92C22×C263C2×C22⋊C411yescharacteristic
93C22×C263#12012yes—
94C2×D263—22no—
95C2×D263—42no—
96C4×C263—22no—
97C4×C263—82no—
98C4×C263C2×C22⋊C411yescharacteristic
99C4×C263C2×C22⋊C411yescharacteristic
100C4×C263#12012yes—
101Dic263—24no—
102Dic263—22no—
103C2×C263—22no—
104C2×C263—21no—
105C2×C263—42no—
106C2×C263#37911yescharacteristic
107D263—42no—
108C263#179611yescharacteristic, complemented, Sylow
109#1796—2631nomaximal, Sylow
110C2×2−1+4—2631no—
111#421—2632no—
112#419—2632no—
113#413—2631no—
114#410D26311yescharacteristic, complemented
1152−1+4—5264no—
1162−1+4—5264no—
117C2×#41—2632no—
118C2×#41—2631no—
119C2×#41—5262no—
120C2×#41—5261no—
121C2×#41C2×D26311yescharacteristic
122C22×Q8—2632no—
123C22×Q8—2631no—
124C22×Q8—5261no—
125C2×M16—2632no—
126#117C2×D26312yes—
127#104—5264no—
128#103—5264no—
129#101—5261no—
130#100—5261no—
131#99—22no—
132#41—22no—
133#41—22no—
134#41—2634no—
135#41—5264no—
136#41—5264no—
137#41—52616no—
138#41—5268no—
139#41—5262no—
140C2×Q8—2632no—
141C2×Q8—2631no—
142C2×Q8—2634no—
143C2×Q8—5264no—
144C2×Q8—5264no—
145C2×Q8—5268no—
146C2×Q8—5262no—
147C2×Q8—5262no—
148C2×Q8—5261no—
149C2×Q8D105211yescharacteristic
150C2×D4—2631no—
151C2×D4—5262no—
152C2×D4—5261no—
153C2×D4C22⋊D26312yes—
154C2×D4D105211yescharacteristic
155C22×C4—5262no—
156C22×C4—5261no—
157C22×C4—5262no—
158C22×C4—5261no—
159C22×C4C4×D26312yes—
160C22×C4C22×D26311yescharacteristic
161M16—5262no—
162M16—5262no—
163C2×C8—5262no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—5261no—
168C23(C2×D263)⋊C412yes—
169C23C2×C22⋊D26311yescharacteristic
170Q8—22no—
171Q8—2634no—
172Q8—2632no—
173Q8—5268no—
174Q8—5262no—
175Q8—5261no—
176Q8—5264no—
177D4—24no—
178D4—22no—
179D4—2632no—
180D4—5268no—
181D4—5264no—
182D4—5261no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—5268no—
187C2×C4—5268no—
188C2×C4—5261no—
189C2×C4—5262no—
190C2×C4—5264no—
191C2×C4—5264no—
192C2×C4(C2×D263)⋊C412yes—
193C2×C4C2×C4×D26311yescharacteristic
194C2×C4D4×D26312yes—
195C2×C4D4×D26312yes—
196C2×C4C2×D105211yescharacteristic
197C8—10522no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—5262no—
202C22—10522no—
203C22C2×(C2×D263)⋊C411yescharacteristic
204C22#2255443812yes—
205C4—22no—
206C4—82no—
207C4—5264no—
208C4—5262no—
209C4C22⋊C4×D26311yescharacteristic
210C4C22⋊C4×D26311yescharacteristic
211C4#2255444012yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—10522no—
216C2#3068179311yescharacteristic
subgroupG/H
centerC2#30681793
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#410×C263C2
socleC2×C263#379
prime radicalC2×#22554517C2
cosocleC22×C4×C263C23
hypercenter#410D263
hypocenterC263#1796
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #30681956C2semidirect
3. #30681946C2semidirect
4. #30681922C2semidirect
5. #410×C263C2semidirect
8. C2×#16862376C4semidirect
12. C22×Dic526C4semidirect
108. C263#1796semidirect
114. #410D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545172
#306819562
#306819462
#306819222
#410×C2632
#1796263