Finite Group Databasebeta

← #46783215

Subgroups — #46783215

Order 33664.

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

normal subgroups only

This group has 338 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×#22554449C211yesmaximal, characteristic
2C2×#22554388C212yesmaximal, complemented
3#30681902C211yesmaximal, characteristic
4#30681706C212yesmaximal, complemented
5C22×M16×C263C211yesmaximal, characteristic
6C22×Dic526C2211yescharacteristic
7C2×#16862360C2212yes—
8#22554449—21no—
9#22554449—21no—
10#22554449—21no—
11#22554449—21no—
12C2×C4⋊Dic263C2211yescharacteristic
13C2×Dic263⋊C4C412yes—
14C2×C22⋊Dic263C412yes—
15#22554388—24no—
16C22⋊(C263⋊C8)—21no—
17C22⋊(C263⋊C8)—21no—
18C23×C4×C263C2211yescharacteristic
19C2×M16×C263—21no—
20C2×M16×C263—24no—
21C2×M16×C263C2212yes—
22C22×C8×C263—21no—
23C2×Dic526—22no—
24C2×Dic526—21no—
25C2×Dic526—21no—
26C2×Dic526—22no—
27C22×Dic263C2×C412yes—
28C22×Dic263C2×C412yes—
29#16862360—22no—
30#16862360—22no—
31C2×C263⋊C8—22no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34Dic263⋊C4—22no—
35Dic263⋊C4—22no—
36C22⋊Dic263—22no—
37C22⋊Dic263—22no—
38C24×C263C2×C411yescharacteristic
39C22×C4×C263—22no—
40C22×C4×C263—22no—
41C22×C4×C263C2×C411yescharacteristic
42C22×C4×C263D411yescharacteristic
43C22×C4×C263D411yescharacteristic
44C22×C4×C263D411yescharacteristic
45C22×C4×C263D411yescharacteristic
46C22×C4×C263C2311yescharacteristic
47M16×C263—24no—
48M16×C263—22no—
49M16×C263D414yes—
50C2×C8×C263—24no—
51C2×C8×C263—22no—
52Dic526—41no—
53Dic526—42no—
54Dic526—41no—
55C2×Dic263—22no—
56C2×Dic263—22no—
57C2×Dic263—24no—
58C2×Dic263—42no—
59C263⋊C8—42no—
60C23×C263—22no—
61C23×C263—22no—
62C23×C263—41no—
63C23×C263C22⋊C411yescharacteristic
64C23×C263C22⋊C411yescharacteristic
65C23×C263C22×C411yescharacteristic
66C2×C4×C263—22no—
67C2×C4×C263—21no—
68C2×C4×C263—21no—
69C2×C4×C263—22no—
70C2×C4×C263—22no—
71C2×C4×C263—21no—
72C2×C4×C263—21no—
73C2×C4×C263C22⋊C411yescharacteristic
74C2×C4×C263C22⋊C411yescharacteristic
75C2×C4×C263C2×D412yes—
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C2×C4×C263#4112yes—
79C8×C263—24no—
80C22×C263—21no—
81C22×C263—21no—
82C22×C263—21no—
83C22×C263—21no—
84C22×C263—21no—
85C22×C263—21no—
86C22×C263—21no—
87C22×C263—44no—
88C22×C263#10112yescomplemented
89C22×C263C2×C22⋊C411yescharacteristic
90C22×C263C4×D412yes—
91C4×C263—21no—
92C4×C263—21no—
93C4×C263#12011yescharacteristic
94C4×C263#12112yes—
95C4×C263#12311yescharacteristic
96Dic263—42no—
97Dic263—42no—
98C2×C263—22no—
99C2×C263—22no—
100C2×C263—41no—
101C2×C263#38611yescharacteristic
102C2×C263C2×#10111yescharacteristic
103C2×C263#41311yescharacteristic
104C263#190111yescharacteristic, complemented, Sylow
105#1901—2631nomaximal, Sylow
106C22×M16D26311yescharacteristic
107C2×C22⋊Q8—2631no—
108C2×#101—2632no—
109#407—2631no—
110#343—2632no—
111C22×Q8—2631no—
112C23×C4C2×D26311yescharacteristic
113C2×M16—21no—
114C2×M16—24no—
115C2×M16—2632no—
116C2×M16C2×D26312yes—
117C22×C8—21no—
118C22⋊Q8—5261no—
119C22⋊Q8—5261no—
120C22⋊Q8—5261no—
121C22⋊Q8—5261no—
122C2×C4⋊C4—2632no—
123C2×C4⋊C4—2631no—
124C2×C22⋊C4—2632no—
125#101—5264no—
126C22⋊C8—5261no—
127C22⋊C8—5261no—
128C24C4×D26311yescharacteristic
129C2×Q8—5262no—
130C2×Q8—5261no—
131C2×Q8—5261no—
132C2×Q8—5262no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—2632no—
136C22×C4—2632no—
137C22×C4C4×D26311yescharacteristic
138C22×C4C22⋊D26311yescharacteristic
139C22×C4C22⋊D26311yescharacteristic
140C22×C4D105211yescharacteristic
141C22×C4D105211yescharacteristic
142C22×C4C22×D26311yescharacteristic
143M16—24no—
144M16—22no—
145M16—5262no—
146M16—5262no—
147M16C22⋊D26314yes—
148C2×C8—24no—
149C2×C8—22no—
150C2×C8—5262no—
151C4⋊C4—5262no—
152C4⋊C4—5262no—
153C4⋊C4—5261no—
154C4⋊C4—5261no—
155C22⋊C4—5262no—
156C22⋊C4—5262no—
157C23—22no—
158C23—22no—
159C23—41no—
160C23(C2×D263)⋊C411yescharacteristic
161C23(C2×D263)⋊C411yescharacteristic
162C23C2×C4×D26311yescharacteristic
163Q8—10521no—
164Q8—10522no—
165Q8—10521no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—5262no—
174C2×C4—5262no—
175C2×C4—5264no—
176C2×C4—10522no—
177C2×C4(C2×D263)⋊C411yescharacteristic
178C2×C4(C2×D263)⋊C411yescharacteristic
179C2×C4C2×C22⋊D26312yes—
180C2×C4C2×C22⋊D26311yescharacteristic
181C2×C4C2×D105211yescharacteristic
182C2×C4#1686237612yes—
183C8—24no—
184C8—10522no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22#2255438812yescomplemented
194C22C2×(C2×D263)⋊C411yescharacteristic
195C22C4×C22⋊D26312yes—
196C4—21no—
197C4—21no—
198C4—10522no—
199C4—10522no—
200C4#2255443911yescharacteristic
201C4#2255444412yes—
202C4#2255445311yescharacteristic
203C2—22no—
204C2—22no—
205C2—41no—
206C2#3068181711yescharacteristic
207C2C2×#2255438811yescharacteristic
208C2#3068192011yescharacteristic
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
FittingC22×M16×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC24×C263C2×C4
cosocleC22×C4×C263C23
hypercenterC22×M16D263
hypocenterC263#1901
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#22554388C2semidirect
4. #30681706C2semidirect
88. C22×C263#101semidirect
104. C263#1901semidirect
193. C22#22554388semidirect

Maximal subgroups

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

subgroupindex
C2×#225544492
C2×#225543882
#306819022
#306817062
C22×M16×C2632
#1901263