Finite Group Databasebeta

← #46784024

Subgroups — #46784024

Order 33664.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#30681986C211yesmaximal, characteristic, complemented
2#30681955C211yesmaximal, characteristic
3#30681947C211yesmaximal, characteristic, complemented
4#30681922C211yesmaximal, characteristic
5C2×#22554389C211yesmaximal, characteristic, complemented
6#30681710C211yesmaximal, characteristic, complemented
7C2×#137×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11#22554429C2211yescharacteristic
12#22554405—22no—
13#22554397—22no—
14#22554394—22no—
15#22554389—22no—
16#22554389—21no—
17#22554387—21no—
18C2×#41×C263C2211yescharacteristic
19C22×Q8×C263C2211yescharacteristic
20#137×C263—22no—
21#137×C263—22no—
22C2×Q16×C263—21no—
23C2×SD16×C263—21no—
24C2×M16×C263C2211yescharacteristic
25#16862360—21no—
26#16862360—21no—
27#16862360—21no—
28#16862360—21no—
29#16862360—21no—
30#16862360D412yes—
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C22⋊Dic263—21no—
36C4×Dic263—21no—
37#41×C263—21no—
38#41×C263—21no—
39#41×C263—21no—
40#41×C263—21no—
41C2×Q8×C263—21no—
42C2×Q8×C263—21no—
43C2×Q8×C263—21no—
44C2×Q8×C263—21no—
45C2×Q8×C263—21no—
46C2×Q8×C263D412yes—
47C2×Q8×C263D411yescharacteristic
48C2×D4×C263—21no—
49C2×D4×C263D411yescharacteristic
50C22×C4×C263—21no—
51C22×C4×C263—21no—
52C22×C4×C263C2311yescharacteristic
53Q16×C263—24no—
54SD16×C263—24no—
55M16×C263—21no—
56M16×C263D412yes—
57C2×C8×C263—21no—
58C2×Dic263—41no—
59C263⋊C8—22no—
60C263⋊C8—41no—
61C263⋊C8—41no—
62C23×C263—21no—
63C23×C263#4111yescharacteristic
64Q8×C263—22no—
65Q8×C263—21no—
66Q8×C263—21no—
67Q8×C263—22no—
68Q8×C263—41no—
69Q8×C263—41no—
70D4×C263—21no—
71D4×C263—21no—
72D4×C263—41no—
73D4×C263—41no—
74C2×C4×C263—22no—
75C2×C4×C263—21no—
76C2×C4×C263—41no—
77C2×C4×C263—41no—
78C2×C4×C263—41no—
79C2×C4×C263—41no—
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263#4111yescharacteristic
85C2×C4×C263#4111yescharacteristic
86C8×C263—22no—
87C22×C263—41no—
88C22×C263—41no—
89C22×C263—81no—
90C22×C263#12111yescharacteristic
91C22×C263#12311yescharacteristic
92C22×C263#12411yescharacteristic
93C4×C263—41no—
94C4×C263—42no—
95C4×C263#12011yescharacteristic
96C4×C263#12111yescharacteristic
97C4×C263#12111yescharacteristic
98C4×C263#12311yescharacteristic
99Dic263—81no—
100C2×C263—21no—
101C2×C263—21no—
102C2×C263—21no—
103C2×C263—81no—
104C2×C263#39411yescharacteristic
105C263#204911yescharacteristic, complemented, Sylow
106#2049—2631nomaximal, Sylow
107C2×#137D26311yescharacteristic
108#430—2631no—
109#421—2631no—
110#419—2631no—
111#413—2631no—
112C2×#101—2631no—
113#344—2631no—
114C2×#41C2×D26311yescharacteristic
115C22×Q8C2×D26311yescharacteristic
116#137—22no—
117#137—22no—
118C2×Q16—21no—
119C2×SD16—21no—
120C2×M16—2631no—
121C2×M16—2631no—
122C2×M16—2631no—
123C2×M16C2×D26311yescharacteristic
124#117—2631no—
125#108—5262no—
126#104—5262no—
127#103—5262no—
128#101—5262no—
129#101—5261no—
130#100—5261no—
131#41—21no—
132#41—21no—
133#41—21no—
134#41—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8C22⋊D26311yescharacteristic
141C2×Q8C22⋊D26312yes—
142C2×D4—21no—
143C2×D4C22⋊D26311yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4C22×D26311yescharacteristic
147Q16—24no—
148SD16—24no—
149M16—21no—
150M16—2632no—
151M16—5261no—
152M16—5261no—
153M16—5261no—
154M16—5261no—
155M16—5261no—
156M16C22⋊D26312yes—
157C2×C8—21no—
158C2×C8—5261no—
159C2×C8—5261no—
160C2×C8—5261no—
161C4⋊C4—5261no—
162C22⋊C4—5261no—
163C42—5261no—
164C23—21no—
165C23#1686237511yescharacteristic
166Q8—22no—
167Q8—21no—
168Q8—21no—
169Q8—22no—
170Q8—41no—
171Q8—41no—
172D4—21no—
173D4—21no—
174D4—41no—
175D4—41no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—10521no—
183C2×C4D4×D26311yescharacteristic
184C2×C4C2×C22⋊D26311yescharacteristic
185C2×C4C2×C22⋊D26311yescharacteristic
186C2×C4C2×C22⋊D26311yescharacteristic
187C2×C4#1686237511yescharacteristic
188C2×C4#1686237511yescharacteristic
189C8—22no—
190C8—5262no—
191C8—10521no—
192C8—10521no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22#2255444211yescharacteristic
197C22#2255445111yescharacteristic
198C22#2255445711yescharacteristic
199C4—41no—
200C4—42no—
201C4—21041no—
202C4#2255443911yescharacteristic
203C4#2255444111yescharacteristic
204C4#2255444211yescharacteristic
205C4#2255445111yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—81no—
210C2#3068185211yescharacteristic
subgroupG/H
centerC2#30681852
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#137×C263C2
socleC2×C263#394
prime radicalC2×#41×C263C22
hypercenterC2×#137D263
hypocenterC263#2049
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. #30681986C2semidirect
3. #30681947C2semidirect
5. C2×#22554389C2semidirect
6. #30681710C2semidirect
105. C263#2049semidirect

Maximal subgroups

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

subgroupindex
#306819862
#306819552
#306819472
#306819222
C2×#225543892
#306817102
C2×#137×C2632
#2049263