Finite Group Databasebeta

← #46783243

Subgroups — #46783243

Order 33664.

310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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#30682416C211yesmaximal, characteristic, complemented
2#30681955C211yesmaximal, characteristic
3#30681947C211yesmaximal, characteristic, complemented
4#30681912C211yesmaximal, characteristic
5#30681709C211yesmaximal, characteristic, complemented
6#30681695C211yesmaximal, characteristic, complemented
7C2×#137×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9Q8×Dic263—22no—
10Q8×Dic263—22no—
11#22554429—22no—
12#22554429C2211yescharacteristic
13#22554429C2211yescharacteristic
14#22554429C2211yescharacteristic
15#22554397—22no—
16#22554394—22no—
17#22554385—22no—
18C2×#41×C263C2211yescharacteristic
19C22×Q8×C263C2211yescharacteristic
20#137×C263—22no—
21#137×C263—22no—
22C2×Q16×C263C412yescomplemented
23C2×SD16×C263C412yescomplemented
24C2×M16×C263C2211yescharacteristic
25#16862360—21no—
26#16862360—21no—
27C2×C263⋊C8—21no—
28C4⋊Dic263—24no—
29C4⋊Dic263—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263—21no—
32C22⋊Dic263—21no—
33C22⋊Dic263—21no—
34C22⋊Dic263D412yes—
35C4×Dic263—24no—
36C4×Dic263—21no—
37C4×Dic263—21no—
38C4×Dic263D412yes—
39#41×C263—21no—
40#41×C263—21no—
41#41×C263—21no—
42#41×C263—21no—
43C2×Q8×C263—21no—
44C2×Q8×C263—21no—
45C2×Q8×C263—21no—
46C2×Q8×C263C2×C411yescharacteristic
47C2×Q8×C263C2×C412yes—
48C2×Q8×C263D412yes—
49C2×Q8×C263D412yes—
50C2×D4×C263—21no—
51C2×D4×C263C2×C411yescharacteristic
52C22×C4×C263—21no—
53C22×C4×C263—21no—
54C22×C4×C263C2311yescharacteristic
55Q16×C263—24no—
56SD16×C263—24no—
57M16×C263—21no—
58M16×C263—21no—
59C2×C8×C263C2×C412yes—
60C2×Dic263—22no—
61C2×Dic263—22no—
62C2×Dic263—41no—
63C263⋊C8—41no—
64C23×C263—21no—
65C23×C263C2×D411yescharacteristic
66Q8×C263—22no—
67Q8×C263—22no—
68Q8×C263—22no—
69Q8×C263—21no—
70Q8×C263—21no—
71Q8×C263C22⋊C414yes—
72D4×C263—21no—
73D4×C263—21no—
74D4×C263—41no—
75D4×C263—41no—
76C2×C4×C263—22no—
77C2×C4×C263—22no—
78C2×C4×C263—22no—
79C2×C4×C263—21no—
80C2×C4×C263—41no—
81C2×C4×C263—41no—
82C2×C4×C263C22×C411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C8×C263—22no—
89C22×C263—41no—
90C22×C263—41no—
91C22×C263—81no—
92C22×C263C4×D411yescharacteristic
93C22×C263#12011yescharacteristic
94C22×C263#12111yescharacteristic
95C4×C263—24no—
96C4×C263—41no—
97C4×C263C2×C22⋊C411yescharacteristic
98C4×C263C4×D411yescharacteristic
99C4×C263#12111yescharacteristic
100C4×C263#12311yescharacteristic
101Dic263—42no—
102Dic263—42no—
103Dic263—81no—
104C2×C263—21no—
105C2×C263—21no—
106C2×C263—21no—
107C2×C263—81no—
108C2×C263#38611yescharacteristic
109C263#190511yescharacteristic, complemented, Sylow
110#1905—2631nomaximal, Sylow
111C2×#137D26311yescharacteristic
112#519—2631no—
113#421—2631no—
114#419—2631no—
115#410—2631no—
116#344—2631no—
117H(3,ℤ/4)—2631no—
118C2×#41C2×D26311yescharacteristic
119C22×Q8C2×D26311yescharacteristic
120#137—22no—
121#137—22no—
122C2×Q16Dic26312yescomplemented
123C2×SD16Dic26312yescomplemented
124C2×M16—2631no—
125C2×M16C2×D26311yescharacteristic
126C4×Q8—5262no—
127C4×Q8—5262no—
128#117—2631no—
129#117—2631no—
130#117—2631no—
131#117—5262no—
132#104—5262no—
133#103—5262no—
134#99—5262no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C2×Dic26311yescharacteristic
143C2×Q8C2×Dic26312yes—
144C2×Q8C22⋊D26312yes—
145C2×Q8C22⋊D26312yes—
146C2×D4—21no—
147C2×D4C2×Dic26311yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4C22×D26311yescharacteristic
151Q16—24no—
152SD16—24no—
153M16—21no—
154M16—21no—
155M16—5261no—
156M16—5261no—
157C2×C8—5261no—
158C2×C8C2×Dic26312yes—
159C4⋊C4—5264no—
160C4⋊C4—5261no—
161C4⋊C4—5261no—
162C4⋊C4—5261no—
163C22⋊C4—2632no—
164C22⋊C4—5261no—
165C22⋊C4—5261no—
166C42—2632no—
167C42—5264no—
168C42—5261no—
169C42—5261no—
170C23—21no—
171C23D4×D26311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—21no—
176Q8—21no—
177Q8C22⋊Dic26314yes—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—5262no—
189C2×C4—5262no—
190C2×C4—10521no—
191C2×C4C22×Dic26311yescharacteristic
192C2×C4D4×D26311yescharacteristic
193C2×C4C2×C22⋊D26311yescharacteristic
194C2×C4C2×C22⋊D26311yescharacteristic
195C2×C4#1686237511yescharacteristic
196C2×C4#1686237511yescharacteristic
197C8—22no—
198C8—10521no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22D4×Dic26311yescharacteristic
203C22#2255443811yescharacteristic
204C22#2255444211yescharacteristic
205C4—24no—
206C4—41no—
207C4—10522no—
208C4—10522no—
209C4—21041no—
210C4C2×C22⋊Dic26311yescharacteristic
211C4D4×Dic26311yescharacteristic
212C4#2255444211yescharacteristic
213C4#2255445111yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#3068181811yescharacteristic
subgroupG/H
centerC2#30681818
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#137×C263C2
socleC2×C263#386
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenterC2×#137D263
hypocenterC263#1905
LCSG ▷ C2×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. #30682416C2semidirect
3. #30681947C2semidirect
5. #30681709C2semidirect
6. #30681695C2semidirect
22. C2×Q16×C263C4semidirect
23. C2×SD16×C263C4semidirect
109. C263#1905semidirect
122. C2×Q16Dic263semidirect
123. C2×SD16Dic263semidirect

Maximal subgroups

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

subgroupindex
#306824162
#306819552
#306819472
#306819122
#306817092
#306816952
C2×#137×C2632
#1905263