Finite Group Databasebeta

← #46782722

Subgroups — #46782722

Order 33664.

536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 121 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#30681955C212yesmaximal, complemented
2#30681947C212yesmaximal, complemented
3#30681922C211yesmaximal, characteristic, complemented
4#30681912C211yesmaximal, characteristic, complemented
5C2×2−1+4×C263C211yesmaximal, characteristic
6C2×#16862360C2212yes—
7#22554429C2212yes—
8#22554397—24no—
9#22554394—24no—
10#22554389—21no—
11#22554387—21no—
12#22554385—22no—
132−1+4×C263—24no—
142−1+4×C263—24no—
15C2×#41×C263—21no—
16C2×#41×C263—22no—
17C2×#41×C263C412yescomplemented
18C2×#41×C263C2211yescharacteristic
19C2×#41×C263C2211yescharacteristic
20C22×Q8×C263—21no—
21C22×Q8×C263C412yescomplemented
22C22×Q8×C263C2211yescharacteristic
23#16862360—22no—
24#16862360—22no—
25C2×C263⋊C8—22no—
26C4⋊Dic263—22no—
27C22⋊Dic263—22no—
28C4×Dic263—22no—
29#41×C263—216no—
30#41×C263—28no—
31#41×C263—24no—
32#41×C263—24no—
33#41×C263—22no—
34#41×C263—22no—
35#41×C263—22no—
36#41×C263D414yes—
37C2×Q8×C263—28no—
38C2×Q8×C263—24no—
39C2×Q8×C263—24no—
40C2×Q8×C263—22no—
41C2×Q8×C263—21no—
42C2×Q8×C263—22no—
43C2×Q8×C263C2×C411yescharacteristic
44C2×Q8×C263C2×C412yes—
45C2×Q8×C263D414yes—
46C2×Q8×C263D411yescharacteristic
47C2×D4×C263—22no—
48C2×D4×C263—21no—
49C2×D4×C263C2×C411yescharacteristic
50C2×D4×C263D412yes—
51C2×D4×C263D411yescharacteristic
52C22×C4×C263—22no—
53C22×C4×C263—21no—
54C22×C4×C263—22no—
55C22×C4×C263—21no—
56C22×C4×C263C2×C412yes—
57C22×C4×C263C2311yescharacteristic
58C2×Dic263—42no—
59C263⋊C8—42no—
60C23×C263—21no—
61C23×C263C22⋊C412yes—
62C23×C263C2×D411yescharacteristic
63Q8×C263—28no—
64Q8×C263—21no—
65Q8×C263—22no—
66Q8×C263—24no—
67Q8×C263—22no—
68Q8×C263C22⋊C412yes—
69Q8×C263C22⋊C414yes—
70D4×C263—28no—
71D4×C263—24no—
72D4×C263—24no—
73D4×C263—21no—
74D4×C263—22no—
75D4×C263C22⋊C412yes—
76C2×C4×C263—28no—
77C2×C4×C263—28no—
78C2×C4×C263—21no—
79C2×C4×C263—22no—
80C2×C4×C263—24no—
81C2×C4×C263—22no—
82C2×C4×C263—22no—
83C2×C4×C263—24no—
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—22no—
91C22×C263—41no—
92C22×C263—42no—
93C22×C263—42no—
94C22×C263C2×C22⋊C411yescharacteristic
95C22×C263#12012yes—
96C4×C263—24no—
97C4×C263—22no—
98C4×C263—22no—
99C4×C263C2×C22⋊C411yescharacteristic
100C4×C263C2×C22⋊C411yescharacteristic
101C4×C263#12012yes—
102Dic263—82no—
103C2×C263—22no—
104C2×C263—21no—
105C2×C263—42no—
106C2×C263—42no—
107C2×C263#37911yescharacteristic
108C263#179611yescharacteristic, complemented, Sylow
109#1796—2631nomaximal, Sylow
110C2×2−1+4D26311yescharacteristic
111#421—2632no—
112#419—2632no—
113#413—2631no—
114#410—2631no—
1152−1+4—24no—
1162−1+4—24no—
117C2×#41—21no—
118C2×#41—22no—
119C2×#41Dic26312yescomplemented
120C2×#41C2×D26311yescharacteristic
121C2×#41C2×D26311yescharacteristic
122C22×Q8—21no—
123C22×Q8Dic26312yescomplemented
124C22×Q8C2×D26311yescharacteristic
125C2×M16—2632no—
126#117—2632no—
127#104—5264no—
128#103—5264no—
129#101—5261no—
130#100—5261no—
131#99—5262no—
132#41—216no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—22no—
137#41—22no—
138#41—22no—
139#41C22⋊D26314yes—
140C2×Q8—28no—
141C2×Q8—24no—
142C2×Q8—24no—
143C2×Q8—22no—
144C2×Q8—21no—
145C2×Q8—22no—
146C2×Q8C2×Dic26311yescharacteristic
147C2×Q8C2×Dic26312yes—
148C2×Q8C22⋊D26314yes—
149C2×Q8C22⋊D26311yescharacteristic
150C2×D4—22no—
151C2×D4—21no—
152C2×D4C2×Dic26311yescharacteristic
153C2×D4C22⋊D26312yes—
154C2×D4C22⋊D26311yescharacteristic
155C22×C4—22no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—21no—
159C22×C4C2×Dic26312yes—
160C22×C4C22×D26311yescharacteristic
161M16—5262no—
162M16—5262no—
163C2×C8—5262no—
164C4⋊C4—5262no—
165C22⋊C4—5262no—
166C42—5262no—
167C23—21no—
168C23C22⋊Dic26312yes—
169C23C2×C22⋊D26311yescharacteristic
170Q8—28no—
171Q8—21no—
172Q8—22no—
173Q8—24no—
174Q8—22no—
175Q8C22⋊Dic26312yes—
176Q8C22⋊Dic26314yes—
177D4—28no—
178D4—24no—
179D4—24no—
180D4—21no—
181D4—22no—
182D4C22⋊Dic26312yes—
183C2×C4—28no—
184C2×C4—28no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—10522no—
192C2×C4C22⋊Dic26312yes—
193C2×C4C22×Dic26311yescharacteristic
194C2×C4C2×C22⋊D26312yes—
195C2×C4C2×C22⋊D26312yes—
196C2×C4C2×C22⋊D26311yescharacteristic
197C8—10522no—
198C22—22no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22C2×C22⋊Dic26311yescharacteristic
204C22#2255443912yes—
205C4—24no—
206C4—22no—
207C4—22no—
208C4—21042no—
209C4C2×C22⋊Dic26311yescharacteristic
210C4C2×C22⋊Dic26311yescharacteristic
211C4#2255443912yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—42no—
216C2#3068179411yescharacteristic
subgroupG/H
centerC2#30681794
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting, prime radicalC2×2−1+4×C263C2
socleC2×C263#379
cosocleC22×C4×C263C23
hypercenterC2×2−1+4D263
hypocenterC263#1796
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #30681955C2semidirect
2. #30681947C2semidirect
3. #30681922C2semidirect
4. #30681912C2semidirect
17. C2×#41×C263C4semidirect
21. C22×Q8×C263C4semidirect
108. C263#1796semidirect
119. C2×#41Dic263semidirect
123. C22×Q8Dic263semidirect

Maximal subgroups

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

subgroupindex
#306819552
#306819472
#306819222
#306819122
C2×2−1+4×C2632
#1796263