Finite Group Databasebeta

← #46783217

Subgroups — #46783217

Order 33664.

304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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×#22554501C211yesmaximal, characteristic
2#30682704C211yesmaximal, characteristic
3#30681956C211yesmaximal, characteristic
4C2×#22554389C211yesmaximal, characteristic, complemented
5#30681708C211yesmaximal, characteristic, complemented
6C263⋊#338C211yesmaximal, characteristic, complemented
7#419×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501—22no—
10#22554501—22no—
11C2×#16862366C412yescomplemented
12C2×#16862363C412yescomplemented
13#22554478—22no—
14#22554476—22no—
15C2×#16862360C2211yescharacteristic
16C2×#16862360C2211yescharacteristic
17C2×#16862360C2211yescharacteristic
18M16×D263—22no—
19#22554398—22no—
20#22554389—22no—
21C22×Q8×C263C2211yescharacteristic
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24#103×C263—22no—
25#16862376—21no—
26#16862376—21no—
27#16862376D412yes—
28#16862376D412yes—
29C2×Dic526C2×C411yescharacteristic
30C2×D1052C2×C411yescharacteristic
31C2×C22⋊D263—21no—
32C2×C4×D263—21no—
33#16862366—24no—
34#16862363—24no—
35#16862360—21no—
36#16862360—21no—
37#16862360—21no—
38#16862360—21no—
39#16862360—21no—
40#16862360D412yes—
41#16862359—24no—
42C2×C263⋊C8—21no—
43C2×C263⋊C8—21no—
44C2×C263⋊C8C2×C412yes—
45C8×D263—24no—
46C2×Q8×C263—21no—
47C2×Q8×C263—21no—
48C2×Q8×C263—21no—
49C2×Q8×C263—21no—
50C2×Q8×C263—21no—
51C2×Q8×C263C2×C412yes—
52C22×C4×C263—21no—
53C22×C4×C263C2311yescharacteristic
54M16×C263—21no—
55M16×C263—21no—
56C2×C8×C263D412yes—
57C4⋊C4×C263—21no—
58C22⋊C4×C263—21no—
59C42×C263—21no—
60C22×D263—21no—
61Dic526—21no—
62Dic526C22⋊C412yes—
63D1052—21no—
64D1052C22⋊C412yes—
65C22⋊D263—22no—
66C22⋊D263—22no—
67C2×Dic263—21no—
68C4×D263—22no—
69C4×D263—22no—
70C263⋊C8—22no—
71C263⋊C8—22no—
72C263⋊C8—41no—
73C23×C263#4111yescharacteristic
74Q8×C263—22no—
75Q8×C263—22no—
76Q8×C263—41no—
77Q8×C263—41no—
78C2×C4×C263—22no—
79C2×C4×C263—41no—
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×C263C2×D411yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C8×C263—22no—
89C22×C263—41no—
90C22×C263C4×D411yescharacteristic
91C22×C263#12111yescharacteristic
92C22×C263#12311yescharacteristic
93C2×D263—22no—
94C2×D263—81no—
95C4×C263—42no—
96C4×C263—81no—
97C4×C263C2×C22⋊C411yescharacteristic
98C4×C263C4×D411yescharacteristic
99C4×C263#12011yescharacteristic
100C4×C263#12111yescharacteristic
101Dic263—22no—
102C2×C263—21no—
103C2×C263—21no—
104C2×C263—21no—
105C2×C263#38611yescharacteristic
106D263—42no—
107C263#190211yescharacteristic, complemented, Sylow
108#1902—2631nomaximal, Sylow
109C2×#137—2631no—
110#568—2631no—
111#421—2631no—
112#419D26311yescharacteristic, complemented
113C2×#101—2631no—
114#344—2631no—
115#338—2631no—
116C2×#41—2631no—
117C22×Q8C2×D26311yescharacteristic
118#137—5262no—
119#137—5262no—
120C2×Q16—2632no—
121C2×SD16—2632no—
122#131—5262no—
123#131—5262no—
124C2×M16—2631no—
125C2×M16—2631no—
126C2×M16—2631no—
127C2×M16—5262no—
128C2×M16C2×D26311yescharacteristic
129#117C2×D26311yescharacteristic
130#104—5262no—
131#103—22no—
132#101—5262no—
133#41—2632no—
134#41—2632no—
135#41—5261no—
136#41—5261no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—2631no—
143C2×Q8C4×D26312yes—
144C2×D4—2631no—
145C2×D4—5261no—
146C22×C4—21no—
147C22×C4—5261no—
148C22×C4C22×D26311yescharacteristic
149Q16—5264no—
150SD16—5264no—
151M16—21no—
152M16—21no—
153M16—2632no—
154M16—5264no—
155M16—5261no—
156M16—5261no—
157M16—5261no—
158M16—5261no—
159M16—5261no—
160C2×C8—2632no—
161C2×C8—5264no—
162C2×C8—5261no—
163C2×C8—5261no—
164C2×C8C22⋊D26312yes—
165C4⋊C4—21no—
166C22⋊C4—21no—
167C42—21no—
168C23—5261no—
169C23#1686237511yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—2632no—
175Q8—5261no—
176D4—2632no—
177D4—5262no—
178D4—5262no—
179D4—5261no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—5261no—
185C2×C4—5262no—
186C2×C4—5262no—
187C2×C4C2×C4×D26311yescharacteristic
188C2×C4D4×D26311yescharacteristic
189C2×C4D4×D26311yescharacteristic
190C2×C4D4×D26311yescharacteristic
191C2×C4C2×C22⋊D26311yescharacteristic
192C2×C4#1686237611yescharacteristic
193C8—22no—
194C8—5262no—
195C8—5262no—
196C8—10521no—
197C22—41no—
198C22—5262no—
199C22—21041no—
200C22(C22⋊D263)⋊C411yescharacteristic
201C22#2255444111yescharacteristic
202C22#2255445211yescharacteristic
203C4—42no—
204C4—81no—
205C4—5262no—
206C4C22⋊C4×D26311yescharacteristic
207C4C4×C22⋊D26311yescharacteristic
208C4#2255443811yescharacteristic
209C4#2255444311yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—10522no—
214C2#3068181411yescharacteristic
subgroupG/H
centerC2#30681814
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#419×C263C2
socleC2×C263#386
prime radicalC2×#16862376C22
cosocleC22×C4×C263C23
hypercenter#419D263
hypocenterC263#1902
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
4. C2×#22554389C2semidirect
5. #30681708C2semidirect
6. C263⋊#338C2semidirect
7. #419×C263C2semidirect
11. C2×#16862366C4semidirect
12. C2×#16862363C4semidirect
107. C263#1902semidirect
112. #419D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545012
#306827042
#306819562
C2×#225543892
#306817082
C263⋊#3382
#419×C2632
#1902263