Finite Group Databasebeta

← #46783219

Subgroups — #46783219

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×#22554503C211yesmaximal, characteristic
2#30682704C211yesmaximal, characteristic
3#30681956C211yesmaximal, characteristic
4#30681946C211yesmaximal, characteristic, complemented
5C2×#22554388C211yesmaximal, characteristic, complemented
6C263⋊#338C211yesmaximal, characteristic, complemented
7#344×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×Dic526C2211yescharacteristic
10#22554503—22no—
11#22554503—22no—
12C2×Dic1052C412yescomplemented
13C2×#16862365C412yescomplemented
14#22554478—22no—
15#22554476—22no—
16C2×#16862360C2211yescharacteristic
17C2×#16862360C2211yescharacteristic
18M16×D263—22no—
19#22554398—22no—
20#22554393—22no—
21#22554388—22no—
22C2×M16×C263C2211yescharacteristic
23C2×M16×C263C2211yescharacteristic
24#117×C263C2211yescharacteristic
25#16862376—21no—
26#16862376—21no—
27#16862376D412yes—
28#16862376D412yes—
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526—21no—
32C2×Dic526—21no—
33C2×Dic526—21no—
34C2×Dic526C2×C412yes—
35C2×Dic526C2×C411yescharacteristic
36C2×D1052C2×C411yescharacteristic
37C2×C22⋊D263—21no—
38C22×Dic263—21no—
39C2×C4×D263—21no—
40Dic1052—24no—
41#16862365—24no—
42#16862360—21no—
43#16862360—21no—
44#16862360—21no—
45#16862360—21no—
46#16862359—24no—
47C2×C263⋊C8—21no—
48C2×C263⋊C8D412yes—
49C8×D263—24no—
50C22×C4×C263C2311yescharacteristic
51M16×C263—21no—
52M16×C263—21no—
53M16×C263—21no—
54M16×C263D412yes—
55C2×C8×C263—21no—
56C2×C8×C263C2×C412yes—
57C4⋊C4×C263—21no—
58C22⋊C4×C263—21no—
59C42×C263—21no—
60C22×D263—21no—
61Dic526—21no—
62Dic526—22no—
63Dic526—22no—
64Dic526—41no—
65Dic526—41no—
66Dic526C22⋊C412yes—
67D1052—21no—
68D1052C22⋊C412yes—
69C22⋊D263—22no—
70C22⋊D263—22no—
71C2×Dic263—21no—
72C2×Dic263—22no—
73C2×Dic263—41no—
74C2×Dic263—41no—
75C4×D263—22no—
76C4×D263—22no—
77C263⋊C8—22no—
78C263⋊C8—41no—
79C23×C263#4111yescharacteristic
80C2×C4×C263—41no—
81C2×C4×C263C22×C411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C8×C263—22no—
88C8×C263—22no—
89C22×C263—41no—
90C22×C263C4×D411yescharacteristic
91C22×C263#12111yescharacteristic
92C22×C263#12311yescharacteristic
93C2×D263—22no—
94C2×D263—81no—
95C4×C263—81no—
96C4×C263C2×C22⋊C411yescharacteristic
97C4×C263C4×D411yescharacteristic
98C4×C263#12011yescharacteristic
99C4×C263#12111yescharacteristic
100Dic263—22no—
101Dic263—42no—
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#419—2631no—
113C2×#101—2631no—
114#344D26311yescharacteristic, complemented
115#338—2631no—
116C2×#41—2631no—
117C22×Q8—2631no—
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—5262no—
127C2×M16C2×D26311yescharacteristic
128C2×M16C2×D26311yescharacteristic
129#117C2×D26311yescharacteristic
130#104—5262no—
131#103—5262no—
132#101—5262no—
133#41—2632no—
134#41—2632no—
135#41—5261no—
136#41—5261no—
137C2×Q8—2631no—
138C2×Q8—2632no—
139C2×Q8—5261no—
140C2×Q8—5261no—
141C2×Q8—5261no—
142C2×Q8—5261no—
143C2×Q8—5261no—
144C2×D4—2631no—
145C2×D4—5261no—
146C22×C4—5261no—
147C22×C4—5261no—
148C22×C4C22×D26311yescharacteristic
149Q16—5264no—
150SD16—5264no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—5264no—
155M16—5261no—
156M16—5261no—
157M16—5261no—
158M16—5261no—
159M16D105212yes—
160C2×C8—21no—
161C2×C8—2632no—
162C2×C8—5264no—
163C2×C8—5261no—
164C2×C8C4×D26312yes—
165C4⋊C4—21no—
166C22⋊C4—21no—
167C42—21no—
168C23—5261no—
169C23#1686237611yescharacteristic
170Q8—2632no—
171Q8—5261no—
172Q8—5262no—
173Q8—5262no—
174Q8—10521no—
175Q8—10521no—
176D4—2632no—
177D4—5262no—
178D4—5262no—
179D4—5261no—
180C2×C4—41no—
181C2×C4—5261no—
182C2×C4—5262no—
183C2×C4—5262no—
184C2×C4—5262no—
185C2×C4—10521no—
186C2×C4—10521no—
187C2×C4C2×C4×D26311yescharacteristic
188C2×C4D4×D26311yescharacteristic
189C2×C4D4×D26311yescharacteristic
190C2×C4D4×D26311yescharacteristic
191C2×C4C2×D105211yescharacteristic
192C2×C4#1686237711yescharacteristic
193C8—22no—
194C8—22no—
195C8—5262no—
196C8—10521no—
197C22—41no—
198C22—5262no—
199C22—21041no—
200C22C4×D105211yescharacteristic
201C22#2255444311yescharacteristic
202C22#2255445511yescharacteristic
203C4—81no—
204C4—5262no—
205C4—10522no—
206C4C22⋊C4×D26311yescharacteristic
207C4#2255443211yescharacteristic
208C4#2255444011yescharacteristic
209C4#2255444511yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—10522no—
214C2#3068181611yescharacteristic
subgroupG/H
centerC2#30681816
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#344×C263C2
socleC2×C263#386
prime radicalC2×#16862376C22
cosocleC22×C4×C263C23
hypercenter#344D263
hypocenterC263#1902
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. #30681946C2semidirect
5. C2×#22554388C2semidirect
6. C263⋊#338C2semidirect
7. #344×C263C2semidirect
12. C2×Dic1052C4semidirect
13. C2×#16862365C4semidirect
107. C263#1902semidirect
114. #344D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545032
#306827042
#306819562
#306819462
C2×#225543882
C263⋊#3382
#344×C2632
#1902263