Finite Group Databasebeta

← #46783266

Subgroups — #46783266

Order 33664.

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

normal subgroups only

This group has 312 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
1#30682704C211yesmaximal, characteristic
2#30682512C211yesmaximal, characteristic
3#30681947C211yesmaximal, characteristic, complemented
4#30681911C211yesmaximal, characteristic
5#30681695C211yesmaximal, characteristic, complemented
6#30681694C211yesmaximal, characteristic, complemented
7#419×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554478—22no—
10#22554476—22no—
11C2×#16862360C2211yescharacteristic
12M16×D263—22no—
13#22554468C412yescomplemented
14#22554459C412yescomplemented
15#22554453—22no—
16#22554446—22no—
17#22554429C2211yescharacteristic
18#22554429C2211yescharacteristic
19#22554394—22no—
20#22554384—22no—
21C22×Q8×C263C2211yescharacteristic
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24#103×C263—22no—
25#16862376—21no—
26#16862376—21no—
27#16862376—21no—
28#16862376—21no—
29C2×Dic526C2×C411yescharacteristic
30C2×D1052C2×C411yescharacteristic
31C2×C22⋊D263D412yes—
32C2×C4×D263D412yes—
33#16862360—21no—
34#16862360—21no—
35#16862359—24no—
36C2×C263⋊C8D412yes—
37C8×D263—24no—
38C4⋊Dic263—21no—
39C4⋊Dic263—21no—
40Dic263⋊C4—24no—
41C22⋊Dic263—21no—
42C22⋊Dic263—21no—
43(C2×D263)⋊C4—24no—
44C4×Dic263—21no—
45C4×Dic263C2×C412yes—
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×D263C22⋊C412yes—
61Dic526—21no—
62Dic526—21no—
63D1052—21no—
64D1052—21no—
65C22⋊D263—22no—
66C22⋊D263—22no—
67C2×Dic263—22no—
68C2×Dic263—41no—
69C2×Dic263C22⋊C412yes—
70C4×D263—22no—
71C4×D263—22no—
72C263⋊C8—22no—
73C23×C263C2×D411yescharacteristic
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×C263#4111yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C8×C263—22no—
89C22×C263—41no—
90C22×C263C2×C22⋊C411yescharacteristic
91C22×C263#12111yescharacteristic
92C22×C263#12111yescharacteristic
93C2×D263—22no—
94C2×D263—42no—
95C4×C263—42no—
96C4×C263—81no—
97C4×C263C4×D411yescharacteristic
98C4×C263C4×D411yescharacteristic
99C4×C263#12011yescharacteristic
100C4×C263#12311yescharacteristic
101Dic263—22no—
102Dic263—42no—
103Dic263—81no—
104C2×C263—21no—
105C2×C263—21no—
106C2×C263—21no—
107C2×C263#38611yescharacteristic
108D263—42no—
109C263#190911yescharacteristic, complemented, Sylow
110#1909—2631nomaximal, Sylow
111#568—2631no—
112#536—2631no—
113#419—2631no—
114#419D26311yescharacteristic, complemented
115#410—2631no—
116H(3,ℤ/4)—2631no—
117H(3,ℤ/4)—2631no—
118C2×#41—2631no—
119C22×Q8C2×D26311yescharacteristic
120#131—5262no—
121#131—5262no—
122C2×M16—2631no—
123C2×M16—5262no—
124C2×M16C2×D26311yescharacteristic
125C4⋊Q8—2632no—
126#124—2632no—
127#123—5262no—
128C22⋊Q8—5262no—
129#117—2631no—
130#117—2631no—
131#117C2×D26311yescharacteristic
132#103—22no—
133#103—5262no—
134#99—5262no—
135#41—5261no—
136#41—5261no—
137#41—5261no—
138#41—5261no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—2631no—
145C2×Q8C4×D26312yes—
146C2×D4—2632no—
147C2×D4—2631no—
148C22×C4—21no—
149C22×C4—2632no—
150C22×C4C22×D26311yescharacteristic
151M16—21no—
152M16—21no—
153M16—5264no—
154M16—5261no—
155M16—5261no—
156C2×C8—2632no—
157C2×C8—5264no—
158C2×C8C22⋊D26312yes—
159C4⋊C4—21no—
160C4⋊C4—5264no—
161C4⋊C4—5261no—
162C4⋊C4—5261no—
163C22⋊C4—21no—
164C22⋊C4—5264no—
165C22⋊C4—5261no—
166C22⋊C4—5261no—
167C42—21no—
168C42—2632no—
169C42—5261no—
170C23—2632no—
171C23D4×D26311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—5261no—
177Q8—5261no—
178D4—5262no—
179D4—5262no—
180D4—5261no—
181D4—5261no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2632no—
187C2×C4—5262no—
188C2×C4—5262no—
189C2×C4—5262no—
190C2×C4—10521no—
191C2×C4C2×C4×D26311yescharacteristic
192C2×C4D4×D26311yescharacteristic
193C2×C4D4×D26311yescharacteristic
194C2×C4C2×C22⋊D26311yescharacteristic
195C2×C4#1686237511yescharacteristic
196C2×C4#1686237611yescharacteristic
197C8—22no—
198C8—5262no—
199C22—41no—
200C22—5262no—
201C22—10522no—
202C22C22⋊C4×D26311yescharacteristic
203C22#2255444111yescharacteristic
204C22#2255444311yescharacteristic
205C4—42no—
206C4—81no—
207C4—5262no—
208C4—10522no—
209C4—21041no—
210C4(C22⋊D263)⋊C411yescharacteristic
211C4C4×C22⋊D26311yescharacteristic
212C4#2255443811yescharacteristic
213C4#2255445211yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—10522no—
218C2#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#1909
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
3. #30681947C2semidirect
5. #30681695C2semidirect
6. #30681694C2semidirect
7. #419×C263C2semidirect
13. #22554468C4semidirect
14. #22554459C4semidirect
109. C263#1909semidirect
114. #419D263semidirect

Maximal subgroups

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

subgroupindex
#306827042
#306825122
#306819472
#306819112
#306816952
#306816942
#419×C2632
#1909263