Finite Group Databasebeta

← #46783271

Subgroups — #46783271

Order 33664.

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

normal subgroups only

This group has 344 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, complemented
2#30682505C211yesmaximal, characteristic
3#30681943C211yesmaximal, characteristic, complemented
4#30681911C211yesmaximal, characteristic, complemented
5#30681695C211yesmaximal, characteristic, complemented
6#30681694C211yesmaximal, characteristic, complemented
7#418×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554478—22no—
10#22554476—22no—
11C2×#16862360C2211yescharacteristic
12M16×D263—22no—
13#22554466C412yescomplemented
14#22554457C412yescomplemented
15#22554441—22no—
16#22554439—22no—
17#22554429C2211yescharacteristic
18#22554429C2211yescharacteristic
19#22554391—22no—
20#22554384—22no—
21C22×D4×C263C2211yescharacteristic
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24#102×C263—22no—
25#16862376—21no—
26#16862376—21no—
27#16862376—21no—
28#16862376—21no—
29C2×Dic526C2×C411yescharacteristic
30C2×D1052C2×C411yescharacteristic
31C2×C22⋊D263—24no—
32C2×C22⋊D263D412yes—
33C2×C4×D263D412yes—
34#16862360—21no—
35#16862360—21no—
36#16862359—24no—
37C2×C263⋊C8D412yescomplemented
38C8×D263—24no—
39C4⋊Dic263—21no—
40C4⋊Dic263—21no—
41C22⋊Dic263—24no—
42C22⋊Dic263—21no—
43C22⋊Dic263—21no—
44C4×Dic263—21no—
45C4×Dic263C2×C412yes—
46C24×C263—21no—
47C2×D4×C263—21no—
48C2×D4×C263—21no—
49C2×D4×C263—21no—
50C2×D4×C263—21no—
51C2×D4×C263—21no—
52C2×D4×C263C2×C412yes—
53C22×C4×C263C2311yescharacteristic
54M16×C263—21no—
55M16×C263—21no—
56C2×C8×C263D412yescomplemented
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—
67C22⋊D263—84no—
68C2×Dic263—22no—
69C2×Dic263—41no—
70C2×Dic263C22⋊C412yes—
71C4×D263—22no—
72C4×D263—22no—
73C263⋊C8—22no—
74C23×C263—22no—
75C23×C263—41no—
76C23×C263—41no—
77C23×C263—82no—
78C23×C263C2×D411yescharacteristic
79D4×C263—22no—
80D4×C263—22no—
81D4×C263—41no—
82D4×C263—41no—
83C2×C4×C263—41no—
84C2×C4×C263C22×C411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C2×C4×C263C2×D411yescharacteristic
88C2×C4×C263#4111yescharacteristic
89C2×C4×C263#4111yescharacteristic
90C8×C263—22no—
91C22×C263—41no—
92C22×C263—44no—
93C22×C263—42no—
94C22×C263—82no—
95C22×C263—82no—
96C22×C263C2×C22⋊C411yescharacteristic
97C22×C263#12111yescharacteristic
98C22×C263#12111yescharacteristic
99C2×D263—22no—
100C2×D263—42no—
101C4×C263—81no—
102C4×C263C4×D411yescharacteristic
103C4×C263C4×D411yescharacteristic
104C4×C263#12011yescharacteristic
105C4×C263#12311yescharacteristic
106Dic263—22no—
107Dic263—42no—
108Dic263—81no—
109C2×C263—21no—
110C2×C263—21no—
111C2×C263—21no—
112C2×C263—82no—
113C2×C263#38611yescharacteristic
114D263—42no—
115C263#191011yescharacteristic, complemented, Sylow
116#1910—2631nomaximal, Sylow
117#568—2631no—
118#535—2631no—
119#418—2631no—
120#418D26311yescharacteristic, complemented
121#410—2631no—
122H(3,ℤ/4)—2631no—
123H(3,ℤ/4)—2631no—
124C2×#41—2631no—
125C22×D4C2×D26311yescharacteristic
126#131—5262no—
127#131—5262no—
128C2×M16—2631no—
129C2×M16—5262no—
130C2×M16C2×D26311yescharacteristic
131#127—2632no—
132#124—2632no—
133#121—5262no—
134#120—5262no—
135#117—2631no—
136#117—2631no—
137#117C2×D26311yescharacteristic
138#102—22no—
139#102—5262no—
140#99—5262no—
141C24—21no—
142#41—5261no—
143#41—5261no—
144#41—5261no—
145#41—5261no—
146C2×Q8—2631no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—2632no—
153C2×D4—2631no—
154C2×D4—5264no—
155C2×D4C4×D26312yes—
156C22×C4—2632no—
157C22×C4C22×D26311yescharacteristic
158M16—21no—
159M16—21no—
160M16—5264no—
161M16—5261no—
162M16—5261no—
163C2×C8—2632no—
164C2×C8—5264no—
165C2×C8C22⋊D26312yescomplemented
166C4⋊C4—21no—
167C4⋊C4—5261no—
168C4⋊C4—5261no—
169C22⋊C4—21no—
170C22⋊C4—5264no—
171C22⋊C4—5261no—
172C22⋊C4—5261no—
173C42—21no—
174C42—2632no—
175C42—5261no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—2632no—
180C23—82no—
181C23D4×D26311yescharacteristic
182Q8—5261no—
183Q8—5261no—
184D4—22no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4—5262no—
189D4—5262no—
190D4—5261no—
191D4—5261no—
192D4—21044no—
193C2×C4—41no—
194C2×C4—2632no—
195C2×C4—5262no—
196C2×C4—5262no—
197C2×C4—5262no—
198C2×C4—10521no—
199C2×C4C2×C4×D26311yescharacteristic
200C2×C4D4×D26311yescharacteristic
201C2×C4D4×D26311yescharacteristic
202C2×C4C2×C22⋊D26311yescharacteristic
203C2×C4#1686237511yescharacteristic
204C2×C4#1686237611yescharacteristic
205C8—22no—
206C8—5262no—
207C22—41no—
208C22—44no—
209C22—42no—
210C22—82no—
211C22—82no—
212C22—5262no—
213C22—10522no—
214C22C22⋊C4×D26311yescharacteristic
215C22#2255444111yescharacteristic
216C22#2255444311yescharacteristic
217C4—81no—
218C4—5262no—
219C4—10522no—
220C4—21041no—
221C4(C22⋊D263)⋊C411yescharacteristic
222C4C4×C22⋊D26311yescharacteristic
223C4#2255443811yescharacteristic
224C4#2255445211yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—82no—
229C2—10522no—
230C2#3068181411yescharacteristic
subgroupG/H
centerC2#30681814
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#418×C263C2
socleC2×C263#386
prime radical#30682505C2
cosocleC22×C4×C263C23
hypercenter#418D263
hypocenterC263#1910
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #30682704C2semidirect
3. #30681943C2semidirect
4. #30681911C2semidirect
5. #30681695C2semidirect
6. #30681694C2semidirect
7. #418×C263C2semidirect
13. #22554466C4semidirect
14. #22554457C4semidirect
37. C2×C263⋊C8D4semidirect
56. C2×C8×C263D4semidirect
115. C263#1910semidirect
120. #418D263semidirect
165. C2×C8C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306827042
#306825052
#306819432
#306819112
#306816952
#306816942
#418×C2632
#1910263