Finite Group Databasebeta

← #46783236

Subgroups — #46783236

Order 33664.

346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 93 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#30682413C211yesmaximal, characteristic, complemented
2#30681955C211yesmaximal, characteristic, complemented
3#30681943C211yesmaximal, characteristic, complemented
4#30681912C211yesmaximal, characteristic, complemented
5#30681709C211yesmaximal, characteristic, complemented
6#30681695C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9D4×Dic263—22no—
10D4×Dic263—22no—
11#22554429C2211yescharacteristic
12#22554429C2211yescharacteristic
13#22554429C2211yescharacteristic
14C2×C22⋊Dic263—22no—
15#22554397—22no—
16#22554391—22no—
17#22554385—22no—
18C2×#41×C263C2211yescharacteristic
19C22×D4×C263C2211yescharacteristic
20AGL(1,ℤ/8)×C263—22no—
21AGL(1,ℤ/8)×C263—22no—
22C2×SD16×C263C412yescomplemented
23C2×D8×C263C412yescomplemented
24C2×M16×C263C2211yescharacteristic
25C22×Dic263—24no—
26#16862360—21no—
27#16862360—21no—
28C2×C263⋊C8—21no—
29C4⋊Dic263—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263—21no—
32C22⋊Dic263—24no—
33C22⋊Dic263—21no—
34C22⋊Dic263—21no—
35C22⋊Dic263D412yes—
36C4×Dic263—21no—
37C4×Dic263—21no—
38C4×Dic263D412yes—
39C24×C263—21no—
40#41×C263—21no—
41#41×C263—21no—
42#41×C263—21no—
43#41×C263—21no—
44C2×Q8×C263C2×C411yescharacteristic, complemented
45C2×D4×C263—21no—
46C2×D4×C263—21no—
47C2×D4×C263—21no—
48C2×D4×C263—21no—
49C2×D4×C263C2×C412yes—
50C2×D4×C263C2×C411yescharacteristic, complemented
51C2×D4×C263D412yes—
52C2×D4×C263D412yes—
53C22×C4×C263—21no—
54C22×C4×C263C2311yescharacteristic
55SD16×C263—24no—
56D8×C263—24no—
57M16×C263—21no—
58M16×C263—21no—
59C2×C8×C263C2×C412yescomplemented
60C2×Dic263—22no—
61C2×Dic263—22no—
62C2×Dic263—41no—
63C2×Dic263—84no—
64C263⋊C8—41no—
65C23×C263—22no—
66C23×C263—22no—
67C23×C263—22no—
68C23×C263—21no—
69C23×C263—82no—
70C23×C263C2×D411yescharacteristic
71Q8×C263—21no—
72Q8×C263—21no—
73D4×C263—21no—
74D4×C263—22no—
75D4×C263—21no—
76D4×C263—22no—
77D4×C263—22no—
78D4×C263—41no—
79D4×C263—41no—
80D4×C263C22⋊C414yes—
81C2×C4×C263—21no—
82C2×C4×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—24no—
92C22×C263—41no—
93C22×C263—44no—
94C22×C263—41no—
95C22×C263—82no—
96C22×C263—82no—
97C22×C263—81no—
98C22×C263C4×D411yescharacteristic
99C22×C263#12011yescharacteristic
100C22×C263#12111yescharacteristic
101C4×C263—41no—
102C4×C263C2×C22⋊C411yescharacteristic
103C4×C263C4×D411yescharacteristic
104C4×C263#12111yescharacteristic
105C4×C263#12311yescharacteristic
106Dic263—42no—
107Dic263—42no—
108Dic263—81no—
109C2×C263—21no—
110C2×C263—21no—
111C2×C263—21no—
112C2×C263—44no—
113C2×C263—81no—
114C2×C263#38611yescharacteristic
115C263#190411yescharacteristic, complemented, Sylow
116#1904—2631nomaximal, Sylow
117C2×AGL(1,ℤ/8)D26311yescharacteristic
118#518—2631no—
119#421—2631no—
120#418—2631no—
121#410—2631no—
122#344—2631no—
123H(3,ℤ/4)—2631no—
124C2×#41C2×D26311yescharacteristic
125C22×D4C2×D26311yescharacteristic
126AGL(1,ℤ/8)—22no—
127AGL(1,ℤ/8)—22no—
128C2×SD16Dic26312yescomplemented
129C2×D8Dic26312yescomplemented
130C2×M16—2631no—
131C2×M16C2×D26311yescharacteristic
132C4×D4—5262no—
133C4×D4—5262no—
134#117—2631no—
135#117—2631no—
136#117—2631no—
137C2×C22⋊C4—5262no—
138#104—5262no—
139#102—5262no—
140#99—5262no—
141C24—21no—
142#41—21no—
143#41—21no—
144#41—21no—
145#41—21no—
146C2×Q8C2×Dic26311yescharacteristic, complemented
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4C2×Dic26312yes—
152C2×D4C2×Dic26311yescharacteristic, complemented
153C2×D4C22⋊D26312yes—
154C2×D4C22⋊D26312yes—
155C22×C4—21no—
156C22×C4—5264no—
157C22×C4C22×D26311yescharacteristic
158SD16—24no—
159D8—24no—
160M16—21no—
161M16—21no—
162M16—5261no—
163M16—5261no—
164C2×C8—5261no—
165C2×C8C2×Dic26312yescomplemented
166C4⋊C4—5261no—
167C4⋊C4—5261no—
168C4⋊C4—5261no—
169C22⋊C4—2632no—
170C22⋊C4—5264no—
171C22⋊C4—5261no—
172C22⋊C4—5261no—
173C42—2632no—
174C42—5261no—
175C42—5261no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—21no—
180C23—82no—
181C23D4×D26311yescharacteristic
182Q8—21no—
183Q8—21no—
184D4—21no—
185D4—22no—
186D4—21no—
187D4—22no—
188D4—22no—
189D4—41no—
190D4—41no—
191D4C22⋊Dic26314yes—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—5262no—
196C2×C4—5262no—
197C2×C4—10521no—
198C2×C4—21044no—
199C2×C4C22×Dic26311yescharacteristic
200C2×C4D4×D26311yescharacteristic
201C2×C4C2×C22⋊D26311yescharacteristic
202C2×C4C2×C22⋊D26311yescharacteristic
203C2×C4#1686237511yescharacteristic
204C2×C4#1686237511yescharacteristic
205C8—22no—
206C8—10521no—
207C22—24no—
208C22—41no—
209C22—44no—
210C22—41no—
211C22—82no—
212C22—82no—
213C22—81no—
214C22D4×Dic26311yescharacteristic
215C22#2255443811yescharacteristic
216C22#2255444211yescharacteristic
217C4—41no—
218C4—10522no—
219C4—10522no—
220C4—21041no—
221C4C2×C22⋊Dic26311yescharacteristic
222C4D4×Dic26311yescharacteristic
223C4#2255444211yescharacteristic
224C4#2255445111yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—44no—
229C2—81no—
230C2#3068181811yescharacteristic
subgroupG/H
centerC2#30681818
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting, prime radicalC2×AGL(1,ℤ/8)×C263C2
socleC2×C263#386
cosocleC22×C4×C263C23
hypercenterC2×AGL(1,ℤ/8)D263
hypocenterC263#1904
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30682413C2semidirect
2. #30681955C2semidirect
3. #30681943C2semidirect
4. #30681912C2semidirect
5. #30681709C2semidirect
6. #30681695C2semidirect
22. C2×SD16×C263C4semidirect
23. C2×D8×C263C4semidirect
44. C2×Q8×C263C2×C4semidirect
50. C2×D4×C263C2×C4semidirect
59. C2×C8×C263C2×C4semidirect
115. C263#1904semidirect
128. C2×SD16Dic263semidirect
129. C2×D8Dic263semidirect
146. C2×Q8C2×Dic263semidirect
152. C2×D4C2×Dic263semidirect
165. C2×C8C2×Dic263semidirect

Maximal subgroups

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

subgroupindex
#306824132
#306819552
#306819432
#306819122
#306817092
#306816952
C2×AGL(1,ℤ/8)×C2632
#1904263