Finite Group Databasebeta

← #46783229

Subgroups — #46783229

Order 33664.

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

normal subgroups only

This group has 324 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#30682705C211yesmaximal, characteristic, complemented
2#30681955C211yesmaximal, characteristic, complemented
3#30681943C211yesmaximal, characteristic, complemented
4C2×#22554387C211yesmaximal, characteristic, complemented
5#30681709C211yesmaximal, characteristic, complemented
6C263⋊#338C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C263C211yesmaximal, characteristic
8#22554477—22no—
9#22554477—22no—
10C2×#16862360—22no—
11C2×#16862360C2211yescharacteristic
12C2×#16862360C2211yescharacteristic
13C2×#16862360C2211yescharacteristic
14#22554429C2211yescharacteristic
15#22554397—22no—
16#22554391—22no—
17#22554387—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
25#16862360—24no—
26#16862360—21no—
27#16862360—21no—
28#16862360—21no—
29#16862360—21no—
30#16862360—21no—
31#16862360D412yes—
32C2×C263⋊C8—24no—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C2×C263⋊C8D412yes—
36C4⋊Dic263—21no—
37C22⋊Dic263—21no—
38C4×Dic263—21no—
39C24×C263—21no—
40#41×C263—21no—
41#41×C263—21no—
42#41×C263D412yes—
43#41×C263D412yes—
44C2×Q8×C263C2×C411yescharacteristic
45C2×D4×C263—21no—
46C2×D4×C263—21no—
47C2×D4×C263—21no—
48C2×D4×C263—21no—
49C2×D4×C263—21no—
50C2×D4×C263—21no—
51C2×D4×C263C2×C412yes—
52C2×D4×C263C2×C411yescharacteristic
53C22×C4×C263—21no—
54C22×C4×C263C2311yescharacteristic
55SD16×C263—24no—
56D8×C263—24no—
57M16×C263—21no—
58M16×C263—21no—
59C2×C8×C263C2×C412yes—
60C2×Dic263—41no—
61C263⋊C8—22no—
62C263⋊C8—22no—
63C263⋊C8—41no—
64C23×C263—21no—
65C23×C263—22no—
66C23×C263—41no—
67C23×C263—41no—
68C23×C263—82no—
69C23×C263#4111yescharacteristic
70Q8×C263—21no—
71Q8×C263C22⋊C412yes—
72D4×C263—22no—
73D4×C263—22no—
74D4×C263—22no—
75D4×C263—21no—
76D4×C263—22no—
77D4×C263—41no—
78D4×C263—41no—
79D4×C263C22⋊C412yes—
80C2×C4×C263—21no—
81C2×C4×C263—22no—
82C2×C4×C263—22no—
83C2×C4×C263C22×C411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C2×C4×C263C2×D411yescharacteristic
88C2×C4×C263#4111yescharacteristic
89C8×C263—22no—
90C22×C263—22no—
91C22×C263—41no—
92C22×C263—42no—
93C22×C263—81no—
94C22×C263—82no—
95C22×C263—82no—
96C22×C263—82no—
97C22×C263C4×D411yescharacteristic
98C22×C263#12111yescharacteristic
99C22×C263#12311yescharacteristic
100C4×C263—22no—
101C4×C263C2×C22⋊C411yescharacteristic
102C4×C263C4×D411yescharacteristic
103C4×C263#12011yescharacteristic
104C4×C263#12111yescharacteristic
105Dic263—81no—
106C2×C263—21no—
107C2×C263—21no—
108C2×C263—21no—
109C2×C263—42no—
110C2×C263—82no—
111C2×C263#38611yescharacteristic
112C263#190311yescharacteristic, complemented, Sylow
113#1903—2631nomaximal, Sylow
114C2×AGL(1,ℤ/8)D26311yescharacteristic
115#568—2631no—
116#421—2631no—
117#418—2631no—
118C2×#100—2631no—
119#344—2631no—
120#338—2631no—
121C2×#41C2×D26311yescharacteristic
122C22×D4C2×D26311yescharacteristic
123AGL(1,ℤ/8)—22no—
124AGL(1,ℤ/8)—22no—
125C2×SD16Dic26312yescomplemented
126C2×D8Dic26312yescomplemented
127#131—5262no—
128#131—5262no—
129C2×M16—2631no—
130C2×M16—2631no—
131C2×M16—2631no—
132C2×M16—5262no—
133C2×M16C2×D26311yescharacteristic
134#117—2631no—
135#104—5262no—
136#102—5262no—
137#100—5262no—
138C24—21no—
139#41—21no—
140#41—21no—
141#41C22⋊D26312yes—
142#41C22⋊D26312yes—
143C2×Q8C2×Dic26311yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4C2×Dic26312yes—
151C2×D4C2×Dic26311yescharacteristic
152C22×C4—21no—
153C22×C4C22×D26311yescharacteristic
154SD16—24no—
155D8—24no—
156M16—21no—
157M16—21no—
158M16—2632no—
159M16—5264no—
160M16—5261no—
161M16—5261no—
162M16—5261no—
163M16—5261no—
164M16—5261no—
165C2×C8—2632no—
166C2×C8—5264no—
167C2×C8—5261no—
168C2×C8—5261no—
169C2×C8C2×Dic26312yes—
170C4⋊C4—5261no—
171C22⋊C4—5261no—
172C42—5261no—
173C23—21no—
174C23—22no—
175C23—41no—
176C23—41no—
177C23—82no—
178C23#1686237511yescharacteristic
179Q8—21no—
180Q8C22⋊Dic26312yes—
181D4—22no—
182D4—22no—
183D4—22no—
184D4—21no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4C22⋊Dic26312yes—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—10521no—
193C2×C4C22×Dic26311yescharacteristic
194C2×C4D4×D26311yescharacteristic
195C2×C4D4×D26311yescharacteristic
196C2×C4C2×C22⋊D26311yescharacteristic
197C2×C4C2×C22⋊D26311yescharacteristic
198C2×C4#1686237511yescharacteristic
199C8—22no—
200C8—5262no—
201C8—5262no—
202C8—10521no—
203C22—22no—
204C22—41no—
205C22—42no—
206C22—81no—
207C22—82no—
208C22—82no—
209C22—82no—
210C22D4×Dic26311yescharacteristic
211C22#2255444211yescharacteristic
212C22#2255445111yescharacteristic
213C4—22no—
214C4—21041no—
215C4C2×C22⋊Dic26311yescharacteristic
216C4D4×Dic26311yescharacteristic
217C4#2255443811yescharacteristic
218C4#2255444211yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—82no—
224C2#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#1903
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. #30682705C2semidirect
2. #30681955C2semidirect
3. #30681943C2semidirect
4. C2×#22554387C2semidirect
5. #30681709C2semidirect
6. C263⋊#338C2semidirect
22. C2×SD16×C263C4semidirect
23. C2×D8×C263C4semidirect
112. C263#1903semidirect
125. C2×SD16Dic263semidirect
126. C2×D8Dic263semidirect

Maximal subgroups

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

subgroupindex
#306827052
#306819552
#306819432
C2×#225543872
#306817092
C263⋊#3382
C2×AGL(1,ℤ/8)×C2632
#1903263