Finite Group Databasebeta

← #46784002

Subgroups — #46784002

Order 33664.

296 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C22×#16862361C211yesmaximal, characteristic
2#30681965C211yesmaximal, characteristic, complemented
3#30681942C211yesmaximal, characteristic, complemented
4C2×#22554387C211yesmaximal, characteristic, complemented
5C2×#22554386C211yesmaximal, characteristic, complemented
6#30681702C211yesmaximal, characteristic, complemented
7#418×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C2×#16862361—22no—
10C2×#16862361—22no—
11C2×#16862361—22no—
12C2×#16862360C2211yescharacteristic
13C2×#16862360C2211yescharacteristic
14C22×C263⋊C8C2211yescharacteristic
15C4⋊(C263⋊C8)—22no—
16#22554390—22no—
17#22554387—22no—
18#22554386—22no—
19C22×D4×C263C2211yescharacteristic
20C2×M16×C263C2211yescharacteristic
21#117×C263C2211yescharacteristic
22#102×C263—22no—
23C23×D263—21no—
24C2×D1052—21no—
25C2×D1052—21no—
26C2×D1052—21no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052D412yes—
30#16862361—28no—
31#16862360—21no—
32#16862360—21no—
33#16862360—21no—
34#16862360—21no—
35C2×C263⋊C8—21no—
36C2×C263⋊C8—21no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8—21no—
39C2×C263⋊C8D412yes—
40C24×C263—21no—
41C2×D4×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45C2×D4×C263—21no—
46C2×D4×C263D412yes—
47C22×C4×C263C2311yescharacteristic
48M16×C263—21no—
49M16×C263—21no—
50C2×C8×C263—21no—
51C4⋊C4×C263D412yes—
52C22⋊C4×C263—21no—
53C42×C263—21no—
54C22×D263—22no—
55C22×D263—41no—
56C22×D263—41no—
57C22×D263—82no—
58D1052—22no—
59D1052—22no—
60D1052—41no—
61D1052—41no—
62C263⋊C8—22no—
63C263⋊C8—41no—
64C263⋊C8—41no—
65C23×C263—22no—
66C23×C263—41no—
67C23×C263—41no—
68C23×C263—82no—
69C23×C263#4111yescharacteristic
70D4×C263—22no—
71D4×C263—22no—
72D4×C263—41no—
73D4×C263—41no—
74C2×C4×C263—22no—
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263#4111yescharacteristic
80C2×C4×C263#4111yescharacteristic
81C8×C263—41no—
82C22×C263—22no—
83C22×C263—42no—
84C22×C263—82no—
85C22×C263—82no—
86C22×C263—82no—
87C22×C263#12111yescharacteristic
88C22×C263#12311yescharacteristic
89C22×C263#12311yescharacteristic
90C2×D263—42no—
91C2×D263—82no—
92C2×D263—82no—
93C2×D263—82no—
94C4×C263—42no—
95C4×C263#12011yescharacteristic
96C4×C263#12111yescharacteristic
97C4×C263#12111yescharacteristic
98C4×C263#12411yescharacteristic
99C2×C263—21no—
100C2×C263—21no—
101C2×C263—82no—
102C2×C263#39411yescharacteristic
103C2×C263#47212yes—
104D263—82no—
105C263#204511yescharacteristic, complemented, Sylow
106#2045—2631nomaximal, Sylow
107C22×D8—2631no—
108#424—2631no—
109#418—2631no—
110#418D26311yescharacteristic, complemented
111C2×#100—2631no—
112C2×#100—2631no—
113#341—2631no—
114C22×D4—2631no—
115C22×D4C2×D26311yescharacteristic
116C2×D8—5262no—
117C2×D8—5262no—
118C2×D8—5262no—
119C2×M16—2631no—
120C2×M16—2631no—
121C2×M16C2×D26311yescharacteristic
122C22×C8—2631no—
123#117C2×D26311yescharacteristic
124C4⋊C8—5262no—
125#102—22no—
126#102—5262no—
127#100—5262no—
128#100—5262no—
129C24—21no—
130C24—5261no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2632no—
137C2×D4—5261no—
138C2×D4—5261no—
139C2×D4—5261no—
140C2×D4—5261no—
141C2×D4—5261no—
142C2×D4D105212yes—
143C22×C4C22×D26311yescharacteristic
144D8—5268no—
145M16—21no—
146M16—21no—
147M16—5261no—
148M16—5261no—
149M16—5261no—
150M16—5261no—
151C2×C8—21no—
152C2×C8—2632no—
153C2×C8—5261no—
154C2×C8—5261no—
155C2×C8—5261no—
156C2×C8—5261no—
157C4⋊C4C22⋊D26312yes—
158C22⋊C4—21no—
159C42—21no—
160C23—22no—
161C23—41no—
162C23—41no—
163C23—82no—
164C23—5262no—
165C23—10521no—
166C23—10521no—
167C23—21042no—
168C23#1686237511yescharacteristic
169D4—22no—
170D4—22no—
171D4—41no—
172D4—41no—
173D4—5262no—
174D4—5262no—
175D4—10521no—
176D4—10521no—
177C2×C4—22no—
178C2×C4D4×D26311yescharacteristic
179C2×C4D4×D26311yescharacteristic
180C2×C4C2×C22⋊D26311yescharacteristic
181C2×C4C2×D105211yescharacteristic
182C2×C4#1686237511yescharacteristic
183C2×C4#1686237611yescharacteristic
184C8—41no—
185C8—5262no—
186C8—10521no—
187C8—10521no—
188C22—22no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—82no—
193C22—10522no—
194C22—21042no—
195C22—21042no—
196C22—21042no—
197C22#2255444211yescharacteristic
198C22#2255445211yescharacteristic
199C22#2255445411yescharacteristic
200C4—42no—
201C4#2255444011yescharacteristic
202C4#2255444111yescharacteristic
203C4#2255444411yescharacteristic
204C4#2255445611yescharacteristic
205C2—21no—
206C2—21no—
207C2—82no—
208C2—21042no—
209C2#3068185411yescharacteristic
210C2#3068220612yes—
subgroupG/H
centerC22#22554442
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#418×C263C2
socleC22×C263#121
prime radicalC22×#16862361C2
hypercenter#418D263
hypocenterC263#2045
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #30681965C2semidirect
3. #30681942C2semidirect
4. C2×#22554387C2semidirect
5. C2×#22554386C2semidirect
6. #30681702C2semidirect
7. #418×C263C2semidirect
105. C263#2045semidirect
110. #418D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623612
#306819652
#306819422
C2×#225543872
C2×#225543862
#306817022
#418×C2632
#2045263