Finite Group Databasebeta

← #46783224

Subgroups — #46783224

Order 33664.

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

normal subgroups only

This group has 324 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
1C2×#22554496C211yesmaximal, characteristic
2#30682704C211yesmaximal, characteristic, complemented
3#30681956C211yesmaximal, characteristic, complemented
4C2×#22554387C211yesmaximal, characteristic, complemented
5#30681708C211yesmaximal, characteristic, complemented
6C263⋊#338C211yesmaximal, characteristic, complemented
7#418×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554496—22no—
10#22554496—22no—
11C2×#16862364C412yescomplemented
12C2×#16862361C412yescomplemented
13#22554478—22no—
14#22554476—22no—
15C2×#16862360C2211yescharacteristic
16C2×#16862360C2211yescharacteristic
17C2×#16862360C2211yescharacteristic
18M16×D263—22no—
19#22554398—22no—
20#22554387—22no—
21C22×D4×C263C2211yescharacteristic
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24#102×C263—22no—
25#16862376—21no—
26#16862376—21no—
27#16862376D412yes—
28#16862376D412yes—
29C2×Dic526C2×C411yescharacteristic
30C2×D1052C2×C411yescharacteristic
31C2×C22⋊D263—21no—
32C2×C4×D263—21no—
33#16862364—24no—
34#16862361—24no—
35#16862360—21no—
36#16862360—21no—
37#16862360—21no—
38#16862360—21no—
39#16862360—21no—
40#16862360D412yes—
41#16862359—24no—
42C2×C263⋊C8—21no—
43C2×C263⋊C8—21no—
44C2×C263⋊C8C2×C412yes—
45C8×D263—24no—
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×C263D412yes—
57C4⋊C4×C263—21no—
58C22⋊C4×C263—21no—
59C42×C263—21no—
60C22×D263—21no—
61Dic526—21no—
62Dic526C22⋊C412yes—
63D1052—21no—
64D1052C22⋊C412yes—
65C22⋊D263—22no—
66C22⋊D263—22no—
67C2×Dic263—21no—
68C4×D263—22no—
69C4×D263—22no—
70C263⋊C8—22no—
71C263⋊C8—22no—
72C263⋊C8—41no—
73C23×C263—22no—
74C23×C263—41no—
75C23×C263—41no—
76C23×C263—82no—
77C23×C263#4111yescharacteristic
78D4×C263—22no—
79D4×C263—22no—
80D4×C263—41no—
81D4×C263—41no—
82C2×C4×C263—41no—
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—41no—
91C22×C263—42no—
92C22×C263—82no—
93C22×C263—82no—
94C22×C263—82no—
95C22×C263C4×D411yescharacteristic
96C22×C263#12111yescharacteristic
97C22×C263#12311yescharacteristic
98C2×D263—22no—
99C2×D263—81no—
100C4×C263—81no—
101C4×C263C2×C22⋊C411yescharacteristic
102C4×C263C4×D411yescharacteristic
103C4×C263#12011yescharacteristic
104C4×C263#12111yescharacteristic
105Dic263—22no—
106C2×C263—21no—
107C2×C263—21no—
108C2×C263—21no—
109C2×C263—82no—
110C2×C263#38611yescharacteristic
111D263—42no—
112C263#190311yescharacteristic, complemented, Sylow
113#1903—2631nomaximal, Sylow
114C2×AGL(1,ℤ/8)—2631no—
115#568—2631no—
116#421—2631no—
117#418D26311yescharacteristic, complemented
118C2×#100—2631no—
119#344—2631no—
120#338—2631no—
121C2×#41—2631no—
122C22×D4C2×D26311yescharacteristic
123AGL(1,ℤ/8)—5262no—
124AGL(1,ℤ/8)—5262no—
125C2×SD16—2632no—
126C2×D8—2632no—
127#131—5262no—
128#131—5262no—
129C2×M16—2631no—
130C2×M16—2631no—
131C2×M16—2631no—
132C2×M16—5262no—
133C2×M16C2×D26311yescharacteristic
134#117C2×D26311yescharacteristic
135#104—5262no—
136#102—22no—
137#100—5262no—
138C24—21no—
139#41—2632no—
140#41—2632no—
141#41—5261no—
142#41—5261no—
143C2×Q8—2631no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—2631no—
150C2×D4—5261no—
151C2×D4C4×D26312yes—
152C22×C4—5261no—
153C22×C4C22×D26311yescharacteristic
154SD16—5264no—
155D8—5264no—
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×C8C22⋊D26312yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—82no—
177C23—5261no—
178C23#1686237511yescharacteristic
179Q8—2632no—
180Q8—5261no—
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185D4—2632no—
186D4—5262no—
187D4—5262no—
188D4—5261no—
189C2×C4—41no—
190C2×C4—5261no—
191C2×C4—5262no—
192C2×C4—5262no—
193C2×C4C2×C4×D26311yescharacteristic
194C2×C4D4×D26311yescharacteristic
195C2×C4D4×D26311yescharacteristic
196C2×C4D4×D26311yescharacteristic
197C2×C4C2×C22⋊D26311yescharacteristic
198C2×C4#1686237611yescharacteristic
199C8—22no—
200C8—5262no—
201C8—5262no—
202C8—10521no—
203C22—41no—
204C22—42no—
205C22—82no—
206C22—82no—
207C22—82no—
208C22—5262no—
209C22—21041no—
210C22(C22⋊D263)⋊C411yescharacteristic
211C22#2255444111yescharacteristic
212C22#2255445211yescharacteristic
213C4—81no—
214C4—5262no—
215C4C22⋊C4×D26311yescharacteristic
216C4C4×C22⋊D26311yescharacteristic
217C4#2255443811yescharacteristic
218C4#2255444311yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—82no—
223C2—10522no—
224C2#3068181411yescharacteristic
subgroupG/H
centerC2#30681814
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#418×C263C2
socleC2×C263#386
prime radicalC2×#22554496C2
cosocleC22×C4×C263C23
hypercenter#418D263
hypocenterC263#1903
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
2. #30682704C2semidirect
3. #30681956C2semidirect
4. C2×#22554387C2semidirect
5. #30681708C2semidirect
6. C263⋊#338C2semidirect
7. #418×C263C2semidirect
11. C2×#16862364C4semidirect
12. C2×#16862361C4semidirect
112. C263#1903semidirect
117. #418D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544962
#306827042
#306819562
C2×#225543872
#306817082
C263⋊#3382
#418×C2632
#1903263