Finite Group Databasebeta

← #46783647

Subgroups — #46783647

Order 33664.

296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16862364C211yesmaximal, characteristic
2C2×#22554405C211yesmaximal, characteristic, complemented
3#30681948C211yesmaximal, characteristic, complemented
4#30681943C211yesmaximal, characteristic
5C2×#22554388C211yesmaximal, characteristic, complemented
6#30681896C211yesmaximal, characteristic, complemented
7C2×#100×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862364—21no—
10C2×#16862364—21no—
11C2×#16862364—22no—
12C2×#16862364C414yescomplemented
13C2×#16862360C2211yescharacteristic
14C22×C263⋊C8C2211yescharacteristic
15#22554429C2211yescharacteristic
16#22554405—22no—
17#22554395—22no—
18#22554391—22no—
19#22554388—22no—
20#22554380—21no—
21C8×Dic263—21no—
22C22×D4×C263C2211yescharacteristic
23C2×M16×C263C2211yescharacteristic
24C2×M16×C263C2211yescharacteristic
25#100×C263—22no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526C2×C412yes—
32C22×Dic263—21no—
33#16862364—24no—
34#16862364—24no—
35#16862360—21no—
36#16862360—21no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8C2×C412yes—
39C2×C263⋊C8D411yescharacteristic
40C2×C263⋊C8D411yescharacteristic
41C2×C263⋊C8D412yes—
42C4⋊Dic263D412yes—
43C22⋊Dic263—21no—
44C4×Dic263—21no—
45C24×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—
52C22×C4×C263C2311yescharacteristic
53M16×C263—21no—
54M16×C263—21no—
55M16×C263—21no—
56M16×C263D412yes—
57C2×C8×C263—21no—
58C2×C8×C263—21no—
59Dic526—22no—
60Dic526—22no—
61Dic526—41no—
62Dic526—41no—
63C2×Dic263—22no—
64C2×Dic263—22no—
65C2×Dic263—41no—
66C2×Dic263—41no—
67C263⋊C8—41no—
68C263⋊C8C22⋊C412yes—
69C263⋊C8C22⋊C412yes—
70C23×C263—22no—
71C23×C263—41no—
72C23×C263—41no—
73C23×C263—82no—
74C23×C263#4111yescharacteristic
75D4×C263—22no—
76D4×C263—22no—
77D4×C263—41no—
78D4×C263—41no—
79C2×C4×C263C22×C411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263#4111yescharacteristic
85C8×C263—22no—
86C8×C263—41no—
87C22×C263—22no—
88C22×C263—42no—
89C22×C263—82no—
90C22×C263—82no—
91C22×C263—82no—
92C22×C263C4×D411yescharacteristic
93C22×C263#12111yescharacteristic
94C22×C263#12411yescharacteristic
95C4×C263C2×C22⋊C411yescharacteristic
96C4×C263C4×D411yescharacteristic
97C4×C263#12111yescharacteristic
98C4×C263#12711yescharacteristic
99Dic263—42no—
100Dic263—42no—
101C2×C263—21no—
102C2×C263—21no—
103C2×C263—82no—
104C2×C263#39011yescharacteristic
105C2×C263#47112yes—
106C263#197711yescharacteristic, complemented, Sylow
107#1977—2631nomaximal, Sylow
108C22×SD16—2631no—
109C2×#108—2631no—
110#419—2631no—
111#418—2631no—
112C2×#101—2631no—
113C2×#100D26311yescharacteristic
114#405—2631no—
115C22×Q8—2631no—
116C22×D4C2×D26311yescharacteristic
117C2×SD16—2634no—
118C2×SD16—5261no—
119C2×SD16—5261no—
120C2×SD16—5262no—
121C2×M16—2631no—
122C2×M16C2×D26311yescharacteristic
123C2×M16C2×D26311yescharacteristic
124C22×C8—2631no—
125#117—2631no—
126#108—5262no—
127#103—5262no—
128#102—5262no—
129#101—5262no—
130#100—22no—
131#97—5261no—
132C4×C8—5261no—
133C24—21no—
134C2×Q8—2632no—
135C2×Q8—5261no—
136C2×Q8—5261no—
137C2×Q8—5261no—
138C2×Q8—5261no—
139C2×Q8—5261no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4C4×D26312yes—
146C22×C4—5261no—
147C22×C4C22×D26311yescharacteristic
148SD16—5264no—
149SD16—5264no—
150M16—21no—
151M16—21no—
152M16—21no—
153M16—5261no—
154M16—5261no—
155M16C22⋊D26312yes—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—2632no—
159C2×C8—2631no—
160C2×C8—2631no—
161C2×C8—2632no—
162C2×C8—5261no—
163C4⋊C4—2632no—
164C22⋊C4—5261no—
165C42—5261no—
166C23—22no—
167C23—41no—
168C23—41no—
169C23—82no—
170C23#1686237611yescharacteristic
171Q8—5262no—
172Q8—5262no—
173Q8—10521no—
174Q8—10521no—
175D4—22no—
176D4—22no—
177D4—41no—
178D4—41no—
179C2×C4—5262no—
180C2×C4—5262no—
181C2×C4—10521no—
182C2×C4—10521no—
183C2×C4C2×C4×D26311yescharacteristic
184C2×C4D4×D26311yescharacteristic
185C2×C4D4×D26311yescharacteristic
186C2×C4D4×D26311yescharacteristic
187C2×C4C2×C22⋊D26311yescharacteristic
188C2×C4#1686237511yescharacteristic
189C8—22no—
190C8—41no—
191C8—2632no—
192C8—2632no—
193C8—10521no—
194C22—22no—
195C22—42no—
196C22—82no—
197C22—82no—
198C22—82no—
199C22C4×C22⋊D26311yescharacteristic
200C22#2255444311yescharacteristic
201C22#2255445611yescharacteristic
202C4—10522no—
203C4—10522no—
204C4C22⋊C4×D26311yescharacteristic
205C4(C22⋊D263)⋊C411yescharacteristic
206C4#2255444211yescharacteristic
207C4#2255446611yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#3068183811yescharacteristic
212C2#3068220012yes—
subgroupG/H
centerC22#22554443
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#100×C263C2
socleC22×C263#121
prime radicalC22×D4×C263C22
cosocleC22×C4×C263C23
hypercenterC2×#100D263
hypocenterC263#1977
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×#22554405C2semidirect
3. #30681948C2semidirect
5. C2×#22554388C2semidirect
6. #30681896C2semidirect
12. C2×#16862364C4semidirect
106. C263#1977semidirect

Maximal subgroups

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

subgroupindex
C22×#168623642
C2×#225544052
#306819482
#306819432
C2×#225543882
#306818962
C2×#100×C2632
#1977263