Finite Group Databasebeta

← #46783218

Subgroups — #46783218

Order 33664.

304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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×#22554500C211yesmaximal, characteristic
2#30682705C211yesmaximal, characteristic
3#30681946C211yesmaximal, characteristic, complemented
4C2×#22554388C211yesmaximal, characteristic, complemented
5#30681708C211yesmaximal, characteristic, complemented
6C263⋊#338C211yesmaximal, characteristic, complemented
7#421×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9#22554500—22no—
10#22554500—22no—
11C2×#16862366C412yescomplemented
12C2×#16862364C412yescomplemented
13#22554477—22no—
14#22554477—22no—
15C2×#16862360—22no—
16C2×#16862360C2211yescharacteristic
17C2×#16862360C2211yescharacteristic
18C2×#16862360C2211yescharacteristic
19#22554393—22no—
20#22554388—22no—
21C2×#41×C263C2211yescharacteristic
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24#104×C263—22no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—21no—
30C2×Dic526C2×C412yes—
31C22×Dic263—21no—
32#16862366—24no—
33#16862364—24no—
34#16862360—24no—
35#16862360—21no—
36#16862360—21no—
37#16862360—21no—
38#16862360—21no—
39#16862360—21no—
40#16862360D412yes—
41C2×C263⋊C8—24no—
42C2×C263⋊C8—21no—
43C2×C263⋊C8C2×C412yes—
44C2×C263⋊C8D412yes—
45#41×C263—21no—
46#41×C263—21no—
47#41×C263D412yes—
48#41×C263D412yes—
49C2×Q8×C263C2×C411yescharacteristic
50C2×D4×C263—21no—
51C2×D4×C263C2×C411yescharacteristic
52C22×C4×C263—21no—
53C22×C4×C263C2311yescharacteristic
54M16×C263—21no—
55M16×C263—21no—
56C2×C8×C263—21no—
57C4⋊C4×C263—21no—
58C22⋊C4×C263—21no—
59C42×C263—21no—
60Dic526—22no—
61Dic526—22no—
62Dic526—41no—
63Dic526—41no—
64C2×Dic263—22no—
65C2×Dic263—41no—
66C2×Dic263—41no—
67C263⋊C8—22no—
68C263⋊C8—22no—
69C263⋊C8—22no—
70C23×C263—21no—
71C23×C263#4111yescharacteristic
72Q8×C263—21no—
73Q8×C263C22⋊C412yes—
74D4×C263—22no—
75D4×C263—22no—
76D4×C263—21no—
77D4×C263C22⋊C412yes—
78C2×C4×C263—21no—
79C2×C4×C263—22no—
80C2×C4×C263—22no—
81C2×C4×C263—41no—
82C2×C4×C263C22×C411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C8×C263—41no—
89C22×C263—22no—
90C22×C263—41no—
91C22×C263—81no—
92C22×C263C4×D411yescharacteristic
93C22×C263#12111yescharacteristic
94C22×C263#12311yescharacteristic
95C4×C263—22no—
96C4×C263—81no—
97C4×C263C2×C22⋊C411yescharacteristic
98C4×C263C4×D411yescharacteristic
99C4×C263#12011yescharacteristic
100C4×C263#12111yescharacteristic
101Dic263—42no—
102C2×C263—21no—
103C2×C263—21no—
104C2×C263—21no—
105C2×C263—42no—
106C2×C263#38611yescharacteristic
107C263#190211yescharacteristic, complemented, Sylow
108#1902—2631nomaximal, Sylow
109C2×#137—2631no—
110#568—2631no—
111#421D26311yescharacteristic
112#419—2631no—
113C2×#101—2631no—
114#344—2631no—
115#338—2631no—
116C2×#41C2×D26311yescharacteristic
117C22×Q8—2631no—
118#137—5262no—
119#137—5262no—
120C2×Q16—2632no—
121C2×SD16—2632no—
122#131—5262no—
123#131—5262no—
124C2×M16—2631no—
125C2×M16—2631no—
126C2×M16—2631no—
127C2×M16—5262no—
128C2×M16C2×D26311yescharacteristic
129#117C2×D26311yescharacteristic
130#104—22no—
131#103—5262no—
132#101—5262no—
133#41—21no—
134#41—21no—
135#41C22⋊D26312yes—
136#41D105212yes—
137C2×Q8—2632no—
138C2×Q8—5261no—
139C2×Q8—5261no—
140C2×Q8—5261no—
141C2×Q8—5261no—
142C2×Q8—5261no—
143C2×Q8C4×D26311yescharacteristic
144C2×D4—21no—
145C2×D4C4×D26311yescharacteristic
146C22×C4—21no—
147C22×C4—5261no—
148C22×C4C22×D26311yescharacteristic
149Q16—5264no—
150SD16—5264no—
151M16—21no—
152M16—21no—
153M16—2632no—
154M16—5264no—
155M16—5261no—
156M16—5261no—
157M16—5261no—
158M16—5261no—
159M16—5261no—
160C2×C8—21no—
161C2×C8—2632no—
162C2×C8—2632no—
163C2×C8—5264no—
164C2×C8—5261no—
165C4⋊C4—21no—
166C22⋊C4—21no—
167C42—21no—
168C23—21no—
169C23#1686237511yescharacteristic
170Q8—21no—
171Q8—5262no—
172Q8—5262no—
173Q8—10521no—
174Q8—10521no—
175Q8(C2×D263)⋊C412yes—
176D4—22no—
177D4—22no—
178D4—21no—
179D4(C2×D263)⋊C412yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—5262no—
185C2×C4—10521no—
186C2×C4—10521no—
187C2×C4C2×C4×D26311yescharacteristic
188C2×C4D4×D26311yescharacteristic
189C2×C4D4×D26311yescharacteristic
190C2×C4C2×C22⋊D26311yescharacteristic
191C2×C4C2×D105211yescharacteristic
192C2×C4#1686237511yescharacteristic
193C8—41no—
194C8—5262no—
195C8—5262no—
196C8—5262no—
197C22—22no—
198C22—41no—
199C22—81no—
200C22(C22⋊D263)⋊C411yescharacteristic
201C22#2255444211yescharacteristic
202C22#2255445411yescharacteristic
203C4—22no—
204C4—81no—
205C4—10522no—
206C4C2×(C2×D263)⋊C411yescharacteristic
207C4(C22⋊D263)⋊C411yescharacteristic
208C4#2255444011yescharacteristic
209C4#2255444211yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—42no—
214C2#3068181511yescharacteristic
subgroupG/H
centerC2#30681815
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#421×C263C2
socleC2×C263#386
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#421D263
hypocenterC263#1902
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
3. #30681946C2semidirect
4. C2×#22554388C2semidirect
5. #30681708C2semidirect
6. C263⋊#338C2semidirect
11. C2×#16862366C4semidirect
12. C2×#16862364C4semidirect
107. C263#1902semidirect

Maximal subgroups

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

subgroupindex
C2×#225545002
#306827052
#306819462
C2×#225543882
#306817082
C263⋊#3382
#421×C2632
#1902263