Finite Group Databasebeta

← #46783238

Subgroups — #46783238

Order 33664.

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

normal subgroups only

This group has 310 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×#22554500C211yesmaximal, characteristic
2#30682415C211yesmaximal, characteristic, complemented
3#30681948C211yesmaximal, characteristic, complemented
4#30681912C211yesmaximal, characteristic
5#30681710C211yesmaximal, characteristic, complemented
6#30681694C211yesmaximal, characteristic, complemented
7#421×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9#22554500—22no—
10#22554500—22no—
11C2×#16862366C412yescomplemented
12C2×#16862364C412yescomplemented
13C2×#16862360C2211yescharacteristic
14C4×Dic526—22no—
15#22554435—22no—
16#22554429C2211yescharacteristic
17#22554429C2211yescharacteristic
18#22554426—22no—
19#22554395—22no—
20#22554385—22no—
21C2×#41×C263C2211yescharacteristic
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24#104×C263—22no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526C2×C412yes—
29C2×Dic526D412yes—
30C2×Dic526D412yes—
31C22×Dic263—21no—
32#16862366—24no—
33#16862364—24no—
34#16862360—21no—
35#16862360—21no—
36C2×C263⋊C8C2×C412yes—
37C4⋊Dic263—21no—
38C4⋊Dic263—21no—
39Dic263⋊C4—24no—
40C22⋊Dic263—21no—
41C22⋊Dic263D412yes—
42C4×Dic263—24no—
43C4×Dic263—21no—
44C4×Dic263—21no—
45#41×C263—21no—
46#41×C263—21no—
47#41×C263—21no—
48#41×C263—21no—
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×C263D412yes—
60Dic526—22no—
61Dic526—22no—
62Dic526—22no—
63Dic526C22⋊C414yes—
64C2×Dic263—22no—
65C2×Dic263—22no—
66C2×Dic263—22no—
67C2×Dic263—22no—
68C2×Dic263—41no—
69C263⋊C8—22no—
70C23×C263—21no—
71C23×C263C2×D411yescharacteristic
72Q8×C263—21no—
73Q8×C263—21no—
74D4×C263—21no—
75D4×C263—21no—
76D4×C263—41no—
77D4×C263—41no—
78C2×C4×C263—21no—
79C2×C4×C263—22no—
80C2×C4×C263—41no—
81C2×C4×C263—41no—
82C2×C4×C263C22×C411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C8×C263—41no—
89C22×C263—41no—
90C22×C263—41no—
91C22×C263—81no—
92C22×C263C4×D411yescharacteristic
93C22×C263#12011yescharacteristic
94C22×C263#12111yescharacteristic
95C4×C263—42no—
96C4×C263—41no—
97C4×C263C2×C22⋊C411yescharacteristic
98C4×C263C4×D411yescharacteristic
99C4×C263#12111yescharacteristic
100C4×C263#12311yescharacteristic
101Dic263—24no—
102Dic263—42no—
103Dic263—81no—
104C2×C263—21no—
105C2×C263—21no—
106C2×C263—21no—
107C2×C263—81no—
108C2×C263#38611yescharacteristic
109C263#190511yescharacteristic, complemented, Sylow
110#1905—2631nomaximal, Sylow
111C2×#137—2631no—
112#519—2631no—
113#421D26311yescharacteristic
114#419—2631no—
115#410—2631no—
116#344—2631no—
117H(3,ℤ/4)—2631no—
118C2×#41C2×D26311yescharacteristic
119C22×Q8—2631no—
120#137—5262no—
121#137—5262no—
122C2×Q16—2632no—
123C2×SD16—2632no—
124C2×M16—2631no—
125C2×M16C2×D26311yescharacteristic
126C4×Q8—5262no—
127C4×Q8—5262no—
128#117—2631no—
129#117—2631no—
130#117—5262no—
131#117C2×D26311yescharacteristic
132#104—22no—
133#103—5262no—
134#99—5262no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—2632no—
140C2×Q8—2632no—
141C2×Q8—2632no—
142C2×Q8—5261no—
143C2×Q8—5261no—
144C2×Q8—5261no—
145C2×Q8C4×D26311yescharacteristic
146C2×D4—21no—
147C2×D4C4×D26311yescharacteristic
148C22×C4—21no—
149C22×C4—5261no—
150C22×C4C22×D26311yescharacteristic
151Q16—5264no—
152SD16—5264no—
153M16—21no—
154M16—21no—
155M16—5261no—
156M16—5261no—
157C2×C8—21no—
158C2×C8—2632no—
159C4⋊C4—21no—
160C4⋊C4—5264no—
161C4⋊C4—5261no—
162C4⋊C4—5261no—
163C22⋊C4—21no—
164C22⋊C4—2632no—
165C22⋊C4—5261no—
166C42—5264no—
167C42—5261no—
168C42—5261no—
169C42C22⋊D26312yes—
170C23—21no—
171C23D4×D26311yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—2634no—
175Q8—5262no—
176Q8—5262no—
177Q8—5262no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—5262no—
187C2×C4—5262no—
188C2×C4—5262no—
189C2×C4—5262no—
190C2×C4—10521no—
191C2×C4C2×C4×D26311yescharacteristic
192C2×C4D4×D26311yescharacteristic
193C2×C4D4×D26311yescharacteristic
194C2×C4C2×C22⋊D26311yescharacteristic
195C2×C4#1686237511yescharacteristic
196C2×C4#1686237611yescharacteristic
197C8—41no—
198C8—5262no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22(C22⋊D263)⋊C411yescharacteristic
203C22#2255443811yescharacteristic
204C22#2255444311yescharacteristic
205C4—42no—
206C4—41no—
207C4—5264no—
208C4—10522no—
209C4—21041no—
210C4C22⋊C4×D26311yescharacteristic
211C4C4×C22⋊D26311yescharacteristic
212C4#2255444111yescharacteristic
213C4#2255445211yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#3068181411yescharacteristic
subgroupG/H
centerC2#30681814
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#421×C263C2
socleC2×C263#386
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#421D263
hypocenterC263#1905
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
2. #30682415C2semidirect
3. #30681948C2semidirect
5. #30681710C2semidirect
6. #30681694C2semidirect
11. C2×#16862366C4semidirect
12. C2×#16862364C4semidirect
109. C263#1905semidirect

Maximal subgroups

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

subgroupindex
C2×#225545002
#306824152
#306819482
#306819122
#306817102
#306816942
#421×C2632
#1905263