Finite Group Databasebeta

← #46783149

Subgroups — #46783149

Order 33664.

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

normal subgroups only

This group has 344 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
1C2×#22554458C211yesmaximal, characteristic
2#30682415C211yesmaximal, characteristic, complemented
3#30681944C211yesmaximal, characteristic
4#30681942C211yesmaximal, characteristic
5C2×#22554388C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7#339×C263C211yesmaximal, characteristic, complemented
8C22×Dic526C2211yescharacteristic
9C22×D1052C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11#22554458—22no—
12#22554458C414yescomplemented
13C4×Dic526—22no—
14#22554435—22no—
15#22554429C2211yescharacteristic
16#22554426—22no—
17C2×(C2×D263)⋊C4—22no—
18#22554392—22no—
19#22554390—22no—
20#22554388—22no—
21C2×M16×C263C2211yescharacteristic
22#117×C263C2211yescharacteristic
23C2×C42×C263C2211yescharacteristic
24C23×D263—21no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526C2×C412yes—
30C2×Dic526D412yes—
31C2×D1052—21no—
32C2×D1052—21no—
33C2×D1052—21no—
34C2×D1052—21no—
35C2×D1052—21no—
36C2×D1052C2×C412yes—
37C22×Dic263D412yes—
38#16862360—21no—
39#16862360—21no—
40C2×C263⋊C8—21no—
41C4⋊Dic263D412yes—
42Dic263⋊C4—24no—
43C22⋊Dic263—21no—
44(C2×D263)⋊C4—28no—
45C4×Dic263—24no—
46C4×Dic263—21no—
47C22×C4×C263—21no—
48C22×C4×C263C2311yescharacteristic
49M16×C263—21no—
50M16×C263—21no—
51C2×C8×C263—21no—
52C4⋊C4×C263D412yes—
53C22⋊C4×C263—21no—
54C42×C263—21no—
55C42×C263—21no—
56C42×C263C2×C412yes—
57C22×D263—22no—
58C22×D263—44no—
59C22×D263—41no—
60C22×D263—41no—
61Dic526—22no—
62Dic526—22no—
63Dic526—22no—
64Dic526—22no—
65D1052—22no—
66D1052—22no—
67D1052—41no—
68D1052—41no—
69C2×Dic263—22no—
70C2×Dic263—22no—
71C2×Dic263—22no—
72C2×Dic263C22⋊C414yes—
73C263⋊C8—41no—
74C23×C263C2×D411yescharacteristic
75C2×C4×C263—22no—
76C2×C4×C263—22no—
77C2×C4×C263—42no—
78C2×C4×C263C22×C411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263#4111yescharacteristic
83C2×C4×C263#4111yescharacteristic
84C8×C263—41no—
85C22×C263—22no—
86C22×C263C2×C22⋊C411yescharacteristic
87C22×C263#12011yescharacteristic
88C22×C263#12311yescharacteristic
89C2×D263—44no—
90C2×D263—42no—
91C2×D263—82no—
92C2×D263—82no—
93C4×C263—42no—
94C4×C263—42no—
95C4×C263C4×D411yescharacteristic
96C4×C263C4×D411yescharacteristic
97C4×C263#12111yescharacteristic
98C4×C263#12111yescharacteristic
99Dic263—24no—
100Dic263—42no—
101C2×C263—21no—
102C2×C263—21no—
103C2×C263#38611yescharacteristic
104C2×C263#45412yes—
105D263—82no—
106C263#188811yescharacteristic, complemented, Sylow
107#1888—2631nomaximal, Sylow
108C2×#124—2631no—
109#519—2631no—
110#418—2631no—
111#418—2631no—
112C2×#101—2631no—
113#339—2631no—
114#339D26311yescharacteristic, complemented
115C22×Q8—2631no—
116C22×D4—2631no—
117C2×M16—2631no—
118C2×M16C2×D26311yescharacteristic
119#124—2634no—
120#124—5262no—
121C4×Q8—5262no—
122C4×Q8—5262no—
123#117—2631no—
124#117—5262no—
125#117C2×D26311yescharacteristic
126C2×C22⋊C4—5262no—
127C2×C42C2×D26311yescharacteristic
128#102—5262no—
129#102—5262no—
130#101—5262no—
131C24—5261no—
132C2×Q8—2632no—
133C2×Q8—2632no—
134C2×Q8—5261no—
135C2×Q8—5261no—
136C2×Q8—5261no—
137C2×Q8—5261no—
138C2×D4—2632no—
139C2×D4—5261no—
140C2×D4—5261no—
141C2×D4—5261no—
142C2×D4—5261no—
143C2×D4—5261no—
144C22×C4—21no—
145C22×C4—2632no—
146C22×C4C22×D26311yescharacteristic
147M16—21no—
148M16—21no—
149M16—5261no—
150M16—5261no—
151C2×C8—21no—
152C2×C8—5261no—
153C4⋊C4—2632no—
154C4⋊C4—5264no—
155C4⋊C4D105212yes—
156C22⋊C4—21no—
157C22⋊C4—5268no—
158C22⋊C4—5261no—
159C42—21no—
160C42—21no—
161C42—5264no—
162C42—5261no—
163C42C4×D26312yes—
164C23—5262no—
165C23—10524no—
166C23—10521no—
167C23—10521no—
168C23D4×D26311yescharacteristic
169Q8—5262no—
170Q8—5262no—
171Q8—5262no—
172Q8—5262no—
173D4—5262no—
174D4—5262no—
175D4—10521no—
176D4—10521no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—2634no—
181C2×C4—5262no—
182C2×C4—5262no—
183C2×C4—5262no—
184C2×C4C2×C4×D26311yescharacteristic
185C2×C4D4×D26311yescharacteristic
186C2×C4D4×D26311yescharacteristic
187C2×C4C2×D105211yescharacteristic
188C2×C4#1686237611yescharacteristic
189C2×C4#1686237711yescharacteristic
190C8—41no—
191C8—10521no—
192C22—22no—
193C22—10524no—
194C22—10522no—
195C22—21042no—
196C22—21042no—
197C22C22⋊C4×D26311yescharacteristic
198C22#2255444011yescharacteristic
199C22#2255445511yescharacteristic
200C4—42no—
201C4—42no—
202C4—5264no—
203C4—10522no—
204C4#2255443211yescharacteristic
205C4C4×D105211yescharacteristic
206C4#2255444311yescharacteristic
207C4#2255444511yescharacteristic
208C2—21no—
209C2—21no—
210C2—21042no—
211C2#3068181611yescharacteristic
212C2#3068211212yes—
subgroupG/H
centerC22#22554440
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#339×C263C2
socleC22×C263#120
prime radicalC22×D1052C22
cosocleC22×C4×C263C23
hypercenter#339D263
hypocenterC263#1888
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #30682415C2semidirect
5. C2×#22554388C2semidirect
6. #30681698C2semidirect
7. #339×C263C2semidirect
12. #22554458C4semidirect
106. C263#1888semidirect
114. #339D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544582
#306824152
#306819442
#306819422
C2×#225543882
#306816982
#339×C2632
#1888263