Finite Group Databasebeta

← #46783099

Subgroups — #46783099

Order 33664.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22554435C211yesmaximal, characteristic, complemented
3C2×#22554395C211yesmaximal, characteristic, complemented
4#30681841C211yesmaximal, characteristic
5#30681700C211yesmaximal, characteristic, complemented
6#30681692C211yesmaximal, characteristic, complemented
7C2×#102×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862364—22no—
10C2×#16862364—22no—
11C2×#16862364C414yescomplemented
12C22×C263⋊C8C2211yescharacteristic
13#22554435—22no—
14#22554435—22no—
15C2×C4⋊Dic263C2211yescharacteristic
16C2×Dic263⋊C4—21no—
17C2×C22⋊Dic263—21no—
18C2×C22⋊Dic263—21no—
19C2×C4×Dic263—21no—
20C2×C4×Dic263C2211yescharacteristic
21#22554395—22no—
22C22×D4×C263C2211yescharacteristic
23C22×C8×C263C2211yescharacteristic
24C2×C4⋊C4×C263C2211yescharacteristic
25#102×C263—22no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526C2×C412yes—
30C2×Dic526D412yes—
31C2×Dic526D412yes—
32C22×Dic263—21no—
33C22×Dic263—21no—
34C22×Dic263D411yescharacteristic
35C22×Dic263D411yescharacteristic
36#16862364—28no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8—21no—
39C2×C263⋊C8C2×C412yes—
40C4⋊Dic263—21no—
41C4⋊Dic263—21no—
42Dic263⋊C4—24no—
43C22⋊Dic263—42no—
44C22⋊Dic263—42no—
45C4×Dic263—24no—
46C4×Dic263—21no—
47C4×Dic263—21no—
48C24×C263—21no—
49C2×D4×C263—21no—
50C2×D4×C263—21no—
51C2×D4×C263—21no—
52C2×D4×C263—21no—
53C2×D4×C263—21no—
54C2×D4×C263C2×C412yes—
55C22×C4×C263—21no—
56C22×C4×C263C2311yescharacteristic
57C2×C8×C263—21no—
58C2×C8×C263—21no—
59C2×C8×C263—21no—
60C4⋊C4×C263—21no—
61C4⋊C4×C263D412yes—
62Dic526—22no—
63Dic526—22no—
64Dic526—22no—
65Dic526C22⋊C414yescomplemented
66C2×Dic263—22no—
67C2×Dic263—21no—
68C2×Dic263—22no—
69C2×Dic263—22no—
70C2×Dic263—21no—
71C2×Dic263—21no—
72C2×Dic263—21no—
73C2×Dic263—21no—
74C2×Dic263—41no—
75C2×Dic263—41no—
76C2×Dic263—41no—
77C2×Dic263SD1612yescomplemented
78C263⋊C8—22no—
79C23×C263—22no—
80C23×C263—41no—
81C23×C263—41no—
82C23×C263—41no—
83C23×C263—41no—
84C23×C263—41no—
85C23×C263—41no—
86C23×C263C2×D411yescharacteristic
87D4×C263—22no—
88D4×C263—22no—
89D4×C263—41no—
90D4×C263—41no—
91C2×C4×C263—22no—
92C2×C4×C263—41no—
93C2×C4×C263—41no—
94C2×C4×C263C22×C411yescharacteristic
95C2×C4×C263C2×D411yescharacteristic
96C2×C4×C263C2×D411yescharacteristic
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263#4111yescharacteristic
99C2×C4×C263#4111yescharacteristic
100C8×C263—41no—
101C22×C263—42no—
102C22×C263—42no—
103C22×C263—42no—
104C22×C263—81no—
105C22×C263—81no—
106C22×C263—81no—
107C22×C263—81no—
108C22×C263C4×D411yescharacteristic
109C22×C263#12011yescharacteristic
110C22×C263#12111yescharacteristic
111C22×C263C2×SD1611yescharacteristic
112C22×C263#13511yescharacteristic
113C22×C263AGL(1,ℤ/8)11yescharacteristic
114C22×C263#13711yescharacteristic
115C4×C263—42no—
116C4×C263C2×C22⋊C411yescharacteristic
117C4×C263C4×D411yescharacteristic
118C4×C263#12111yescharacteristic
119C4×C263#12311yescharacteristic
120Dic263—24no—
121Dic263—22no—
122Dic263—41no—
123Dic263—81no—
124C2×C263—82no—
125C2×C263#38611yescharacteristic
126C2×C263C4×SD1611yescharacteristic
127C2×C263#44011yescharacteristic
128C2×C263#44811yescharacteristic
129C2×C263#44911yescharacteristic
130C2×C263#46011yescharacteristic
131C2×C263#46411yescharacteristic
132C263#188011yescharacteristic, complemented, Sylow
133#1880—2631nomaximal, Sylow
134C22×SD16—2631no—
135C2×C4×Q8—2631no—
136C2×#103—2631no—
137C2×#102D26311yescharacteristic
138#390—2631no—
139#340—2631no—
140#336—2631no—
141C22×Q8—2631no—
142C22×D4C2×D26311yescharacteristic
143C2×SD16—2634no—
144C2×SD16—5262no—
145C2×SD16—5262no—
146C22×C8—2631no—
147C22×C8C2×D26311yescharacteristic
148C4×Q8—5262no—
149C4×Q8—5262no—
150C2×C4⋊C4—2631no—
151C2×C4⋊C4—5261no—
152C2×C4⋊C4C2×D26311yescharacteristic
153C2×C22⋊C4—5261no—
154C2×C22⋊C4—5261no—
155C2×C42—2631no—
156C2×C42—5261no—
157#103—5262no—
158#102—22no—
159C24—21no—
160C2×Q8—2632no—
161C2×Q8—2632no—
162C2×Q8—2632no—
163C2×Q8—5261no—
164C2×Q8—5261no—
165C2×Q8—5261no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4C4×D26312yes—
172C22×C4—21no—
173C22×C4—2631no—
174C22×C4—2631no—
175C22×C4—5261no—
176C22×C4—5261no—
177C22×C4C22×D26311yescharacteristic
178SD16—5268no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—2632no—
183C2×C8—5261no—
184C2×C8—5261no—
185C4⋊C4—21no—
186C4⋊C4—5264no—
187C4⋊C4—5261no—
188C4⋊C4—5261no—
189C4⋊C4C22⋊D26312yes—
190C22⋊C4—10522no—
191C22⋊C4—10522no—
192C42—5264no—
193C42—5261no—
194C42—5261no—
195C23—22no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23D4×D26311yescharacteristic
203Q8—2634no—
204Q8—5262no—
205Q8—5262no—
206Q8—5262no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2632no—
215C2×C4—5262no—
216C2×C4—5261no—
217C2×C4—5262no—
218C2×C4—5262no—
219C2×C4—5261no—
220C2×C4—5261no—
221C2×C4—5261no—
222C2×C4—5261no—
223C2×C4—10521no—
224C2×C4—10521no—
225C2×C4—10521no—
226C2×C4C2×C4×D26311yescharacteristic
227C2×C4D4×D26311yescharacteristic
228C2×C4D4×D26311yescharacteristic
229C2×C4C2×C22⋊D26311yescharacteristic
230C2×C4#1686237511yescharacteristic
231C2×C4#1686237611yescharacteristic
232C8—41no—
233C8—5262no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22(C22⋊D263)⋊C411yescharacteristic
242C22#2255443811yescharacteristic
243C22#2255444311yescharacteristic
244C22SD16×D26311yescharacteristic
245C22#2255448911yescharacteristic
246C22#2255449411yescharacteristic
247C22#2255449911yescharacteristic
248C4—42no—
249C4—5264no—
250C4—5262no—
251C4—10521no—
252C4—21041no—
253C4C22⋊C4×D26311yescharacteristic
254C4C4×C22⋊D26311yescharacteristic
255C4#2255444111yescharacteristic
256C4#2255445211yescharacteristic
257C2—82no—
258C2#3068181411yescharacteristic
259C2#3068202911yescharacteristic
260C2#3068203511yescharacteristic
261C2#3068207511yescharacteristic
262C2#3068208011yescharacteristic
263C2#3068213711yescharacteristic
264C2#3068215911yescharacteristic
subgroupG/H
centerC23D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#102×C263C2
socleC23×C263C2×D4
prime radicalC22×D4×C263C22
cosocleC22×C4×C263C23
hypercenterC2×#102D263
hypocenterC263#1880
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#22554435C2semidirect
3. C2×#22554395C2semidirect
5. #30681700C2semidirect
6. #30681692C2semidirect
11. C2×#16862364C4semidirect
65. Dic526C22⋊C4semidirect
77. C2×Dic263SD16semidirect
132. C263#1880semidirect

Maximal subgroups

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

subgroupindex
C22×#168623642
C2×#225544352
C2×#225543952
#306818412
#306817002
#306816922
C2×#102×C2632
#1880263