Finite Group Databasebeta

← #46783887

Subgroups — #46783887

Order 33664.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#22554469C211yesmaximal, characteristic
2C2×#22554395C211yesmaximal, characteristic
3C2×#22554393C211yesmaximal, characteristic
4#30681843C211yesmaximal, characteristic
5#30681700C211yesmaximal, characteristic
6#30681692C211yesmaximal, characteristic
7#340×C263C211yesmaximal, characteristic
8C22×Dic526—21no—
9C22×Dic526C2211yescharacteristic
10C22×C263⋊C8C2211yescharacteristic
11#22554469—22no—
12#22554469—22no—
13C2×C4⋊Dic263C2211yescharacteristic
14C2×Dic263⋊C4—21no—
15C2×C4×Dic263C2211yescharacteristic
16#22554395—22no—
17#22554393—22no—
18C263⋊#95—21no—
19C263⋊#95—21no—
20C22×C8×C263C2211yescharacteristic
21C2×C4⋊C4×C263C2211yescharacteristic
22C2×C4⋊C4×C263C2211yescharacteristic
23C2×Dic526—24no—
24C2×Dic526—21no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—42no—
30C2×Dic526—42no—
31C2×Dic526Q812yescomplemented
32C22×Dic263—21no—
33C22×Dic263—21no—
34C22×Dic263D411yescharacteristic
35C22×Dic263D411yescharacteristic
36C2×C263⋊C8—21no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8—21no—
39C4⋊Dic263—21no—
40C4⋊Dic263D412yes—
41Dic263⋊C4—24no—
42C4×Dic263—21no—
43C4×Dic263—21no—
44C22×C4×C263—21no—
45C22×C4×C263—21no—
46C22×C4×C263C2311yescharacteristic
47C2×C8×C263—21no—
48C2×C8×C263—21no—
49C2×C8×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263D412yes—
54Dic526—22no—
55Dic526—22no—
56Dic526—48no—
57Dic526—41no—
58Dic526—41no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—21no—
63C2×Dic263—22no—
64C2×Dic263—22no—
65C2×Dic263—41no—
66C2×Dic263—41no—
67C2×Dic263—41no—
68C2×Dic263—41no—
69C2×Dic263SD1612yes—
70C2×Dic263Q1612yes—
71C263⋊C8—41no—
72C23×C263C2×D411yescharacteristic
73C2×C4×C263—22no—
74C2×C4×C263—41no—
75C2×C4×C263—41no—
76C2×C4×C263—41no—
77C2×C4×C263—41no—
78C2×C4×C263—41no—
79C2×C4×C263C2×D411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×Q811yescharacteristic
82C2×C4×C263#4111yescharacteristic
83C2×C4×C263#4111yescharacteristic
84C2×C4×C263#4111yescharacteristic
85C8×C263—41no—
86C22×C263#12011yescharacteristic
87C22×C263C22⋊Q811yescharacteristic
88C22×C263#12411yescharacteristic
89C22×C263C2×SD1611yescharacteristic
90C22×C263C2×Q1611yescharacteristic
91C22×C263AGL(1,ℤ/8)11yescharacteristic
92C22×C263#13711yescharacteristic
93C4×C263—42no—
94C4×C263—81no—
95C4×C263C22⋊Q811yescharacteristic
96C4×C263C22⋊Q811yescharacteristic
97C4×C263#12411yescharacteristic
98C4×C263#12411yescharacteristic
99Dic263—22no—
100Dic263—22no—
101Dic263—42no—
102Dic263—42no—
103C2×C263#39311yescharacteristic
104C2×C263#45011yescharacteristic
105C2×C263#45111yescharacteristic
106C2×C263#47511yescharacteristic
107C2×C263#47711yescharacteristic
108C2×C263#48711yescharacteristic
109C2×C263#48911yescharacteristic
110C263#202411yescharacteristic, complemented, Sylow
111#2024—2631nomaximal, Sylow
112C2×C4⋊Q8—2631no—
113C2×#103—2631no—
114C2×#103—2631no—
115#391—2631no—
116#340—2631no—
117#340D26311yescharacteristic
118#336—2631no—
119C22×Q8—2631no—
120C22×Q8—5261no—
121C22×C8—2631no—
122C22×C8C2×D26311yescharacteristic
123C4⋊Q8—5262no—
124C4⋊Q8—5262no—
125C2×C4⋊C4—2631no—
126C2×C4⋊C4—5261no—
127C2×C4⋊C4C2×D26311yescharacteristic
128C2×C4⋊C4C2×D26311yescharacteristic
129C2×C42—2631no—
130#103—5262no—
131#103—5262no—
132#95—5261no—
133#95—5261no—
134C2×Q8—2632no—
135C2×Q8—5264no—
136C2×Q8—5261no—
137C2×Q8—5261no—
138C2×Q8—5261no—
139C2×Q8—5261no—
140C2×Q8—5261no—
141C2×Q8—10522no—
142C2×Q8—10522no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2631no—
146C22×C4—2631no—
147C22×C4—5261no—
148C22×C4—5261no—
149C22×C4C22×D26311yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—5261no—
154C2×C8—5261no—
155C2×C8—5261no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—2632no—
160C4⋊C4—5264no—
161C4⋊C4—5261no—
162C4⋊C4D105212yes—
163C42—5261no—
164C42—5261no—
165C23D4×D26311yescharacteristic
166Q8—5262no—
167Q8—5262no—
168Q8—10528no—
169Q8—10521no—
170Q8—10521no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2632no—
178C2×C4—2632no—
179C2×C4—5261no—
180C2×C4—5261no—
181C2×C4—5261no—
182C2×C4—5261no—
183C2×C4—5262no—
184C2×C4—5262no—
185C2×C4—10521no—
186C2×C4—10521no—
187C2×C4—10521no—
188C2×C4—10521no—
189C2×C4D4×D26311yescharacteristic
190C2×C4C2×D105211yescharacteristic
191C2×C4Q8×D26311yescharacteristic
192C2×C4#1686237511yescharacteristic
193C2×C4#1686237611yescharacteristic
194C2×C4#1686237611yescharacteristic
195C8—41no—
196C8—10521no—
197C22#2255444011yescharacteristic
198C22#2255444811yescharacteristic
199C22#2255445611yescharacteristic
200C22SD16×D26311yescharacteristic
201C22Q16×D26311yescharacteristic
202C22#2255449411yescharacteristic
203C22#2255449911yescharacteristic
204C4—42no—
205C4—81no—
206C4—5262no—
207C4—5262no—
208C4—10522no—
209C4—10522no—
210C4#2255444811yescharacteristic
211C4#2255445011yescharacteristic
212C4#2255445611yescharacteristic
213C4#2255445811yescharacteristic
214C2#3068185111yescharacteristic
215C2#3068209011yescharacteristic
216C2#3068209511yescharacteristic
217C2#3068222211yescharacteristic
218C2#3068223211yescharacteristic
219C2#3068228711yescharacteristic
220C2#3068229611yescharacteristic
subgroupG/H
centerC23D4×D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#340×C263C2
socle, prime radicalC23×C263C2×D4
hypercenter#340D263
hypocenterC263#2024
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic526Q8semidirect
110. C263#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#225544692
C2×#225543952
C2×#225543932
#306818432
#306817002
#306816922
#340×C2632
#2024263