Finite Group Databasebeta

← #46782761

Subgroups — #46782761

Order 33664.

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

normal subgroups only

This group has 292 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
1C2×#22554435C211yesmaximal, characteristic
2C2×Dic263⋊C8C211yesmaximal, characteristic
3C2×#22554395C211yesmaximal, characteristic
4C2×#22554393C211yesmaximal, characteristic
5#30681803C211yesmaximal, characteristic
6#30681700C211yesmaximal, characteristic
7#340×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C22×C263⋊C8C2211yescharacteristic
10#22554435—22no—
11#22554435C414yescomplemented
12C2×C4⋊Dic263C2211yescharacteristic
13C2×Dic263⋊C4—21no—
14C2×C4×Dic263—21no—
15C2×C4×Dic263C2211yescharacteristic
16Dic263⋊C8—22no—
17#22554395—22no—
18#22554393—22no—
19C263⋊#95—21no—
20C263⋊#95—21no—
21C22×C8×C263C2211yescharacteristic
22C2×C4⋊C4×C263C2211yescharacteristic
23C2×C4⋊C4×C263C2211yescharacteristic
24C2×Dic526—21no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526C2×C412yes—
28C2×Dic526D412yes—
29C2×Dic526Q812yes—
30C22×Dic263—21no—
31C22×Dic263—21no—
32C22×Dic263D411yescharacteristic
33C22×Dic263D411yescharacteristic
34C2×C263⋊C8—21no—
35C2×C263⋊C8—21no—
36C2×C263⋊C8—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263—21no—
39Dic263⋊C4—24no—
40C4×Dic263—24no—
41C4×Dic263C2×C412yes—
42C4×Dic263D412yes—
43C22×C4×C263—21no—
44C22×C4×C263—21no—
45C22×C4×C263C2311yescharacteristic
46C2×C8×C263—21no—
47C2×C8×C263—21no—
48C2×C8×C263—21no—
49C4⋊C4×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263C2×C412yes—
53Dic526—22no—
54Dic526—22no—
55Dic526—22no—
56Dic526C4⋊C414yes—
57C2×Dic263—22no—
58C2×Dic263—22no—
59C2×Dic263—22no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—21no—
63C2×Dic263—21no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C2×Dic263—41no—
67C2×Dic263C22⋊C412yes—
68C2×Dic263C22⋊C412yes—
69C263⋊C8—41no—
70C23×C263C2×D411yescharacteristic
71C2×C4×C263—22no—
72C2×C4×C263—41no—
73C2×C4×C263—41no—
74C2×C4×C263—41no—
75C2×C4×C263—41no—
76C2×C4×C263—41no—
77C2×C4×C263C22×C411yescharacteristic
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C2×C4×C263C2×Q811yescharacteristic
81C2×C4×C263#4111yescharacteristic
82C2×C4×C263#4111yescharacteristic
83C8×C263—41no—
84C22×C263C2×C22⋊C411yescharacteristic
85C22×C263#12111yescharacteristic
86C22×C263C22⋊Q811yescharacteristic
87C22×C263#13511yescharacteristic
88C22×C263#13511yescharacteristic
89C22×C263#13711yescharacteristic
90C22×C263#13711yescharacteristic
91C4×C263—42no—
92C4×C263—81no—
93C4×C263C2×C4⋊C411yescharacteristic
94C4×C263#11711yescharacteristic
95C4×C263#12111yescharacteristic
96C4×C263C22⋊Q811yescharacteristic
97Dic263—24no—
98Dic263—22no—
99Dic263—22no—
100Dic263—81no—
101C2×C263#38011yescharacteristic
102C2×C263#41611yescharacteristic
103C2×C263#41911yescharacteristic
104C2×C263#46411yescharacteristic
105C2×C263#46411yescharacteristic
106C2×C263#47911yescharacteristic
107C2×C263#47911yescharacteristic
108C263#180511yescharacteristic, complemented, Sylow
109#1805—2631nomaximal, Sylow
110C2×C4×Q8—2631no—
111C2×C4⋊C8—2631no—
112C2×#103—2631no—
113C2×#103—2631no—
114#382—2631no—
115#340—2631no—
116#340D26311yescharacteristic
117C22×Q8—2631no—
118C22×C8—2631no—
119C22×C8C2×D26311yescharacteristic
120C4×Q8—2634no—
121C4×Q8—5262no—
122C2×C4⋊C4—2631no—
123C2×C4⋊C4—5261no—
124C2×C4⋊C4C2×D26311yescharacteristic
125C2×C4⋊C4C2×D26311yescharacteristic
126C2×C42—2631no—
127C2×C42—5261no—
128C4⋊C8—5262no—
129#103—5262no—
130#103—5262no—
131#95—5261no—
132#95—5261no—
133C2×Q8—2632no—
134C2×Q8—2632no—
135C2×Q8—2632no—
136C2×Q8—5261no—
137C2×Q8—5261no—
138C2×Q8—5261no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—2631no—
142C22×C4—2631no—
143C22×C4—5261no—
144C22×C4—5261no—
145C22×C4C22×D26311yescharacteristic
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—5261no—
150C2×C8—5261no—
151C2×C8—5261no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—5264no—
156C4⋊C4—5261no—
157C4⋊C4—5261no—
158C4⋊C4C4×D26312yes—
159C42—2632no—
160C42—2632no—
161C42—5264no—
162C23D4×D26311yescharacteristic
163Q8—2634no—
164Q8—5262no—
165Q8—5262no—
166Q8—5262no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2632no—
174C2×C4—2632no—
175C2×C4—5262no—
176C2×C4—5262no—
177C2×C4—5262no—
178C2×C4—5261no—
179C2×C4—5261no—
180C2×C4—5261no—
181C2×C4—5261no—
182C2×C4—10521no—
183C2×C4—10521no—
184C2×C4—10521no—
185C2×C4C2×C4×D26311yescharacteristic
186C2×C4D4×D26311yescharacteristic
187C2×C4D4×D26311yescharacteristic
188C2×C4Q8×D26311yescharacteristic
189C2×C4#1686237611yescharacteristic
190C2×C4#1686237611yescharacteristic
191C8—41no—
192C8—10521no—
193C22C22⋊C4×D26311yescharacteristic
194C22#2255444311yescharacteristic
195C22#2255444811yescharacteristic
196C22#2255448911yescharacteristic
197C22#2255449111yescharacteristic
198C22#2255449911yescharacteristic
199C22#2255450211yescharacteristic
200C4—42no—
201C4—81no—
202C4—5262no—
203C4—5262no—
204C4—5264no—
205C4—21041no—
206C4C4⋊C4×D26311yescharacteristic
207C4#2255442711yescharacteristic
208C4#2255444311yescharacteristic
209C4#2255444811yescharacteristic
210C2#3068179711yescharacteristic
211C2#3068193111yescharacteristic
212C2#3068194511yescharacteristic
213C2#3068215911yescharacteristic
214C2#3068216311yescharacteristic
215C2#3068224411yescharacteristic
216C2#3068224811yescharacteristic
subgroupG/H
centerC23D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#340×C263C2
socle, prime radicalC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenter#340D263
hypocenterC263#1805
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #22554435C4semidirect
108. C263#1805semidirect

Maximal subgroups

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

subgroupindex
C2×#225544352
C2×Dic263⋊C82
C2×#225543952
C2×#225543932
#306818032
#306817002
#340×C2632
#1805263