Finite Group Databasebeta

← #46783322

Subgroups — #46783322

Order 33664.

230 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 95 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×#22554401C211yesmaximal, characteristic
2C4×C4⋊Dic263C211yesmaximal, characteristic
3#30681700C211yesmaximal, characteristic
4#30681700C211yesmaximal, characteristic
5#30681700C211yesmaximal, characteristic
6#30681693C211yesmaximal, characteristic
7#389×C263C211yesmaximal, characteristic
8C22×C263⋊C8C2211yescharacteristic
9C22×C263⋊C8C2211yescharacteristic
10C2×C4⋊Dic263C2211yescharacteristic
11C2×C4⋊Dic263C2211yescharacteristic
12C2×C4×Dic263—21no—
13#22554401C414yescomplemented
14C263⋊#95—21no—
15C2×C4⋊C4×C263—21no—
16C2×C4⋊C4×C263C2211yescharacteristic
17C2×C4⋊C4×C263C2211yescharacteristic
18C2×C42×C263C2211yescharacteristic
19#95×C263—21no—
20C22×Dic263—21no—
21C22×Dic263—21no—
22C2×C263⋊C8—21no—
23C2×C263⋊C8—21no—
24C2×C263⋊C8—21no—
25C2×C263⋊C8—21no—
26C2×C263⋊C8—21no—
27C2×C263⋊C8C2×C412yes—
28C4⋊Dic263—21no—
29C4⋊Dic263—21no—
30C4⋊Dic263C2×C412yes—
31C4⋊Dic263Q812yes—
32C4×Dic263—42no—
33C22×C4×C263—21no—
34C22×C4×C263—21no—
35C22×C4×C263D411yescharacteristic
36C22×C4×C263D411yescharacteristic
37C22×C4×C263C2311yescharacteristic
38C4⋊C4×C263—21no—
39C4⋊C4×C263—21no—
40C4⋊C4×C263—21no—
41C4⋊C4×C263—42no—
42C4⋊C4×C263C2×C412yes—
43C42×C263—21no—
44C42×C263—21no—
45C2×Dic263—22no—
46C2×Dic263—22no—
47C2×Dic263—41no—
48C2×Dic263—41no—
49C2×Dic263—41no—
50C2×Dic263—41no—
51C263⋊C8—22no—
52C263⋊C8—41no—
53C23×C263C2×D411yescharacteristic
54C2×C4×C263—21no—
55C2×C4×C263—21no—
56C2×C4×C263—22no—
57C2×C4×C263—21no—
58C2×C4×C263—21no—
59C2×C4×C263—21no—
60C2×C4×C263—41no—
61C2×C4×C263—41no—
62C2×C4×C263—41no—
63C2×C4×C263—41no—
64C2×C4×C263—41no—
65C2×C4×C263SD1612yes—
66C2×C4×C263C22×C411yescharacteristic
67C2×C4×C263C2×Q811yescharacteristic
68C2×C4×C263#4111yescharacteristic
69C2×C4×C263#4111yescharacteristic
70C2×C4×C263#4111yescharacteristic
71C2×C4×C263#4111yescharacteristic
72C22×C263C4×D411yescharacteristic
73C22×C263C22⋊Q811yescharacteristic
74C22×C263#12311yescharacteristic
75C22×C263C2×SD1611yescharacteristic
76C22×C263#13511yescharacteristic
77C22×C263AGL(1,ℤ/8)11yescharacteristic
78C22×C263#13711yescharacteristic
79C4×C263—22no—
80C4×C263—42no—
81C4×C263—41no—
82C4×C263—81no—
83C4×C263#11711yescharacteristic
84C4×C263C4×Q811yescharacteristic
85C4×C263#12511yescharacteristic
86C4×C263#12611yescharacteristic
87Dic263—42no—
88Dic263—42no—
89C2×C263#38711yescharacteristic
90C2×C263C4×SD1611yescharacteristic
91C2×C263#44011yescharacteristic
92C2×C263#47511yescharacteristic
93C2×C263#47811yescharacteristic
94C2×C263#48111yescharacteristic
95C2×C263#48511yescharacteristic
96C263#191911yescharacteristic, complemented, Sylow
97#1919—2631nomaximal, Sylow
98C2×#106—2631no—
99#389D26311yescharacteristic
100C4×C4⋊C4—2631no—
101#340—2631no—
102#340—2631no—
103#340—2631no—
104#336—2631no—
105C22×C8—2631no—
106C22×C8—2631no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—2631no—
109C2×C4⋊C4—2631no—
110C2×C4⋊C4C2×D26311yescharacteristic
111C2×C4⋊C4C2×D26311yescharacteristic
112C2×C42—5261no—
113C2×C42C2×D26311yescharacteristic
114#106—2634no—
115#95—21no—
116#95—5261no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—5261no—
120C22×C4—5261no—
121C22×C4C22⋊D26311yescharacteristic
122C22×C4C22⋊D26311yescharacteristic
123C22×C4C22×D26311yescharacteristic
124C2×C8—2632no—
125C2×C8—5261no—
126C2×C8—5261no—
127C2×C8—5261no—
128C2×C8—5261no—
129C2×C8—5261no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—42no—
134C4⋊C4—2632no—
135C4⋊C4—2632no—
136C4⋊C4—5261no—
137C4⋊C4—5261no—
138C4⋊C4C4×D26312yes—
139C42—21no—
140C42—21no—
141C42—10522no—
142C23C2×C22⋊D26311yescharacteristic
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—22no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—5262no—
155C2×C4—5262no—
156C2×C4—10521no—
157C2×C4—10521no—
158C2×C4—10521no—
159C2×C4—10521no—
160C2×C4#1686236412yes—
161C2×C4C2×C4×D26311yescharacteristic
162C2×C4Q8×D26311yescharacteristic
163C2×C4#1686237511yescharacteristic
164C2×C4#1686237511yescharacteristic
165C2×C4#1686237611yescharacteristic
166C2×C4#1686237711yescharacteristic
167C8—5262no—
168C8—10521no—
169C22C4×C22⋊D26311yescharacteristic
170C22#2255444611yescharacteristic
171C22#2255445111yescharacteristic
172C22C2×#1686236411yescharacteristic
173C22#2255449011yescharacteristic
174C22#2255449511yescharacteristic
175C22#2255450111yescharacteristic
176C4—22no—
177C4—41no—
178C4—42no—
179C4—81no—
180C4—10522no—
181C4—10522no—
182C4#2255442811yescharacteristic
183C4#2255443511yescharacteristic
184C4#2255446011yescharacteristic
185C4#2255446511yescharacteristic
186C2#3068181911yescharacteristic
187C2C4×#1686236411yescharacteristic
188C2#3068203611yescharacteristic
189C2#3068222011yescharacteristic
190C2#3068223511yescharacteristic
191C2#3068225411yescharacteristic
192C2#3068227611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#389×C263C2
socle, prime radicalC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenter#389D263
hypocenterC263#1919
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
13. #22554401C4semidirect
96. C263#1919semidirect

Maximal subgroups

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

subgroupindex
C2×#225544012
C4×C4⋊Dic2632
#306817002
#306816932
#389×C2632
#1919263