Finite Group Databasebeta

← #46783334

Subgroups — #46783334

Order 33664.

230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#30681837C211yesmaximal, characteristic
2C4⋊C4×Dic263C211yesmaximal, characteristic
3#30681701C211yesmaximal, characteristic
4#30681700C211yesmaximal, characteristic
5#30681700C211yesmaximal, characteristic
6#30681692C211yesmaximal, characteristic
7C2×#106×C263C211yesmaximal, characteristic
8C22×C263⋊C8C2211yescharacteristic
9C2×C4⋊Dic263—21no—
10C2×C4⋊Dic263C2211yescharacteristic
11C2×C4⋊Dic263C2211yescharacteristic
12C2×C4×Dic263—21no—
13C2×C4×Dic263C2211yescharacteristic
14C263⋊#95—21no—
15C263⋊#95—21no—
16C22×C8×C263C2211yescharacteristic
17C2×C4⋊C4×C263C2211yescharacteristic
18C2×C4⋊C4×C263C2211yescharacteristic
19#106×C263C414yescomplemented
20C22×Dic263—21no—
21C22×Dic263—21no—
22C22×Dic263D411yescharacteristic
23C22×Dic263D411yescharacteristic
24C2×C263⋊C8—21no—
25C2×C263⋊C8—21no—
26C2×C263⋊C8—21no—
27C4⋊Dic263—21no—
28C4⋊Dic263—21no—
29C4⋊Dic263—21no—
30C4⋊Dic263—42no—
31C4⋊Dic263Q812yes—
32C4×Dic263—21no—
33C4×Dic263—21no—
34C4×Dic263—42no—
35C22×C4×C263—21no—
36C22×C4×C263—21no—
37C22×C4×C263C2311yescharacteristic
38C2×C8×C263—21no—
39C2×C8×C263—21no—
40C2×C8×C263C2×C412yes—
41C4⋊C4×C263—21no—
42C4⋊C4×C263—21no—
43C4⋊C4×C263C2×C412yes—
44C4⋊C4×C263C2×C412yes—
45C2×Dic263—21no—
46C2×Dic263—21no—
47C2×Dic263—22no—
48C2×Dic263—21no—
49C2×Dic263—21no—
50C2×Dic263—21no—
51C2×Dic263—41no—
52C2×Dic263—41no—
53C2×Dic263—41no—
54C2×Dic263—41no—
55C2×Dic263—41no—
56C2×Dic263SD1612yes—
57C263⋊C8—41no—
58C23×C263C2×D411yescharacteristic
59C2×C4×C263—22no—
60C2×C4×C263—22no—
61C2×C4×C263—41no—
62C2×C4×C263—41no—
63C2×C4×C263—41no—
64C2×C4×C263—41no—
65C2×C4×C263C22×C411yescharacteristic
66C2×C4×C263C2×Q811yescharacteristic
67C2×C4×C263#4111yescharacteristic
68C2×C4×C263#4111yescharacteristic
69C2×C4×C263#4111yescharacteristic
70C2×C4×C263#4111yescharacteristic
71C8×C263—22no—
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—42no—
80C4×C263—42no—
81C4×C263#11711yescharacteristic
82C4×C263C4×Q811yescharacteristic
83C4×C263#12511yescharacteristic
84C4×C263#12611yescharacteristic
85Dic263—22no—
86Dic263—42no—
87Dic263—41no—
88Dic263—81no—
89C2×C263#38711yescharacteristic
90C2×C263C4×SD1611yescharacteristic
91C2×C263#44011yescharacteristic
92C2×C263#47611yescharacteristic
93C2×C263#47911yescharacteristic
94C2×C263#48211yescharacteristic
95C2×C263#48311yescharacteristic
96C263#192011yescharacteristic, complemented, Sylow
97#1920—2631nomaximal, Sylow
98C2×#106D26311yescharacteristic
99#389—2631no—
100C4×C4⋊C4—2631no—
101#340—2631no—
102#340—2631no—
103#340—2631no—
104#336—2631no—
105C22×C8—2631no—
106C22×C8C2×D26311yescharacteristic
107C2×C4⋊C4—2631no—
108C2×C4⋊C4—2631no—
109C2×C4⋊C4—5261no—
110C2×C4⋊C4C2×D26311yescharacteristic
111C2×C4⋊C4C2×D26311yescharacteristic
112C2×C42—2631no—
113C2×C42—5261no—
114#106Dic26314yescomplemented
115#95—5261no—
116#95—5261no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—2631no—
120C22×C4—2631no—
121C22×C4—5261no—
122C22×C4—5261no—
123C22×C4C22×D26311yescharacteristic
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—5261no—
127C2×C8—5261no—
128C2×C8—5261no—
129C2×C8C2×Dic26312yes—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2632no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C4⋊C4—5261no—
136C4⋊C4—10522no—
137C4⋊C4C2×Dic26312yes—
138C4⋊C4C2×Dic26312yes—
139C42—5261no—
140C42—5261no—
141C42—10522no—
142C23D4×D26311yescharacteristic
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—2632no—
150C2×C4—5261no—
151C2×C4—5261no—
152C2×C4—5262no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—5261no—
156C2×C4—10521no—
157C2×C4—10521no—
158C2×C4—10521no—
159C2×C4—10521no—
160C2×C4—10521no—
161C2×C4C22×Dic26311yescharacteristic
162C2×C4Q8×D26311yescharacteristic
163C2×C4#1686237511yescharacteristic
164C2×C4#1686237611yescharacteristic
165C2×C4#1686237611yescharacteristic
166C2×C4#1686237711yescharacteristic
167C8—22no—
168C8—10521no—
169C22D4×Dic26311yescharacteristic
170C22#2255444811yescharacteristic
171C22#2255445511yescharacteristic
172C22SD16×D26311yescharacteristic
173C22#2255449111yescharacteristic
174C22#2255449711yescharacteristic
175C22#2255449911yescharacteristic
176C4—42no—
177C4—42no—
178C4—5262no—
179C4—10522no—
180C4—10521no—
181C4—21041no—
182C4#2255442911yescharacteristic
183C4Q8×Dic26311yescharacteristic
184C4#2255446011yescharacteristic
185C4#2255446511yescharacteristic
186C2#3068182411yescharacteristic
187C2SD16×Dic26311yescharacteristic
188C2#3068203911yescharacteristic
189C2#3068222711yescharacteristic
190C2#3068224811yescharacteristic
191C2#3068226411yescharacteristic
192C2#3068227011yescharacteristic
subgroupG/H
centerC23D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#106×C263C2
socle, prime radicalC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenterC2×#106D263
hypocenterC263#1920
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
19. #106×C263C4semidirect
96. C263#1920semidirect
114. #106Dic263semidirect

Maximal subgroups

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

subgroupindex
#306818372
C4⋊C4×Dic2632
#306817012
#306817002
#306816922
C2×#106×C2632
#1920263