Finite Group Databasebeta

← #46784103

Subgroups — #46784103

Order 33664.

228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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×#22554405C211yesmaximal, characteristic, complemented
2#30681980C211yesmaximal, characteristic, complemented
3#30681966C211yesmaximal, characteristic, complemented
4#30681943C211yesmaximal, characteristic
5C2×#22554391C211yesmaximal, characteristic
6#30681706C211yesmaximal, characteristic, complemented
7C2×#100×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9C22×C263⋊C8C2211yescharacteristic
10#22554429C2211yescharacteristic
11C2×C4⋊Dic263C2211yescharacteristic
12#22554405—22no—
13#22554404—21no—
14#22554402—21no—
15Dic263⋊C8—22no—
16#22554391—22no—
17#22554391—21no—
18#22554391—21no—
19C22×D4×C263C2211yescharacteristic
20C2×M16×C263C2211yescharacteristic
21C2×M16×C263C2211yescharacteristic
22#100×C263—22no—
23C22×Dic263—21no—
24#16862360—21no—
25#16862360—21no—
26C2×C263⋊C8—21no—
27C2×C263⋊C8—21no—
28C2×C263⋊C8—21no—
29C2×C263⋊C8D412yes—
30C4⋊Dic263—21no—
31C4⋊Dic263—21no—
32C4⋊Dic263D411yescharacteristic
33C4⋊Dic263D411yescharacteristic
34C22⋊Dic263—21no—
35C4×Dic263—21no—
36C24×C263—21no—
37C2×D4×C263—21no—
38C2×D4×C263—21no—
39C2×D4×C263—21no—
40C2×D4×C263—21no—
41C2×D4×C263—21no—
42C2×D4×C263Q812yes—
43C22×C4×C263C2311yescharacteristic
44M16×C263—21no—
45M16×C263—21no—
46M16×C263—21no—
47M16×C263D412yes—
48C2×C8×C263—21no—
49C2×C8×C263—21no—
50C2×Dic263—21no—
51C2×Dic263—21no—
52C2×Dic263—41no—
53C2×Dic263—81no—
54C263⋊C8—22no—
55C263⋊C8—41no—
56C23×C263—22no—
57C23×C263—41no—
58C23×C263—41no—
59C23×C263—81no—
60C23×C263—81no—
61C23×C263#4111yescharacteristic
62D4×C263—22no—
63D4×C263—22no—
64D4×C263—41no—
65D4×C263—41no—
66C2×C4×C263C2×D411yescharacteristic
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×Q811yescharacteristic
70C2×C4×C263#4111yescharacteristic
71C2×C4×C263#4111yescharacteristic
72C8×C263—22no—
73C8×C263—41no—
74C22×C263—21no—
75C22×C263—21no—
76C22×C263—42no—
77C22×C263—82no—
78C22×C263—82no—
79C22×C263—81no—
80C22×C263—81no—
81C22×C263#12111yescharacteristic
82C22×C263C22⋊Q811yescharacteristic
83C22×C263#12611yescharacteristic
84C4×C263#12111yescharacteristic
85C4×C263#12111yescharacteristic
86C4×C263C22⋊Q811yescharacteristic
87C4×C263C22⋊Q811yescharacteristic
88Dic263—41no—
89Dic263—41no—
90Dic263—81no—
91C2×C263—21no—
92C2×C263—21no—
93C2×C263—82no—
94C2×C263#39611yescharacteristic
95C2×C263#47111yescharacteristic
96C2×C263#47211yescharacteristic
97C263#206311yescharacteristic, complemented, Sylow
98#2063—2631nomaximal, Sylow
99C2×#108—2631no—
100#428—2631no—
101#424—2631no—
102#418—2631no—
103C2×#102—2631no—
104C2×#100D26311yescharacteristic
105#343—2631no—
106C22×D4C2×D26311yescharacteristic
107C2×M16—2631no—
108C2×M16C2×D26311yescharacteristic
109C2×M16C2×D26311yescharacteristic
110C22×C8—2631no—
111#117—2631no—
112C2×C4⋊C4—2631no—
113#108—5262no—
114#107—5261no—
115#106—5261no—
116C4⋊C8—5262no—
117#102—5261no—
118#102—5261no—
119#102—5262no—
120#100—22no—
121C24—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4Dic52612yes—
128C22×C4—5261no—
129C22×C4C22×D26311yescharacteristic
130M16—21no—
131M16—21no—
132M16—21no—
133M16—5261no—
134M16—5261no—
135M16C22⋊D26312yes—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—2632no—
139C2×C8—5261no—
140C2×C8—5261no—
141C2×C8—5261no—
142C4⋊C4—2631no—
143C4⋊C4—2631no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C22⋊C4—5261no—
147C42—5261no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—81no—
152C23—81no—
153C23#1686237611yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—5261no—
159C2×C4—5261no—
160C2×C4—10521no—
161C2×C4—21041no—
162C2×C4D4×D26311yescharacteristic
163C2×C4D4×D26311yescharacteristic
164C2×C4C2×C22⋊D26311yescharacteristic
165C2×C4C2×Dic52611yescharacteristic
166C2×C4#1686237511yescharacteristic
167C2×C4#1686237511yescharacteristic
168C8—22no—
169C8—41no—
170C8—5262no—
171C8—10521no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—82no—
176C22—82no—
177C22—81no—
178C22—81no—
179C22#2255444311yescharacteristic
180C22#2255444911yescharacteristic
181C22#2255446311yescharacteristic
182C4—10521no—
183C4—10521no—
184C4—21041no—
185C4#2255444111yescharacteristic
186C4#2255444211yescharacteristic
187C4#2255444711yescharacteristic
188C4#2255444711yescharacteristic
189C2—21no—
190C2—21no—
191C2—82no—
192C2#3068186111yescharacteristic
193C2#3068220011yescharacteristic
194C2#3068220711yescharacteristic
subgroupG/H
centerC22#22554443
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#100×C263C2
socleC22×C263#121
prime radicalC22×D4×C263C22
hypercenterC2×#100D263
hypocenterC263#2063
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#22554405C2semidirect
2. #30681980C2semidirect
3. #30681966C2semidirect
6. #30681706C2semidirect
97. C263#2063semidirect

Maximal subgroups

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

subgroupindex
C2×#225544052
#306819802
#306819662
#306819432
C2×#225543912
#306817062
C2×#100×C2632
#2063263