Finite Group Databasebeta

← #46784102

Subgroups — #46784102

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
1#30681980C211yesmaximal, characteristic, complemented
2#30681964C211yesmaximal, characteristic, complemented
3#30681944C211yesmaximal, characteristic
4C2×#22554392C211yesmaximal, characteristic
5C2×#22554386C211yesmaximal, characteristic
6#30681706C211yesmaximal, characteristic, complemented
7C2×#108×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554429C2211yescharacteristic
11C2×C4⋊Dic263C2211yescharacteristic
12#22554404—21no—
13#22554402—21no—
14Dic263⋊C8—22no—
15#22554392—21no—
16#22554392—21no—
17#22554392—22no—
18#22554386—22no—
19C2×M16×C263C2211yescharacteristic
20C2×M16×C263C2211yescharacteristic
21C22×C8×C263C2211yescharacteristic
22#108×C263—22no—
23C23×D263—21no—
24C2×D1052—21no—
25C2×D1052—21no—
26C2×D1052—21no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052Q812yes—
30C22×Dic263—21no—
31#16862360—21no—
32#16862360—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263D411yescharacteristic
37C4⋊Dic263D411yescharacteristic
38C22⋊Dic263—21no—
39C4×Dic263—21no—
40C22×C4×C263C2311yescharacteristic
41M16×C263—21no—
42M16×C263—21no—
43M16×C263—21no—
44M16×C263D412yes—
45C2×C8×C263—21no—
46C2×C8×C263—21no—
47C2×C8×C263—21no—
48C2×C8×C263—21no—
49C2×C8×C263D412yes—
50C22×D263—22no—
51C22×D263—41no—
52C22×D263—41no—
53C22×D263—81no—
54C22×D263—81no—
55D1052—22no—
56D1052—22no—
57D1052—41no—
58D1052—41no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—41no—
62C2×Dic263—81no—
63C263⋊C8—41no—
64C23×C263#4111yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263C2×D411yescharacteristic
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×Q811yescharacteristic
69C2×C4×C263#4111yescharacteristic
70C2×C4×C263#4111yescharacteristic
71C8×C263—22no—
72C8×C263—22no—
73C8×C263—41no—
74C22×C263—21no—
75C22×C263—21no—
76C22×C263#12111yescharacteristic
77C22×C263C22⋊Q811yescharacteristic
78C22×C263#12611yescharacteristic
79C2×D263—42no—
80C2×D263—82no—
81C2×D263—81no—
82C2×D263—81no—
83C2×D263—82no—
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#39611yescharacteristic
94C2×C263#47111yescharacteristic
95C2×C263#47211yescharacteristic
96D263—82no—
97C263#206311yescharacteristic, complemented, Sylow
98#2063—2631nomaximal, Sylow
99C2×#108D26311yescharacteristic, complemented
100#428—2631no—
101#424—2631no—
102#418—2631no—
103C2×#102—2631no—
104C2×#100—2631no—
105#343—2631no—
106C22×D4—2631no—
107C2×M16—2631no—
108C2×M16C2×D26311yescharacteristic
109C2×M16C2×D26311yescharacteristic
110C22×C8C2×D26311yescharacteristic
111#117—2631no—
112C2×C4⋊C4—2631no—
113#108—22no—
114#107—5261no—
115#106—5261no—
116C4⋊C8—5262no—
117#102—5261no—
118#102—5261no—
119#102—5262no—
120#100—5262no—
121C24—5261no—
122C2×D4—2632no—
123C2×D4—5261no—
124C2×D4—5261no—
125C2×D4—5261no—
126C2×D4—5261no—
127C2×D4—5261no—
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—21no—
139C2×C8—21no—
140C2×C8—5261no—
141C2×C8D105212yes—
142C4⋊C4—2631no—
143C4⋊C4—2631no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C22⋊C4—5261no—
147C42—5261no—
148C23—5262no—
149C23—10521no—
150C23—10521no—
151C23—21041no—
152C23—21041no—
153C23#1686237711yescharacteristic
154D4—5262no—
155D4—5262no—
156D4—10521no—
157D4—10521no—
158C2×C4—5261no—
159C2×C4—5261no—
160C2×C4—10521no—
161C2×C4—21041no—
162C2×C4D4×D26311yescharacteristic
163C2×C4C2×C22⋊D26311yescharacteristic
164C2×C4C2×D105211yescharacteristic
165C2×C4Q8×D26311yescharacteristic
166C2×C4#1686237511yescharacteristic
167C2×C4#1686237611yescharacteristic
168C8—22no—
169C8—22no—
170C8—41no—
171C8—10521no—
172C22—21no—
173C22—21no—
174C22—10522no—
175C22—21042no—
176C22—21042no—
177C22—21041no—
178C22—21041no—
179C22#2255444511yescharacteristic
180C22#2255444611yescharacteristic
181C22#2255446511yescharacteristic
182C4—10521no—
183C4—10521no—
184C4—21041no—
185C4#2255444211yescharacteristic
186C4#2255444411yescharacteristic
187C4#2255444811yescharacteristic
188C4#2255445011yescharacteristic
189C2—21no—
190C2—21no—
191C2—21042no—
192C2#3068186011yescharacteristic
193C2#3068220211yescharacteristic
194C2#3068220911yescharacteristic
subgroupG/H
centerC22#22554445
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#108×C263C2
socleC22×C263#121
prime radicalC22×D1052C22
hypercenterC2×#108D263
hypocenterC263#2063
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
1. #30681980C2semidirect
2. #30681964C2semidirect
6. #30681706C2semidirect
7. C2×#108×C263C2semidirect
97. C263#2063semidirect
99. C2×#108D263semidirect

Maximal subgroups

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

subgroupindex
#306819802
#306819642
#306819442
C2×#225543922
C2×#225543862
#306817062
C2×#108×C2632
#2063263