Finite Group Databasebeta

← #46810846

Subgroups — #46810846

Order 34432.

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

normal subgroups only

This group has 552 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×#22575501C211yesmaximal, characteristic
2C2×#22575379C212yesmaximal, complemented
3#31770607C212yesmaximal, complemented
4#31770512C211yesmaximal, characteristic, complemented
5C2×#101×C269C211yesmaximal, characteristic, complemented
6#22575501—24no—
7#22575501—22no—
8#22575501C414yescomplemented
9C2×#16864403—22no—
10C2×#16864402—22no—
11C2×#16864402C2212yes—
12C2×Q8×D269—22no—
13C2×C4⋊Dic269C2211yescharacteristic
14C2×C4×Dic269C2211yescharacteristic
15#22575379—24no—
16#22575378—22no—
17#22575375—22no—
18#22575360—22no—
19C22×Q8×C269C2211yescharacteristic
20C2×M16×C269C2212yes—
21#101×C269—22no—
22#16864403—28no—
23#16864403—28no—
24#16864402—28no—
25#16864402—28no—
26#16864402—22no—
27#16864402—22no—
28#16864402C2×C414yes—
29#16864402D414yes—
30C2×Dic538—22no—
31C2×Dic538D412yes—
32Q8×D269—28no—
33Q8×D269—28no—
34C2×D1076—22no—
35C2×D1076D412yes—
36C2×C22⋊D269—22no—
37C22×Dic269—21no—
38C22×Dic269—21no—
39C2×C4×D269—24no—
40C2×C4×D269—22no—
41C4⋊Dic269—22no—
42C4×Dic269—22no—
43C2×Q8×C269—22no—
44C2×Q8×C269—22no—
45C2×Q8×C269C2×C412yes—
46C2×Q8×C269D412yes—
47C22×C4×C269D412yes—
48C22×C4×C269C2311yescharacteristic
49M16×C269—22no—
50M16×C269—22no—
51C2×C8×C269—22no—
52C22×D269—22no—
53Dic538—28no—
54Dic538—22no—
55Dic538C22⋊C414yes—
56D1076—28no—
57D1076—22no—
58D1076C22⋊C414yes—
59C22⋊D269—24no—
60C22⋊D269—24no—
61C2×Dic269—22no—
62C2×Dic269—22no—
63C2×Dic269—41no—
64C2×Dic269—41no—
65C2×Dic269—42no—
66C2×Dic269—41no—
67C4×D269—216no—
68C4×D269—24no—
69C4×D269—24no—
70C23×C269C2×D411yescharacteristic
71Q8×C269—24no—
72Q8×C269—24no—
73C2×C4×C269—22no—
74C2×C4×C269—22no—
75C2×C4×C269C22⋊C414yes—
76C2×C4×C269C22×C411yescharacteristic
77C2×C4×C269C2×D412yes—
78C2×C4×C269C2×D412yes—
79C2×C4×C269C2×D411yescharacteristic
80C8×C269—42no—
81C22×C269—21no—
82C22×C269—21no—
83C22×C269C2×C22⋊C411yescharacteristic
84C22×C269#12011yescharacteristic
85C22×C269#12011yescharacteristic
86C2×D269—24no—
87C2×D269—42no—
88C2×D269—42no—
89C4×C269—24no—
90C4×C269C2×C22⋊C412yes—
91C4×C269#12012yes—
92Dic269—24no—
93Dic269—42no—
94Dic269—81no—
95C2×C269—21no—
96C2×C269—21no—
97C2×C269#37911yescharacteristic
98C2×C269#45411yescharacteristic
99C2×C269#45611yescharacteristic
100D269—44no—
101C269#179311yescharacteristic, complemented, Sylow
102#1793—2691nomaximal, Sylow
103C2×2−1+4—2691no—
104C2×#104—2692no—
105#417—2692no—
106C2×#101D26911yescharacteristic, complemented
107#391—2691no—
1082−1+4—2694no—
1092−1+4—5384no—
1102−1+4—5382no—
111C2×#41—2692no—
112C2×#41—5382no—
113C2×#41—5382no—
114C22×Q8—5382no—
115C22×Q8C2×D26911yescharacteristic
116C2×M16C2×D26912yes—
117C2×C4⋊C4—2691no—
118C2×C42—2691no—
119#104—5384no—
120#103—5382no—
121#102—5382no—
122#101—22no—
123#95—5382no—
124#41—2694no—
125#41—2694no—
126#41—5388no—
127#41—5388no—
128#41—5388no—
129#41—5388no—
130#41—5382no—
131#41—5382no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—2692no—
135C2×Q8—5382no—
136C2×Q8—5388no—
137C2×Q8—5388no—
138C2×Q8C4×D26912yes—
139C2×Q8C22⋊D26912yes—
140C2×D4—2692no—
141C2×D4—5382no—
142C2×D4—5382no—
143C22×C4—5384no—
144C22×C4—5382no—
145C22×C4—5381no—
146C22×C4—5381no—
147C22×C4D107612yes—
148C22×C4C22×D26911yescharacteristic
149M16—22no—
150M16—22no—
151C2×C8—22no—
152C4⋊C4—5382no—
153C42—5382no—
154C23—5382no—
155C23C2×D107611yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—2694no—
159Q8—5388no—
160Q8—5382no—
161D4—2694no—
162D4—5388no—
163D4—5384no—
164D4—5384no—
165D4—5382no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—53816no—
169C2×C4—5382no—
170C2×C4—5384no—
171C2×C4—5384no—
172C2×C4—5382no—
173C2×C4—10761no—
174C2×C4—10761no—
175C2×C4—10762no—
176C2×C4—10761no—
177C2×C4#1686437914yes—
178C2×C4C2×C4×D26911yescharacteristic
179C2×C4D4×D26912yes—
180C2×C4D4×D26912yes—
181C2×C4C2×C22⋊D26911yescharacteristic
182C8—42no—
183C22—21no—
184C22—21no—
185C22—5384no—
186C22—10762no—
187C22—10762no—
188C22C2×#1686437911yescharacteristic
189C22#2257542311yescharacteristic
190C22#2257542311yescharacteristic
191C4—24no—
192C4—5384no—
193C4—10762no—
194C4—21521no—
195C4C22⋊C4×D26912yes—
196C4#2257542112yes—
197C2—21no—
198C2—21no—
199C2—10764no—
200C2#3177046011yescharacteristic
201C2#3177078011yescharacteristic
202C2#3177079011yescharacteristic
subgroupG/H
centerC22#22575423
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
FittingC2×#101×C269C2
socleC22×C269#120
prime radicalC2×#22575501C2
cosocleC22×C4×C269C23
hypercenterC2×#101D269
hypocenterC269#1793
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#22575379C2semidirect
3. #31770607C2semidirect
4. #31770512C2semidirect
5. C2×#101×C269C2semidirect
8. #22575501C4semidirect
101. C269#1793semidirect
106. C2×#101D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225755012
C2×#225753792
#317706072
#317705122
C2×#101×C2692
#1793269