Finite Group Databasebeta

← #46810011

Subgroups — #46810011

Order 34432.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#31771276C211yesmaximal, characteristic
2#31770979C211yesmaximal, characteristic, complemented
3#31770897C211yesmaximal, characteristic, complemented
4#31770348C211yesmaximal, characteristic, complemented
5#31770335C211yesmaximal, characteristic, complemented
6D4⋊#14524130C211yesmaximal, characteristic, complemented
7#476×C269C211yesmaximal, characteristic, complemented
8C2×#16864402—21no—
9C2×#16864389—22no—
10#22575450C2211yescharacteristic
11#22575449—21no—
12#22575427—21no—
13#22575426—22no—
14C4×Dic538C2211yescharacteristic
15#22575415—21no—
16#22575386—21no—
17C4⋊#14524130C2211yescharacteristic
18#22575376—21no—
19C4×#14524130C2211yescharacteristic
20C4⋊Q8×C269C2211yescharacteristic
21C4×D4×C269C2211yescharacteristic
22#106×C269—21no—
23C4⋊C8×C269C2211yescharacteristic
24#102×C269—21no—
25#16864402—42no—
26#16864402—42no—
27C2×Dic538D411yescharacteristic
28C2×D1076—21no—
29C2×D1076—21no—
30C2×D1076D412yes—
31C2×C22⋊D269—22no—
32C2×C22⋊D269—22no—
33C2×C4×D269—22no—
34#16864389—44no—
35C2×#14524130—21no—
36C2×#14524130—21no—
37C4⋊Dic269D411yescharacteristic
38#16864381—21no—
39#16864379—22no—
40C4×Dic269—21no—
41C2×Q8×C269—21no—
42C2×D4×C269D411yescharacteristic
43C22×C4×C269—21no—
44C2×C8×C269—21no—
45C4⋊C4×C269—21no—
46C4⋊C4×C269—21no—
47C4⋊C4×C269D411yescharacteristic
48C22⋊C4×C269—21no—
49C42×C269C2311yescharacteristic
50C22×D269—22no—
51Dic538—21no—
52Dic538SD1612yescomplemented
53D1076—42no—
54D1076—41no—
55D1076—41no—
56D1076—41no—
57D1076—41no—
58C22⋊D269—44no—
59C22⋊D269—82no—
60C2×Dic269—21no—
61C2×Dic269—21no—
62C4×D269—44no—
63#14524130—22no—
64#14524130—41no—
65C23×C269—21no—
66Q8×C269—42no—
67D4×C269—21no—
68D4×C269—21no—
69C2×C4×C269—21no—
70C2×C4×C269—41no—
71C2×C4×C269—41no—
72C2×C4×C269—41no—
73C2×C4×C269C2×D411yescharacteristic
74C2×C4×C269C2×D411yescharacteristic
75C2×C4×C269C2×D411yescharacteristic
76C8×C269—41no—
77C22×C269—41no—
78C22×C269—41no—
79C22×C269—41no—
80C22×C269#12011yescharacteristic
81C2×D269—42no—
82C2×D269—42no—
83C2×D269—42no—
84C4×C269—21no—
85C4×C269—41no—
86C4×C269—81no—
87C4×C269C2×SD1611yescharacteristic
88C4×C269#13511yescharacteristic
89C4×C269AGL(1,ℤ/8)11yescharacteristic
90C4×C269#13711yescharacteristic
91Dic269—22no—
92Dic269—41no—
93C2×C269—81no—
94C2×C269#45011yescharacteristic
95C2×C269#45211yescharacteristic
96C2×C269#45311yescharacteristic
97D269—82no—
98C269#163111yescharacteristic, complemented, Sylow
99#1631—2691nomaximal, Sylow
100#550—2691no—
101#492—2691no—
102#477—2691no—
103#476D26911yescharacteristic, complemented
104#331—2691no—
105Q8⋊C8—2691no—
106D4⋊C8—2691no—
107C2×#41—5381no—
108C2×SD16—5382no—
109C4⋊Q8C2×D26911yescharacteristic
110#127—2691no—
111#127—5381no—
112#121—5382no—
113#121—5381no—
114C4×Q8—2691no—
115C4×D4—5381no—
116C4×D4C2×D26911yescharacteristic
117#107—5381no—
118#106—21no—
119C4⋊C8—2691no—
120C4⋊C8C2×D26911yescharacteristic
121#103—5381no—
122#102—21no—
123C4×C8—2691no—
124#41—10762no—
125#41—10762no—
126C2×Q8—21no—
127C2×Q8—2691no—
128C2×D4—2692no—
129C2×D4—5382no—
130C2×D4—5382no—
131C2×D4—5381no—
132C2×D4—5381no—
133C2×D4C22⋊D26911yescharacteristic
134C22×C4—21no—
135C22×C4—5382no—
136SD16—10764no—
137C2×C8—21no—
138C2×C8—5381no—
139C2×C8—5381no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—2691no—
143C4⋊C4—5381no—
144C4⋊C4C22⋊D26911yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—5382no—
147C42—5381no—
148C42C22×D26911yescharacteristic
149C23—21no—
150C23—5382no—
151Q8—42no—
152Q8—2692no—
153Q8—5381no—
154D4—21no—
155D4—21no—
156D4—10762no—
157D4—10764no—
158D4—10761no—
159D4—10761no—
160D4—10761no—
161D4—10761no—
162D4—21522no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—5381no—
168C2×C4—5381no—
169C2×C4—10764no—
170C2×C4D4×D26911yescharacteristic
171C2×C4D4×D26911yescharacteristic
172C2×C4C2×C22⋊D26911yescharacteristic
173C8—41no—
174C8—5382no—
175C8—10761no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—10762no—
180C22—10762no—
181C22—10762no—
182C22#2257542111yescharacteristic
183C4—21no—
184C4—41no—
185C4—81no—
186C4—5382no—
187C4—10761no—
188C4SD16×D26911yescharacteristic
189C4#2257547311yescharacteristic
190C4#2257548011yescharacteristic
191C4#2257548411yescharacteristic
192C2—81no—
193C2—21522no—
194C2#3177075411yescharacteristic
195C2#3177076511yescharacteristic
196C2#3177077111yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#476×C269C2
socleC22×C269#120
prime radical#31771276C2
hypercenter#476D269
hypocenterC269#1631
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31770979C2semidirect
3. #31770897C2semidirect
4. #31770348C2semidirect
5. #31770335C2semidirect
6. D4⋊#14524130C2semidirect
7. #476×C269C2semidirect
52. Dic538SD16semidirect
98. C269#1631semidirect
103. #476D269semidirect

Maximal subgroups

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

subgroupindex
#317712762
#317709792
#317708972
#317703482
#317703352
D4⋊#145241302
#476×C2692
#1631269