Finite Group Databasebeta

← #46838376

Subgroups — #46838376

Order 34688.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#31774647C211yesmaximal, characteristic, complemented
2#31774087C212yesmaximal
3#31773692C211yesmaximal, characteristic, complemented
4#31773688C212yesmaximal, complemented
5#455×C271C211yesmaximal, characteristic
6#22576158—21no—
7#22576153—22no—
8#22576152—21no—
9#22576141—22no—
10#22576141C2212yes—
11#22576137—22no—
12#22576075—22no—
13#22576075C2212yes—
14H(5,𝔽2)×C271C2211yescharacteristic
15#137×C271—21no—
16#124×C271C2211yescharacteristic
17#104×C271—21no—
18#100×C271C2211yescharacteristic
19C2×Dic542—21no—
20C22×Dic271D412yes—
21C4⋊Dic271—21no—
22C4⋊Dic271—21no—
23Dic271⋊C4—22no—
24Dic271⋊C4—22no—
25Dic271⋊C4—22no—
26Dic271⋊C4—42no—
27C22⋊Dic271—22no—
28C22⋊Dic271—22no—
29C22⋊Dic271—42no—
30C22⋊Dic271D412yes—
31C4×Dic271—21no—
32#41×C271—21no—
33#41×C271—41no—
34C2×Q8×C271D411yescharacteristic
35C2×D4×C271—22no—
36C2×D4×C271—41no—
37C2×D4×C271C2311yescharacteristic
38Q16×C271—41no—
39SD16×C271—41no—
40M16×C271—21no—
41C22⋊C4×C271—22no—
42C42×C271D411yescharacteristic
43Dic542—81no—
44C2×Dic271—22no—
45C2×Dic271—22no—
46C2×Dic271—42no—
47C2×Dic271—42no—
48C23×C271—22no—
49C23×C271C2×D412yes—
50Q8×C271—21no—
51Q8×C271—41no—
52D4×C271—21no—
53D4×C271—41no—
54D4×C271—42no—
55D4×C271—41no—
56C2×C4×C271—22no—
57C2×C4×C271—21no—
58C2×C4×C271—21no—
59C2×C4×C271—41no—
60C2×C4×C271C2×D411yescharacteristic
61C8×C271—41no—
62C22×C271—22no—
63C22×C271—42no—
64C22×C271—41no—
65C22×C271—82no—
66C22×C271#12011yescharacteristic
67C4×C271—21no—
68C4×C271—41no—
69C4×C271—41no—
70C4×C271—41no—
71Dic271—42no—
72Dic271—42no—
73Dic271—82no—
74C2×C271—21no—
75C2×C271—42no—
76C2×C271—81no—
77C2×C271B(4,𝔽2)11yescharacteristic
78C271#220111yescharacteristic, complemented, Sylow
79#2201—2711nomaximal, Sylow
80#563—2711no—
81#458—2712no—
82#455D27111yescharacteristic
83#354—2711no—
84#352—2712no—
85H(5,𝔽2)C2×D27111yescharacteristic
86#137—21no—
87C4⋊Q8—5421no—
88#126—5422no—
89#125—5421no—
90#124C2×D27111yescharacteristic
91#123—2712no—
92#123—5422no—
93C22⋊Q8—5422no—
94#104—21no—
95#100C2×D27111yescharacteristic
96#99—2712no—
97#99—5422no—
98#41—21no—
99#41—41no—
100C2×Q8—5421no—
101C2×Q8C22⋊D27111yescharacteristic
102C2×D4—22no—
103C2×D4—41no—
104C2×D4C22×D27111yescharacteristic
105C22×C4—2712no—
106Q16—41no—
107SD16—41no—
108M16—21no—
109C4⋊C4—5422no—
110C4⋊C4—5422no—
111C4⋊C4—5421no—
112C4⋊C4—5421no—
113C4⋊C4—5422no—
114C4⋊C4—10842no—
115C22⋊C4—22no—
116C22⋊C4—2712no—
117C22⋊C4—5422no—
118C22⋊C4—5422no—
119C22⋊C4—10842no—
120C42—5421no—
121C42C22⋊D27111yescharacteristic
122C23—22no—
123C23D4×D27112yes—
124Q8—21no—
125Q8—41no—
126Q8—21681no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—5422no—
136C2×C4—5422no—
137C2×C4—10842no—
138C2×C4—10842no—
139C2×C4C2×C22⋊D27111yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#2257612811yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—10842no—
151C4—10842no—
152C4—21682no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#3177408311yescharacteristic
subgroupG/H
centerC2#31774083
commutator, cosocleC2×D4×C271C23
FrattiniC2×D4C22×D271
Fitting#455×C271C2
socleC2×C271B(4,𝔽2)
prime radicalH(5,𝔽2)×C271C22
hypercenter#455D271
hypocenterC271#2201
LCSG ▷ C2×D4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #31774647C2semidirect
3. #31773692C2semidirect
4. #31773688C2semidirect
78. C271#2201semidirect

Maximal subgroups

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

subgroupindex
#317746472
#317740872
#317736922
#317736882
#455×C2712
#2201271