Finite Group Databasebeta

← #49094413

Subgroups — #49094413

Order 35968.

216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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#31823811C211yesmaximal, characteristic, complemented
2#31823663C211yesmaximal, characteristic, complemented
3#31823658C211yesmaximal, characteristic
4#31823209C211yesmaximal, characteristic, complemented
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic, complemented
7#556×C281C211yesmaximal, characteristic, complemented
8C2×#17985125—21no—
9C2×#17985123—21no—
10#22582876C2211yescharacteristic
11C4⋊#14555886C2211yescharacteristic
12C4⋊#14555886C2211yescharacteristic
13#22582799—21no—
14#22582799—21no—
15#22582799—22no—
16C4×#14555886C2211yescharacteristic
17C4⋊Q8×C281C2211yescharacteristic
18#126×C281—22no—
19#124×C281—21no—
20C22⋊Q8×C281—21no—
21C4×Q8×C281—21no—
22C4×Q8×C281C2211yescharacteristic
23C4×D4×C281C2211yescharacteristic
24#117×C281—21no—
25C2×D1124—21no—
26C2×D1124—21no—
27C2×D1124—21no—
28#17985125—42no—
29#17985123—42no—
30C2×#14555886—21no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C2×Q8×C281—21no—
34C2×Q8×C281D411yescharacteristic
35C2×D4×C281D411yescharacteristic
36C22×C4×C281—21no—
37C4⋊C4×C281—22no—
38C4⋊C4×C281—21no—
39C4⋊C4×C281—21no—
40C4⋊C4×C281D411yescharacteristic
41C4⋊C4×C281D411yescharacteristic
42C4⋊C4×C281D412yes—
43C22⋊C4×C281—22no—
44C22⋊C4×C281—22no—
45C22⋊C4×C281—21no—
46C42×C281—22no—
47C42×C281—21no—
48C42×C281C2311yescharacteristic
49C22×D281—41no—
50D1124—42no—
51D1124—41no—
52D1124—41no—
53D1124—41no—
54D1124—41no—
55#14555886—41no—
56#14555886—41no—
57#14555886—41no—
58C23×C281—21no—
59Q8×C281—21no—
60Q8×C281—21no—
61Q8×C281—41no—
62Q8×C281—41no—
63D4×C281—21no—
64D4×C281—21no—
65C2×C4×C281—21no—
66C2×C4×C281—21no—
67C2×C4×C281—21no—
68C2×C4×C281—22no—
69C2×C4×C281—41no—
70C2×C4×C281—41no—
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C22×C281—41no—
75C22×C281—41no—
76C22×C281—41no—
77C22×C281#12011yescharacteristic
78C2×D281—81no—
79C2×D281—81no—
80C2×D281—81no—
81C4×C281—21no—
82C4×C281—41no—
83C4×C281—41no—
84C4×C281—42no—
85C4×C281—41no—
86C4×C281#13511yescharacteristic
87C4×C281#13511yescharacteristic
88C4×C281AGL(1,ℤ/8)11yescharacteristic
89C4×C281AGL(1,ℤ/8)11yescharacteristic
90C2×C281—81no—
91C2×C281#44911yescharacteristic
92C2×C281#44911yescharacteristic
93C2×C281#45411yescharacteristic
94D281—161no—
95C281#162811yescharacteristic, complemented, Sylow
96#1628—2811nomaximal, Sylow
97#556D28111yescharacteristic, complemented
98#486—2811no—
99#460—2811no—
100#459—2811no—
101#332—2811no—
102Q8⋊C8—2811no—
103D4⋊C8—2811no—
104C2×SD16—5621no—
105C2×D8—5621no—
106C4⋊Q8C2×D28111yescharacteristic
107#127—2811no—
108#126—22no—
109#124—21no—
110C22⋊Q8—21no—
111C4×Q8—21no—
112C4×Q8C2×D28111yescharacteristic
113C4×D4C2×D28111yescharacteristic
114#117—21no—
115C4⋊C8—2811no—
116C4⋊C8—2811no—
117#102—5621no—
118#102—5621no—
119#102—5622no—
120C4×C8—2811no—
121C2×Q8—21no—
122C2×Q8C22⋊D28111yescharacteristic
123C2×D4—5621no—
124C2×D4—5621no—
125C2×D4—5621no—
126C2×D4C22⋊D28111yescharacteristic
127C22×C4—21no—
128SD16—11242no—
129D8—11242no—
130C2×C8—5621no—
131C2×C8—5621no—
132C2×C8—5621no—
133C4⋊C4—22no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4C22⋊D28111yescharacteristic
137C4⋊C4C22⋊D28111yescharacteristic
138C4⋊C4C22⋊D28112yes—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—21no—
142C42—22no—
143C42—21no—
144C42C22×D28111yescharacteristic
145C23—21no—
146C23—11241no—
147Q8—21no—
148Q8—21no—
149Q8—41no—
150Q8—41no—
151D4—21no—
152D4—21no—
153D4—11242no—
154D4—11241no—
155D4—11241no—
156D4—11241no—
157D4—11241no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4C2×C22⋊D28111yescharacteristic
165C2×C4C2×C22⋊D28111yescharacteristic
166C2×C4C2×C22⋊D28111yescharacteristic
167C8—11241no—
168C8—11241no—
169C8—11241no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—22481no—
174C22—22481no—
175C22—22481no—
176C22#2258284811yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—41no—
181C4—42no—
182C4#2258289911yescharacteristic
183C4#2258289911yescharacteristic
184C4#2258290411yescharacteristic
185C4#2258290411yescharacteristic
186C2—81no—
187C2—44961no—
188C2#3182360811yescharacteristic
189C2#3182360811yescharacteristic
190C2#3182363611yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#556×C281C2
socleC22×C281#120
prime radical#31823658C2
hypercenter#556D281
hypocenterC281#1628
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #31823811C2semidirect
2. #31823663C2semidirect
4. #31823209C2semidirect
5. Q8⋊#14555886C2semidirect
6. D4⋊#14555886C2semidirect
7. #556×C281C2semidirect
95. C281#1628semidirect
97. #556D281semidirect

Maximal subgroups

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

subgroupindex
#318238112
#318236632
#318236582
#318232092
Q8⋊#145558862
D4⋊#145558862
#556×C2812
#1628281