Finite Group Databasebeta

← #49094374

Subgroups — #49094374

Order 35968.

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

normal subgroups only

This group has 236 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#31824173C211yesmaximal, characteristic, complemented
2#31823835C211yesmaximal, characteristic, complemented
3#31823655C211yesmaximal, characteristic
4#31823211C211yesmaximal, characteristic, complemented
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#460×C281C211yesmaximal, characteristic, complemented
8C2×#17985126—22no—
9C2×#17985123—21no—
10#22582879C2211yescharacteristic
11#22582871—21no—
12#22582857—22no—
13#22582855—21no—
14C4×D1124—21no—
15C4×D1124C2211yescharacteristic
16C4⋊C4×D281—21no—
17C4⋊#14555886C2211yescharacteristic
18#22582800—21no—
19C4×#14555886C2211yescharacteristic
20C2×SD16×C281—21no—
21#127×C281C2211yescharacteristic
22C4×Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24#102×C281—21no—
25C2×Dic562D412yes—
26C2×D1124D411yescharacteristic
27C2×C4×D281—22no—
28C2×C4×D281—21no—
29#17985126—44no—
30#17985123—42no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281D411yescharacteristic
36#17985117—22no—
37#17985117—22no—
38#17985115—22no—
39#17985115—21no—
40C2×Q8×C281D411yescharacteristic
41C2×D4×C281—21no—
42C2×D4×C281—21no—
43C2×D4×C281—21no—
44SD16×C281—42no—
45C2×C8×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281D411yescharacteristic
48C42×C281—21no—
49C42×C281C2311yescharacteristic
50C22×D281—21no—
51Dic562—42no—
52D1124—21no—
53D1124SD1612yescomplemented
54C2×Dic281—21no—
55C2×Dic281—22no—
56C4×D281—41no—
57C4×D281—41no—
58C4×D281—82no—
59#14555886—22no—
60#14555886—41no—
61C23×C281—41no—
62Q8×C281—21no—
63Q8×C281—21no—
64D4×C281—42no—
65D4×C281—41no—
66D4×C281—41no—
67D4×C281—41no—
68D4×C281—41no—
69C2×C4×C281—21no—
70C2×C4×C281—21no—
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C8×C281—41no—
75C22×C281—81no—
76C22×C281—81no—
77C22×C281—81no—
78C22×C281#12011yescharacteristic
79C2×D281—22no—
80C2×D281—41no—
81C2×D281—41no—
82C4×C281—21no—
83C4×C281—41no—
84C4×C281—41no—
85C4×C281C2×SD1611yescharacteristic
86C4×C281#13511yescharacteristic
87C4×C281AGL(1,ℤ/8)11yescharacteristic
88C4×C281#13711yescharacteristic
89Dic281—41no—
90Dic281—42no—
91C2×C281—161no—
92C2×C281#44811yescharacteristic
93C2×C281#44911yescharacteristic
94C2×C281#45311yescharacteristic
95D281—42no—
96C281#162211yescharacteristic, complemented, Sylow
97#1622—2811nomaximal, Sylow
98#554—2811no—
99#492—2811no—
100#460D28111yescharacteristic, complemented
101#459—2811no—
102#333—2811no—
103Q8⋊C8—2811no—
104D4⋊C8—2811no—
105C2×SD16—21no—
106C2×SD16—5622no—
107C2×D8—5621no—
108C4⋊Q8—2811no—
109#127C2×D28111yescharacteristic
110#125—5621no—
111C22⋊Q8—5622no—
112C22⋊Q8—5621no—
113C4×Q8C2×D28111yescharacteristic
114C4×D4—2811no—
115C4×D4—5621no—
116C2×C4⋊C4—5621no—
117C4⋊C8—2811no—
118C4⋊C8C2×D28111yescharacteristic
119#102—21no—
120#102—5621no—
121C4×C8—2811no—
122C2×Q8—2812no—
123C2×Q8C22⋊D28111yescharacteristic
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2811no—
128C22×C4—5622no—
129C22×C4—5621no—
130SD16—42no—
131SD16—11244no—
132D8—11242no—
133C2×C8—21no—
134C2×C8—5621no—
135C2×C8—5621no—
136C4⋊C4—21no—
137C4⋊C4—2811no—
138C4⋊C4—5622no—
139C4⋊C4—5622no—
140C4⋊C4—5621no—
141C4⋊C4—5621no—
142C4⋊C4C22⋊D28111yescharacteristic
143C22⋊C4—5622no—
144C22⋊C4—5621no—
145C42—21no—
146C42C22×D28111yescharacteristic
147C23—41no—
148C23—5621no—
149Q8—21no—
150Q8—21no—
151Q8—11242no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2812no—
158D4—5621no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—5621no—
162C2×C4—5622no—
163C2×C4—11241no—
164C2×C4—11241no—
165C2×C4—22482no—
166C2×C4D4×D28111yescharacteristic
167C2×C4D4×D28111yescharacteristic
168C2×C4C2×C22⋊D28111yescharacteristic
169C8—41no—
170C8—5622no—
171C8—11241no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—5622no—
176C22—11241no—
177C22—11241no—
178C22#2258284711yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—11242no—
183C4—11241no—
184C4SD16×D28111yescharacteristic
185C4#2258289911yescharacteristic
186C4#2258290511yescharacteristic
187C4#2258290811yescharacteristic
188C2—161no—
189C2—11242no—
190C2#3182360011yescharacteristic
191C2#3182360611yescharacteristic
192C2#3182362911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#460×C281C2
socleC22×C281#120
prime radical#31823655C2
hypercenter#460D281
hypocenterC281#1622
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #31824173C2semidirect
2. #31823835C2semidirect
4. #31823211C2semidirect
5. Q8⋊#14555886C2semidirect
6. #31823190C2semidirect
7. #460×C281C2semidirect
53. D1124SD16semidirect
96. C281#1622semidirect
100. #460D281semidirect

Maximal subgroups

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

subgroupindex
#318241732
#318238352
#318236552
#318232112
Q8⋊#145558862
#318231902
#460×C2812
#1622281