Finite Group Databasebeta

← #49096407

Subgroups — #49096407

Order 35968.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#31824263C211yesmaximal, characteristic, complemented
2#31824261C212yesmaximal, complemented
3#31823429C212yesmaximal, complemented
4#31823221C211yesmaximal, characteristic, complemented
5#408×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2212yes—
7#22582912—22no—
8#22582910—22no—
9#22582909—22no—
10#22582907—22no—
11#22582905—22no—
12#22582904—22no—
13#22582901—22no—
14#22582899—24no—
15C2×#17985122C2212yes—
16#22582791—24no—
17C2×#41×C281C2211yescharacteristic
18C2×M16×C281C2211yescharacteristic
19C22×C8×C281C2211yescharacteristic
20C22⋊C8×C281—22no—
21#17985138—22no—
22#17985138—22no—
23#17985138—22no—
24#17985138—22no—
25C2×Dic562D412yes—
26C2×D1124D412yes—
27C2×C22⋊D281—22no—
28C2×C4×D281—22no—
29Dic1124—22no—
30#17985128—24no—
31#17985127—24no—
32#17985126—24no—
33#17985125—24no—
34D2248—22no—
35#17985123—24no—
36#17985122—22no—
37#17985122—22no—
38C2×#14555886D414yes—
39#41×C281—22no—
40#41×C281—22no—
41C2×Q8×C281D411yescharacteristic
42C2×D4×C281—21no—
43C2×D4×C281D411yescharacteristic
44C22×C4×C281—21no—
45C22×C4×C281C2311yescharacteristic
46M16×C281—22no—
47C2×C8×C281—22no—
48C2×C8×C281—21no—
49C2×C8×C281D412yes—
50C22×D281—22no—
51Dic562—22no—
52Dic562—22no—
53D1124—22no—
54D1124—22no—
55C22⋊D281—42no—
56C22⋊D281—42no—
57C2×Dic281—22no—
58C4×D281—42no—
59C4×D281—42no—
60#14555886—24no—
61C23×C281—21no—
62C23×C281#4111yescharacteristic
63Q8×C281—22no—
64D4×C281—22no—
65D4×C281—42no—
66C2×C4×C281—21no—
67C2×C4×C281—41no—
68C2×C4×C281—41no—
69C2×C4×C281C2×D412yes—
70C2×C4×C281C2×D412yes—
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C8×C281—22no—
74C8×C281—41no—
75C22×C281—41no—
76C22×C281—42no—
77C22×C281—41no—
78C22×C281#12112yes—
79C22×C281#12111yescharacteristic
80C2×D281—44no—
81C2×D281—42no—
82C4×C281—41no—
83C4×C281#12011yescharacteristic
84C4×C281#12012yes—
85C4×C281#12711yescharacteristic
86Dic281—42no—
87C2×C281—22no—
88C2×C281—21no—
89C2×C281—81no—
90C2×C281#39211yescharacteristic
91D281—82no—
92C281#201711yescharacteristic, complemented, Sylow
93#2017—2811nomaximal, Sylow
94#575—2812no—
95#575—2811no—
96#408—2812no—
97#408D28111yescharacteristic, complemented
98#338—2811no—
99C2×#41—2812no—
100C2×#41C2×D28111yescharacteristic
101#137—5622no—
102#137—5622no—
103#137—5622no—
104AGL(1,ℤ/8)—5622no—
105AGL(1,ℤ/8)—5622no—
106AGL(1,ℤ/8)—5622no—
107#135—5624no—
108#135—5622no—
109C2×M16—2812no—
110C2×M16C2×D28111yescharacteristic
111C22×C8C2×D28111yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—5624no—
114#41—22no—
115#41—22no—
116#41—5622no—
117#41—5622no—
118#41—5622no—
119#41—5622no—
120C2×Q8—2812no—
121C2×Q8D112411yescharacteristic
122C2×D4—21no—
123C2×D4—2812no—
124C2×D4—5622no—
125C2×D4D112411yescharacteristic
126C22×C4—21no—
127C22×C4—5622no—
128C22×C4C22×D28111yescharacteristic
129Q16—5622no—
130Q16—5624no—
131SD16—5624no—
132SD16—5624no—
133SD16—5624no—
134D8—5622no—
135D8—5624no—
136M16—22no—
137M16—5622no—
138M16—5622no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—2814no—
142C2×C8C22⋊D28112yes—
143C23—21no—
144C23—5622no—
145C23#1798513811yescharacteristic
146Q8—22no—
147Q8—5622no—
148Q8—5622no—
149D4—22no—
150D4—42no—
151D4—5622no—
152D4—5622no—
153D4—11242no—
154D4—11242no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—5622no—
159C2×C4—11242no—
160C2×C4—11242no—
161C2×C4D4×D28112yes—
162C2×C4D4×D28112yes—
163C2×C4C2×C22⋊D28111yescharacteristic
164C2×C4C2×D112411yescharacteristic
165C8—22no—
166C8—41no—
167C8—5624no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—11244no—
172C22—11242no—
173C22#2258285212yes—
174C22#2258285311yescharacteristic
175C4—41no—
176C4—11242no—
177C4#2258284711yescharacteristic
178C4#2258284912yes—
179C4#2258287511yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—22482no—
184C2#3182337211yescharacteristic
subgroupG/H
centerC4#22582875
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#408×C281C2
socleC2×C281#392
hypercenter#408D281
hypocenterC281#2017
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #31824263C2semidirect
2. #31824261C2semidirect
3. #31823429C2semidirect
4. #31823221C2semidirect
5. #408×C281C2semidirect
92. C281#2017semidirect
97. #408D281semidirect

Maximal subgroups

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

subgroupindex
#318242632
#318242612
#318234292
#318232212
#408×C2812
#2017281