Finite Group Databasebeta

← #49096406

Subgroups — #49096406

Order 35968.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#31824261C212yesmaximal, complemented
2#31823431C211yesmaximal, characteristic, complemented
3#31823430C212yesmaximal, complemented
4#31823221C211yesmaximal, characteristic, complemented
5#575×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2211yescharacteristic
7#22582910—22no—
8#22582909—22no—
9#22582905—22no—
10#22582904—22no—
11#22582899—24no—
12C2×#17985122C2212yes—
13C22×#14555886C2211yescharacteristic
14C22⋊#14555886—24no—
15#22582791—22no—
16C2×#41×C281C2212yes—
17#137×C281—22no—
18AGL(1,ℤ/8)×C281—22no—
19#135×C281—22no—
20C2×M16×C281C2211yescharacteristic
21#17985138—22no—
22#17985138—22no—
23C2×Dic562D411yescharacteristic
24C2×D1124D411yescharacteristic
25C2×C22⋊D281—21no—
26C2×C4×D281—21no—
27#17985128—24no—
28#17985126—24no—
29#17985125—24no—
30#17985123—24no—
31#17985122—22no—
32#17985122—22no—
33C2×#14555886—21no—
34C2×#14555886—22no—
35C2×#14555886D414yes—
36#41×C281—22no—
37#41×C281—22no—
38#41×C281—22no—
39#41×C281—22no—
40C2×Q8×C281D412yes—
41C2×D4×C281—22no—
42C2×D4×C281D412yes—
43C22×C4×C281—22no—
44C22×C4×C281C2311yescharacteristic
45Q16×C281—22no—
46SD16×C281—24no—
47D8×C281—22no—
48M16×C281—22no—
49C2×C8×C281D412yes—
50C22×D281—21no—
51Dic562—22no—
52D1124—22no—
53C22⋊D281—42no—
54C2×Dic281—21no—
55C4×D281—41no—
56C4×D281—41no—
57#14555886—24no—
58#14555886—41no—
59C23×C281—22no—
60C23×C281#4111yescharacteristic
61Q8×C281—22no—
62Q8×C281—22no—
63D4×C281—22no—
64D4×C281—22no—
65D4×C281—42no—
66D4×C281—42no—
67C2×C4×C281—22no—
68C2×C4×C281—42no—
69C2×C4×C281—42no—
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D412yes—
72C2×C4×C281C2×D412yes—
73C2×C4×C281C2×D411yescharacteristic
74C8×C281—22no—
75C22×C281—41no—
76C22×C281—44no—
77C22×C281—42no—
78C22×C281#12111yescharacteristic
79C22×C281#12112yes—
80C2×D281—42no—
81C2×D281—41no—
82C4×C281—42no—
83C4×C281#12012yes—
84C4×C281#12011yescharacteristic
85C4×C281#12711yescharacteristic
86Dic281—41no—
87C2×C281—21no—
88C2×C281—22no—
89C2×C281—82no—
90C2×C281#39211yescharacteristic
91D281—81no—
92C281#201711yescharacteristic, complemented, Sylow
93#2017—2811nomaximal, Sylow
94#575—2812no—
95#575D28111yescharacteristic, complemented
96#408—2812no—
97#408—2811no—
98#338—2811no—
99C2×#41—2811no—
100C2×#41C2×D28112yes—
101#137—22no—
102#137—5622no—
103#137—5622no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—5622no—
106AGL(1,ℤ/8)—5622no—
107#135—22no—
108#135—5624no—
109C2×M16—2812no—
110C2×M16C2×D28111yescharacteristic
111C22×C8—2811no—
112C22⋊C8—5624no—
113C22⋊C8—5622no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—5622no—
119#41—5622no—
120C2×Q8—2811no—
121C2×Q8C22⋊D28112yes—
122C2×D4—22no—
123C2×D4—2811no—
124C2×D4—5621no—
125C2×D4C22⋊D28112yes—
126C22×C4—22no—
127C22×C4—5621no—
128C22×C4C22×D28111yescharacteristic
129Q16—22no—
130Q16—5624no—
131SD16—24no—
132SD16—5624no—
133SD16—5624no—
134D8—22no—
135D8—5624no—
136M16—22no—
137M16—5622no—
138M16—5622no—
139C2×C8—2814no—
140C2×C8—5622no—
141C2×C8—5621no—
142C2×C8C22⋊D28112yes—
143C23—22no—
144C23—5621no—
145C23#1798513711yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—5622no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—5622no—
154D4—11242no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—5621no—
159C2×C4—11241no—
160C2×C4—11241no—
161C2×C4D4×D28111yescharacteristic
162C2×C4D4×D28112yes—
163C2×C4C2×C22⋊D28112yes—
164C2×C4C2×C22⋊D28111yescharacteristic
165C8—22no—
166C8—5624no—
167C8—11241no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—11242no—
172C22—11241no—
173C22#2258285011yescharacteristic
174C22#2258285112yes—
175C4—42no—
176C4—11241no—
177C4#2258284712yes—
178C4#2258284811yescharacteristic
179C4#2258287511yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—22481no—
184C2#3182337111yescharacteristic
subgroupG/H
centerC4#22582875
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#575×C281C2
socleC2×C281#392
hypercenter#575D281
hypocenterC281#2017
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #31824261C2semidirect
2. #31823431C2semidirect
3. #31823430C2semidirect
4. #31823221C2semidirect
5. #575×C281C2semidirect
92. C281#2017semidirect
95. #575D281semidirect

Maximal subgroups

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

subgroupindex
#318242612
#318234312
#318234302
#318232212
#575×C2812
#2017281