Finite Group Databasebeta

← #49095721

Subgroups — #49095721

Order 35968.

342 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 89 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#31823970C211yesmaximal, characteristic
2#31823447C211yesmaximal, characteristic, complemented
3#31823426C212yesmaximal, complemented
4#31823234C212yesmaximal, complemented
5#568×C281C211yesmaximal, characteristic, complemented
6C22×C4×D281C2211yescharacteristic
7C2×#17985122C2212yes—
8#22582860C412yes—
9#22582855—21no—
10#22582850—21no—
11#22582847C412yes—
12C4×C22⋊D281—22no—
13#22582838C2211yescharacteristic
14#22582798—21no—
15#22582796—21no—
16#22582791—24no—
17C2×#41×C281C2211yescharacteristic
18#131×C281—24no—
19C2×M16×C281—22no—
20C2×M16×C281C2212yes—
21C23×D281C2×C411yescharacteristic
22C2×C22⋊D281—22no—
23C22×Dic281C2×C411yescharacteristic
24C2×C4×D281—22no—
25C2×C4×D281—21no—
26C2×C4×D281—21no—
27C2×C4×D281—22no—
28#17985122—22no—
29#17985122—22no—
30C2×#14555886—22no—
31C4⋊Dic281—21no—
32#17985117—22no—
33C22⋊Dic281—22no—
34C22⋊Dic281C2×C412yes—
35#17985115—22no—
36C4×Dic281—21no—
37#41×C281—22no—
38#41×C281—22no—
39C2×Q8×C281D411yescharacteristic
40C2×D4×C281C2×C412yes—
41C2×D4×C281D411yescharacteristic
42C22×C4×C281D412yes—
43C22×C4×C281C2311yescharacteristic
44M16×C281—24no—
45M16×C281—22no—
46M16×C281—22no—
47C2×C8×C281—24no—
48C2×C8×C281D414yescomplemented
49C22×D281—21no—
50C22×D281—22no—
51C22×D281—42no—
52C22⋊D281—44no—
53C2×Dic281—22no—
54C2×Dic281—21no—
55C2×Dic281—22no—
56C4×D281—41no—
57C4×D281—42no—
58C4×D281—41no—
59#14555886—42no—
60C23×C281C22⋊C412yes—
61C23×C281C22×C411yescharacteristic
62Q8×C281—22no—
63D4×C281—24no—
64D4×C281—22no—
65C2×C4×C281—22no—
66C2×C4×C281—22no—
67C2×C4×C281C22⋊C412yes—
68C2×C4×C281C2×D412yes—
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281#4112yes—
72C8×C281—24no—
73C22×C281—22no—
74C22×C281—41no—
75C22×C281—42no—
76C22×C281C2×C22⋊C411yescharacteristic
77C22×C281C4×D412yes—
78C2×D281—22no—
79C2×D281—24no—
80C2×D281—41no—
81C2×D281—42no—
82C2×D281—41no—
83C4×C281—22no—
84C4×C281#12011yescharacteristic
85C4×C281#12112yes—
86C4×C281#12311yescharacteristic
87Dic281—42no—
88Dic281—41no—
89C2×C281—21no—
90C2×C281—22no—
91C2×C281—42no—
92C2×C281#38611yescharacteristic
93D281—42no—
94C281#189111yescharacteristic, complemented, Sylow
95#1891—2811nomaximal, Sylow
96#568D28111yescharacteristic, complemented
97#525—2811no—
98#413—2811no—
99#407—2812no—
100#344—2812no—
101C2×#41C2×D28111yescharacteristic
102C23×C4—2811no—
103#131—24no—
104C2×M16—22no—
105C2×M16—2812no—
106C2×M16C2×D28112yes—
107#123—2812no—
108C22⋊Q8—5621no—
109#121—5621no—
110#120—2812no—
111C4×D4—5622no—
112#117—2811no—
113#101—5621no—
114#100—5621no—
115C22⋊C8—5624no—
116C24—2811no—
117#41—22no—
118#41—22no—
119C2×Q8D112411yescharacteristic
120C2×D4—5622no—
121C2×D4C4×D28112yes—
122C2×D4D112411yescharacteristic
123C22×C4—2811no—
124C22×C4—5622no—
125C22×C4—5621no—
126C22×C4—5621no—
127C22×C4—5622no—
128C22×C4C22⋊D28112yes—
129C22×C4C22×D28111yescharacteristic
130M16—24no—
131M16—22no—
132M16—22no—
133M16—5622no—
134M16—5622no—
135C2×C8—24no—
136C2×C8—5622no—
137C2×C8C22⋊D28114yescomplemented
138C4⋊C4—5622no—
139C4⋊C4—5621no—
140C22⋊C4—2812no—
141C22⋊C4—5622no—
142C22⋊C4—5622no—
143C42—5621no—
144C23—5621no—
145C23—5622no—
146C23—11242no—
147C23#1798511512yes—
148C23C2×C4×D28111yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—11244no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—5622no—
156C2×C4—5621no—
157C2×C4—5622no—
158C2×C4—11241no—
159C2×C4—11242no—
160C2×C4—11241no—
161C2×C4#1798511512yes—
162C2×C4C2×C22⋊D28112yes—
163C2×C4C2×C22⋊D28111yescharacteristic
164C2×C4C2×D112411yescharacteristic
165C2×C4#1798513812yes—
166C8—24no—
167C8—11242no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—5622no—
172C22—5624no—
173C22—11241no—
174C22—11242no—
175C22—11241no—
176C22C2×#1798511511yescharacteristic
177C22C4×C22⋊D28112yes—
178C4—22no—
179C4—11242no—
180C4—11241no—
181C4#2258284811yescharacteristic
182C4#2258285312yes—
183C4#2258286211yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—11242no—
188C2#3182334211yescharacteristic
subgroupG/H
centerC4#22582848
commutatorC23×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#568×C281C2
socleC2×C281#386
prime radical#31823970C2
cosocleC22×C4×C281C23
hypercenter#568D281
hypocenterC281#1891
LCSG ▷ C23×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #31823447C2semidirect
3. #31823426C2semidirect
4. #31823234C2semidirect
5. #568×C281C2semidirect
48. C2×C8×C281D4semidirect
94. C281#1891semidirect
96. #568D281semidirect
137. C2×C8C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318239702
#318234472
#318234262
#318232342
#568×C2812
#1891281