Finite Group Databasebeta

← #49094322

Subgroups — #49094322

Order 35968.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#31824025C211yesmaximal, characteristic
2#31823781C212yesmaximal, complemented
3#31823196C212yesmaximal, complemented
4#31823187C211yesmaximal, characteristic, complemented
5#399×C281C211yesmaximal, characteristic, complemented
6C22×C22⋊D281—21no—
7#22582863—22no—
8#22582853—21no—
9#22582853C2212yes—
10#22582849—22no—
11#22582810—22no—
12#22582799—22no—
13C22⋊#14555886C2212yescomplemented
14C2×C4⋊C4×C281—21no—
15C2×C4⋊C4×C281C2211yescharacteristic, complemented
16C2×C22⋊C4×C281—21no—
17C2×C22⋊C4×C281C2211yescharacteristic
18#95×C281C2211yescharacteristic, complemented
19C23×D281—21no—
20C2×D1124—21no—
21C2×D1124D412yes—
22C2×C22⋊D281—22no—
23C2×C22⋊D281—22no—
24C2×C22⋊D281—42no—
25C2×C22⋊D281—42no—
26C22×Dic281—21no—
27C2×#14555886—22no—
28C4⋊Dic281—21no—
29C4⋊Dic281D412yes—
30#17985115—22no—
31#17985115—22no—
32C24×C281D411yescharacteristic
33C22×C4×C281—21no—
34C22×C4×C281—21no—
35C22×C4×C281D411yescharacteristic
36C22×C4×C281C2311yescharacteristic
37C4⋊C4×C281—22no—
38C4⋊C4×C281—42no—
39C22⋊C4×C281—22no—
40C22⋊C4×C281—42no—
41C22×D281—22no—
42C22×D281—42no—
43C22×D281—81no—
44C22×D281—81no—
45D1124—42no—
46D1124—81no—
47C22⋊D281—44no—
48C22⋊D281—42no—
49C22⋊D281—42no—
50C2×Dic281—22no—
51C2×Dic281—42no—
52#14555886—42no—
53C23×C281—21no—
54C23×C281—21no—
55C23×C281—41no—
56C23×C281—41no—
57C23×C281SD1612yes—
58C23×C281C2×D411yescharacteristic
59C2×C4×C281—22no—
60C2×C4×C281—21no—
61C2×C4×C281—41no—
62C2×C4×C281—41no—
63C2×C4×C281—41no—
64C2×C4×C281—41no—
65C2×C4×C281—41no—
66C2×C4×C281—41no—
67C2×C4×C281—41no—
68C2×C4×C281C2×D412yes—
69C22×C281—21no—
70C22×C281—21no—
71C22×C281—22no—
72C22×C281—42no—
73C22×C281—41no—
74C22×C281—41no—
75C22×C281—81no—
76C22×C281#12011yescharacteristic
77C22×C281C2×SD1611yescharacteristic
78C22×C281AGL(1,ℤ/8)11yescharacteristic
79C2×D281—42no—
80C2×D281—42no—
81C2×D281—42no—
82C2×D281—84no—
83C4×C281—22no—
84C4×C281—42no—
85C4×C281—41no—
86C4×C281—81no—
87Dic281—42no—
88C2×C281—21no—
89C2×C281—21no—
90C2×C281—42no—
91C2×C281#45011yescharacteristic
92C2×C281#45311yescharacteristic
93C2×C281#45811yescharacteristic
94D281—82no—
95C281#161311yescharacteristic, complemented, Sylow
96#1613—2811nomaximal, Sylow
97#534—2811no—
98#481—2812no—
99#399D28111yescharacteristic, complemented
100#327—2812no—
101#323—2811no—
102C22×D4—5621no—
103#123—5622no—
104#121—2812no—
105#121—5621no—
106#120—5622no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4C2×D28111yescharacteristic, complemented
109C2×C22⋊C4—21no—
110C2×C22⋊C4C2×D28111yescharacteristic
111#106—5622no—
112#102—5622no—
113C22⋊C8—2812no—
114#95C2×D28111yescharacteristic, complemented
115C24—5621no—
116C24C22⋊D28111yescharacteristic
117C2×D4—2812no—
118C2×D4—5621no—
119C2×D4—5622no—
120C2×D4—5622no—
121C2×D4—11242no—
122C2×D4—11242no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—5621no—
126C22×C4C22⋊D28111yescharacteristic
127C22×C4C22×D28111yescharacteristic
128C2×C8—5622no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—2812no—
132C4⋊C4—5621no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C22⋊C4—5622no—
136C22⋊C4—5622no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—5622no—
142C23—11242no—
143C23—22481no—
144C23—22481no—
145C23#1798512512yes—
146C23C2×C22⋊D28111yescharacteristic
147D4—11242no—
148D4—11244no—
149D4—11242no—
150D4—11242no—
151D4—22481no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5622no—
162C2×C4—11242no—
163C2×C4D4×D28112yes—
164C8—11242no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—11242no—
173C22—11242no—
174C22—11242no—
175C22—22484no—
176C22#2258284711yescharacteristic
177C22C2×#1798512511yescharacteristic
178C22#2258290411yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—11242no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—22482no—
188C2#3182361311yescharacteristic
189C2#3182363011yescharacteristic
190C2#3182365211yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#399×C281C2
socleC22×C281#120
prime radical#31824025C2
hypercenter#399D281
hypocenterC281#1613
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #31823781C2semidirect
3. #31823196C2semidirect
4. #31823187C2semidirect
5. #399×C281C2semidirect
13. C22⋊#14555886C22semidirect
15. C2×C4⋊C4×C281C22semidirect
18. #95×C281C22semidirect
95. C281#1613semidirect
99. #399D281semidirect
108. C2×C4⋊C4C2×D281semidirect
114. #95C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318240252
#318237812
#318231962
#318231872
#399×C2812
#1613281