Finite Group Databasebeta

← #49094298

Subgroups — #49094298

Order 35968.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#31824060C211yesmaximal, characteristic
2#31823793C211yesmaximal, characteristic, complemented
3#31823776C211yesmaximal, characteristic
4#31823199C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic
6#31823189C211yesmaximal, characteristic, complemented
7#398×C281C211yesmaximal, characteristic, complemented
8#22582874—21no—
9#22582869—21no—
10#22582864—21no—
11#22582862—21no—
12#22582858C2211yescharacteristic
13#22582857—21no—
14#22582853C2211yescharacteristic
15C4×C22⋊D281—21no—
16#22582812—21no—
17#22582810—21no—
18#22582802—21no—
19#22582799—21no—
20C22⋊#14555886C2211yescharacteristic
21C22⋊#14555886C2211yescharacteristic
22C2×C4⋊C4×C281—21no—
23C2×C4⋊C4×C281C2211yescharacteristic
24C2×C4⋊C4×C281C2211yescharacteristic
25#95×C281—21no—
26#95×C281C2211yescharacteristic
27C2×Dic562D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—21no—
30C2×C4×D281—21no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C4⋊Dic281D411yescharacteristic
34C4⋊Dic281D411yescharacteristic
35#17985117—21no—
36#17985117—21no—
37#17985117—21no—
38#17985117—21no—
39C22⋊Dic281—21no—
40#17985115—21no—
41#17985115—21no—
42#17985115—21no—
43#17985115—21no—
44C4×Dic281—21no—
45C22×C4×C281—21no—
46C22×C4×C281—21no—
47C22×C4×C281D411yescharacteristic
48C22×C4×C281D411yescharacteristic
49C22×C4×C281C2311yescharacteristic
50C4⋊C4×C281—21no—
51C4⋊C4×C281—21no—
52C4⋊C4×C281—21no—
53C4⋊C4×C281—21no—
54C4⋊C4×C281—42no—
55C22×D281—21no—
56Dic562—41no—
57D1124—41no—
58C22⋊D281—41no—
59C22⋊D281—41no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—21no—
63C4×D281—81no—
64#14555886—41no—
65#14555886—41no—
66C23×C281C2×D411yescharacteristic
67C2×C4×C281—22no—
68C2×C4×C281—21no—
69C2×C4×C281—21no—
70C2×C4×C281—21no—
71C2×C4×C281—21no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281—41no—
75C2×C4×C281—41no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281—41no—
79C2×C4×C281C2×D411yescharacteristic
80C2×C4×C281C2×D411yescharacteristic
81C22×C281—21no—
82C22×C281—21no—
83C22×C281#12011yescharacteristic
84C22×C281#13511yescharacteristic
85C22×C281AGL(1,ℤ/8)11yescharacteristic
86C2×D281—41no—
87C2×D281—41no—
88C2×D281—41no—
89C4×C281—21no—
90C4×C281—21no—
91C4×C281—42no—
92C4×C281—41no—
93C4×C281—41no—
94C4×C281—81no—
95Dic281—41no—
96Dic281—41no—
97Dic281—41no—
98C2×C281—21no—
99C2×C281—21no—
100C2×C281#44911yescharacteristic
101C2×C281#45611yescharacteristic
102C2×C281#45811yescharacteristic
103D281—81no—
104C281#160911yescharacteristic, complemented, Sylow
105#1609—2811nomaximal, Sylow
106#539—2811no—
107#483—2811no—
108#480—2811no—
109#398D28111yescharacteristic, complemented
110#328—2811no—
111#327—2811no—
112#324—2811no—
113#126—5621no—
114#125—5621no—
115#123—5621no—
116#123—5621no—
117C22⋊Q8—2811no—
118C22⋊Q8—5621no—
119#121—2811no—
120C4×D4—5621no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D28111yescharacteristic
123C2×C4⋊C4C2×D28111yescharacteristic
124#107—5621no—
125#106—5621no—
126#103—5621no—
127#102—5621no—
128C22⋊C8—2811no—
129C22⋊C8—2811no—
130#95—21no—
131#95C2×D28111yescharacteristic
132C2×Q8—2811no—
133C2×D4—2811no—
134C2×D4—5621no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—5621no—
138C22×C4C22⋊D28111yescharacteristic
139C22×C4C22⋊D28111yescharacteristic
140C22×C4C22×D28111yescharacteristic
141C2×C8—5621no—
142C2×C8—5621no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—2811no—
149C4⋊C4—2811no—
150C4⋊C4—5621no—
151C4⋊C4—5621no—
152C4⋊C4—5621no—
153C4⋊C4—5621no—
154C22⋊C4—5621no—
155C22⋊C4—5621no—
156C22⋊C4—5621no—
157C22⋊C4—5621no—
158C22⋊C4—5621no—
159C42—5621no—
160C23—5621no—
161C23C2×C22⋊D28111yescharacteristic
162Q8—11241no—
163D4—11241no—
164D4—11241no—
165D4—11241no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—5621no—
179C2×C4—5621no—
180C2×C4—5621no—
181C2×C4—22481no—
182C2×C4D4×D28111yescharacteristic
183C2×C4D4×D28111yescharacteristic
184C8—11241no—
185C8—11241no—
186C22—21no—
187C22—21no—
188C22—11241no—
189C22—11241no—
190C22—11241no—
191C22#2258284711yescharacteristic
192C22#2258289911yescharacteristic
193C22#2258290511yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—11241no—
201C4—11241no—
202C4—11241no—
203C2—21no—
204C2—21no—
205C2—22481no—
206C2#3182360611yescharacteristic
207C2#3182364511yescharacteristic
208C2#3182365211yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#398×C281C2
socleC22×C281#120
prime radical#22582853C22
hypercenter#398D281
hypocenterC281#1609
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #31823793C2semidirect
4. #31823199C2semidirect
6. #31823189C2semidirect
7. #398×C281C2semidirect
104. C281#1609semidirect
109. #398D281semidirect

Maximal subgroups

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

subgroupindex
#318240602
#318237932
#318237762
#318231992
#318231962
#318231892
#398×C2812
#1609281