Finite Group Databasebeta

← #49094493

Subgroups — #49094493

Order 35968.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824133C211yesmaximal, characteristic
2#31823740C211yesmaximal, characteristic, complemented
3#31823670C211yesmaximal, characteristic, complemented
4#31823207C211yesmaximal, characteristic, complemented
5#31823195C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic, complemented
7#486×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9C2×#17985128—21no—
10#22582875—21no—
11#22582851—22no—
12#22582850—21no—
13C4×Dic562C2211yescharacteristic
14C4×D1124C2211yescharacteristic
15D4×Dic281—21no—
16#22582812—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582803—21no—
20#22582799—21no—
21C4⋊Q8×C281C2211yescharacteristic
22#127×C281C2211yescharacteristic
23#102×C281—22no—
24C4×C8×C281C2211yescharacteristic
25#17985137—42no—
26#17985137—42no—
27C2×Dic562D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—22no—
30C2×C22⋊D281—22no—
31C22×Dic281—22no—
32C2×C4×D281—21no—
33#17985128—42no—
34C2×#14555886—21no—
35C2×#14555886—21no—
36C4⋊Dic281D411yescharacteristic
37C4⋊Dic281D411yescharacteristic
38#17985117—21no—
39C22⋊Dic281—22no—
40#17985115—21no—
41C4×Dic281—21no—
42C2×Q8×C281—21no—
43C2×D4×C281—21no—
44C2×D4×C281—21no—
45C2×D4×C281D412yes—
46C2×C8×C281—21no—
47C4⋊C4×C281—21no—
48C4⋊C4×C281—21no—
49C42×C281C2311yescharacteristic
50C22×D281—21no—
51Dic562—21no—
52Dic562D812yes—
53D1124—21no—
54D1124—21no—
55C22⋊D281—44no—
56C22⋊D281—82no—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—44no—
61C4×D281—41no—
62C4×D281—41no—
63#14555886—41no—
64#14555886—41no—
65C23×C281—22no—
66Q8×C281—41no—
67Q8×C281—41no—
68D4×C281—42no—
69D4×C281—41no—
70D4×C281—41no—
71D4×C281—41no—
72D4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C2×C4×C281C2×D411yescharacteristic
77C8×C281—41no—
78C22×C281—42no—
79C22×C281—42no—
80C22×C281—42no—
81C22×C281#12011yescharacteristic
82C2×D281—41no—
83C2×D281—41no—
84C2×D281—41no—
85C4×C281—21no—
86C4×C281—81no—
87C4×C281C2×D811yescharacteristic
88C4×C281#13511yescharacteristic
89C4×C281AGL(1,ℤ/8)11yescharacteristic
90C4×C281#13711yescharacteristic
91Dic281—22no—
92Dic281—41no—
93Dic281—41no—
94C2×C281—82no—
95C2×C281#44711yescharacteristic
96C2×C281#45211yescharacteristic
97C2×C281#45511yescharacteristic
98D281—81no—
99C281#164111yescharacteristic, complemented, Sylow
100#1641—2811nomaximal, Sylow
101#550—2811no—
102#486D28111yescharacteristic, complemented
103#474—2811no—
104#462—2811no—
105#331—2811no—
106Q8⋊C8—2811no—
107D4⋊C8—2811no—
108C2×#41—5621no—
109C2×Q16—5621no—
110C4⋊Q8C2×D28111yescharacteristic
111#127—5621no—
112#127C2×D28111yescharacteristic
113#121—5621no—
114#121—5622no—
115C4×Q8—2811no—
116C4×D4—2811no—
117C4×D4—5621no—
118#107—5621no—
119C4⋊C8—2811no—
120C4⋊C8—2811no—
121#103—5621no—
122#102—22no—
123#102—5621no—
124C4×C8C2×D28111yescharacteristic
125#41—11242no—
126#41—11242no—
127C2×Q8—21no—
128C2×Q8—2811no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2811no—
132C2×D4—5622no—
133C2×D4—5622no—
134C2×D4C22⋊D28112yes—
135C22×C4—5622no—
136C22×C4—5621no—
137Q16—11242no—
138C2×C8—21no—
139C2×C8—5621no—
140C2×C8—5621no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2811no—
144C4⋊C4—2811no—
145C4⋊C4—5621no—
146C22⋊C4—5622no—
147C22⋊C4—5621no—
148C42—5621no—
149C42C22×D28111yescharacteristic
150C23—22no—
151C23—5621no—
152Q8—41no—
153Q8—41no—
154Q8—2812no—
155Q8—5621no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—5621no—
162D4—5621no—
163D4—11244no—
164D4—22482no—
165C2×C4—41no—
166C2×C4—5621no—
167C2×C4—5621no—
168C2×C4—5621no—
169C2×C4—11244no—
170C2×C4—11241no—
171C2×C4—11241no—
172C2×C4D4×D28111yescharacteristic
173C2×C4D4×D28111yescharacteristic
174C2×C4C2×C22⋊D28111yescharacteristic
175C8—41no—
176C8—11241no—
177C8—11241no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—11241no—
182C22—11241no—
183C22—11241no—
184C22#2258284711yescharacteristic
185C4—21no—
186C4—81no—
187C4—5622no—
188C4—11241no—
189C4—11241no—
190C4D8×D28111yescharacteristic
191C4#2258290011yescharacteristic
192C4#2258290311yescharacteristic
193C4#2258290811yescharacteristic
194C2—82no—
195C2—22481no—
196C2#3182359511yescharacteristic
197C2#3182362211yescharacteristic
198C2#3182364011yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#486×C281C2
socleC22×C281#120
prime radical#31824133C2
hypercenter#486D281
hypocenterC281#1641
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #31823740C2semidirect
3. #31823670C2semidirect
4. #31823207C2semidirect
5. #31823195C2semidirect
6. #31823192C2semidirect
7. #486×C281C2semidirect
99. C281#1641semidirect
102. #486D281semidirect

Maximal subgroups

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

subgroupindex
#318241332
#318237402
#318236702
#318232072
#318231952
#318231922
#486×C2812
#1641281