Finite Group Databasebeta

← #49094600

Subgroups — #49094600

Order 35968.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#31824217C211yesmaximal, characteristic, complemented
2#31823850C211yesmaximal, characteristic
3#31823827C211yesmaximal, characteristic, complemented
4#31823205C211yesmaximal, characteristic, complemented
5#31823204C211yesmaximal, characteristic, complemented
6#31823202C211yesmaximal, characteristic, complemented
7#490×C281C211yesmaximal, characteristic, complemented
8C2×#17985126—21no—
9C2×#17985123—21no—
10#22582878—21no—
11#22582874—21no—
12#22582874—21no—
13#22582871C2211yescharacteristic
14#22582867C2211yescharacteristic
15#22582864—21no—
16#22582859—21no—
17#22582857—21no—
18#22582800—21no—
19#22582800—21no—
20#22582790C2211yescharacteristic
21#22582790C2211yescharacteristic
22#127×C281C2211yescharacteristic
23#125×C281C2211yescharacteristic
24#102×C281—21no—
25#102×C281—21no—
26#97×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×Dic562D411yescharacteristic
29C2×D1124D411yescharacteristic
30C2×C4×D281—21no—
31#17985126—42no—
32#17985123—42no—
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281D411yescharacteristic
37C4⋊Dic281D411yescharacteristic
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41#17985115—21no—
42#17985115—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46C4×Dic281—21no—
47C2×D4×C281—21no—
48C2×D4×C281—21no—
49C2×D4×C281—21no—
50C2×C8×C281—21no—
51C4⋊C4×C281—21no—
52C4⋊C4×C281—21no—
53C4⋊C4×C281D411yescharacteristic
54C4⋊C4×C281D411yescharacteristic
55C42×C281C2311yescharacteristic
56C22×D281—21no—
57Dic562—41no—
58Dic562—81no—
59D1124—41no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—21no—
63C4×D281—81no—
64#14555886—22no—
65#14555886—41no—
66C23×C281—41no—
67D4×C281—42no—
68D4×C281—42no—
69D4×C281—41no—
70D4×C281—41no—
71C2×C4×C281—21no—
72C2×C4×C281—21no—
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C8×C281—41no—
77C22×C281—81no—
78C22×C281—81no—
79C22×C281—81no—
80C22×C281#12011yescharacteristic
81C2×D281—41no—
82C2×D281—41no—
83C2×D281—41no—
84C4×C281—21no—
85C4×C281—21no—
86C4×C281—21no—
87C4×C281—41no—
88C4×C281—41no—
89Dic281—41no—
90Dic281—41no—
91Dic281—41no—
92C2×C281—161no—
93C2×C281#45311yescharacteristic
94C2×C281#45411yescharacteristic
95C2×C281#45411yescharacteristic
96D281—81no—
97C281#165711yescharacteristic, complemented, Sylow
98#1657—2811nomaximal, Sylow
99#563—2811no—
100#496—2811no—
101#490—2811no—
102#490D28111yescharacteristic, complemented
103#330—2811no—
104#330—2811no—
105#329—2811no—
106C2×SD16—5621no—
107C2×D8—5621no—
108C4⋊Q8—5621no—
109#127C2×D28111yescharacteristic
110#126—5621no—
111#126—5621no—
112#125—2811no—
113#125C2×D28111yescharacteristic
114#124—2811no—
115#123—5621no—
116C22⋊Q8—5621no—
117C22⋊Q8—5621no—
118#102—21no—
119#102—21no—
120#102—5621no—
121#102—5621no—
122#97—2811no—
123#97—2811no—
124#97C2×D28111yescharacteristic
125C2×Q8—2811no—
126C2×Q8—5621no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—2811no—
131C22×C4—5621no—
132SD16—11242no—
133D8—11242no—
134C2×C8—21no—
135C2×C8—5621no—
136C2×C8—5621no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2811no—
140C4⋊C4—2811no—
141C4⋊C4—5621no—
142C4⋊C4—5621no—
143C4⋊C4—5621no—
144C4⋊C4—5621no—
145C4⋊C4C22⋊D28111yescharacteristic
146C4⋊C4C22⋊D28111yescharacteristic
147C22⋊C4—5621no—
148C22⋊C4—5621no—
149C22⋊C4—5621no—
150C22⋊C4—5621no—
151C22⋊C4—5621no—
152C42—5621no—
153C42C22×D28111yescharacteristic
154C23—41no—
155C23—5621no—
156Q8—11241no—
157Q8—22481no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—11241no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—5621no—
166C2×C4—5621no—
167C2×C4—5621no—
168C2×C4—22481no—
169C2×C4D4×D28111yescharacteristic
170C2×C4D4×D28111yescharacteristic
171C2×C4C2×C22⋊D28111yescharacteristic
172C8—41no—
173C8—5622no—
174C8—11241no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—11241no—
179C22—11241no—
180C22—11241no—
181C22#2258284711yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—11241no—
188C4—11241no—
189C4—11241no—
190C2—161no—
191C2—22481no—
192C2#3182362911yescharacteristic
193C2#3182363411yescharacteristic
194C2#3182363511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#490×C281C2
socleC22×C281#120
prime radical#31823850C2
hypercenter#490D281
hypocenterC281#1657
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31824217C2semidirect
3. #31823827C2semidirect
4. #31823205C2semidirect
5. #31823204C2semidirect
6. #31823202C2semidirect
7. #490×C281C2semidirect
97. C281#1657semidirect
102. #490D281semidirect

Maximal subgroups

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

subgroupindex
#318242172
#318238502
#318238272
#318232052
#318232042
#318232022
#490×C2812
#1657281