Finite Group Databasebeta

← #49094308

Subgroups — #49094308

Order 35968.

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

normal subgroups only

This group has 254 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#31824044C211yesmaximal, characteristic
2#31823777C212yesmaximal, complemented
3#31823393C211yesmaximal, characteristic, complemented
4#31823198C212yesmaximal, complemented
5#324×C281C211yesmaximal, characteristic, complemented
6C2×#17985138—21no—
7#22582859—22no—
8#22582854—22no—
9#22582853—21no—
10#22582853C2212yes—
11C2×C4⋊Dic281C2211yescharacteristic
12C2×#17985117—21no—
13#22582813—22no—
14#22582801—22no—
15#22582786—21no—
16#22582786C2211yescharacteristic
17C2×C4⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19#17985138—42no—
20#17985138—42no—
21C2×Dic562—21no—
22C2×D1124—21no—
23C2×D1124—21no—
24C2×D1124D412yes—
25C2×C22⋊D281—22no—
26C22×Dic281—21no—
27C22×Dic281—21no—
28C2×C4×D281—22no—
29C4⋊Dic281—21no—
30C4⋊Dic281—22no—
31C4⋊Dic281D412yes—
32#17985117—42no—
33#17985115—22no—
34#17985115—22no—
35C22×C4×C281D411yescharacteristic
36C22×C4×C281D411yescharacteristic
37C22×C4×C281C2311yescharacteristic
38C2×C8×C281—22no—
39C4⋊C4×C281—22no—
40C22×D281—22no—
41Dic562—42no—
42D1124—42no—
43D1124—42no—
44D1124—81no—
45C22⋊D281—42no—
46C22⋊D281—42no—
47C2×Dic281—22no—
48C2×Dic281—22no—
49C2×Dic281—41no—
50C2×Dic281—41no—
51C2×Dic281—41no—
52C2×Dic281—41no—
53C2×Dic281—41no—
54C4×D281—44no—
55C23×C281C2×D411yescharacteristic
56C2×C4×C281—21no—
57C2×C4×C281—21no—
58C2×C4×C281—21no—
59C2×C4×C281—41no—
60C2×C4×C281—41no—
61C2×C4×C281D812yes—
62C2×C4×C281C2×D412yes—
63C8×C281—42no—
64C22×C281—21no—
65C22×C281—21no—
66C22×C281#12011yescharacteristic
67C22×C281C2×D811yescharacteristic
68C22×C281AGL(1,ℤ/8)11yescharacteristic
69C2×D281—42no—
70C2×D281—42no—
71C2×D281—42no—
72C4×C281—22no—
73C4×C281—22no—
74C4×C281—41no—
75Dic281—42no—
76Dic281—42no—
77Dic281—81no—
78C2×C281—21no—
79C2×C281—21no—
80C2×C281#44711yescharacteristic
81C2×C281#45611yescharacteristic
82C2×C281#45811yescharacteristic
83D281—82no—
84C281#161011yescharacteristic, complemented, Sylow
85#1610—2811nomaximal, Sylow
86#537—2811no—
87#480—2812no—
88#398—2811no—
89#327—2812no—
90#324D28111yescharacteristic, complemented
91C2×#41—5621no—
92C22⋊Q8—5622no—
93#121—2812no—
94#121—5622no—
95#121—5621no—
96C2×C4⋊C4—2811no—
97C2×C4⋊C4—5621no—
98C2×C4⋊C4C2×D28111yescharacteristic
99#107—5622no—
100#102—5622no—
101C22⋊C8C2×D28112yes—
102#95—2811no—
103#95—5621no—
104#41—11242no—
105#41—11242no—
106C2×Q8—5621no—
107C2×D4—2812no—
108C2×D4—5621no—
109C2×D4—5621no—
110C2×D4—5622no—
111C22×C4—5622no—
112C22×C4—5621no—
113C22×C4—5621no—
114C22×C4D112411yescharacteristic
115C22×C4D112411yescharacteristic
116C22×C4C22×D28111yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—2812no—
120C4⋊C4—5621no—
121C4⋊C4—5622no—
122C4⋊C4—11242no—
123C22⋊C4—5622no—
124C22⋊C4—5622no—
125C23—5622no—
126C23C2×D112411yescharacteristic
127Q8—11242no—
128D4—11242no—
129D4—11242no—
130D4—11242no—
131D4—11242no—
132D4—22481no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—5622no—
139C2×C4—5622no—
140C2×C4—11244no—
141C2×C4—11241no—
142C2×C4—11241no—
143C2×C4—11241no—
144C2×C4—11241no—
145C2×C4—11241no—
146C2×C4D224812yes—
147C2×C4D4×D28112yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—11242no—
152C22—11242no—
153C22—11242no—
154C22#2258284911yescharacteristic
155C22C2×D224811yescharacteristic
156C22#2258290711yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—11242no—
161C4—11242no—
162C4—22481no—
163C2—21no—
164C2—21no—
165C2—22482no—
166C2#3182359911yescharacteristic
167C2#3182364811yescharacteristic
168C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281#120
prime radical#31824044C2
hypercenter#324D281
hypocenterC281#1610
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #31823777C2semidirect
3. #31823393C2semidirect
4. #31823198C2semidirect
5. #324×C281C2semidirect
84. C281#1610semidirect
90. #324D281semidirect

Maximal subgroups

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

subgroupindex
#318240442
#318237772
#318233932
#318231982
#324×C2812
#1610281