Finite Group Databasebeta

← #49094245

Subgroups — #49094245

Order 35968.

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

normal subgroups only

This group has 266 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#31824094C211yesmaximal, characteristic, complemented
2#31823616C212yesmaximal
3#31823380C211yesmaximal, characteristic
4#31823201C212yesmaximal, complemented
5#324×C281C211yesmaximal, characteristic, complemented
6C22×D1124C2211yescharacteristic
7C2×#17985127—22no—
8#22582878—22no—
9#22582870—22no—
10#22582858—21no—
11#22582858C2212yes—
12#22582838—21no—
13C2×#17985115—21no—
14C2×#17985115—21no—
15#22582801—22no—
16#22582786C2211yescharacteristic
17C2×C4⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C23×D281—21no—
20C2×Dic562—21no—
21C2×Dic562D412yes—
22C2×D1124—22no—
23C2×D1124—42no—
24C22×Dic281—21no—
25#17985127—44no—
26C4⋊Dic281—21no—
27C4⋊Dic281—21no—
28C4⋊Dic281—21no—
29C4⋊Dic281D412yes—
30#17985117—22no—
31#17985117—22no—
32C22⋊Dic281—22no—
33#17985115—42no—
34#17985115—42no—
35C4×Dic281—22no—
36C22×C4×C281D411yescharacteristic
37C22×C4×C281D411yescharacteristic
38C22×C4×C281C2311yescharacteristic
39C2×C8×C281—22no—
40C4⋊C4×C281—22no—
41C22×D281—22no—
42C22×D281—41no—
43C22×D281—41no—
44C22×D281—41no—
45C22×D281—41no—
46C22×D281—41no—
47C22×D281—41no—
48Dic562—42no—
49Dic562—81no—
50D1124—24no—
51D1124—42no—
52C2×Dic281—22no—
53C2×Dic281—22no—
54C2×Dic281—41no—
55C2×Dic281—41no—
56C2×Dic281—41no—
57C23×C281C2×D411yescharacteristic
58C2×C4×C281—21no—
59C2×C4×C281—21no—
60C2×C4×C281—21no—
61C2×C4×C281—41no—
62C2×C4×C281—41no—
63C2×C4×C281SD1612yescomplemented
64C2×C4×C281C2×D412yes—
65C8×C281—42no—
66C22×C281—21no—
67C22×C281—21no—
68C22×C281#12011yescharacteristic
69C22×C281C2×SD1611yescharacteristic
70C22×C281#13711yescharacteristic
71C2×D281—42no—
72C2×D281—42no—
73C2×D281—42no—
74C2×D281—81no—
75C2×D281—81no—
76C2×D281—81no—
77C2×D281—81no—
78C4×C281—22no—
79C4×C281—22no—
80C4×C281—41no—
81Dic281—42no—
82Dic281—42no—
83Dic281—81no—
84C2×C281—21no—
85C2×C281—21no—
86C2×C281#44811yescharacteristic
87C2×C281#45411yescharacteristic
88C2×C281B(4,𝔽2)11yescharacteristic
89D281—82no—
90C281#159911yescharacteristic, complemented, Sylow
91#1599—2811nomaximal, Sylow
92#544—2811no—
93#450—2812no—
94#394—2811no—
95#328—2812no—
96#324D28111yescharacteristic, complemented
97C22×D4—2811no—
98C2×SD16—5622no—
99C4⋊Q8—5622no—
100#125—5622no—
101C22⋊Q8—2812no—
102C22⋊Q8—5621no—
103#117—5621no—
104C2×C4⋊C4C2×D28111yescharacteristic
105C2×C22⋊C4—5621no—
106C2×C22⋊C4—5621no—
107#102—5622no—
108C22⋊C8C2×D28112yes—
109#95—2811no—
110C24—5621no—
111C2×Q8—2812no—
112C2×Q8—5621no—
113C2×D4—5622no—
114C2×D4—11242no—
115C22×C4—5621no—
116C22×C4D112411yescharacteristic
117C22×C4D112411yescharacteristic
118C22×C4C22×D28111yescharacteristic
119SD16—11244no—
120C2×C8—22no—
121C4⋊C4—22no—
122C4⋊C4—2812no—
123C4⋊C4—5622no—
124C4⋊C4—5621no—
125C4⋊C4—5621no—
126C4⋊C4—5621no—
127C4⋊C4—5622no—
128C22⋊C4—5622no—
129C22⋊C4—11242no—
130C22⋊C4—11242no—
131C42—5622no—
132C23—5622no—
133C23—11241no—
134C23—11241no—
135C23—11241no—
136C23—11241no—
137C23—11241no—
138C23—11241no—
139C23C2×D112411yescharacteristic
140Q8—11242no—
141Q8—22481no—
142D4—5624no—
143D4—11242no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—5622no—
150C2×C4—5622no—
151C2×C4—11241no—
152C2×C4—11241no—
153C2×C4—11241no—
154C2×C4#1798512712yescomplemented
155C2×C4D4×D28112yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—11242no—
160C22—11242no—
161C22—11242no—
162C22—22481no—
163C22—22481no—
164C22—22481no—
165C22—22481no—
166C22#2258284911yescharacteristic
167C22C2×#1798512711yescharacteristic
168C22#2258291211yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—11242no—
173C4—11242no—
174C4—22481no—
175C2—21no—
176C2—21no—
177C2—22482no—
178C2#3182360411yescharacteristic
179C2#3182363811yescharacteristic
180C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281#120
prime radicalC22×D1124C22
hypercenter#324D281
hypocenterC281#1599
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
1. #31824094C2semidirect
4. #31823201C2semidirect
5. #324×C281C2semidirect
63. C2×C4×C281SD16semidirect
90. C281#1599semidirect
96. #324D281semidirect
154. C2×C4#17985127semidirect

Maximal subgroups

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

subgroupindex
#318240942
#318236162
#318233802
#318232012
#324×C2812
#1599281