Finite Group Databasebeta

← #49096987

Subgroups — #49096987

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#31824014C211yesmaximal, characteristic
2#31823446C212yesmaximal, complemented
3#31823262C211yesmaximal, characteristic, complemented
4#31823259C212yesmaximal, complemented
5#356×C281C211yesmaximal, characteristic, complemented
6C2×#17985139C411yescharacteristic
7C2×#17985139C2211yescharacteristic
8M16×D281—22no—
9#22582876C411yescharacteristic
10#22582868C411yescharacteristic
11#22582868C2211yescharacteristic
12#22582854—22no—
13#22582841—22no—
14C42×D281C411yescharacteristic
15#22582798C2212yes—
16#22582795—22no—
17C4⋊Q8×C281C2211yescharacteristic
18#101×C281C2212yes—
19#17985139—41no—
20#17985139—41no—
21#17985139—41no—
22#17985139—41no—
23C2×D1124—22no—
24C2×D1124—21no—
25C2×D1124C2×C411yescharacteristic
26C2×D1124C2×C411yescharacteristic
27C2×D1124D412yes—
28C2×C4×D281—21no—
29C2×C4×D281—21no—
30C2×C4×D281C2×C411yescharacteristic
31C2×C4×D281D412yes—
32#17985122—22no—
33#17985121—42no—
34C8×D281—42no—
35#17985115—22no—
36#17985115—22no—
37C4×Dic281—21no—
38C4×Dic281C2×C411yescharacteristic
39C2×Q8×C281C2×C411yescharacteristic
40C2×Q8×C281C2311yescharacteristic
41M16×C281—22no—
42C4⋊C4×C281—22no—
43C42×C281C2×C411yescharacteristic
44C22×D281—21no—
45C22×D281C22⋊C412yes—
46C22×D281C22⋊C411yescharacteristic
47D1124—41no—
48D1124—42no—
49D1124—41no—
50D1124—44no—
51D1124—42no—
52C2×Dic281—21no—
53C2×Dic281C22⋊C411yescharacteristic
54C4×D281—22no—
55C4×D281—22no—
56C4×D281—21no—
57C4×D281—21no—
58C4×D281—42no—
59C4×D281—41no—
60C4×D281—41no—
61#14555886—42no—
62Q8×C281—41no—
63Q8×C281—41no—
64C2×C4×C281—21no—
65C2×C4×C281—21no—
66C2×C4×C281C22×C411yescharacteristic
67C2×C4×C281C2×D412yes—
68C8×C281—42no—
69C22×C281C2×C22⋊C411yescharacteristic
70C2×D281—21no—
71C2×D281—22no—
72C2×D281—41no—
73C2×D281—42no—
74C2×D281—42no—
75C2×D281—41no—
76C4×C281—22no—
77C4×C281—22no—
78C4×C281—21no—
79C4×C281—41no—
80Dic281—41no—
81Dic281#9911yescharacteristic
82Dic281#9911yescharacteristic
83C2×C281—21no—
84C2×C281C2×#9911yescharacteristic
85D281—41no—
86D281—42no—
87D281—81no—
88C281#213211yescharacteristic, complemented, Sylow
89#2132—2811nomaximal, Sylow
90#532—2811no—
91#413—2812no—
92#356—2811no—
93#356D28111yescharacteristic, complemented
94#355—2812no—
95C2×#41—2811no—
96C2×#41—2811no—
97C2×M16—5622no—
98C4⋊Q8C2×D28111yescharacteristic
99#127—2811no—
100#124—2811no—
101#124—2811no—
102#121—5622no—
103C4×D4—5622no—
104C2×C42—2811no—
105#101—2812no—
106#101C2×D28112yes—
107#100—5622no—
108#41—11241no—
109#41—11241no—
110#41—11241no—
111#41—11241no—
112C2×Q8C4×D28111yescharacteristic
113C2×Q8C22×D28111yescharacteristic
114C2×D4—2811no—
115C2×D4—2811no—
116C2×D4—2812no—
117C2×D4—5622no—
118C2×D4—5621no—
119C22×C4—2811no—
120C22×C4—2812no—
121C22×C4—5621no—
122C22×C4—5621no—
123M16—22no—
124M16—5622no—
125M16—11242no—
126C2×C8—11242no—
127C4⋊C4—22no—
128C22⋊C4—5622no—
129C22⋊C4—5622no—
130C42—2811no—
131C42—5621no—
132C42C4×D28111yescharacteristic
133C23—2812no—
134C23—2811no—
135C23—5621no—
136Q8—41no—
137Q8—41no—
138D4—11242no—
139D4—11241no—
140D4—11241no—
141D4—11244no—
142D4—11242no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2811no—
146C2×C4—5622no—
147C2×C4—5622no—
148C2×C4—5621no—
149C2×C4—5621no—
150C2×C4—5621no—
151C2×C4—11242no—
152C2×C4—11241no—
153C2×C4—11241no—
154C2×C4C2×C4×D28111yescharacteristic
155C2×C4D4×D28112yes—
156C8—42no—
157C8—11242no—
158C22—5621no—
159C22—5622no—
160C22—11241no—
161C22—11242no—
162C22—11242no—
163C22—11241no—
164C22C22⋊C4×D28111yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—2811no—
170C4—2811no—
171C4—11241no—
172C2—21no—
173C2—11241no—
174C2—11242no—
175C2—22481no—
176C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×Q8C22×D281
Fitting#356×C281C2
socleC2×C281C2×#99
prime radical#31824014C2
cosocleC2×Q8×C281C23
hypercenter#356D281
hypocenterC281#2132
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #31823446C2semidirect
3. #31823262C2semidirect
4. #31823259C2semidirect
5. #356×C281C2semidirect
88. C281#2132semidirect
93. #356D281semidirect

Maximal subgroups

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

subgroupindex
#318240142
#318234462
#318232622
#318232592
#356×C2812
#2132281