Finite Group Databasebeta

← #49094007

Subgroups — #49094007

Order 35968.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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#31823519C211yesmaximal, characteristic, complemented
3#31823515C211yesmaximal, characteristic, complemented
4#31823209C211yesmaximal, characteristic, complemented
5#31823206C211yesmaximal, characteristic, complemented
6#31823206C211yesmaximal, characteristic, complemented
7#332×C281C211yesmaximal, characteristic, complemented
8C2×#17985139—21no—
9#22582876C2211yescharacteristic
10#22582868—21no—
11#22582854—21no—
12#22582854C412yes—
13#22582841—21no—
14#22582841C412yes—
15C42×D281C2211yescharacteristic
16C4⋊#14555886C2211yescharacteristic
17C4⋊#14555886C2211yescharacteristic
18#22582791—21no—
19#22582791—21no—
20#22582789—21no—
21C8×Dic281—21no—
22C4⋊Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25#17985139—42no—
26#17985139—42no—
27C2×D1124—22no—
28C2×D1124—21no—
29C2×D1124—21no—
30C2×D1124C2×C412yes—
31C2×C4×D281—22no—
32C2×C4×D281C2×C411yescharacteristic
33C2×C4×D281D411yescharacteristic
34C2×C4×D281D411yescharacteristic
35C2×#14555886—21no—
36C2×#14555886—21no—
37#17985115—22no—
38#17985115—22no—
39C4×Dic281C2×C411yescharacteristic
40C4×Dic281D411yescharacteristic
41C4×Dic281D411yescharacteristic
42C2×Q8×C281—21no—
43C2×C8×C281—21no—
44C2×C8×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281C2×C412yes—
47C42×C281C2311yescharacteristic
48C22×D281—22no—
49C22×D281C22⋊C411yescharacteristic
50D1124—42no—
51D1124—44no—
52D1124—41no—
53D1124—41no—
54D1124—41no—
55D1124—41no—
56C2×Dic281C22⋊C411yescharacteristic
57C2×Dic281C22⋊C411yescharacteristic
58C2×Dic281C22⋊C411yescharacteristic
59C4×D281—21no—
60C4×D281—21no—
61C4×D281—21no—
62C4×D281—21no—
63C4×D281—41no—
64C4×D281—44no—
65#14555886—41no—
66#14555886—41no—
67Q8×C281—41no—
68Q8×C281—41no—
69C2×C4×C281—22no—
70C2×C4×C281C22×C411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C8×C281—41no—
74C8×C281—41no—
75C22×C281C2×C22⋊C411yescharacteristic
76C2×D281—21no—
77C2×D281—21no—
78C2×D281—21no—
79C2×D281—42no—
80C2×D281—42no—
81C2×D281—42no—
82C4×C281—21no—
83C4×C281—42no—
84C4×C281#13511yescharacteristic
85C4×C281#13511yescharacteristic
86C4×C281AGL(1,ℤ/8)11yescharacteristic
87C4×C281AGL(1,ℤ/8)11yescharacteristic
88Dic281—21no—
89Dic281—21no—
90Dic281—21no—
91C2×C281#41311yescharacteristic
92C2×C281#41611yescharacteristic
93C2×C281#41811yescharacteristic
94D281—41no—
95D281—82no—
96C281#155311yescharacteristic, complemented, Sylow
97#1553—2811nomaximal, Sylow
98#532—2811no—
99#432—2811no—
100#431—2811no—
101#332—2811no—
102#332D28111yescharacteristic, complemented
103#331—2811no—
104#331—2811no—
105C2×#41—5621no—
106C4⋊Q8C2×D28111yescharacteristic
107#127—2811no—
108#124—5621no—
109#121—2812no—
110#121—5621no—
111C4×D4—2812no—
112C4×D4—5621no—
113C2×C42—2811no—
114C4⋊C8—2811no—
115C4⋊C8—2811no—
116C4⋊C8C2×D28111yescharacteristic
117C4⋊C8C2×D28111yescharacteristic
118C22⋊C8—5621no—
119C22⋊C8—5621no—
120#97—5621no—
121C4×C8—5621no—
122#41—11242no—
123#41—11242no—
124C2×Q8—21no—
125C2×D4—2812no—
126C2×D4—5622no—
127C2×D4—5621no—
128C2×D4—5621no—
129C22×C4—2811no—
130C22×C4—2811no—
131C22×C4—2811no—
132C22×C4—5622no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5621no—
136C2×C8—5621no—
137C4⋊C4—21no—
138C4⋊C4C4×D28112yes—
139C22⋊C4—5622no—
140C22⋊C4—5622no—
141C42—2811no—
142C42—2811no—
143C42—2811no—
144C42C22×D28111yescharacteristic
145C23—2811no—
146C23—5622no—
147Q8—41no—
148Q8—41no—
149D4—11242no—
150D4—11244no—
151D4—11241no—
152D4—11241no—
153D4—11241no—
154D4—11241no—
155C2×C4—22no—
156C2×C4—2811no—
157C2×C4—2811no—
158C2×C4—2811no—
159C2×C4—5621no—
160C2×C4—5621no—
161C2×C4—5621no—
162C2×C4—5621no—
163C2×C4—11241no—
164C2×C4—11244no—
165C2×C4C2×C4×D28111yescharacteristic
166C2×C4D4×D28111yescharacteristic
167C2×C4D4×D28111yescharacteristic
168C8—41no—
169C8—41no—
170C8—11241no—
171C8—11241no—
172C22—5621no—
173C22—5621no—
174C22—5621no—
175C22—11242no—
176C22—11242no—
177C22—11242no—
178C22C22⋊C4×D28111yescharacteristic
179C4—21no—
180C4—42no—
181C4—5621no—
182C4—5621no—
183C4—5621no—
184C4#2258290011yescharacteristic
185C4#2258290211yescharacteristic
186C4#2258290311yescharacteristic
187C4#2258290611yescharacteristic
188C2—11241no—
189C2—22482no—
190C2#3182344611yescharacteristic
191C2#3182345811yescharacteristic
192C2#3182346611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D281
commutatorC2×C4×C281C22×C4
FrattiniC42C22×D281
Fitting#332×C281C2
socleC22×C281C2×C22⋊C4
prime radical#31824014C2
cosocleC42×C281C23
hypercenter#332D281
hypocenterC281#1553
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31823519C2semidirect
3. #31823515C2semidirect
4. #31823209C2semidirect
5. #31823206C2semidirect
6. #31823206C2semidirect
7. #332×C281C2semidirect
96. C281#1553semidirect
102. #332D281semidirect

Maximal subgroups

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

subgroupindex
#318240142
#318235192
#318235152
#318232092
#318232062
#332×C2812
#1553281