Finite Group Databasebeta

← #49094024

Subgroups — #49094024

Order 35968.

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

normal subgroups only

This group has 246 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#31823485C211yesmaximal, characteristic, complemented
4#31823209C211yesmaximal, characteristic, complemented
5#31823206C211yesmaximal, characteristic, complemented
6#31823206C211yesmaximal, characteristic, complemented
7#332×C281C211yesmaximal, characteristic, complemented
8C2×#17985139—21no—
9C2×#17985121—21no—
10#22582876C2211yescharacteristic
11#22582868—21no—
12#22582854—21no—
13#22582854C412yes—
14#22582841—21no—
15#22582841C412yes—
16C42×D281C2211yescharacteristic
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582808—21no—
20#22582791—21no—
21#22582789—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
35#17985121—42no—
36C2×#14555886—21no—
37C2×#14555886—21no—
38#17985115—22no—
39#17985115—22no—
40C4×Dic281C2×C411yescharacteristic
41C4×Dic281D411yescharacteristic
42C4×Dic281D411yescharacteristic
43C2×Q8×C281—21no—
44C2×C8×C281—21no—
45C2×C8×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281C2×C412yes—
48C42×C281C2311yescharacteristic
49C22×D281—22no—
50C22×D281C22⋊C411yescharacteristic
51D1124—42no—
52D1124—44no—
53D1124—41no—
54D1124—41no—
55D1124—41no—
56D1124—41no—
57C2×Dic281C22⋊C411yescharacteristic
58C2×Dic281C22⋊C411yescharacteristic
59C2×Dic281C22⋊C411yescharacteristic
60C4×D281—21no—
61C4×D281—21no—
62C4×D281—21no—
63C4×D281—21no—
64C4×D281—41no—
65C4×D281—44no—
66#14555886—41no—
67#14555886—41no—
68Q8×C281—41no—
69Q8×C281—41no—
70C2×C4×C281—22no—
71C2×C4×C281C22×C411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C8×C281—41no—
75C8×C281—41no—
76C22×C281C2×C22⋊C411yescharacteristic
77C2×D281—21no—
78C2×D281—21no—
79C2×D281—21no—
80C2×D281—42no—
81C2×D281—42no—
82C2×D281—42no—
83C4×C281—21no—
84C4×C281—42no—
85C4×C281AGL(1,ℤ/8)11yescharacteristic
86C4×C281AGL(1,ℤ/8)11yescharacteristic
87C4×C281AGL(1,ℤ/8)11yescharacteristic
88C4×C281#13711yescharacteristic
89Dic281—21no—
90Dic281—21no—
91Dic281—21no—
92C2×C281#41311yescharacteristic
93C2×C281#41711yescharacteristic
94C2×C281#41811yescharacteristic
95D281—41no—
96D281—82no—
97C281#155711yescharacteristic, complemented, Sylow
98#1557—2811nomaximal, Sylow
99#532—2811no—
100#432—2811no—
101#423—2811no—
102#332—2811no—
103#332D28111yescharacteristic, complemented
104#331—2811no—
105#331—2811no—
106C2×#41—5621no—
107C2×M16—5621no—
108C4⋊Q8C2×D28111yescharacteristic
109#127—2811no—
110#124—5621no—
111#121—2812no—
112#121—5621no—
113C4×D4—2812no—
114C4×D4—5621no—
115C2×C42—2811no—
116C4⋊C8—2811no—
117C4⋊C8—2811no—
118C4⋊C8—5621no—
119C4⋊C8C2×D28111yescharacteristic
120C4⋊C8C2×D28111yescharacteristic
121C22⋊C8—5621no—
122#97—5621no—
123#41—11242no—
124#41—11242no—
125C2×Q8—21no—
126C2×D4—2812no—
127C2×D4—5622no—
128C2×D4—5621no—
129C2×D4—5621no—
130C22×C4—2811no—
131C22×C4—2811no—
132C22×C4—2811no—
133C22×C4—5622no—
134M16—11242no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—5621no—
138C2×C8—5621no—
139C4⋊C4—21no—
140C4⋊C4C4×D28112yes—
141C22⋊C4—5622no—
142C22⋊C4—5622no—
143C42—2811no—
144C42—2811no—
145C42—2811no—
146C42C22×D28111yescharacteristic
147C23—2811no—
148C23—5622no—
149Q8—41no—
150Q8—41no—
151D4—11242no—
152D4—11244no—
153D4—11241no—
154D4—11241no—
155D4—11241no—
156D4—11241no—
157C2×C4—22no—
158C2×C4—2811no—
159C2×C4—2811no—
160C2×C4—2811no—
161C2×C4—5621no—
162C2×C4—5621no—
163C2×C4—5621no—
164C2×C4—5621no—
165C2×C4—11241no—
166C2×C4—11244no—
167C2×C4C2×C4×D28111yescharacteristic
168C2×C4D4×D28111yescharacteristic
169C2×C4D4×D28111yescharacteristic
170C8—41no—
171C8—41no—
172C8—11241no—
173C8—11241no—
174C22—5621no—
175C22—5621no—
176C22—5621no—
177C22—11242no—
178C22—11242no—
179C22—11242no—
180C22C22⋊C4×D28111yescharacteristic
181C4—21no—
182C4—42no—
183C4—5621no—
184C4—5621no—
185C4—5621no—
186C4#2258290311yescharacteristic
187C4#2258290611yescharacteristic
188C4#2258290611yescharacteristic
189C4#2258291111yescharacteristic
190C2—11241no—
191C2—22482no—
192C2#3182344611yescharacteristic
193C2#3182346311yescharacteristic
194C2#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#1557
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. #31823485C2semidirect
4. #31823209C2semidirect
5. #31823206C2semidirect
6. #31823206C2semidirect
7. #332×C281C2semidirect
97. C281#1557semidirect
103. #332D281semidirect

Maximal subgroups

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

subgroupindex
#318240142
#318235192
#318234852
#318232092
#318232062
#332×C2812
#1557281