Finite Group Databasebeta

← #49094005

Subgroups — #49094005

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#31824011C211yesmaximal, characteristic
2#31823519C211yesmaximal, characteristic, complemented
3#31823515C211yesmaximal, characteristic, complemented
4#31823210C211yesmaximal, characteristic, complemented
5#31823208C211yesmaximal, characteristic, complemented
6#31823207C211yesmaximal, characteristic, complemented
7#331×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9#22582879C2211yescharacteristic
10#22582866—21no—
11#22582850—21no—
12#22582850C412yes—
13D4×Dic281—21no—
14D4×Dic281C412yes—
15C42×D281C2211yescharacteristic
16C4⋊#14555886C2211yescharacteristic
17C4⋊#14555886C2211yescharacteristic
18#22582791—21no—
19#22582791—21no—
20#22582789—21no—
21C8×Dic281—21no—
22#127×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25#17985137—42no—
26#17985137—42no—
27C2×Dic562—21no—
28C2×C22⋊D281—22no—
29C22×Dic281—22no—
30C2×C4×D281C2×C411yescharacteristic
31C2×C4×D281D411yescharacteristic
32C2×C4×D281D411yescharacteristic
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281C2×C412yes—
37C22⋊Dic281—22no—
38C22⋊Dic281—22no—
39C4×Dic281C2×C411yescharacteristic
40C4×Dic281D411yescharacteristic
41C4×Dic281D411yescharacteristic
42C2×D4×C281—21no—
43C2×D4×C281—21no—
44C2×D4×C281C2×C412yes—
45C2×C8×C281—21no—
46C2×C8×C281—21no—
47C42×C281C2311yescharacteristic
48C22×D281C22⋊C411yescharacteristic
49Dic562—41no—
50Dic562—41no—
51C22⋊D281—44no—
52C2×Dic281—22no—
53C2×Dic281—44no—
54C2×Dic281C22⋊C411yescharacteristic
55C2×Dic281C22⋊C411yescharacteristic
56C2×Dic281C22⋊C411yescharacteristic
57C4×D281—21no—
58C4×D281—21no—
59C4×D281—21no—
60C4×D281—21no—
61C4×D281—41no—
62#14555886—41no—
63#14555886—41no—
64C23×C281—22no—
65D4×C281—42no—
66D4×C281—41no—
67D4×C281—41no—
68D4×C281—41no—
69D4×C281—41no—
70C2×C4×C281C22×C411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C8×C281—41no—
74C8×C281—41no—
75C22×C281—42no—
76C22×C281—42no—
77C22×C281—42no—
78C22×C281C2×C22⋊C411yescharacteristic
79C2×D281—21no—
80C2×D281—21no—
81C2×D281—21no—
82C4×C281—21no—
83C4×C281#13511yescharacteristic
84C4×C281#13511yescharacteristic
85C4×C281AGL(1,ℤ/8)11yescharacteristic
86C4×C281AGL(1,ℤ/8)11yescharacteristic
87Dic281—21no—
88Dic281—21no—
89Dic281—21no—
90Dic281—42no—
91C2×C281—82no—
92C2×C281#41311yescharacteristic
93C2×C281#41611yescharacteristic
94C2×C281#41811yescharacteristic
95D281—41no—
96C281#155311yescharacteristic, complemented, Sylow
97#1553—2811nomaximal, Sylow
98#532—2811no—
99#432—2811no—
100#431—2811no—
101#332—2811no—
102#332—2811no—
103#331—2811no—
104#331D28111yescharacteristic, complemented
105C2×#41—5621no—
106C4⋊Q8—2811no—
107#127C2×D28111yescharacteristic
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—5621no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—5622no—
128C2×D4C4×D28112yes—
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—2812no—
138C4⋊C4—5621no—
139C22⋊C4—5622no—
140C22⋊C4—5622no—
141C42—2811no—
142C42—2811no—
143C42—2811no—
144C42C22×D28111yescharacteristic
145C23—22no—
146C23—2811no—
147Q8—11241no—
148Q8—11241no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—11244no—
155C2×C4—2811no—
156C2×C4—2811no—
157C2×C4—2811no—
158C2×C4—5621no—
159C2×C4—5621no—
160C2×C4—5621no—
161C2×C4—5621no—
162C2×C4—5622no—
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—42no—
173C22—42no—
174C22—42no—
175C22—5621no—
176C22—5621no—
177C22—5621no—
178C22C22⋊C4×D28111yescharacteristic
179C4—21no—
180C4—5621no—
181C4—5621no—
182C4—5621no—
183C4—11242no—
184C4#2258289811yescharacteristic
185C4#2258290011yescharacteristic
186C4#2258290311yescharacteristic
187C4#2258290611yescharacteristic
188C2—82no—
189C2—11241no—
190C2#3182344411yescharacteristic
191C2#3182345611yescharacteristic
192C2#3182346611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D281
commutatorC2×C4×C281C22×C4
FrattiniC42C22×D281
Fitting#331×C281C2
socleC22×C281C2×C22⋊C4
prime radical#31824011C2
cosocleC42×C281C23
hypercenter#331D281
hypocenterC281#1553
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31823519C2semidirect
3. #31823515C2semidirect
4. #31823210C2semidirect
5. #31823208C2semidirect
6. #31823207C2semidirect
7. #331×C281C2semidirect
96. C281#1553semidirect
104. #331D281semidirect

Maximal subgroups

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

subgroupindex
#318240112
#318235192
#318235152
#318232102
#318232082
#318232072
#331×C2812
#1553281