Finite Group Databasebeta

← #49093995

Subgroups — #49093995

Order 35968.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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
3C4⋊C8×D281C211yesmaximal, characteristic, complemented
4#31823211C211yesmaximal, characteristic, complemented
5#31823211C211yesmaximal, characteristic, complemented
6#31823207C211yesmaximal, characteristic, complemented
7#331×C281C211yesmaximal, characteristic, complemented
8C2×#17985137C412yes—
9C2×C8×D281—21no—
10#22582879C2211yescharacteristic
11#22582866C412yes—
12#22582850—21no—
13#22582850—21no—
14D4×Dic281—21no—
15D4×Dic281—21no—
16C42×D281C2211yescharacteristic
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582808—21no—
20#22582791—21no—
21#22582789—21no—
22#127×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25#17985137—44no—
26C2×Dic562C2×C412yes—
27C2×C22⋊D281—22no—
28C22×Dic281—22no—
29C2×C4×D281C2×C411yescharacteristic
30C2×C4×D281D411yescharacteristic
31C2×C4×D281D411yescharacteristic
32C2×#14555886—21no—
33C2×#14555886—21no—
34C8×D281—42no—
35C4⋊Dic281—21no—
36C4⋊Dic281—21no—
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—42no—
50C22⋊D281—44no—
51C2×Dic281—22no—
52C2×Dic281—44no—
53C2×Dic281C22⋊C411yescharacteristic
54C2×Dic281C22⋊C411yescharacteristic
55C2×Dic281C22⋊C411yescharacteristic
56C4×D281—22no—
57C4×D281—21no—
58C4×D281—21no—
59C4×D281—21no—
60C4×D281—21no—
61#14555886—41no—
62#14555886—41no—
63C23×C281—22no—
64D4×C281—42no—
65D4×C281—41no—
66D4×C281—41no—
67D4×C281—41no—
68D4×C281—41no—
69C2×C4×C281C22×C411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C8×C281—41no—
73C8×C281—41no—
74C22×C281—42no—
75C22×C281—42no—
76C22×C281—42no—
77C22×C281C2×C22⋊C411yescharacteristic
78C2×D281—21no—
79C2×D281—21no—
80C2×D281#10012yes—
81C4×C281—21no—
82C4×C281#13511yescharacteristic
83C4×C281#13511yescharacteristic
84C4×C281AGL(1,ℤ/8)11yescharacteristic
85C4×C281#13711yescharacteristic
86Dic281—21no—
87Dic281—21no—
88Dic281—21no—
89Dic281—42no—
90C2×C281—82no—
91C2×C281C2×#10011yescharacteristic
92C2×C281#41611yescharacteristic
93C2×C281#41711yescharacteristic
94D281—22no—
95C281#155111yescharacteristic, complemented, Sylow
96#1551—2811nomaximal, Sylow
97#532—2811no—
98#432—2811no—
99C2×C4⋊C8—2811no—
100#333—2811no—
101#333—2811no—
102#331—2811no—
103#331D28111yescharacteristic, complemented
104C2×#41—2812no—
105C22×C8—5621no—
106C4⋊Q8—2811no—
107#127C2×D28111yescharacteristic
108#124—2812no—
109#121—5621no—
110#121—5621no—
111C4×D4—5621no—
112C4×D4—5621no—
113C2×C42—2811no—
114C4⋊C8—2811no—
115C4⋊C8—2811no—
116C4⋊C8—5621no—
117C4⋊C8C2×D28111yescharacteristic
118C4⋊C8C2×D28111yescharacteristic
119C22⋊C8—5621no—
120#97—5621no—
121#41—11244no—
122C2×Q8—2812no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—5622no—
126C2×D4C4×D28112yes—
127C22×C4—2811no—
128C22×C4—2811no—
129C22×C4—2811no—
130C22×C4—5622no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5621no—
134C2×C8—5621no—
135C2×C8—11242no—
136C4⋊C4—5621no—
137C4⋊C4—5621no—
138C22⋊C4—5622no—
139C22⋊C4—5622no—
140C42—2811no—
141C42—2811no—
142C42—2811no—
143C42C22×D28111yescharacteristic
144C23—22no—
145C23—2811no—
146Q8—11242no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—11244no—
153C2×C4—2811no—
154C2×C4—2811no—
155C2×C4—2811no—
156C2×C4—5622no—
157C2×C4—5621no—
158C2×C4—5621no—
159C2×C4—5621no—
160C2×C4—5621no—
161C2×C4—5622no—
162C2×C4—11244no—
163C2×C4C2×C4×D28111yescharacteristic
164C2×C4D4×D28111yescharacteristic
165C2×C4D4×D28111yescharacteristic
166C8—41no—
167C8—41no—
168C8—11241no—
169C8—11241no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—2812no—
174C22—5621no—
175C22—5621no—
176C22C22⋊C4×D28111yescharacteristic
177C4—21no—
178C4—5621no—
179C4—5621no—
180C4—5621no—
181C4—11242no—
182C4#2258289811yescharacteristic
183C4#2258290011yescharacteristic
184C4#2258290311yescharacteristic
185C4#2258290811yescharacteristic
186C2—82no—
187C2—5622no—
188C2#100×D28111yescharacteristic
189C2#3182345611yescharacteristic
190C2#3182346111yescharacteristic
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#1551
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. C4⋊C8×D281C2semidirect
4. #31823211C2semidirect
5. #31823211C2semidirect
6. #31823207C2semidirect
7. #331×C281C2semidirect
95. C281#1551semidirect
103. #331D281semidirect

Maximal subgroups

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

subgroupindex
#318240112
#318235192
C4⋊C8×D2812
#318232112
#318232072
#331×C2812
#1551281