Finite Group Databasebeta

← #49094532

Subgroups — #49094532

Order 35968.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#31824179C211yesmaximal, characteristic
2#31823813C211yesmaximal, characteristic, complemented
3#31823744C211yesmaximal, characteristic, complemented
4#31823669C211yesmaximal, characteristic, complemented
5#31823190C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#333×C281C211yesmaximal, characteristic, complemented
8C2×#17985127—21no—
9#22582879C2211yescharacteristic
10#22582868—22no—
11#22582854—21no—
12#22582854—21no—
13C4×D1124C2211yescharacteristic
14C4×D1124C2211yescharacteristic
15#22582837—21no—
16#22582837—21no—
17#22582813—21no—
18#22582804—21no—
19#22582803—22no—
20#22582801—21no—
21C4×#14555886C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25C2×Dic562—21no—
26C2×D1124—22no—
27C2×D1124D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C4×D281—21no—
30C2×C4×D281—21no—
31#17985127—42no—
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281D411yescharacteristic
36C4⋊Dic281D411yescharacteristic
37#17985115—22no—
38#17985115—22no—
39#17985115—21no—
40#17985115—21no—
41C4×Dic281—22no—
42C2×Q8×C281D412yes—
43C2×C8×C281—21no—
44C2×C8×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C42×C281C2311yescharacteristic
48C22×D281—21no—
49C22×D281—21no—
50Dic562—41no—
51Dic562—41no—
52D1124—21no—
53D1124—21no—
54D1124—21no—
55D1124—21no—
56D1124—82no—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—41no—
60C4×D281—41no—
61C4×D281—41no—
62C4×D281—41no—
63C4×D281—41no—
64#14555886—41no—
65Q8×C281—42no—
66C2×C4×C281—22no—
67C2×C4×C281C2×D411yescharacteristic
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C8×C281—41no—
71C8×C281—41no—
72C22×C281#12011yescharacteristic
73C2×D281—41no—
74C2×D281—41no—
75C2×D281—41no—
76C2×D281—41no—
77C2×D281—41no—
78C2×D281—41no—
79C4×C281—21no—
80C4×C281—42no—
81C4×C281#13511yescharacteristic
82C4×C281#13511yescharacteristic
83C4×C281AGL(1,ℤ/8)11yescharacteristic
84C4×C281#13711yescharacteristic
85Dic281—41no—
86Dic281—41no—
87Dic281—81no—
88C2×C281#44911yescharacteristic
89C2×C281#45211yescharacteristic
90C2×C281#45511yescharacteristic
91D281—81no—
92D281—81no—
93C281#164611yescharacteristic, complemented, Sylow
94#1646—2811nomaximal, Sylow
95#555—2811no—
96#487—2811no—
97#474—2811no—
98#461—2811no—
99#333D28111yescharacteristic, complemented
100D4⋊C8—2811no—
101D4⋊C8—2811no—
102C2×SD16—5621no—
103C4⋊Q8—2811no—
104C4⋊Q8C2×D28111yescharacteristic
105#124—5622no—
106#121—5621no—
107#121—5621no—
108C4×D4—2811no—
109C4×D4—2811no—
110#117—5621no—
111#117—5621no—
112#107—5621no—
113C4⋊C8C2×D28111yescharacteristic
114C4⋊C8C2×D28111yescharacteristic
115#103—5621no—
116#103—5622no—
117#102—5621no—
118C4×C8—2811no—
119C2×Q8—5621no—
120C2×Q8D112412yes—
121C2×D4—2811no—
122C2×D4—2811no—
123C2×D4—5622no—
124C22×C4—5621no—
125C22×C4—5621no—
126SD16—11242no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—5621no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2811no—
133C4⋊C4—2811no—
134C4⋊C4—5621no—
135C4⋊C4—5621no—
136C22⋊C4—5622no—
137C22⋊C4—5622no—
138C22⋊C4—5621no—
139C22⋊C4—5621no—
140C42—5622no—
141C42C22×D28111yescharacteristic
142C23—5621no—
143C23—5621no—
144Q8—42no—
145Q8—11241no—
146Q8—11241no—
147D4—5621no—
148D4—5621no—
149D4—5621no—
150D4—5621no—
151D4—22482no—
152C2×C4—22no—
153C2×C4—5621no—
154C2×C4—5621no—
155C2×C4—11241no—
156C2×C4—11241no—
157C2×C4—11241no—
158C2×C4—11241no—
159C2×C4—11241no—
160C2×C4D4×D28111yescharacteristic
161C2×C4D4×D28111yescharacteristic
162C2×C4C2×D112411yescharacteristic
163C8—41no—
164C8—41no—
165C8—11241no—
166C22—11241no—
167C22—11241no—
168C22—11241no—
169C22—11241no—
170C22—11241no—
171C22—11241no—
172C22#2258284911yescharacteristic
173C4—21no—
174C4—42no—
175C4—11241no—
176C4—11241no—
177C4—22481no—
178C4#2258290011yescharacteristic
179C4#2258290211yescharacteristic
180C4#2258290611yescharacteristic
181C4#2258291111yescharacteristic
182C2—22481no—
183C2—22481no—
184C2#3182361111yescharacteristic
185C2#3182362811yescharacteristic
186C2#3182364311yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#333×C281C2
socleC22×C281#120
prime radical#31824179C2
hypercenter#333D281
hypocenterC281#1646
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31823813C2semidirect
3. #31823744C2semidirect
4. #31823669C2semidirect
5. #31823190C2semidirect
6. #31823190C2semidirect
7. #333×C281C2semidirect
93. C281#1646semidirect
99. #333D281semidirect

Maximal subgroups

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

subgroupindex
#318241792
#318238132
#318237442
#318236692
#318231902
#333×C2812
#1646281