Finite Group Databasebeta

← #49094528

Subgroups — #49094528

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#31823740C211yesmaximal, characteristic, complemented
3#31823665C211yesmaximal, characteristic, complemented
4#31823212C211yesmaximal, characteristic, complemented
5#31823192C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic, complemented
7#487×C281C211yesmaximal, characteristic, complemented
8C2×#17985125—21no—
9#22582868—22no—
10#22582854—21no—
11#22582854—21no—
12C4×D1124C2211yescharacteristic
13C4×D1124C2211yescharacteristic
14#22582837—21no—
15#22582837—21no—
16#22582812—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582803—21no—
20#22582799—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23#103×C281—22no—
24C4×C8×C281C2211yescharacteristic
25C2×D1124—22no—
26C2×D1124D411yescharacteristic
27C2×D1124D411yescharacteristic
28C2×C4×D281—21no—
29C2×C4×D281—21no—
30#17985125—42no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C4⋊Dic281D411yescharacteristic
34C4⋊Dic281D411yescharacteristic
35#17985115—22no—
36#17985115—22no—
37#17985115—21no—
38#17985115—21no—
39C4×Dic281—22no—
40C2×Q8×C281—21no—
41C2×Q8×C281D412yes—
42C2×C8×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C42×C281C2311yescharacteristic
48C22×D281—21no—
49C22×D281—21no—
50D1124—21no—
51D1124—21no—
52D1124—21no—
53D1124—21no—
54D1124—82no—
55C2×Dic281—21no—
56C2×Dic281—21no—
57C4×D281—41no—
58C4×D281—41no—
59C4×D281—41no—
60C4×D281—41no—
61#14555886—41no—
62#14555886—41no—
63Q8×C281—42no—
64Q8×C281—41no—
65Q8×C281—41no—
66C2×C4×C281—22no—
67C2×C4×C281—41no—
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
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—81no—
82C4×C281#13511yescharacteristic
83C4×C281#13511yescharacteristic
84C4×C281AGL(1,ℤ/8)11yescharacteristic
85C4×C281#13711yescharacteristic
86Dic281—41no—
87Dic281—41no—
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#487D28111yescharacteristic, complemented
97#474—2811no—
98#461—2811no—
99#333—2811no—
100D4⋊C8—2811no—
101D4⋊C8—2811no—
102C2×SD16—5621no—
103C4⋊Q8C2×D28111yescharacteristic
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⋊C8—2811no—
114C4⋊C8—2811no—
115#103—22no—
116#103—5621no—
117#102—5621no—
118C4×C8C2×D28111yescharacteristic
119C2×Q8—21no—
120C2×Q8C22⋊D28112yes—
121C2×D4—2811no—
122C2×D4—2811no—
123C2×D4—5622no—
124C22×C4—5621no—
125C22×C4—5621no—
126SD16—11242no—
127C2×C8—21no—
128C2×C8—5621no—
129C2×C8—5621no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2811no—
135C4⋊C4—2811no—
136C22⋊C4—5622no—
137C22⋊C4—5622no—
138C22⋊C4—5621no—
139C22⋊C4—5621no—
140C42—5622no—
141C42C22×D28111yescharacteristic
142C23—5621no—
143C23—5621no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—5621no—
148D4—5621no—
149D4—5621no—
150D4—5621no—
151D4—22482no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—5621no—
155C2×C4—5621no—
156C2×C4—11241no—
157C2×C4—11241no—
158C2×C4—11241no—
159C2×C4—11241no—
160C2×C4D4×D28111yescharacteristic
161C2×C4D4×D28111yescharacteristic
162C2×C4C2×C22⋊D28111yescharacteristic
163C8—41no—
164C8—11241no—
165C8—11241no—
166C22—11241no—
167C22—11241no—
168C22—11241no—
169C22—11241no—
170C22—11241no—
171C22—11241no—
172C22#2258284711yescharacteristic
173C4—21no—
174C4—42no—
175C4—81no—
176C4—11241no—
177C4—11241no—
178C4#2258290011yescharacteristic
179C4#2258290211yescharacteristic
180C4#2258290611yescharacteristic
181C4#2258291111yescharacteristic
182C2—22481no—
183C2—22481no—
184C2#3182360711yescharacteristic
185C2#3182362411yescharacteristic
186C2#3182364011yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#487×C281C2
socleC22×C281#120
prime radical#31824179C2
hypercenter#487D281
hypocenterC281#1646
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #31823740C2semidirect
3. #31823665C2semidirect
4. #31823212C2semidirect
5. #31823192C2semidirect
6. #31823192C2semidirect
7. #487×C281C2semidirect
93. C281#1646semidirect
96. #487D281semidirect

Maximal subgroups

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

subgroupindex
#318241792
#318237402
#318236652
#318232122
#318231922
#487×C2812
#1646281