Finite Group Databasebeta

← #49094451

Subgroups — #49094451

Order 35968.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824116C211yesmaximal, characteristic
2#31823750C211yesmaximal, characteristic, complemented
3#31823750C211yesmaximal, characteristic, complemented
4#31823209C211yesmaximal, characteristic, complemented
5#31823192C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic, complemented
7#487×C281C211yesmaximal, characteristic, complemented
8C2×#17985139—21no—
9#22582864—22no—
10#22582855—21no—
11#22582854—21no—
12C4×D1124C2211yescharacteristic
13C4×D1124C2211yescharacteristic
14C4⋊C4×D281—21no—
15#22582810—21no—
16#22582810—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582799—21no—
20#22582799—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23#103×C281—22no—
24C4×C8×C281C2211yescharacteristic
25#17985139—42no—
26#17985139—42no—
27C2×D1124—22no—
28C2×D1124D411yescharacteristic
29C2×D1124D411yescharacteristic
30C2×C4×D281—22no—
31C2×C4×D281—21no—
32C2×C4×D281—21no—
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281D411yescharacteristic
36C4⋊Dic281D411yescharacteristic
37#17985117—22no—
38#17985115—22no—
39#17985115—21no—
40#17985115—21no—
41C2×Q8×C281—21no—
42C2×Q8×C281—21no—
43C2×C8×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281D412yes—
48C42×C281C2311yescharacteristic
49C22×D281—21no—
50C22×D281—21no—
51D1124—21no—
52D1124—21no—
53D1124—21no—
54D1124—44no—
55D1124SD1612yes—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C4×D281—44no—
59C4×D281—41no—
60C4×D281—41no—
61C4×D281—41no—
62C4×D281—41no—
63#14555886—41no—
64#14555886—41no—
65Q8×C281—42no—
66Q8×C281—41no—
67Q8×C281—41no—
68C2×C4×C281—22no—
69C2×C4×C281—41no—
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C8×C281—41no—
74C22×C281#12011yescharacteristic
75C2×D281—22no—
76C2×D281—41no—
77C2×D281—41no—
78C2×D281—41no—
79C2×D281—41no—
80C2×D281—41no—
81C4×C281—21no—
82C4×C281—42no—
83C4×C281—81no—
84C4×C281C2×SD1611yescharacteristic
85C4×C281#13511yescharacteristic
86C4×C281AGL(1,ℤ/8)11yescharacteristic
87C4×C281#13711yescharacteristic
88Dic281—41no—
89Dic281—41no—
90C2×C281#45011yescharacteristic
91C2×C281#45211yescharacteristic
92C2×C281#45411yescharacteristic
93D281—42no—
94D281—81no—
95C281#163511yescharacteristic, complemented, Sylow
96#1635—2811nomaximal, Sylow
97#547—2811no—
98#487D28111yescharacteristic, complemented
99#476—2811no—
100#476—2811no—
101#332—2811no—
102D4⋊C8—2811no—
103D4⋊C8—2811no—
104C2×#41—5621no—
105C4⋊Q8C2×D28111yescharacteristic
106C4⋊Q8C2×D28111yescharacteristic
107#123—5622no—
108C22⋊Q8—5621no—
109#121—5621no—
110C4×D4—2811no—
111C4×D4—2811no—
112C2×C4⋊C4—5621no—
113#106—5621no—
114#106—5621no—
115C4⋊C8—2811no—
116C4⋊C8—2811no—
117#103—22no—
118#102—5621no—
119#102—5621no—
120C4×C8C2×D28111yescharacteristic
121#41—11242no—
122#41—11242no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—2811no—
126C2×D4—2811no—
127C2×D4—5622no—
128C22×C4—5622no—
129C22×C4—5621no—
130C22×C4—5621no—
131C2×C8—21no—
132C2×C8—5621no—
133C2×C8—5621no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—2811no—
138C4⋊C4—2811no—
139C4⋊C4—5622no—
140C4⋊C4C22⋊D28112yes—
141C22⋊C4—5622no—
142C22⋊C4—5621no—
143C22⋊C4—5621no—
144C42C22×D28111yescharacteristic
145C23—5621no—
146C23—5621no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—2812no—
151D4—5621no—
152D4—5621no—
153D4—5621no—
154D4—11244no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—5621no—
158C2×C4—5621no—
159C2×C4—11244no—
160C2×C4—11241no—
161C2×C4—11241no—
162C2×C4—11241no—
163C2×C4—11241no—
164C2×C4D4×D28111yescharacteristic
165C2×C4D4×D28111yescharacteristic
166C2×C4C2×C22⋊D28111yescharacteristic
167C8—41no—
168C8—11241no—
169C8—11241no—
170C22—5622no—
171C22—11241no—
172C22—11241no—
173C22—11241no—
174C22—11241no—
175C22—11241no—
176C22#2258284711yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—11241no—
181C4—11241no—
182C4SD16×D28111yescharacteristic
183C4#2258290211yescharacteristic
184C4#2258290611yescharacteristic
185C4#2258291111yescharacteristic
186C2—11242no—
187C2—22481no—
188C2#3182361211yescharacteristic
189C2#3182362411yescharacteristic
190C2#3182363511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#487×C281C2
socleC22×C281#120
prime radical#31824116C2
hypercenter#487D281
hypocenterC281#1635
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. #31823750C2semidirect
3. #31823750C2semidirect
4. #31823209C2semidirect
5. #31823192C2semidirect
6. #31823192C2semidirect
7. #487×C281C2semidirect
95. C281#1635semidirect
98. #487D281semidirect

Maximal subgroups

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

subgroupindex
#318241162
#318237502
#318232092
#318231922
#487×C2812
#1635281