Finite Group Databasebeta

← #49094584

Subgroups — #49094584

Order 35968.

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

normal subgroups only

This group has 240 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#31823740C211yesmaximal, characteristic, complemented
3#31823665C211yesmaximal, characteristic, complemented
4#31823209C211yesmaximal, characteristic, complemented
5#31823192C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic, complemented
7#498×C281C211yesmaximal, characteristic, complemented
8C2×#17985139—21no—
9C2×#17985125—21no—
10#22582864—22no—
11#22582855—21no—
12#22582854—21no—
13C4×D1124C2211yescharacteristic
14C4×D1124C2211yescharacteristic
15C4⋊C4×D281—21no—
16#22582812—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582803—21no—
20#22582799—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23#106×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—
33#17985125—42no—
34C2×#14555886—21no—
35C2×#14555886—21no—
36C4⋊Dic281D411yescharacteristic
37C4⋊Dic281D411yescharacteristic
38#17985117—22no—
39#17985115—22no—
40#17985115—21no—
41#17985115—21no—
42C2×Q8×C281—21no—
43C2×Q8×C281—21no—
44C2×C8×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281—21no—
48C4⋊C4×C281D412yes—
49C42×C281C2311yescharacteristic
50C22×D281—21no—
51C22×D281—21no—
52D1124—21no—
53D1124—21no—
54D1124—21no—
55D1124—44no—
56D1124SD1612yescomplemented
57C2×Dic281—21no—
58C2×Dic281—21no—
59C4×D281—44no—
60C4×D281—41no—
61C4×D281—41no—
62C4×D281—41no—
63C4×D281—41no—
64#14555886—41no—
65#14555886—41no—
66Q8×C281—41no—
67Q8×C281—41no—
68Q8×C281—41no—
69Q8×C281—41no—
70C2×C4×C281—22no—
71C2×C4×C281—41no—
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281C2×D411yescharacteristic
75C8×C281—22no—
76C22×C281#12011yescharacteristic
77C2×D281—22no—
78C2×D281—41no—
79C2×D281—41no—
80C2×D281—41no—
81C2×D281—41no—
82C2×D281—41no—
83C4×C281—21no—
84C4×C281—42no—
85C4×C281—81no—
86C4×C281C2×SD1611yescharacteristic
87C4×C281#13511yescharacteristic
88C4×C281AGL(1,ℤ/8)11yescharacteristic
89C4×C281AGL(1,ℤ/8)11yescharacteristic
90Dic281—41no—
91Dic281—41no—
92C2×C281#44911yescharacteristic
93C2×C281#45011yescharacteristic
94C2×C281#45611yescharacteristic
95D281—42no—
96D281—81no—
97C281#165411yescharacteristic, complemented, Sylow
98#1654—2811nomaximal, Sylow
99#547—2811no—
100#498D28111yescharacteristic, complemented
101#474—2811no—
102#461—2811no—
103#332—2811no—
104D4⋊C8—2811no—
105D4⋊C8—2811no—
106C2×#41—5621no—
107C2×SD16—5621no—
108C4⋊Q8C2×D28111yescharacteristic
109C4⋊Q8C2×D28111yescharacteristic
110#123—5622no—
111C22⋊Q8—5621no—
112#121—5621no—
113C4×D4—2811no—
114C4×D4—2811no—
115C2×C4⋊C4—5621no—
116#107—5621no—
117#106—22no—
118C4⋊C8—2811no—
119C4⋊C8—2811no—
120#103—5621no—
121#102—5621no—
122C4×C8C2×D28111yescharacteristic
123#41—11242no—
124#41—11242no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×D4—2811no—
128C2×D4—2811no—
129C2×D4—5622no—
130C22×C4—5622no—
131C22×C4—5621no—
132C22×C4—5621no—
133SD16—11242no—
134C2×C8—21no—
135C2×C8—5621no—
136C2×C8—5621no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—2811no—
141C4⋊C4—2811no—
142C4⋊C4—5622no—
143C4⋊C4C22⋊D28112yes—
144C22⋊C4—5622no—
145C22⋊C4—5621no—
146C22⋊C4—5621no—
147C42C22×D28111yescharacteristic
148C23—5621no—
149C23—5621no—
150Q8—41no—
151Q8—41no—
152Q8—41no—
153Q8—41no—
154D4—2812no—
155D4—5621no—
156D4—5621no—
157D4—5621no—
158D4—11244no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—5621no—
162C2×C4—5621no—
163C2×C4—11244no—
164C2×C4—11241no—
165C2×C4—11241no—
166C2×C4—11241no—
167C2×C4—11241no—
168C2×C4D4×D28111yescharacteristic
169C2×C4D4×D28111yescharacteristic
170C2×C4C2×C22⋊D28111yescharacteristic
171C8—22no—
172C8—11241no—
173C8—11241no—
174C22—5622no—
175C22—11241no—
176C22—11241no—
177C22—11241no—
178C22—11241no—
179C22—11241no—
180C22#2258284711yescharacteristic
181C4—21no—
182C4—42no—
183C4—81no—
184C4—11241no—
185C4—11241no—
186C4SD16×D28111yescharacteristic
187C4#2258290011yescharacteristic
188C4#2258290611yescharacteristic
189C4#2258290611yescharacteristic
190C2—11242no—
191C2—22481no—
192C2#3182360711yescharacteristic
193C2#3182361211yescharacteristic
194C2#3182364511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#498×C281C2
socleC22×C281#120
prime radical#31824116C2
hypercenter#498D281
hypocenterC281#1654
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #31823740C2semidirect
3. #31823665C2semidirect
4. #31823209C2semidirect
5. #31823192C2semidirect
6. #31823192C2semidirect
7. #498×C281C2semidirect
56. D1124SD16semidirect
97. C281#1654semidirect
100. #498D281semidirect

Maximal subgroups

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

subgroupindex
#318241162
#318237402
#318236652
#318232092
#318231922
#498×C2812
#1654281