Finite Group Databasebeta

← #49094539

Subgroups — #49094539

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#31823866C211yesmaximal, characteristic, complemented
3#31823744C211yesmaximal, characteristic, complemented
4#31823669C211yesmaximal, characteristic, complemented
5#31823190C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#332×C281C211yesmaximal, characteristic, complemented
8C2×#17985139—21no—
9C2×#17985127—21no—
10#22582879C2211yescharacteristic
11#22582864—22no—
12#22582855—21no—
13#22582854—21no—
14C4×D1124C2211yescharacteristic
15C4×D1124C2211yescharacteristic
16C4⋊C4×D281—21no—
17#22582813—21no—
18#22582812—22no—
19#22582804—21no—
20#22582801—21no—
21C4×#14555886C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25#17985139—42no—
26#17985139—42no—
27C2×Dic562—21no—
28C2×D1124—22no—
29C2×D1124D411yescharacteristic
30C2×D1124D411yescharacteristic
31C2×C4×D281—22no—
32C2×C4×D281—21no—
33C2×C4×D281—21no—
34#17985127—42no—
35C2×#14555886—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281—21no—
38C4⋊Dic281D411yescharacteristic
39C4⋊Dic281D411yescharacteristic
40#17985117—22no—
41#17985115—22no—
42#17985115—21no—
43#17985115—21no—
44C2×Q8×C281—21no—
45C2×C8×C281—21no—
46C2×C8×C281—21no—
47C4⋊C4×C281—21no—
48C4⋊C4×C281D412yes—
49C42×C281C2311yescharacteristic
50C22×D281—21no—
51C22×D281—21no—
52Dic562—41no—
53Dic562—41no—
54D1124—21no—
55D1124—21no—
56D1124—21no—
57D1124—44no—
58D1124D812yes—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—41no—
62C4×D281—44no—
63C4×D281—41no—
64C4×D281—41no—
65C4×D281—41no—
66C4×D281—41no—
67#14555886—22no—
68Q8×C281—41no—
69Q8×C281—41no—
70C2×C4×C281—22no—
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C8×C281—41no—
75C8×C281—41no—
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×C281C2×D811yescharacteristic
86C4×C281#13511yescharacteristic
87C4×C281AGL(1,ℤ/8)11yescharacteristic
88C4×C281#13711yescharacteristic
89Dic281—41no—
90Dic281—41no—
91Dic281—81no—
92C2×C281#44711yescharacteristic
93C2×C281#45211yescharacteristic
94C2×C281#45611yescharacteristic
95D281—42no—
96D281—81no—
97C281#164711yescharacteristic, complemented, Sylow
98#1647—2811nomaximal, Sylow
99#547—2811no—
100#500—2811no—
101#474—2811no—
102#461—2811no—
103#332D28111yescharacteristic, complemented
104D4⋊C8—2811no—
105D4⋊C8—2811no—
106C2×#41—5621no—
107C2×SD16—5621no—
108C4⋊Q8—2811no—
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#107—5622no—
118C4⋊C8C2×D28111yescharacteristic
119C4⋊C8C2×D28111yescharacteristic
120#103—5621no—
121#102—5621no—
122C4×C8—2811no—
123#41—11242no—
124#41—11242no—
125C2×Q8—21no—
126C2×Q8—5621no—
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—21no—
136C2×C8—5621no—
137C4⋊C4—21no—
138C4⋊C4—2811no—
139C4⋊C4—2811no—
140C4⋊C4—5622no—
141C4⋊C4—5621no—
142C4⋊C4—5621no—
143C4⋊C4D112412yes—
144C22⋊C4—5622no—
145C22⋊C4—5621no—
146C22⋊C4—5621no—
147C42C22×D28111yescharacteristic
148C23—5621no—
149C23—5621no—
150Q8—41no—
151Q8—41no—
152Q8—11241no—
153Q8—11241no—
154D4—2812no—
155D4—5621no—
156D4—5621no—
157D4—5621no—
158D4—11244no—
159C2×C4—22no—
160C2×C4—5621no—
161C2×C4—5621no—
162C2×C4—11244no—
163C2×C4—11241no—
164C2×C4—11241no—
165C2×C4—11241no—
166C2×C4—11241no—
167C2×C4—11241no—
168C2×C4D4×D28111yescharacteristic
169C2×C4D4×D28111yescharacteristic
170C2×C4C2×D112411yescharacteristic
171C8—41no—
172C8—41no—
173C8—5622no—
174C22—5622no—
175C22—11241no—
176C22—11241no—
177C22—11241no—
178C22—11241no—
179C22—11241no—
180C22#2258284911yescharacteristic
181C4—21no—
182C4—42no—
183C4—11241no—
184C4—11241no—
185C4—22481no—
186C4D8×D28111yescharacteristic
187C4#2258290011yescharacteristic
188C4#2258290611yescharacteristic
189C4#2258291111yescharacteristic
190C2—11242no—
191C2—22481no—
192C2#3182359811yescharacteristic
193C2#3182362811yescharacteristic
194C2#3182364811yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#332×C281C2
socleC22×C281#120
prime radical#31824116C2
hypercenter#332D281
hypocenterC281#1647
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31823866C2semidirect
3. #31823744C2semidirect
4. #31823669C2semidirect
5. #31823190C2semidirect
6. #31823190C2semidirect
7. #332×C281C2semidirect
97. C281#1647semidirect
103. #332D281semidirect

Maximal subgroups

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

subgroupindex
#318241162
#318238662
#318237442
#318236692
#318231902
#332×C2812
#1647281