Finite Group Databasebeta

← #49094536

Subgroups — #49094536

Order 35968.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#31824117C211yesmaximal, characteristic
2#31823866C211yesmaximal, characteristic, complemented
3#31823740C211yesmaximal, characteristic, complemented
4#31823210C211yesmaximal, characteristic, complemented
5D4⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#461×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9#22582879C2211yescharacteristic
10#22582863—22no—
11#22582859—21no—
12#22582853—21no—
13C4×D1124C2211yescharacteristic
14C2×C4⋊Dic281—21no—
15#22582812—21no—
16#22582812—22no—
17C4⋊#14555886C2211yescharacteristic
18#22582799—21no—
19C4×#14555886C2211yescharacteristic
20C2×SD16×C281—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4×D4×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24#103×C281—21no—
25#17985137—42no—
26#17985137—42no—
27C2×Dic562—21no—
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—22no—
30C22×Dic281—22no—
31C2×C4×D281—21no—
32C2×#14555886—21no—
33C2×#14555886—21no—
34C4⋊Dic281—22no—
35C4⋊Dic281—21no—
36C4⋊Dic281D411yescharacteristic
37C4⋊Dic281D412yes—
38#17985115—22no—
39#17985115—21no—
40C2×Q8×C281—21no—
41C2×D4×C281D411yescharacteristic
42C22×C4×C281—21no—
43SD16×C281—42no—
44C2×C8×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281D411yescharacteristic
48C22⋊C4×C281—21no—
49C42×C281C2311yescharacteristic
50C22×D281—21no—
51Dic562—41no—
52Dic562—41no—
53D1124—21no—
54D1124—21no—
55C22⋊D281—44no—
56C2×Dic281—21no—
57C2×Dic281—22no—
58C2×Dic281—44no—
59C4×D281—41no—
60C4×D281—41no—
61#14555886—22no—
62#14555886—41no—
63C23×C281—21no—
64Q8×C281—41no—
65Q8×C281—41no—
66D4×C281—21no—
67D4×C281D812yes—
68C2×C4×C281—21no—
69C2×C4×C281—41no—
70C2×C4×C281—41no—
71C2×C4×C281—41no—
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281C2×D411yescharacteristic
75C8×C281—41no—
76C22×C281—22no—
77C22×C281—41no—
78C22×C281—41no—
79C22×C281#12011yescharacteristic
80C2×D281—41no—
81C2×D281—41no—
82C2×D281—41no—
83C4×C281—21no—
84C4×C281—41no—
85C4×C281—81no—
86C4×C281C2×D811yescharacteristic
87C4×C281#13511yescharacteristic
88C4×C281AGL(1,ℤ/8)11yescharacteristic
89C4×C281#13711yescharacteristic
90Dic281—41no—
91Dic281—42no—
92C2×C281—42no—
93C2×C281#44711yescharacteristic
94C2×C281#45211yescharacteristic
95C2×C281#45611yescharacteristic
96D281—81no—
97C281#164711yescharacteristic, complemented, Sylow
98#1647—2811nomaximal, Sylow
99#547—2811no—
100#500—2811no—
101#474—2811no—
102#461D28111yescharacteristic, complemented
103#332—2811no—
104D4⋊C8—2811no—
105D4⋊C8—2811no—
106C2×#41—5621no—
107C2×SD16—21no—
108C4⋊Q8—2811no—
109C4⋊Q8C2×D28111yescharacteristic
110#123—5622no—
111C22⋊Q8—5621no—
112#121—5621no—
113C4×D4—2811no—
114C4×D4C2×D28111yescharacteristic
115C2×C4⋊C4—5621no—
116#107—5621no—
117#107—5622no—
118C4⋊C8—2811no—
119C4⋊C8C2×D28111yescharacteristic
120#103—21no—
121#102—5621no—
122C4×C8—2811no—
123#41—11242no—
124#41—11242no—
125C2×Q8—21no—
126C2×Q8—5621no—
127C2×D4—2811no—
128C2×D4—5622no—
129C2×D4C22⋊D28111yescharacteristic
130C22×C4—21no—
131C22×C4—5622no—
132C22×C4—5621no—
133SD16—42no—
134C2×C8—21no—
135C2×C8—5621no—
136C2×C8—5621no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2811no—
140C4⋊C4—2812no—
141C4⋊C4—5622no—
142C4⋊C4—5621no—
143C4⋊C4C22⋊D28111yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—5622no—
146C22⋊C4—5621no—
147C42C22×D28111yescharacteristic
148C23—21no—
149C23—5621no—
150Q8—41no—
151Q8—41no—
152Q8—11241no—
153Q8—11241no—
154D4—21no—
155D4—5621no—
156D4—5621no—
157D4—11244no—
158D4#1798512312yes—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—5621no—
164C2×C4—5622no—
165C2×C4—11244no—
166C2×C4—11241no—
167C2×C4—11241no—
168C2×C4D4×D28111yescharacteristic
169C2×C4D4×D28111yescharacteristic
170C2×C4C2×C22⋊D28111yescharacteristic
171C8—41no—
172C8—5622no—
173C8—11241no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—11241no—
178C22—11241no—
179C22—11241no—
180C22#2258284711yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—11241no—
185C4—11242no—
186C4C2×#1798512311yescharacteristic
187C4#2258290011yescharacteristic
188C4#2258290411yescharacteristic
189C4#2258290811yescharacteristic
190C2—42no—
191C2—22481no—
192C2#3182359611yescharacteristic
193C2#3182362211yescharacteristic
194C2#3182364411yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#461×C281C2
socleC22×C281#120
prime radical#31824117C2
hypercenter#461D281
hypocenterC281#1647
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #31823866C2semidirect
3. #31823740C2semidirect
4. #31823210C2semidirect
5. D4⋊#14555886C2semidirect
6. #31823190C2semidirect
7. #461×C281C2semidirect
97. C281#1647semidirect
102. #461D281semidirect

Maximal subgroups

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

subgroupindex
#318241172
#318238662
#318237402
#318232102
D4⋊#145558862
#318231902
#461×C2812
#1647281