Finite Group Databasebeta

← #49094620

Subgroups — #49094620

Order 35968.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#31823873C211yesmaximal, characteristic, complemented
2#31823858C211yesmaximal, characteristic, complemented
3#31823822C211yesmaximal, characteristic, complemented
4#31823205C211yesmaximal, characteristic, complemented
5#31823203C211yesmaximal, characteristic, complemented
6#31823203C211yesmaximal, characteristic, complemented
7#562×C281C211yesmaximal, characteristic
8C2×#17985128—21no—
9C2×#17985126—21no—
10#22582879C2211yescharacteristic
11#22582812—21no—
12#22582810—21no—
13#22582803—21no—
14#22582800—21no—
15#22582790C2211yescharacteristic
16#22582790C2211yescharacteristic
17#22582790C2211yescharacteristic
18#125×C281C2211yescharacteristic
19#124×C281C2211yescharacteristic
20#124×C281C2211yescharacteristic
21#123×C281—21no—
22#123×C281—21no—
23C22⋊Q8×C281—21no—
24C22⋊Q8×C281—21no—
25#121×C281—21no—
26#121×C281—21no—
27C2×Dic562—21no—
28#17985128—42no—
29#17985126—42no—
30C2×#14555886—21no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281—21no—
35C2×Q8×C281D411yescharacteristic
36C2×Q8×C281D411yescharacteristic
37C2×D4×C281—21no—
38C2×D4×C281—21no—
39C2×D4×C281D411yescharacteristic
40C2×D4×C281D411yescharacteristic
41C22×C4×C281—21no—
42C22×C4×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281D411yescharacteristic
48C4⋊C4×C281D411yescharacteristic
49C22⋊C4×C281—21no—
50C22⋊C4×C281—21no—
51C22⋊C4×C281—21no—
52C22⋊C4×C281—21no—
53C22⋊C4×C281—21no—
54C22⋊C4×C281—21no—
55C42×C281C2311yescharacteristic
56Dic562—41no—
57Dic562—41no—
58C2×Dic281—41no—
59#14555886—22no—
60#14555886—22no—
61#14555886—41no—
62C23×C281—21no—
63C23×C281—21no—
64Q8×C281—41no—
65Q8×C281—41no—
66D4×C281—41no—
67D4×C281—41no—
68D4×C281—81no—
69D4×C281—81no—
70C2×C4×C281—21no—
71C2×C4×C281—21no—
72C2×C4×C281—21no—
73C2×C4×C281—21no—
74C2×C4×C281—81no—
75C2×C4×C281—81no—
76C2×C4×C281C2×D411yescharacteristic
77C2×C4×C281C2×D411yescharacteristic
78C2×C4×C281C2×D411yescharacteristic
79C22×C281—41no—
80C22×C281—41no—
81C22×C281—41no—
82C22×C281—41no—
83C22×C281—41no—
84C22×C281—41no—
85C22×C281#12011yescharacteristic
86C4×C281—21no—
87C4×C281—21no—
88C4×C281—21no—
89C4×C281—41no—
90C4×C281—41no—
91C4×C281—41no—
92C4×C281—41no—
93Dic281—81no—
94C2×C281—81no—
95C2×C281—81no—
96C2×C281#45311yescharacteristic
97C2×C281#45511yescharacteristic
98C2×C281#45611yescharacteristic
99C281#166111yescharacteristic, complemented, Sylow
100#1661—2811nomaximal, Sylow
101#562D28111yescharacteristic
102#501—2811no—
103#497—2811no—
104#489—2811no—
105#330—2811no—
106#329—2811no—
107#329—2811no—
108C2×Q16—5621no—
109C2×SD16—5621no—
110C4⋊Q8—2811no—
111#125C2×D28111yescharacteristic
112#124C2×D28111yescharacteristic
113#124C2×D28111yescharacteristic
114#123—21no—
115#123—21no—
116C22⋊Q8—21no—
117C22⋊Q8—21no—
118#121—21no—
119#121—21no—
120#107—5621no—
121#106—5621no—
122#103—5621no—
123#102—5621no—
124#97—2811no—
125#97—2811no—
126#97—2811no—
127C2×Q8—5621no—
128C2×Q8C22⋊D28111yescharacteristic
129C2×Q8C22⋊D28111yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4C22⋊D28111yescharacteristic
133C2×D4C22⋊D28111yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136Q16—11242no—
137SD16—11242no—
138C2×C8—5621no—
139C2×C8—5621no—
140C2×C8—5621no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—5621no—
146C4⋊C4—5621no—
147C4⋊C4C22⋊D28111yescharacteristic
148C4⋊C4C22⋊D28111yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D28111yescharacteristic
156C23—21no—
157C23—21no—
158Q8—41no—
159Q8—41no—
160Q8—11241no—
161Q8—11241no—
162D4—41no—
163D4—41no—
164D4—81no—
165D4—81no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—11241no—
173C2×C4C2×C22⋊D28111yescharacteristic
174C2×C4C2×C22⋊D28111yescharacteristic
175C2×C4C2×C22⋊D28111yescharacteristic
176C8—5622no—
177C8—5622no—
178C8—11241no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22#2258284811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—22481no—
194C2—81no—
195C2—81no—
196C2#3182363111yescharacteristic
197C2#3182364111yescharacteristic
198C2#3182364611yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting, prime radical#562×C281C2
socleC22×C281#120
hypercenter#562D281
hypocenterC281#1661
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #31823873C2semidirect
2. #31823858C2semidirect
3. #31823822C2semidirect
4. #31823205C2semidirect
5. #31823203C2semidirect
6. #31823203C2semidirect
99. C281#1661semidirect

Maximal subgroups

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

subgroupindex
#318238732
#318238582
#318238222
#318232052
#318232032
#562×C2812
#1661281