Finite Group Databasebeta

← #49094621

Subgroups — #49094621

Order 35968.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#31824207C211yesmaximal, characteristic
2#31823872C211yesmaximal, characteristic, complemented
3#31823858C211yesmaximal, characteristic, complemented
4#31823823C211yesmaximal, characteristic, complemented
5#31823204C211yesmaximal, characteristic, complemented
6#31823202C211yesmaximal, characteristic, complemented
7#329×C281C211yesmaximal, characteristic, complemented
8C2×#17985128—21no—
9C2×#17985126—21no—
10#22582879C2211yescharacteristic
11#22582871C2211yescharacteristic
12#22582867C2211yescharacteristic
13#22582863—21no—
14#22582861—21no—
15#22582856—21no—
16#22582855—21no—
17#22582852—21no—
18#22582851—21no—
19#22582813—21no—
20#22582811—21no—
21#22582804—21no—
22#22582801—21no—
23#22582790C2211yescharacteristic
24#124×C281C2211yescharacteristic
25#97×C281C2211yescharacteristic
26#97×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×Dic562D411yescharacteristic
29C2×D1124D411yescharacteristic
30C2×C22⋊D281—21no—
31C2×C22⋊D281—21no—
32C22×Dic281—21no—
33C2×C4×D281—21no—
34#17985128—42no—
35#17985126—42no—
36C2×#14555886—21no—
37C4⋊Dic281—21no—
38C4⋊Dic281—21no—
39C4⋊Dic281—21no—
40C4⋊Dic281D411yescharacteristic
41C4⋊Dic281D411yescharacteristic
42#17985117—21no—
43#17985117—21no—
44#17985117—21no—
45C22⋊Dic281—21no—
46#17985115—21no—
47#17985115—21no—
48#17985115—21no—
49C2×Q8×C281D411yescharacteristic
50C2×D4×C281D411yescharacteristic
51C2×C8×C281—21no—
52C2×C8×C281—21no—
53C22⋊C4×C281—21no—
54C22⋊C4×C281—21no—
55C42×C281C2311yescharacteristic
56C22×D281—21no—
57Dic562—41no—
58Dic562—41no—
59Dic562—41no—
60D1124—41no—
61C22⋊D281—81no—
62C22⋊D281—81no—
63C2×Dic281—21no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—41no—
67C2×Dic281—81no—
68C4×D281—81no—
69#14555886—22no—
70C23×C281—21no—
71Q8×C281—41no—
72D4×C281—41no—
73C2×C4×C281—21no—
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C2×C4×C281C2×D411yescharacteristic
77C8×C281—22no—
78C8×C281—41no—
79C22×C281—41no—
80C22×C281—41no—
81C22×C281—41no—
82C22×C281#12011yescharacteristic
83C2×D281—41no—
84C2×D281—41no—
85C2×D281—41no—
86C4×C281—21no—
87C4×C281—21no—
88C4×C281—21no—
89C4×C281—41no—
90Dic281—41no—
91Dic281—41no—
92Dic281—41no—
93Dic281—81no—
94C2×C281—81no—
95C2×C281#45311yescharacteristic
96C2×C281#45511yescharacteristic
97C2×C281#45611yescharacteristic
98D281—81no—
99C281#166111yescharacteristic, complemented, Sylow
100#1661—2811nomaximal, Sylow
101#562—2811no—
102#501—2811no—
103#497—2811no—
104#489—2811no—
105#330—2811no—
106#329—2811no—
107#329D28111yescharacteristic, complemented
108C2×Q16—5621no—
109C2×SD16—5621no—
110C4⋊Q8—2811no—
111#125—2811no—
112#124—2811no—
113#124C2×D28111yescharacteristic
114#123—5621no—
115#123—5621no—
116C22⋊Q8—5621no—
117C22⋊Q8—5621no—
118#121—5621no—
119#121—5621no—
120#107—5621no—
121#106—5621no—
122#103—5621no—
123#102—5621no—
124#97—2811no—
125#97C2×D28111yescharacteristic
126#97C2×D28111yescharacteristic
127C2×Q8—2811no—
128C2×Q8—5621no—
129C2×Q8D112411yescharacteristic
130C2×D4—2811no—
131C2×D4—5621no—
132C2×D4—5621no—
133C2×D4D112411yescharacteristic
134C22×C4—5621no—
135C22×C4—5621no—
136Q16—11242no—
137SD16—11242no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5621no—
141C4⋊C4—2811no—
142C4⋊C4—2811no—
143C4⋊C4—5621no—
144C4⋊C4—5621no—
145C4⋊C4—5621no—
146C4⋊C4—5621no—
147C4⋊C4—5621no—
148C4⋊C4—5621no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—5621no—
152C22⋊C4—5621no—
153C22⋊C4—5621no—
154C22⋊C4—5621no—
155C42C22×D28111yescharacteristic
156C23—21no—
157C23—5621no—
158Q8—41no—
159Q8—11241no—
160Q8—11241no—
161Q8—11241no—
162D4—41no—
163D4—11241no—
164D4—22481no—
165D4—22481no—
166C2×C4—21no—
167C2×C4—5621no—
168C2×C4—5621no—
169C2×C4—5621no—
170C2×C4—11241no—
171C2×C4—22481no—
172C2×C4—22481no—
173C2×C4D4×D28111yescharacteristic
174C2×C4D4×D28111yescharacteristic
175C2×C4C2×D112411yescharacteristic
176C8—22no—
177C8—41no—
178C8—5622no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—11241no—
183C22—11241no—
184C22—11241no—
185C22#2258284911yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—11241no—
191C4—11241no—
192C4—11241no—
193C4—22481no—
194C2—81no—
195C2—22481no—
196C2#3182363311yescharacteristic
197C2#3182364211yescharacteristic
198C2#3182364711yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#329×C281C2
socleC22×C281#120
prime radical#31824207C2
hypercenter#329D281
hypocenterC281#1661
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31823872C2semidirect
3. #31823858C2semidirect
4. #31823823C2semidirect
5. #31823204C2semidirect
6. #31823202C2semidirect
7. #329×C281C2semidirect
99. C281#1661semidirect
107. #329D281semidirect

Maximal subgroups

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

subgroupindex
#318242072
#318238722
#318238582
#318238232
#318232042
#318232022
#329×C2812
#1661281