Finite Group Databasebeta

← #49094594

Subgroups — #49094594

Order 35968.

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

normal subgroups only

This group has 230 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, complemented
2#31823850C211yesmaximal, characteristic, complemented
3#31823827C211yesmaximal, characteristic, complemented
4#31823204C211yesmaximal, characteristic, complemented
5#31823203C211yesmaximal, characteristic, complemented
6#31823202C211yesmaximal, characteristic, complemented
7#496×C281C211yesmaximal, characteristic, complemented
8C2×#17985126—21no—
9C2×#17985123—21no—
10#22582871C2211yescharacteristic
11#22582867C2211yescharacteristic
12#22582863—21no—
13#22582861—21no—
14#22582856—21no—
15#22582855—21no—
16#22582852—21no—
17#22582851—21no—
18#22582800—21no—
19#22582800—21no—
20#22582790C2211yescharacteristic
21#22582790C2211yescharacteristic
22C2×SD16×C281—21no—
23C2×D8×C281—21no—
24#127×C281C2211yescharacteristic
25#124×C281C2211yescharacteristic
26#97×C281C2211yescharacteristic
27C2×Dic562D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—21no—
30C2×C22⋊D281—21no—
31C22×Dic281—21no—
32C2×C4×D281—21no—
33#17985126—42no—
34#17985123—42no—
35C2×#14555886—21no—
36C2×#14555886—21no—
37C4⋊Dic281—21no—
38C4⋊Dic281D411yescharacteristic
39C4⋊Dic281D411yescharacteristic
40#17985117—21no—
41#17985117—21no—
42#17985117—21no—
43C22⋊Dic281—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47C2×Q8×C281D411yescharacteristic
48C2×D4×C281—21no—
49C2×D4×C281—21no—
50C2×D4×C281—21no—
51C2×D4×C281D411yescharacteristic
52SD16×C281—42no—
53D8×C281—42no—
54C2×C8×C281—21no—
55C22⋊C4×C281—21no—
56C22⋊C4×C281—21no—
57C42×C281C2311yescharacteristic
58C22×D281—21no—
59Dic562—41no—
60D1124—41no—
61C22⋊D281—81no—
62C22⋊D281—81no—
63C2×Dic281—21no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—81no—
67C4×D281—81no—
68#14555886—22no—
69#14555886—41no—
70C23×C281—21no—
71C23×C281—41no—
72Q8×C281—41no—
73D4×C281—41no—
74D4×C281—41no—
75D4×C281—41no—
76D4×C281—42no—
77D4×C281—41no—
78D4×C281—41no—
79C2×C4×C281—21no—
80C2×C4×C281C2×D411yescharacteristic
81C2×C4×C281C2×D411yescharacteristic
82C2×C4×C281C2×D411yescharacteristic
83C8×C281—22no—
84C22×C281—41no—
85C22×C281—41no—
86C22×C281—41no—
87C22×C281—81no—
88C22×C281—81no—
89C22×C281—81no—
90C22×C281#12011yescharacteristic
91C2×D281—41no—
92C2×D281—41no—
93C2×D281—41no—
94C4×C281—21no—
95C4×C281—21no—
96C4×C281—21no—
97C4×C281—41no—
98Dic281—41no—
99Dic281—41no—
100Dic281—41no—
101C2×C281—81no—
102C2×C281—161no—
103C2×C281#45311yescharacteristic
104C2×C281#45311yescharacteristic
105C2×C281#45411yescharacteristic
106D281—81no—
107C281#165611yescharacteristic, complemented, Sylow
108#1656—2811nomaximal, Sylow
109#562—2811no—
110#496—2811no—
111#496D28111yescharacteristic, complemented
112#490—2811no—
113#330—2811no—
114#329—2811no—
115#329—2811no—
116C2×SD16—21no—
117C2×SD16—5621no—
118C2×D8—21no—
119C2×D8—5621no—
120#127C2×D28111yescharacteristic
121#125—2811no—
122#124—2811no—
123#124C2×D28111yescharacteristic
124#123—5621no—
125#123—5621no—
126C22⋊Q8—5621no—
127C22⋊Q8—5621no—
128#121—5621no—
129#121—5621no—
130#102—5621no—
131#102—5621no—
132#97—2811no—
133#97—2811no—
134#97C2×D28111yescharacteristic
135C2×Q8—2811no—
136C2×Q8C22⋊D28111yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—2811no—
141C2×D4—5621no—
142C2×D4—5621no—
143C2×D4C22⋊D28111yescharacteristic
144C22×C4—5621no—
145C22×C4—5621no—
146SD16—42no—
147SD16—11242no—
148D8—42no—
149D8—11242no—
150C2×C8—21no—
151C2×C8—5621no—
152C2×C8—5621no—
153C4⋊C4—2811no—
154C4⋊C4—2811no—
155C4⋊C4—5621no—
156C4⋊C4—5621no—
157C4⋊C4—5621no—
158C4⋊C4—5621no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—5621no—
162C22⋊C4—5621no—
163C22⋊C4—5621no—
164C22⋊C4—5621no—
165C42C22×D28111yescharacteristic
166C23—21no—
167C23—41no—
168C23—5621no—
169Q8—41no—
170Q8—11241no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—41no—
176D4—42no—
177D4—11241no—
178D4—22481no—
179D4—22481no—
180C2×C4—21no—
181C2×C4—5621no—
182C2×C4—5621no—
183C2×C4—5621no—
184C2×C4—22481no—
185C2×C4—22481no—
186C2×C4D4×D28111yescharacteristic
187C2×C4D4×D28111yescharacteristic
188C2×C4C2×C22⋊D28111yescharacteristic
189C8—22no—
190C8—5622no—
191C8—11241no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22—81no—
197C22—81no—
198C22—11241no—
199C22—11241no—
200C22—11241no—
201C22#2258284711yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—11241no—
207C4—11241no—
208C4—11241no—
209C2—81no—
210C2—161no—
211C2—22481no—
212C2#3182362911yescharacteristic
213C2#3182363011yescharacteristic
214C2#3182363411yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#496×C281C2
socleC22×C281#120
hypercenter#496D281
hypocenterC281#1656
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #31824207C2semidirect
2. #31823850C2semidirect
3. #31823827C2semidirect
4. #31823204C2semidirect
5. #31823203C2semidirect
6. #31823202C2semidirect
7. #496×C281C2semidirect
107. C281#1656semidirect
111. #496D281semidirect

Maximal subgroups

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

subgroupindex
#318242072
#318238502
#318238272
#318232042
#318232032
#318232022
#496×C2812
#1656281