Finite Group Databasebeta

← #49094611

Subgroups — #49094611

Order 35968.

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

normal subgroups only

This group has 228 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#31824205C211yesmaximal, characteristic
2#31823857C211yesmaximal, characteristic, complemented
3#31823823C211yesmaximal, characteristic, complemented
4#31823822C211yesmaximal, characteristic, complemented
5#31823202C211yesmaximal, characteristic, complemented
6#31823202C211yesmaximal, characteristic, complemented
7#329×C281C211yesmaximal, characteristic, complemented
8C2×Dic1124—21no—
9C2×#17985127—21no—
10#22582879C2211yescharacteristic, complemented
11#22582868—21no—
12#22582867C2211yescharacteristic
13#22582867C2211yescharacteristic
14#22582865—21no—
15#22582865—21no—
16#22582849—21no—
17#22582849—21no—
18#22582847—21no—
19#22582804—21no—
20#22582803—21no—
21#22582801—21no—
22#22582800—21no—
23#22582790C2211yescharacteristic, complemented
24#124×C281C2211yescharacteristic
25#97×C281C2211yescharacteristic, complemented
26#97×C281C2211yescharacteristic, complemented
27C23×D281—21no—
28C2×Dic562—21no—
29C2×Dic562D411yescharacteristic
30C2×Dic562D411yescharacteristic
31C2×D1124—21no—
32C2×D1124D411yescharacteristic
33C2×D1124D411yescharacteristic
34C2×C22⋊D281—21no—
35C2×C22⋊D281—21no—
36Dic1124—42no—
37#17985127—42no—
38C2×#14555886—21no—
39C4⋊Dic281—21no—
40C4⋊Dic281—21no—
41C22⋊Dic281—21no—
42#17985115—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—21no—
48C4×Dic281—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—
57C22×D281—21no—
58C22×D281—81no—
59C22×D281—81no—
60C22×D281—81no—
61Dic562—41no—
62Dic562—41no—
63Dic562—41no—
64Dic562—41no—
65D1124—41no—
66D1124—41no—
67D1124—81no—
68C22⋊D281—81no—
69C22⋊D281—81no—
70C2×Dic281—21no—
71C2×Dic281—21no—
72C2×Dic281—41no—
73#14555886—41no—
74C23×C281—21no—
75Q8×C281—41no—
76D4×C281—41no—
77C2×C4×C281—21no—
78C2×C4×C281C2×D411yescharacteristic
79C2×C4×C281C2×D411yescharacteristic
80C2×C4×C281C2×D411yescharacteristic
81C8×C281—22no—
82C8×C281—41no—
83C22×C281—41no—
84C22×C281—41no—
85C22×C281—41no—
86C22×C281#12011yescharacteristic
87C2×D281—41no—
88C2×D281—41no—
89C2×D281—41no—
90C2×D281—41no—
91C2×D281—41no—
92C2×D281—41no—
93C2×D281—84no—
94C4×C281—21no—
95C4×C281—21no—
96C4×C281—21no—
97C4×C281—41no—
98Dic281—41no—
99Dic281—41no—
100Dic281—81no—
101C2×C281—81no—
102C2×C281#45311yescharacteristic
103C2×C281#45511yescharacteristic
104C2×C281#45511yescharacteristic
105D281—81no—
106D281—81no—
107C281#165911yescharacteristic, complemented, Sylow
108#1659—2811nomaximal, Sylow
109H(3,𝔽4)—2811no—
110#497—2811no—
111#489—2811no—
112#489—2811no—
113#329—2811no—
114#329—2811no—
115#329D28111yescharacteristic, complemented
116C2×Q16—5621no—
117C2×SD16—5621no—
118C4⋊Q8—2811no—
119#124—2811no—
120#124—2811no—
121#124—5621no—
122#124—5621no—
123#124—5621no—
124#124C2×D28111yescharacteristic
125#120—5621no—
126#120—5621no—
127#120—5621no—
128#103—5621no—
129#103—5621no—
130#102—5621no—
131#102—5621no—
132#97—2811no—
133#97C2×D28111yescharacteristic, complemented
134#97C2×D28111yescharacteristic, complemented
135C24—5621no—
136C2×Q8—2811no—
137C2×Q8—2811no—
138C2×Q8—5621no—
139C2×Q8D112411yescharacteristic
140C2×D4—2811no—
141C2×D4—2811no—
142C2×D4—5621no—
143C2×D4—5621no—
144C2×D4—5621no—
145C2×D4D112411yescharacteristic
146Q16—11242no—
147SD16—11242no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—5621no—
151C4⋊C4—5621no—
152C4⋊C4—5621no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—5621no—
156C22⋊C4—5621no—
157C22⋊C4—5621no—
158C22⋊C4—5621no—
159C22⋊C4—5621no—
160C22⋊C4—5621no—
161C22⋊C4—5621no—
162C42—5621no—
163C42C22×D28111yescharacteristic
164C23—21no—
165C23—5621no—
166C23—5621no—
167C23—22481no—
168C23—22481no—
169C23—22481no—
170Q8—41no—
171Q8—11241no—
172Q8—11241no—
173Q8—11241no—
174Q8—11241no—
175D4—41no—
176D4—11241no—
177D4—11241no—
178D4—22481no—
179D4—22481no—
180D4—22481no—
181C2×C4—21no—
182C2×C4—5621no—
183C2×C4—5621no—
184C2×C4—11241no—
185C2×C4D4×D28111yescharacteristic
186C2×C4D4×D28111yescharacteristic
187C2×C4C2×D112411yescharacteristic
188C8—22no—
189C8—41no—
190C8—11241no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—11241no—
195C22—11241no—
196C22—11241no—
197C22—11241no—
198C22—11241no—
199C22—11241no—
200C22—22484no—
201C22#2258284911yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—11241no—
207C4—11241no—
208C4—22481no—
209C2—81no—
210C2—22481no—
211C2—22481no—
212C2#3182363211yescharacteristic
213C2#3182364211yescharacteristic
214C2#3182364311yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#329×C281C2
socleC22×C281#120
prime radical#31824205C2
hypercenter#329D281
hypocenterC281#1659
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. #31823857C2semidirect
3. #31823823C2semidirect
4. #31823822C2semidirect
5. #31823202C2semidirect
6. #31823202C2semidirect
7. #329×C281C2semidirect
10. #22582879C22semidirect
23. #22582790C22semidirect
25. #97×C281C22semidirect
26. #97×C281C22semidirect
107. C281#1659semidirect
115. #329D281semidirect
133. #97C2×D281semidirect
134. #97C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318242052
#318238572
#318238232
#318238222
#318232022
#329×C2812
#1659281