Finite Group Databasebeta

← #49094241

Subgroups — #49094241

Order 35968.

266 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 51 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#31824092C211yesmaximal, characteristic, complemented
2#31823614C211yesmaximal, characteristic
3#31823377C211yesmaximal, characteristic
4#31823201C211yesmaximal, characteristic, complemented
5#31823200C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#450×C281C211yesmaximal, characteristic
8C2×#17985126—21no—
9#22582878—21no—
10#22582877—21no—
11#22582869—21no—
12#22582869—21no—
13#22582858C2211yescharacteristic
14#22582856—21no—
15#22582835—21no—
16C2×#17985117C2211yescharacteristic
17C2×C22⋊Dic281—21no—
18C2×C22⋊Dic281—21no—
19#22582800—21no—
20C22⋊#14555886C2211yescharacteristic
21#22582786C2211yescharacteristic
22C22×D4×C281C2211yescharacteristic
23C2×SD16×C281—21no—
24C22⋊Q8×C281C2211yescharacteristic
25#102×C281—21no—
26C22⋊C8×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×Dic562D411yescharacteristic
29C22×Dic281—21no—
30C22×Dic281D411yescharacteristic
31C22×Dic281D411yescharacteristic
32#17985126—42no—
33C2×#14555886—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281D411yescharacteristic
36#17985117—21no—
37#17985117—21no—
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41#17985117—21no—
42#17985117—21no—
43C22⋊Dic281—21no—
44C22⋊Dic281—42no—
45C22⋊Dic281—42no—
46C4×Dic281—21no—
47C4×Dic281—21no—
48C24×C281—21no—
49C2×Q8×C281D411yescharacteristic
50C2×D4×C281—21no—
51C2×D4×C281—21no—
52C2×D4×C281—42no—
53C22×C4×C281C2311yescharacteristic
54SD16×C281—42no—
55C2×C8×C281—21no—
56C4⋊C4×C281—21no—
57C4⋊C4×C281D411yescharacteristic
58C22⋊C4×C281—21no—
59Dic562—41no—
60Dic562—81no—
61C2×Dic281—21no—
62C2×Dic281—21no—
63C2×Dic281—21no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—41no—
67C2×Dic281—41no—
68C2×Dic281—41no—
69C2×Dic281—41no—
70C2×Dic281SD1612yescomplemented
71#14555886—41no—
72C23×C281—22no—
73C23×C281—41no—
74C23×C281—41no—
75C23×C281—41no—
76C23×C281—41no—
77C23×C281—41no—
78C23×C281—41no—
79C23×C281C2×D411yescharacteristic
80Q8×C281—41no—
81D4×C281—22no—
82D4×C281—22no—
83D4×C281—41no—
84D4×C281—41no—
85C2×C4×C281—21no—
86C2×C4×C281—21no—
87C2×C4×C281—41no—
88C2×C4×C281C2×D411yescharacteristic
89C2×C4×C281C2×D411yescharacteristic
90C8×C281—41no—
91C22×C281—21no—
92C22×C281—21no—
93C22×C281—42no—
94C22×C281—42no—
95C22×C281—42no—
96C22×C281—81no—
97C22×C281—81no—
98C22×C281—81no—
99C22×C281—81no—
100C22×C281#12011yescharacteristic
101C22×C281C2×SD1611yescharacteristic
102C22×C281#13711yescharacteristic
103C4×C281—21no—
104C4×C281—21no—
105C4×C281—41no—
106C4×C281—41no—
107Dic281—22no—
108Dic281—41no—
109Dic281—41no—
110Dic281—41no—
111Dic281—81no—
112C2×C281—21no—
113C2×C281—21no—
114C2×C281—82no—
115C2×C281#44811yescharacteristic
116C2×C281#45411yescharacteristic
117C2×C281B(4,𝔽2)11yescharacteristic
118C281#159911yescharacteristic, complemented, Sylow
119#1599—2811nomaximal, Sylow
120#544—2811no—
121#450—2811no—
122#450D28111yescharacteristic
123#394—2811no—
124#328—2811no—
125#328—2811no—
126#324—2811no—
127C22×D4C2×D28111yescharacteristic
128C2×SD16—21no—
129C2×SD16—5621no—
130C4⋊Q8—5621no—
131C4⋊Q8—5621no—
132#125—5621no—
133#125—5621no—
134C22⋊Q8—2811no—
135C22⋊Q8—5621no—
136C22⋊Q8C2×D28111yescharacteristic
137#117—5621no—
138C2×C4⋊C4—2811no—
139C2×C22⋊C4—5621no—
140C2×C22⋊C4—5621no—
141#102—21no—
142#102—5621no—
143C22⋊C8—2811no—
144C22⋊C8C2×D28111yescharacteristic
145#95—2811no—
146C24—21no—
147C2×Q8—2811no—
148C2×Q8—5621no—
149C2×Q8C22⋊D28111yescharacteristic
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—42no—
153C22×C4—2811no—
154C22×C4—2811no—
155C22×C4—5621no—
156C22×C4C22×D28111yescharacteristic
157SD16—42no—
158SD16—11242no—
159C2×C8—21no—
160C2×C8—5621no—
161C4⋊C4—21no—
162C4⋊C4—2811no—
163C4⋊C4—5621no—
164C4⋊C4—5621no—
165C4⋊C4—5621no—
166C4⋊C4—5621no—
167C4⋊C4—5621no—
168C4⋊C4—5621no—
169C4⋊C4—5621no—
170C4⋊C4—5621no—
171C4⋊C4C22⋊D28111yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—5621no—
174C22⋊C4—11242no—
175C22⋊C4—11242no—
176C42—5621no—
177C42—5621no—
178C23—22no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23D4×D28111yescharacteristic
186Q8—41no—
187Q8—11241no—
188Q8—22481no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—2812no—
197C2×C4—5621no—
198C2×C4—5621no—
199C2×C4—5621no—
200C2×C4—5621no—
201C2×C4—5621no—
202C2×C4—11241no—
203C2×C4—11241no—
204C2×C4—11241no—
205C2×C4—11241no—
206C2×C4D4×D28111yescharacteristic
207C2×C4C2×C22⋊D28111yescharacteristic
208C8—41no—
209C8—11241no—
210C22—21no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—81no—
216C22—81no—
217C22—81no—
218C22—81no—
219C22#2258284711yescharacteristic
220C22SD16×D28111yescharacteristic
221C22#2258290811yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—5622no—
227C4—11241no—
228C4—11241no—
229C4—11241no—
230C4—22481no—
231C2—21no—
232C2—21no—
233C2—82no—
234C2#3182360011yescharacteristic
235C2#3182363411yescharacteristic
236C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#450×C281C2
socleC22×C281#120
prime radicalC22×D4×C281C22
hypercenter#450D281
hypocenterC281#1599
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #31824092C2semidirect
4. #31823201C2semidirect
5. #31823200C2semidirect
6. #31823188C2semidirect
70. C2×Dic281SD16semidirect
118. C281#1599semidirect

Maximal subgroups

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

subgroupindex
#318240922
#318236142
#318233772
#318232012
#318232002
#318231882
#450×C2812
#1599281