Finite Group Databasebeta

← #49096555

Subgroups — #49096555

Order 35968.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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#31824025C211yesmaximal, characteristic
2C2×#22582793C212yesmaximal, complemented
3#31823340C212yesmaximal, complemented
4#31823335C211yesmaximal, characteristic, complemented
5#342×C281C211yesmaximal, characteristic, complemented
6C22×C22⋊D281C2212yes—
7C23×Dic281C2211yescharacteristic
8#22582863—22no—
9#22582853—21no—
10#22582853—21no—
11#22582849—22no—
12C2×#17985117—21no—
13C2×C22⋊Dic281C2211yescharacteristic
14C2×#17985115—22no—
15#22582793—24no—
16#22582786—22no—
17#22582786—21no—
18C2×C22⋊C4×C281C2212yes—
19C2×C22⋊C4×C281C2211yescharacteristic
20C23×D281D412yes—
21C2×D1124—21no—
22C2×D1124—21no—
23C2×C22⋊D281—22no—
24C2×C22⋊D281—22no—
25C2×C22⋊D281—22no—
26C2×C22⋊D281—22no—
27C2×C22⋊D281—22no—
28C2×C22⋊D281—22no—
29C22×Dic281—22no—
30C22×Dic281—21no—
31C22×Dic281—21no—
32C22×Dic281—42no—
33C22×Dic281D412yes—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36#17985117—42no—
37C22⋊Dic281—21no—
38C22⋊Dic281D412yescomplemented
39#17985115—22no—
40#17985115—22no—
41#17985115—44no—
42C24×C281C2311yescharacteristic
43C22×C4×C281—22no—
44C22×C4×C281D411yescharacteristic
45C22×C4×C281D411yescharacteristic
46C22⋊C4×C281—22no—
47C22⋊C4×C281—22no—
48C22⋊C4×C281—22no—
49C22×D281—22no—
50C22×D281—22no—
51C22×D281—22no—
52C22×D281—42no—
53C22×D281—42no—
54D1124—81no—
55D1124—81no—
56C22⋊D281—42no—
57C22⋊D281—42no—
58C22⋊D281—42no—
59C22⋊D281—42no—
60C2×Dic281—24no—
61C2×Dic281—22no—
62C2×Dic281—22no—
63C2×Dic281—22no—
64C2×Dic281—22no—
65C2×Dic281—22no—
66C2×Dic281—41no—
67C2×Dic281—41no—
68C2×Dic281—41no—
69C2×Dic281—42no—
70C2×Dic281—41no—
71C23×C281—41no—
72C23×C281—41no—
73C23×C281C2×D412yes—
74C23×C281C2×D411yescharacteristic
75C23×C281C2×D411yescharacteristic
76C23×C281#4112yes—
77C23×C281#4111yescharacteristic
78C2×C4×C281—21no—
79C2×C4×C281—21no—
80C2×C4×C281—41no—
81C2×C4×C281—41no—
82C2×C4×C281—42no—
83C2×C4×C281—42no—
84C2×C4×C281—42no—
85C22×C281—21no—
86C22×C281—22no—
87C22×C281—21no—
88C22×C281—22no—
89C22×C281—41no—
90C22×C281—42no—
91C22×C281—41no—
92C22×C281#12011yescharacteristic
93C22×C281#12112yes—
94C22×C281#12111yescharacteristic
95C22×C281#12312yes—
96C22×C281#12411yescharacteristic
97C2×D281—44no—
98C2×D281—42no—
99C2×D281—42no—
100C2×D281—42no—
101C2×D281—82no—
102C4×C281—41no—
103C4×C281—41no—
104C4×C281—82no—
105Dic281—42no—
106Dic281—42no—
107Dic281—42no—
108C2×C281—21no—
109C2×C281—22no—
110C2×C281—22no—
111C2×C281—21no—
112C2×C281#39411yescharacteristic
113C2×C281B(4,𝔽2)11yescharacteristic
114C2×C281#45811yescharacteristic
115D281—82no—
116C281#204411yescharacteristic, complemented, Sylow
117#2044—2811nomaximal, Sylow
118#534—2811no—
119C2×#99—2812no—
120#386—2812no—
121#385—2811no—
122#342D28111yescharacteristic, complemented
123C22×D4—2812no—
124C23×C4—2811no—
125#123—5622no—
126#121—5621no—
127#121—5621no—
128#120—5622no—
129C2×C4⋊C4—5621no—
130C2×C22⋊C4—2811no—
131C2×C22⋊C4—5622no—
132C2×C22⋊C4C2×D28112yes—
133C2×C22⋊C4C2×D28111yescharacteristic
134#99—5624no—
135#95—5622no—
136#95—5621no—
137C24—2812no—
138C24C22×D28111yescharacteristic
139C2×D4—5621no—
140C2×D4—5621no—
141C2×D4—5622no—
142C2×D4—5622no—
143C2×D4—5622no—
144C2×D4—5622no—
145C2×D4—5622no—
146C2×D4—5622no—
147C22×C4—22no—
148C22×C4—2812no—
149C22×C4—5622no—
150C22×C4—5621no—
151C22×C4—5621no—
152C22×C4—11242no—
153C22×C4D112411yescharacteristic
154C22×C4D112411yescharacteristic
155C4⋊C4—5621no—
156C4⋊C4—5621no—
157C4⋊C4—11242no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—2812no—
162C22⋊C4—5622no—
163C22⋊C4—5622no—
164C22⋊C4—5621no—
165C22⋊C4—11244no—
166C23—41no—
167C23—41no—
168C23—5622no—
169C23—5622no—
170C23—5622no—
171C23—11242no—
172C23—11242no—
173C23D4×D28112yes—
174C23D4×D28111yescharacteristic
175C23C2×D112411yescharacteristic
176C23#1798513812yes—
177C23#1798513911yescharacteristic
178D4—11242no—
179D4—11242no—
180D4—11242no—
181D4—11242no—
182D4—22481no—
183D4—22481no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—5624no—
192C2×C4—5622no—
193C2×C4—5622no—
194C2×C4—5622no—
195C2×C4—5622no—
196C2×C4—5622no—
197C2×C4—11241no—
198C2×C4—11241no—
199C2×C4—11242no—
200C2×C4—11241no—
201C2×C4—11241no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—42no—
208C22—41no—
209C22—11244no—
210C22—11242no—
211C22—11242no—
212C22—11242no—
213C22—22482no—
214C22#2258284911yescharacteristic
215C22#2258285212yes—
216C22#2258285411yescharacteristic
217C22#2258286412yes—
218C22#2258286711yescharacteristic
219C4—41no—
220C4—41no—
221C4—82no—
222C4—11242no—
223C4—11242no—
224C4—11242no—
225C2—22no—
226C2—21no—
227C2—22no—
228C2—21no—
229C2—22482no—
230C2#3182338111yescharacteristic
231C2#3182365111yescharacteristic
232C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC24×C281C23
FrattiniC24C22×D281
Fitting#342×C281C2
socleC22×C281#120
prime radical#31824025C2
hypercenter#342D281
hypocenterC281#2044
LCSG ▷ C24×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#22582793C2semidirect
3. #31823340C2semidirect
4. #31823335C2semidirect
5. #342×C281C2semidirect
38. C22⋊Dic281D4semidirect
116. C281#2044semidirect
122. #342D281semidirect

Maximal subgroups

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

subgroupindex
#318240252
C2×#225827932
#318233402
#318233352
#342×C2812
#2044281