Finite Group Databasebeta

← #49098640

Subgroups — #49098640

Order 35968.

864 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×#17985138C211yesmaximal, characteristic
2C2×#22582863C212yesmaximal, complemented
3C22×#17985117C211yesmaximal, characteristic, complemented
4#31823384C212yesmaximal, complemented
5#31823381C212yesmaximal, complemented
6#31823340C212yesmaximal, complemented
7#31823337C214yesmaximal, complemented
8#381×C281C211yesmaximal, characteristic, complemented
9C2×#17985138—28no—
10C2×#17985138—24no—
11C22×Dic562C2211yescharacteristic
12C22×D1124C2211yescharacteristic
13C22×C22⋊D281C2212yes—
14C23×Dic281C2211yescharacteristic
15C23×Dic281C2211yescharacteristic
16C22×C4×D281C2212yes—
17#22582863—28no—
18C2×C4⋊Dic281C2214yes—
19C2×#17985117—24no—
20C2×#17985117C2212yes—
21C2×#17985117C2212yes—
22C2×#17985115C2214yes—
23C2×#17985115C2214yes—
24#22582786C2214yes—
25C23×C4×C281C2211yescharacteristic
26C2×C22⋊C4×C281C2212yes—
27#95×C281C2212yes—
28#95×C281C2212yes—
29C23×D281C2312yes—
30#17985138—232no—
31C2×Dic562—24no—
32C2×Dic562—22no—
33C2×D1124—24no—
34C2×D1124—22no—
35C2×C22⋊D281—24no—
36C2×C22⋊D281—24no—
37C2×C22⋊D281D418yes—
38C22×Dic281—24no—
39C22×Dic281—22no—
40C22×Dic281—22no—
41C22×Dic281—24no—
42C22×Dic281C2312yes—
43C22×Dic281C2312yes—
44C22×Dic281C2312yes—
45C2×C4×D281—24no—
46C2×C4×D281—24no—
47C2×C4×D281—24no—
48C4⋊Dic281—28no—
49#17985117—24no—
50#17985117—24no—
51#17985115—28no—
52#17985115—28no—
53C24×C281C2311yescharacteristic
54C22×C4×C281—24no—
55C22×C4×C281D414yes—
56C22×C4×C281C2314yes—
57C22×C4×C281C2311yescharacteristic
58C22×C4×C281C2311yescharacteristic
59C22⋊C4×C281—24no—
60C22×D281—22no—
61C22×D281—22no—
62C22×D281—24no—
63C22×D281—24no—
64C22×D281C2×D414yes—
65Dic562—28no—
66D1124—28no—
67C22⋊D281—216no—
68C2×Dic281—28no—
69C2×Dic281—22no—
70C2×Dic281—22no—
71C2×Dic281—22no—
72C2×Dic281—22no—
73C2×Dic281—24no—
74C2×Dic281—22no—
75C2×Dic281—44no—
76C2×Dic281C2×D414yes—
77C2×Dic281#4114yescomplemented
78C4×D281—216no—
79C23×C281—22no—
80C23×C281—22no—
81C23×C281C2×D414yes—
82C23×C281C2×D412yes—
83C23×C281C2411yescharacteristic
84C2×C4×C281—28no—
85C2×C4×C281—22no—
86C2×C4×C281—22no—
87C2×C4×C281—24no—
88C2×C4×C281—24no—
89C2×C4×C281—24no—
90C2×C4×C281C2×D412yes—
91C2×C4×C281C2×D412yes—
92C22×C281—22no—
93C22×C281—22no—
94C22×C281—28no—
95C22×C281#12014yes—
96C22×C281C22×D412yes—
97C22×C281C22×D411yescharacteristic
98C22×C281C2×#4112yes—
99C22×C2812−1+412yes—
100C2×D281—24no—
101C2×D281—28no—
102C2×D281—42no—
103C2×D281—42no—
104C2×D281—44no—
105C4×C281—22no—
106C4×C281—22no—
107C4×C281—44no—
108Dic281—24no—
109Dic281—24no—
110Dic281—42no—
111C2×C281—24no—
112C2×C281C2×#12011yescharacteristic
113C2×C281#52511yescharacteristic
114C2×C281#53611yescharacteristic
115C2×C281#54714yes—
116D281—44no—
117C281#240611yescharacteristic, complemented, Sylow
118#2406—2811nomaximal, Sylow
119C22×#41—2811no—
120C2×#123—2812no—
121C22×C4⋊C4—2811no—
122#395—2812no—
123#394—2812no—
124#386—2812no—
125#385—2814no—
126#381D28111yescharacteristic, complemented
127C2×#41—5628no—
128C2×#41—5624no—
129C22×Q8—2811no—
130C22×D4—2812no—
131C22×D4—2811no—
132C23×C4—2811no—
133C23×C4—2811no—
134C23×C4—2812no—
135C23×C4C2×D28111yescharacteristic
136#123—5628no—
137C2×C4⋊C4—2812no—
138C2×C4⋊C4—2812no—
139C2×C4⋊C4—2814no—
140C2×C4⋊C4—5624no—
141C2×C22⋊C4—2814no—
142C2×C22⋊C4—2814no—
143C2×C22⋊C4C2×D28112yes—
144#95—2814no—
145#95C2×D28112yes—
146#95C2×D28112yes—
147C24—2812no—
148C24C22×D28111yescharacteristic
149#41—56232no—
150C2×Q8—5624no—
151C2×Q8—5622no—
152C2×D4—2818no—
153C2×D4—5624no—
154C2×D4—5624no—
155C2×D4—5624no—
156C2×D4—5622no—
157C22×C4—24no—
158C22×C4—2812no—
159C22×C4—2812no—
160C22×C4—2812no—
161C22×C4—5624no—
162C22×C4—5624no—
163C22×C4—5624no—
164C22×C4—5622no—
165C22×C4—5624no—
166C22×C4—5624no—
167C22×C4—5622no—
168C22×C4D112414yes—
169C22×C4C22×D28114yes—
170C22×C4C22×D28111yescharacteristic
171C22×C4C22×D28111yescharacteristic
172C4⋊C4—5628no—
173C4⋊C4—5624no—
174C4⋊C4—5624no—
175C22⋊C4—24no—
176C22⋊C4—5628no—
177C22⋊C4—5628no—
178C23—22no—
179C23—22no—
180C23—2814no—
181C23—5622no—
182C23—5622no—
183C23—5624no—
184C23—5624no—
185C23D4×D28114yes—
186C23C2×D112412yes—
187C23C23×D28111yescharacteristic
188Q8—5628no—
189D4—5628no—
190D4—56216no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—2814no—
198C2×C4—2814no—
199C2×C4—56216no—
200C2×C4—5628no—
201C2×C4—5622no—
202C2×C4—5622no—
203C2×C4—5622no—
204C2×C4—5622no—
205C2×C4—5624no—
206C2×C4—5622no—
207C2×C4—11244no—
208C2×C4C2×D112412yes—
209C2×C4C2×D112412yes—
210C22—22no—
211C22—22no—
212C22—28no—
213C22—5624no—
214C22—5628no—
215C22—11242no—
216C22—11242no—
217C22—11244no—
218C22#2258284914yes—
219C22C2×D4×D28112yes—
220C22C22×D112411yescharacteristic
221C22#41×D28112yes—
222C22#2258292612yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—5624no—
227C4—5624no—
228C4—11242no—
229C2—24no—
230C2—11244no—
231C2C2×#2258284911yescharacteristic
232C2#3182397511yescharacteristic
233C2#3182403911yescharacteristic
234C2#3182411114yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#381×C281C2
prime radicalC22×#17985138C2
hypercenter#381D281
hypocenterC281#2406
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#22582863C2semidirect
3. C22×#17985117C2semidirect
4. #31823384C2semidirect
5. #31823381C2semidirect
6. #31823340C2semidirect
7. #31823337C2semidirect
8. #381×C281C2semidirect
77. C2×Dic281#41semidirect
117. C281#2406semidirect
126. #381D281semidirect

Maximal subgroups

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

subgroupindex
C22×#179851382
C2×#225828632
C22×#179851172
#318233842
#318233812
#318233402
#318233372
#381×C2812
#2406281