Finite Group Databasebeta

← #49098595

Subgroups — #49098595

Order 35968.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C2×#22582844C211yesmaximal, characteristic
2C2×#22582844C211yesmaximal, characteristic
3#31823397C212yesmaximal
4#31823394C211yesmaximal, characteristic
5#31823384C211yesmaximal, characteristic
6#31823383C211yesmaximal, characteristic
7#31823383C212yesmaximal
8C4⋊C4×Dic281C212yesmaximal
9#31823314C212yesmaximal
10#31823308C211yesmaximal, characteristic
11#398×C281C211yesmaximal, characteristic
12C22×Dic562C2211yescharacteristic
13C22×Dic562C2211yescharacteristic
14#22582844—24no—
15#22582844—24no—
16C2×C4⋊Dic281C2212yes—
17C2×#17985117C2212yes—
18C2×#17985117C2212yes—
19C2×#17985117C2212yes—
20C2×#17985117C2211yescharacteristic
21C2×#17985117C2211yescharacteristic
22C2×C4×Dic281C2211yescharacteristic
23C2×C4×Dic281C2212yes—
24C2×C4×Dic281C2211yescharacteristic
25C2×C4×Dic281C2211yescharacteristic
26C2×C4×Dic281C2212yes—
27#22582786C2212yes—
28#22582786C2212yes—
29#22582786C2211yescharacteristic
30#22582786C2212yes—
31#22582786C2212yes—
32C2×C4⋊C4×C281C2211yescharacteristic
33C2×C4⋊C4×C281C2212yes—
34C2×C4⋊C4×C281C2211yescharacteristic
35#95×C281C2211yescharacteristic
36#95×C281C2212yes—
37C2×Dic562—22no—
38C2×Dic562—22no—
39C2×Dic562—24no—
40C2×Dic562—22no—
41C2×Dic562—22no—
42C22×Dic281C2311yescharacteristic
43C22×Dic281C2311yescharacteristic
44C22×Dic281C2312yes—
45C22×Dic281C2311yescharacteristic
46C22×Dic281C2312yes—
47C22×Dic281C2311yescharacteristic
48C4⋊Dic281—24no—
49#17985117—24no—
50#17985117—22no—
51#17985117—24no—
52#17985117—24no—
53#17985117—22no—
54C4×Dic281—22no—
55C4×Dic281—22no—
56C4×Dic281—24no—
57C4×Dic281D414yes—
58C4×Dic281Q818yescomplemented
59C22×C4×C281C2312yes—
60C22×C4×C281C2311yescharacteristic
61C22×C4×C281C2311yescharacteristic
62C22×C4×C281C2312yes—
63C22×C4×C281C2311yescharacteristic
64C4⋊C4×C281—22no—
65C4⋊C4×C281—22no—
66C4⋊C4×C281—24no—
67Dic562—28no—
68Dic562—28no—
69C2×Dic281—22no—
70C2×Dic281—21no—
71C2×Dic281—22no—
72C2×Dic281—22no—
73C2×Dic281—21no—
74C2×Dic281—22no—
75C2×Dic281—21no—
76C2×Dic281—21no—
77C2×Dic281—21no—
78C2×Dic281—22no—
79C2×Dic281C2×D412yes—
80C2×Dic281C2×D412yes—
81C2×Dic281C2×Q814yes—
82C2×Dic281C2×Q814yes—
83C2×Dic281#4112yes—
84C2×Dic281#4114yes—
85C23×C281C2411yescharacteristic
86C2×C4×C281—21no—
87C2×C4×C281—22no—
88C2×C4×C281—22no—
89C2×C4×C281—22no—
90C2×C4×C281—21no—
91C2×C4×C281—22no—
92C2×C4×C281—21no—
93C2×C4×C281—22no—
94C2×C4×C281—22no—
95C2×C4×C281—22no—
96C2×C4×C281C2×D412yes—
97C2×C4×C281C2×Q814yes—
98C2×C4×C281#4112yes—
99C22×C281C22×D411yescharacteristic
100C22×C281C22×Q812yes—
101C22×C281C2×#4112yes—
102C22×C281C2×#4111yescharacteristic
103C22×C281C2×#4111yescharacteristic
104C4×C281—22no—
105C4×C281—22no—
106C4×C281—24no—
107C4×C281—41no—
108C4×C281—42no—
109Dic281—22no—
110Dic281—24no—
111Dic281—22no—
112Dic281—24no—
113Dic281—41no—
114Dic281C4⋊Q814yes—
115C2×C281#52511yescharacteristic
116C2×C281#52511yescharacteristic
117C2×C281C2×C4⋊Q811yescharacteristic
118C2×C281#53312yes—
119C2×C281#53312yes—
120C281#239911yescharacteristic, complemented, Sylow
121#2399—2811nomaximal, Sylow
122C2×C4×Q8—2811no—
123C2×C4×Q8—2811no—
124#398—2811no—
125#398—2812no—
126#398D28111yescharacteristic
127#395—2812no—
128#395—2811no—
129#395—2811no—
130C4×C4⋊C4—2812no—
131C4×C4⋊C4—2812no—
132#376—2811no—
133C22×Q8—2811no—
134C22×Q8—2811no—
135C4×Q8—5624no—
136C4×Q8—5624no—
137C2×C4⋊C4—2812no—
138C2×C4⋊C4—2811no—
139C2×C4⋊C4—2811no—
140C2×C4⋊C4—2812no—
141C2×C4⋊C4—2812no—
142C2×C4⋊C4—2812no—
143C2×C4⋊C4C2×D28111yescharacteristic
144C2×C4⋊C4C2×D28111yescharacteristic
145C2×C4⋊C4C2×D28112yes—
146C2×C42—2811no—
147C2×C42—2812no—
148C2×C42—2812no—
149C2×C42—2811no—
150C2×C42—2811no—
151#95—2811no—
152#95—2812no—
153#95—2812no—
154#95—2812no—
155#95—2812no—
156#95C2×D28111yescharacteristic
157#95C2×D28112yes—
158C2×Q8—5622no—
159C2×Q8—5624no—
160C2×Q8—5622no—
161C2×Q8—5622no—
162C2×Q8—5622no—
163C22×C4—2811no—
164C22×C4—2812no—
165C22×C4—2811no—
166C22×C4—2812no—
167C22×C4—2811no—
168C22×C4—2811no—
169C22×C4C22×D28112yes—
170C22×C4C22×D28111yescharacteristic
171C22×C4C22×D28111yescharacteristic
172C22×C4C22×D28112yes—
173C22×C4C22×D28111yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—5624no—
178C4⋊C4—5624no—
179C4⋊C4—5624no—
180C4⋊C4—5622no—
181C4⋊C4—5624no—
182C4⋊C4—5622no—
183C42—2814no—
184C42—2818no—
185C42—5622no—
186C42—5622no—
187C42—5624no—
188C23C23×D28111yescharacteristic
189Q8—5628no—
190Q8—5628no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—2812no—
202C2×C4—2814no—
203C2×C4—2812no—
204C2×C4—2814no—
205C2×C4—2814no—
206C2×C4—2812no—
207C2×C4—5622no—
208C2×C4—5621no—
209C2×C4—5622no—
210C2×C4—5622no—
211C2×C4—5622no—
212C2×C4—5621no—
213C2×C4—5621no—
214C2×C4—5621no—
215C2×C4—5621no—
216C2×C4—5622no—
217C2×C4D4×D28112yes—
218C2×C4Q8×D28114yes—
219C2×C4#1798513712yes—
220C22C2×D4×D28111yescharacteristic
221C22C2×Q8×D28112yes—
222C22#41×D28112yes—
223C22#41×D28111yescharacteristic
224C22C2×#1798513711yescharacteristic
225C4—22no—
226C4—22no—
227C4—24no—
228C4—41no—
229C4—42no—
230C4—2814no—
231C4—5624no—
232C4—5622no—
233C4—5622no—
234C4—5624no—
235C4—11241no—
236C2#3182397111yescharacteristic
237C2#3182397311yescharacteristic
238C2C4⋊Q8×D28111yescharacteristic
239C2#3182401512yes—
240C2#3182401912yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, prime radical, cosocleC23×C281C24
Fitting#398×C281C2
hypercenter#398D281
hypocenterC281#2399
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
58. C4×Dic281Q8semidirect
120. C281#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#225828442
#318233972
#318233942
#318233842
#318233832
C4⋊C4×Dic2812
#318233142
#318233082
#398×C2812
#2399281