Finite Group Databasebeta

← #49098576

Subgroups — #49098576

Order 35968.

528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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, complemented
2C2×#22582837C211yesmaximal, characteristic
3#31823398C211yesmaximal, characteristic
4#31823397C212yesmaximal, complemented
5#31823387C212yesmaximal
6#31823383C211yesmaximal, characteristic, complemented
7#31823376C211yesmaximal, characteristic
8#31823314C212yesmaximal, complemented
9#31823314C211yesmaximal, characteristic, complemented
10#31823310C212yesmaximal
11#400×C281C211yesmaximal, characteristic, complemented
12C22×Dic562C2211yescharacteristic
13C22×C4×D281C2211yescharacteristic
14#22582844—24no—
15#22582837—24no—
16C2×C4⋊Dic281C2211yescharacteristic
17C2×#17985117C2212yes—
18C2×#17985117C2212yes—
19C2×#17985117C2212yes—
20C2×#17985117C2212yes—
21C2×#17985115C2212yes—
22C2×#17985115C2211yescharacteristic
23C2×#17985115C2211yescharacteristic
24C2×#17985115C2212yes—
25C2×C4×Dic281C2211yescharacteristic
26C2×C4×Dic281C2212yes—
27C2×C4×Dic281C2212yes—
28C2×C4×Dic281C2211yescharacteristic
29#22582786C2212yes—
30#22582786C2212yes—
31#22582786C2211yescharacteristic
32C2×C4⋊C4×C281C2211yescharacteristic
33C2×C4⋊C4×C281C2211yescharacteristic
34#95×C281C2211yescharacteristic
35#95×C281C2212yes—
36#95×C281C2212yes—
37C23×D281C2311yescharacteristic
38C2×Dic562—24no—
39C2×Dic562—22no—
40C22×Dic281C2311yescharacteristic
41C22×Dic281C2311yescharacteristic
42C22×Dic281C2312yes—
43C22×Dic281C2312yes—
44C22×Dic281C2311yescharacteristic
45C2×C4×D281—22no—
46C2×C4×D281—22no—
47C2×C4×D281Q814yescomplemented
48C4⋊Dic281—22no—
49#17985117—24no—
50#17985117—24no—
51#17985117—24no—
52#17985117—24no—
53#17985115—22no—
54#17985115—24no—
55#17985115—24no—
56#17985115—22no—
57C4×Dic281—22no—
58C4×Dic281—24no—
59C4×Dic281—24no—
60C4×Dic281D414yes—
61C22×C4×C281C2312yes—
62C22×C4×C281C2311yescharacteristic
63C22×C4×C281C2312yes—
64C22×C4×C281C2311yescharacteristic
65C22×C4×C281C2311yescharacteristic
66C4⋊C4×C281—22no—
67C4⋊C4×C281—22no—
68C22×D281—21no—
69C22×D281—22no—
70C22×D281—22no—
71C22×D281—21no—
72C22×D281C2×Q812yes—
73Dic562—28no—
74C2×Dic281—22no—
75C2×Dic281—22no—
76C2×Dic281—22no—
77C2×Dic281—22no—
78C2×Dic281—22no—
79C2×Dic281—21no—
80C2×Dic281—22no—
81C2×Dic281C2×D412yes—
82C2×Dic281C2×D412yes—
83C2×Dic281C2×Q812yes—
84C2×Dic281#4114yes—
85C2×Dic281#4114yes—
86C2×Dic281#4112yes—
87C4×D281—28no—
88C23×C281C2411yescharacteristic
89C2×C4×C281—21no—
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×C281—22no—
97C2×C4×C281—22no—
98C2×C4×C281—22no—
99C2×C4×C281—22no—
100C2×C4×C281C2×D412yes—
101C2×C4×C281C2×Q812yes—
102C22×C281C22×D411yescharacteristic
103C22×C281C22×Q811yescharacteristic
104C22×C281C2×#4111yescharacteristic
105C22×C281C2×#4112yes—
106C22×C281C2×#4112yes—
107C2×D281—22no—
108C2×D281—24no—
109C2×D281—41no—
110C2×D281—42no—
111C2×D281—41no—
112C4×C281—22no—
113C4×C281—22no—
114C4×C281—41no—
115C4×C281—42no—
116C4×C281—42no—
117Dic281—24no—
118Dic281—24no—
119Dic281—22no—
120Dic281—41no—
121Dic281C22⋊Q814yes—
122C2×C281C2×C22⋊Q811yescharacteristic
123C2×C281#52511yescharacteristic
124C2×C281#52912yes—
125C2×C281#53211yescharacteristic
126C2×C281#53312yes—
127D281—42no—
128C281#239611yescharacteristic, complemented, Sylow
129#2396—2811nomaximal, Sylow
130C2×C4×Q8—2811no—
131C2×#117—2811no—
132#400D28111yescharacteristic, complemented
133#399—2811no—
134#398—2812no—
135#396—2812no—
136#395—2811no—
137#393—2811no—
138C4×C4⋊C4—2812no—
139C4×C4⋊C4—2811no—
140C4×C22⋊C4—2812no—
141C22×Q8—2811no—
142C23×C4—2811no—
143C4×Q8—5624no—
144#117—5624no—
145C2×C4⋊C4—2811no—
146C2×C4⋊C4—2812no—
147C2×C4⋊C4—2812no—
148C2×C4⋊C4—2812no—
149C2×C4⋊C4—2812no—
150C2×C4⋊C4C2×D28111yescharacteristic
151C2×C4⋊C4C2×D28111yescharacteristic
152C2×C22⋊C4—2811no—
153C2×C22⋊C4—2811no—
154C2×C22⋊C4—2812no—
155C2×C22⋊C4—2812no—
156C2×C42—2811no—
157C2×C42—2811no—
158C2×C42—2812no—
159C2×C42—2812no—
160#95—2812no—
161#95—2812no—
162#95—2811no—
163#95C2×D28112yes—
164#95C2×D28111yescharacteristic
165#95C2×D28112yes—
166C24—2811no—
167C2×Q8—5624no—
168C2×Q8—5622no—
169C22×C4—2811no—
170C22×C4—2812no—
171C22×C4—2812no—
172C22×C4—2811no—
173C22×C4—2814no—
174C22×C4—2811no—
175C22×C4—5622no—
176C22×C4—5622no—
177C22×C4C22×D28112yes—
178C22×C4C22×D28111yescharacteristic
179C22×C4C22×D28112yes—
180C22×C4C22×D28111yescharacteristic
181C22×C4C22×D28111yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—5624no—
185C4⋊C4—5624no—
186C4⋊C4—5624no—
187C4⋊C4—5624no—
188C4⋊C4—5622no—
189C22⋊C4—5624no—
190C22⋊C4—5624no—
191C22⋊C4—5622no—
192C22⋊C4—5622no—
193C42—2814no—
194C42—5624no—
195C42—5622no—
196C42—5624no—
197C23—2812no—
198C23—5621no—
199C23—5622no—
200C23—5622no—
201C23—5621no—
202C23C23×D28111yescharacteristic
203Q8—5628no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—2812no—
216C2×C4—2812no—
217C2×C4—2812no—
218C2×C4—2812no—
219C2×C4—2814no—
220C2×C4—2814no—
221C2×C4—5628no—
222C2×C4—5622no—
223C2×C4—5622no—
224C2×C4—5622no—
225C2×C4—5622no—
226C2×C4—5622no—
227C2×C4—5621no—
228C2×C4—5622no—
229C2×C4D4×D28112yes—
230C2×C4Q8×D28112yes—
231C22—5622no—
232C22—5624no—
233C22—11241no—
234C22—11242no—
235C22—11241no—
236C22C2×D4×D28111yescharacteristic
237C22C2×Q8×D28111yescharacteristic
238C22#41×D28111yescharacteristic
239C22#41×D28112yes—
240C22#41×D28112yes—
241C4—22no—
242C4—22no—
243C4—41no—
244C4—42no—
245C4—42no—
246C4—2814no—
247C4—5624no—
248C4—5624no—
249C4—5622no—
250C4—11241no—
251C2—11242no—
252C2C22⋊Q8×D28111yescharacteristic
253C2#3182397111yescharacteristic
254C2#3182399612yes—
255C2#3182401211yescharacteristic
256C2#3182401912yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#400×C281C2
prime radicalC23×D281C23
hypercenter#400D281
hypocenterC281#2396
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#22582844C2semidirect
4. #31823397C2semidirect
6. #31823383C2semidirect
8. #31823314C2semidirect
9. #31823314C2semidirect
11. #400×C281C2semidirect
47. C2×C4×D281Q8semidirect
128. C281#2396semidirect
132. #400D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828442
C2×#225828372
#318233982
#318233972
#318233872
#318233832
#318233762
#318233142
#318233102
#400×C2812
#2396281