Finite Group Databasebeta

← #49098568

Subgroups — #49098568

Order 35968.

560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 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×#22582839C211yesmaximal, characteristic
2C2×#22582837C211yesmaximal, characteristic, complemented
3#31823401C211yesmaximal, characteristic, complemented
4#31823395C211yesmaximal, characteristic, complemented
5#31823389C212yesmaximal, complemented
6#31823388C211yesmaximal, characteristic, complemented
7#31823379C212yesmaximal
8C4⋊C4×Dic281C212yesmaximal, complemented
9C22⋊C4×Dic281C212yesmaximal, complemented
10#31823310C211yesmaximal, characteristic, complemented
11#399×C281C211yesmaximal, characteristic, complemented
12C22×C22⋊D281C2211yescharacteristic
13C23×Dic281C2211yescharacteristic
14C22×C4×D281C2211yescharacteristic
15#22582839—24no—
16#22582837—24no—
17C2×C4⋊Dic281C2212yes—
18C2×C4⋊Dic281C2211yescharacteristic
19C2×#17985117C2211yescharacteristic
20C2×C22⋊Dic281C2212yes—
21C2×#17985115C2212yes—
22C2×#17985115C2212yes—
23C2×#17985115C2211yescharacteristic
24C2×C4×Dic281C2212yes—
25C2×C4×Dic281C2211yescharacteristic
26C2×C4×Dic281C2212yes—
27#22582786C2212yes—
28#22582786C2212yes—
29#22582786C2211yescharacteristic
30#22582786C2212yes—
31#22582786C2212yes—
32C2×C4⋊C4×C281C2212yes—
33C2×C4⋊C4×C281C2211yescharacteristic
34C2×C22⋊C4×C281C2212yes—
35C2×C22⋊C4×C281C2211yescharacteristic
36#95×C281C2211yescharacteristic
37C23×D281C2311yescharacteristic
38C2×C22⋊D281—22no—
39C2×C22⋊D281—22no—
40C2×C22⋊D281—22no—
41C22×Dic281—22no—
42C22×Dic281—24no—
43C22×Dic281C2312yes—
44C22×Dic281C2311yescharacteristic
45C22×Dic281C2312yes—
46C22×Dic281C2311yescharacteristic
47C22×Dic281C2311yescharacteristic
48C2×C4×D281—24no—
49C2×C4×D281D414yes—
50C4⋊Dic281—24no—
51C4⋊Dic281—22no—
52#17985117—22no—
53C22⋊Dic281—24no—
54#17985115—24no—
55#17985115—22no—
56#17985115—24no—
57C4×Dic281—24no—
58C4×Dic281—22no—
59C4×Dic281—24no—
60C24×C281C2311yescharacteristic
61C22×C4×C281C2311yescharacteristic
62C22×C4×C281C2312yes—
63C22×C4×C281C2311yescharacteristic
64C22×C4×C281C2312yes—
65C4⋊C4×C281—22no—
66C4⋊C4×C281—24no—
67C22⋊C4×C281—22no—
68C22⋊C4×C281—24no—
69C22×D281—22no—
70C22×D281—22no—
71C22×D281—21no—
72C22×D281—21no—
73C22×D281C2×D412yes—
74C22⋊D281—28no—
75C2×Dic281—21no—
76C2×Dic281—21no—
77C2×Dic281—22no—
78C2×Dic281—21no—
79C2×Dic281—22no—
80C2×Dic281—22no—
81C2×Dic281—22no—
82C2×Dic281—22no—
83C2×Dic281—22no—
84C2×Dic281—22no—
85C2×Dic281—44no—
86C2×Dic281C2×D412yes—
87C2×Dic281#4112yes—
88C2×Dic281#4114yes—
89C4×D281—28no—
90C23×C281—21no—
91C23×C281—22no—
92C23×C281—22no—
93C23×C281—21no—
94C23×C281#4112yes—
95C23×C281C2411yescharacteristic
96C2×C4×C281—22no—
97C2×C4×C281—22no—
98C2×C4×C281—22no—
99C2×C4×C281—21no—
100C2×C4×C281—22no—
101C2×C4×C281—22no—
102C2×C4×C281—22no—
103C2×C4×C281—22no—
104C2×C4×C281C2×D412yes—
105C2×C4×C281#4114yes—
106C22×C281—22no—
107C22×C281—24no—
108C22×C281—41no—
109C22×C281—42no—
110C22×C281—41no—
111C22×C281C22×D411yescharacteristic
112C22×C281C2×#4112yes—
113C22×C281C2×#4111yescharacteristic
114C22×C281C2×#4112yes—
115C22×C281C2×#4111yescharacteristic
116C2×D281—22no—
117C2×D281—22no—
118C2×D281—22no—
119C2×D281—42no—
120C2×D281—42no—
121C4×C281—22no—
122C4×C281—24no—
123C4×C281—41no—
124C4×C281—42no—
125Dic281—22no—
126Dic281—41no—
127Dic281—42no—
128Dic281—42no—
129Dic281#12314yes—
130C2×C281—42no—
131C2×C281C2×#12311yescharacteristic
132C2×C281#52511yescharacteristic
133C2×C281#52912yes—
134C2×C281#52912yes—
135C2×C281#53211yescharacteristic
136D281—42no—
137C281#239511yescharacteristic, complemented, Sylow
138#2395—2811nomaximal, Sylow
139C2×C4×D4—2811no—
140C2×#117—2811no—
141#400—2811no—
142#399D28111yescharacteristic, complemented
143#398—2811no—
144#397—2812no—
145#397—2811no—
146#394—2812no—
147C4×C4⋊C4—2812no—
148C4×C22⋊C4—2812no—
149C4×C22⋊C4—2811no—
150C22×D4—2811no—
151C23×C4—2811no—
152C23×C4—2811no—
153C4×D4—5624no—
154#117—5624no—
155C2×C4⋊C4—2811no—
156C2×C4⋊C4—2811no—
157C2×C4⋊C4—2812no—
158C2×C4⋊C4C2×D28111yescharacteristic
159C2×C4⋊C4C2×D28112yes—
160C2×C22⋊C4—2812no—
161C2×C22⋊C4—2812no—
162C2×C22⋊C4—2811no—
163C2×C22⋊C4—2812no—
164C2×C22⋊C4C2×D28111yescharacteristic
165C2×C22⋊C4C2×D28112yes—
166C2×C42—2812no—
167C2×C42—2811no—
168C2×C42—2812no—
169#95—2812no—
170#95—2811no—
171#95—2812no—
172#95—2812no—
173#95—2812no—
174#95C2×D28111yescharacteristic
175C24—2811no—
176C24C22×D28111yescharacteristic
177C2×D4—5622no—
178C2×D4—5622no—
179C2×D4—5622no—
180C22×C4—2811no—
181C22×C4—2811no—
182C22×C4—2814no—
183C22×C4—2812no—
184C22×C4—2811no—
185C22×C4—2812no—
186C22×C4—5624no—
187C22×C4—5622no—
188C22×C4—5624no—
189C22×C4C22×D28111yescharacteristic
190C22×C4C22×D28112yes—
191C22×C4C22×D28111yescharacteristic
192C22×C4C22×D28112yes—
193C4⋊C4—22no—
194C4⋊C4—24no—
195C4⋊C4—5624no—
196C4⋊C4—5622no—
197C4⋊C4—5622no—
198C22⋊C4—22no—
199C22⋊C4—24no—
200C22⋊C4—5624no—
201C22⋊C4—5622no—
202C22⋊C4—5624no—
203C22⋊C4—5624no—
204C42—5624no—
205C42—5624no—
206C42—5622no—
207C23—21no—
208C23—22no—
209C23—21no—
210C23—22no—
211C23—2812no—
212C23—5622no—
213C23—5621no—
214C23—5622no—
215C23—5621no—
216C23#1798513912yes—
217C23C23×D28111yescharacteristic
218D4—5628no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—2812no—
228C2×C4—2814no—
229C2×C4—2812no—
230C2×C4—5628no—
231C2×C4—5621no—
232C2×C4—5621no—
233C2×C4—5622no—
234C2×C4—5621no—
235C2×C4—5622no—
236C2×C4—5622no—
237C2×C4—5622no—
238C2×C4—5622no—
239C2×C4—5622no—
240C2×C4—5622no—
241C2×C4—11244no—
242C2×C4D4×D28112yes—
243C2×C4#1798513714yes—
244C22—22no—
245C22—24no—
246C22—41no—
247C22—42no—
248C22—41no—
249C22—5622no—
250C22—5622no—
251C22—5622no—
252C22—11242no—
253C22—11242no—
254C22C2×D4×D28111yescharacteristic
255C22#41×D28112yes—
256C22#41×D28111yescharacteristic
257C22C2×#1798513712yes—
258C22C2×#1798513911yescharacteristic
259C4—22no—
260C4—24no—
261C4—41no—
262C4—42no—
263C4—2814no—
264C4—5622no—
265C4—11241no—
266C4—11242no—
267C4—11242no—
268C2—42no—
269C2—11242no—
270C2#123×D28111yescharacteristic
271C2#3182397611yescharacteristic
272C2#3182399012yes—
273C2#3182399912yes—
274C2#3182401111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#399×C281C2
prime radicalC22×C22⋊D281C22
hypercenter#399D281
hypocenterC281#2395
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#22582837C2semidirect
3. #31823401C2semidirect
4. #31823395C2semidirect
5. #31823389C2semidirect
6. #31823388C2semidirect
8. C4⋊C4×Dic281C2semidirect
9. C22⋊C4×Dic281C2semidirect
10. #31823310C2semidirect
11. #399×C281C2semidirect
137. C281#2395semidirect
142. #399D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828392
C2×#225828372
#318234012
#318233952
#318233892
#318233882
#318233792
C4⋊C4×Dic2812
C22⋊C4×Dic2812
#318233102
#399×C2812
#2395281