Finite Group Databasebeta

← #49098585

Subgroups — #49098585

Order 35968.

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

normal subgroups only

This group has 568 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×Q8×Dic281C211yesmaximal, characteristic, complemented
2C2×#22582839C211yesmaximal, characteristic
3#31823405C212yesmaximal, complemented
4#31823390C211yesmaximal, characteristic, complemented
5#31823388C211yesmaximal, characteristic, complemented
6#31823379C212yesmaximal
7#31823374C211yesmaximal, characteristic, complemented
8C22⋊C4×Dic281C212yesmaximal, complemented
9#31823310C212yesmaximal, complemented
10#31823308C211yesmaximal, characteristic, complemented
11#393×C281C211yesmaximal, characteristic, complemented
12C22×C22⋊D281C2211yescharacteristic
13C23×Dic281C2211yescharacteristic
14C22×C4×D281C2211yescharacteristic
15Q8×Dic281—24no—
16#22582839—24no—
17C2×C4⋊Dic281C2212yes—
18C2×C4⋊Dic281C2211yescharacteristic
19C2×#17985117C2211yescharacteristic
20C2×C22⋊Dic281C2212yes—
21C2×#17985115C2212yes—
22C2×#17985115C2211yescharacteristic
23C2×#17985115C2212yes—
24C2×C4×Dic281C2212yes—
25C2×C4×Dic281C2212yes—
26C2×C4×Dic281C2211yescharacteristic
27#22582786C2211yescharacteristic
28#22582786C2212yes—
29#22582786C2212yes—
30#22582786C2212yes—
31#22582786C2212yes—
32C22×Q8×C281C2211yescharacteristic
33C2×C22⋊C4×C281C2212yes—
34C2×C22⋊C4×C281C2211yescharacteristic
35#95×C281C2211yescharacteristic
36#95×C281C2212yes—
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—22no—
49C2×C4×D281—24no—
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—24no—
59C4×Dic281D414yes—
60C24×C281C2311yescharacteristic
61C2×Q8×C281—22no—
62C2×Q8×C281—24no—
63C22×C4×C281C2312yes—
64C22×C4×C281C2311yescharacteristic
65C22×C4×C281C2311yescharacteristic
66C22×C4×C281C2312yes—
67C22⋊C4×C281—22no—
68C22⋊C4×C281—24no—
69C22×D281—21no—
70C22×D281—22no—
71C22×D281—22no—
72C22×D281—21no—
73C22×D281#4112yes—
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×Dic281C2×D412yes—
88C2×Dic281#4114yes—
89C4×D281—44no—
90C23×C281—21no—
91C23×C281—22no—
92C23×C281—22no—
93C23×C281—21no—
94C23×C281#4112yes—
95C23×C281C2411yescharacteristic
96Q8×C281—28no—
97C2×C4×C281—22no—
98C2×C4×C281—22no—
99C2×C4×C281—22no—
100C2×C4×C281—21no—
101C2×C4×C281—22no—
102C2×C4×C281—22no—
103C2×C4×C281—22no—
104C2×C4×C281—22no—
105C2×C4×C281C2×D412yes—
106C2×C4×C281#4114yes—
107C22×C281—22no—
108C22×C281—24no—
109C22×C281—41no—
110C22×C281—41no—
111C22×C281—42no—
112C22×C281C22×D411yescharacteristic
113C22×C281C2×#4111yescharacteristic
114C22×C281C2×#4112yes—
115C22×C281C2×#4112yes—
116C22×C281C2×#4111yescharacteristic
117C2×D281—22no—
118C2×D281—24no—
119C2×D281—41no—
120C2×D281—41no—
121C2×D281—42no—
122C4×C281—22no—
123C4×C281—24no—
124C4×C281—41no—
125C4×C281—42no—
126Dic281—22no—
127Dic281—42no—
128Dic281—41no—
129Dic281—42no—
130Dic281#12414yes—
131C2×C281—42no—
132C2×C281#52511yescharacteristic
133C2×C281#52511yescharacteristic
134C2×C281C2×#12411yescharacteristic
135C2×C281#52912yes—
136C2×C281#52912yes—
137D281—42no—
138C281#239811yescharacteristic, complemented, Sylow
139#2398—2811nomaximal, Sylow
140C2×C4×Q8—2811no—
141C2×C4×D4—2811no—
142#400—2812no—
143#397—2811no—
144#397—2811no—
145#394—2812no—
146#393—2811no—
147#393D28111yescharacteristic, complemented
148C4×C22⋊C4—2812no—
149C4×C22⋊C4—2812no—
150#376—2811no—
151C22×Q8C2×D28111yescharacteristic
152C22×D4—2811no—
153C23×C4—2811no—
154C23×C4—2811no—
155C4×Q8—5624no—
156C4×D4—5624no—
157C2×C4⋊C4—2811no—
158C2×C4⋊C4—2812no—
159C2×C4⋊C4—2811no—
160C2×C22⋊C4—2812no—
161C2×C22⋊C4—2811no—
162C2×C22⋊C4—2812no—
163C2×C22⋊C4—2812no—
164C2×C22⋊C4C2×D28111yescharacteristic
165C2×C22⋊C4C2×D28112yes—
166C2×C42—2811no—
167C2×C42—2812no—
168C2×C42—2812no—
169#95—2811no—
170#95—2812no—
171#95—2812no—
172#95—2812no—
173#95—2812no—
174#95C2×D28111yescharacteristic
175#95C2×D28112yes—
176C24—2811no—
177C24C22×D28111yescharacteristic
178C2×Q8—22no—
179C2×Q8—24no—
180C2×D4—5622no—
181C2×D4—5622no—
182C2×D4—5622no—
183C22×C4—2811no—
184C22×C4—2811no—
185C22×C4—2812no—
186C22×C4—2811no—
187C22×C4—2812no—
188C22×C4—5622no—
189C22×C4—5624no—
190C22×C4—5622no—
191C22×C4—5624no—
192C22×C4C22×D28112yes—
193C22×C4C22×D28111yescharacteristic
194C22×C4C22×D28111yescharacteristic
195C22×C4C22×D28112yes—
196C4⋊C4—5622no—
197C4⋊C4—5624no—
198C4⋊C4—5622no—
199C22⋊C4—22no—
200C22⋊C4—24no—
201C22⋊C4—5624no—
202C22⋊C4—5624no—
203C22⋊C4—5622no—
204C22⋊C4—5624no—
205C42—2814no—
206C42—5624no—
207C42—5624no—
208C23—21no—
209C23—22no—
210C23—21no—
211C23—22no—
212C23—2812no—
213C23—5621no—
214C23—5622no—
215C23—5622no—
216C23—5621no—
217C23#1798513912yes—
218C23C23×D28111yescharacteristic
219Q8—28no—
220D4—5628no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—2812no—
230C2×C4—2814no—
231C2×C4—2812no—
232C2×C4—5621no—
233C2×C4—5621no—
234C2×C4—5622no—
235C2×C4—5621no—
236C2×C4—5622no—
237C2×C4—5622no—
238C2×C4—5622no—
239C2×C4—5622no—
240C2×C4—5622no—
241C2×C4—5622no—
242C2×C4—11244no—
243C2×C4—11244no—
244C2×C4D4×D28112yes—
245C2×C4#1798513714yes—
246C22—22no—
247C22—24no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—5622no—
252C22—5624no—
253C22—11241no—
254C22—11241no—
255C22—11242no—
256C22C2×D4×D28111yescharacteristic
257C22#41×D28111yescharacteristic
258C22#41×D28112yes—
259C22C2×#1798513712yes—
260C22C2×#1798513911yescharacteristic
261C4—22no—
262C4—24no—
263C4—41no—
264C4—42no—
265C4—2814no—
266C4—5622no—
267C4—11242no—
268C4—11241no—
269C4—11242no—
270C2—42no—
271C2—11242no—
272C2#3182396911yescharacteristic
273C2#3182397611yescharacteristic
274C2#124×D28111yescharacteristic
275C2#3182399212yes—
276C2#3182399912yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#393×C281C2
prime radicalC22×C22⋊D281C22
hypercenter#393D281
hypocenterC281#2398
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic281C2semidirect
3. #31823405C2semidirect
4. #31823390C2semidirect
5. #31823388C2semidirect
7. #31823374C2semidirect
8. C22⋊C4×Dic281C2semidirect
9. #31823310C2semidirect
10. #31823308C2semidirect
11. #393×C281C2semidirect
138. C281#2398semidirect
147. #393D281semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic2812
C2×#225828392
#318234052
#318233902
#318233882
#318233792
#318233742
C22⋊C4×Dic2812
#318233102
#318233082
#393×C2812
#2398281