Finite Group Databasebeta

← #49098542

Subgroups — #49098542

Order 35968.

696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 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×D4×Dic281C211yesmaximal, characteristic, complemented
2C2×#22582839C212yesmaximal, complemented
3C2×#22582837C211yesmaximal, characteristic, complemented
4#31823393C211yesmaximal, characteristic, complemented
5#31823390C211yesmaximal, characteristic, complemented
6#31823386C212yesmaximal, complemented
7#31823378C212yesmaximal, complemented
8#31823371C211yesmaximal, characteristic
9#31823314C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic281C212yesmaximal, complemented
11#394×C281C211yesmaximal, characteristic, complemented
12C22×C22⋊D281C2212yes—
13C23×Dic281C2212yes—
14C22×C4×D281C2211yescharacteristic
15D4×Dic281—24no—
16#22582839—28no—
17#22582837—24no—
18C2×C4⋊Dic281C2211yescharacteristic
19C2×C4⋊Dic281C2211yescharacteristic
20C2×#17985117C2212yes—
21C2×#17985117C2212yes—
22C2×C22⋊Dic281C2212yes—
23C2×C22⋊Dic281C2212yes—
24C2×#17985115C2211yescharacteristic
25C2×#17985115C2211yescharacteristic
26C2×#17985115C2212yes—
27C2×C4×Dic281C2211yescharacteristic
28C2×C4×Dic281C2212yes—
29C2×C4×Dic281C2211yescharacteristic
30#22582786C2211yescharacteristic
31#22582786C2212yes—
32#22582786C2212yes—
33C22×D4×C281C2211yescharacteristic
34C2×C4⋊C4×C281C2211yescharacteristic
35C2×C22⋊C4×C281C2212yes—
36C2×C22⋊C4×C281C2212yes—
37#95×C281C2211yescharacteristic
38C23×D281C2311yescharacteristic
39C2×C22⋊D281—24no—
40C2×C22⋊D281—24no—
41C2×C22⋊D281—24no—
42C22×Dic281—24no—
43C22×Dic281—24no—
44C22×Dic281—24no—
45C22×Dic281C2311yescharacteristic
46C22×Dic281C2312yes—
47C22×Dic281C2311yescharacteristic
48C22×Dic281C2312yes—
49C22×Dic281C2311yescharacteristic
50C2×C4×D281—22no—
51C2×C4×D281—22no—
52C2×C4×D281D414yescomplemented
53C4⋊Dic281—22no—
54C4⋊Dic281—22no—
55#17985117—24no—
56#17985117—24no—
57C22⋊Dic281—24no—
58C22⋊Dic281—24no—
59#17985115—24no—
60#17985115—22no—
61#17985115—22no—
62C4×Dic281—22no—
63C4×Dic281—24no—
64C4×Dic281D414yescomplemented
65C24×C281C2312yes—
66C2×D4×C281—24no—
67C2×D4×C281—22no—
68C22×C4×C281C2311yescharacteristic
69C22×C4×C281C2312yes—
70C22×C4×C281C2311yescharacteristic
71C22×C4×C281C2311yescharacteristic
72C4⋊C4×C281—22no—
73C22⋊C4×C281—24no—
74C22⋊C4×C281—24no—
75C22×D281—21no—
76C22×D281—21no—
77C22×D281—22no—
78C22×D281—22no—
79C22×D281C2×D412yes—
80C22⋊D281—216no—
81C2×Dic281—22no—
82C2×Dic281—22no—
83C2×Dic281—22no—
84C2×Dic281—21no—
85C2×Dic281—22no—
86C2×Dic281—22no—
87C2×Dic281—22no—
88C2×Dic281—22no—
89C2×Dic281—48no—
90C2×Dic281C2×D412yes—
91C2×Dic281C2×D412yes—
92C2×Dic281C2×D412yes—
93C2×Dic281#4114yes—
94C2×Dic281#4112yes—
95C4×D281—28no—
96C23×C281—22no—
97C23×C281—22no—
98C23×C281—22no—
99C23×C281—22no—
100C23×C281—22no—
101C23×C281—22no—
102C23×C281#4114yes—
103C23×C281C2411yescharacteristic
104D4×C281—28no—
105C2×C4×C281—21no—
106C2×C4×C281—22no—
107C2×C4×C281—21no—
108C2×C4×C281—22no—
109C2×C4×C281—21no—
110C2×C4×C281—22no—
111C2×C4×C281—22no—
112C2×C4×C281—22no—
113C2×C4×C281C2×D412yes—
114C2×C4×C281C2×D412yes—
115C22×C281—24no—
116C22×C281—24no—
117C22×C281—24no—
118C22×C281—42no—
119C22×C281—42no—
120C22×C281—42no—
121C22×C281—42no—
122C22×C281C22×D411yescharacteristic
123C22×C281C22×D411yescharacteristic
124C22×C281C2×#4111yescharacteristic
125C22×C281C2×#4112yes—
126C22×C281C2×#4112yes—
127C2×D281—22no—
128C2×D281—24no—
129C2×D281—41no—
130C2×D281—42no—
131C2×D281—41no—
132C4×C281—22no—
133C4×C281—22no—
134C4×C281—41no—
135C4×C281—42no—
136Dic281—24no—
137Dic281—22no—
138Dic281—42no—
139Dic281—41no—
140Dic281#12114yes—
141C2×C281—44no—
142C2×C281C2×#12111yescharacteristic
143C2×C281#52511yescharacteristic
144C2×C281#52512yes—
145C2×C281#52912yes—
146C2×C281#53211yescharacteristic
147D281—42no—
148C281#239211yescharacteristic, complemented, Sylow
149#2392—2811nomaximal, Sylow
150C2×C4×D4—2811no—
151C2×C4×D4—2812no—
152C2×#117—2811no—
153#398—2811no—
154#397—2811no—
155#396—2812no—
156#394—2812no—
157#394D28111yescharacteristic, complemented
158#392—2811no—
159C4×C4⋊C4—2811no—
160C4×C22⋊C4—2812no—
161C22×D4—2812no—
162C22×D4C2×D28111yescharacteristic
163C23×C4—2811no—
164C23×C4—2812no—
165C4×D4—5624no—
166C4×D4—5628no—
167#117—5624no—
168C2×C4⋊C4—2811no—
169C2×C4⋊C4—2812no—
170C2×C4⋊C4—2811no—
171C2×C4⋊C4—2812no—
172C2×C4⋊C4C2×D28111yescharacteristic
173C2×C22⋊C4—2812no—
174C2×C22⋊C4—2812no—
175C2×C22⋊C4—2811no—
176C2×C22⋊C4—2811no—
177C2×C22⋊C4—2812no—
178C2×C22⋊C4C2×D28112yes—
179C2×C22⋊C4C2×D28112yes—
180C2×C42—2811no—
181C2×C42—2811no—
182C2×C42—2812no—
183#95—2812no—
184#95—2812no—
185#95—2811no—
186#95C2×D28111yescharacteristic
187C24—2811no—
188C24C22×D28112yes—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—5624no—
192C2×D4—5624no—
193C2×D4—5624no—
194C22×C4—2811no—
195C22×C4—2812no—
196C22×C4—2811no—
197C22×C4—2814no—
198C22×C4—2811no—
199C22×C4—2812no—
200C22×C4—5622no—
201C22×C4—5622no—
202C22×C4—5624no—
203C22×C4—5624no—
204C22×C4—5624no—
205C22×C4C22×D28111yescharacteristic
206C22×C4C22×D28112yes—
207C22×C4C22×D28111yescharacteristic
208C22×C4C22×D28111yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—5624no—
211C4⋊C4—5622no—
212C4⋊C4—5624no—
213C4⋊C4—5622no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—5622no—
217C22⋊C4—5624no—
218C22⋊C4—5624no—
219C22⋊C4—5624no—
220C22⋊C4—5622no—
221C42—2814no—
222C42—5622no—
223C42—5624no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—2812no—
231C23—5621no—
232C23—5621no—
233C23—5622no—
234C23—5622no—
235C23#1798513714yes—
236C23C23×D28111yescharacteristic
237D4—28no—
238D4—56216no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—2812no—
248C2×C4—2812no—
249C2×C4—2812no—
250C2×C4—2812no—
251C2×C4—2814no—
252C2×C4—5628no—
253C2×C4—5622no—
254C2×C4—5622no—
255C2×C4—5622no—
256C2×C4—5621no—
257C2×C4—5622no—
258C2×C4—5622no—
259C2×C4—5622no—
260C2×C4—5622no—
261C2×C4—11248no—
262C2×C4D4×D28112yes—
263C2×C4D4×D28112yes—
264C22—24no—
265C22—24no—
266C22—24no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—5622no—
272C22—5624no—
273C22—11241no—
274C22—11242no—
275C22—11241no—
276C22C2×D4×D28111yescharacteristic
277C22C2×D4×D28111yescharacteristic
278C22#41×D28111yescharacteristic
279C22#41×D28112yes—
280C22C2×#1798513712yes—
281C4—22no—
282C4—22no—
283C4—41no—
284C4—42no—
285C4—2814no—
286C4—5624no—
287C4—5622no—
288C4—11242no—
289C4—11241no—
290C2—44no—
291C2—11242no—
292C2#121×D28111yescharacteristic
293C2#3182396911yescharacteristic
294C2#3182397312yes—
295C2#3182399012yes—
296C2#3182401211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#394×C281C2
prime radical#31823371C2
hypercenter#394D281
hypocenterC281#2392
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic281C2semidirect
2. C2×#22582839C2semidirect
3. C2×#22582837C2semidirect
4. #31823393C2semidirect
5. #31823390C2semidirect
6. #31823386C2semidirect
7. #31823378C2semidirect
9. #31823314C2semidirect
10. C22⋊C4×Dic281C2semidirect
11. #394×C281C2semidirect
52. C2×C4×D281D4semidirect
64. C4×Dic281D4semidirect
148. C281#2392semidirect
157. #394D281semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic2812
C2×#225828392
C2×#225828372
#318233932
#318233902
#318233862
#318233782
#318233712
#318233142
C22⋊C4×Dic2812
#394×C2812
#2392281