Finite Group Databasebeta

← #49098515

Subgroups — #49098515

Order 35968.

944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C22×#17985137C211yesmaximal, characteristic, complemented
2C2×D4×Dic281C212yesmaximal, complemented
3C2×#22582839C211yesmaximal, characteristic, complemented
4#31823384C211yesmaximal, characteristic, complemented
5#31823379C212yesmaximal, complemented
6#31823377C211yesmaximal, characteristic, complemented
7#31823375C211yesmaximal, characteristic, complemented
8#31823371C212yesmaximal, complemented
9C22⋊C4×Dic281C212yesmaximal, complemented
10#31823310C211yesmaximal, characteristic, complemented
11#392×C281C211yesmaximal, characteristic, complemented
12C2×#17985137—28no—
13C2×#17985137—24no—
14C22×Dic562C2211yescharacteristic
15C22×C22⋊D281C2211yescharacteristic
16C22×C22⋊D281C2212yes—
17C23×Dic281C2211yescharacteristic
18C23×Dic281C2212yes—
19C22×C4×D281C2211yescharacteristic
20D4×Dic281—28no—
21#22582839—24no—
22C2×C4⋊Dic281C2212yes—
23C2×#17985117C2211yescharacteristic
24C2×C22⋊Dic281C2212yes—
25C2×C22⋊Dic281C2212yes—
26C2×C22⋊Dic281C2212yes—
27C2×#17985115C2212yes—
28C2×#17985115C2211yescharacteristic
29C2×C4×Dic281C2211yescharacteristic
30C2×C4×Dic281C2212yes—
31#22582786C2212yes—
32#22582786C2211yescharacteristic
33#22582786C2212yes—
34C22×D4×C281C2212yes—
35C22×D4×C281C2211yescharacteristic
36C2×C22⋊C4×C281C2211yescharacteristic
37C2×C22⋊C4×C281C2212yes—
38#95×C281C2211yescharacteristic
39C23×D281C2311yescharacteristic
40#17985137—232no—
41C2×Dic562—24no—
42C2×Dic562—22no—
43C2×C22⋊D281—22no—
44C2×C22⋊D281—24no—
45C2×C22⋊D281—24no—
46C2×C22⋊D281—22no—
47C2×C22⋊D281—24no—
48C2×C22⋊D281—22no—
49C22×Dic281—24no—
50C22×Dic281—24no—
51C22×Dic281—22no—
52C22×Dic281—24no—
53C22×Dic281D418yescomplemented
54C22×Dic281C2312yes—
55C22×Dic281C2311yescharacteristic
56C22×Dic281C2312yes—
57C22×Dic281C2311yescharacteristic
58C22×Dic281C2311yescharacteristic
59C2×C4×D281—24no—
60C2×C4×D281D414yescomplemented
61C4⋊Dic281—24no—
62#17985117—22no—
63C22⋊Dic281—24no—
64C22⋊Dic281—24no—
65C22⋊Dic281—24no—
66#17985115—22no—
67#17985115—24no—
68C4×Dic281—22no—
69C4×Dic281—24no—
70C24×C281C2312yes—
71C24×C281C2311yescharacteristic
72C2×D4×C281—24no—
73C2×D4×C281—24no—
74C2×D4×C281—24no—
75C2×D4×C281—22no—
76C2×D4×C281—24no—
77C22×C4×C281C2311yescharacteristic
78C22×C4×C281C2311yescharacteristic
79C22×C4×C281C2312yes—
80C22⋊C4×C281—22no—
81C22⋊C4×C281—24no—
82C22×D281—22no—
83C22×D281—22no—
84C22×D281—21no—
85C22×D281—21no—
86C22×D281C2×D412yes—
87Dic562—28no—
88C22⋊D281—28no—
89C22⋊D281—216no—
90C2×Dic281—21no—
91C2×Dic281—22no—
92C2×Dic281—22no—
93C2×Dic281—21no—
94C2×Dic281—216no—
95C2×Dic281—22no—
96C2×Dic281—21no—
97C2×Dic281—22no—
98C2×Dic281—22no—
99C2×Dic281—22no—
100C2×Dic281—44no—
101C2×Dic281C2×D414yes—
102C2×Dic281C2×D414yes—
103C2×Dic281C2×D412yes—
104C2×Dic281#4112yescomplemented
105C4×D281—28no—
106C23×C281—21no—
107C23×C281—22no—
108C23×C281—22no—
109C23×C281—22no—
110C23×C281—22no—
111C23×C281—22no—
112C23×C281—22no—
113C23×C281—22no—
114C23×C281—22no—
115C23×C281—21no—
116C23×C281C2×D414yes—
117C23×C281#4112yescomplemented
118C23×C281C2411yescharacteristic
119D4×C281—216no—
120D4×C281—28no—
121C2×C4×C281—22no—
122C2×C4×C281—22no—
123C2×C4×C281—22no—
124C2×C4×C281—21no—
125C2×C4×C281—22no—
126C2×C4×C281C2×D412yes—
127C2×C4×C281#4114yescomplemented
128C22×C281—24no—
129C22×C281—24no—
130C22×C281—24no—
131C22×C281—22no—
132C22×C281—24no—
133C22×C281—41no—
134C22×C281—42no—
135C22×C281—42no—
136C22×C281—42no—
137C22×C281—42no—
138C22×C281—41no—
139C22×C281—42no—
140C22×C281C22×D412yes—
141C22×C281C22×D411yescharacteristic
142C22×C281C2×#4111yescharacteristic
143C22×C281C2×#4111yescharacteristic
144C22×C281C2×#4112yes—
145C2×D281—22no—
146C2×D281—22no—
147C2×D281—22no—
148C2×D281—42no—
149C2×D281—42no—
150C4×C281—22no—
151C4×C281—24no—
152C4×C281—41no—
153Dic281—24no—
154Dic281—22no—
155Dic281—41no—
156Dic281—42no—
157Dic281#12014yes—
158C2×C281—44no—
159C2×C281—42no—
160C2×C281C2×#12011yescharacteristic
161C2×C281#52512yes—
162C2×C281#52511yescharacteristic
163C2×C281#53212yes—
164C2×C281#53211yescharacteristic
165D281—42no—
166C281#238811yescharacteristic, complemented, Sylow
167#2388—2811nomaximal, Sylow
168C22×#41—2811no—
169C2×C4×D4—2812no—
170C2×C4×D4—2811no—
171#395—2811no—
172#394—2811no—
173#394—2812no—
174#393—2811no—
175#392—2812no—
176#392D28111yescharacteristic, complemented
177C4×C22⋊C4—2812no—
178C4×C22⋊C4—2811no—
179C2×#41—5628no—
180C2×#41—5624no—
181C22×Q8—2811no—
182C22×D4—2811no—
183C22×D4—2812no—
184C22×D4C2×D28112yes—
185C22×D4C2×D28111yescharacteristic
186C23×C4—2812no—
187C23×C4—2811no—
188C23×C4—2811no—
189C4×D4—5624no—
190C4×D4—5628no—
191C2×C4⋊C4—2811no—
192C2×C4⋊C4—2812no—
193C2×C22⋊C4—2812no—
194C2×C22⋊C4—2812no—
195C2×C22⋊C4—2812no—
196C2×C22⋊C4—2811no—
197C2×C22⋊C4—2812no—
198C2×C22⋊C4C2×D28111yescharacteristic
199C2×C22⋊C4C2×D28112yes—
200C2×C42—2811no—
201C2×C42—2812no—
202#95—2812no—
203#95—2812no—
204#95—2811no—
205#95C2×D28111yescharacteristic
206C24—2811no—
207C24C22×D28112yes—
208C24C22×D28111yescharacteristic
209#41—56232no—
210C2×Q8—5624no—
211C2×Q8—5622no—
212C2×D4—24no—
213C2×D4—24no—
214C2×D4—24no—
215C2×D4—22no—
216C2×D4—24no—
217C2×D4—5622no—
218C2×D4—5624no—
219C2×D4—5622no—
220C2×D4—5624no—
221C2×D4—5624no—
222C2×D4—5622no—
223C22×C4—2811no—
224C22×C4—2818no—
225C22×C4—2811no—
226C22×C4—2812no—
227C22×C4—2814no—
228C22×C4—2812no—
229C22×C4—2811no—
230C22×C4—5624no—
231C22×C4—5624no—
232C22×C4—5624no—
233C22×C4—5622no—
234C22×C4—5624no—
235C22×C4C22×D28111yescharacteristic
236C22×C4C22×D28111yescharacteristic
237C22×C4C22×D28112yes—
238C4⋊C4—5624no—
239C4⋊C4—5622no—
240C22⋊C4—22no—
241C22⋊C4—24no—
242C22⋊C4—5622no—
243C22⋊C4—5624no—
244C22⋊C4—5624no—
245C22⋊C4—5624no—
246C22⋊C4—5624no—
247C42—5624no—
248C42—5622no—
249C23—21no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—2812no—
260C23—5622no—
261C23—5621no—
262C23—5622no—
263C23—5621no—
264C23D4×D28114yes—
265C23#1798513712yescomplemented
266C23C23×D28111yescharacteristic
267Q8—5628no—
268D4—28no—
269D4—216no—
270D4—56216no—
271D4—5628no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—2814no—
278C2×C4—2812no—
279C2×C4—2814no—
280C2×C4—2812no—
281C2×C4—5628no—
282C2×C4—56216no—
283C2×C4—5621no—
284C2×C4—5622no—
285C2×C4—5622no—
286C2×C4—5621no—
287C2×C4—5622no—
288C2×C4—5622no—
289C2×C4—5621no—
290C2×C4—5622no—
291C2×C4—5622no—
292C2×C4—11244no—
293C2×C4D4×D28112yes—
294C2×C4#1798513714yescomplemented
295C22—24no—
296C22—24no—
297C22—24no—
298C22—22no—
299C22—24no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—42no—
307C22—5622no—
308C22—5622no—
309C22—5622no—
310C22—11242no—
311C22—11242no—
312C22C2×D4×D28112yes—
313C22C2×D4×D28111yescharacteristic
314C22#41×D28111yescharacteristic
315C22C2×#1798513711yescharacteristic
316C22C2×#1798513712yes—
317C4—22no—
318C4—24no—
319C4—41no—
320C4—2814no—
321C4—5624no—
322C4—5622no—
323C4—11241no—
324C4—11242no—
325C2—44no—
326C2—42no—
327C2—11242no—
328C2#120×D28111yescharacteristic
329C2#3182396912yes—
330C2#3182397311yescharacteristic
331C2#3182400812yes—
332C2#3182401111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#392×C281C2
hypercenter#392D281
hypocenterC281#2388
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#17985137C2semidirect
2. C2×D4×Dic281C2semidirect
3. C2×#22582839C2semidirect
4. #31823384C2semidirect
5. #31823379C2semidirect
6. #31823377C2semidirect
7. #31823375C2semidirect
8. #31823371C2semidirect
9. C22⋊C4×Dic281C2semidirect
10. #31823310C2semidirect
11. #392×C281C2semidirect
53. C22×Dic281D4semidirect
60. C2×C4×D281D4semidirect
104. C2×Dic281#41semidirect
117. C23×C281#41semidirect
127. C2×C4×C281#41semidirect
166. C281#2388semidirect
176. #392D281semidirect
265. C23#17985137semidirect
294. C2×C4#17985137semidirect

Maximal subgroups

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

subgroupindex
C22×#179851372
C2×D4×Dic2812
C2×#225828392
#318233842
#318233792
#318233772
#318233752
#318233712
C22⋊C4×Dic2812
#318233102
#392×C2812
#2388281