Finite Group Databasebeta

← #49098517

Subgroups — #49098517

Order 35968.

944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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×#22582841C211yesmaximal, characteristic, complemented
3C2×#22582839C212yesmaximal, complemented
4#31823383C211yesmaximal, characteristic, complemented
5#31823378C212yesmaximal, complemented
6#31823376C211yesmaximal, characteristic, complemented
7#31823372C212yesmaximal, complemented
8#31823371C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic281C212yesmaximal, complemented
10#31823310C211yesmaximal, characteristic, complemented
11#394×C281C211yesmaximal, characteristic, complemented
12C2×#17985137—28no—
13C2×#17985137—24no—
14C22×Dic562C2211yescharacteristic
15C22×D1124C2211yescharacteristic
16C22×C22⋊D281C2212yes—
17C22×C22⋊D281C2212yes—
18C23×Dic281C2212yes—
19C22×C4×D281C2211yescharacteristic
20C22×C4×D281C2211yescharacteristic
21#22582841—24no—
22#22582839—28no—
23C2×#17985117C2212yes—
24C2×C22⋊Dic281C2212yes—
25C2×#17985115C2211yescharacteristic
26C2×#17985115C2212yes—
27C2×#17985115C2212yes—
28C2×#17985115C2211yescharacteristic
29C2×C4×Dic281C2212yes—
30C2×C4×Dic281C2211yescharacteristic
31#22582786C2211yescharacteristic
32#22582786C2212yes—
33#22582786C2212yes—
34C22×D4×C281C2211yescharacteristic
35C2×C4⋊C4×C281C2211yescharacteristic
36C2×C22⋊C4×C281C2212yes—
37C2×C22⋊C4×C281C2212yes—
38#95×C281C2211yescharacteristic
39C23×D281C2311yescharacteristic
40C23×D281C2311yescharacteristic
41#17985137—232no—
42C2×Dic562—24no—
43C2×Dic562—22no—
44C2×D1124—22no—
45C2×D1124—22no—
46C2×D1124—22no—
47C2×C22⋊D281—24no—
48C2×C22⋊D281—24no—
49C2×C22⋊D281—24no—
50C2×C22⋊D281—24no—
51C2×C22⋊D281—24no—
52C2×C22⋊D281—24no—
53C22×Dic281—24no—
54C22×Dic281—24no—
55C22×Dic281D418yescomplemented
56C22×Dic281C2311yescharacteristic
57C22×Dic281C2312yes—
58C22×Dic281C2312yes—
59C22×Dic281C2311yescharacteristic
60C2×C4×D281—24no—
61C2×C4×D281—24no—
62C2×C4×D281—22no—
63C2×C4×D281D414yescomplemented
64#17985117—24no—
65C22⋊Dic281—24no—
66#17985115—22no—
67#17985115—24no—
68#17985115—24no—
69#17985115—22no—
70C4×Dic281—24no—
71C4×Dic281—22no—
72C24×C281C2312yes—
73C2×D4×C281—24no—
74C2×D4×C281—22no—
75C22×C4×C281C2312yes—
76C22×C4×C281C2311yescharacteristic
77C22×C4×C281C2311yescharacteristic
78C22×C4×C281C2311yescharacteristic
79C4⋊C4×C281—22no—
80C22⋊C4×C281—24no—
81C22⋊C4×C281—24no—
82C22×D281—22no—
83C22×D281—21no—
84C22×D281—22no—
85C22×D281—22no—
86C22×D281—22no—
87C22×D281—21no—
88C22×D281—21no—
89C22×D281—21no—
90C22×D281C2×D412yes—
91C22×D281#4112yescomplemented
92Dic562—28no—
93D1124—28no—
94C22⋊D281—216no—
95C22⋊D281—216no—
96C2×Dic281—22no—
97C2×Dic281—22no—
98C2×Dic281—22no—
99C2×Dic281—22no—
100C2×Dic281—216no—
101C2×Dic281—21no—
102C2×Dic281—22no—
103C2×Dic281C2×D414yes—
104C2×Dic281C2×D414yes—
105C2×Dic281C2×D412yes—
106C2×Dic281#4114yescomplemented
107C4×D281—28no—
108C4×D281—44no—
109C23×C281—22no—
110C23×C281—22no—
111C23×C281—22no—
112C23×C281—22no—
113C23×C281—22no—
114C23×C281—22no—
115C23×C281C2×D414yes—
116C23×C281C2411yescharacteristic
117D4×C281—28no—
118C2×C4×C281—21no—
119C2×C4×C281—22no—
120C2×C4×C281—21no—
121C2×C4×C281—22no—
122C2×C4×C281—22no—
123C2×C4×C281—21no—
124C2×C4×C281—22no—
125C2×C4×C281—22no—
126C2×C4×C281C2×D412yes—
127C2×C4×C281#4112yescomplemented
128C22×C281—24no—
129C22×C281—24no—
130C22×C281—24no—
131C22×C281—42no—
132C22×C281—42no—
133C22×C281—42no—
134C22×C281—42no—
135C22×C281C22×D412yes—
136C22×C281C22×D411yescharacteristic
137C22×C281C2×#4111yescharacteristic
138C22×C281C2×#4112yes—
139C22×C281C2×#4111yescharacteristic
140C2×D281—22no—
141C2×D281—24no—
142C2×D281—22no—
143C2×D281—22no—
144C2×D281—22no—
145C2×D281—41no—
146C2×D281—42no—
147C2×D281—42no—
148C2×D281—42no—
149C2×D281—41no—
150C4×C281—22no—
151C4×C281—22no—
152C4×C281—41no—
153C4×C281—42no—
154Dic281—24no—
155Dic281—24no—
156Dic281—41no—
157Dic281#12014yes—
158C2×C281—44no—
159C2×C281C2×#12011yescharacteristic
160C2×C281#52512yes—
161C2×C281#52511yescharacteristic
162C2×C281#53212yes—
163C2×C281#53211yescharacteristic
164D281—42no—
165D281—42no—
166C281#238811yescharacteristic, complemented, Sylow
167#2388—2811nomaximal, Sylow
168C22×#41—2811no—
169C2×C4×D4—2811no—
170C2×C4×D4—2812no—
171#395—2811no—
172#394—2812no—
173#394D28111yescharacteristic, complemented
174#393—2811no—
175#392—2811no—
176#392—2812no—
177C4×C22⋊C4—2812no—
178C4×C22⋊C4—2811no—
179C2×#41—5628no—
180C2×#41—5624no—
181C22×Q8—2811no—
182C22×D4—2812no—
183C22×D4—2812no—
184C22×D4—2811no—
185C22×D4C2×D28111yescharacteristic
186C23×C4—2812no—
187C23×C4—2811no—
188C23×C4—2811no—
189C4×D4—5628no—
190C4×D4—5624no—
191C2×C4⋊C4—2812no—
192C2×C4⋊C4C2×D28111yescharacteristic
193C2×C22⋊C4—2812no—
194C2×C22⋊C4—2812no—
195C2×C22⋊C4—2811no—
196C2×C22⋊C4—2811no—
197C2×C22⋊C4—2812no—
198C2×C22⋊C4C2×D28112yes—
199C2×C22⋊C4C2×D28112yes—
200C2×C42—2812no—
201C2×C42—2811no—
202#95—2811no—
203#95—2812no—
204#95—2812no—
205#95C2×D28111yescharacteristic
206C24—2811no—
207C24—2811no—
208C24C22×D28112yes—
209#41—56232no—
210C2×Q8—5624no—
211C2×Q8—5622no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—5622no—
215C2×D4—5622no—
216C2×D4—5624no—
217C2×D4—5624no—
218C2×D4—5624no—
219C2×D4—5624no—
220C2×D4—5624no—
221C2×D4—5624no—
222C2×D4—5622no—
223C22×C4—2811no—
224C22×C4—2818no—
225C22×C4—2812no—
226C22×C4—2812no—
227C22×C4—2814no—
228C22×C4—2811no—
229C22×C4—5624no—
230C22×C4—5624no—
231C22×C4—5622no—
232C22×C4—5624no—
233C22×C4—5624no—
234C22×C4C22×D28112yes—
235C22×C4C22×D28111yescharacteristic
236C22×C4C22×D28111yescharacteristic
237C22×C4C22×D28111yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—5624no—
240C22⋊C4—24no—
241C22⋊C4—24no—
242C22⋊C4—5624no—
243C22⋊C4—5624no—
244C22⋊C4—5622no—
245C22⋊C4—5624no—
246C22⋊C4—5622no—
247C42—5622no—
248C42—5624no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—2812no—
256C23—2812no—
257C23—5622no—
258C23—5621no—
259C23—5622no—
260C23—5622no—
261C23—5622no—
262C23—5621no—
263C23—5621no—
264C23—5621no—
265C23D4×D28114yes—
266C23C23×D28111yescharacteristic
267Q8—5628no—
268D4—28no—
269D4—5628no—
270D4—56216no—
271D4—56216no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—2814no—
281C2×C4—2812no—
282C2×C4—2814no—
283C2×C4—2814no—
284C2×C4—5628no—
285C2×C4—56216no—
286C2×C4—5622no—
287C2×C4—5622no—
288C2×C4—5622no—
289C2×C4—5622no—
290C2×C4—5621no—
291C2×C4—5622no—
292C2×C4—11244no—
293C2×C4D4×D28112yes—
294C2×C4#1798513712yescomplemented
295C22—24no—
296C22—24no—
297C22—24no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—5622no—
303C22—5624no—
304C22—5622no—
305C22—5622no—
306C22—5622no—
307C22—11241no—
308C22—11242no—
309C22—11242no—
310C22—11242no—
311C22—11241no—
312C22C2×D4×D28112yes—
313C22C2×D4×D28111yescharacteristic
314C22#41×D28111yescharacteristic
315C22#41×D28112yes—
316C22C2×#1798513711yescharacteristic
317C4—22no—
318C4—22no—
319C4—41no—
320C4—42no—
321C4—2814no—
322C4—5624no—
323C4—5624no—
324C4—11241no—
325C2—44no—
326C2—11242no—
327C2—11242no—
328C2#120×D28111yescharacteristic
329C2#3182397112yes—
330C2#3182397311yescharacteristic
331C2#3182400812yes—
332C2#3182401211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#394×C281C2
hypercenter#394D281
hypocenterC281#2388
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×#17985137C2semidirect
2. C2×#22582841C2semidirect
3. C2×#22582839C2semidirect
4. #31823383C2semidirect
5. #31823378C2semidirect
6. #31823376C2semidirect
7. #31823372C2semidirect
8. #31823371C2semidirect
9. C22⋊C4×Dic281C2semidirect
10. #31823310C2semidirect
11. #394×C281C2semidirect
55. C22×Dic281D4semidirect
63. C2×C4×D281D4semidirect
91. C22×D281#41semidirect
106. C2×Dic281#41semidirect
127. C2×C4×C281#41semidirect
166. C281#2388semidirect
173. #394D281semidirect
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×#225828412
C2×#225828392
#318233832
#318233782
#318233762
#318233722
#318233712
C22⋊C4×Dic2812
#318233102
#394×C2812
#2388281