Finite Group Databasebeta

← #49098623

Subgroups — #49098623

Order 35968.

1056 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 159 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×#17985139C211yesmaximal, characteristic, complemented
2C2×#22582849C212yesmaximal, complemented
3C2×C22⋊C4×D281C211yesmaximal, characteristic, complemented
4#31823374C211yesmaximal, characteristic, complemented
5#31823373C211yesmaximal, characteristic, complemented
6#31823372C211yesmaximal, characteristic, complemented
7#31823341C212yesmaximal, complemented
8#31823341C212yesmaximal, complemented
9#31823339C212yesmaximal, complemented
10#31823325C211yesmaximal, characteristic, complemented
11#393×C281C211yesmaximal, characteristic, complemented
12C24×D281C2211yescharacteristic
13C2×#17985139—28no—
14C2×#17985139—24no—
15C22×D1124C2212yes—
16C22×D1124C2212yes—
17C22×D1124C2211yescharacteristic, complemented
18C22×C22⋊D281C2212yes—
19C22×C4×D281C2211yescharacteristic
20C22×C4×D281C2211yescharacteristic
21C22×C4×D281C2212yescomplemented
22#22582849—28no—
23C2×C22⋊Dic281C2211yescharacteristic
24C2×#17985115C2211yescharacteristic
25C2×#17985115C2212yes—
26C2×#17985115C2211yescharacteristic
27C2×#17985115C2212yes—
28C2×#17985115C2212yescomplemented
29C2×#17985115C2212yescomplemented
30C22⋊C4×D281—24no—
31#22582786C2211yescharacteristic, complemented
32#22582786C2212yescomplemented
33#22582786C2212yescomplemented
34C22×Q8×C281C2211yescharacteristic, complemented
35C2×C22⋊C4×C281C2211yescharacteristic
36C2×C22⋊C4×C281C2212yes—
37#95×C281C2211yescharacteristic, complemented
38#95×C281C2212yescomplemented
39C23×D281—22no—
40C23×D281—22no—
41C23×D281—24no—
42C23×D281—22no—
43C23×D281—42no—
44C23×D281C2312yes—
45C23×D281C2311yescharacteristic
46C23×D281C2311yescharacteristic
47#17985139—232no—
48C2×D1124—24no—
49C2×D1124—24no—
50C2×D1124—24no—
51C2×D1124—24no—
52C2×D1124—24no—
53C2×D1124—22no—
54C2×D1124—42no—
55C2×D1124D418yescomplemented
56C2×C22⋊D281—24no—
57C2×C22⋊D281—24no—
58C2×C22⋊D281—42no—
59C22×Dic281C2312yes—
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2311yescharacteristic
62C2×C4×D281—24no—
63C2×C4×D281—24no—
64C2×C4×D281—24no—
65C2×C4×D281—22no—
66C2×C4×D281—24no—
67C2×C4×D281—42no—
68C2×C4×D281D414yescomplemented
69C22⋊Dic281—22no—
70#17985115—24no—
71#17985115—22no—
72#17985115—22no—
73#17985115—24no—
74#17985115—42no—
75#17985115—42no—
76C24×C281C2311yescharacteristic
77C2×Q8×C281—24no—
78C2×Q8×C281—22no—
79C22×C4×C281C2312yes—
80C22×C4×C281C2311yescharacteristic
81C22×C4×C281C2311yescharacteristic
82C22×C4×C281C2312yes—
83C22⋊C4×C281—22no—
84C22⋊C4×C281—24no—
85C22×D281—21no—
86C22×D281—21no—
87C22×D281—22no—
88C22×D281—28no—
89C22×D281—21no—
90C22×D281—22no—
91C22×D281—22no—
92C22×D281—22no—
93C22×D281—22no—
94C22×D281—22no—
95C22×D281—21no—
96C22×D281—22no—
97C22×D281—22no—
98C22×D281—22no—
99C22×D281—48no—
100C22×D281—48no—
101C22×D281—44no—
102C22×D281—44no—
103C22×D281C2×D414yes—
104C22×D281C2×D414yes—
105C22×D281C2×D412yes—
106C22×D281#4112yescomplemented
107D1124—28no—
108D1124—216no—
109D1124—48no—
110C22⋊D281—48no—
111C2×Dic281—22no—
112C2×Dic281—22no—
113C2×Dic281—21no—
114C2×Dic281—22no—
115C2×Dic281—22no—
116C2×Dic281—22no—
117C2×Dic281C2×D412yes—
118C4×D281—216no—
119C4×D281—28no—
120C4×D281—44no—
121C23×C281—21no—
122C23×C281—22no—
123C23×C281—21no—
124C23×C281—22no—
125C23×C281#4112yescomplemented
126C23×C281C2411yescharacteristic
127Q8×C281—28no—
128C2×C4×C281—22no—
129C2×C4×C281—22no—
130C2×C4×C281—22no—
131C2×C4×C281—21no—
132C2×C4×C281—22no—
133C2×C4×C281—22no—
134C2×C4×C281—22no—
135C2×C4×C281—22no—
136C2×C4×C281C2×D414yes—
137C2×C4×C281C2×D412yes—
138C22×C281—22no—
139C22×C281—24no—
140C22×C281—41no—
141C22×C281—41no—
142C22×C281—42no—
143C22×C281C22×D411yescharacteristic
144C22×C281C22×D412yes—
145C22×C281C2×#4111yescharacteristic
146C22×C281C2×#4111yescharacteristic
147C22×C281H(5,𝔽2)12yes—
148C2×D281—22no—
149C2×D281—22no—
150C2×D281—24no—
151C2×D281—24no—
152C2×D281—24no—
153C2×D281—22no—
154C2×D281—24no—
155C2×D281—24no—
156C2×D281—24no—
157C2×D281—416no—
158C2×D281—41no—
159C2×D281—42no—
160C2×D281—42no—
161C2×D281—41no—
162C2×D281—42no—
163C2×D281—42no—
164C2×D281—42no—
165C2×D281#12014yes—
166C4×C281—24no—
167C4×C281—22no—
168C4×C281—41no—
169C4×C281—42no—
170Dic281—22no—
171Dic281—41no—
172Dic281—42no—
173C2×C281—42no—
174C2×C281C2×#12011yescharacteristic
175C2×C281#52511yescharacteristic
176C2×C281#53511yescharacteristic
177C2×C281#54612yes—
178C2×C281#54612yes—
179D281—24no—
180D281—44no—
181D281—42no—
182C281#240411yescharacteristic, complemented, Sylow
183#2404—2811nomaximal, Sylow
184C22×#41—2811no—
185C2×#120—2812no—
186C22×C22⋊C4—2811no—
187#393—2811no—
188#393D28111yescharacteristic, complemented
189#392—2811no—
190#392—2811no—
191#386—2812no—
192#386—2812no—
193#386—2812no—
194#381—2811no—
195C25—2811no—
196C2×#41—5624no—
197C2×#41—5628no—
198C22×Q8C2×D28111yescharacteristic, complemented
199C22×D4—2812no—
200C22×D4—2812no—
201C22×D4—2811no—
202C22×D4—2812no—
203C23×C4—2811no—
204C23×C4—2812no—
205C23×C4—2811no—
206#120—5628no—
207C2×C22⋊C4—2811no—
208C2×C22⋊C4—2811no—
209C2×C22⋊C4—2811no—
210C2×C22⋊C4—2812no—
211C2×C22⋊C4—2812no—
212C2×C22⋊C4—2812no—
213C2×C22⋊C4—2812no—
214C2×C22⋊C4—5624no—
215C2×C22⋊C4C2×D28111yescharacteristic
216C2×C22⋊C4C2×D28112yes—
217#95—2812no—
218#95—2811no—
219#95—2812no—
220#95C2×D28111yescharacteristic, complemented
221#95C2×D28112yescomplemented
222C24—2811no—
223C24—2811no—
224C24—2812no—
225C24—5622no—
226C24—5622no—
227C24—5624no—
228C24—5622no—
229C24—11242no—
230C24C22×D28111yescharacteristic
231#41—56232no—
232C2×Q8—22no—
233C2×Q8—24no—
234C2×D4—2818no—
235C2×D4—5624no—
236C2×D4—5624no—
237C2×D4—5624no—
238C2×D4—5624no—
239C2×D4—5624no—
240C2×D4—5624no—
241C2×D4—5624no—
242C2×D4—5622no—
243C2×D4—11242no—
244C2×D4—11242no—
245C22×C4—2811no—
246C22×C4—2814no—
247C22×C4—2812no—
248C22×C4—2811no—
249C22×C4—5624no—
250C22×C4—5624no—
251C22×C4—5624no—
252C22×C4—5622no—
253C22×C4—5624no—
254C22×C4—11242no—
255C22×C4C22×D28112yes—
256C22×C4C22×D28111yescharacteristic
257C22×C4C22×D28111yescharacteristic
258C22×C4C22×D28112yes—
259C22⋊C4—22no—
260C22⋊C4—24no—
261C22⋊C4—5622no—
262C22⋊C4—5624no—
263C22⋊C4—5622no—
264C22⋊C4—5622no—
265C22⋊C4—5624no—
266C22⋊C4—11242no—
267C22⋊C4—11242no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—2814no—
273C23—2812no—
274C23—2814no—
275C23—2812no—
276C23—5628no—
277C23—5621no—
278C23—5621no—
279C23—5622no—
280C23—5621no—
281C23—5622no—
282C23—5622no—
283C23—5622no—
284C23—5622no—
285C23—5622no—
286C23—5621no—
287C23—5622no—
288C23—5622no—
289C23—5622no—
290C23—11248no—
291C23—11244no—
292C23—11248no—
293C23—11244no—
294C23#1798513912yescomplemented
295C23C23×D28111yescharacteristic
296Q8—28no—
297D4—56216no—
298D4—5628no—
299D4—11248no—
300D4—11248no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—2812no—
310C2×C4—5628no—
311C2×C4—56216no—
312C2×C4—5622no—
313C2×C4—5621no—
314C2×C4—5622no—
315C2×C4—5622no—
316C2×C4—5622no—
317C2×C4—5622no—
318C2×C4—11244no—
319C2×C4D4×D28112yes—
320C2×C4D4×D28114yes—
321C22—22no—
322C22—24no—
323C22—41no—
324C22—41no—
325C22—42no—
326C22—2814no—
327C22—5622no—
328C22—5622no—
329C22—5624no—
330C22—5624no—
331C22—5624no—
332C22—5622no—
333C22—5624no—
334C22—5624no—
335C22—5624no—
336C22—112416no—
337C22—11241no—
338C22—11242no—
339C22—11241no—
340C22—11242no—
341C22—11242no—
342C22—11242no—
343C22—11242no—
344C22C2×D4×D28111yescharacteristic
345C22C2×D4×D28112yes—
346C22#41×D28111yescharacteristic
347C22C2×#1798513911yescharacteristic
348C22#2258292512yes—
349C4—22no—
350C4—24no—
351C4—41no—
352C4—42no—
353C4—5622no—
354C4—11241no—
355C4—11242no—
356C2—42no—
357C2—5624no—
358C2—11242no—
359C2—11244no—
360C2#120×D28111yescharacteristic
361C2#3182397611yescharacteristic
362C2#3182403111yescharacteristic
363C2#3182410412yes—
364C2#3182410612yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#393×C281C2
hypercenter#393D281
hypocenterC281#2404
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×#17985139C2semidirect
2. C2×#22582849C2semidirect
3. C2×C22⋊C4×D281C2semidirect
4. #31823374C2semidirect
5. #31823373C2semidirect
6. #31823372C2semidirect
7. #31823341C2semidirect
8. #31823341C2semidirect
9. #31823339C2semidirect
10. #31823325C2semidirect
11. #393×C281C2semidirect
17. C22×D1124C22semidirect
21. C22×C4×D281C22semidirect
28. C2×#17985115C22semidirect
29. C2×#17985115C22semidirect
31. #22582786C22semidirect
32. #22582786C22semidirect
33. #22582786C22semidirect
34. C22×Q8×C281C22semidirect
37. #95×C281C22semidirect
38. #95×C281C22semidirect
55. C2×D1124D4semidirect
68. C2×C4×D281D4semidirect
106. C22×D281#41semidirect
125. C23×C281#41semidirect
182. C281#2404semidirect
188. #393D281semidirect
198. C22×Q8C2×D281semidirect
220. #95C2×D281semidirect
221. #95C2×D281semidirect
294. C23#17985139semidirect

Maximal subgroups

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

subgroupindex
C22×#179851392
C2×#225828492
C2×C22⋊C4×D2812
#318233742
#318233732
#318233722
#318233412
#318233392
#318233252
#393×C2812
#2404281