Finite Group Databasebeta

← #49096368

Subgroups — #49096368

Order 35968.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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
1#31824261C211yesmaximal, characteristic, complemented
2#31823974C211yesmaximal, characteristic, complemented
3#31823481C211yesmaximal, characteristic, complemented
4#31823480C211yesmaximal, characteristic, complemented
5#31823427C211yesmaximal, characteristic, complemented
6#31823219C211yesmaximal, characteristic, complemented
7#525×C281C211yesmaximal, characteristic, complemented
8C2×#17985138C2211yescharacteristic
9#22582910—21no—
10#22582909—21no—
11#22582905—21no—
12#22582904—21no—
13#22582899—22no—
14C2×#17985122C2211yescharacteristic
15C2×#17985122C2211yescharacteristic
16#22582862—21no—
17#22582858—21no—
18#22582853—21no—
19#22582848—21no—
20C4×C22⋊D281—22no—
21#22582838C2211yescharacteristic
22#22582807—22no—
23#22582806—22no—
24C22⋊#14555886—22no—
25C2×#41×C281C2211yescharacteristic
26C23×C4×C281C2211yescharacteristic
27#123×C281—21no—
28C22⋊Q8×C281—21no—
29#121×C281—21no—
30#120×C281—21no—
31C4×D4×C281—22no—
32#117×C281C2211yescharacteristic
33#17985138—21no—
34#17985138—21no—
35#17985138—21no—
36#17985138—21no—
37C2×Dic562D411yescharacteristic, complemented
38C2×D1124D411yescharacteristic, complemented
39C2×C22⋊D281—22no—
40C2×C22⋊D281—21no—
41C2×C4×D281—21no—
42#17985128—22no—
43#17985126—22no—
44#17985125—22no—
45#17985123—22no—
46#17985122—21no—
47#17985122—21no—
48#17985122—21no—
49#17985122—21no—
50C2×#14555886—21no—
51C2×#14555886D412yescomplemented
52C4⋊Dic281—21no—
53#17985117—22no—
54C22⋊Dic281—22no—
55C22⋊Dic281—21no—
56#17985115—22no—
57C4×Dic281D412yescomplemented
58C24×C281D411yescharacteristic
59#41×C281—21no—
60#41×C281—21no—
61#41×C281—21no—
62#41×C281—21no—
63C2×Q8×C281D411yescharacteristic, complemented
64C2×D4×C281—22no—
65C2×D4×C281—21no—
66C2×D4×C281D411yescharacteristic, complemented
67C22×C4×C281—21no—
68C22×C4×C281—21no—
69C22×C4×C281—21no—
70C22×C4×C281—21no—
71C22×C4×C281—21no—
72C22×C4×C281—21no—
73C22×C4×C281—21no—
74C22×C4×C281D411yescharacteristic
75C22×C4×C281C2311yescharacteristic
76C4⋊C4×C281—22no—
77C4⋊C4×C281—21no—
78C22⋊C4×C281—22no—
79C22⋊C4×C281—22no—
80C22⋊C4×C281—21no—
81C42×C281D412yescomplemented
82C22×D281—21no—
83Dic562—21no—
84Dic562—21no—
85D1124—21no—
86D1124—21no—
87C22⋊D281—44no—
88C22⋊D281—41no—
89C22⋊D281—41no—
90C2×Dic281—22no—
91C2×Dic281—21no—
92C4×D281—41no—
93C4×D281—41no—
94#14555886—22no—
95#14555886—41no—
96C23×C281—21no—
97C23×C281—21no—
98C23×C281—21no—
99C23×C281—21no—
100C23×C281—42no—
101C23×C281C2×D411yescharacteristic
102Q8×C281—21no—
103Q8×C281—21no—
104D4×C281—21no—
105D4×C281—21no—
106D4×C281—44no—
107D4×C281—41no—
108D4×C281—41no—
109C2×C4×C281—22no—
110C2×C4×C281—21no—
111C2×C4×C281—21no—
112C2×C4×C281—21no—
113C2×C4×C281—21no—
114C2×C4×C281—41no—
115C2×C4×C281—41no—
116C2×C4×C281—41no—
117C2×C4×C281—41no—
118C2×C4×C281—41no—
119C2×C4×C281—41no—
120C2×C4×C281C2×D411yescharacteristic
121C2×C4×C281C2×D411yescharacteristic
122C2×C4×C281C2×D411yescharacteristic
123C2×C4×C281C2×D411yescharacteristic
124C2×C4×C281C2×D411yescharacteristic
125C2×C4×C281#4111yescharacteristic
126C22×C281—22no—
127C22×C281—22no—
128C22×C281—22no—
129C22×C281—41no—
130C22×C281—41no—
131C22×C281—41no—
132C22×C281—41no—
133C22×C281—42no—
134C22×C281—41no—
135C22×C281—41no—
136C22×C281#12011yescharacteristic
137C22×C281#12011yescharacteristic
138C22×C281#12111yescharacteristic
139C2×D281—42no—
140C2×D281—41no—
141C4×C281—42no—
142C4×C281—41no—
143C4×C281—41no—
144C4×C281#12011yescharacteristic
145C4×C281#12111yescharacteristic
146C4×C281#12111yescharacteristic
147C4×C281#12711yescharacteristic
148Dic281—42no—
149Dic281—41no—
150C2×C281—21no—
151C2×C281—21no—
152C2×C281—21no—
153C2×C281—42no—
154C2×C281—81no—
155C2×C281#39211yescharacteristic
156D281—81no—
157C281#201011yescharacteristic, complemented, Sylow
158#2010—2811nomaximal, Sylow
159#575—2811no—
160#525—2811no—
161#525D28111yescharacteristic, complemented
162#421—2811no—
163#421—2811no—
164#407—2811no—
165H(3,ℤ/4)—2811no—
166C2×#41—2811no—
167C2×#41C2×D28111yescharacteristic
168C23×C4C2×D28111yescharacteristic
169#137—5621no—
170#137—5621no—
171AGL(1,ℤ/8)—5621no—
172AGL(1,ℤ/8)—5621no—
173#135—5622no—
174C2×M16—2811no—
175C2×M16—2811no—
176#123—21no—
177#123—5621no—
178C22⋊Q8—21no—
179C22⋊Q8—5621no—
180#121—21no—
181#121—5621no—
182#120—21no—
183#120—5621no—
184C4×D4—22no—
185C4×D4—5622no—
186#117—2811no—
187#117C2×D28111yescharacteristic
188#104—5622no—
189#104—5622no—
190C22⋊C8—5622no—
191C24C22⋊D28111yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—5621no—
197#41—5621no—
198#41—5621no—
199#41—5621no—
200C2×Q8—2811no—
201C2×Q8C22⋊D28111yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—2811no—
205C2×D4—5622no—
206C2×D4—5621no—
207C2×D4C22⋊D28111yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—5621no—
216C22×C4C22⋊D28111yescharacteristic
217C22×C4C22×D28111yescharacteristic
218Q16—5622no—
219SD16—5622no—
220SD16—5622no—
221D8—5622no—
222M16—5621no—
223M16—5621no—
224M16—5621no—
225M16—5621no—
226C2×C8—2812no—
227C2×C8—5621no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—5622no—
231C4⋊C4—5621no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—5622no—
236C22⋊C4—5622no—
237C22⋊C4—5621no—
238C42—2812no—
239C42C22⋊D28112yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—5621no—
246C23C2×C22⋊D28111yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—5621no—
250Q8—5621no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—5621no—
257D4—5621no—
258D4—11244no—
259D4—11241no—
260D4—11241no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—5622no—
273C2×C4—5621no—
274C2×C4—11241no—
275C2×C4—11241no—
276C2×C4D4×D28111yescharacteristic
277C2×C4D4×D28111yescharacteristic
278C2×C4D4×D28111yescharacteristic
279C2×C4C2×C22⋊D28111yescharacteristic
280C2×C4C2×C22⋊D28111yescharacteristic
281C2×C4#1798513711yescharacteristic
282C8—5622no—
283C8—11241no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—11242no—
295C22—11241no—
296C22#2258284711yescharacteristic
297C22#2258284811yescharacteristic
298C22#2258285111yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—11242no—
303C4—11241no—
304C4#2258284711yescharacteristic
305C4#2258285011yescharacteristic
306C4#2258285111yescharacteristic
307C4#2258287511yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—22481no—
314C2#3182337111yescharacteristic
subgroupG/H
centerC4#22582875
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#525×C281C2
socleC2×C281#392
hypercenter#525D281
hypocenterC281#2010
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #31824261C2semidirect
2. #31823974C2semidirect
3. #31823481C2semidirect
4. #31823480C2semidirect
5. #31823427C2semidirect
6. #31823219C2semidirect
7. #525×C281C2semidirect
37. C2×Dic562D4semidirect
38. C2×D1124D4semidirect
51. C2×#14555886D4semidirect
57. C4×Dic281D4semidirect
63. C2×Q8×C281D4semidirect
66. C2×D4×C281D4semidirect
81. C42×C281D4semidirect
157. C281#2010semidirect
161. #525D281semidirect
201. C2×Q8C22⋊D281semidirect
207. C2×D4C22⋊D281semidirect
239. C42C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318242612
#318239742
#318234812
#318234802
#318234272
#318232192
#525×C2812
#2010281