Finite Group Databasebeta

← #49096369

Subgroups — #49096369

Order 35968.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#31823975C211yesmaximal, characteristic, complemented
3#31823970C211yesmaximal, characteristic, complemented
4#31823479C211yesmaximal, characteristic, complemented
5#31823426C211yesmaximal, characteristic, complemented
6#31823219C211yesmaximal, characteristic, complemented
7#421×C281C211yesmaximal, characteristic, complemented
8C2×#17985138C2211yescharacteristic
9C22×C4×D281C2211yescharacteristic
10#22582910—21no—
11#22582909—21no—
12#22582905—21no—
13#22582904—21no—
14#22582899—22no—
15C2×#17985122C2211yescharacteristic
16#22582863—21no—
17#22582860—21no—
18#22582859—21no—
19#22582855—21no—
20#22582854—21no—
21#22582850—21no—
22#22582849—21no—
23#22582847—21no—
24C4×D1124—22no—
25C4×C22⋊D281—22no—
26#22582838C2211yescharacteristic
27#22582805—22no—
28#22582791—22no—
29C2×#41×C281C2211yescharacteristic
30C2×M16×C281C2211yescharacteristic
31#117×C281C2211yescharacteristic
32#104×C281—22no—
33C23×D281D411yescharacteristic
34#17985138—21no—
35#17985138—21no—
36#17985138—21no—
37#17985138—21no—
38C2×Dic562D411yescharacteristic, complemented
39C2×D1124—22no—
40C2×D1124D411yescharacteristic, complemented
41C2×C22⋊D281—22no—
42C2×C22⋊D281—21no—
43C22×Dic281D411yescharacteristic
44C2×C4×D281—21no—
45C2×C4×D281—21no—
46C2×C4×D281—21no—
47C2×C4×D281—21no—
48C2×C4×D281—21no—
49C2×C4×D281—21no—
50C2×C4×D281—21no—
51#17985128—22no—
52#17985126—22no—
53#17985125—22no—
54#17985123—22no—
55#17985122—21no—
56#17985122—21no—
57C2×#14555886D412yescomplemented
58C4⋊Dic281—22no—
59C4⋊Dic281—21no—
60#17985117—22no—
61C22⋊Dic281—22no—
62C22⋊Dic281—21no—
63#17985115—22no—
64#17985115—22no—
65#17985115—22no—
66C4×Dic281D412yescomplemented
67#41×C281—21no—
68#41×C281—21no—
69#41×C281—21no—
70#41×C281—21no—
71C2×Q8×C281D411yescharacteristic, complemented
72C2×D4×C281—21no—
73C2×D4×C281D411yescharacteristic, complemented
74C22×C4×C281—21no—
75C22×C4×C281C2311yescharacteristic
76M16×C281—21no—
77M16×C281—21no—
78C2×C8×C281—21no—
79C4⋊C4×C281—21no—
80C22⋊C4×C281—21no—
81C42×C281D412yescomplemented
82C22×D281—21no—
83C22×D281—21no—
84C22×D281—21no—
85C22×D281—21no—
86C22×D281—42no—
87Dic562—21no—
88Dic562—21no—
89D1124—21no—
90D1124—21no—
91D1124—44no—
92C22⋊D281—44no—
93C22⋊D281—41no—
94C22⋊D281—41no—
95C2×Dic281—22no—
96C2×Dic281—21no—
97C2×Dic281—21no—
98C2×Dic281—21no—
99C2×Dic281—21no—
100C4×D281—41no—
101C4×D281—41no—
102C4×D281—41no—
103C4×D281—41no—
104C4×D281—41no—
105C4×D281—41no—
106#14555886—22no—
107C23×C281—21no—
108C23×C281C2×D411yescharacteristic
109Q8×C281—21no—
110Q8×C281—21no—
111D4×C281—21no—
112D4×C281—21no—
113D4×C281—41no—
114D4×C281—41no—
115C2×C4×C281—22no—
116C2×C4×C281—21no—
117C2×C4×C281—41no—
118C2×C4×C281—41no—
119C2×C4×C281C2×D411yescharacteristic
120C2×C4×C281C2×D411yescharacteristic
121C2×C4×C281C2×D411yescharacteristic
122C2×C4×C281C2×D411yescharacteristic
123C2×C4×C281C2×D411yescharacteristic
124C2×C4×C281#4111yescharacteristic
125C8×C281—41no—
126C22×C281—41no—
127C22×C281—42no—
128C22×C281—41no—
129C22×C281#12011yescharacteristic
130C22×C281#12011yescharacteristic
131C22×C281#12111yescharacteristic
132C2×D281—22no—
133C2×D281—22no—
134C2×D281—22no—
135C2×D281—41no—
136C2×D281—41no—
137C2×D281—41no—
138C2×D281—41no—
139C2×D281—42no—
140C2×D281—41no—
141C4×C281—42no—
142C4×C281—41no—
143C4×C281#12011yescharacteristic
144C4×C281#12111yescharacteristic
145C4×C281#12111yescharacteristic
146C4×C281#12711yescharacteristic
147Dic281—42no—
148Dic281—41no—
149Dic281—41no—
150C2×C281—21no—
151C2×C281—21no—
152C2×C281—21no—
153C2×C281—81no—
154C2×C281#39211yescharacteristic
155D281—42no—
156D281—81no—
157C281#201011yescharacteristic, complemented, Sylow
158#2010—2811nomaximal, Sylow
159#575—2811no—
160#525—2811no—
161#525—2811no—
162#421—2811no—
163#421D28111yescharacteristic, complemented
164#407—2811no—
165H(3,ℤ/4)—2811no—
166C2×#41—2811no—
167C2×#41C2×D28111yescharacteristic
168C23×C4—2811no—
169#137—5621no—
170#137—5621no—
171AGL(1,ℤ/8)—5621no—
172AGL(1,ℤ/8)—5621no—
173#135—5622no—
174C2×M16—2811no—
175C2×M16C2×D28111yescharacteristic
176#123—5621no—
177#123—5621no—
178C22⋊Q8—5621no—
179C22⋊Q8—5621no—
180#121—5621no—
181#121—5621no—
182#120—5621no—
183#120—5621no—
184C4×D4—5622no—
185C4×D4—5622no—
186#117—2811no—
187#117C2×D28111yescharacteristic
188#104—22no—
189#104—5622no—
190C22⋊C8—5622no—
191C24—2811no—
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×Q8D112411yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—2811no—
204C2×D4—5622no—
205C2×D4—5622no—
206C2×D4—5621no—
207C2×D4D112411yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—2811no—
210C22×C4—5621no—
211C22×C4—5621no—
212C22×C4—5621no—
213C22×C4—5621no—
214C22×C4—5621no—
215C22×C4—5621no—
216C22×C4—5621no—
217C22×C4C22×D28111yescharacteristic
218Q16—5622no—
219SD16—5622no—
220SD16—5622no—
221D8—5622no—
222M16—21no—
223M16—21no—
224M16—5621no—
225M16—5621no—
226C2×C8—21no—
227C2×C8—2812no—
228C4⋊C4—21no—
229C4⋊C4—5622no—
230C4⋊C4—5622no—
231C4⋊C4—5621no—
232C22⋊C4—21no—
233C22⋊C4—5622no—
234C22⋊C4—5622no—
235C22⋊C4—5622no—
236C22⋊C4—5622no—
237C22⋊C4—5621no—
238C42—2812no—
239C42C22⋊D28112yescomplemented
240C23—21no—
241C23—5621no—
242C23—5621no—
243C23—5621no—
244C23—5621no—
245C23—11242no—
246C23D4×D28111yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—5621no—
250Q8—5621no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—5621no—
256D4—5621no—
257D4—11244no—
258D4—11244no—
259D4—11241no—
260D4—11241no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—5621no—
266C2×C4—5621no—
267C2×C4—5622no—
268C2×C4—5621no—
269C2×C4—5621no—
270C2×C4—11241no—
271C2×C4—11241no—
272C2×C4—11241no—
273C2×C4—11241no—
274C2×C4—11241no—
275C2×C4—11241no—
276C2×C4D4×D28111yescharacteristic
277C2×C4D4×D28111yescharacteristic
278C2×C4D4×D28111yescharacteristic
279C2×C4C2×C22⋊D28111yescharacteristic
280C2×C4C2×D112411yescharacteristic
281C2×C4#1798513811yescharacteristic
282C8—41no—
283C8—5622no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—5622no—
288C22—5622no—
289C22—5622no—
290C22—11241no—
291C22—11241no—
292C22—11241no—
293C22—11242no—
294C22—11241no—
295C22—11241no—
296C22#2258284711yescharacteristic
297C22#2258284911yescharacteristic
298C22#2258285211yescharacteristic
299C4—42no—
300C4—41no—
301C4—11242no—
302C4—11241no—
303C4—11241no—
304C4#2258284911yescharacteristic
305C4#2258285211yescharacteristic
306C4#2258285311yescharacteristic
307C4#2258287511yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—11242no—
313C2—22481no—
314C2#3182337211yescharacteristic
subgroupG/H
centerC4#22582875
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#421×C281C2
socleC2×C281#392
hypercenter#421D281
hypocenterC281#2010
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #31824261C2semidirect
2. #31823975C2semidirect
3. #31823970C2semidirect
4. #31823479C2semidirect
5. #31823426C2semidirect
6. #31823219C2semidirect
7. #421×C281C2semidirect
38. C2×Dic562D4semidirect
40. C2×D1124D4semidirect
57. C2×#14555886D4semidirect
66. C4×Dic281D4semidirect
71. C2×Q8×C281D4semidirect
73. C2×D4×C281D4semidirect
81. C42×C281D4semidirect
157. C281#2010semidirect
163. #421D281semidirect
201. C2×Q8D1124semidirect
207. C2×D4D1124semidirect
239. C42C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318242612
#318239752
#318239702
#318234792
#318234262
#318232192
#421×C2812
#2010281