Finite Group Databasebeta

← #19134896

Subgroups — #19134896

Order 5504.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×M16×D43C211yesmaximal, characteristic, complemented
2#14583411C211yesmaximal, characteristic
3C2×#13063253C211yesmaximal, characteristic, complemented
4C2×#13063251C211yesmaximal, characteristic, complemented
5C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6#14582658C211yesmaximal, characteristic, complemented
7C43×#339C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×C4×D43C2211yescharacteristic
10C2×#10621877C2211yescharacteristic
11C2×#10621872—21no—
12M16×D43—22no—
13M16×D43—22no—
14C2×C8×D43—21no—
15#13063309—21no—
16#13063305C411yescharacteristic, complemented
17#13063305C411yescharacteristic, complemented
18#13063300C411yescharacteristic, complemented
19#13063300C411yescharacteristic, complemented
20#13063295—21no—
21C4×D172—21no—
22C4×D172—21no—
23C2×(C2×D43)⋊C4—21no—
24C2×C4×Dic43C2211yescharacteristic
25#13063253—22no—
26#13063251—22no—
27C43⋊#95—21no—
28C2×M16×C43C2211yescharacteristic
29#117×C43C2211yescharacteristic
30C2×C42×C43C2211yescharacteristic
31C23×D43D411yescharacteristic
32C22×C4×C43—21no—
33C22×C4×C43C2311yescharacteristic
34C2×C22⋊D43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37#10621898—21no—
38#10621898—21no—
39#10621898—21no—
40#10621898—21no—
41C2×D172—21no—
42C2×D172—21no—
43C2×D172C2×C411yescharacteristic
44C2×C4×D43—21no—
45C2×C4×D43—21no—
46C2×C4×D43—21no—
47C2×C4×D43—21no—
48C2×C4×D43—21no—
49C2×C4×D43C2×C411yescharacteristic
50C2×C4×D43C2×C411yescharacteristic
51C2×C4×D43D411yescharacteristic
52C2×C4×D43D411yescharacteristic
53C2×Dic86C2×C411yescharacteristic
54M16×C43—21no—
55M16×C43D412yescomplemented
56C2×C8×C43—21no—
57C4⋊C4×C43C2×C411yescharacteristic
58C4⋊C4×C43C2×C411yescharacteristic
59C22⋊C4×C43—21no—
60C42×C43—21no—
61C42×C43—21no—
62C42×C43—21no—
63(C2×D43)⋊C4—24no—
64(C2×D43)⋊C4—21no—
65(C2×D43)⋊C4—21no—
66(C2×D43)⋊C4—21no—
67(C2×D43)⋊C4—21no—
68C4⋊Dic43—21no—
69C4⋊Dic43—21no—
70C4×Dic43—21no—
71C4×Dic43—21no—
72#10621877—21no—
73#10621877D412yescomplemented
74C2×C43⋊C8—21no—
75#10621872—24no—
76C8×D43—24no—
77C23×C43C2×D411yescharacteristic
78C22×D43—21no—
79C22×D43—21no—
80C22×D43—22no—
81C22×D43—21no—
82C22×D43—41no—
83C22×D43C22⋊C411yescharacteristic
84C22×D43C22⋊C411yescharacteristic
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43C22×C411yescharacteristic
91C2×C4×C43C2×D411yescharacteristic
92C2×C4×C43C2×D411yescharacteristic
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43#4111yescharacteristic
95C2×C4×C43#4111yescharacteristic
96C22⋊D43—41no—
97C22⋊D43—41no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—22no—
101C2×Dic43—21no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43C22⋊C411yescharacteristic
105C2×Dic43C22⋊C411yescharacteristic
106D172—21no—
107D172—21no—
108D172—42no—
109D172—42no—
110C4×D43—21no—
111C4×D43—21no—
112C4×D43—21no—
113C4×D43—21no—
114C4×D43—21no—
115C4×D43—21no—
116C4×D43—21no—
117C4×D43—21no—
118C4×D43—41no—
119C4×D43—41no—
120Dic86—21no—
121Dic86—21no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43C2×C22⋊C411yescharacteristic
127C22×C43#12111yescharacteristic
128C22×C43#12111yescharacteristic
129C2×D43—21no—
130C2×D43—21no—
131C2×D43—21no—
132C2×D43—21no—
133C2×D43—21no—
134C2×D43—42no—
135C2×D43—42no—
136C2×D43—41no—
137C2×D43—41no—
138C2×D43—41no—
139C2×D43#10412yescomplemented
140C4×C43—42no—
141C4×C43—41no—
142C4×C43—41no—
143C4×C43C4×D411yescharacteristic
144C4×C43C4×D411yescharacteristic
145C4×C43#12011yescharacteristic
146C4×C43#12311yescharacteristic
147Dic43—21no—
148Dic43—21no—
149Dic43—42no—
150Dic43—41no—
151#1871—431nomaximal, Sylow
152C2×C43—21no—
153C2×C43—21no—
154C2×C43#38611yescharacteristic
155C2×C43C2×#10411yescharacteristic
156C2×C43#42111yescharacteristic
157D43—22no—
158D43—41no—
159D43—81no—
160C22×M16—431no—
161#525—431no—
162C2×#104—431no—
163C2×#104—431no—
164C4×C22⋊C4—431no—
165#339—431no—
166#339D4311yescharacteristic, complemented
167C43#187111yescharacteristic, complemented, Sylow
168C2×#41—431no—
169C23×C4—431no—
170C2×M16—431no—
171C2×M16—861no—
172C2×M16—862no—
173C2×M16—862no—
174C2×M16C2×D4311yescharacteristic
175C22×C8—861no—
176#123—861no—
177C22⋊Q8—431no—
178C22⋊Q8—431no—
179#121—431no—
180#121—431no—
181#120—861no—
182C4×D4—861no—
183C4×D4—861no—
184#117C2×D4311yescharacteristic
185C2×C22⋊C4—861no—
186C2×C42—431no—
187C2×C42C2×D4311yescharacteristic
188#104—862no—
189#104—862no—
190#95—861no—
191C24—431no—
192#41—861no—
193#41—861no—
194#41—861no—
195#41—861no—
196C2×Q8—431no—
197C2×D4—431no—
198C2×D4—861no—
199C2×D4—861no—
200C2×D4—861no—
201C22×C4—21no—
202C22×C4—431no—
203C22×C4—431no—
204C22×C4—431no—
205C22×C4—431no—
206C22×C4—431no—
207C22×C4—861no—
208C22×C4—861no—
209C22×C4—861no—
210C22×C4—861no—
211C22×C4—861no—
212C22×C4—861no—
213C22×C4C22×D4311yescharacteristic
214M16—21no—
215M16—432no—
216M16—864no—
217M16—861no—
218M16D17212yescomplemented
219C2×C8—21no—
220C2×C8—864no—
221C2×C8—861no—
222C4⋊C4—861no—
223C4⋊C4—861no—
224C4⋊C4C4×D4311yescharacteristic
225C4⋊C4C4×D4311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—861no—
228C22⋊C4—861no—
229C22⋊C4—861no—
230C22⋊C4—861no—
231C22⋊C4—864no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—861no—
236C42—861no—
237C23—431no—
238C23—431no—
239C23—862no—
240C23—861no—
241C23—861no—
242C23—861no—
243C23—1721no—
244C23D4×D4311yescharacteristic
245Q8—861no—
246Q8—861no—
247D4—861no—
248D4—861no—
249D4—1722no—
250D4—1722no—
251D4—1721no—
252D4—1721no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—431no—
259C2×C4—431no—
260C2×C4—861no—
261C2×C4—861no—
262C2×C4—861no—
263C2×C4—861no—
264C2×C4—861no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—861no—
269C2×C4—861no—
270C2×C4—862no—
271C2×C4—861no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4C2×C4×D4311yescharacteristic
277C2×C4C2×D17211yescharacteristic
278C2×C4#1062189811yescharacteristic
279C2×C4D4×D4311yescharacteristic
280C2×C4D4×D4311yescharacteristic
281C2×C4#1062190211yescharacteristic
282C8—22no—
283C8—862no—
284C22—21no—
285C22—21no—
286C22—432no—
287C22—861no—
288C22—861no—
289C22—861no—
290C22—861no—
291C22—861no—
292C22—1722no—
293C22—1722no—
294C22—1721no—
295C22—1721no—
296C22—1721no—
297C22C22⋊C4×D4311yescharacteristic
298C22#1306329811yescharacteristic
299C22#1306330011yescharacteristic
300C4—42no—
301C4—41no—
302C4—41no—
303C4—861no—
304C4—861no—
305C4—1722no—
306C4—1721no—
307C4#1306328711yescharacteristic
308C4C4×D17211yescharacteristic
309C4#1306329511yescharacteristic
310C4#1306331011yescharacteristic
311C2—21no—
312C2—21no—
313C2—862no—
314C2—3441no—
315C2—1721no—
316C2#1458277711yescharacteristic
317C2#104×D4311yescharacteristic
318C2#1458291411yescharacteristic
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#339C2
socleC22×C43C2×C22⋊C4
hypercenter#339D43
hypocenterC43#1871
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×M16×D43C2semidirect
3. C2×#13063253C2semidirect
4. C2×#13063251C2semidirect
5. C4×(C2×D43)⋊C4C2semidirect
6. #14582658C2semidirect
7. C43×#339C2semidirect
16. #13063305C4semidirect
17. #13063305C4semidirect
18. #13063300C4semidirect
19. #13063300C4semidirect
55. M16×C43D4semidirect
73. #10621877D4semidirect
139. C2×D43#104semidirect
166. #339D43semidirect
167. C43#1871semidirect
218. M16D172semidirect