Finite Group Databasebeta

← #19140480

Subgroups — #19140480

Order 5504.

620 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×C22⋊D43C211yesmaximal, characteristic, complemented
2#14582837C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic, complemented
4#14582813C211yesmaximal, characteristic, complemented
5#14582813C212yesmaximal, complemented
6#14582807C212yesmaximal, complemented
7#14582807C211yesmaximal, characteristic, complemented
8#14582787C212yesmaximal, complemented
9#14582775C212yesmaximal, complemented
10#14582762C211yesmaximal, characteristic, complemented
11C2×#121×C43C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C22×C22⋊D43C2212yes—
14C22×C4×D43C2211yescharacteristic
15C4×C22⋊D43—24no—
16C2×Dic43⋊C4C2211yescharacteristic
17C2×Dic43⋊C4C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2211yescharacteristic
20C2×C22⋊Dic43C2212yes—
21C2×C22⋊Dic43C2212yes—
22C2×C22⋊Dic43C2212yes—
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×C4×Dic43C2211yescharacteristic
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2212yes—
31C22×D4×C43C2212yes—
32C22×D4×C43C2211yescharacteristic
33C23×C4×C43C2211yescharacteristic
34#121×C43—24no—
35C2×C4⋊C4×C43C2211yescharacteristic
36C2×C22⋊C4×C43C2212yes—
37C24×C43C2312yes—
38C24×C43C2311yescharacteristic
39C23×D43C2311yescharacteristic
40C2×D4×C43—22no—
41C2×D4×C43—24no—
42C2×D4×C43—42no—
43C2×D4×C43—42no—
44C2×D4×C43—42no—
45C22×C4×C43—42no—
46C22×C4×C43D414yescomplemented
47C22×C4×C43C2312yes—
48C22×C4×C43C2311yescharacteristic
49C22×C4×C43C2311yescharacteristic
50C2×C22⋊D43—22no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—24no—
54C2×C22⋊D43—42no—
55C2×C22⋊D43—42no—
56C22×Dic43C2312yes—
57C22×Dic43C2312yes—
58C22×Dic43C2311yescharacteristic
59C22×Dic43C2311yescharacteristic
60C22×Dic43C2311yescharacteristic
61C2×C4×D43—22no—
62C2×C4×D43—42no—
63C4⋊C4×C43—22no—
64C22⋊C4×C43—24no—
65C22⋊Dic43—24no—
66C22⋊Dic43—22no—
67C22⋊Dic43—42no—
68C22⋊Dic43—42no—
69C22⋊Dic43—42no—
70(C2×D43)⋊C4—22no—
71(C2×D43)⋊C4—42no—
72Dic43⋊C4—22no—
73Dic43⋊C4—42no—
74C4×Dic43—22no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—22no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43C2×D412yes—
87C23×C43C2411yescharacteristic
88C22×D43—21no—
89C22×D43—21no—
90C22×D43—22no—
91C22×D43—22no—
92C22×D43#4112yes—
93D4×C43—44no—
94D4×C43—48no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—44no—
101C2×C4×C43C2×D412yes—
102C2×C4×C43C2×D412yes—
103C22⋊D43—28no—
104C22⋊D43—48no—
105C2×Dic43—21no—
106C2×Dic43—21no—
107C2×Dic43—21no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43#4112yes—
118C4×D43—44no—
119C22×C43—22no—
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—42no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—42no—
131C22×C43C22×D411yescharacteristic
132C22×C43C2×#4111yescharacteristic
133C22×C43C2×#4111yescharacteristic
134C22×C43H(5,𝔽2)12yes—
135C22×C43H(5,𝔽2)12yes—
136C2×D43—22no—
137C2×D43—24no—
138C2×D43—41no—
139C2×D43—41no—
140C2×D43—42no—
141C4×C43—22no—
142C4×C43—22no—
143C4×C43—42no—
144Dic43—22no—
145Dic43—41no—
146Dic43—41no—
147Dic43—42no—
148Dic43—42no—
149#2635—431nomaximal, Sylow
150C2×C43—42no—
151C2×C43—82no—
152C2×C43#52511yescharacteristic
153C2×C43#53411yescharacteristic
154C2×C43#53511yescharacteristic
155C2×C43#53812yes—
156C2×C43#54012yes—
157D43—42no—
158C2×#121D4311yescharacteristic, complemented
159C2×C4×D4—431no—
160#400—431no—
161#399—431no—
162#394—431no—
163#394—432no—
164#392—431no—
165#392—432no—
166#388—432no—
167#386—432no—
168#381—431no—
169C43#263511yescharacteristic, complemented, Sylow
170C22×D4—431no—
171C22×D4—432no—
172C22×D4C2×D4312yes—
173C22×D4C2×D4311yescharacteristic
174C23×C4—431no—
175C23×C4C2×D4311yescharacteristic
176#121—24no—
177C4×D4—864no—
178C2×C4⋊C4—431no—
179C2×C4⋊C4—432no—
180C2×C4⋊C4C2×D4311yescharacteristic
181C2×C22⋊C4—431no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4—431no—
184C2×C22⋊C4—432no—
185C2×C22⋊C4—432no—
186C2×C22⋊C4—432no—
187C2×C22⋊C4—432no—
188C2×C22⋊C4C2×D4312yes—
189C2×C42—431no—
190#95—432no—
191#95—431no—
192#95—431no—
193#95—432no—
194#95—432no—
195C24—431no—
196C24C22×D4312yes—
197C24C22×D4311yescharacteristic
198C2×D4—24no—
199C2×D4—22no—
200C2×D4—42no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—862no—
204C2×D4—862no—
205C2×D4—862no—
206C2×D4—864no—
207C2×D4—1722no—
208C2×D4—1722no—
209C22×C4—42no—
210C22×C4—431no—
211C22×C4—432no—
212C22×C4—432no—
213C22×C4—431no—
214C22×C4—431no—
215C22×C4—862no—
216C22×C4—1722no—
217C22×C4C22⋊D4314yescomplemented
218C22×C4C22×D4312yes—
219C22×C4C22×D4311yescharacteristic
220C22×C4C22×D4311yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—862no—
223C4⋊C4—1722no—
224C22⋊C4—24no—
225C22⋊C4—864no—
226C22⋊C4—862no—
227C22⋊C4—862no—
228C22⋊C4—1722no—
229C22⋊C4—1722no—
230C22⋊C4—1722no—
231C22⋊C4—1722no—
232C42—862no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—432no—
245C23—861no—
246C23—861no—
247C23—862no—
248C23—862no—
249C23C2×C22⋊D4312yes—
250C23C23×D4311yescharacteristic
251D4—44no—
252D4—48no—
253D4—868no—
254D4—1728no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—44no—
261C2×C4—432no—
262C2×C4—861no—
263C2×C4—861no—
264C2×C4—861no—
265C2×C4—861no—
266C2×C4—862no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4—1724no—
275C2×C4C2×C22⋊D4312yes—
276C2×C4C2×C22⋊D4312yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—862no—
290C22—864no—
291C22—1721no—
292C22—1721no—
293C22—1722no—
294C22C22×C22⋊D4311yescharacteristic
295C22#41×D4311yescharacteristic
296C22#41×D4311yescharacteristic
297C22#1306337012yes—
298C22#1306337012yes—
299C4—22no—
300C4—22no—
301C4—42no—
302C4—862no—
303C4—1721no—
304C4—1721no—
305C4—1722no—
306C4—1722no—
307C2—42no—
308C2—82no—
309C2—1722no—
310C2#1458340611yescharacteristic
311C2#1458345811yescharacteristic
312C2#1458346611yescharacteristic
313C2#1458348112yes—
314C2#1458349912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#121×C43C2
hypercenterC2×#121D43
hypocenterC43#2635
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D43C2semidirect
2. #14582837C2semidirect
3. #14582834C2semidirect
4. #14582813C2semidirect
5. #14582813C2semidirect
6. #14582807C2semidirect
7. #14582807C2semidirect
8. #14582787C2semidirect
9. #14582775C2semidirect
10. #14582762C2semidirect
11. C2×#121×C43C2semidirect
46. C22×C4×C43D4semidirect
158. C2×#121D43semidirect
169. C43#2635semidirect
217. C22×C4C22⋊D43semidirect