Finite Group Databasebeta

← #19140479

Subgroups — #19140479

Order 5504.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13063299C211yesmaximal, characteristic, complemented
2#14582838C211yesmaximal, characteristic, complemented
3#14582835C211yesmaximal, characteristic, complemented
4#14582816C211yesmaximal, characteristic, complemented
5#14582814C212yesmaximal, complemented
6#14582808C211yesmaximal, characteristic, complemented
7#14582807C212yesmaximal, complemented
8#14582790C212yesmaximal, complemented
9#14582778C212yesmaximal, complemented
10#14582762C211yesmaximal, characteristic, complemented
11C2×C4×D4×C43C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2212yes—
14C22×C22⋊D43C2212yes—
15#13063299—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2211yescharacteristic
27C43⋊#95C2212yes—
28C43⋊#95C2211yescharacteristic
29C22×D4×C43C2211yescharacteristic
30C23×C4×C43C2211yescharacteristic
31C23×C4×C43C2211yescharacteristic
32C4×D4×C43—24no—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2211yescharacteristic
36C2×C42×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C24×C43C2311yescharacteristic
39C23×D43C2312yes—
40C2×D4×C43—22no—
41C2×D4×C43—22no—
42C2×D4×C43—22no—
43C22×C4×C43—22no—
44C22×C4×C43—42no—
45C22×C4×C43—42no—
46C22×C4×C43D414yescomplemented
47C22×C4×C43C2311yescharacteristic
48C22×C4×C43C2311yescharacteristic
49C22×C4×C43C2311yescharacteristic
50C22×C4×C43C2311yescharacteristic
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—24no—
53C2×C22⋊D43—24no—
54C2×C22⋊D43—42no—
55C2×C22⋊D43—42no—
56C2×C22⋊D43—42no—
57C2×C22⋊D43—42no—
58C22×Dic43C2312yes—
59C22×Dic43C2312yes—
60C22×Dic43C2312yes—
61C2×D172—22no—
62C2×D172—42no—
63C4⋊C4×C43—22no—
64C22⋊C4×C43—22no—
65C22⋊C4×C43—22no—
66C42×C43—22no—
67C22⋊Dic43—42no—
68C22⋊Dic43—42no—
69(C2×D43)⋊C4—24no—
70(C2×D43)⋊C4—24no—
71(C2×D43)⋊C4—42no—
72(C2×D43)⋊C4—42no—
73C4⋊Dic43—22no—
74Dic43⋊C4—42no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—21no—
78C23×C43—21no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43C2×D412yes—
84C23×C43#4112yes—
85C23×C43C2411yescharacteristic
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—22no—
90C22×D43—22no—
91C22×D43—22no—
92C22×D43—22no—
93D4×C43—28no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—44no—
103C2×C4×C43—44no—
104C2×C4×C43C2×D412yes—
105C2×C4×C43C2×D412yes—
106C2×C4×C43#4112yes—
107C22⋊D43—48no—
108C22⋊D43—48no—
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—22no—
118D172—44no—
119C22×C43—22no—
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—24no—
124C22×C43—41no—
125C22×C43—41no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43C22×D411yescharacteristic
130C22×C43C2×#4111yescharacteristic
131C22×C43C2×#4111yescharacteristic
132C22×C43H(5,𝔽2)12yes—
133C22×C43H(5,𝔽2)12yes—
134C2×D43—42no—
135C2×D43—42no—
136C2×D43—42no—
137C2×D43—42no—
138C2×D43—42no—
139C2×D43—42no—
140C2×D43—42no—
141C4×C43—22no—
142C4×C43—22no—
143C4×C43—22no—
144C4×C43—41no—
145C4×C43—41no—
146Dic43—42no—
147Dic43—42no—
148Dic43—42no—
149#2635—431nomaximal, Sylow
150C2×C43—42no—
151C2×C43—42no—
152C2×C43#52511yescharacteristic
153C2×C43#53411yescharacteristic
154C2×C43#53511yescharacteristic
155C2×C43#53812yes—
156C2×C43#54012yes—
157D43—82no—
158C2×#121—431no—
159C2×C4×D4D4311yescharacteristic, complemented
160#400—431no—
161#399—431no—
162#394—431no—
163#394—432no—
164#392—432no—
165#392—431no—
166#388—432no—
167#386—432no—
168#381—431no—
169C43#263511yescharacteristic, complemented, Sylow
170C22×D4—432no—
171C22×D4—432no—
172C22×D4—431no—
173C22×D4C2×D4311yescharacteristic
174C23×C4C2×D4311yescharacteristic
175C23×C4C2×D4311yescharacteristic
176#121—864no—
177C4×D4—24no—
178C2×C4⋊C4—431no—
179C2×C4⋊C4—432no—
180C2×C4⋊C4C2×D4311yescharacteristic
181C2×C22⋊C4—432no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4—432no—
184C2×C22⋊C4—432no—
185C2×C22⋊C4—432no—
186C2×C22⋊C4—432no—
187C2×C22⋊C4C2×D4311yescharacteristic
188C2×C22⋊C4C2×D4311yescharacteristic
189C2×C42C2×D4311yescharacteristic
190#95—432no—
191#95—431no—
192#95—431no—
193#95—432no—
194#95—432no—
195C24—432no—
196C24C22×D4311yescharacteristic
197C24C22×D4311yescharacteristic
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—864no—
202C2×D4—864no—
203C2×D4—862no—
204C2×D4—1722no—
205C2×D4—1722no—
206C2×D4—1722no—
207C2×D4—1722no—
208C2×D4—1722no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—432no—
213C22×C4—432no—
214C22×C4—432no—
215C22×C4C22⋊D4314yescomplemented
216C22×C4C22×D4311yescharacteristic
217C22×C4C22×D4311yescharacteristic
218C22×C4C22×D4311yescharacteristic
219C22×C4C22×D4311yescharacteristic
220C22×C4C22×D4311yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—862no—
223C4⋊C4—1722no—
224C22⋊C4—22no—
225C22⋊C4—22no—
226C22⋊C4—864no—
227C22⋊C4—864no—
228C22⋊C4—1722no—
229C22⋊C4—1722no—
230C22⋊C4—1722no—
231C22⋊C4—1722no—
232C42—22no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—862no—
242C23—862no—
243C23—862no—
244C23—862no—
245C23—862no—
246C23—862no—
247C23—862no—
248C23#1062189812yes—
249C23C2×C22⋊D4312yes—
250C23C23×D4311yescharacteristic
251D4—28no—
252D4—1724no—
253D4—1728no—
254D4—1728no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—862no—
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#1062189812yes—
275C2×C4C2×C22⋊D4312yes—
276C2×C4C2×C22⋊D4312yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—24no—
282C22—41no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—1722no—
288C22—1722no—
289C22—1722no—
290C22—1722no—
291C22—1722no—
292C22—1722no—
293C22—1722no—
294C22C22×C22⋊D4311yescharacteristic
295C22C2×#1062189811yescharacteristic
296C22C2×#1062189811yescharacteristic
297C22#1306337012yes—
298C22#1306337112yes—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—41no—
304C4—1722no—
305C4—1722no—
306C4—1722no—
307C2—42no—
308C2—42no—
309C2—3442no—
310C2#1458341011yescharacteristic
311C2#1458345811yescharacteristic
312C2#1458346311yescharacteristic
313C2#1458348212yes—
314C2#1458350012yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×C4×D4×C43C2
hypercenterC2×C4×D4D43
hypocenterC43#2635
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13063299C2semidirect
2. #14582838C2semidirect
3. #14582835C2semidirect
4. #14582816C2semidirect
5. #14582814C2semidirect
6. #14582808C2semidirect
7. #14582807C2semidirect
8. #14582790C2semidirect
9. #14582778C2semidirect
10. #14582762C2semidirect
11. C2×C4×D4×C43C2semidirect
46. C22×C4×C43D4semidirect
159. C2×C4×D4D43semidirect
169. C43#2635semidirect
215. C22×C4C22⋊D43semidirect