Finite Group Databasebeta

← #19140347

Subgroups — #19140347

Order 5504.

728 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13063321C211yesmaximal, characteristic, complemented
2C2×#13063298C212yesmaximal, complemented
3C2×#13063283C211yesmaximal, characteristic, complemented
4#14582816C211yesmaximal, characteristic, complemented
5#14582815C212yesmaximal, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582808C212yesmaximal, complemented
8#14582807C211yesmaximal, characteristic, complemented
9#14582799C212yesmaximal, complemented
10#14582763C211yesmaximal, characteristic, complemented
11C43×#394C211yesmaximal, characteristic, complemented
12C22×D172C2212yes—
13C22×D172C2211yescharacteristic
14C22×C22⋊D43C2212yes—
15C22×C22⋊D43C2212yes—
16C22×C22⋊D43C2212yes—
17C22×C4×D43C2211yescharacteristic
18#13063321—24no—
19#13063298—28no—
20#13063283—24no—
21C2×C4⋊Dic43C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2212yes—
29C2×C4×Dic43C2211yescharacteristic
30C2×C4×Dic43C2211yescharacteristic
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C22×D4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36C2×C22⋊C4×C43C2212yes—
37#95×C43C2211yescharacteristic
38C24×C43C2312yes—
39C23×D43C2312yes—
40C23×D43C2311yescharacteristic
41C2×D4×C43—22no—
42C2×D4×C43—42no—
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—24no—
48C2×C22⋊D43—24no—
49C2×C22⋊D43—24no—
50C2×C22⋊D43—24no—
51C2×C22⋊D43—24no—
52C2×C22⋊D43—42no—
53C2×C22⋊D43—42no—
54C2×C22⋊D43—42no—
55C2×C22⋊D43—42no—
56C22×Dic43C2312yes—
57C22×Dic43C2311yescharacteristic
58C22×Dic43C2311yescharacteristic
59C22×Dic43C2311yescharacteristic
60C2×D172—22no—
61C2×D172—24no—
62C2×D172—42no—
63C2×D172—42no—
64C2×D172—42no—
65C2×C4×D43—22no—
66C2×C4×D43—22no—
67C2×C4×D43D414yescomplemented
68C4⋊C4×C43—22no—
69C22⋊C4×C43—24no—
70C22⋊C4×C43—42no—
71C22⋊Dic43—42no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—24no—
74(C2×D43)⋊C4—22no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—42no—
77C4⋊Dic43—22no—
78Dic43⋊C4—24no—
79C4×Dic43—22no—
80C4×Dic43D414yescomplemented
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43—22no—
87C23×C43—22no—
88C23×C43C2411yescharacteristic
89C22×D43—21no—
90C22×D43—21no—
91C22×D43—22no—
92C22×D43—22no—
93C22×D43—22no—
94C22×D43—22no—
95C22×D43—22no—
96C22×D43—22no—
97C22×D43—22no—
98C22×D43—22no—
99C22×D43—22no—
100C22×D43C2×D412yes—
101D4×C43—44no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43C2×D412yes—
111C2×C4×C43C2×D412yes—
112C22⋊D43—48no—
113C22⋊D43—48no—
114C22⋊D43—48no—
115C2×Dic43—22no—
116C2×Dic43—21no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—22no—
120C2×Dic43—22no—
121C2×Dic43C2×D412yes—
122C2×Dic43C2×D412yes—
123C2×Dic43C2×D412yes—
124C2×Dic43#4112yes—
125D172—44no—
126D172—48no—
127C4×D43—28no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—42no—
131C22×C43—42no—
132C22×C43—42no—
133C22×C43—42no—
134C22×C43—42no—
135C22×C43C22×D411yescharacteristic
136C22×C43C22×D411yescharacteristic
137C22×C43C2×#4111yescharacteristic
138C22×C43H(5,𝔽2)12yes—
139C22×C43H(5,𝔽2)12yes—
140C2×D43—22no—
141C2×D43—24no—
142C2×D43—41no—
143C2×D43—41no—
144C2×D43—42no—
145C2×D43—42no—
146C2×D43—42no—
147C2×D43—42no—
148C2×D43—42no—
149C2×D43—42no—
150C2×D43—42no—
151C2×D43—42no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—42no—
155C4×C43—41no—
156Dic43—22no—
157Dic43—41no—
158Dic43—42no—
159Dic43#12114yes—
160#2619—431nomaximal, Sylow
161C2×C43—82no—
162C2×C43C2×#12111yescharacteristic
163C2×C43#53511yescharacteristic
164C2×C43#53512yes—
165C2×C43#53511yescharacteristic
166C2×C43#54012yes—
167D43—42no—
168D43—82no—
169C2×#127—431no—
170C2×#121—432no—
171C2×#117—431no—
172#394—431no—
173#394—432no—
174#394D4311yescharacteristic, complemented
175#392—431no—
176#392—432no—
177#392—431no—
178#390—432no—
179#382—431no—
180C43#261911yescharacteristic, complemented, Sylow
181C22×D4—432no—
182C22×D4—432no—
183C22×D4—432no—
184C22×D4—432no—
185C22×D4—431no—
186C22×D4C2×D4311yescharacteristic
187C23×C4—431no—
188#127—864no—
189#121—868no—
190#117—864no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—432no—
193C2×C4⋊C4C2×D4311yescharacteristic
194C2×C22⋊C4—431no—
195C2×C22⋊C4—431no—
196C2×C22⋊C4—432no—
197C2×C22⋊C4—432no—
198C2×C22⋊C4—432no—
199C2×C22⋊C4—432no—
200C2×C22⋊C4C2×D4312yes—
201C2×C22⋊C4C2×D4312yes—
202C2×C42—431no—
203C2×C42—431no—
204#95—432no—
205#95—431no—
206#95C2×D4311yescharacteristic
207C24—431no—
208C24—432no—
209C24C22×D4312yes—
210C2×D4—22no—
211C2×D4—42no—
212C2×D4—864no—
213C2×D4—864no—
214C2×D4—864no—
215C2×D4—864no—
216C2×D4—864no—
217C2×D4—864no—
218C2×D4—862no—
219C2×D4—1722no—
220C2×D4—1722no—
221C2×D4—1722no—
222C2×D4—1722no—
223C2×D4—1722no—
224C2×D4—1722no—
225C2×D4—1722no—
226C22×C4—431no—
227C22×C4—431no—
228C22×C4—434no—
229C22×C4—432no—
230C22×C4—431no—
231C22×C4—862no—
232C22×C4—862no—
233C22×C4C22×D4312yes—
234C22×C4C22×D4311yescharacteristic
235C22×C4C22×D4311yescharacteristic
236C22×C4C22×D4311yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—862no—
239C4⋊C4—864no—
240C22⋊C4—24no—
241C22⋊C4—42no—
242C22⋊C4—862no—
243C22⋊C4—862no—
244C22⋊C4—864no—
245C22⋊C4—1722no—
246C22⋊C4—1722no—
247C22⋊C4—1722no—
248C42—434no—
249C42—862no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—432no—
258C23—861no—
259C23—861no—
260C23—862no—
261C23—862no—
262C23—862no—
263C23—862no—
264C23—862no—
265C23—862no—
266C23—862no—
267C23—862no—
268C23—862no—
269C23C23×D4311yescharacteristic
270D4—44no—
271D4—1724no—
272D4—1728no—
273D4—1728no—
274D4—1728no—
275D4—1728no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—432no—
285C2×C4—432no—
286C2×C4—432no—
287C2×C4—432no—
288C2×C4—868no—
289C2×C4—862no—
290C2×C4—861no—
291C2×C4—862no—
292C2×C4—862no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4D4×D4312yes—
296C2×C4D4×D4312yes—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—862no—
305C22—864no—
306C22—1722no—
307C22—1722no—
308C22—1722no—
309C22—1722no—
310C22—1722no—
311C22—1722no—
312C22—1722no—
313C22—1721no—
314C22—1721no—
315C22—1722no—
316C22C2×D4×D4311yescharacteristic
317C22C2×D4×D4311yescharacteristic
318C22#41×D4311yescharacteristic
319C22#1306337012yes—
320C22#1306337112yes—
321C4—22no—
322C4—22no—
323C4—41no—
324C4—42no—
325C4—434no—
326C4—862no—
327C4—1722no—
328C4—1721no—
329C2—82no—
330C2—3442no—
331C2—1722no—
332C2#121×D4311yescharacteristic
333C2#1458346411yescharacteristic
334C2#1458346512yes—
335C2#1458346711yescharacteristic
336C2#1458350112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2619
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13063321C2semidirect
2. C2×#13063298C2semidirect
3. C2×#13063283C2semidirect
4. #14582816C2semidirect
5. #14582815C2semidirect
6. #14582809C2semidirect
7. #14582808C2semidirect
8. #14582807C2semidirect
9. #14582799C2semidirect
10. #14582763C2semidirect
11. C43×#394C2semidirect
67. C2×C4×D43D4semidirect
80. C4×Dic43D4semidirect
174. #394D43semidirect
180. C43#2619semidirect