Finite Group Databasebeta

← #19140372

Subgroups — #19140372

Order 5504.

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

normal subgroups only

This group has 702 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×#13063293C211yesmaximal, characteristic
2C22×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
3#14582828C212yesmaximal, complemented
4#14582826C212yesmaximal, complemented
5#14582815C212yesmaximal, complemented
6#14582814C212yesmaximal, complemented
7#14582779C211yesmaximal, characteristic, complemented
8#14582774C211yesmaximal, characteristic, complemented
9#14582772C211yesmaximal, characteristic, complemented
10#14582754C211yesmaximal, characteristic, complemented
11C43×#386C211yesmaximal, characteristic, complemented
12C24×D43C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14C22×C22⋊D43C2211yescharacteristic
15C23×Dic43C2211yescharacteristic
16#13063293—24no—
17C2×C4⋊Dic43C2212yescomplemented
18C2×Dic43⋊C4C2212yescomplemented
19C2×C22⋊Dic43C2211yescharacteristic
20C2×C22⋊Dic43C2211yescharacteristic
21C2×C22⋊Dic43C2212yescomplemented
22C2×(C2×D43)⋊C4—24no—
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2212yes—
29C43⋊#95C2212yescomplemented
30C43⋊#95C2212yescomplemented
31C43⋊#95C2212yescomplemented
32C22×D4×C43C2211yescharacteristic
33C23×C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yescomplemented
36#95×C43C2212yescomplemented
37C24×C43C2311yescharacteristic
38C24×C43C2311yescharacteristic
39C23×D43—22no—
40C23×D43—22no—
41C23×D43—42no—
42C23×D43—42no—
43C23×D43D414yes—
44C23×D43C2311yescharacteristic
45C23×D43C2311yescharacteristic
46C2×D4×C43—22no—
47C2×D4×C43—22no—
48C2×D4×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43—42no—
51C22×C4×C43C2311yescharacteristic
52C22×C4×C43C2312yes—
53C22×C4×C43C2312yes—
54C2×C22⋊D43—22no—
55C2×C22⋊D43—22no—
56C2×C22⋊D43—42no—
57C2×C22⋊D43—42no—
58C22×Dic43—22no—
59C22×Dic43—42no—
60C22×Dic43C2312yes—
61C22×Dic43C2312yes—
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22⋊C4×C43—22no—
65C22⋊C4×C43—42no—
66C22⋊Dic43—22no—
67C22⋊Dic43—22no—
68C22⋊Dic43—42no—
69(C2×D43)⋊C4—24no—
70(C2×D43)⋊C4—24no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—42no—
74(C2×D43)⋊C4—42no—
75C4⋊Dic43—42no—
76Dic43⋊C4—42no—
77C23×C43—22no—
78C23×C43—22no—
79C23×C43—21no—
80C23×C43—21no—
81C23×C43—21no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43C2×D412yes—
85C23×C43#4112yes—
86C23×C43#4112yes—
87C23×C43C2411yescharacteristic
88C22×D43—28no—
89C22×D43—21no—
90C22×D43—21no—
91C22×D43—21no—
92C22×D43—21no—
93C22×D43—22no—
94C22×D43—22no—
95C22×D43—22no—
96C22×D43—22no—
97C22×D43—44no—
98C22×D43—44no—
99C22×D43—48no—
100C22×D43—48no—
101C22×D43C2×D412yes—
102C22×D43C2×D412yes—
103D4×C43—44no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—44no—
114C22⋊D43—44no—
115C22⋊D43—44no—
116C2×Dic43—22no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—22no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—44no—
127C22×C43—22no—
128C22×C43—22no—
129C22×C43—24no—
130C22×C43—24no—
131C22×C43—41no—
132C22×C43—41no—
133C22×C43—41no—
134C22×C43—42no—
135C22×C43—42no—
136C22×C43#12314yes—
137C22×C43C22×D411yescharacteristic
138C22×C43C2×#4111yescharacteristic
139C22×C43C2×#4111yescharacteristic
140C22×C43H(5,𝔽2)12yes—
141C22×C43H(5,𝔽2)12yes—
142C2×D43—22no—
143C2×D43—22no—
144C2×D43—22no—
145C2×D43—22no—
146C2×D43—22no—
147C2×D43—22no—
148C2×D43—416no—
149C2×D43—42no—
150C2×D43—42no—
151C2×D43—42no—
152C2×D43—42no—
153C4×C43—41no—
154C4×C43—42no—
155C4×C43—42no—
156Dic43—42no—
157Dic43—41no—
158Dic43—41no—
159Dic43—42no—
160#2622—431nomaximal, Sylow
161C2×C43—24no—
162C2×C43—81no—
163C2×C43C2×#12311yescharacteristic
164C2×C43#53411yescharacteristic
165C2×C43#53411yescharacteristic
166C2×C43#53812yes—
167C2×C43#53812yes—
168D43—42no—
169D43—42no—
170C2×#120—431no—
171C22×C22⋊C4—431no—
172#397—432no—
173#397—432no—
174#394—432no—
175#394—432no—
176#386—431no—
177#386D4311yescharacteristic, complemented
178#385—431no—
179#385—431no—
180#379—431no—
181C43#262211yescharacteristic, complemented, Sylow
182C25—431no—
183C22×D4—431no—
184C22×D4—431no—
185C22×D4C2×D4311yescharacteristic
186C23×C4—431no—
187C23×C4C2×D4311yescharacteristic
188#120—864no—
189C2×C4⋊C4—432no—
190C2×C4⋊C4—432no—
191C2×C22⋊C4—431no—
192C2×C22⋊C4—431no—
193C2×C22⋊C4—432no—
194C2×C22⋊C4—432no—
195C2×C22⋊C4—431no—
196C2×C22⋊C4—431no—
197C2×C22⋊C4—432no—
198C2×C22⋊C4—432no—
199C2×C22⋊C4—432no—
200C2×C22⋊C4—864no—
201C2×C22⋊C4C2×D4311yescharacteristic
202C2×C22⋊C4C2×D4312yescomplemented
203#95—432no—
204#95—432no—
205#95—432no—
206#95C2×D4312yescomplemented
207C24—431no—
208C24—431no—
209C24—434no—
210C24—862no—
211C24—862no—
212C24—1722no—
213C24—1722no—
214C24C22×D4311yescharacteristic
215C24C22×D4311yescharacteristic
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—862no—
220C2×D4—862no—
221C2×D4—1722no—
222C2×D4—1722no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—432no—
226C22×C4—432no—
227C22×C4—431no—
228C22×C4—431no—
229C22×C4—862no—
230C22×C4—1722no—
231C22×C4C22×D4311yescharacteristic
232C22×C4C22×D4312yes—
233C22×C4C22×D4312yes—
234C4⋊C4—1722no—
235C4⋊C4—1722no—
236C22⋊C4—22no—
237C22⋊C4—42no—
238C22⋊C4—864no—
239C22⋊C4—864no—
240C22⋊C4—862no—
241C22⋊C4—862no—
242C22⋊C4—862no—
243C22⋊C4—862no—
244C22⋊C4—1722no—
245C22⋊C4—1722no—
246C22⋊C4—1722no—
247C23—22no—
248C23—22no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—22no—
253C23—22no—
254C23—432no—
255C23—432no—
256C23—868no—
257C23—861no—
258C23—861no—
259C23—861no—
260C23—861no—
261C23—862no—
262C23—862no—
263C23—862no—
264C23—862no—
265C23—1724no—
266C23—1724no—
267C23—1728no—
268C23—1728no—
269C23#1062189812yes—
270C23D4×D4312yes—
271C23#1062190012yes—
272C23C23×D4311yescharacteristic
273D4—44no—
274D4—1724no—
275D4—1724no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—862no—
287C2×C4—861no—
288C2×C4—861no—
289C2×C4—862no—
290C2×C4—862no—
291C2×C4—862no—
292C2×C4—862no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4—862no—
296C2×C4—1724no—
297C22—22no—
298C22—22no—
299C22—24no—
300C22—24no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—862no—
307C22—862no—
308C22—862no—
309C22—862no—
310C22—862no—
311C22—862no—
312C22—17216no—
313C22—1722no—
314C22—1722no—
315C22—1722no—
316C22—1722no—
317C22#1306330714yes—
318C22C2×D4×D4311yescharacteristic
319C22C2×#1062190011yescharacteristic
320C22C2×#1062189811yescharacteristic
321C22#1306337012yes—
322C22#1306337112yes—
323C4—41no—
324C4—42no—
325C4—42no—
326C4—1721no—
327C4—1722no—
328C4—1721no—
329C4—1722no—
330C2—24no—
331C2—81no—
332C2—1722no—
333C2—1722no—
334C2C2×#1306330711yescharacteristic
335C2#1458345911yescharacteristic
336C2#1458346011yescharacteristic
337C2#1458348212yes—
338C2#1458348612yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#386C2
hypercenter#386D43
hypocenterC43#2622
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×(C2×D43)⋊C4C2semidirect
3. #14582828C2semidirect
4. #14582826C2semidirect
5. #14582815C2semidirect
6. #14582814C2semidirect
7. #14582779C2semidirect
8. #14582774C2semidirect
9. #14582772C2semidirect
10. #14582754C2semidirect
11. C43×#386C2semidirect
17. C2×C4⋊Dic43C22semidirect
18. C2×Dic43⋊C4C22semidirect
21. C2×C22⋊Dic43C22semidirect
29. C43⋊#95C22semidirect
30. C43⋊#95C22semidirect
31. C43⋊#95C22semidirect
35. C2×C22⋊C4×C43C22semidirect
36. #95×C43C22semidirect
177. #386D43semidirect
181. C43#2622semidirect
202. C2×C22⋊C4C2×D43semidirect
206. #95C2×D43semidirect