Finite Group Databasebeta

← #19135002

Subgroups — #19135002

Order 5504.

578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13063295C211yesmaximal, characteristic
2#14583372C211yesmaximal, characteristic, complemented
3C2×#13063239C211yesmaximal, characteristic, complemented
4#14582754C211yesmaximal, characteristic, complemented
5#14582754C211yesmaximal, characteristic, complemented
6#14582665C211yesmaximal, characteristic, complemented
7C43×#342C211yesmaximal, characteristic, complemented
8C24×D43C2211yescharacteristic
9C22×D172—21no—
10C22×C22⋊D43C2211yescharacteristic
11#13063295—22no—
12#13063295C414yescomplemented
13C4×C22⋊D43—22no—
14(C22⋊D43)⋊C4—22no—
15#13063281—21no—
16C2×C22⋊Dic43C2211yescharacteristic
17C2×C22⋊Dic43C2211yescharacteristic
18C2×(C2×D43)⋊C4—21no—
19C2×(C2×D43)⋊C4—22no—
20C2×(C2×D43)⋊C4—22no—
21C22⋊C4×D43—21no—
22#13063239—22no—
23C2×C22⋊C4×C43C2211yescharacteristic
24C2×C22⋊C4×C43C2211yescharacteristic
25C2×C22⋊C4×C43C2211yescharacteristic
26C24×C43C2311yescharacteristic
27C23×D43—21no—
28C23×D43—21no—
29C23×D43—21no—
30C23×D43—21no—
31C23×D43—21no—
32C23×D43—21no—
33C23×D43—44no—
34C23×D43C2×C412yescomplemented
35C23×D43D411yescharacteristic
36C22×C4×C43—21no—
37C22×C4×C43—21no—
38C22×C4×C43D412yescomplemented
39C2×C22⋊D43—21no—
40C2×C22⋊D43—21no—
41C2×C22⋊D43—21no—
42C2×C22⋊D43—21no—
43C2×C22⋊D43C2×C412yes—
44C2×C22⋊D43D412yes—
45C22×Dic43—21no—
46C22×Dic43D411yescharacteristic
47C22×Dic43D412yescomplemented
48C2×D172—24no—
49C2×D172—44no—
50C2×C4×D43—22no—
51C22⋊C4×C43—21no—
52C22⋊C4×C43—21no—
53C22⋊C4×C43—21no—
54C22⋊C4×C43—21no—
55C22⋊C4×C43—21no—
56C22⋊C4×C43C2×C412yescomplemented
57C22⋊Dic43—21no—
58C22⋊Dic43—21no—
59C22⋊Dic43—21no—
60C22⋊Dic43—21no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—44no—
64(C2×D43)⋊C4—44no—
65Dic43⋊C4—22no—
66C4×Dic43—22no—
67C23×C43—42no—
68C23×C43C22×C411yescharacteristic
69C23×C43C2×D411yescharacteristic
70C23×C43C2×D411yescharacteristic
71C23×C43C2×D411yescharacteristic
72C23×C43C2×D411yescharacteristic
73C23×C43#4111yescharacteristic
74C23×C43#4111yescharacteristic
75C22×D43—24no—
76C22×D43—24no—
77C22×D43—24no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—21no—
82C22×D43—21no—
83C22×D43—44no—
84C22×D43—44no—
85C22×D43—44no—
86C22×D43—44no—
87C22×D43—42no—
88C22×D43—42no—
89C22×D43—42no—
90C22×D43—41no—
91C22×D43—41no—
92C22×D43—41no—
93C22×D43—41no—
94C22×D43—42no—
95C22×D43C22⋊C412yescomplemented
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—41no—
102C22⋊D43—22no—
103C22⋊D43—22no—
104C22⋊D43—22no—
105C22⋊D43—22no—
106C2×Dic43—21no—
107C2×Dic43—21no—
108C2×Dic43—22no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111C2×Dic43—41no—
112C2×Dic43C22⋊C412yescomplemented
113D172—48no—
114C4×D43—82no—
115C22×C43—22no—
116C22×C43—22no—
117C22×C43—22no—
118C22×C43—41no—
119C22×C43—41no—
120C22×C43—41no—
121C22×C43—41no—
122C22×C43C2×C22⋊C411yescharacteristic
123C22×C43C4×D411yescharacteristic
124C22×C43C4×D411yescharacteristic
125C22×C43#12011yescharacteristic
126C22×C43#12111yescharacteristic
127C22×C43#12111yescharacteristic
128C22×C43#12311yescharacteristic
129C2×D43—24no—
130C2×D43—24no—
131C2×D43—24no—
132C2×D43—22no—
133C2×D43—44no—
134C2×D43—42no—
135C2×D43—44no—
136C2×D43—42no—
137C2×D43—42no—
138C2×D43—44no—
139C2×D43—42no—
140C2×D43—44no—
141C2×D43—42no—
142C2×D43—42no—
143C2×D43—81no—
144C4×C43—42no—
145C4×C43—42no—
146C4×C43—81no—
147Dic43—22no—
148Dic43—42no—
149Dic43—81no—
150#1889—431nomaximal, Sylow
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—21no—
154C2×C43—21no—
155C2×C43—21no—
156C2×C43—21no—
157C2×C43#38611yescharacteristic
158C2×C43B(4,𝔽2)12yes—
159D43—44no—
160D43—42no—
161C2×#120—431no—
162#518—431no—
163C2×#99—431no—
164#379—431no—
165#379—431no—
166#342—431no—
167#342D4311yescharacteristic, complemented
168C43#188911yescharacteristic, complemented, Sylow
169C25—431no—
170C22×D4—431no—
171C22×D4—861no—
172#120—434no—
173#120—862no—
174C4×D4—862no—
175C4×D4—862no—
176#117—861no—
177C2×C22⋊C4—431no—
178C2×C22⋊C4—431no—
179C2×C22⋊C4—861no—
180C2×C22⋊C4—861no—
181C2×C22⋊C4—862no—
182C2×C22⋊C4—862no—
183C2×C22⋊C4C2×D4311yescharacteristic
184C2×C22⋊C4C2×D4311yescharacteristic
185C2×C22⋊C4C2×D4311yescharacteristic
186#99—862no—
187C24—431no—
188C24—432no—
189C24—861no—
190C24—861no—
191C24—861no—
192C24—861no—
193C24—861no—
194C24—861no—
195C24—1724no—
196C24C22×D4311yescharacteristic
197C2×D4—432no—
198C2×D4—432no—
199C2×D4—864no—
200C2×D4—861no—
201C2×D4—861no—
202C2×D4—861no—
203C2×D4—861no—
204C2×D4—1724no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—431no—
208C22×C4—432no—
209C22×C4—862no—
210C22×C4—861no—
211C22×C4D17212yescomplemented
212C4⋊C4—862no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—21no—
218C22⋊C4—864no—
219C22⋊C4—862no—
220C22⋊C4—861no—
221C22⋊C4—861no—
222C22⋊C4—861no—
223C22⋊C4—861no—
224C22⋊C4—1724no—
225C22⋊C4—1724no—
226C22⋊C4C4×D4312yescomplemented
227C42—862no—
228C23—42no—
229C23—432no—
230C23—864no—
231C23—864no—
232C23—864no—
233C23—861no—
234C23—862no—
235C23—862no—
236C23—862no—
237C23—861no—
238C23—1722no—
239C23—1722no—
240C23—1722no—
241C23—1722no—
242C23—1724no—
243C23—1724no—
244C23—1724no—
245C23—1724no—
246C23—1721no—
247C23—1721no—
248C23—1721no—
249C23—1721no—
250C23C2×C4×D4311yescharacteristic
251C23C2×D17211yescharacteristic
252C23#1062189811yescharacteristic
253C23D4×D4311yescharacteristic
254C23D4×D4311yescharacteristic
255C23D4×D4311yescharacteristic
256C23#1062190211yescharacteristic
257D4—862no—
258D4—862no—
259D4—862no—
260D4—862no—
261D4—1728no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—432no—
269C2×C4—861no—
270C2×C4—861no—
271C2×C4—862no—
272C2×C4—3442no—
273C2×C4—1722no—
274C2×C4—1721no—
275C2×C4—1722no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—864no—
284C22—864no—
285C22—864no—
286C22—862no—
287C22—3441no—
288C22—1722no—
289C22—1722no—
290C22—1724no—
291C22—1724no—
292C22—1722no—
293C22—1722no—
294C22—1724no—
295C22—1722no—
296C22—1724no—
297C22—1722no—
298C22C22⋊C4×D4311yescharacteristic
299C22#1306328711yescharacteristic
300C22C4×D17211yescharacteristic
301C22#1306329511yescharacteristic
302C22#1306329811yescharacteristic
303C22#1306330011yescharacteristic
304C22#1306331011yescharacteristic
305C4—42no—
306C4—42no—
307C4—81no—
308C4—862no—
309C4—3441no—
310C4—1722no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—1724no—
318C2—1722no—
319C2#1458277711yescharacteristic
320C2#1458308712yes—
subgroupG/H
centerC22#13063295
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43#120
hypercenter#342D43
hypocenterC43#1889
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #14583372C2semidirect
3. C2×#13063239C2semidirect
4. #14582754C2semidirect
5. #14582754C2semidirect
6. #14582665C2semidirect
7. C43×#342C2semidirect
12. #13063295C4semidirect
34. C23×D43C2×C4semidirect
38. C22×C4×C43D4semidirect
47. C22×Dic43D4semidirect
56. C22⋊C4×C43C2×C4semidirect
95. C22×D43C22⋊C4semidirect
112. C2×Dic43C22⋊C4semidirect
167. #342D43semidirect
168. C43#1889semidirect
211. C22×C4D172semidirect
226. C22⋊C4C4×D43semidirect