Finite Group Databasebeta

← #19134508

Subgroups — #19134508

Order 5504.

880 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×D4×D43C211yesmaximal, characteristic
2C2×#13063240C211yesmaximal, characteristic, complemented
3C2×#13063239C212yesmaximal, complemented
4#14582754C212yesmaximal, complemented
5C2×#99×C43C211yesmaximal, characteristic, complemented
6C24×D43C411yescharacteristic, complemented
7C24×D43C2211yescharacteristic
8C22×D172C411yescharacteristic, complemented
9C22×C22⋊D43C411yescharacteristic, complemented
10C22×C22⋊D43C2211yescharacteristic
11C2×D4×D43—24no—
12C2×D4×D43—22no—
13C2×D4×D43—22no—
14C2×D4×D43—24no—
15C22×C4×D43C411yescharacteristic, complemented
16C2×C22⋊Dic43C2212yescomplemented
17C2×(C2×D43)⋊C4—24no—
18#13063240—22no—
19#13063239—24no—
20C22×D4×C43C2211yescharacteristic
21C2×C22⋊C4×C43C2212yescomplemented
22#99×C43—22no—
23C24×C43C2×C411yescharacteristic
24C24×C43C2311yescharacteristic
25C23×D43—22no—
26C23×D43—21no—
27C23×D43—22no—
28C23×D43—21no—
29C23×D43—22no—
30C23×D43—22no—
31C23×D43—44no—
32C23×D43—44no—
33C23×D43C2×C411yescharacteristic
34C23×D43C2×C411yescharacteristic
35C23×D43C2×C411yescharacteristic
36C23×D43D414yes—
37C2×D4×C43—22no—
38C2×D4×C43—22no—
39C2×D4×C43D412yes—
40C2×D4×C43D412yes—
41C22×C4×C43—22no—
42C22×C4×C43C2×C411yescharacteristic
43C2×C22⋊D43—22no—
44C2×C22⋊D43—22no—
45C2×C22⋊D43—21no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—21no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43D414yes—
50C22×Dic43—22no—
51C22×Dic43C2×C411yescharacteristic
52D4×D43—216no—
53D4×D43—216no—
54C2×D172—22no—
55C2×D172—22no—
56C2×D172—22no—
57C2×C4×D43—22no—
58C2×C4×D43—22no—
59C2×C4×D43—22no—
60C22⋊C4×C43—22no—
61C22⋊C4×C43—22no—
62C22⋊Dic43—22no—
63C22⋊Dic43—22no—
64(C2×D43)⋊C4—48no—
65C23×C43—21no—
66C23×C43—21no—
67C23×C43—42no—
68C23×C43—42no—
69C23×C43C22⋊C412yescomplemented
70C23×C43C22×C411yescharacteristic
71C23×C43C2×D411yescharacteristic
72C23×C43C2×D412yes—
73C23×C43C2×D412yes—
74C23×C43C2×D411yescharacteristic
75C22×D43—21no—
76C22×D43—21no—
77C22×D43—24no—
78C22×D43—28no—
79C22×D43—21no—
80C22×D43—21no—
81C22×D43—21no—
82C22×D43—21no—
83C22×D43—24no—
84C22×D43—24no—
85C22×D43—28no—
86C22×D43—42no—
87C22×D43—44no—
88C22×D43—44no—
89C22×D43—48no—
90C22×D43—44no—
91C22×D43—48no—
92C22×D43—48no—
93C22×D43—44no—
94C22×D43—44no—
95C22×D43—42no—
96C22×D43C22⋊C412yes—
97C22×D43C22⋊C412yes—
98C22×D43C22⋊C412yescomplemented
99D4×C43—24no—
100D4×C43—24no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—44no—
104C2×C4×C43—42no—
105C2×C4×C43C22⋊C412yescomplemented
106C22⋊D43—28no—
107C22⋊D43—24no—
108C22⋊D43—24no—
109C2×Dic43—21no—
110C2×Dic43—21no—
111C2×Dic43—44no—
112C2×Dic43—42no—
113C2×Dic43C22⋊C412yescomplemented
114D172—28no—
115C4×D43—28no—
116C22×C43—22no—
117C22×C43—24no—
118C22×C43—22no—
119C22×C43—41no—
120C22×C43—42no—
121C22×C43—41no—
122C22×C43—42no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43C2×C22⋊C411yescharacteristic
126C22×C43C2×C22⋊C411yescharacteristic
127C22×C43C2×C22⋊C411yescharacteristic
128C22×C43#12012yes—
129C22×C43#12012yes—
130C2×D43—24no—
131C2×D43—24no—
132C2×D43—22no—
133C2×D43—22no—
134C2×D43—22no—
135C2×D43—22no—
136C2×D43—24no—
137C2×D43—48no—
138C2×D43—48no—
139C2×D43—416no—
140C2×D43—42no—
141C2×D43—42no—
142C2×D43—42no—
143C2×D43—42no—
144C2×D43—42no—
145C2×D43#9914yescomplemented
146C4×C43—22no—
147C4×C43—82no—
148Dic43—22no—
149Dic43—82no—
150#1781—431nomaximal, Sylow
151C2×C43—22no—
152C2×C43—22no—
153C2×C43—21no—
154C2×C43—21no—
155C2×C43—42no—
156C2×C43#37911yescharacteristic
157C2×C43C2×#9912yes—
158D43—24no—
159D43—42no—
160D43—42no—
161C23×D4—431no—
162C2×#99—431no—
163C2×#99—432no—
164C2×#99D4311yescharacteristic, complemented
165#379—432no—
166C43#178111yescharacteristic, complemented, Sylow
167C25—431no—
168C25—431no—
169C22×D4—431no—
170C22×D4—431no—
171C22×D4—431no—
172C22×D4—864no—
173C22×D4—864no—
174C22×D4—862no—
175C22×D4—862no—
176C22×D4C2×D4311yescharacteristic
177C23×C4—431no—
178C2×C22⋊C4—432no—
179C2×C22⋊C4—864no—
180C2×C22⋊C4C2×D4312yescomplemented
181#99—22no—
182#99—864no—
183#99—862no—
184C24—431no—
185C24—434no—
186C24—431no—
187C24—431no—
188C24—862no—
189C24—862no—
190C24—862no—
191C24—861no—
192C24—862no—
193C24—861no—
194C24—1724no—
195C24—1724no—
196C24C4×D4311yescharacteristic
197C24C22×D4311yescharacteristic
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—434no—
201C2×D4—862no—
202C2×D4—862no—
203C2×D4—862no—
204C2×D4—8616no—
205C2×D4—8616no—
206C2×D4—862no—
207C2×D4—862no—
208C2×D4—861no—
209C2×D4—862no—
210C2×D4—861no—
211C2×D4—862no—
212C2×D4D17212yes—
213C2×D4C22⋊D4312yes—
214C22×C4—22no—
215C22×C4—431no—
216C22×C4—862no—
217C22×C4—862no—
218C22×C4—862no—
219C22×C4—862no—
220C22×C4C4×D4311yescharacteristic
221C22⋊C4—22no—
222C22⋊C4—22no—
223C22⋊C4—862no—
224C22⋊C4—862no—
225C22⋊C4—1728no—
226C23—21no—
227C23—21no—
228C23—42no—
229C23—42no—
230C23—432no—
231C23—432no—
232C23—432no—
233C23—864no—
234C23—868no—
235C23—868no—
236C23—861no—
237C23—861no—
238C23—861no—
239C23—861no—
240C23—861no—
241C23—861no—
242C23—864no—
243C23—864no—
244C23—1724no—
245C23—1722no—
246C23—1722no—
247C23—1724no—
248C23—1724no—
249C23—1728no—
250C23—1724no—
251C23—1728no—
252C23—1728no—
253C23—1724no—
254C23(C2×D43)⋊C412yescomplemented
255C23C2×C4×D4311yescharacteristic
256C23C2×D17211yescharacteristic
257C23D4×D4312yes—
258C23D4×D4312yes—
259C23C2×C22⋊D4311yescharacteristic
260D4—24no—
261D4—24no—
262D4—868no—
263D4—868no—
264D4—864no—
265D4—864no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—432no—
271C2×C4—868no—
272C2×C4—861no—
273C2×C4—861no—
274C2×C4—1724no—
275C2×C4—1722no—
276C2×C4(C2×D43)⋊C412yescomplemented
277C22—24no—
278C22—22no—
279C22—22no—
280C22—41no—
281C22—42no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—434no—
287C22—864no—
288C22—864no—
289C22—862no—
290C22—862no—
291C22—864no—
292C22—862no—
293C22—862no—
294C22—1728no—
295C22—1728no—
296C22—1722no—
297C22—1722no—
298C22—1722no—
299C22—1722no—
300C22—17216no—
301C22—1722no—
302C22C22⋊C4×D4311yescharacteristic
303C22C22⋊C4×D4311yescharacteristic
304C22C2×(C2×D43)⋊C411yescharacteristic
305C22#1306329312yes—
306C22#1306329512yes—
307C4—22no—
308C4—82no—
309C4—862no—
310C4—3442no—
311C2—22no—
312C2—22no—
313C2—21no—
314C2—21no—
315C2—42no—
316C2—864no—
317C2—1722no—
318C2—1722no—
319C2#1458275411yescharacteristic
320C2#99×D4312yes—
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC2×#99×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC2×#99D43
hypocenterC43#1781
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#13063240C2semidirect
3. C2×#13063239C2semidirect
4. #14582754C2semidirect
5. C2×#99×C43C2semidirect
6. C24×D43C4semidirect
8. C22×D172C4semidirect
9. C22×C22⋊D43C4semidirect
15. C22×C4×D43C4semidirect
16. C2×C22⋊Dic43C22semidirect
21. C2×C22⋊C4×C43C22semidirect
69. C23×C43C22⋊C4semidirect
98. C22×D43C22⋊C4semidirect
105. C2×C4×C43C22⋊C4semidirect
113. C2×Dic43C22⋊C4semidirect
145. C2×D43#99semidirect
164. C2×#99D43semidirect
166. C43#1781semidirect
180. C2×C22⋊C4C2×D43semidirect
254. C23(C2×D43)⋊C4semidirect
276. C2×C4(C2×D43)⋊C4semidirect