Finite Group Databasebeta

← #19137913

Subgroups — #19137913

Order 5504.

1056 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10621900C211yesmaximal, characteristic, complemented
2C2×#13063295C211yesmaximal, characteristic, complemented
3C2×#13063293C211yesmaximal, characteristic, complemented
4C22×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5#14582812C212yesmaximal, complemented
6#14582808C212yesmaximal, complemented
7#14582778C211yesmaximal, characteristic, complemented
8#14582777C212yesmaximal, complemented
9#14582776C212yesmaximal, complemented
10#14582760C211yesmaximal, characteristic, complemented
11C43×#386C211yesmaximal, characteristic, complemented
12C24×D43C2211yescharacteristic
13C2×#10621900—24no—
14C2×#10621900—24no—
15C2×#10621900—24no—
16C22×Dic86C2211yescharacteristic, complemented
17C22×D172C2212yes—
18C22×C22⋊D43C2212yes—
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic, complemented
21C23×Dic43C2211yescharacteristic
22C23×Dic43C2211yescharacteristic, complemented
23C22×C4×D43C2211yescharacteristic, complemented
24#13063295—24no—
25#13063293—24no—
26C2×C22⋊Dic43C2211yescharacteristic
27C2×(C2×D43)⋊C4—24no—
28C2×(C2×D43)⋊C4C2212yes—
29C2×(C2×D43)⋊C4C2212yes—
30C2×(C2×D43)⋊C4C2212yes—
31C2×(C2×D43)⋊C4C2212yes—
32C2×(C2×D43)⋊C4C2212yescomplemented
33C43⋊#95C2212yescomplemented
34C43⋊#95C2212yescomplemented
35C43⋊#95C2212yescomplemented
36C22×D4×C43C2211yescharacteristic
37C23×C4×C43C2211yescharacteristic
38C2×C22⋊C4×C43C2211yescharacteristic
39C2×C22⋊C4×C43C2212yescomplemented
40#95×C43C2212yescomplemented
41C24×C43C2311yescharacteristic
42C24×C43C2311yescharacteristic
43C23×D43—22no—
44C23×D43—24no—
45C23×D43—22no—
46C23×D43—22no—
47C23×D43—42no—
48C23×D43C2311yescharacteristic
49C23×D43C2312yes—
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43D414yescomplemented
53C22×C4×C43—22no—
54C22×C4×C43—42no—
55C22×C4×C43C2312yes—
56C22×C4×C43C2312yes—
57C22×C4×C43C2311yescharacteristic
58C2×C22⋊D43—22no—
59C2×C22⋊D43—22no—
60C2×C22⋊D43—22no—
61C2×C22⋊D43—22no—
62C2×C22⋊D43—24no—
63C2×C22⋊D43—22no—
64C2×C22⋊D43—24no—
65C2×C22⋊D43—42no—
66C2×C22⋊D43D414yescomplemented
67C22×Dic43—22no—
68C22×Dic43—22no—
69C22×Dic43—22no—
70C22×Dic43—22no—
71C22×Dic43—22no—
72C22×Dic43D414yescomplemented
73C22×Dic43C2312yes—
74C22×Dic43C2311yescharacteristic
75C22×Dic43C2311yescharacteristic
76C22×Dic43C2311yescharacteristic
77#10621900—232no—
78C2×D172—24no—
79C2×D172—24no—
80C2×D172—42no—
81C2×C4×D43—22no—
82C2×C4×D43—22no—
83C2×C4×D43—22no—
84C2×Dic86—22no—
85C2×Dic86—22no—
86C2×Dic86—22no—
87C22⋊C4×C43—22no—
88C22⋊C4×C43—42no—
89C22⋊Dic43—22no—
90(C2×D43)⋊C4—24no—
91(C2×D43)⋊C4—24no—
92(C2×D43)⋊C4—24no—
93(C2×D43)⋊C4—24no—
94(C2×D43)⋊C4—42no—
95C23×C43—22no—
96C23×C43—22no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—22no—
100C23×C43—22no—
101C23×C43C2×D412yes—
102C23×C43C2×D412yes—
103C23×C43C2×D412yes—
104C23×C43C2×D412yes—
105C23×C43C2411yescharacteristic
106C22×D43—28no—
107C22×D43—22no—
108C22×D43—22no—
109C22×D43—22no—
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—22no—
113C22×D43—22no—
114C22×D43—22no—
115C22×D43—22no—
116C22×D43—22no—
117C22×D43—48no—
118C22×D43—48no—
119C22×D43—44no—
120C22×D43—44no—
121C22×D43C2×D412yes—
122C22×D43#4114yescomplemented
123D4×C43—28no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—44no—
133C2×C4×C43C2×D412yes—
134C22⋊D43—28no—
135C22⋊D43—28no—
136C22⋊D43—48no—
137C2×Dic43—28no—
138C2×Dic43—28no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—22no—
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43C2×D412yes—
149C2×Dic43C2×D412yes—
150C2×Dic43C2×D412yes—
151D172—48no—
152C4×D43—28no—
153Dic86—28no—
154C22×C43—22no—
155C22×C43—22no—
156C22×C43—24no—
157C22×C43—24no—
158C22×C43—22no—
159C22×C43—24no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—42no—
163C22×C43#12014yes—
164C22×C43C22×D411yescharacteristic
165C22×C43C22×D411yescharacteristic
166C22×C43C22×D411yescharacteristic
167C22×C43C2×#4112yes—
168C22×C43H(5,𝔽2)12yes—
169C2×D43—22no—
170C2×D43—24no—
171C2×D43—24no—
172C2×D43—24no—
173C2×D43—24no—
174C2×D43—416no—
175C2×D43—42no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—42no—
179C2×D43—42no—
180C2×D43—42no—
181C2×D43—42no—
182C4×C43—22no—
183C4×C43—42no—
184C4×C43—42no—
185Dic43—22no—
186Dic43—22no—
187Dic43—22no—
188Dic43—42no—
189#2404—431nomaximal, Sylow
190C2×C43—24no—
191C2×C43—42no—
192C2×C43C2×#12011yescharacteristic
193C2×C43#52511yescharacteristic
194C2×C43#53511yescharacteristic
195C2×C43#54612yes—
196C2×C43#54612yes—
197D43—42no—
198D43—44no—
199C22×#41—431no—
200C2×#120—431no—
201C2×#120—431no—
202C22×C22⋊C4—431no—
203#393—432no—
204#392—432no—
205#386—431no—
206#386—432no—
207#386—432no—
208#386D4311yescharacteristic, complemented
209#381—431no—
210C43#240411yescharacteristic, complemented, Sylow
211C25—431no—
212C2×#41—864no—
213C2×#41—864no—
214C2×#41—864no—
215C22×Q8—431no—
216C22×D4—431no—
217C22×D4—431no—
218C22×D4—432no—
219C22×D4—432no—
220C22×D4C2×D4311yescharacteristic
221C23×C4—431no—
222C23×C4—431no—
223C23×C4—431no—
224C23×C4C2×D4311yescharacteristic
225#120—864no—
226#120—864no—
227C2×C22⋊C4—431no—
228C2×C22⋊C4—432no—
229C2×C22⋊C4—432no—
230C2×C22⋊C4—432no—
231C2×C22⋊C4—432no—
232C2×C22⋊C4—432no—
233C2×C22⋊C4—864no—
234C2×C22⋊C4C2×D4311yescharacteristic
235C2×C22⋊C4C2×D4312yescomplemented
236#95—432no—
237#95—432no—
238#95—432no—
239#95C2×D4312yescomplemented
240C24—432no—
241C24—431no—
242C24—864no—
243C24—862no—
244C24—862no—
245C24—862no—
246C24—1722no—
247C24C22×D4311yescharacteristic
248C24C22×D4311yescharacteristic
249#41—8632no—
250C2×Q8—862no—
251C2×Q8—862no—
252C2×Q8—862no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—434no—
256C2×D4—864no—
257C2×D4—864no—
258C2×D4—862no—
259C2×D4—862no—
260C2×D4—862no—
261C2×D4—862no—
262C2×D4—862no—
263C2×D4—864no—
264C2×D4—864no—
265C2×D4—1722no—
266C2×D4—1722no—
267C2×D4D17214yescomplemented
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—434no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—432no—
275C22×C4—862no—
276C22×C4—862no—
277C22×C4—862no—
278C22×C4—862no—
279C22×C4—862no—
280C22×C4—862no—
281C22×C4—862no—
282C22×C4—862no—
283C22×C4C22×D4312yes—
284C22×C4C22×D4312yes—
285C22×C4C22×D4311yescharacteristic
286C22⋊C4—22no—
287C22⋊C4—42no—
288C22⋊C4—864no—
289C22⋊C4—864no—
290C22⋊C4—864no—
291C22⋊C4—862no—
292C22⋊C4—864no—
293C22⋊C4—1722no—
294C23—22no—
295C23—22no—
296C23—21no—
297C23—21no—
298C23—22no—
299C23—22no—
300C23—432no—
301C23—434no—
302C23—868no—
303C23—862no—
304C23—862no—
305C23—861no—
306C23—862no—
307C23—861no—
308C23—862no—
309C23—862no—
310C23—862no—
311C23—862no—
312C23—862no—
313C23—1728no—
314C23—1728no—
315C23—1724no—
316C23—1724no—
317C23C2×D17212yes—
318C23C2×D17212yes—
319C23D4×D4312yes—
320C23D4×D4312yes—
321C23C23×D4311yescharacteristic
322Q8—868no—
323D4—28no—
324D4—868no—
325D4—868no—
326D4—1728no—
327D4—1728no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—44no—
337C2×C4—432no—
338C2×C4—432no—
339C2×C4—432no—
340C2×C4—868no—
341C2×C4—868no—
342C2×C4—868no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4C2×D17212yes—
353C22—22no—
354C22—22no—
355C22—24no—
356C22—24no—
357C22—22no—
358C22—24no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—862no—
363C22—864no—
364C22—864no—
365C22—864no—
366C22—864no—
367C22—17216no—
368C22—1722no—
369C22—1721no—
370C22—1722no—
371C22—1721no—
372C22—1722no—
373C22—1722no—
374C22—1722no—
375C22#1306329514yes—
376C22C2×D4×D4311yescharacteristic
377C22C2×D4×D4311yescharacteristic
378C22C22×D17211yescharacteristic
379C22#41×D4312yes—
380C22#1306337012yes—
381C4—22no—
382C4—42no—
383C4—42no—
384C4—862no—
385C4—862no—
386C4—862no—
387C4—1722no—
388C2—24no—
389C2—42no—
390C2—1724no—
391C2—1722no—
392C2C2×#1306329511yescharacteristic
393C2#1458340711yescharacteristic
394C2#1458346411yescharacteristic
395C2#1458353812yes—
396C2#1458354412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#386C2
hypercenter#386D43
hypocenterC43#2404
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#10621900C2semidirect
2. C2×#13063295C2semidirect
3. C2×#13063293C2semidirect
4. C22×(C2×D43)⋊C4C2semidirect
5. #14582812C2semidirect
6. #14582808C2semidirect
7. #14582778C2semidirect
8. #14582777C2semidirect
9. #14582776C2semidirect
10. #14582760C2semidirect
11. C43×#386C2semidirect
16. C22×Dic86C22semidirect
20. C22×C22⋊D43C22semidirect
22. C23×Dic43C22semidirect
23. C22×C4×D43C22semidirect
32. C2×(C2×D43)⋊C4C22semidirect
33. C43⋊#95C22semidirect
34. C43⋊#95C22semidirect
35. C43⋊#95C22semidirect
39. C2×C22⋊C4×C43C22semidirect
40. #95×C43C22semidirect
52. C2×D4×C43D4semidirect
66. C2×C22⋊D43D4semidirect
72. C22×Dic43D4semidirect
122. C22×D43#41semidirect
208. #386D43semidirect
210. C43#2404semidirect
235. C2×C22⋊C4C2×D43semidirect
239. #95C2×D43semidirect
267. C2×D4D172semidirect