Finite Group Databasebeta

← #19140330

Subgroups — #19140330

Order 5504.

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

normal subgroups only

This group has 824 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×#13063300C211yesmaximal, characteristic, complemented
2C2×#13063295C212yesmaximal, complemented
3C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
4#14582825C211yesmaximal, characteristic, complemented
5#14582817C212yesmaximal, complemented
6#14582814C212yesmaximal, complemented
7#14582809C211yesmaximal, characteristic, complemented
8#14582808C211yesmaximal, characteristic, complemented
9#14582777C212yesmaximal, complemented
10#14582758C211yesmaximal, characteristic, complemented
11C43×#397C211yesmaximal, characteristic, complemented
12C24×D43C2211yescharacteristic
13C22×D172C2212yes—
14C22×D172C2212yes—
15C22×D172C2211yescharacteristic, complemented
16C22×C22⋊D43C2212yes—
17C22×C4×D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19#13063300—24no—
20#13063295—28no—
21C2×Dic43⋊C4C2212yescomplemented
22C2×C22⋊Dic43C2211yescharacteristic
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yescomplemented
28C2×(C2×D43)⋊C4C2212yescomplemented
29C2×(C2×D43)⋊C4C2212yescomplemented
30C22⋊C4×D43—24no—
31C43⋊#95C2211yescharacteristic, complemented
32C43⋊#95C2212yescomplemented
33C2×C4⋊C4×C43C2211yescharacteristic, complemented
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic, complemented
37#95×C43C2212yescomplemented
38C24×C43C2311yescharacteristic
39C23×D43—22no—
40C23×D43—22no—
41C23×D43—42no—
42C23×D43—42no—
43C23×D43D414yescomplemented
44C23×D43C2312yes—
45C23×D43C2311yescharacteristic
46C23×D43C2311yescharacteristic
47C22×C4×C43C2311yescharacteristic
48C22×C4×C43C2312yes—
49C22×C4×C43C2312yes—
50C22×C4×C43C2311yescharacteristic
51C2×C22⋊D43—24no—
52C2×C22⋊D43—42no—
53C2×C22⋊D43—42no—
54C22×Dic43C2312yes—
55C22×Dic43C2311yescharacteristic
56C22×Dic43C2311yescharacteristic
57C2×D172—22no—
58C2×D172—24no—
59C2×D172—24no—
60C2×D172—24no—
61C2×D172—24no—
62C2×D172—42no—
63C2×D172—42no—
64C2×D172—42no—
65C2×C4×D43—22no—
66C2×C4×D43—42no—
67C2×C4×D43—42no—
68C2×C4×D43D414yescomplemented
69C4⋊C4×C43—22no—
70C22⋊C4×C43—22no—
71C22⋊C4×C43—24no—
72C22⋊Dic43—22no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—22no—
75(C2×D43)⋊C4—24no—
76(C2×D43)⋊C4—24no—
77(C2×D43)⋊C4—24no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—42no—
80Dic43⋊C4—42no—
81C23×C43—21no—
82C23×C43—21no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43C2×D412yes—
86C23×C43C2411yescharacteristic
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—21no—
90C22×D43—21no—
91C22×D43—22no—
92C22×D43—22no—
93C22×D43—28no—
94C22×D43—22no—
95C22×D43—22no—
96C22×D43—22no—
97C22×D43—22no—
98C22×D43—22no—
99C22×D43—22no—
100C22×D43—22no—
101C22×D43—48no—
102C22×D43—44no—
103C22×D43—44no—
104C22×D43—48no—
105C22×D43C2×D412yes—
106C22×D43C2×D412yes—
107C22×D43C2×D412yes—
108C22×D43#4112yes—
109C2×C4×C43—22no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43C2×D412yes—
119C22⋊D43—48no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—21no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43C2×D412yes—
127D172—44no—
128D172—48no—
129D172—48no—
130C4×D43—44no—
131C4×D43—44no—
132C22×C43—22no—
133C22×C43—24no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—42no—
137C22×C43C22×D411yescharacteristic
138C22×C43C22×D411yescharacteristic
139C22×C43C2×#4111yescharacteristic
140C22×C43H(5,𝔽2)12yes—
141C22×C43H(5,𝔽2)12yes—
142C2×D43—24no—
143C2×D43—22no—
144C2×D43—22no—
145C2×D43—24no—
146C2×D43—22no—
147C2×D43—24no—
148C2×D43—416no—
149C2×D43—41no—
150C2×D43—41no—
151C2×D43—42no—
152C2×D43—42no—
153C2×D43—42no—
154C2×D43—42no—
155C2×D43—42no—
156C2×D43—42no—
157C2×D43—42no—
158C2×D43—42no—
159C2×D43#12114yes—
160C4×C43—22no—
161C4×C43—42no—
162C4×C43—42no—
163C4×C43—41no—
164Dic43—22no—
165Dic43—42no—
166Dic43—41no—
167#2617—431nomaximal, Sylow
168C2×C43—42no—
169C2×C43C2×#12111yescharacteristic
170C2×C43#53411yescharacteristic
171C2×C43#53412yes—
172C2×C43#53511yescharacteristic
173C2×C43#53812yes—
174D43—24no—
175D43—42no—
176D43—82no—
177C2×#121—431no—
178C2×#120—432no—
179C22×C22⋊C4—431no—
180#397—431no—
181#397D4311yescharacteristic, complemented
182#394—432no—
183#394—432no—
184#392—431no—
185#392—431no—
186#386—432no—
187#380—431no—
188C43#261711yescharacteristic, complemented, Sylow
189C25—431no—
190C22×D4—432no—
191C22×D4—432no—
192C22×D4—432no—
193C22×D4—431no—
194C23×C4—431no—
195C23×C4—431no—
196#121—864no—
197#120—868no—
198C2×C4⋊C4—432no—
199C2×C4⋊C4C2×D4311yescharacteristic, complemented
200C2×C22⋊C4—431no—
201C2×C22⋊C4—431no—
202C2×C22⋊C4—431no—
203C2×C22⋊C4—432no—
204C2×C22⋊C4—432no—
205C2×C22⋊C4—432no—
206C2×C22⋊C4—432no—
207C2×C22⋊C4—432no—
208C2×C22⋊C4—864no—
209C2×C22⋊C4C2×D4311yescharacteristic
210C2×C22⋊C4C2×D4312yes—
211#95—431no—
212#95—432no—
213#95C2×D4311yescharacteristic, complemented
214#95C2×D4312yescomplemented
215C24—431no—
216C24—431no—
217C24—434no—
218C24—432no—
219C24—862no—
220C24—862no—
221C24—1722no—
222C24—1722no—
223C24C22×D4311yescharacteristic
224C2×D4—864no—
225C2×D4—864no—
226C2×D4—864no—
227C2×D4—864no—
228C2×D4—864no—
229C2×D4—862no—
230C2×D4—1722no—
231C2×D4—1722no—
232C2×D4—1722no—
233C2×D4—1722no—
234C2×D4—1722no—
235C22×C4—431no—
236C22×C4—434no—
237C22×C4—431no—
238C22×C4—432no—
239C22×C4—862no—
240C22×C4—1722no—
241C22×C4—1722no—
242C22×C4C22×D4312yes—
243C22×C4C22×D4311yescharacteristic
244C22×C4C22×D4312yes—
245C22×C4C22×D4311yescharacteristic
246C4⋊C4—22no—
247C4⋊C4—1722no—
248C22⋊C4—24no—
249C22⋊C4—22no—
250C22⋊C4—862no—
251C22⋊C4—864no—
252C22⋊C4—864no—
253C22⋊C4—864no—
254C22⋊C4—862no—
255C22⋊C4—862no—
256C22⋊C4—1722no—
257C22⋊C4—1722no—
258C23—21no—
259C23—21no—
260C23—22no—
261C23—22no—
262C23—432no—
263C23—432no—
264C23—432no—
265C23—432no—
266C23—868no—
267C23—862no—
268C23—862no—
269C23—861no—
270C23—861no—
271C23—862no—
272C23—862no—
273C23—862no—
274C23—862no—
275C23—862no—
276C23—862no—
277C23—862no—
278C23—862no—
279C23—862no—
280C23—1728no—
281C23—1724no—
282C23—1724no—
283C23—1728no—
284C23D4×D4312yes—
285C23C23×D4311yescharacteristic
286D4—1724no—
287D4—1728no—
288D4—1728no—
289D4—1728no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—432no—
300C2×C4—862no—
301C2×C4—861no—
302C2×C4—862no—
303C2×C4—862no—
304C2×C4—862no—
305C2×C4—862no—
306C2×C4—1724no—
307C2×C4—1724no—
308C2×C4D4×D4312yes—
309C22—22no—
310C22—24no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—434no—
315C22—862no—
316C22—864no—
317C22—862no—
318C22—864no—
319C22—862no—
320C22—864no—
321C22—17216no—
322C22—1722no—
323C22—1722no—
324C22—1722no—
325C22—1722no—
326C22—1722no—
327C22—1722no—
328C22—1722no—
329C22—1721no—
330C22—1721no—
331C22—1722no—
332C22C2×D4×D4311yescharacteristic
333C22C2×D4×D4311yescharacteristic
334C22#41×D4311yescharacteristic
335C22#1306337112yes—
336C22#1306337112yes—
337C4—22no—
338C4—42no—
339C4—42no—
340C4—41no—
341C4—862no—
342C4—1722no—
343C4—1721no—
344C2—42no—
345C2—864no—
346C2—3442no—
347C2—1722no—
348C2#121×D4311yescharacteristic
349C2#1458346011yescharacteristic
350C2#1458346012yes—
351C2#1458346711yescharacteristic
352C2#1458348812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2617
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13063300C2semidirect
2. C2×#13063295C2semidirect
3. C2×C22⋊C4×D43C2semidirect
4. #14582825C2semidirect
5. #14582817C2semidirect
6. #14582814C2semidirect
7. #14582809C2semidirect
8. #14582808C2semidirect
9. #14582777C2semidirect
10. #14582758C2semidirect
11. C43×#397C2semidirect
15. C22×D172C22semidirect
21. C2×Dic43⋊C4C22semidirect
27. C2×(C2×D43)⋊C4C22semidirect
28. C2×(C2×D43)⋊C4C22semidirect
29. C2×(C2×D43)⋊C4C22semidirect
31. C43⋊#95C22semidirect
32. C43⋊#95C22semidirect
33. C2×C4⋊C4×C43C22semidirect
36. #95×C43C22semidirect
37. #95×C43C22semidirect
43. C23×D43D4semidirect
68. C2×C4×D43D4semidirect
181. #397D43semidirect
188. C43#2617semidirect
199. C2×C4⋊C4C2×D43semidirect
213. #95C2×D43semidirect
214. #95C2×D43semidirect