Finite Group Databasebeta

← #19140318

Subgroups — #19140318

Order 5504.

932 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10621900C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic, complemented
3C2×#13063297C212yesmaximal, complemented
4#14582812C211yesmaximal, characteristic, complemented
5#14582811C211yesmaximal, characteristic, complemented
6#14582808C212yesmaximal, complemented
7#14582807C211yesmaximal, characteristic, complemented
8#14582807C212yesmaximal, complemented
9#14582758C211yesmaximal, characteristic, complemented
10#14582757C212yesmaximal, complemented
11C43×#392C211yesmaximal, characteristic, complemented
12C2×#10621900—28no—
13C2×#10621900—24no—
14C22×Dic86C2211yescharacteristic
15C22×D172C2211yescharacteristic
16C22×C22⋊D43C2212yes—
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2212yes—
20C23×Dic43C2212yes—
21C22×C4×D43C2211yescharacteristic
22#13063298—24no—
23#13063297—28no—
24C2×Dic43⋊C4C2212yes—
25C2×Dic43⋊C4C2211yescharacteristic
26C2×C22⋊Dic43C2212yes—
27C2×C22⋊Dic43C2212yes—
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2212yes—
30C2×(C2×D43)⋊C4C2212yes—
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C43⋊#95C2212yes—
34C22×D4×C43C2211yescharacteristic
35C22×D4×C43C2212yes—
36C2×C22⋊C4×C43C2211yescharacteristic
37C2×C22⋊C4×C43C2212yes—
38#95×C43C2211yescharacteristic
39C24×C43C2311yescharacteristic
40C24×C43C2312yes—
41C23×D43C2311yescharacteristic
42C23×D43C2311yescharacteristic
43C2×D4×C43—22no—
44C2×D4×C43—24no—
45C2×D4×C43—24no—
46C2×D4×C43—42no—
47C2×D4×C43—42no—
48C22×C4×C43C2312yes—
49C22×C4×C43C2311yescharacteristic
50C22×C4×C43C2311yescharacteristic
51C2×C22⋊D43—24no—
52C2×C22⋊D43—24no—
53C2×C22⋊D43—22no—
54C2×C22⋊D43—24no—
55C2×C22⋊D43—24no—
56C2×C22⋊D43—24no—
57C2×C22⋊D43—22no—
58C2×C22⋊D43—42no—
59C2×C22⋊D43—42no—
60C2×C22⋊D43—42no—
61C22×Dic43—24no—
62C22×Dic43—24no—
63C22×Dic43D418yescomplemented
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2312yes—
66C22×Dic43C2312yes—
67C22×Dic43C2311yescharacteristic
68#10621900—232no—
69C2×D172—22no—
70C2×D172—42no—
71C2×C4×D43—24no—
72C2×C4×D43D414yescomplemented
73C2×Dic86—22no—
74C2×Dic86—24no—
75C22⋊C4×C43—22no—
76C22⋊C4×C43—42no—
77C22⋊Dic43—24no—
78C22⋊Dic43—42no—
79(C2×D43)⋊C4—22no—
80(C2×D43)⋊C4—24no—
81(C2×D43)⋊C4—42no—
82Dic43⋊C4—24no—
83Dic43⋊C4—22no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43—22no—
87C23×C43—22no—
88C23×C43—22no—
89C23×C43—22no—
90C23×C43—22no—
91C23×C43—21no—
92C23×C43—22no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43C2×D414yes—
96C23×C43C2411yescharacteristic
97C22×D43—22no—
98C22×D43—21no—
99C22×D43—22no—
100C22×D43—21no—
101C22×D43—21no—
102C22×D43—22no—
103C22×D43—22no—
104C22×D43—21no—
105C22×D43—21no—
106C22×D43C2×D412yes—
107D4×C43—28no—
108D4×C43—48no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—21no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43C2×D412yes—
116C22⋊D43—216no—
117C22⋊D43—44no—
118C22⋊D43—48no—
119C22⋊D43—44no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—216no—
123C2×Dic43—21no—
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—22no—
128C2×Dic43C2×D414yes—
129C2×Dic43C2×D414yes—
130C2×Dic43C2×D412yes—
131D172—44no—
132C4×D43—28no—
133Dic86—28no—
134C22×C43—24no—
135C22×C43—24no—
136C22×C43—24no—
137C22×C43—42no—
138C22×C43—42no—
139C22×C43—42no—
140C22×C43—42no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—42no—
144C22×C43—42no—
145C22×C43—41no—
146C22×C43C22×D412yes—
147C22×C43C22×D411yescharacteristic
148C22×C43H(5,𝔽2)12yes—
149C22×C43H(5,𝔽2)11yescharacteristic
150C22×C432−1+411yescharacteristic
151C2×D43—22no—
152C2×D43—22no—
153C2×D43—22no—
154C2×D43—42no—
155C2×D43—42no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—42no—
159C2×D43—42no—
160C2×D43—41no—
161C4×C43—22no—
162C4×C43—41no—
163C4×C43—42no—
164Dic43—24no—
165Dic43—41no—
166Dic43—42no—
167Dic43#12014yes—
168#2615—431nomaximal, Sylow
169C2×C43—44no—
170C2×C43—81no—
171C2×C43C2×#12011yescharacteristic
172C2×C43#53511yescharacteristic
173C2×C43#53512yes—
174C2×C43#53712yes—
175C2×C43#53711yescharacteristic
176D43—42no—
177D43—81no—
178C22×#41—431no—
179C2×#121—432no—
180C2×#121—431no—
181#393—431no—
182#393—431no—
183#392—432no—
184#392—431no—
185#392—432no—
186#392D4311yescharacteristic, complemented
187#380—432no—
188#380—431no—
189C43#261511yescharacteristic, complemented, Sylow
190C2×#41—868no—
191C2×#41—864no—
192C22×Q8—431no—
193C22×D4—431no—
194C22×D4—432no—
195C22×D4—431no—
196C22×D4—432no—
197C22×D4—431no—
198C22×D4C2×D4311yescharacteristic
199C22×D4C2×D4312yes—
200C23×C4—432no—
201C23×C4—431no—
202#121—864no—
203#121—868no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—432no—
206C2×C22⋊C4—432no—
207C2×C22⋊C4—432no—
208C2×C22⋊C4—431no—
209C2×C22⋊C4—432no—
210C2×C22⋊C4—432no—
211C2×C22⋊C4C2×D4311yescharacteristic
212C2×C22⋊C4C2×D4312yes—
213#95—432no—
214#95—432no—
215#95—431no—
216#95C2×D4311yescharacteristic
217C24—431no—
218C24—431no—
219C24C22×D4311yescharacteristic
220C24C22×D4312yes—
221#41—8632no—
222C2×Q8—864no—
223C2×Q8—862no—
224C2×D4—24no—
225C2×D4—24no—
226C2×D4—22no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—862no—
230C2×D4—864no—
231C2×D4—862no—
232C2×D4—864no—
233C2×D4—864no—
234C2×D4—864no—
235C2×D4—862no—
236C2×D4—864no—
237C2×D4—1722no—
238C2×D4—1722no—
239C2×D4—1722no—
240C2×D4—1722no—
241C22×C4—431no—
242C22×C4—438no—
243C22×C4—432no—
244C22×C4—434no—
245C22×C4—432no—
246C22×C4—431no—
247C22×C4—864no—
248C22×C4—864no—
249C22×C4—864no—
250C22×C4C22×D4311yescharacteristic
251C22×C4C22×D4312yes—
252C22×C4C22×D4311yescharacteristic
253C4⋊C4—862no—
254C4⋊C4—864no—
255C22⋊C4—22no—
256C22⋊C4—42no—
257C22⋊C4—864no—
258C22⋊C4—864no—
259C22⋊C4—862no—
260C22⋊C4—1722no—
261C22⋊C4—1722no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—21no—
273C23—432no—
274C23—862no—
275C23—861no—
276C23—862no—
277C23—861no—
278C23—861no—
279C23—862no—
280C23—862no—
281C23—861no—
282C23—861no—
283C23D4×D4314yes—
284C23C23×D4311yescharacteristic
285Q8—868no—
286D4—28no—
287D4—48no—
288D4—8616no—
289D4—1724no—
290D4—1724no—
291D4—1728no—
292D4—1724no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—432no—
300C2×C4—434no—
301C2×C4—434no—
302C2×C4—868no—
303C2×C4—8616no—
304C2×C4—862no—
305C2×C4—862no—
306C2×C4—861no—
307C2×C4—862no—
308C2×C4—862no—
309C2×C4—862no—
310C2×C4—862no—
311C2×C4D4×D4312yes—
312C22—24no—
313C22—24no—
314C22—24no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—42no—
323C22—41no—
324C22—862no—
325C22—862no—
326C22—862no—
327C22—1721no—
328C22—1721no—
329C22—1722no—
330C22—1722no—
331C22—1721no—
332C22—1722no—
333C22—1722no—
334C22C2×D4×D4311yescharacteristic
335C22C2×D4×D4312yes—
336C22#1306337012yes—
337C22#1306337011yescharacteristic
338C22#1306337211yescharacteristic
339C4—22no—
340C4—41no—
341C4—42no—
342C4—434no—
343C4—864no—
344C4—1721no—
345C4—1722no—
346C2—44no—
347C2—81no—
348C2—3441no—
349C2—1722no—
350C2#120×D4311yescharacteristic
351C2#1458346211yescharacteristic
352C2#1458346412yes—
353C2#1458347612yes—
354C2#1458347811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2615
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#10621900C2semidirect
2. C2×#13063298C2semidirect
3. C2×#13063297C2semidirect
4. #14582812C2semidirect
5. #14582811C2semidirect
6. #14582808C2semidirect
7. #14582807C2semidirect
8. #14582807C2semidirect
9. #14582758C2semidirect
10. #14582757C2semidirect
11. C43×#392C2semidirect
63. C22×Dic43D4semidirect
72. C2×C4×D43D4semidirect
186. #392D43semidirect
189. C43#2615semidirect