Finite Group Databasebeta

← #19138206

Subgroups — #19138206

Order 5504.

914 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 161 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×#10621902C211yesmaximal, characteristic, complemented
2C2×#13063310C211yesmaximal, characteristic, complemented
3C2×#13063300C212yesmaximal, complemented
4#14582816C211yesmaximal, characteristic, complemented
5#14582810C211yesmaximal, characteristic, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582777C212yesmaximal, complemented
8#14582777C212yesmaximal, complemented
9#14582770C212yesmaximal, complemented
10#95×D43C211yesmaximal, characteristic, complemented
11C43×#395C211yesmaximal, characteristic, complemented
12C2×#10621902—28no—
13C2×#10621902—24no—
14C22×D172C2211yescharacteristic
15C22×D172C2211yescharacteristic
16C22×D172C2212yes—
17C22×D172C2212yes—
18C22×C4×D43C2212yes—
19C22×C4×D43C2212yes—
20C22×C4×D43C2211yescharacteristic
21#13063310—24no—
22#13063300—28no—
23C2×Dic43⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2212yes—
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C43⋊#95C2212yes—
34C22×Q8×C43C2211yescharacteristic
35C2×C4⋊C4×C43C2211yescharacteristic
36C2×C4⋊C4×C43C2212yes—
37#95×C43C2211yescharacteristic
38#95×C43C2212yes—
39C23×D43C2311yescharacteristic
40C23×D43C2312yes—
41C23×D43C2311yescharacteristic
42C2×Q8×C43—24no—
43C2×Q8×C43—22no—
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2312yes—
47C22×C4×C43C2311yescharacteristic
48C22×C4×C43C2312yes—
49C22×Dic43C2312yes—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52#10621902—232no—
53C2×D172—22no—
54C2×D172—24no—
55C2×D172—24no—
56C2×D172—24no—
57C2×D172—24no—
58C2×D172—24no—
59C2×D172—24no—
60C2×D172—22no—
61C2×D172—42no—
62C2×D172D418yescomplemented
63C2×C4×D43—24no—
64C2×C4×D43—24no—
65C2×C4×D43—24no—
66C2×C4×D43—24no—
67C2×C4×D43—24no—
68C2×C4×D43—24no—
69C2×C4×D43—42no—
70C2×C4×D43D414yescomplemented
71C4⋊C4×C43—24no—
72C4⋊C4×C43—22no—
73(C2×D43)⋊C4—24no—
74(C2×D43)⋊C4—22no—
75(C2×D43)⋊C4—24no—
76(C2×D43)⋊C4—22no—
77(C2×D43)⋊C4—24no—
78(C2×D43)⋊C4—22no—
79(C2×D43)⋊C4—42no—
80Dic43⋊C4—22no—
81C23×C43C2411yescharacteristic
82C22×D43—22no—
83C22×D43—21no—
84C22×D43—21no—
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—22no—
90C22×D43—22no—
91C22×D43—21no—
92C22×D43—22no—
93C22×D43—22no—
94C22×D43—21no—
95C22×D43—21no—
96C22×D43C2×D414yes—
97C22×D43C2×D412yes—
98C22×D43C2×D414yes—
99Q8×C43—28no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43C2×D414yes—
111C2×C4×C43C2×D412yes—
112C2×C4×C43#4114yescomplemented
113C2×Dic43—22no—
114C2×Dic43—21no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43C2×D412yes—
120D172—28no—
121D172—216no—
122D172—48no—
123D172—44no—
124C4×D43—216no—
125C4×D43—28no—
126C4×D43—48no—
127C22×C43C22×D411yescharacteristic
128C22×C43C22×D412yes—
129C22×C43C2×#4112yes—
130C22×C43H(5,𝔽2)11yescharacteristic
131C22×C432−1+411yescharacteristic
132C2×D43—22no—
133C2×D43—22no—
134C2×D43—24no—
135C2×D43—24no—
136C2×D43—24no—
137C2×D43—24no—
138C2×D43—24no—
139C2×D43—42no—
140C2×D43—42no—
141C2×D43—42no—
142C2×D43—42no—
143C2×D43—41no—
144C2×D43—41no—
145C2×D43—41no—
146C2×D43—42no—
147C2×D43—42no—
148C2×D43#12014yes—
149C4×C43—24no—
150C4×C43—22no—
151C4×C43—24no—
152C4×C43—41no—
153C4×C43—41no—
154Dic43—22no—
155Dic43—41no—
156Dic43—42no—
157#2430—431nomaximal, Sylow
158C2×C43C2×#12011yescharacteristic
159C2×C43#53211yescharacteristic
160C2×C43#53711yescharacteristic
161C2×C43#54612yes—
162C2×C43#54712yes—
163D43—24no—
164D43—44no—
165D43—81no—
166C22×#41—431no—
167C2×#123—431no—
168C2×#121—432no—
169#395D4311yescharacteristic, complemented
170#394—431no—
171#393—431no—
172#392—431no—
173#386—432no—
174#386—432no—
175#385—432no—
176C2×#95—431no—
177C43#243011yescharacteristic, complemented, Sylow
178C2×#41—864no—
179C2×#41—868no—
180C22×Q8C2×D4311yescharacteristic
181C22×D4—432no—
182C22×D4—431no—
183C22×D4—431no—
184C22×D4—432no—
185C23×C4—431no—
186C23×C4—432no—
187C23×C4—432no—
188#123—864no—
189#121—868no—
190C2×C4⋊C4—431no—
191C2×C4⋊C4C2×D4312yes—
192C2×C4⋊C4C2×D4311yescharacteristic
193C2×C22⋊C4—432no—
194C2×C22⋊C4—432no—
195C2×C22⋊C4—431no—
196C2×C22⋊C4—431no—
197C2×C22⋊C4—431no—
198C2×C22⋊C4—432no—
199C2×C22⋊C4—432no—
200#95—432no—
201#95—431no—
202#95—432no—
203#95C2×D4311yescharacteristic
204#95C2×D4312yes—
205C24—431no—
206C24—432no—
207C24—431no—
208#41—8632no—
209C2×Q8—22no—
210C2×Q8—24no—
211C2×D4—438no—
212C2×D4—864no—
213C2×D4—864no—
214C2×D4—864no—
215C2×D4—864no—
216C2×D4—864no—
217C2×D4—862no—
218C2×D4—862no—
219C2×D4—864no—
220C2×D4—1722no—
221C22×C4—431no—
222C22×C4—434no—
223C22×C4—432no—
224C22×C4—431no—
225C22×C4—864no—
226C22×C4—864no—
227C22×C4—864no—
228C22×C4—864no—
229C22×C4—864no—
230C22×C4—864no—
231C22×C4—1722no—
232C22×C4C22×D4311yescharacteristic
233C22×C4C22×D4311yescharacteristic
234C22×C4C22×D4311yescharacteristic
235C22×C4C22×D4312yes—
236C22×C4C22×D4312yes—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—862no—
240C22⋊C4—862no—
241C22⋊C4—864no—
242C22⋊C4—862no—
243C22⋊C4—864no—
244C22⋊C4—862no—
245C22⋊C4—864no—
246C22⋊C4—1722no—
247C23—432no—
248C23—434no—
249C23—434no—
250C23—862no—
251C23—861no—
252C23—861no—
253C23—862no—
254C23—862no—
255C23—862no—
256C23—862no—
257C23—862no—
258C23—862no—
259C23—861no—
260C23—862no—
261C23—862no—
262C23—861no—
263C23—861no—
264C23C23×D4311yescharacteristic
265Q8—28no—
266D4—8616no—
267D4—868no—
268D4—1728no—
269D4—1724no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—432no—
281C2×C4—868no—
282C2×C4—8616no—
283C2×C4—862no—
284C2×C4—861no—
285C2×C4—862no—
286C2×C4—862no—
287C2×C4—862no—
288C2×C4—862no—
289C2×C4—1728no—
290C2×C4D4×D4312yes—
291C2×C4D4×D4314yes—
292C2×C4#1062190214yescomplemented
293C22—434no—
294C22—864no—
295C22—862no—
296C22—862no—
297C22—864no—
298C22—864no—
299C22—864no—
300C22—864no—
301C22—1722no—
302C22—1721no—
303C22—1721no—
304C22—1721no—
305C22—1722no—
306C22—1722no—
307C22—1722no—
308C22—1722no—
309C22—1722no—
310C22C2×D4×D4312yes—
311C22C2×D4×D4311yescharacteristic
312C22C2×#1062190212yes—
313C22#1306337111yescharacteristic
314C22#1306337311yescharacteristic
315C4—22no—
316C4—24no—
317C4—24no—
318C4—41no—
319C4—41no—
320C4—862no—
321C4—1721no—
322C4—1722no—
323C2—864no—
324C2—3441no—
325C2—1724no—
326C2#120×D4311yescharacteristic
327C2#1458345011yescharacteristic
328C2#1458347911yescharacteristic
329C2#1458354012yes—
330C2#1458355212yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2430
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C22×#10621902C2semidirect
2. C2×#13063310C2semidirect
3. C2×#13063300C2semidirect
4. #14582816C2semidirect
5. #14582810C2semidirect
6. #14582809C2semidirect
7. #14582777C2semidirect
8. #14582777C2semidirect
9. #14582770C2semidirect
10. #95×D43C2semidirect
11. C43×#395C2semidirect
62. C2×D172D4semidirect
70. C2×C4×D43D4semidirect
112. C2×C4×C43#41semidirect
169. #395D43semidirect
177. C43#2430semidirect
292. C2×C4#10621902semidirect