Finite Group Databasebeta

← #19139530

Subgroups — #19139530

Order 5504.

760 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13063311C211yesmaximal, characteristic, complemented
2C2×#13063303C212yesmaximal, complemented
3C2×#13063298C212yesmaximal, complemented
4C2×#13063287C211yesmaximal, characteristic, complemented
5#14582834C211yesmaximal, characteristic, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582808C211yesmaximal, characteristic, complemented
8#14582800C212yesmaximal, complemented
9#14582799C212yesmaximal, complemented
10#14582750C211yesmaximal, characteristic, complemented
11C43×#399C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C22×D172C2212yes—
15C22×C22⋊D43C2211yescharacteristic
16C22×C22⋊D43C2212yes—
17C22×C4×D43C2212yes—
18#13063311—24no—
19#13063303—28no—
20#13063298—28no—
21#13063287—24no—
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2212yes—
24C2×C22⋊Dic43C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×(C2×D43)⋊C4C2212yes—
29C2×(C2×D43)⋊C4C2212yes—
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×C4×Dic43C2212yes—
32C2×C4×Dic43C2211yescharacteristic
33C43⋊#95C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35C2×C4⋊C4×C43C2211yescharacteristic
36C2×C22⋊C4×C43C2212yes—
37C2×C22⋊C4×C43C2211yescharacteristic
38#95×C43C2211yescharacteristic
39C24×C43C2311yescharacteristic
40C23×D43C2311yescharacteristic
41C23×D43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2312yes—
46C2×C22⋊D43—24no—
47C2×C22⋊D43—24no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43—24no—
50C2×C22⋊D43—42no—
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2312yes—
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2311yescharacteristic
55C2×D172—22no—
56C2×D172—24no—
57C2×D172—24no—
58C2×D172—24no—
59C2×D172—42no—
60C2×C4×D43—24no—
61C2×C4×D43—24no—
62C2×C4×D43—24no—
63C2×Dic86—24no—
64C2×Dic86—22no—
65C4⋊C4×C43—22no—
66C4⋊C4×C43—24no—
67C22⋊C4×C43—24no—
68C22⋊C4×C43—22no—
69C22⋊Dic43—22no—
70(C2×D43)⋊C4—24no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4—24no—
73(C2×D43)⋊C4—24no—
74(C2×D43)⋊C4—24no—
75(C2×D43)⋊C4—22no—
76Dic43⋊C4—24no—
77Dic43⋊C4D418yescomplemented
78C4×Dic43—42no—
79C4×Dic43D414yescomplemented
80C23×C43—21no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—21no—
84C23×C43—21no—
85C23×C43C2411yescharacteristic
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—22no—
90C22×D43—22no—
91C22×D43—22no—
92C22×D43—21no—
93C22×D43—22no—
94C22×D43—22no—
95C22×D43—21no—
96C22×D43—21no—
97C22×D43#4114yes—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—21no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43C2×D412yes—
107C2×C4×C43C2×D414yes—
108C22⋊D43—48no—
109C22⋊D43—44no—
110C2×Dic43—22no—
111C2×Dic43—21no—
112C2×Dic43—22no—
113C2×Dic43—21no—
114C2×Dic43—22no—
115C2×Dic43—21no—
116C2×Dic43C2×D412yes—
117C2×Dic43C2×D414yes—
118C2×Dic43C2×D412yes—
119C2×Dic43C2×D414yes—
120D172—28no—
121D172—48no—
122C4×D43—48no—
123Dic86—44no—
124C22×C43—41no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43C22×D411yescharacteristic
130C22×C43C22×D412yes—
131C22×C43C2×#4112yes—
132C22×C43H(5,𝔽2)11yescharacteristic
133C22×C432−1+411yescharacteristic
134C2×D43—24no—
135C2×D43—24no—
136C2×D43—24no—
137C2×D43—42no—
138C2×D43—42no—
139C2×D43—42no—
140C2×D43—42no—
141C2×D43—41no—
142C2×D43—41no—
143C2×D43—41no—
144C2×D43—42no—
145C2×D43—42no—
146C4×C43—22no—
147C4×C43—24no—
148C4×C43—41no—
149C4×C43—42no—
150Dic43—22no—
151Dic43—24no—
152Dic43—41no—
153Dic43#12714yes—
154#2540—431nomaximal, Sylow
155C2×C43—81no—
156C2×C43#52511yescharacteristic
157C2×C43C2×#12711yescharacteristic
158C2×C43#53711yescharacteristic
159C2×C43#54612yes—
160C2×C43#54812yes—
161D43—44no—
162D43—81no—
163C2×#124—431no—
164C2×C22⋊Q8—432no—
165C2×#121—432no—
166C2×C4×D4—431no—
167#399—431no—
168#399D4311yescharacteristic, complemented
169#392—431no—
170#392—431no—
171#390—432no—
172#390—432no—
173C4×C4⋊C4—431no—
174C43#254011yescharacteristic, complemented, Sylow
175C22×Q8—431no—
176C22×D4—431no—
177C22×D4—432no—
178C22×D4—431no—
179C22×D4—432no—
180C23×C4—432no—
181#124—864no—
182C22⋊Q8—868no—
183#121—868no—
184C4×D4—864no—
185C2×C4⋊C4—432no—
186C2×C4⋊C4—432no—
187C2×C4⋊C4C2×D4311yescharacteristic
188C2×C4⋊C4C2×D4312yes—
189C2×C22⋊C4—431no—
190C2×C22⋊C4—432no—
191C2×C22⋊C4—432no—
192C2×C22⋊C4—432no—
193C2×C22⋊C4—432no—
194C2×C22⋊C4—431no—
195C2×C22⋊C4—431no—
196C2×C22⋊C4C2×D4312yes—
197C2×C22⋊C4C2×D4311yescharacteristic
198C2×C42—431no—
199C2×C42—432no—
200#95—431no—
201#95C2×D4311yescharacteristic
202C24—432no—
203C24—431no—
204C24C22×D4311yescharacteristic
205C2×Q8—864no—
206C2×Q8—862no—
207C2×D4—864no—
208C2×D4—864no—
209C2×D4—864no—
210C2×D4—864no—
211C2×D4—862no—
212C2×D4—864no—
213C2×D4—862no—
214C2×D4—864no—
215C2×D4—1722no—
216C2×D4—1722no—
217C22×C4—431no—
218C22×C4—432no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—864no—
222C22×C4—864no—
223C22×C4—864no—
224C22×C4C22×D4311yescharacteristic
225C22×C4C22×D4312yes—
226C22×C4C22×D4311yescharacteristic
227C22×C4C22×D4312yes—
228C4⋊C4—22no—
229C4⋊C4—24no—
230C4⋊C4—438no—
231C4⋊C4—864no—
232C22⋊C4—24no—
233C22⋊C4—22no—
234C22⋊C4—864no—
235C22⋊C4—864no—
236C22⋊C4—864no—
237C22⋊C4—862no—
238C22⋊C4—862no—
239C22⋊C4—864no—
240C22⋊C4—862no—
241C42—434no—
242C42—1722no—
243C23—21no—
244C23—22no—
245C23—22no—
246C23—21no—
247C23—21no—
248C23—434no—
249C23—862no—
250C23—862no—
251C23—862no—
252C23—862no—
253C23—862no—
254C23—862no—
255C23—861no—
256C23—862no—
257C23—862no—
258C23—861no—
259C23—861no—
260C23C23×D4311yescharacteristic
261Q8—1724no—
262D4—868no—
263D4—1728no—
264D4—1724no—
265D4—1728no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—432no—
275C2×C4—434no—
276C2×C4—432no—
277C2×C4—434no—
278C2×C4—862no—
279C2×C4—861no—
280C2×C4—862no—
281C2×C4—861no—
282C2×C4—861no—
283C2×C4—862no—
284C2×C4—1728no—
285C2×C4D4×D4312yes—
286C2×C4D4×D4314yes—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—864no—
293C22—864no—
294C22—864no—
295C22—1722no—
296C22—1721no—
297C22—1721no—
298C22—1721no—
299C22—1722no—
300C22—1722no—
301C22—1722no—
302C22—1722no—
303C22—1722no—
304C22C2×D4×D4312yes—
305C22C2×D4×D4311yescharacteristic
306C22#41×D4312yes—
307C22#1306337111yescharacteristic
308C22#1306337311yescharacteristic
309C4—22no—
310C4—24no—
311C4—42no—
312C4—41no—
313C4—434no—
314C4—862no—
315C4—864no—
316C4—1721no—
317C2—81no—
318C2—3441no—
319C2—1724no—
320C2#1458340711yescharacteristic
321C2#127×D4311yescharacteristic
322C2#1458347911yescharacteristic
323C2#1458354112yes—
324C2#1458355912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2540
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13063311C2semidirect
2. C2×#13063303C2semidirect
3. C2×#13063298C2semidirect
4. C2×#13063287C2semidirect
5. #14582834C2semidirect
6. #14582809C2semidirect
7. #14582808C2semidirect
8. #14582800C2semidirect
9. #14582799C2semidirect
10. #14582750C2semidirect
11. C43×#399C2semidirect
77. Dic43⋊C4D4semidirect
79. C4×Dic43D4semidirect
168. #399D43semidirect
174. C43#2540semidirect