Finite Group Databasebeta

← #19139528

Subgroups — #19139528

Order 5504.

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

normal subgroups only

This group has 760 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
1C2×#13063311C211yesmaximal, characteristic, complemented
2C2×#13063302C212yesmaximal, complemented
3C2×#13063297C212yesmaximal, complemented
4C2×D4×Dic43C211yesmaximal, characteristic, complemented
5#14582836C211yesmaximal, characteristic, complemented
6#14582835C211yesmaximal, characteristic, complemented
7#14582807C211yesmaximal, characteristic, complemented
8#14582802C212yesmaximal, complemented
9#14582799C212yesmaximal, complemented
10#14582750C211yesmaximal, characteristic, complemented
11C43×#392C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14C22×C22⋊D43C2212yes—
15C23×Dic43C2212yes—
16#13063311—24no—
17#13063302—28no—
18#13063297—28no—
19D4×Dic43—24no—
20C2×C4⋊Dic43C2212yes—
21C2×C4⋊Dic43C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2212yes—
24C2×C22⋊Dic43C2212yes—
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2212yes—
27C2×C22⋊Dic43C2212yes—
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2212yes—
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×C4×Dic43C2212yes—
32C2×C4×Dic43C2211yescharacteristic
33C43⋊#95C2211yescharacteristic
34C22×D4×C43C2211yescharacteristic
35C22×D4×C43C2212yes—
36C2×C22⋊C4×C43C2212yes—
37C2×C22⋊C4×C43C2211yescharacteristic
38#95×C43C2211yescharacteristic
39C24×C43C2311yescharacteristic
40C24×C43C2312yes—
41C23×D43C2311yescharacteristic
42C2×D4×C43—22no—
43C2×D4×C43—24no—
44C2×D4×C43—24no—
45C2×D4×C43—24no—
46C2×D4×C43—42no—
47C22×C4×C43C2311yescharacteristic
48C22×C4×C43C2311yescharacteristic
49C22×C4×C43C2312yes—
50C2×C22⋊D43—24no—
51C2×C22⋊D43—24no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—24no—
54C2×C22⋊D43—42no—
55C22×Dic43—24no—
56C22×Dic43—24no—
57C22×Dic43—24no—
58C22×Dic43C2311yescharacteristic
59C22×Dic43C2312yes—
60C22×Dic43C2312yes—
61C22×Dic43C2311yescharacteristic
62C22×Dic43C2311yescharacteristic
63C2×Dic86—24no—
64C2×Dic86—22no—
65C22⋊C4×C43—24no—
66C22⋊C4×C43—22no—
67C22⋊Dic43—24no—
68C22⋊Dic43—24no—
69C22⋊Dic43—24no—
70C22⋊Dic43—22no—
71(C2×D43)⋊C4—24no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43—24no—
76Dic43⋊C4—24no—
77Dic43⋊C4D418yescomplemented
78C4×Dic43—42no—
79C4×Dic43D414yescomplemented
80C23×C43—22no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43—21no—
87C23×C43—22no—
88C23×C43—22no—
89C23×C43—21no—
90C23×C43—21no—
91C23×C43#4114yes—
92C23×C43C2411yescharacteristic
93C22×D43—21no—
94C22×D43—22no—
95C22×D43—22no—
96C22×D43—21no—
97C22×D43—21no—
98D4×C43—28no—
99D4×C43—48no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—21no—
105C2×C4×C43C2×D412yes—
106C2×C4×C43C2×D414yes—
107C22⋊D43—48no—
108C22⋊D43—44no—
109C2×Dic43—22no—
110C2×Dic43—21no—
111C2×Dic43—22no—
112C2×Dic43—21no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—21no—
117C2×Dic43—22no—
118C2×Dic43—48no—
119C2×Dic43C2×D412yes—
120C2×Dic43C2×D414yes—
121C2×Dic43C2×D412yes—
122C2×Dic43C2×D414yes—
123Dic86—44no—
124C22×C43—24no—
125C22×C43—24no—
126C22×C43—24no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—42no—
131C22×C43—41no—
132C22×C43—41no—
133C22×C43—41no—
134C22×C43—42no—
135C22×C43—42no—
136C22×C43C22×D411yescharacteristic
137C22×C43C22×D412yes—
138C22×C43C2×#4112yes—
139C22×C43H(5,𝔽2)11yescharacteristic
140C22×C432−1+411yescharacteristic
141C2×D43—41no—
142C2×D43—41no—
143C2×D43—41no—
144C2×D43—42no—
145C2×D43—42no—
146C4×C43—22no—
147C4×C43—24no—
148C4×C43—41no—
149Dic43—22no—
150Dic43—24no—
151Dic43—41no—
152Dic43—42no—
153Dic43#12714yes—
154#2540—431nomaximal, Sylow
155C2×C43—44no—
156C2×C43—81no—
157C2×C43#52511yescharacteristic
158C2×C43C2×#12711yescharacteristic
159C2×C43#53711yescharacteristic
160C2×C43#54612yes—
161C2×C43#54812yes—
162D43—81no—
163C2×#124—431no—
164C2×C22⋊Q8—432no—
165C2×#121—432no—
166C2×C4×D4—431no—
167#399—431no—
168#399—431no—
169#392—431no—
170#392D4311yescharacteristic, complemented
171#390—432no—
172#390—432no—
173C4×C4⋊C4—431no—
174C43#254011yescharacteristic, complemented, Sylow
175C22×Q8—431no—
176C22×D4—431no—
177C22×D4—432no—
178C22×D4C2×D4311yescharacteristic
179C22×D4C2×D4312yes—
180C23×C4—432no—
181#124—864no—
182C22⋊Q8—868no—
183#121—868no—
184C4×D4—864no—
185C2×C4⋊C4—432no—
186C2×C4⋊C4—431no—
187C2×C4⋊C4—432no—
188C2×C4⋊C4—432no—
189C2×C22⋊C4—432no—
190C2×C22⋊C4—432no—
191C2×C22⋊C4—432no—
192C2×C22⋊C4—431no—
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—431no—
203C24C22×D4311yescharacteristic
204C24C22×D4312yes—
205C2×Q8—864no—
206C2×Q8—862no—
207C2×D4—24no—
208C2×D4—24no—
209C2×D4—22no—
210C2×D4—24no—
211C2×D4—42no—
212C2×D4—864no—
213C2×D4—864no—
214C2×D4—862no—
215C2×D4—864no—
216C2×D4—1722no—
217C22×C4—431no—
218C22×C4—432no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—432no—
222C22×C4—864no—
223C22×C4—864no—
224C22×C4—864no—
225C22×C4C22×D4311yescharacteristic
226C22×C4C22×D4311yescharacteristic
227C22×C4C22×D4312yes—
228C4⋊C4—438no—
229C4⋊C4—864no—
230C4⋊C4—862no—
231C4⋊C4—864no—
232C22⋊C4—24no—
233C22⋊C4—22no—
234C22⋊C4—862no—
235C22⋊C4—864no—
236C22⋊C4—864no—
237C22⋊C4—864no—
238C22⋊C4—862no—
239C22⋊C4—864no—
240C22⋊C4—862no—
241C42—434no—
242C42—1722no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—21no—
250C23—22no—
251C23—22no—
252C23—21no—
253C23—21no—
254C23—861no—
255C23—862no—
256C23—862no—
257C23—861no—
258C23—861no—
259C23#1062190014yes—
260C23C23×D4311yescharacteristic
261Q8—1724no—
262D4—28no—
263D4—48no—
264D4—1724no—
265D4—1728no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—432no—
272C2×C4—434no—
273C2×C4—432no—
274C2×C4—434no—
275C2×C4—862no—
276C2×C4—861no—
277C2×C4—862no—
278C2×C4—861no—
279C2×C4—862no—
280C2×C4—861no—
281C2×C4—862no—
282C2×C4—862no—
283C2×C4—862no—
284C2×C4—1728no—
285C2×C4D4×D4312yes—
286C2×C4D4×D4314yes—
287C22—24no—
288C22—24no—
289C22—24no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—42no—
299C22—1722no—
300C22—1721no—
301C22—1721no—
302C22—1721no—
303C22—1722no—
304C22C2×D4×D4312yes—
305C22C2×D4×D4311yescharacteristic
306C22C2×#1062190012yes—
307C22#1306337011yescharacteristic
308C22#1306337211yescharacteristic
309C4—22no—
310C4—24no—
311C4—41no—
312C4—434no—
313C4—862no—
314C4—864no—
315C4—1722no—
316C4—1721no—
317C2—44no—
318C2—81no—
319C2—3441no—
320C2#1458340511yescharacteristic
321C2#127×D4311yescharacteristic
322C2#1458347811yescharacteristic
323C2#1458353612yes—
324C2#1458355512yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2540
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13063311C2semidirect
2. C2×#13063302C2semidirect
3. C2×#13063297C2semidirect
4. C2×D4×Dic43C2semidirect
5. #14582836C2semidirect
6. #14582835C2semidirect
7. #14582807C2semidirect
8. #14582802C2semidirect
9. #14582799C2semidirect
10. #14582750C2semidirect
11. C43×#392C2semidirect
77. Dic43⋊C4D4semidirect
79. C4×Dic43D4semidirect
170. #392D43semidirect
174. C43#2540semidirect