Finite Group Databasebeta

← #19140323

Subgroups — #19140323

Order 5504.

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

normal subgroups only

This group has 816 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
2C2×#13063303C211yesmaximal, characteristic, complemented
3C2×#13063302C212yesmaximal, complemented
4#14582820C211yesmaximal, characteristic, complemented
5#14582819C211yesmaximal, characteristic, complemented
6#14582815C212yesmaximal, complemented
7#14582814C212yesmaximal, complemented
8#14582813C211yesmaximal, characteristic, complemented
9#14582758C211yesmaximal, characteristic, complemented
10#14582757C212yesmaximal, complemented
11C43×#394C211yesmaximal, characteristic, complemented
12C2×#10621900—28no—
13C2×#10621900—24no—
14C22×Dic86C2211yescharacteristic
15C22×Dic86C2211yescharacteristic
16C22×C22⋊D43C2212yes—
17C23×Dic43C2212yes—
18C22×C4×D43C2211yescharacteristic
19#13063303—24no—
20#13063302—28no—
21C2×C4⋊Dic43C2212yes—
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2212yes—
24C2×Dic43⋊C4C2212yes—
25C2×Dic43⋊C4C2211yescharacteristic
26C2×C22⋊Dic43C2212yes—
27C2×C22⋊Dic43C2212yes—
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2212yes—
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C43⋊#95C2212yes—
34C22×D4×C43C2211yescharacteristic
35C2×C4⋊C4×C43C2211yescharacteristic
36C2×C22⋊C4×C43C2212yes—
37C2×C22⋊C4×C43C2212yes—
38#95×C43C2211yescharacteristic
39C24×C43C2312yes—
40C23×D43C2311yescharacteristic
41C2×D4×C43—22no—
42C2×D4×C43—24no—
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—24no—
48C2×C22⋊D43—24no—
49C2×C22⋊D43—24no—
50C22×Dic43—24no—
51C22×Dic43—24no—
52C22×Dic43D418yes—
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2312yes—
55C22×Dic43C2311yescharacteristic
56C22×Dic43C2312yes—
57C22×Dic43C2311yescharacteristic
58#10621900—232no—
59C2×C4×D43—24no—
60C2×C4×D43D414yes—
61C2×Dic86—22no—
62C2×Dic86—24no—
63C2×Dic86—24no—
64C2×Dic86—22no—
65C4⋊C4×C43—22no—
66C22⋊C4×C43—24no—
67C22⋊C4×C43—42no—
68C22⋊Dic43—24no—
69C22⋊Dic43—42no—
70(C2×D43)⋊C4—22no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4—42no—
73C4⋊Dic43—24no—
74Dic43⋊C4—22no—
75Dic43⋊C4—24no—
76Dic43⋊C4—24no—
77Dic43⋊C4—22no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43C2×D414yes—
85C23×C43C2411yescharacteristic
86C22×D43—22no—
87C22×D43—21no—
88C22×D43—22no—
89C22×D43—21no—
90C22×D43C2×D412yes—
91D4×C43—28no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43C2×D412yes—
102C22⋊D43—216no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—216no—
106C2×Dic43—21no—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—21no—
112C2×Dic43—22no—
113C2×Dic43—21no—
114C2×Dic43C2×D414yes—
115C2×Dic43C2×D414yes—
116C2×Dic43C2×D412yes—
117C4×D43—28no—
118Dic86—28no—
119Dic86—44no—
120C22×C43—24no—
121C22×C43—24no—
122C22×C43—24no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43C22×D412yes—
128C22×C43C22×D411yescharacteristic
129C22×C43H(5,𝔽2)11yescharacteristic
130C22×C432−1+412yes—
131C22×C432−1+411yescharacteristic
132C2×D43—22no—
133C2×D43—22no—
134C2×D43—22no—
135C2×D43—42no—
136C2×D43—42no—
137C4×C43—22no—
138C4×C43—41no—
139C4×C43—42no—
140C4×C43—41no—
141Dic43—24no—
142Dic43—41no—
143Dic43—42no—
144Dic43—41no—
145Dic43#12014yes—
146#2616—431nomaximal, Sylow
147C2×C43—44no—
148C2×C43C2×#12011yescharacteristic
149C2×C43#53611yescharacteristic
150C2×C43#53612yes—
151C2×C43#53712yes—
152C2×C43#53711yescharacteristic
153D43—42no—
154C22×#41—431no—
155C2×C22⋊Q8—431no—
156C2×C22⋊Q8—432no—
157#395—431no—
158#395—431no—
159#394—431no—
160#394—432no—
161#394—432no—
162#394D4311yescharacteristic, complemented
163#380—432no—
164#380—431no—
165C43#261611yescharacteristic, complemented, Sylow
166C2×#41—868no—
167C2×#41—864no—
168C22×Q8—431no—
169C22×Q8—431no—
170C22×D4—432no—
171C22×D4C2×D4311yescharacteristic
172C23×C4—432no—
173C23×C4—431no—
174C22⋊Q8—868no—
175C22⋊Q8—864no—
176C2×C4⋊C4—431no—
177C2×C4⋊C4—432no—
178C2×C4⋊C4—432no—
179C2×C4⋊C4—431no—
180C2×C4⋊C4—432no—
181C2×C4⋊C4C2×D4311yescharacteristic
182C2×C22⋊C4—432no—
183C2×C22⋊C4—431no—
184C2×C22⋊C4—431no—
185C2×C22⋊C4—432no—
186C2×C22⋊C4—432no—
187C2×C22⋊C4C2×D4312yes—
188C2×C22⋊C4C2×D4312yes—
189#95—432no—
190#95—432no—
191#95—431no—
192#95C2×D4311yescharacteristic
193C24—431no—
194C24C22×D4312yes—
195#41—8632no—
196C2×Q8—864no—
197C2×Q8—864no—
198C2×Q8—862no—
199C2×Q8—862no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—864no—
203C2×D4—864no—
204C2×D4—864no—
205C22×C4—431no—
206C22×C4—438no—
207C22×C4—432no—
208C22×C4—434no—
209C22×C4—432no—
210C22×C4—431no—
211C22×C4—431no—
212C22×C4—864no—
213C22×C4—864no—
214C22×C4—864no—
215C22×C4C22×D4311yescharacteristic
216C22×C4C22×D4312yes—
217C22×C4C22×D4311yescharacteristic
218C22×C4C22×D4311yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—864no—
221C4⋊C4—864no—
222C4⋊C4—862no—
223C4⋊C4—864no—
224C4⋊C4—862no—
225C22⋊C4—24no—
226C22⋊C4—42no—
227C22⋊C4—862no—
228C22⋊C4—862no—
229C22⋊C4—864no—
230C22⋊C4—1722no—
231C22⋊C4—1722no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—432no—
239C23—862no—
240C23—861no—
241C23—862no—
242C23—861no—
243C23D4×D4314yes—
244C23C23×D4311yescharacteristic
245Q8—868no—
246Q8—1724no—
247D4—28no—
248D4—8616no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—432no—
259C2×C4—434no—
260C2×C4—434no—
261C2×C4—868no—
262C2×C4—8616no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—862no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4—861no—
271C2×C4—862no—
272C2×C4—861no—
273C2×C4D4×D4312yes—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—862no—
282C22—862no—
283C22—862no—
284C22—1722no—
285C22—1722no—
286C22C2×D4×D4311yescharacteristic
287C22C2×D4×D4312yes—
288C22#1306337011yescharacteristic
289C22#1306337212yes—
290C22#1306337211yescharacteristic
291C4—22no—
292C4—41no—
293C4—42no—
294C4—41no—
295C4—434no—
296C4—864no—
297C4—1721no—
298C4—1722no—
299C4—1721no—
300C2—44no—
301C2—1722no—
302C2#120×D4311yescharacteristic
303C2#1458346911yescharacteristic
304C2#1458347112yes—
305C2#1458347612yes—
306C2#1458347811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2616
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13063303C2semidirect
3. C2×#13063302C2semidirect
4. #14582820C2semidirect
5. #14582819C2semidirect
6. #14582815C2semidirect
7. #14582814C2semidirect
8. #14582813C2semidirect
9. #14582758C2semidirect
10. #14582757C2semidirect
11. C43×#394C2semidirect
162. #394D43semidirect
165. C43#2616semidirect