Finite Group Databasebeta

← #19140341

Subgroups — #19140341

Order 5504.

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

normal subgroups only

This group has 632 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×#13063308C211yesmaximal, characteristic, complemented
2C2×#13063297C211yesmaximal, characteristic
3C22×C4⋊Dic43C211yesmaximal, characteristic, complemented
4#14582832C212yesmaximal, complemented
5#14582822C212yesmaximal, complemented
6#14582821C212yesmaximal, complemented
7#14582815C212yesmaximal, complemented
8#14582779C211yesmaximal, characteristic, complemented
9#14582776C211yesmaximal, characteristic, complemented
10#14582757C211yesmaximal, characteristic, complemented
11C2×#123×C43C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14C23×Dic43C2211yescharacteristic
15C23×Dic43C2211yescharacteristic
16#13063308—24no—
17#13063297—24no—
18C2×C4⋊Dic43—24no—
19C2×C4⋊Dic43C2212yes—
20C2×C4⋊Dic43C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2212yes—
24C2×C22⋊Dic43C2211yescharacteristic
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C43⋊#95C2212yes—
33C22×D4×C43C2211yescharacteristic
34C23×C4×C43C2211yescharacteristic
35#123×C43—24no—
36C2×C4⋊C4×C43C2212yes—
37C2×C22⋊C4×C43C2212yes—
38C2×C22⋊C4×C43C2211yescharacteristic
39C24×C43C2311yescharacteristic
40C24×C43C2311yescharacteristic
41C23×D43C2311yescharacteristic
42C2×D4×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—22no—
45C22×C4×C43—22no—
46C22×C4×C43—22no—
47C22×C4×C43D414yescomplemented
48C22×C4×C43C2312yes—
49C22×C4×C43C2311yescharacteristic
50C22×C4×C43C2312yes—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—22no—
54C2×C22⋊D43—22no—
55C2×C22⋊D43—42no—
56C22×Dic43—22no—
57C22×Dic43—42no—
58C22×Dic43—42no—
59C22×Dic43D414yes—
60C22×Dic43C2312yes—
61C22×Dic43C2312yes—
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C4⋊C4×C43—24no—
66C22⋊C4×C43—24no—
67C22⋊C4×C43—22no—
68C22⋊Dic43—22no—
69C22⋊Dic43—22no—
70C22⋊Dic43—42no—
71(C2×D43)⋊C4—24no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—42no—
74C4⋊Dic43—24no—
75C4⋊Dic43—24no—
76Dic43⋊C4—24no—
77Dic43⋊C4—22no—
78Dic43⋊C4—42no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43—21no—
82C23×C43—21no—
83C23×C43—21no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43C2×D412yes—
87C23×C43C2×D412yes—
88C23×C43#4112yes—
89C23×C43C2411yescharacteristic
90C22×D43—21no—
91C22×D43—21no—
92C22×D43—21no—
93C22×D43—22no—
94C22×D43—22no—
95D4×C43—44no—
96C2×C4×C43—28no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43C2×D414yes—
106C22⋊D43—44no—
107C22⋊D43—44no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—21no—
111C2×Dic43—22no—
112C2×Dic43—21no—
113C2×Dic43—22no—
114C2×Dic43—21no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—44no—
120C2×Dic43—44no—
121C2×Dic43C2×D412yes—
122C2×Dic43C2×D412yes—
123C22×C43—22no—
124C22×C43—22no—
125C22×C43—24no—
126C22×C43—24no—
127C22×C43—41no—
128C22×C43—41no—
129C22×C43—41no—
130C22×C43—42no—
131C22×C43—42no—
132C22×C43#12114yes—
133C22×C43C22×D411yescharacteristic
134C22×C43C22×D411yescharacteristic
135C22×C43C2×#4111yescharacteristic
136C22×C43H(5,𝔽2)12yes—
137C22×C432−1+412yes—
138C2×D43—41no—
139C2×D43—41no—
140C2×D43—41no—
141C2×D43—42no—
142C2×D43—42no—
143C4×C43—24no—
144C4×C43—41no—
145C4×C43—42no—
146Dic43—22no—
147Dic43—22no—
148Dic43—41no—
149Dic43—42no—
150Dic43—42no—
151#2618—431nomaximal, Sylow
152C2×C43—24no—
153C2×C43—81no—
154C2×C43C2×#12111yescharacteristic
155C2×C43#53411yescharacteristic
156C2×C43#53611yescharacteristic
157C2×C43#53712yes—
158C2×C43#53912yes—
159D43—81no—
160C2×#123—431no—
161C2×#123D4311yescharacteristic, complemented
162C2×#121—431no—
163C22×C4⋊C4—431no—
164#398—432no—
165#396—432no—
166#396—432no—
167#394—432no—
168#386—431no—
169#386—431no—
170#380—431no—
171C43#261811yescharacteristic, complemented, Sylow
172C22×D4—431no—
173C22×D4—431no—
174C22×D4C2×D4311yescharacteristic
175C23×C4—431no—
176C23×C4—431no—
177C23×C4C2×D4311yescharacteristic
178#123—24no—
179#123—864no—
180#121—864no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—432no—
183C2×C4⋊C4—431no—
184C2×C4⋊C4—432no—
185C2×C4⋊C4—432no—
186C2×C4⋊C4—864no—
187C2×C4⋊C4C2×D4312yes—
188C2×C22⋊C4—431no—
189C2×C22⋊C4—431no—
190C2×C22⋊C4—431no—
191C2×C22⋊C4—432no—
192C2×C22⋊C4—432no—
193C2×C22⋊C4—432no—
194C2×C22⋊C4C2×D4311yescharacteristic
195C2×C22⋊C4C2×D4312yes—
196#95—432no—
197#95—432no—
198#95—432no—
199C24—431no—
200C24C22×D4311yescharacteristic
201C24C22×D4311yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—862no—
206C2×D4—862no—
207C2×D4—862no—
208C2×D4—862no—
209C2×D4—1722no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—431no—
213C22×C4—431no—
214C22×C4—434no—
215C22×C4—432no—
216C22×C4—432no—
217C22×C4—431no—
218C22×C4—862no—
219C22×C4—1722no—
220C22×C4—1722no—
221C22×C4C22⋊D4314yescomplemented
222C22×C4C22×D4312yes—
223C22×C4C22×D4311yescharacteristic
224C22×C4C22×D4312yes—
225C4⋊C4—24no—
226C4⋊C4—864no—
227C4⋊C4—864no—
228C4⋊C4—862no—
229C4⋊C4—864no—
230C4⋊C4—1722no—
231C22⋊C4—22no—
232C22⋊C4—24no—
233C22⋊C4—862no—
234C22⋊C4—862no—
235C22⋊C4—862no—
236C22⋊C4—864no—
237C22⋊C4—1722no—
238C22⋊C4—1722no—
239C23—22no—
240C23—22no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—22no—
245C23—22no—
246C23—861no—
247C23—861no—
248C23—861no—
249C23—862no—
250C23—862no—
251C23D4×D4312yes—
252C23#1062190012yes—
253C23C2×C22⋊D4312yes—
254C23C23×D4311yescharacteristic
255D4—44no—
256D4—1724no—
257D4—1724no—
258C2×C4—28no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—432no—
268C2×C4—432no—
269C2×C4—862no—
270C2×C4—862no—
271C2×C4—861no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4—861no—
275C2×C4—861no—
276C2×C4—862no—
277C2×C4—862no—
278C2×C4—862no—
279C2×C4—862no—
280C2×C4—1724no—
281C2×C4—1724no—
282C2×C4C2×C22⋊D4314yes—
283C22—22no—
284C22—22no—
285C22—24no—
286C22—24no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—42no—
292C22—1721no—
293C22—1721no—
294C22—1721no—
295C22—1722no—
296C22—1722no—
297C22#1306329714yes—
298C22C2×D4×D4311yescharacteristic
299C22C22×C22⋊D4311yescharacteristic
300C22C2×#1062190011yescharacteristic
301C22#1306337112yes—
302C22#1306337212yes—
303C4—24no—
304C4—41no—
305C4—42no—
306C4—862no—
307C4—862no—
308C4—1721no—
309C4—1722no—
310C4—1722no—
311C2—24no—
312C2—81no—
313C2—3441no—
314C2C2×#1306329711yescharacteristic
315C2#1458346011yescharacteristic
316C2#1458347111yescharacteristic
317C2#1458347712yes—
318C2#1458349312yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#123×C43C2
hypercenterC2×#123D43
hypocenterC43#2618
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#13063308C2semidirect
3. C22×C4⋊Dic43C2semidirect
4. #14582832C2semidirect
5. #14582822C2semidirect
6. #14582821C2semidirect
7. #14582815C2semidirect
8. #14582779C2semidirect
9. #14582776C2semidirect
10. #14582757C2semidirect
11. C2×#123×C43C2semidirect
47. C22×C4×C43D4semidirect
161. C2×#123D43semidirect
171. C43#2618semidirect
221. C22×C4C22⋊D43semidirect