Finite Group Databasebeta

← #19140485

Subgroups — #19140485

Order 5504.

620 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 131 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×#13063300C211yesmaximal, characteristic, complemented
2C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
3#14582837C211yesmaximal, characteristic, complemented
4#14582817C211yesmaximal, characteristic, complemented
5#14582816C212yesmaximal, complemented
6#14582808C211yesmaximal, characteristic, complemented
7#14582808C212yesmaximal, complemented
8#14582789C212yesmaximal, complemented
9#14582776C212yesmaximal, complemented
10#14582761C211yesmaximal, characteristic, complemented
11C43×#399C211yesmaximal, characteristic, complemented
12C22×D172C2212yes—
13C22×D172C2211yescharacteristic
14C22×C22⋊D43C2211yescharacteristic
15C22×C22⋊D43C2212yes—
16C23×Dic43C2211yescharacteristic
17C22×C4×D43C2211yescharacteristic
18#13063300—24no—
19(C22⋊D43)⋊C4—24no—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2312yes—
39C23×D43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—22no—
45C2×C22⋊D43—22no—
46C2×C22⋊D43—24no—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—42no—
49C2×C22⋊D43—42no—
50C22×Dic43—22no—
51C22×Dic43—42no—
52C22×Dic43C2312yes—
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2311yescharacteristic
55C22×Dic43C2311yescharacteristic
56C2×D172—22no—
57C2×D172—24no—
58C2×D172—42no—
59C2×D172—42no—
60C2×D172—42no—
61C2×C4×D43—42no—
62C2×C4×D43D414yescomplemented
63C4⋊C4×C43—22no—
64C4⋊C4×C43—42no—
65C22⋊C4×C43—22no—
66C22⋊C4×C43—42no—
67(C2×D43)⋊C4—24no—
68(C2×D43)⋊C4—24no—
69(C2×D43)⋊C4—22no—
70(C2×D43)⋊C4—42no—
71(C2×D43)⋊C4—42no—
72(C2×D43)⋊C4—42no—
73Dic43⋊C4—22no—
74C4×Dic43—22no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—22no—
78C23×C43—22no—
79C23×C43#4112yes—
80C23×C43C2411yescharacteristic
81C22×D43—21no—
82C22×D43—21no—
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—22no—
90C22×D43—22no—
91C22×D43—22no—
92C22×D43C2×D412yes—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43C2×D412yes—
103C22⋊D43—28no—
104C22⋊D43—48no—
105C2×Dic43—21no—
106C2×Dic43—21no—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—44no—
114C2×Dic43C2×D412yes—
115C2×Dic43#4112yes—
116D172—44no—
117D172—48no—
118C4×D43—44no—
119C22×C43—22no—
120C22×C43—24no—
121C22×C43—41no—
122C22×C43—41no—
123C22×C43—42no—
124C22×C43C22×D411yescharacteristic
125C22×C43C2×#4111yescharacteristic
126C22×C43C2×#4111yescharacteristic
127C22×C43H(5,𝔽2)12yes—
128C22×C43H(5,𝔽2)12yes—
129C2×D43—22no—
130C2×D43—22no—
131C2×D43—22no—
132C2×D43—42no—
133C2×D43—42no—
134C2×D43—42no—
135C2×D43—42no—
136C2×D43—42no—
137C2×D43—42no—
138C2×D43—42no—
139C2×D43—42no—
140C2×D43—42no—
141C4×C43—22no—
142C4×C43—42no—
143C4×C43—41no—
144C4×C43—42no—
145Dic43—22no—
146Dic43—22no—
147Dic43—41no—
148Dic43—42no—
149#2635—431nomaximal, Sylow
150C2×C43—42no—
151C2×C43#52511yescharacteristic
152C2×C43#53411yescharacteristic
153C2×C43#53511yescharacteristic
154C2×C43#53812yes—
155C2×C43#54012yes—
156D43—42no—
157D43—82no—
158C2×#121—431no—
159C2×C4×D4—431no—
160#400—431no—
161#399D4311yescharacteristic, complemented
162#394—432no—
163#394—431no—
164#392—431no—
165#392—432no—
166#388—432no—
167#386—432no—
168#381—431no—
169C43#263511yescharacteristic, complemented, Sylow
170C22×D4—431no—
171C22×D4—432no—
172C22×D4—432no—
173C22×D4—431no—
174C23×C4—431no—
175C23×C4—431no—
176#121—864no—
177C4×D4—864no—
178C2×C4⋊C4—431no—
179C2×C4⋊C4C2×D4311yescharacteristic
180C2×C4⋊C4C2×D4312yes—
181C2×C22⋊C4—431no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4—432no—
184C2×C22⋊C4—432no—
185C2×C22⋊C4—432no—
186C2×C22⋊C4—432no—
187C2×C22⋊C4C2×D4311yescharacteristic
188C2×C22⋊C4C2×D4312yes—
189C2×C42—431no—
190#95—432no—
191#95—431no—
192#95—432no—
193#95—432no—
194#95C2×D4311yescharacteristic
195C24—431no—
196C24—432no—
197C24C22×D4311yescharacteristic
198C2×D4—864no—
199C2×D4—862no—
200C2×D4—862no—
201C2×D4—862no—
202C2×D4—864no—
203C2×D4—862no—
204C2×D4—1722no—
205C2×D4—1722no—
206C2×D4—1722no—
207C2×D4—1722no—
208C2×D4—1722no—
209C22×C4—431no—
210C22×C4—431no—
211C22×C4—434no—
212C22×C4—432no—
213C22×C4—431no—
214C22×C4—862no—
215C22×C4—1722no—
216C22×C4—1722no—
217C22×C4C22×D4312yes—
218C22×C4C22×D4312yes—
219C22×C4C22×D4311yescharacteristic
220C22×C4C22×D4311yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—42no—
223C4⋊C4—862no—
224C22⋊C4—22no—
225C22⋊C4—42no—
226C22⋊C4—864no—
227C22⋊C4—864no—
228C22⋊C4—862no—
229C22⋊C4—1722no—
230C22⋊C4—1722no—
231C22⋊C4—1722no—
232C42—862no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—432no—
238C23—861no—
239C23—861no—
240C23—862no—
241C23—862no—
242C23—862no—
243C23—862no—
244C23—862no—
245C23—862no—
246C23—862no—
247C23—862no—
248C23—862no—
249C23#1062190212yes—
250C23C23×D4311yescharacteristic
251D4—868no—
252D4—1724no—
253D4—1728no—
254D4—1728no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—432no—
265C2×C4—432no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—862no—
269C2×C4—861no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4—1724no—
275C2×C4—1724no—
276C2×C4D4×D4312yes—
277C22—22no—
278C22—24no—
279C22—41no—
280C22—41no—
281C22—42no—
282C22—862no—
283C22—862no—
284C22—862no—
285C22—1722no—
286C22—1722no—
287C22—1722no—
288C22—1722no—
289C22—1722no—
290C22—1722no—
291C22—1722no—
292C22—1722no—
293C22—1722no—
294C22C2×D4×D4311yescharacteristic
295C22#41×D4311yescharacteristic
296C22C2×#1062190211yescharacteristic
297C22#1306337012yes—
298C22#1306337112yes—
299C4—22no—
300C4—42no—
301C4—41no—
302C4—42no—
303C4—862no—
304C4—862no—
305C4—1721no—
306C4—1722no—
307C2—42no—
308C2—3442no—
309C2—1722no—
310C2#1458341211yescharacteristic
311C2#1458346011yescharacteristic
312C2#1458346211yescharacteristic
313C2#1458348912yes—
314C2#1458350112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2635
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13063300C2semidirect
2. C2×(C22⋊D43)⋊C4C2semidirect
3. #14582837C2semidirect
4. #14582817C2semidirect
5. #14582816C2semidirect
6. #14582808C2semidirect
7. #14582808C2semidirect
8. #14582789C2semidirect
9. #14582776C2semidirect
10. #14582761C2semidirect
11. C43×#399C2semidirect
62. C2×C4×D43D4semidirect
161. #399D43semidirect
169. C43#2635semidirect