Finite Group Databasebeta

← #19137998

Subgroups — #19137998

Order 5504.

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

normal subgroups only

This group has 610 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×#13063306C211yesmaximal, characteristic
2C2×#13063281C211yesmaximal, characteristic, complemented
3C22×Dic43⋊C4C211yesmaximal, characteristic, complemented
4#14582830C212yesmaximal, complemented
5#14582822C212yesmaximal, complemented
6#14582795C212yesmaximal, complemented
7#14582787C212yesmaximal, complemented
8#14582779C211yesmaximal, characteristic
9#14582774C211yesmaximal, characteristic, complemented
10#14582762C211yesmaximal, characteristic, complemented
11C2×#123×C43C211yesmaximal, characteristic
12C23×Dic43C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14#13063306—24no—
15#13063281—24no—
16C2×C4⋊Dic43C2212yes—
17C2×Dic43⋊C4—24no—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×Dic43⋊C4C2211yescharacteristic
23C2×C22⋊Dic43C2211yescharacteristic
24C2×C22⋊Dic43C2212yes—
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2211yescharacteristic
27C2×C22⋊Dic43C2211yescharacteristic
28C2×C4×Dic43C2212yes—
29C43⋊#95C2212yes—
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
41C2×D4×C43—22no—
42C2×D4×C43—22no—
43C2×D4×C43—22no—
44C22×C4×C43—22no—
45C22×C4×C43—22no—
46C22×C4×C43—22no—
47C22×C4×C43C2312yes—
48C22×C4×C43C2311yescharacteristic
49C22×C4×C43C2312yes—
50C22×Dic43—24no—
51C22×Dic43—22no—
52C22×Dic43—22no—
53C22×Dic43—22no—
54C22×Dic43D414yes—
55C22×Dic43C2311yescharacteristic
56C22×Dic43C2312yes—
57C22×Dic43C2311yescharacteristic
58C22×Dic43C2311yescharacteristic
59C22×Dic43C2311yescharacteristic
60C22×Dic43C2312yes—
61C4⋊C4×C43—24no—
62C22⋊C4×C43—24no—
63C22⋊C4×C43D414yes—
64C22⋊Dic43—22no—
65C22⋊Dic43—22no—
66C22⋊Dic43—24no—
67C22⋊Dic43—22no—
68C22⋊Dic43—22no—
69C4⋊Dic43—24no—
70Dic43⋊C4—24no—
71Dic43⋊C4—24no—
72Dic43⋊C4—24no—
73Dic43⋊C4—22no—
74Dic43⋊C4—22no—
75C4×Dic43—24no—
76C23×C43—22no—
77C23×C43—22no—
78C23×C43—21no—
79C23×C43—21no—
80C23×C43—22no—
81C23×C43—21no—
82C23×C43—22no—
83C23×C43C2×D412yes—
84C23×C43C2×D412yes—
85C23×C43#4112yes—
86C23×C43C2411yescharacteristic
87D4×C43—44no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—44no—
97C2×C4×C43C2×D414yes—
98C2×Dic43—28no—
99C2×Dic43—28no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—21no—
106C2×Dic43—22no—
107C2×Dic43—21no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43C2×D412yes—
114C2×Dic43C2×D412yes—
115C2×Dic43#4114yes—
116C22×C43—22no—
117C22×C43—22no—
118C22×C43—24no—
119C22×C43—24no—
120C22×C43—41no—
121C22×C43—41no—
122C22×C43—41no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43#12114yes—
126C22×C43C22×D411yescharacteristic
127C22×C43C22×D411yescharacteristic
128C22×C43C2×#4112yes—
129C22×C43C2×#4111yescharacteristic
130C22×C432−1+412yes—
131C4×C43—24no—
132C4×C43—42no—
133C4×C43—41no—
134Dic43—22no—
135Dic43—22no—
136Dic43—24no—
137Dic43—41no—
138Dic43—41no—
139Dic43—42no—
140#2413—431nomaximal, Sylow
141C2×C43—24no—
142C2×C43—81no—
143C2×C43C2×#12111yescharacteristic
144C2×C43#52511yescharacteristic
145C2×C43#53611yescharacteristic
146C2×C43#54712yes—
147C2×C43#55212yes—
148C2×#123—431no—
149C2×#123D4311yescharacteristic
150C2×#117—431no—
151C22×C4⋊C4—431no—
152#398—432no—
153#396—432no—
154#389—432no—
155#388—432no—
156#386—431no—
157#385—431no—
158#381—431no—
159C43#241311yescharacteristic, complemented, Sylow
160C22×D4C2×D4311yescharacteristic
161C23×C4—431no—
162C23×C4—431no—
163C23×C4C2×D4311yescharacteristic
164#123—24no—
165#123—864no—
166#117—864no—
167C2×C4⋊C4—432no—
168C2×C4⋊C4—432no—
169C2×C4⋊C4—432no—
170C2×C4⋊C4—431no—
171C2×C4⋊C4—431no—
172C2×C4⋊C4—432no—
173C2×C4⋊C4—864no—
174C2×C4⋊C4C2×D4312yes—
175C2×C22⋊C4—431no—
176C2×C22⋊C4—431no—
177C2×C22⋊C4—431no—
178C2×C22⋊C4—431no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4C2×D4312yes—
181C2×C22⋊C4C2×D4311yescharacteristic
182C2×C42—432no—
183#95—432no—
184#95—432no—
185#95—432no—
186#95—432no—
187C24C22×D4311yescharacteristic
188C24C22×D4311yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—434no—
196C22×C4—432no—
197C22×C4—431no—
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—432no—
201C22×C4—431no—
202C22×C4—864no—
203C22×C4—862no—
204C22×C4—862no—
205C22×C4—862no—
206C22×C4C22×D4312yes—
207C22×C4C22×D4311yescharacteristic
208C22×C4C22×D4312yes—
209C4⋊C4—24no—
210C4⋊C4—864no—
211C4⋊C4—864no—
212C4⋊C4—862no—
213C4⋊C4—862no—
214C4⋊C4—864no—
215C4⋊C4—864no—
216C22⋊C4—24no—
217C22⋊C4—862no—
218C22⋊C4—862no—
219C22⋊C4—864no—
220C22⋊C4—862no—
221C22⋊C4—862no—
222C22⋊C4C22⋊D4314yes—
223C42—864no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—21no—
228C23—22no—
229C23—21no—
230C23—22no—
231C23D4×D4312yes—
232C23#1062190012yes—
233C23C2×C22⋊D4312yes—
234C23C23×D4311yescharacteristic
235D4—44no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—44no—
245C2×C4—432no—
246C2×C4—432no—
247C2×C4—434no—
248C2×C4—868no—
249C2×C4—868no—
250C2×C4—862no—
251C2×C4—861no—
252C2×C4—861no—
253C2×C4—862no—
254C2×C4—861no—
255C2×C4—861no—
256C2×C4—861no—
257C2×C4—861no—
258C2×C4—862no—
259C2×C4—862no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4C2×C22⋊D4314yes—
264C22—24no—
265C22—22no—
266C22—22no—
267C22—24no—
268C22—42no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22#1306329614yes—
274C22C2×D4×D4311yescharacteristic
275C22C22×C22⋊D4311yescharacteristic
276C22#41×D4312yes—
277C22C2×#1062190011yescharacteristic
278C22#1306337212yes—
279C4—24no—
280C4—42no—
281C4—41no—
282C4—862no—
283C4—862no—
284C4—864no—
285C4—1721no—
286C4—1721no—
287C4—1722no—
288C2—24no—
289C2—81no—
290C2C2×#1306329611yescharacteristic
291C2#1458340711yescharacteristic
292C2#1458347111yescharacteristic
293C2#1458354812yes—
294C2#1458358612yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#123×C43C2
hypercenterC2×#123D43
hypocenterC43#2413
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#13063281C2semidirect
3. C22×Dic43⋊C4C2semidirect
4. #14582830C2semidirect
5. #14582822C2semidirect
6. #14582795C2semidirect
7. #14582787C2semidirect
9. #14582774C2semidirect
10. #14582762C2semidirect
159. C43#2413semidirect