Finite Group Databasebeta

← #19142923

Subgroups — #19142923

Order 5504.

688 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063309C211yesmaximal, characteristic, complemented
2C2×#13063306C211yesmaximal, characteristic, complemented
3C2×#13063297C211yesmaximal, characteristic
4C22×C4×Dic43C211yesmaximal, characteristic, complemented
5#14582799C212yesmaximal, complemented
6#14582796C212yesmaximal, complemented
7#14582792C212yesmaximal, complemented
8#14582788C212yesmaximal, complemented
9#14582778C211yesmaximal, characteristic, complemented
10#14582757C211yesmaximal, characteristic, complemented
11C43×#386C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14C23×Dic43C2211yescharacteristic
15C23×Dic43C2211yescharacteristic
16#13063309—24no—
17#13063306—24no—
18#13063297—24no—
19C2×C4⋊Dic43C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×C22⋊Dic43C2211yescharacteristic
24C2×C22⋊Dic43C2212yes—
25C2×C22⋊Dic43C2211yescharacteristic
26C2×(C2×D43)⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2212yes—
29C2×C4×Dic43—24no—
30C2×C4×Dic43C2212yes—
31C2×C4×Dic43C2212yes—
32C43⋊#95C2212yes—
33C43⋊#95C2212yes—
34C22×D4×C43C2211yescharacteristic
35C23×C4×C43C2211yescharacteristic
36C2×C22⋊C4×C43C2212yes—
37C2×C22⋊C4×C43C2211yescharacteristic
38#95×C43C2212yes—
39C24×C43C2311yescharacteristic
40C24×C43C2311yescharacteristic
41C23×D43C2311yescharacteristic
42C2×D4×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—22no—
45C22×C4×C43—24no—
46C22×C4×C43—22no—
47C22×C4×C43C2311yescharacteristic
48C22×C4×C43C2312yes—
49C22×C4×C43C2312yes—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—24no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—22no—
54C2×C22⋊D43—22no—
55C22×Dic43—24no—
56C22×Dic43—22no—
57C22×Dic43—22no—
58C22×Dic43D414yes—
59C22×Dic43D414yescomplemented
60C22×Dic43C2312yes—
61C22×Dic43C2311yescharacteristic
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2312yes—
64C22×Dic43C2311yescharacteristic
65C22⋊C4×C43—24no—
66C22⋊C4×C43—22no—
67C22⋊Dic43—22no—
68C22⋊Dic43—24no—
69C22⋊Dic43—22no—
70(C2×D43)⋊C4—24no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4—24no—
73C4⋊Dic43—24no—
74Dic43⋊C4—22no—
75Dic43⋊C4—24no—
76Dic43⋊C4—24no—
77C4×Dic43—24no—
78C4×Dic43—24no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43—21no—
82C23×C43—21no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43—21no—
86C23×C43C2×D412yes—
87C23×C43C2×D412yes—
88C23×C43#4112yes—
89C23×C43C2411yescharacteristic
90C22×D43—21no—
91C22×D43—21no—
92C22×D43—22no—
93C22×D43—22no—
94C22×D43—21no—
95D4×C43—44no—
96C2×C4×C43—28no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—21no—
105C2×C4×C43#4114yes—
106C22⋊D43—44no—
107C22⋊D43—44no—
108C2×Dic43—28no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—28no—
113C2×Dic43—22no—
114C2×Dic43—21no—
115C2×Dic43—21no—
116C2×Dic43—22no—
117C2×Dic43—22no—
118C2×Dic43—21no—
119C2×Dic43C2×D412yes—
120C2×Dic43C2×D414yes—
121C2×Dic43C2×D412yes—
122C2×Dic43#4114yes—
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×#4112yes—
136C22×C43C2×#4112yes—
137C22×C43C2×#4111yescharacteristic
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—24no—
147Dic43—22no—
148Dic43—41no—
149Dic43—42no—
150Dic43#12314yescomplemented
151#2854—431nomaximal, Sylow
152C2×C43—24no—
153C2×C43—81no—
154C2×C43C2×#12111yescharacteristic
155C2×C43C2×#12311yescharacteristic
156C2×C43#52511yescharacteristic
157C2×C43#52912yes—
158C2×C43#53212yes—
159D43—81no—
160C2×#123—431no—
161C2×#123—431no—
162C2×#121—431no—
163C22×C42—431no—
164#390—432no—
165#389—432no—
166#388—432no—
167#388—432no—
168#386—431no—
169#386D4311yescharacteristic, complemented
170#380—431no—
171C43#285411yescharacteristic, complemented, Sylow
172C22×D4—431no—
173C22×D4—431no—
174C22×D4C2×D4311yescharacteristic
175C23×C4—431no—
176C23×C4—431no—
177C23×C4C2×D4311yescharacteristic
178#123—864no—
179#123—864no—
180#121—864no—
181C2×C4⋊C4—431no—
182C2×C4⋊C4—432no—
183C2×C4⋊C4—432no—
184C2×C4⋊C4—432no—
185C2×C22⋊C4—431no—
186C2×C22⋊C4—431no—
187C2×C22⋊C4—432no—
188C2×C22⋊C4—431no—
189C2×C22⋊C4—432no—
190C2×C22⋊C4—432no—
191C2×C22⋊C4C2×D4311yescharacteristic
192C2×C22⋊C4C2×D4312yes—
193C2×C42—432no—
194C2×C42—432no—
195C2×C42—864no—
196#95—432no—
197#95—432no—
198#95C2×D4312yes—
199C24—431no—
200C24C22×D4311yescharacteristic
201C24C22×D4311yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—862no—
206C2×D4—864no—
207C2×D4—862no—
208C2×D4—862no—
209C2×D4—862no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—431no—
213C22×C4—434no—
214C22×C4—434no—
215C22×C4—431no—
216C22×C4—432no—
217C22×C4—432no—
218C22×C4—431no—
219C22×C4—864no—
220C22×C4—862no—
221C22×C4—862no—
222C22×C4C22×D4312yes—
223C22×C4C22×D4311yescharacteristic
224C22×C4C22×D4312yes—
225C4⋊C4—862no—
226C4⋊C4—864no—
227C4⋊C4—864no—
228C4⋊C4—864no—
229C22⋊C4—22no—
230C22⋊C4—24no—
231C22⋊C4—862no—
232C22⋊C4—864no—
233C22⋊C4—862no—
234C22⋊C4—864no—
235C22⋊C4—862no—
236C22⋊C4—864no—
237C42—864no—
238C42—864no—
239C23—22no—
240C23—22no—
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23—21no—
246C23—861no—
247C23—861no—
248C23—862no—
249C23—862no—
250C23—861no—
251C23#1062189812yes—
252C23D4×D4312yes—
253C23D4×D4312yes—
254C23C23×D4311yescharacteristic
255D4—44no—
256D4—1724no—
257D4—1724no—
258C2×C4—28no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—432no—
268C2×C4—434no—
269C2×C4—432no—
270C2×C4—434no—
271C2×C4—868no—
272C2×C4—868no—
273C2×C4—862no—
274C2×C4—862no—
275C2×C4—862no—
276C2×C4—862no—
277C2×C4—861no—
278C2×C4—861no—
279C2×C4—862no—
280C2×C4—862no—
281C2×C4—861no—
282C2×C4#1062190014yes—
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#1306329814yes—
298C22C2×D4×D4311yescharacteristic
299C22C2×D4×D4311yescharacteristic
300C22#41×D4312yes—
301C22C2×#1062190012yes—
302C22C2×#1062189811yescharacteristic
303C4—24no—
304C4—41no—
305C4—42no—
306C4—434no—
307C4—864no—
308C4—862no—
309C4—1721no—
310C4—1722no—
311C2—24no—
312C2—81no—
313C2—3441no—
314C2C2×#1306329811yescharacteristic
315C2#123×D4311yescharacteristic
316C2#1458340511yescharacteristic
317C2#1458342912yes—
318C2#1458344412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#386C2
hypercenter#386D43
hypocenterC43#2854
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13063309C2semidirect
2. C2×#13063306C2semidirect
4. C22×C4×Dic43C2semidirect
5. #14582799C2semidirect
6. #14582796C2semidirect
7. #14582792C2semidirect
8. #14582788C2semidirect
9. #14582778C2semidirect
10. #14582757C2semidirect
11. C43×#386C2semidirect
59. C22×Dic43D4semidirect
150. Dic43#123semidirect
169. #386D43semidirect
171. C43#2854semidirect