Finite Group Databasebeta

← #19135134

Subgroups — #19135134

Order 5504.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#14583458C211yesmaximal, characteristic
2#14583372C211yesmaximal, characteristic, complemented
3C2×#13063240C211yesmaximal, characteristic, complemented
4C2×#13063239C211yesmaximal, characteristic, complemented
5#14582666C211yesmaximal, characteristic, complemented
6#14582665C211yesmaximal, characteristic, complemented
7C2×#99×C43C211yesmaximal, characteristic, complemented
8C22×C22⋊D43C2211yescharacteristic
9#13063308C412yescomplemented
10#13063306—21no—
11#13063297—22no—
12#13063294C412yescomplemented
13#13063293—21no—
14C4×C22⋊D43—22no—
15(C22⋊D43)⋊C4—22no—
16#13063281—21no—
17C2×C22⋊Dic43C2211yescharacteristic
18C2×C22⋊Dic43C2211yescharacteristic
19C2×C22⋊Dic43C2211yescharacteristic
20C22⋊C4×D43—21no—
21#13063240—22no—
22#13063239—22no—
23C22×D4×C43C2211yescharacteristic
24C2×C22⋊C4×C43C2211yescharacteristic
25C2×C22⋊C4×C43C2211yescharacteristic
26#99×C43—22no—
27C24×C43C2×C411yescharacteristic, complemented
28C24×C43C2311yescharacteristic
29C23×D43D411yescharacteristic
30C2×D4×C43—21no—
31C2×D4×C43—21no—
32C2×D4×C43—21no—
33C2×D4×C43—21no—
34C2×D4×C43—21no—
35C2×D4×C43—21no—
36C22×C4×C43—21no—
37C22×C4×C43—21no—
38C22×C4×C43C2×C411yescharacteristic, complemented
39C2×C22⋊D43—21no—
40C2×C22⋊D43—21no—
41C2×C22⋊D43—21no—
42C2×C22⋊D43—21no—
43C2×C22⋊D43—22no—
44C2×C22⋊D43C2×C412yes—
45C2×C22⋊D43D412yes—
46C22×Dic43—21no—
47C22×Dic43—21no—
48C22×Dic43—21no—
49C22×Dic43D411yescharacteristic
50C2×C4×D43—22no—
51C22⋊C4×C43—21no—
52C22⋊C4×C43—21no—
53C22⋊C4×C43—21no—
54C22⋊C4×C43D412yescomplemented
55C22⋊Dic43—22no—
56C22⋊Dic43—21no—
57C22⋊Dic43—21no—
58C22⋊Dic43—21no—
59C22⋊Dic43—21no—
60C22⋊Dic43C2×C412yescomplemented
61C22⋊Dic43D412yescomplemented
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66C4×Dic43—22no—
67C23×C43—21no—
68C23×C43—21no—
69C23×C43—21no—
70C23×C43—81no—
71C23×C43—81no—
72C23×C43C22×C411yescharacteristic
73C23×C43C2×D411yescharacteristic
74C23×C43C2×D411yescharacteristic
75C23×C43C2×D411yescharacteristic
76C23×C43C2×D411yescharacteristic
77C23×C43#4111yescharacteristic
78C23×C43#4111yescharacteristic
79C22×D43—21no—
80C22×D43—21no—
81C22×D43—81no—
82C22×D43C22⋊C412yes—
83D4×C43—41no—
84D4×C43—41no—
85D4×C43—41no—
86D4×C43—41no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—41no—
92C2×C4×C43—81no—
93C2×C4×C43—81no—
94C22⋊D43—22no—
95C22⋊D43—22no—
96C22⋊D43—22no—
97C22⋊D43—22no—
98C22⋊D43—82no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—41no—
104C2×Dic43—81no—
105C2×Dic43—81no—
106C2×Dic43—81no—
107C2×Dic43C22⋊C412yes—
108C4×D43—82no—
109C22×C43—41no—
110C22×C43—41no—
111C22×C43—41no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43—41no—
115C22×C43—41no—
116C22×C43—42no—
117C22×C43—41no—
118C22×C43—81no—
119C22×C43—81no—
120C22×C43C2×C22⋊C411yescharacteristic
121C22×C43C4×D411yescharacteristic
122C22×C43C4×D411yescharacteristic
123C22×C43#12011yescharacteristic
124C22×C43#12111yescharacteristic
125C22×C43#12111yescharacteristic
126C22×C43#12311yescharacteristic
127C2×D43—22no—
128C2×D43—42no—
129C2×D43—42no—
130C2×D43—81no—
131C4×C43—42no—
132C4×C43—41no—
133C4×C43—81no—
134Dic43—22no—
135Dic43—42no—
136Dic43—42no—
137Dic43—81no—
138#1913—431nomaximal, Sylow
139C2×C43—21no—
140C2×C43—21no—
141C2×C43—21no—
142C2×C43—21no—
143C2×C43—21no—
144C2×C43—21no—
145C2×C43—21no—
146C2×C43—81no—
147C2×C43#38611yescharacteristic
148D43—42no—
149#534—431no—
150#518—431no—
151C2×#99—431no—
152C2×#99—431no—
153C2×#99D4311yescharacteristic, complemented
154#342—431no—
155#342—431no—
156C43#191311yescharacteristic, complemented, Sylow
157C22×D4—431no—
158C22×D4C2×D4311yescharacteristic
159#123—432no—
160#123—861no—
161#121—862no—
162#120—432no—
163#120—861no—
164C4×D4—862no—
165C4×D4—862no—
166#117—861no—
167C2×C22⋊C4—431no—
168C2×C22⋊C4—431no—
169C2×C22⋊C4—431no—
170C2×C22⋊C4—861no—
171C2×C22⋊C4C2×D4311yescharacteristic
172C2×C22⋊C4C2×D4311yescharacteristic
173#99—22no—
174#99—862no—
175#99—862no—
176C24—431no—
177C24C4×D4311yescharacteristic, complemented
178C24C22×D4311yescharacteristic
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—432no—
186C2×D4—432no—
187C2×D4—861no—
188C2×D4—861no—
189C2×D4—861no—
190C2×D4—861no—
191C2×D4—862no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—431no—
195C22×C4—862no—
196C22×C4—861no—
197C22×C4—861no—
198C22×C4—861no—
199C22×C4C4×D4311yescharacteristic, complemented
200C4⋊C4—862no—
201C4⋊C4—862no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—432no—
206C22⋊C4—432no—
207C22⋊C4—862no—
208C22⋊C4—862no—
209C22⋊C4—862no—
210C22⋊C4—861no—
211C22⋊C4—861no—
212C22⋊C4—861no—
213C22⋊C4—861no—
214C22⋊C4C22⋊D4312yescomplemented
215C42—862no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—81no—
220C23—81no—
221C23—432no—
222C23—861no—
223C23—861no—
224C23—3441no—
225C23C2×C4×D4311yescharacteristic
226C23#1062189811yescharacteristic
227C23D4×D4311yescharacteristic
228C23D4×D4311yescharacteristic
229C23D4×D4311yescharacteristic
230C23#1062190011yescharacteristic
231C23C2×C22⋊D4311yescharacteristic
232D4—41no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—862no—
237D4—862no—
238D4—862no—
239D4—862no—
240D4—3442no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—432no—
249C2×C4—861no—
250C2×C4—861no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—3442no—
254C2×C4—3441no—
255C2×C4—3441no—
256C2×C4—3441no—
257C2×C4—1721no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—81no—
268C22—81no—
269C22—862no—
270C22—3441no—
271C22—1722no—
272C22—1722no—
273C22C22⋊C4×D4311yescharacteristic
274C22(C22⋊D43)⋊C411yescharacteristic
275C22C4×C22⋊D4311yescharacteristic
276C22#1306329311yescharacteristic
277C22#1306329611yescharacteristic
278C22#1306329811yescharacteristic
279C22#1306330711yescharacteristic
280C4—42no—
281C4—41no—
282C4—81no—
283C4—862no—
284C4—3441no—
285C4—1722no—
286C4—1722no—
287C2—21no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2—81no—
295C2—1722no—
296C2#1458277511yescharacteristic
subgroupG/H
centerC2#14582775
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC2×#99×C43C2
socleC2×C43#386
hypercenterC2×#99D43
hypocenterC43#1913
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #14583372C2semidirect
3. C2×#13063240C2semidirect
4. C2×#13063239C2semidirect
5. #14582666C2semidirect
6. #14582665C2semidirect
7. C2×#99×C43C2semidirect
9. #13063308C4semidirect
12. #13063294C4semidirect
27. C24×C43C2×C4semidirect
38. C22×C4×C43C2×C4semidirect
54. C22⋊C4×C43D4semidirect
60. C22⋊Dic43C2×C4semidirect
61. C22⋊Dic43D4semidirect
153. C2×#99D43semidirect
156. C43#1913semidirect
177. C24C4×D43semidirect
199. C22×C4C4×D43semidirect
214. C22⋊C4C22⋊D43semidirect