Finite Group Databasebeta

← #19135047

Subgroups — #19135047

Order 5504.

598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13063295C211yesmaximal, characteristic
2C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
3C2×#13063239C211yesmaximal, characteristic, complemented
4C2×#13063239C211yesmaximal, characteristic, complemented
5#14582754C211yesmaximal, characteristic, complemented
6#14582666C211yesmaximal, characteristic, complemented
7C43×#342C211yesmaximal, characteristic, complemented
8C24×D43C2211yescharacteristic
9C22×D172C412yescomplemented
10C22×C22⋊D43C2211yescharacteristic
11C22×C4×D43—21no—
12#13063295—21no—
13#13063295—22no—
14#13063295—21no—
15C2×C22⋊Dic43C2211yescharacteristic
16C2×C22⋊Dic43C2211yescharacteristic
17C2×(C2×D43)⋊C4—21no—
18C2×(C2×D43)⋊C4—22no—
19C2×(C2×D43)⋊C4C412yescomplemented
20C22⋊C4×D43—22no—
21C22⋊C4×D43—22no—
22#13063239—22no—
23#13063239—22no—
24C2×C22⋊C4×C43C2211yescharacteristic
25C2×C22⋊C4×C43C2211yescharacteristic
26C2×C22⋊C4×C43C2211yescharacteristic
27C24×C43C2311yescharacteristic
28C23×D43—21no—
29C23×D43—21no—
30C23×D43—21no—
31C23×D43—21no—
32C23×D43—44no—
33C23×D43C2×C412yes—
34C23×D43C2×C411yescharacteristic, complemented
35C23×D43D411yescharacteristic
36C23×D43D412yes—
37C23×D43D411yescharacteristic
38C22×C4×C43—21no—
39C22×C4×C43—21no—
40C22×C4×C43C2×C412yescomplemented
41C2×C22⋊D43—21no—
42C2×C22⋊D43—21no—
43C2×C22⋊D43—21no—
44C2×C22⋊D43—21no—
45C2×C22⋊D43—21no—
46C2×C22⋊D43—21no—
47C22×Dic43—21no—
48C22×Dic43—21no—
49C22×Dic43C2×C411yescharacteristic, complemented
50C2×D172—22no—
51C2×D172—22no—
52C2×D172—44no—
53C2×C4×D43—24no—
54C2×C4×D43—44no—
55C22⋊C4×C43—21no—
56C22⋊C4×C43—21no—
57C22⋊C4×C43—21no—
58C22⋊C4×C43—21no—
59C22⋊C4×C43—21no—
60C22⋊C4×C43D412yescomplemented
61C22⋊Dic43—21no—
62C22⋊Dic43—21no—
63C22⋊Dic43—21no—
64C22⋊Dic43D412yescomplemented
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—22no—
67(C2×D43)⋊C4—22no—
68(C2×D43)⋊C4—44no—
69C23×C43—42no—
70C23×C43C22×C411yescharacteristic
71C23×C43C2×D411yescharacteristic
72C23×C43C2×D411yescharacteristic
73C23×C43C2×D411yescharacteristic
74C23×C43C2×D411yescharacteristic
75C23×C43#4111yescharacteristic
76C23×C43#4111yescharacteristic
77C22×D43—21no—
78C22×D43—21no—
79C22×D43—24no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—21no—
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—21no—
86C22×D43—24no—
87C22×D43—24no—
88C22×D43—21no—
89C22×D43—21no—
90C22×D43—21no—
91C22×D43—42no—
92C22×D43—42no—
93C22×D43—42no—
94C22×D43—44no—
95C22×D43—44no—
96C22×D43—44no—
97C22×D43—44no—
98C22×D43—42no—
99C22×D43C22⋊C412yes—
100C22×D43C22⋊C412yes—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—41no—
107C22⋊D43—41no—
108C22⋊D43—41no—
109C22⋊D43—41no—
110C22⋊D43—41no—
111C2×Dic43—21no—
112C2×Dic43—21no—
113C2×Dic43—21no—
114C2×Dic43—22no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—41no—
118D172—44no—
119D172—44no—
120C4×D43—48no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—41no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43—41no—
128C22×C43C2×C22⋊C411yescharacteristic
129C22×C43C4×D411yescharacteristic
130C22×C43C4×D411yescharacteristic
131C22×C43#12011yescharacteristic
132C22×C43#12111yescharacteristic
133C22×C43#12111yescharacteristic
134C22×C43#12311yescharacteristic
135C2×D43—24no—
136C2×D43—24no—
137C2×D43—22no—
138C2×D43—22no—
139C2×D43—22no—
140C2×D43—22no—
141C2×D43—22no—
142C2×D43—44no—
143C2×D43—44no—
144C2×D43—44no—
145C2×D43—44no—
146C2×D43—42no—
147C2×D43—42no—
148C2×D43—41no—
149C2×D43—42no—
150C2×D43—81no—
151C2×D43—81no—
152C2×D43#9914yescomplemented
153C4×C43—42no—
154C4×C43—42no—
155C4×C43—81no—
156Dic43—42no—
157Dic43—41no—
158Dic43—81no—
159#1898—431nomaximal, Sylow
160C2×C43—21no—
161C2×C43—21no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43#38611yescharacteristic
167C2×C43C2×#9912yes—
168D43—24no—
169D43—42no—
170D43—81no—
171C2×#120—431no—
172C22×C22⋊C4—431no—
173C2×#99—431no—
174C2×#99—431no—
175#379—431no—
176#342—431no—
177#342D4311yescharacteristic, complemented
178C43#189811yescharacteristic, complemented, Sylow
179C25—431no—
180C22×D4—431no—
181C22×D4—432no—
182C23×C4—861no—
183#120—861no—
184#120—862no—
185#120—861no—
186C2×C22⋊C4—431no—
187C2×C22⋊C4—432no—
188C2×C22⋊C4—431no—
189C2×C22⋊C4—862no—
190C2×C22⋊C4—861no—
191C2×C22⋊C4—862no—
192C2×C22⋊C4—862no—
193C2×C22⋊C4C2×D4311yescharacteristic
194C2×C22⋊C4C2×D4311yescharacteristic
195C2×C22⋊C4C2×D4311yescharacteristic
196#99—862no—
197#99—862no—
198C24—431no—
199C24—432no—
200C24—432no—
201C24—431no—
202C24—431no—
203C24—861no—
204C24—861no—
205C24—861no—
206C24—861no—
207C24—1724no—
208C24C22×D4311yescharacteristic
209C2×D4—862no—
210C2×D4—862no—
211C2×D4—861no—
212C2×D4—861no—
213C2×D4—861no—
214C2×D4—861no—
215C2×D4—861no—
216C2×D4—861no—
217C2×D4—1724no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—431no—
221C22×C4—864no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4—1724no—
225C22×C4C4×D4312yescomplemented
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—432no—
232C22⋊C4—862no—
233C22⋊C4—862no—
234C22⋊C4—864no—
235C22⋊C4—861no—
236C22⋊C4—861no—
237C22⋊C4—861no—
238C22⋊C4—1724no—
239C22⋊C4D17212yescomplemented
240C23—42no—
241C23—432no—
242C23—432no—
243C23—864no—
244C23—864no—
245C23—864no—
246C23—861no—
247C23—861no—
248C23—862no—
249C23—862no—
250C23—861no—
251C23—862no—
252C23—862no—
253C23—861no—
254C23—861no—
255C23—861no—
256C23—861no—
257C23—1722no—
258C23—1722no—
259C23—1722no—
260C23—1722no—
261C23—1724no—
262C23—1724no—
263C23—1724no—
264C23—1724no—
265C23C2×C4×D4311yescharacteristic
266C23C2×D17211yescharacteristic
267C23#1062189811yescharacteristic
268C23D4×D4311yescharacteristic
269C23D4×D4311yescharacteristic
270C23D4×D4311yescharacteristic
271C23#1062190211yescharacteristic
272D4—1724no—
273D4—1724no—
274D4—1721no—
275D4—1721no—
276D4—1721no—
277D4—1721no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—861no—
285C2×C4—861no—
286C2×C4—861no—
287C2×C4—862no—
288C2×C4—1728no—
289C2×C4—1722no—
290C2×C4—1721no—
291C2×C4—1722no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—434no—
300C22—864no—
301C22—864no—
302C22—862no—
303C22—862no—
304C22—862no—
305C22—862no—
306C22—862no—
307C22—3441no—
308C22—3441no—
309C22—1724no—
310C22—1724no—
311C22—1724no—
312C22—1724no—
313C22—1722no—
314C22—1722no—
315C22—1722no—
316C22—1721no—
317C22C22⋊C4×D4311yescharacteristic
318C22#1306328711yescharacteristic
319C22C4×D17211yescharacteristic
320C22#1306329511yescharacteristic
321C22#1306329811yescharacteristic
322C22#1306330011yescharacteristic
323C22#1306331011yescharacteristic
324C4—42no—
325C4—42no—
326C4—81no—
327C4—3441no—
328C4—1722no—
329C4—1721no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2—21no—
335C2—21no—
336C2—864no—
337C2—3441no—
338C2—1722no—
339C2#1458277711yescharacteristic
340C2#99×D4312yes—
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43C2×C22⋊C4
hypercenter#342D43
hypocenterC43#1898
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D43C2semidirect
3. C2×#13063239C2semidirect
4. C2×#13063239C2semidirect
5. #14582754C2semidirect
6. #14582666C2semidirect
7. C43×#342C2semidirect
9. C22×D172C4semidirect
19. C2×(C2×D43)⋊C4C4semidirect
34. C23×D43C2×C4semidirect
40. C22×C4×C43C2×C4semidirect
49. C22×Dic43C2×C4semidirect
60. C22⋊C4×C43D4semidirect
64. C22⋊Dic43D4semidirect
152. C2×D43#99semidirect
177. #342D43semidirect
178. C43#1898semidirect
225. C22×C4C4×D43semidirect
239. C22⋊C4D172semidirect