Finite Group Databasebeta

← #19144796

Subgroups — #19144796

Order 5504.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583504C211yesmaximal, characteristic, complemented
2#14583379C211yesmaximal, characteristic, complemented
3#14583218C211yesmaximal, characteristic, complemented
4#14583213C211yesmaximal, characteristic, complemented
5#14583207C211yesmaximal, characteristic, complemented
6#14583200C211yesmaximal, characteristic, complemented
7#14583100C211yesmaximal, characteristic, complemented
8#14583095C211yesmaximal, characteristic, complemented
9#14583046C211yesmaximal, characteristic, complemented
10#14583046C211yesmaximal, characteristic, complemented
11#14583012C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13C4×#10621873C211yesmaximal, characteristic, complemented
14C4×D344C211yesmaximal, characteristic, complemented
15C43×#433C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×D344C2211yescharacteristic
20C2×D344C2211yescharacteristic
21#13063322C2211yescharacteristic
22#13063317C2211yescharacteristic
23#13063310—21no—
24#13063310—21no—
25#13063299C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063298—21no—
28#13063298—21no—
29C4×Dic86C2211yescharacteristic
30C4×Dic86C2211yescharacteristic
31C4×D172C2211yescharacteristic
32C4×D172C2211yescharacteristic
33C4×D172C2211yescharacteristic
34C4×D172C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36(C22⋊D43)⋊C4—21no—
37#13063283—21no—
38C2×C4⋊Dic43C2211yescharacteristic
39C4⋊C4×D43—21no—
40#13063259C2211yescharacteristic
41#13063259C2211yescharacteristic
42#13063257C2211yescharacteristic
43#13063257C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic
52#117×C43C2211yescharacteristic
53C4⋊C8×C43C2211yescharacteristic
54C4⋊C8×C43C2211yescharacteristic
55C22⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57#97×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C2×C22⋊D43—21no—
61C2×C22⋊D43—21no—
62C2×C22⋊D43—21no—
63C22×Dic43—21no—
64#10621898—22no—
65#10621898—22no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172C2311yescharacteristic
69C2×D172C2311yescharacteristic
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×Dic86C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43D411yescharacteristic
82C4⋊C4×C43D411yescharacteristic
83C22⋊C4×C43D411yescharacteristic
84C22⋊C4×C43D411yescharacteristic
85C42×C43C2311yescharacteristic
86C42×C43C2311yescharacteristic
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104D344—22no—
105D344—22no—
106#10621873—22no—
107#10621873—22no—
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43C2×D411yescharacteristic
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2411yescharacteristic
120C22⋊D43—24no—
121C22⋊D43—81no—
122C22⋊D43—81no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—81no—
129D172—21no—
130D172—21no—
131D172—21no—
132D172—21no—
133D172—21no—
134D172—81no—
135D172—81no—
136D172#4112yes—
137C4×D43—24no—
138C4×D43—81no—
139C4×D43—81no—
140C4×D43—81no—
141C4×D43—81no—
142Dic86—21no—
143Dic86#4112yes—
144C8×C43—21no—
145C8×C43—21no—
146C8×C43—21no—
147C8×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43C22×D411yescharacteristic
152C2×D43—22no—
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43C2×#4111yescharacteristic
167C4×C43C2×#4111yescharacteristic
168Dic43—22no—
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172Dic43—41no—
173#3119—431nomaximal, Sylow
174C2×C43—41no—
175C2×C43#52511yescharacteristic
176C2×C43#57611yescharacteristic
177C2×C43#57711yescharacteristic
178D43—42no—
179D43—81no—
180D43—81no—
181#540—431no—
182#520—431no—
183#481—431no—
184#480—431no—
185#479—431no—
186#478—431no—
187#460—431no—
188#459—431no—
189#449—431no—
190#449—431no—
191#442—431no—
192#440—431no—
193C4×SD16—431no—
194C4×D8—431no—
195#433D4311yescharacteristic, complemented
196C43#311911yescharacteristic, complemented, Sylow
197C2×#41—431no—
198C2×SD16—431no—
199C2×SD16—431no—
200C2×D8—431no—
201C2×D8—431no—
202#127—431no—
203#125—431no—
204#123—861no—
205#123—861no—
206#121—431no—
207#121—431no—
208#121—861no—
209#121—861no—
210C4×Q8—431no—
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—861no—
217C4×D4—861no—
218#117—861no—
219#117C2×D4311yescharacteristic
220C2×C4⋊C4—431no—
221C2×C4⋊C4—861no—
222#107—431no—
223#107—431no—
224#106—431no—
225#106—431no—
226C4⋊C8C2×D4311yescharacteristic
227C4⋊C8C2×D4311yescharacteristic
228#103—431no—
229#103—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102—431no—
236C22⋊C8C2×D4311yescharacteristic
237C22⋊C8C2×D4311yescharacteristic
238#97C2×D4311yescharacteristic
239C4×C8C2×D4311yescharacteristic
240#41—862no—
241#41—862no—
242C2×Q8—431no—
243C2×D4—431no—
244C2×D4—431no—
245C2×D4—431no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4—861no—
250C2×D4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4C22×D4311yescharacteristic
258SD16—862no—
259SD16—862no—
260D8—862no—
261D8—862no—
262C2×C8C22×D4311yescharacteristic
263C2×C8C22×D4311yescharacteristic
264C2×C8C22×D4311yescharacteristic
265C2×C8C22×D4311yescharacteristic
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4D17211yescharacteristic
276C4⋊C4D17211yescharacteristic
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4D17211yescharacteristic
284C22⋊C4D17211yescharacteristic
285C42—861no—
286C42—861no—
287C42C22×D4311yescharacteristic
288C42C22×D4311yescharacteristic
289C23—861no—
290C23—861no—
291C23—861no—
292C23C2×D17211yescharacteristic
293Q8—432no—
294Q8—861no—
295D4—432no—
296D4—864no—
297D4—861no—
298D4—861no—
299D4—861no—
300D4—861no—
301D4—861no—
302D4—3441no—
303D4—3441no—
304D4—3441no—
305D4—3441no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—864no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—3441no—
315C2×C4—3441no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4C2×D17211yescharacteristic
320C2×C4C2×D17211yescharacteristic
321C2×C4C2×D17211yescharacteristic
322C2×C4C2×D17211yescharacteristic
323C2×C4C2×D17211yescharacteristic
324C2×C4C23×D4311yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—862no—
333C22—1721no—
334C22—1721no—
335C22—1721no—
336C22—1721no—
337C22—1721no—
338C22—1721no—
339C22—1721no—
340C22—1721no—
341C22C22×D17211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—862no—
348C4—1721no—
349C4—1721no—
350C4—1721no—
351C4—1721no—
352C4#41×D4311yescharacteristic
353C4#41×D4311yescharacteristic
354C2—41no—
355C2—3441no—
356C2—3441no—
357C2—1722no—
358C2#1458341111yescharacteristic
359C2#1458370411yescharacteristic
360C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#433C2
socleC22×C43C22×D4
hypercenter#433D43
hypocenterC43#3119
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14583504C2semidirect
2. #14583379C2semidirect
3. #14583218C2semidirect
4. #14583213C2semidirect
5. #14583207C2semidirect
6. #14583200C2semidirect
7. #14583100C2semidirect
8. #14583095C2semidirect
9. #14583046C2semidirect
10. #14583046C2semidirect
11. #14583012C2semidirect
12. #14583001C2semidirect
13. C4×#10621873C2semidirect
14. C4×D344C2semidirect
15. C43×#433C2semidirect
195. #433D43semidirect
196. C43#3119semidirect