Finite Group Databasebeta

← #19144845

Subgroups — #19144845

Order 5504.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583510C211yesmaximal, characteristic, complemented
2#14583371C211yesmaximal, characteristic
3#14583239C211yesmaximal, characteristic, complemented
4#14583238C211yesmaximal, characteristic, complemented
5#14583200C211yesmaximal, characteristic, complemented
6#14583199C211yesmaximal, characteristic, complemented
7#14583101C211yesmaximal, characteristic, complemented
8#14583048C211yesmaximal, characteristic
9#14583048C211yesmaximal, characteristic
10#14583002C211yesmaximal, characteristic, complemented
11#14583000C211yesmaximal, characteristic, complemented
12SD16×Dic43C211yesmaximal, characteristic, complemented
13#14582984C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic, complemented
15C43×#461C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19#13063320—21no—
20#13063320—21no—
21#13063317C2211yescharacteristic, complemented
22#13063315—21no—
23#13063315—21no—
24#13063301C2211yescharacteristic
25#13063301C2211yescharacteristic
26Q8×Dic43C2211yescharacteristic, complemented
27Q8×Dic43C2211yescharacteristic, complemented
28C4×D172C2211yescharacteristic
29D4×Dic43C2211yescharacteristic
30#13063287C2211yescharacteristic
31C4×C22⋊D43—21no—
32(C22⋊D43)⋊C4—21no—
33#13063283C2211yescharacteristic
34#13063282C2211yescharacteristic
35C2×(C2×D43)⋊C4—21no—
36C22⋊C4×D43—21no—
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C4⋊Q8×C43C2211yescharacteristic, complemented
55C4×D4×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#103×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C2×C22⋊D43—21no—
65C22×Dic43—21no—
66D4×D43—22no—
67D4×D43—22no—
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72SD16×C43—22no—
73SD16×C43—22no—
74C2×C8×C43C2311yescharacteristic
75C2×C8×C43C2311yescharacteristic
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C42×C43C2311yescharacteristic
81C22⋊Dic43—21no—
82#10621884—22no—
83#10621884—22no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4D411yescharacteristic
90(C2×D43)⋊C4D411yescharacteristic
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C22×D43—21no—
110C22×D43—24no—
111C22×D43—81no—
112C22×D43—81no—
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118D4×C43—21no—
119D4×C43#4112yes—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—81no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—24no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—81no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—21no—
136D172#4112yes—
137C4×D43—21no—
138C4×D43—21no—
139C4×D43—81no—
140C4×D43—81no—
141C8×C43—21no—
142C8×C43—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—22no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43C22×D411yescharacteristic
149C2×D43—21no—
150C2×D43—22no—
151C2×D43—21no—
152C2×D43—21no—
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—84no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43C2×#4111yescharacteristic
162C4×C43C2×#4111yescharacteristic
163Dic43—21no—
164Dic43—21no—
165Dic43—21no—
166Dic43—41no—
167Dic43—41no—
168Dic43—41no—
169#3123—431nomaximal, Sylow
170C2×C43—42no—
171C2×C43#52511yescharacteristic
172C2×C43#57711yescharacteristic
173C2×C43#57711yescharacteristic
174D43—41no—
175D43—42no—
176#541—431no—
177#518—431no—
178#485—431no—
179#485—431no—
180#478—431no—
181#478—431no—
182#461—431no—
183#461D4311yescharacteristic, complemented
184#450—431no—
185#450—431no—
186#440—431no—
187#440—431no—
188C4×SD16—431no—
189C4×SD16—431no—
190#433—431no—
191C43#312311yescharacteristic, complemented, Sylow
192C22×D4—431no—
193C2×SD16—431no—
194C2×SD16—431no—
195C2×SD16C2×D4311yescharacteristic
196C2×SD16C2×D4311yescharacteristic
197C4⋊Q8C2×D4311yescharacteristic, complemented
198#126—861no—
199#126—861no—
200#125—431no—
201#125—861no—
202#125—861no—
203C22⋊Q8—431no—
204C22⋊Q8—431no—
205C4×Q8—431no—
206C4×Q8—431no—
207C4×D4—431no—
208C4×D4—431no—
209C4×D4—431no—
210C4×D4—861no—
211C4×D4—861no—
212C4×D4C2×D4311yescharacteristic
213#117—431no—
214#117—431no—
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217#107—431no—
218#107—431no—
219#106—431no—
220#106—431no—
221C4⋊C8—431no—
222C4⋊C8C2×D4311yescharacteristic, complemented
223#103—431no—
224#103—431no—
225#103C2×D4311yescharacteristic, complemented
226#103C2×D4311yescharacteristic, complemented
227#102—431no—
228#102—431no—
229#102—431no—
230#102—431no—
231C22⋊C8—431no—
232C22⋊C8—431no—
233#97—431no—
234C4×C8—431no—
235C24—861no—
236C2×Q8C22×D4311yescharacteristic
237C2×Q8C22×D4311yescharacteristic
238C2×D4—431no—
239C2×D4—861no—
240C2×D4—862no—
241C2×D4—862no—
242C2×D4C22×D4311yescharacteristic
243C22×C4—21no—
244C22×C4—431no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248SD16—22no—
249SD16—22no—
250SD16—862no—
251SD16—862no—
252C2×C8—431no—
253C2×C8—431no—
254C2×C8C22×D4311yescharacteristic
255C2×C8C22×D4311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—431no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4C22×D4311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—431no—
272C22⋊C4—431no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C42—431no—
280C42—861no—
281C42—861no—
282C42—861no—
283C42C22×D4311yescharacteristic
284C23—21no—
285C23—431no—
286C23—864no—
287C23—861no—
288C23—3441no—
289C23—3441no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—432no—
296D4—864no—
297D4—861no—
298D4#1062190012yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—431no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—3441no—
312C2×C4—3441no—
313C2×C4—3441no—
314C2×C4D4×D4311yescharacteristic
315C2×C4D4×D4311yescharacteristic
316C2×C4C23×D4311yescharacteristic
317C8—21no—
318C8—21no—
319C8—861no—
320C8—861no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—861no—
325C22—862no—
326C22—861no—
327C22—861no—
328C22—3444no—
329C22—1721no—
330C22—1721no—
331C22C2×D4×D4311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—861no—
338C4—861no—
339C4—861no—
340C4—1721no—
341C4—1721no—
342C4—1721no—
343C4#41×D4311yescharacteristic
344C4C2×#1062190011yescharacteristic
345C2—42no—
346C2—1721no—
347C2—1722no—
348C2#1458340911yescharacteristic
349C2#1458370511yescharacteristic
350C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#461C2
socleC22×C43C22×D4
hypercenter#461D43
hypocenterC43#3123
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #14583510C2semidirect
3. #14583239C2semidirect
4. #14583238C2semidirect
5. #14583200C2semidirect
6. #14583199C2semidirect
7. #14583101C2semidirect
10. #14583002C2semidirect
11. #14583000C2semidirect
12. SD16×Dic43C2semidirect
13. #14582984C2semidirect
14. #14582959C2semidirect
15. C43×#461C2semidirect
21. #13063317C22semidirect
26. Q8×Dic43C22semidirect
27. Q8×Dic43C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063249C22semidirect
43. #13063249C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
54. C4⋊Q8×C43C22semidirect
56. C4⋊C8×C43C22semidirect
57. #103×C43C22semidirect
58. #103×C43C22semidirect
183. #461D43semidirect
191. C43#3123semidirect
197. C4⋊Q8C2×D43semidirect
222. C4⋊C8C2×D43semidirect
225. #103C2×D43semidirect
226. #103C2×D43semidirect