Finite Group Databasebeta

← #19144506

Subgroups — #19144506

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583406C211yesmaximal, characteristic
2#117×D43C211yesmaximal, characteristic, complemented
3#14583239C211yesmaximal, characteristic, complemented
4#14583238C211yesmaximal, characteristic, complemented
5#14583233C211yesmaximal, characteristic, complemented
6#14583228C211yesmaximal, characteristic, complemented
7#14583222C211yesmaximal, characteristic, complemented
8#14583221C211yesmaximal, characteristic, complemented
9#14583216C211yesmaximal, characteristic, complemented
10#14583211C211yesmaximal, characteristic, complemented
11#14582937C211yesmaximal, characteristic, complemented
12#14582935C211yesmaximal, characteristic, complemented
13#14582895C211yesmaximal, characteristic, complemented
14C2×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C43×#416C211yesmaximal, characteristic, complemented
16C22×C4×D43C2211yescharacteristic
17C22×C43⋊C8C2211yescharacteristic
18#13063306—21no—
19#13063301C2211yescharacteristic
20#13063301C2211yescharacteristic
21#13063296C2211yescharacteristic
22#13063296C2211yescharacteristic
23#13063293—21no—
24C4×C22⋊D43—21no—
25C4×C22⋊D43—21no—
26#13063284C2211yescharacteristic
27#13063284C2211yescharacteristic
28#13063283C2211yescharacteristic
29#13063283C2211yescharacteristic
30#13063282—21no—
31#13063281—21no—
32C4⋊C4×D43C2211yescharacteristic
33C4⋊C4×D43C2211yescharacteristic
34C22⋊C4×D43—21no—
35C42×D43—21no—
36#13063259C2211yescharacteristic, complemented
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063258C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41#13063257C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063256C2211yescharacteristic, complemented
44#13063249C2211yescharacteristic, complemented
45#13063249C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54#117×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43D411yescharacteristic
60#41×C43—22no—
61#41×C43—22no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C22×Dic43D411yescharacteristic
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43D411yescharacteristic
75C2×C4×D43D411yescharacteristic
76C2×C4×D43C2311yescharacteristic
77C2×C4×D43C2311yescharacteristic
78C2×C8×C43—22no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C42×C43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—22no—
111C22×D43—22no—
112C22×D43—41no—
113C22×D43C2×D411yescharacteristic
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—42no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—42no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43#4112yes—
126C2×C4×C43#4112yes—
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—42no—
129C22⋊D43—42no—
130C2×Dic43—22no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C4×D43—22no—
138C4×D43—22no—
139C4×D43—21no—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—42no—
144C4×D43—42no—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43#12312yes—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—44no—
162C2×D43#13512yes—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43#12312yes—
167C4×C43C2×#4111yescharacteristic
168C4×C43C2×#4111yescharacteristic
169Dic43—21no—
170Dic43—21no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174Dic43—41no—
175#3091—431nomaximal, Sylow
176C2×C43—22no—
177C2×C43—81no—
178C2×C43C2×#12311yescharacteristic
179C2×C43C2×#13511yescharacteristic
180C2×C43#57511yescharacteristic
181D43—22no—
182D43—41no—
183#525—431no—
184C2×#117—431no—
185#485—431no—
186#485—431no—
187#484—431no—
188#483—431no—
189#482—431no—
190#482—431no—
191#481—431no—
192#480—431no—
193#427—431no—
194#427—431no—
195#416—431no—
196#416D4311yescharacteristic, complemented
197C2×C22⋊C8—431no—
198C43#309111yescharacteristic, complemented, Sylow
199C2×#41C2×D4311yescharacteristic
200C23×C4—431no—
201C22×C8—431no—
202C22×C8C2×D4311yescharacteristic
203#123—861no—
204C22⋊Q8—431no—
205C22⋊Q8—431no—
206#121—431no—
207#121—431no—
208#120—861no—
209C4×D4—861no—
210C4×D4—861no—
211#117—431no—
212#117—431no—
213#117—431no—
214#117—431no—
215#117—861no—
216#117—861no—
217#117C2×D4311yescharacteristic
218C2×C4⋊C4—431no—
219C2×C4⋊C4—431no—
220C2×C22⋊C4—861no—
221C2×C42—861no—
222#107—431no—
223#107—431no—
224#107—431no—
225#107—431no—
226#106—431no—
227#106—431no—
228#106—431no—
229#106—431no—
230#103—431no—
231#103—431no—
232#103C2×D4311yescharacteristic, complemented
233#103C2×D4311yescharacteristic, complemented
234#102—431no—
235#102—431no—
236#102C2×D4311yescharacteristic, complemented
237#102C2×D4311yescharacteristic, complemented
238C22⋊C8—431no—
239C22⋊C8—431no—
240C22⋊C8—431no—
241C22⋊C8—431no—
242C24—431no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D4311yescharacteristic
246C2×D4—21no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C22×C4—21no—
251C22×C4—431no—
252C22×C4—431no—
253C22×C4—431no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—862no—
259C22×C4—862no—
260C22×C4C22×D4311yescharacteristic
261C2×C8—22no—
262C2×C8—431no—
263C2×C8—431no—
264C2×C8—862no—
265C2×C8C22×D4311yescharacteristic
266C2×C8C22×D4311yescharacteristic
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—431no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—21no—
287C42—861no—
288C42—861no—
289C42—861no—
290C42—861no—
291C23—21no—
292C23—431no—
293C23—431no—
294C23—862no—
295C23—862no—
296C23—1721no—
297C23D4×D4311yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—1722no—
304D4—1722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—862no—
312C2×C4—862no—
313C2×C4—862no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—1722no—
323C2×C4—1722no—
324C2×C4#1062189812yes—
325C2×C4D4×D4311yescharacteristic
326C2×C4#1062190012yes—
327C2×C4C23×D4311yescharacteristic
328C8—21no—
329C8—21no—
330C8—861no—
331C8—861no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—432no—
338C22—861no—
339C22—861no—
340C22—861no—
341C22—861no—
342C22—861no—
343C22—1724no—
344C22#1306330712yes—
345C22C2×D4×D4311yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—861no—
350C4—861no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4—1721no—
355C4#1306330712yes—
356C4C2×#1062190011yescharacteristic
357C4C2×#1062189811yescharacteristic
358C2—22no—
359C2—81no—
360C2—862no—
361C2—1721no—
362C2C2×#1306330711yescharacteristic
363C2#135×D4311yescharacteristic
364C2#1458369611yescharacteristic
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#416C2
socleC22×C43C22×D4
hypercenter#416D43
hypocenterC43#3091
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D43C2semidirect
3. #14583239C2semidirect
4. #14583238C2semidirect
5. #14583233C2semidirect
6. #14583228C2semidirect
7. #14583222C2semidirect
8. #14583221C2semidirect
9. #14583216C2semidirect
10. #14583211C2semidirect
11. #14582937C2semidirect
12. #14582935C2semidirect
13. #14582895C2semidirect
14. C2×(C2×D43)⋊C8C2semidirect
15. C43×#416C2semidirect
36. #13063259C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063258C22semidirect
40. #13063257C22semidirect
41. #13063257C22semidirect
42. #13063256C22semidirect
43. #13063256C22semidirect
44. #13063249C22semidirect
45. #13063249C22semidirect
46. #13063246C22semidirect
47. #13063246C22semidirect
55. #103×C43C22semidirect
56. #103×C43C22semidirect
57. #102×C43C22semidirect
58. #102×C43C22semidirect
196. #416D43semidirect
198. C43#3091semidirect
232. #103C2×D43semidirect
233. #103C2×D43semidirect
236. #102C2×D43semidirect
237. #102C2×D43semidirect