Finite Group Databasebeta

← #19146763

Subgroups — #19146763

Order 5504.

388 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#14583602C211yesmaximal, characteristic
2Q8×D172C211yesmaximal, characteristic, complemented
3#14583269C211yesmaximal, characteristic, complemented
4#14583243C211yesmaximal, characteristic, complemented
5#14583236C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583105C211yesmaximal, characteristic, complemented
9#14583039C211yesmaximal, characteristic, complemented
10#14583039C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582906C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#479C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×#10621872C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063325—21no—
24#13063325C2211yescharacteristic
25#13063320—21no—
26#13063310—21no—
27#13063305—21no—
28#13063305—21no—
29#13063305C2211yescharacteristic
30#13063305C2211yescharacteristic
31#13063300—21no—
32#13063300C2211yescharacteristic
33#13063300C2211yescharacteristic
34C4×D172—21no—
35C4×D172C2211yescharacteristic
36C4×D172C2211yescharacteristic
37#13063287—21no—
38#13063283C2211yescharacteristic
39C4⋊C4×D43C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52#125×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60Q8×D43—22no—
61Q8×D43—22no—
62Q8×D43—41no—
63Q8×D43—41no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172D411yescharacteristic
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43C2311yescharacteristic
73C2×C4×D43C2311yescharacteristic
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86C2311yescharacteristic
77C2×Dic86C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C42×C43—21no—
87C42×C43C2311yescharacteristic
88#10621884—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4D411yescharacteristic
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43D411yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107#10621873—41no—
108#10621873—41no—
109#10621872—41no—
110C8×D43—41no—
111C22×D43—21no—
112C22×D43C2×D411yescharacteristic
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43#4112yes—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2411yescharacteristic
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128D172—22no—
129D172—21no—
130D172—21no—
131D172—42no—
132D172—81no—
133C4×D43—21no—
134C4×D43—21no—
135C4×D43—21no—
136C4×D43—21no—
137C4×D43—42no—
138C4×D43—42no—
139C4×D43—81no—
140C4×D43—81no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145Dic86—42no—
146Dic86—42no—
147C8×C43—21no—
148C8×C43—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43C22×D411yescharacteristic
152C2×D43—21no—
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—21no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43#13712yes—
161C4×C43—22no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43C2×#4111yescharacteristic
168C4×C43H(5,𝔽2)11yescharacteristic
169Dic43—21no—
170Dic43—21no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3320—431nomaximal, Sylow
175C2×C43#54611yescharacteristic
176C2×C43C2×#13711yescharacteristic
177C2×C43#57711yescharacteristic
178D43—22no—
179D43—41no—
180D43—81no—
181#553—431no—
182D4×Q8—431no—
183#491—431no—
184#485—431no—
185#484—431no—
186#479D4311yescharacteristic, complemented
187#468—431no—
188#465—431no—
189#461—431no—
190#448—431no—
191#448—431no—
192#440—431no—
193#435—431no—
194#419—431no—
195C2×#103—431no—
196C43#332011yescharacteristic, complemented, Sylow
197C22×Q8—431no—
198C22×Q8—431no—
199C2×SD16—431no—
200C2×SD16—431no—
201C2×SD16—431no—
202C2×M16—431no—
203C22×C8—431no—
204C4⋊Q8—431no—
205C4⋊Q8—861no—
206#126—861no—
207#125C2×D4311yescharacteristic
208#123—861no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212C22⋊Q8—861no—
213#121—431no—
214#121—431no—
215#121—861no—
216C4×Q8C2×D4311yescharacteristic
217C4×D4—431no—
218C4×D4—431no—
219C4×D4—861no—
220C4×D4—861no—
221#117—431no—
222C2×C4⋊C4—431no—
223#107—431no—
224#107C2×D4311yescharacteristic
225#106C2×D4311yescharacteristic
226C4⋊C8C2×D4311yescharacteristic
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103C2×D4311yescharacteristic
235#103C2×D4311yescharacteristic
236#102—431no—
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240C2×Q8—431no—
241C2×Q8—431no—
242C2×Q8—861no—
243C2×Q8—861no—
244C2×Q8—862no—
245C2×Q8—862no—
246C2×Q8—1721no—
247C2×Q8—1721no—
248C2×Q8C22×D4311yescharacteristic
249C2×D4—431no—
250C2×D4—431no—
251C2×D4—861no—
252C2×D4—861no—
253C22×C4—431no—
254C22×C4—431no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259SD16—862no—
260SD16—1721no—
261SD16—1721no—
262M16—1721no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—1721no—
266C2×C8C22×D4311yescharacteristic
267C2×C8C22×D4311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—431no—
272C4⋊C4—431no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4C22×D4311yescharacteristic
279C4⋊C4C22×D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C22⋊C4—431no—
282C22⋊C4—431no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C42—21no—
290C42—861no—
291C42C22×D4311yescharacteristic
292C23—431no—
293C23—431no—
294C23—861no—
295Q8—21no—
296Q8—861no—
297Q8—861no—
298Q8—861no—
299Q8—861no—
300Q8—1722no—
301Q8—1722no—
302Q8#1062190212yes—
303D4—862no—
304D4—861no—
305D4—861no—
306D4—3441no—
307D4—1722no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4D4×D4311yescharacteristic
326C2×C4D4×D4311yescharacteristic
327C2×C4C23×D4311yescharacteristic
328C8—21no—
329C8—21no—
330C8—861no—
331C8—861no—
332C22—432no—
333C22—861no—
334C22—861no—
335C22—861no—
336C22—861no—
337C22—861no—
338C22—1721no—
339C22—1721no—
340C22—1721no—
341C22C2×D4×D4311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—861no—
349C4—861no—
350C4—1721no—
351C4—1721no—
352C4—1721no—
353C4C2×#1062190211yescharacteristic
354C4#1306337111yescharacteristic
355C2—862no—
356C2—3441no—
357C2—1721no—
358C2#1458354011yescharacteristic
359C2#137×D4311yescharacteristic
360C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#479C2
socleC22×C43C22×D4
hypercenter#479D43
hypocenterC43#3320
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. Q8×D172C2semidirect
3. #14583269C2semidirect
4. #14583243C2semidirect
5. #14583236C2semidirect
6. #14583146C2semidirect
7. #14583129C2semidirect
8. #14583105C2semidirect
9. #14583039C2semidirect
10. #14583039C2semidirect
11. #14582997C2semidirect
12. #14582969C2semidirect
13. #14582906C2semidirect
14. #103×D43C2semidirect
15. C43×#479C2semidirect
186. #479D43semidirect
196. C43#3320semidirect