Finite Group Databasebeta

← #19146106

Subgroups — #19146106

Order 5504.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063356C211yesmaximal, characteristic, complemented
2C22×#10621884C211yesmaximal, characteristic, complemented
3#14583545C211yesmaximal, characteristic
4#14583291C211yesmaximal, characteristic, complemented
5#14583147C211yesmaximal, characteristic, complemented
6#14583138C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583101C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583055C211yesmaximal, characteristic, complemented
11#14583049C211yesmaximal, characteristic, complemented
12#14583038C211yesmaximal, characteristic, complemented
13#14582997C211yesmaximal, characteristic, complemented
14#14582971C211yesmaximal, characteristic, complemented
15D4×Q8×C43C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18#13063356—24no—
19C2×#10621885C2211yescharacteristic, complemented
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621885C2211yescharacteristic, complemented
22C2×#10621884—24no—
23C2×#10621884C2211yescharacteristic
24C2×#10621884C2211yescharacteristic
25C2×#10621884C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27C2×#10621884C2211yescharacteristic
28C2×#10621884C2211yescharacteristic
29C2×#10621877C2211yescharacteristic, complemented
30C22×C43⋊C8C2211yescharacteristic
31#13063313C2211yescharacteristic
32#13063310—21no—
33#13063304C2211yescharacteristic
34#13063299C2211yescharacteristic
35#13063298—21no—
36#13063293—21no—
37C4×D172C2211yescharacteristic
38C22⋊C4×D43—21no—
39#13063258C2211yescharacteristic, complemented
40C4⋊(C43⋊C8)C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C22⋊(C43⋊C8)C2211yescharacteristic, complemented
49#13063236C2211yescharacteristic, complemented
50C22×Q8×C43C2211yescharacteristic
51C22×Q8×C43C2211yescharacteristic, complemented
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43C2211yescharacteristic, complemented
54C22⋊Q8×C43—21no—
55C22⋊Q8×C43—21no—
56C22⋊Q8×C43C2211yescharacteristic
57C22⋊Q8×C43C2211yescharacteristic, complemented
58C4×Q8×C43C2211yescharacteristic, complemented
59C4×D4×C43—21no—
60C4×D4×C43C2211yescharacteristic
61C23×D43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—22no—
65C2×Q8×C43—22no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43C2311yescharacteristic
69C2×Q8×C43C2311yescharacteristic
70C2×Q8×C43C2311yescharacteristic
71C2×D4×C43D411yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2311yescharacteristic
75C22×C4×C43C2311yescharacteristic
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78#10621898—22no—
79#10621898—41no—
80C2×D172—21no—
81C2×D172—22no—
82C2×D172—41no—
83C2×D172C2311yescharacteristic
84C2×D172C2311yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×Dic86C2311yescharacteristic
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43D411yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊C4×C43D411yescharacteristic
98C22⋊C4×C43D411yescharacteristic
99C42×C43—21no—
100C42×C43C2311yescharacteristic
101C22⋊Dic43—21no—
102#10621885—22no—
103#10621885—22no—
104#10621885—41no—
105#10621884—22no—
106#10621884—22no—
107#10621884—22no—
108#10621884—22no—
109#10621884—41no—
110#10621884D414yescomplemented
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—21no—
114(C2×D43)⋊C4—21no—
115C4⋊Dic43C2311yescharacteristic
116Dic43⋊C4—21no—
117#10621877—22no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121C2×C43⋊C8C2311yescharacteristic
122C2×C43⋊C8C2311yescharacteristic
123C23×C43C2×D411yescharacteristic
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—81no—
130Q8×C43—21no—
131Q8×C43—21no—
132Q8×C43—21no—
133Q8×C43—21no—
134Q8×C43—21no—
135Q8×C43—42no—
136Q8×C43—42no—
137Q8×C43C2×D412yes—
138D4×C43—22no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43C2×D411yescharacteristic
150C2×C4×C43C2×D411yescharacteristic
151C2×C4×C43C2×D411yescharacteristic
152C2×C4×C43C2×D411yescharacteristic
153C2×C4×C43C2411yescharacteristic
154C22⋊D43—42no—
155C22⋊D43—81no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158D172—21no—
159D172—21no—
160D172—21no—
161D172—42no—
162D172C2×D412yes—
163C4×D43—42no—
164C4×D43—81no—
165Dic86—21no—
166Dic86—21no—
167C43⋊C8—21no—
168C43⋊C8—21no—
169C43⋊C8—21no—
170C43⋊C8C2×D412yes—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43#13712yescomplemented
177C22×C43C22×D411yescharacteristic
178C2×D43—22no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—84no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—22no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43C22×D411yescharacteristic
194C4×C43H(5,𝔽2)11yescharacteristic
195Dic43—41no—
196Dic43—41no—
197#3266—431nomaximal, Sylow
198C2×C43—22no—
199C2×C43—41no—
200C2×C43D4211yescharacteristic
201C2×C43C2×#13711yescharacteristic
202C2×C43#57711yescharacteristic
203D43—42no—
204D43—81no—
205C2×#137—431no—
206C22×SD16—431no—
207D4×Q8D4311yescharacteristic, complemented
208#546—431no—
209#497—431no—
210#468—431no—
211#467—431no—
212#464—431no—
213#461—431no—
214#452—431no—
215#451—431no—
216#450—431no—
217#448—431no—
218#440—431no—
219#435—431no—
220C43#326611yescharacteristic, complemented, Sylow
221C2×#41—431no—
222C22×Q8C2×D4311yescharacteristic
223C22×Q8C2×D4311yescharacteristic, complemented
224C22×D4—431no—
225#137—864no—
226C2×Q16—431no—
227C2×Q16—431no—
228C2×Q16—431no—
229C2×SD16—431no—
230C2×SD16—431no—
231C2×SD16—431no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—864no—
236C2×M16—431no—
237C22×C8—431no—
238C4⋊Q8—21no—
239C4⋊Q8C2×D4311yescharacteristic, complemented
240#124—431no—
241#123—861no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—431no—
245C22⋊Q8C2×D4311yescharacteristic
246C22⋊Q8C2×D4311yescharacteristic, complemented
247#121—431no—
248#121—861no—
249#120—861no—
250C4×Q8C2×D4311yescharacteristic, complemented
251C4×D4—21no—
252C4×D4—431no—
253C4×D4C2×D4311yescharacteristic
254C2×C22⋊C4—861no—
255#107—431no—
256C4⋊C8—431no—
257#103—431no—
258#103—431no—
259#103—431no—
260#103—431no—
261#102—431no—
262#102—431no—
263C22⋊C8—431no—
264C22⋊C8—431no—
265#97—431no—
266C24—861no—
267#41—862no—
268#41—1721no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—431no—
276C2×Q8C22×D4311yescharacteristic
277C2×Q8C22×D4311yescharacteristic
278C2×Q8C22×D4311yescharacteristic
279C2×D4—431no—
280C2×D4—431no—
281C2×D4—862no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—1721no—
286C2×D4C22⋊D4311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4C22×D4311yescharacteristic
292C22×C4C22×D4311yescharacteristic
293Q16—862no—
294Q16—862no—
295Q16—1721no—
296SD16—434no—
297SD16—862no—
298SD16—862no—
299SD16—862no—
300SD16—862no—
301SD16—1721no—
302M16—862no—
303C2×C8—431no—
304C2×C8—431no—
305C2×C8—431no—
306C2×C8—431no—
307C2×C8—862no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—431no—
314C4⋊C4—861no—
315C4⋊C4C22⋊D4311yescharacteristic
316C4⋊C4C22×D4311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4C22⋊D4311yescharacteristic
325C22⋊C4C22⋊D4311yescharacteristic
326C42—21no—
327C42C22×D4311yescharacteristic
328C23—861no—
329C23—861no—
330C23—3441no—
331C23—1722no—
332C23—1722no—
333C23C2×C22⋊D4311yescharacteristic
334C23C2×C22⋊D4311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—42no—
342Q8—861no—
343Q8—861no—
344Q8D4×D4312yes—
345D4—22no—
346D4—432no—
347D4—861no—
348D4—861no—
349D4—861no—
350D4—3441no—
351D4—1722no—
352D4—1722no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—3441no—
366C2×C4—1722no—
367C2×C4C2×C22⋊D4311yescharacteristic
368C2×C4C2×C22⋊D4311yescharacteristic
369C2×C4C2×C22⋊D4311yescharacteristic
370C2×C4C2×C22⋊D4311yescharacteristic
371C2×C4C23×D4311yescharacteristic
372C8—432no—
373C8—861no—
374C8—861no—
375C8—861no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—862no—
382C22—3444no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22—1721no—
388C22#1306335612yescomplemented
389C22C22×C22⋊D4311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—1721no—
399C4—1721no—
400C4C2×D4×D4311yescharacteristic
401C4#1306337011yescharacteristic
402C2—22no—
403C2—41no—
404C2—3441no—
405C2—1722no—
406C2D4×C22⋊D4311yescharacteristic
407C2C2×#1306335611yescharacteristic
408C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingD4×Q8×C43C2
socleC22×C43C22×D4
hypercenterD4×Q8D43
hypocenterC43#3266
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13063356C2semidirect
2. C22×#10621884C2semidirect
4. #14583291C2semidirect
5. #14583147C2semidirect
6. #14583138C2semidirect
7. #14583121C2semidirect
8. #14583101C2semidirect
9. #14583059C2semidirect
10. #14583055C2semidirect
11. #14583049C2semidirect
12. #14583038C2semidirect
13. #14582997C2semidirect
14. #14582971C2semidirect
15. D4×Q8×C43C2semidirect
19. C2×#10621885C22semidirect
20. C2×#10621885C22semidirect
21. C2×#10621885C22semidirect
29. C2×#10621877C22semidirect
39. #13063258C22semidirect
40. C4⋊(C43⋊C8)C22semidirect
41. #13063249C22semidirect
42. #13063249C22semidirect
43. #13063249C22semidirect
44. #13063248C22semidirect
48. C22⋊(C43⋊C8)C22semidirect
49. #13063236C22semidirect
51. C22×Q8×C43C22semidirect
53. C4⋊Q8×C43C22semidirect
57. C22⋊Q8×C43C22semidirect
58. C4×Q8×C43C22semidirect
110. #10621884D4semidirect
176. C22×C43#137semidirect
207. D4×Q8D43semidirect
220. C43#3266semidirect
223. C22×Q8C2×D43semidirect
239. C4⋊Q8C2×D43semidirect
246. C22⋊Q8C2×D43semidirect
250. C4×Q8C2×D43semidirect
388. C22#13063356semidirect