Finite Group Databasebeta

← #19146099

Subgroups — #19146099

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×SD16×D43C211yesmaximal, characteristic, complemented
2Q8×C22⋊D43C211yesmaximal, characteristic, complemented
3#14583537C211yesmaximal, characteristic
4#14583292C211yesmaximal, characteristic, complemented
5#14583145C211yesmaximal, characteristic, complemented
6#14583137C211yesmaximal, characteristic, complemented
7#14583123C211yesmaximal, characteristic, complemented
8#14583102C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583053C211yesmaximal, characteristic, complemented
11#14583048C211yesmaximal, characteristic, complemented
12#14583038C211yesmaximal, characteristic, complemented
13#14583000C211yesmaximal, characteristic, complemented
14#14582968C211yesmaximal, characteristic, complemented
15C2×#137×C43C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23SD16×D43—24no—
24C2×C8×D43C2211yescharacteristic
25#13063323—21no—
26#13063323C2211yescharacteristic, complemented
27#13063314C2211yescharacteristic
28#13063308—21no—
29#13063304—21no—
30#13063304C2211yescharacteristic, complemented
31#13063301—21no—
32#13063301C2211yescharacteristic
33#13063301C2211yescharacteristic
34#13063299C2211yescharacteristic
35#13063297—21no—
36#13063293—21no—
37Q8×Dic43C2211yescharacteristic, complemented
38D4×Dic43C2211yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43C2211yescharacteristic
41C2×(C2×D43)⋊C4—21no—
42#13063259C2211yescharacteristic, complemented
43Dic43⋊C8C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063249C2211yescharacteristic, complemented
46#13063249C2211yescharacteristic, complemented
47#13063249C2211yescharacteristic, complemented
48#13063247C2211yescharacteristic
49#13063246C2211yescharacteristic
50C22⋊(C43⋊C8)C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic
52#13063235C2211yescharacteristic, complemented
53C2×#41×C43C2211yescharacteristic
54C22×Q8×C43C2211yescharacteristic, complemented
55#137×C43—24no—
56C2×Q16×C43C2211yescharacteristic, complemented
57C2×Q16×C43C2211yescharacteristic, complemented
58C2×SD16×C43C2211yescharacteristic
59C2×SD16×C43C2211yescharacteristic
60C2×M16×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62#41×C43—22no—
63#41×C43—41no—
64C2×Q8×C43—21no—
65C2×Q8×C43—22no—
66C2×Q8×C43—41no—
67C2×Q8×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×Q8×C43C2311yescharacteristic
70C2×D4×C43—21no—
71C2×D4×C43C2311yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2311yescharacteristic
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C2×C22⋊D43D411yescharacteristic
78C22×Dic43—21no—
79Q8×D43—22no—
80Q8×D43—41no—
81D4×D43—22no—
82D4×D43—41no—
83C2×D172C2311yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43C2311yescharacteristic
86C2×Dic86—21no—
87C2×Dic86C2311yescharacteristic
88Q16×C43—22no—
89Q16×C43—22no—
90SD16×C43—22no—
91SD16×C43D414yescomplemented
92M16×C43—22no—
93C2×C8×C43C2311yescharacteristic
94C2×C8×C43C2311yescharacteristic
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43D411yescharacteristic
98#10621885—41no—
99#10621884—22no—
100#10621884—41no—
101#10621883—22no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4D411yescharacteristic
108C4⋊Dic43—21no—
109C4⋊Dic43C2311yescharacteristic
110C4⋊Dic43C2311yescharacteristic
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116Dic43⋊C4D411yescharacteristic
117C4×Dic43—21no—
118C4×Dic43C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121#10621873—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—42no—
127C22×D43—42no—
128C22×D43—81no—
129C22×D43C2×D411yescharacteristic
130Q8×C43—21no—
131Q8×C43—21no—
132Q8×C43—21no—
133Q8×C43—21no—
134Q8×C43—21no—
135Q8×C43—42no—
136Q8×C43C2×D412yes—
137D4×C43—21no—
138D4×C43—42no—
139D4×C43C2×D412yes—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43C2×D411yescharacteristic
148C2×C4×C43C2411yescharacteristic
149C22⋊D43—22no—
150C22⋊D43—42no—
151C22⋊D43—81no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—81no—
156C2×Dic43C2×D411yescharacteristic
157C2×Dic43C2×D411yescharacteristic
158C2×Dic43C2×D411yescharacteristic
159D172—21no—
160D172—21no—
161C4×D43—21no—
162C4×D43—21no—
163C4×D43—42no—
164Dic86—21no—
165Dic86—21no—
166Dic86—42no—
167C8×C43—21no—
168C8×C43C2×D412yes—
169C43⋊C8—21no—
170C43⋊C8—21no—
171C22×C43—22no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43C22×D411yescharacteristic
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—84no—
184C2×D43#13712yescomplemented
185C4×C43—22no—
186C4×C43—21no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43C22×D411yescharacteristic
190C4×C43H(5,𝔽2)11yescharacteristic
191Dic43—21no—
192Dic43—21no—
193Dic43—21no—
194Dic43—41no—
195Dic43—41no—
196Dic43—41no—
197#3266—431nomaximal, Sylow
198C2×C43—42no—
199C2×C43—41no—
200C2×C43D4211yescharacteristic
201C2×C43C2×#13711yescharacteristic
202C2×C43#57711yescharacteristic
203D43—22no—
204D43—81no—
205C2×#137D4311yescharacteristic, complemented
206C22×SD16—431no—
207D4×Q8—431no—
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×#41C2×D4311yescharacteristic
222C22×Q8—431no—
223C22×Q8C2×D4311yescharacteristic, complemented
224C22×D4—431no—
225#137—24no—
226C2×Q16—431no—
227C2×Q16C2×D4311yescharacteristic, complemented
228C2×Q16C2×D4311yescharacteristic, complemented
229C2×SD16—431no—
230C2×SD16—431no—
231C2×SD16—431no—
232C2×SD16—431no—
233C2×SD16—864no—
234C2×SD16C2×D4311yescharacteristic
235C2×SD16C2×D4311yescharacteristic
236C2×M16C2×D4311yescharacteristic, complemented
237C22×C8—431no—
238C4⋊Q8—431no—
239C4⋊Q8—861no—
240#124—431no—
241#123—861no—
242C22⋊Q8—431no—
243C22⋊Q8—431no—
244C22⋊Q8—431no—
245C22⋊Q8—861no—
246C22⋊Q8—861no—
247#121—431no—
248#121—861no—
249#120—861no—
250C4×Q8—431no—
251C4×D4—431no—
252C4×D4—431no—
253C4×D4—861no—
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—22no—
268#41—41no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—431no—
273C2×Q8—861no—
274C2×Q8—862no—
275C2×Q8—1721no—
276C2×Q8C22×D4311yescharacteristic
277C2×Q8C22×D4311yescharacteristic
278C2×Q8C22×D4311yescharacteristic
279C2×D4—21no—
280C2×D4—431no—
281C2×D4—431no—
282C2×D4—861no—
283C2×D4—862no—
284C2×D4—861no—
285C2×D4—1721no—
286C2×D4C22×D4311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—431no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4C22×D4311yescharacteristic
293Q16—22no—
294Q16—22no—
295Q16—1721no—
296SD16—22no—
297SD16—862no—
298SD16—862no—
299SD16—862no—
300SD16—1721no—
301SD16C22⋊D4314yescomplemented
302M16—22no—
303C2×C8—431no—
304C2×C8—431no—
305C2×C8—862no—
306C2×C8C22×D4311yescharacteristic
307C2×C8C22×D4311yescharacteristic
308C4⋊C4—431no—
309C4⋊C4—431no—
310C4⋊C4—431no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C22⋊C4—431no—
318C22⋊C4—431no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C42—431no—
327C42—861no—
328C23—21no—
329C23—431no—
330C23—861no—
331C23—3441no—
332C23—1722no—
333C23—1722no—
334C23D4×D4311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—861no—
342Q8—861no—
343Q8—1722no—
344Q8C2×C22⋊D4312yes—
345D4—21no—
346D4—42no—
347D4—862no—
348D4—861no—
349D4—861no—
350D4—3441no—
351D4—1722no—
352D4C2×C22⋊D4312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—431no—
361C2×C4—431no—
362C2×C4—431no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—3441no—
369C2×C4—1722no—
370C2×C4D4×D4311yescharacteristic
371C2×C4C23×D4311yescharacteristic
372C8—21no—
373C8—861no—
374C8—861no—
375C8C2×C22⋊D4312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—432no—
383C22—861no—
384C22—861no—
385C22—3444no—
386C22—1721no—
387C22—1721no—
388C22—1721no—
389C22C2×D4×D4311yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—861no—
395C4—861no—
396C4—861no—
397C4—1721no—
398C4—1721no—
399C4—1721no—
400C4C22×C22⋊D4311yescharacteristic
401C4#1306337011yescharacteristic
402C2—41no—
403C2—42no—
404C2—862no—
405C2—3441no—
406C2D4×C22⋊D4311yescharacteristic
407C2#137×D4311yescharacteristic
408C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#137×C43C2
socleC22×C43C22×D4
hypercenterC2×#137D43
hypocenterC43#3266
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D43C2semidirect
2. Q8×C22⋊D43C2semidirect
4. #14583292C2semidirect
5. #14583145C2semidirect
6. #14583137C2semidirect
7. #14583123C2semidirect
8. #14583102C2semidirect
9. #14583061C2semidirect
10. #14583053C2semidirect
11. #14583048C2semidirect
12. #14583038C2semidirect
13. #14583000C2semidirect
14. #14582968C2semidirect
15. C2×#137×C43C2semidirect
18. C2×#10621885C22semidirect
26. #13063323C22semidirect
30. #13063304C22semidirect
37. Q8×Dic43C22semidirect
42. #13063259C22semidirect
43. Dic43⋊C8C22semidirect
44. #13063250C22semidirect
45. #13063249C22semidirect
46. #13063249C22semidirect
47. #13063249C22semidirect
50. C22⋊(C43⋊C8)C22semidirect
52. #13063235C22semidirect
54. C22×Q8×C43C22semidirect
56. C2×Q16×C43C22semidirect
57. C2×Q16×C43C22semidirect
60. C2×M16×C43C22semidirect
91. SD16×C43D4semidirect
184. C2×D43#137semidirect
205. C2×#137D43semidirect
220. C43#3266semidirect
223. C22×Q8C2×D43semidirect
227. C2×Q16C2×D43semidirect
228. C2×Q16C2×D43semidirect
236. C2×M16C2×D43semidirect
301. SD16C22⋊D43semidirect