Finite Group Databasebeta

← #13058484

Subgroups — #13058484

Order 1344.

692 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊D7C211yesmaximal, characteristic, complemented
2C2×D7×D12C211yesmaximal, characteristic, complemented
3#10621367C211yesmaximal, characteristic, complemented
4C7×#882C211yesmaximal, characteristic, complemented
5C3×#6446C211yesmaximal, characteristic, complemented
6#10621139C211yesmaximal, characteristic, complemented
7#10621132C211yesmaximal, characteristic, complemented
8#10621119C211yesmaximal, characteristic, complemented
9#10621037C211yesmaximal, characteristic, complemented
10#10621035C211yesmaximal, characteristic, complemented
11#10621028C211yesmaximal, characteristic, complemented
12#10621009C211yesmaximal, characteristic, complemented
13#10620989C211yesmaximal, characteristic, complemented
14#10620985C211yesmaximal, characteristic, complemented
15#10620982C211yesmaximal, characteristic, complemented
16#90280—31nomaximal, Hall
17C23×D3×C7C2211yescharacteristic, complemented
18C22×D3×D7C2211yescharacteristic
19C22×D3×D7C2211yescharacteristic, complemented
20C2×#4268C2211yescharacteristic, complemented
21C2×#4268C2211yescharacteristic, complemented
22C2×D84C2211yescharacteristic, complemented
23C2×C4×D21C2211yescharacteristic, complemented
24C2×C7×#67C2211yescharacteristic, complemented
25C2×C7×D12C2211yescharacteristic
26C2×C7×D12C2211yescharacteristic, complemented
27C2×C3×C22⋊D7C2211yescharacteristic
28C2×C3×C4×D7C2211yescharacteristic, complemented
29D3×C22⋊D7—24no—
30C2×#4247C2211yescharacteristic
31C2×#4247C2211yescharacteristic, complemented
32C2×#4247C2211yescharacteristic, complemented
33C2×#4247C2211yescharacteristic, complemented
34C2×#4245C2211yescharacteristic
35C2×D21⋊C4C2211yescharacteristic, complemented
36C2×D3×Dic7C2211yescharacteristic, complemented
37D7×D12—24no—
38C3×C7×C22⋊C4C2211yescharacteristic, complemented
39#66631C2211yescharacteristic, complemented
40#66629C2211yescharacteristic, complemented
41C7×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C7×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×C22⋊Dic7C2211yescharacteristic, complemented
44C3×(C2×D7)⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic7C2211yescharacteristic, complemented
46C3×Dic7⋊C4C2211yescharacteristic, complemented
47Dic3⋊Dic7C2211yescharacteristic, complemented
48#66575C2211yescharacteristic, complemented
49(C2×D3)⋊Dic7C2211yescharacteristic, complemented
50(C2×D3)⋊Dic7C2211yescharacteristic, complemented
51(C2×D3)⋊Dic7C2211yescharacteristic, complemented
52(C2×D3)⋊Dic7C2211yescharacteristic, complemented
53(C2×D7)⋊Dic3C2211yescharacteristic, complemented
54C22×C22⋊D7—31no—
55C2×D4×D7—31no—
56C7×#120—31no—
57#6516—31no—
58#6501—31no—
59#6501—31no—
60#6500—31no—
61#6500—31no—
62#6498—31no—
63#6449—31no—
64#6447—31no—
65#6447—31no—
66#6446—31no—
67#6446D311yescharacteristic, complemented
68D7×C22⋊C4—31no—
69#5653—71nomaximal, Hall
70C23×C3×C7C2311yescharacteristic
71C22×D21C2311yescharacteristic
72C22×D21C2311yescharacteristic
73C22×D3×C7—22no—
74C22×D3×C7—41no—
75C22×D3×C7—41no—
76C22×D3×C7C2311yescharacteristic
77C22×D3×C7C2311yescharacteristic
78C22×D3×C7C2311yescharacteristic
79C22×C3×D7C2311yescharacteristic
80C2×D3×D7—22no—
81C2×D3×D7—41no—
82C2×D3×D7—41no—
83C2×D3×D7—41no—
84C2×D3×D7—41no—
85C2×D3×D7D414yescomplemented
86C2×C3×C4×C7C2311yescharacteristic
87C2×C3×C4×C7C2311yescharacteristic
88#4268—22no—
89#4268—41no—
90C2×Dic21C2311yescharacteristic
91C2×Dic21C2311yescharacteristic
92D84—22no—
93C4×D21—41no—
94C7×#67—41no—
95C2×C7×Dic3C2311yescharacteristic
96C7×D12—22no—
97C7×D12—41no—
98C3×C22⋊D7—22no—
99C2×C3×Dic7C2311yescharacteristic
100C2×C3×Dic7C2311yescharacteristic
101C2×C3×Dic7C2311yescharacteristic
102C3×C4×D7—22no—
103#4247—22no—
104#4247—22no—
105#4247—22no—
106#4247—41no—
107#4245—22no—
108D21⋊C4—41no—
109D3×Dic7—22no—
110C24×C7—31no—
111C23×D7—31no—
112C23×D7—31no—
113C2×C7×D4—31no—
114C2×C7×D4—31no—
115C2×C7×D4—31no—
116C2×C22⋊D7—31no—
117C2×C22⋊D7—31no—
118C2×C22⋊D7—31no—
119C2×C22⋊D7—31no—
120C2×C22⋊D7—31no—
121C2×C22⋊D7—31no—
122C2×C22⋊D7—31no—
123C2×C22⋊D7—64no—
124C2×C22⋊D7C2×D311yescharacteristic
125C22×Dic7—31no—
126D4×D7—64no—
127C2×D28—31no—
128C2×C4×D7—31no—
129C2×C4×D7—31no—
130C2×C4×D7C2×D311yescharacteristic, complemented
131C7×C22⋊C4—31no—
132C7×C22⋊C4—31no—
133C7×C22⋊C4C2×D311yescharacteristic, complemented
134C22⋊Dic7—31no—
135C22⋊Dic7—31no—
136C22⋊Dic7—31no—
137C22⋊Dic7—31no—
138C22⋊Dic7C2×D311yescharacteristic, complemented
139(C2×D7)⋊C4—31no—
140(C2×D7)⋊C4—31no—
141(C2×D7)⋊C4—31no—
142(C2×D7)⋊C4C2×D311yescharacteristic, complemented
143C4⋊Dic7—31no—
144C4⋊Dic7C2×D311yescharacteristic, complemented
145Dic7⋊C4—31no—
146Dic7⋊C4C2×D311yescharacteristic, complemented
147C2×D3×D4—71no—
148C22×D12—71no—
149C3×#123—71no—
150#937—71no—
151#929—71no—
152#895—71no—
153#895—71no—
154#894—71no—
155#894—71no—
156#884—71no—
157#884—71no—
158#882—71no—
159#882—71no—
160#882D711yescharacteristic, complemented
161D3×C22⋊C4—71no—
162C22×C3×C7—21no—
163C22×C3×C7—21no—
164C22×C3×C7—21no—
165C22×C3×C7C2411yescharacteristic
166C2×D21—21no—
167C2×D21—21no—
168C2×D21—21no—
169C2×D21—21no—
170C2×D21—21no—
171C2×D21C2×D412yes—
172C2×D3×C7—21no—
173C2×D3×C7—21no—
174C2×D3×C7—21no—
175C2×D3×C7—21no—
176C2×D3×C7—21no—
177C2×D3×C7—21no—
178C2×D3×C7—21no—
179C2×D3×C7—21no—
180C2×D3×C7—44no—
181C2×D3×C7C2×D412yes—
182C2×C3×D7—21no—
183C2×C3×D7—21no—
184C2×C3×D7C2×D412yes—
185D3×D7—44no—
186D3×D7—44no—
187C3×C4×C7—21no—
188C3×C4×C7—21no—
189Dic21—21no—
190Dic21—21no—
191C3×Dic7—21no—
192C3×Dic7—21no—
193C3×Dic7—21no—
194C7×Dic3—21no—
195#534—211noSylow
196C23×C7—31no—
197C23×C7—31no—
198C23×C7—31no—
199C23×C7—62no—
200C23×C7—121no—
201C23×C7—121no—
202C23×C7C22×D311yescharacteristic
203C22×D7—31no—
204C22×D7—34no—
205C22×D7—31no—
206C22×D7—62no—
207C22×D7—121no—
208C22×D7—121no—
209C22×D7—121no—
210C22×D7—121no—
211C22×D7C22×D311yescharacteristic
212C7×D4—62no—
213C7×D4—121no—
214C7×D4—121no—
215C2×C4×C7—31no—
216C2×C4×C7C22×D311yescharacteristic
217C2×C4×C7C22×D311yescharacteristic
218C22⋊D7—22no—
219C22⋊D7—62no—
220C22⋊D7—62no—
221C22⋊D7—62no—
222C22⋊D7—62no—
223C22⋊D7—62no—
224C22⋊D7—121no—
225C22⋊D7—121no—
226C2×Dic7—31no—
227C2×Dic7—31no—
228C2×Dic7—62no—
229C2×Dic7C22×D311yescharacteristic
230C2×Dic7C22×D311yescharacteristic
231C2×Dic7C22×D311yescharacteristic
232D28—62no—
233C4×D7—22no—
234C4×D7—121no—
235C4×D7—121no—
236C23×D3—71no—
237C23×D3—71no—
238C23×D3C2×D711yescharacteristic, complemented
239C2×C3×D4—71no—
240C22×C3×C4—71no—
241C2×#67—71no—
242C2×#67—71no—
243C2×#67—71no—
244C2×#67C2×D711yescharacteristic, complemented
245D3×D4—144no—
246C2×D12—71no—
247C2×D12—71no—
248C2×D12—71no—
249C2×D12—71no—
250C2×D12—71no—
251C2×D12—144no—
252C2×D12C2×D711yescharacteristic
253C2×D12C2×D711yescharacteristic, complemented
254C2×C4×D3—71no—
255C2×C4×D3—71no—
256C2×C4×D3—71no—
257C3×C4⋊C4—71no—
258C3×C4⋊C4—71no—
259C3×C22⋊C4—71no—
260C3×C22⋊C4—71no—
261C3×C22⋊C4C2×D711yescharacteristic, complemented
262#217—71no—
263(C2×D3)⋊C4—71no—
264(C2×D3)⋊C4—71no—
265(C2×D3)⋊C4—71no—
266(C2×D3)⋊C4—71no—
267(C2×D3)⋊C4—71no—
268(C2×D3)⋊C4—71no—
269(C2×D3)⋊C4C2×D711yescharacteristic, complemented
270(C2×D3)⋊C4C2×D711yescharacteristic, complemented
271Dic3⋊C4—71no—
272Dic3⋊C4—71no—
273C2×C3×C7—41no—
274C2×C3×C7C22×D411yescharacteristic
275C2×C3×C7H(5,𝔽2)11yescharacteristic
276C2×C3×C7H(5,𝔽2)11yescharacteristic
277D21—22no—
278D21—41no—
279C3×D7—22no—
280D3×C7—22no—
281D3×C7—41no—
282D3×C7—41no—
283C22×D4—211no—
284C22×D4—211no—
285#123—71no—
286#123—211no—
287#123—211no—
288#123—211no—
289#121—211no—
290#121—211no—
291#121—211no—
292#121—211no—
293#120—31no—
294#120—211no—
295#120—211no—
296#120—211no—
297C2×C22⋊C4—211no—
298C22×C7—21no—
299C22×C7—21no—
300C22×C7—21no—
301C22×C7—32no—
302C22×C7—61no—
303C22×C7—61no—
304C22×C7—61no—
305C22×C7—61no—
306C22×C7—61no—
307C22×C7—61no—
308C22×C7—61no—
309C22×C7—61no—
310C22×C7—124no—
311C22×C7C23×D311yescharacteristic
312C2×D7—21no—
313C2×D7—21no—
314C2×D7—32no—
315C2×D7—61no—
316C2×D7—61no—
317C2×D7—61no—
318C2×D7—61no—
319C2×D7—61no—
320C2×D7—124no—
321C2×D7—124no—
322C2×D7D3×D412yes—
323C4×C7—21no—
324C4×C7—21no—
325C4×C7—61no—
326Dic7—21no—
327Dic7—21no—
328Dic7—21no—
329Dic7—61no—
330Dic7—61no—
331C23×C3—71no—
332C23×C3C22×D711yescharacteristic
333C22×D3—22no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—71no—
337C22×D3—74no—
338C22×D3—71no—
339C22×D3—142no—
340C22×D3—281no—
341C22×D3—281no—
342C22×D3—281no—
343C22×D3—281no—
344C22×D3C22×D711yescharacteristic
345C22×D3C22×D711yescharacteristic
346C22×D3C22×D711yescharacteristic
347C3×D4—142no—
348C2×C3×C4—71no—
349C2×C3×C4—71no—
350C2×C3×C4—71no—
351C2×C3×C4—142no—
352C2×C3×C4C22×D711yescharacteristic
353C2×C3×C4C22×D711yescharacteristic
354#67—41no—
355#67—142no—
356#67—142no—
357#67—281no—
358C2×Dic3—71no—
359C2×Dic3—71no—
360C2×Dic3C22×D711yescharacteristic
361D12—22no—
362D12—41no—
363D12—142no—
364D12—142no—
365D12—142no—
366D12—142no—
367D12—281no—
368C4×D3—142no—
369C4×D3—281no—
370C4×D3—281no—
371C3×C7#53411yescharacteristic, complemented, Hall
372C24—31no—
373C24—211no—
374C24—211no—
375C2×D4—31no—
376C2×D4—31no—
377C2×D4—31no—
378C2×D4—71no—
379C2×D4—211no—
380C2×D4—211no—
381C2×D4—211no—
382C2×D4—211no—
383C2×D4—211no—
384C2×D4—211no—
385C2×D4—211no—
386C2×D4—211no—
387C2×D4—424no—
388C2×D4—424no—
389C22×C4—71no—
390C22×C4—211no—
391C22×C4—211no—
392C22×C4—211no—
393C4⋊C4—71no—
394C4⋊C4—71no—
395C4⋊C4—211no—
396C4⋊C4—211no—
397C22⋊C4—31no—
398C22⋊C4—31no—
399C22⋊C4—71no—
400C22⋊C4—71no—
401C22⋊C4—211no—
402C22⋊C4—211no—
403C22⋊C4—211no—
404C22⋊C4—211no—
405C22⋊C4—211no—
406C22⋊C4—211no—
407C22⋊C4—211no—
408C22⋊C4D3×D711yescharacteristic, complemented
409C2×C7—41no—
410C2×C7—62no—
411C2×C7—121no—
412C2×C7—121no—
413C2×C7C2×D3×D411yescharacteristic
414C2×C7#100911yescharacteristic
415C2×C7#100911yescharacteristic
416D7—22no—
417D7—62no—
418D7—121no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—72no—
423C22×C3—141no—
424C22×C3—141no—
425C22×C3C23×D711yescharacteristic
426C2×D3—21no—
427C2×D3—21no—
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—21no—
431C2×D3—21no—
432C2×D3—21no—
433C2×D3—21no—
434C2×D3—44no—
435C2×D3—72no—
436C2×D3—141no—
437C2×D3—141no—
438C2×D3—141no—
439C2×D3—141no—
440C2×D3—141no—
441C2×D3—284no—
442C2×D3—284no—
443C2×D3D4×D712yes—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—141no—
447C3×C4—141no—
448C3×C4—141no—
449Dic3—21no—
450Dic3—141no—
451Dic3—141no—
452C23—31no—
453C23—31no—
454C23—31no—
455C23—62no—
456C23—71no—
457C23—121no—
458C23—121no—
459C23—214no—
460C23—211no—
461C23—211no—
462C23—422no—
463C23—841no—
464C23—841no—
465C23—841no—
466C23—841no—
467C23C2×D3×D711yescharacteristic
468D4—62no—
469D4—121no—
470D4—121no—
471D4—142no—
472D4—422no—
473D4—422no—
474D4—422no—
475D4—422no—
476D4—422no—
477D4—422no—
478D4—841no—
479D4—841no—
480C2×C4—31no—
481C2×C4—71no—
482C2×C4—71no—
483C2×C4—71no—
484C2×C4—142no—
485C2×C4—211no—
486C2×C4—211no—
487C2×C4—422no—
488C2×C4—841no—
489C2×C4—841no—
490C2×C4C2×D3×D711yescharacteristic
491C2×C4C2×D3×D711yescharacteristic
492C7#565311yescharacteristic, complemented, Sylow
493C2×C3—41no—
494C2×C3—142no—
495C2×C3C2×D4×D711yescharacteristic
496C2×C3#654811yescharacteristic
497C2×C3#654811yescharacteristic
498D3—22no—
499D3—41no—
500D3—41no—
501D3—142no—
502D3—281no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—32no—
507C22—61no—
508C22—61no—
509C22—61no—
510C22—61no—
511C22—61no—
512C22—61no—
513C22—61no—
514C22—61no—
515C22—72no—
516C22—124no—
517C22—141no—
518C22—141no—
519C22—212no—
520C22—421no—
521C22—421no—
522C22—421no—
523C22—421no—
524C22—421no—
525C22—844no—
526C22—844no—
527C22C22×D3×D711yescharacteristic
528C4—21no—
529C4—21no—
530C4—61no—
531C4—141no—
532C4—141no—
533C4—141no—
534C4—421no—
535C4—421no—
536C3#9028011yescharacteristic, complemented, Sylow
537C2—41no—
538C2—62no—
539C2—121no—
540C2—121no—
541C2—142no—
542C2—422no—
543C2—841no—
544C2#1062156511yescharacteristic
545C2D3×D4×D711yescharacteristic
546C2#1062157411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C22⋊C4C22
hypercenterC22⋊C4D3×D7
hypocenterC3×C7#534
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×C22⋊D7C2semidirect
2. C2×D7×D12C2semidirect
3. #10621367C2semidirect
4. C7×#882C2semidirect
5. C3×#6446C2semidirect
6. #10621139C2semidirect
7. #10621132C2semidirect
8. #10621119C2semidirect
9. #10621037C2semidirect
10. #10621035C2semidirect
11. #10621028C2semidirect
12. #10621009C2semidirect
13. #10620989C2semidirect
14. #10620985C2semidirect
15. #10620982C2semidirect
17. C23×D3×C7C22semidirect
19. C22×D3×D7C22semidirect
20. C2×#4268C22semidirect
21. C2×#4268C22semidirect
22. C2×D84C22semidirect
23. C2×C4×D21C22semidirect
24. C2×C7×#67C22semidirect
26. C2×C7×D12C22semidirect
28. C2×C3×C4×D7C22semidirect
31. C2×#4247C22semidirect
32. C2×#4247C22semidirect
33. C2×#4247C22semidirect
35. C2×D21⋊C4C22semidirect
36. C2×D3×Dic7C22semidirect
38. C3×C7×C22⋊C4C22semidirect
39. #66631C22semidirect
40. #66629C22semidirect
41. C7×(C2×D3)⋊C4C22semidirect
42. C7×(C2×D3)⋊C4C22semidirect
43. C3×C22⋊Dic7C22semidirect
44. C3×(C2×D7)⋊C4C22semidirect
45. C3×C4⋊Dic7C22semidirect
46. C3×Dic7⋊C4C22semidirect
47. Dic3⋊Dic7C22semidirect
48. #66575C22semidirect
49. (C2×D3)⋊Dic7C22semidirect
50. (C2×D3)⋊Dic7C22semidirect
51. (C2×D3)⋊Dic7C22semidirect
52. (C2×D3)⋊Dic7C22semidirect
53. (C2×D7)⋊Dic3C22semidirect
67. #6446D3semidirect
85. C2×D3×D7D4semidirect
130. C2×C4×D7C2×D3semidirect
133. C7×C22⋊C4C2×D3semidirect
138. C22⋊Dic7C2×D3semidirect
142. (C2×D7)⋊C4C2×D3semidirect
144. C4⋊Dic7C2×D3semidirect
146. Dic7⋊C4C2×D3semidirect
160. #882D7semidirect
238. C23×D3C2×D7semidirect
244. C2×#67C2×D7semidirect
253. C2×D12C2×D7semidirect
261. C3×C22⋊C4C2×D7semidirect
269. (C2×D3)⋊C4C2×D7semidirect
270. (C2×D3)⋊C4C2×D7semidirect
371. C3×C7#534semidirect
408. C22⋊C4D3×D7semidirect
492. C7#5653semidirect
536. C3#90280semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D3×C22⋊D72
C2×D7×D122
#106213672
C7×#8822
C3×#64462
#106211392
#106211322
#106211192
#106210372
#106210352
#106210282
#106210092
#106209892
#106209852
#106209822
#902803
#56537