Finite Group Databasebeta

← #14222271

Subgroups — #14222271

Order 1792.

2218 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#518C211yesmaximal, characteristic, complemented
2#11742806C211yesmaximal, characteristic, complemented
3#11741483C212yesmaximal, complemented
4#11739990C214yesmaximal, complemented
5#11739987C214yesmaximal, complemented
6#11739986C218yesmaximal, complemented
7#11739752C212yesmaximal, complemented
8#11739741C212yesmaximal, complemented
9C4×#6495C214yesmaximal, complemented
10#11739661C212yesmaximal, complemented
11#11739654C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C7×#518—24no—
14C7×#518C2214yes—
15C7×#518C2214yes—
16C2×C4×C7×D4—22no—
17C2×C4×C7×D4C2212yes—
18C2×C4×C7×D4C2212yes—
19C2×C7×#117C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C22×C7×C22⋊C4—22no—
22C2×#6495C2214yes—
23#90482C2212yes—
24#90226C2212yescomplemented
25#90225C2214yescomplemented
26#90219—24no—
27#90209C2212yescomplemented
28#90206—22no—
29#90185—22no—
30#90168C2211yescharacteristic, complemented
31C4×#1157C2212yescomplemented
32#90161C2211yescharacteristic, complemented
33#89990C2218yes—
34#89989C2218yes—
35#89987C2214yes—
36#89979C2212yes—
37#89791C2214yescomplemented
38#89790C2218yescomplemented
39C4×#1142C2218yescomplemented
40#89788C2218yescomplemented
41#89787C2214yescomplemented
42#89786C2218yescomplemented
43C4×#1141C2218yescomplemented
44#89781C2218yescomplemented
45#89780C2214yescomplemented
46#89779C2214yescomplemented
47#89775C2218yescomplemented
48#89772C2214yescomplemented
49#89772C2214yescomplemented
50#89768C2218yescomplemented
51#89738C2214yescomplemented
52#89736C2214yescomplemented
53#89696C2212yescomplemented
54C4×#1136C2212yescomplemented
55#60564—71nomaximal, Sylow
56C25×C7—21no—
57C22×C7×D4—28no—
58C22×C7×D4—21no—
59C22×C7×D4—22no—
60C22×C7×D4C2314yes—
61C22×C7×D4C2312yes—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7C2311yescharacteristic
65C2×#1157C2312yes—
66C4×C7×D4—28no—
67C4×C7×D4—28no—
68C4×C7×D4—22no—
69C4×C7×D4—22no—
70C4×C7×D4—24no—
71C4×C7×D4C2314yes—
72C4×C7×D4C2314yes—
73C4×C7×D4C2318yes—
74C7×#117—22no—
75C7×#117D414yes—
76C7×#117C2314yes—
77C7×#117C2312yes—
78C7×#117C2312yes—
79C2×C7×C4⋊C4D412yes—
80C2×C7×C4⋊C4C2312yes—
81C2×C7×C22⋊C4—21no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—28no—
85C2×C7×C22⋊C4—28no—
86C2×C7×C22⋊C4D412yes—
87C2×C42×C7—21no—
88C2×C42×C7C2311yescharacteristic
89C2×C42×C7C2311yescharacteristic
90#6516—22no—
91C2×#1142C2318yes—
92#6495—216no—
93C2×#1141C2318yes—
94#6493—22no—
95#6493C2314yes—
96#6492—22no—
97C4×C22⋊D7—24no—
98C4×C22⋊D7—24no—
99#6489C2312yes—
100#6487—22no—
101#6487C2314yes—
102C2×#1136C2314yes—
103#6461—24no—
104#6459—24no—
105#6457—24no—
106#6452—24no—
107#6448—24no—
108#6447—24no—
109#6446—24no—
110#6442—24no—
111#6438C2312yescomplemented
112#6437C2311yescharacteristic, complemented
113C4×D28—22no—
114C4×D28C2314yescomplemented
115#6435—22no—
116C42×D7—22no—
117#6433C2312yescomplemented
118#6432C2311yescharacteristic, complemented
119#6432C2312yescomplemented
120C4×Dic14—22no—
121C4×Dic14C2314yescomplemented
122#6406C2318yes—
123#6406C2318yes—
124C22⋊(C7⋊C8)C2318yes—
125#6384C2318yescomplemented
126#6383C2318yescomplemented
127#6382C2318yescomplemented
128#6381C2318yescomplemented
129C4⋊(C7⋊C8)C2314yescomplemented
130C4⋊(C7⋊C8)C2314yescomplemented
131#6377C2314yescomplemented
132C4×C7⋊C8C2314yescomplemented
133#3455—71no—
134C2×#518D711yescharacteristic, complemented
135#3123—74no—
136#3122—74no—
137#3118—78no—
138#3093—72no—
139#3077—72no—
140#3036—72no—
141#3003—72no—
142C4×AGL(1,ℤ/8)—74no—
143#2921—71no—
144C24×C7—28no—
145C24×C7—22no—
146C24×C7—24no—
147C24×C7—84no—
148C24×C7C2×D411yescharacteristic
149C2×C7×D4—28no—
150C2×C7×D4—216no—
151C2×C7×D4—216no—
152C2×C7×D4—24no—
153C2×C7×D4—22no—
154C2×C7×D4—24no—
155C2×C7×D4#4118yes—
156C2×C7×D4C2414yes—
157C22×C4×C7—24no—
158C22×C4×C7—22no—
159C22×C4×C7—28no—
160C22×C4×C7—24no—
161C22×C4×C7—24no—
162C22×C4×C7—84no—
163C22×C4×C7—84no—
164C22×C4×C7C2×D412yes—
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2412yes—
169C22×C4×C7C2411yescharacteristic
170C2×C22⋊D7—22no—
171C2×C22⋊D7—24no—
172#1157—28no—
173C2×D28—22no—
174C2×D28C2412yes—
175C2×C4×D7—22no—
176C2×C4×D7—24no—
177C2×Dic14—22no—
178C2×Dic14C2412yes—
179C7×C4⋊C4—22no—
180C7×C4⋊C4C2×D414yes—
181C7×C4⋊C4C2×D414yes—
182C7×C4⋊C4C2414yes—
183C7×C22⋊C4—24no—
184C7×C22⋊C4—28no—
185C7×C22⋊C4—24no—
186C7×C22⋊C4—24no—
187C7×C22⋊C4C2×D414yes—
188C7×C22⋊C4C2×D414yes—
189C42×C7—24no—
190C42×C7C2×D412yes—
191C42×C7C2×D412yes—
192C42×C7C2412yes—
193C42×C7C2411yescharacteristic
194C42×C7C2411yescharacteristic
195C22⋊Dic7—24no—
196C22⋊Dic7—22no—
197#1142—216no—
198#1141—216no—
199(C2×D7)⋊C4—24no—
200(C2×D7)⋊C4—24no—
201(C2×D7)⋊C4—24no—
202C4⋊Dic7—22no—
203C4⋊Dic7—22no—
204C4⋊Dic7C2414yes—
205Dic7⋊C4—24no—
206Dic7⋊C4—24no—
207Dic7⋊C4—24no—
208C4×Dic7—22no—
209C4×Dic7—24no—
210#1136—28no—
211C2×C7⋊C8C2418yes—
212C23×D4C2×D711yescharacteristic
213C2×AGL(1,ℤ/8)—74no—
214#542—74no—
215#541—72no—
216#540—72no—
217#539—142no—
218#538—142no—
219#533—71no—
220#532—71no—
221#529—144no—
222#525—72no—
223#518—24no—
224#518C2×D714yes—
225#518C2×D714yes—
226C4×#41—72no—
227C2×C4×D4—22no—
228C2×C4×D4C2×D712yes—
229C2×C4×D4C2×D712yes—
230C2×#117C2×D711yescharacteristic
231C2×#117C2×D711yescharacteristic
232C22×C22⋊C4—22no—
233#485—78no—
234#482—78no—
235#478—78no—
236#476—74no—
237#474—74no—
238#463—78no—
239#461—74no—
240#459—74no—
241#450—78no—
242#447—78no—
243#442—78no—
244#440—78no—
245C4×SD16—78no—
246C4×D8—78no—
247#433—74no—
248#433—74no—
249#428—74no—
250#423—72no—
251#418—74no—
252#417—74no—
253#407—72no—
254C4×M16—72no—
255C23×C7—216no—
256C23×C7—22no—
257C23×C7—28no—
258C23×C7—24no—
259C23×C7—42no—
260C23×C7—44no—
261C23×C7—44no—
262C23×C7—88no—
263C23×C7—816no—
264C23×C7C22×D412yes—
265C23×C7C22×D411yescharacteristic
266C22×D7—22no—
267C7×D4—216no—
268C7×D4—28no—
269C7×D4—24no—
270C7×D4C2×#4118yes—
271C2×C4×C7—22no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—24no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—44no—
278C2×C4×C7—84no—
279C2×C4×C7—88no—
280C2×C4×C7—84no—
281C2×C4×C7C22×D414yes—
282C2×C4×C7C22×D412yes—
283C2×C4×C7C22×D412yes—
284C2×C4×C7C22×D412yes—
285C2×C4×C7C22×D411yescharacteristic
286C2×C4×C7C2×#4114yes—
287C2×C4×C7C2511yescharacteristic
288C22⋊D7—44no—
289C22⋊D7—84no—
290C2×Dic7—22no—
291C2×Dic7—24no—
292D28—24no—
293D28—82no—
294C4×D7—44no—
295C4×D7—84no—
296Dic14—24no—
297Dic14—82no—
298C7⋊C8—28no—
299C25—21no—
300C2×#41—72no—
301C22×D4—28no—
302C22×D4—21no—
303C22×D4—22no—
304C22×D4C22×D714yes—
305C22×D4C22×D712yes—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4C22×D711yescharacteristic
309AGL(1,ℤ/8)—1416no—
310C2×SD16—78no—
311C2×D8—78no—
312C2×M16—74no—
313C4⋊Q8—72no—
314C4⋊Q8—71no—
315#127—71no—
316#126—144no—
317#126—144no—
318#125—72no—
319#125—144no—
320#124—72no—
321#124—144no—
322#123—142no—
323#123—144no—
324#123—144no—
325C22⋊Q8—74no—
326C22⋊Q8—142no—
327C22⋊Q8—144no—
328#121—74no—
329#121—142no—
330#121—144no—
331#120—142no—
332C4×Q8—74no—
333C4×Q8—142no—
334C4×D4—28no—
335C4×D4—28no—
336C4×D4—24no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—74no—
340C4×D4—144no—
341C4×D4—144no—
342C4×D4—142no—
343C4×D4C22×D718yes—
344C4×D4C22×D714yes—
345C4×D4C22×D714yes—
346#117—22no—
347#117—72no—
348#117—142no—
349#117C22⋊D714yes—
350#117C22×D714yes—
351#117C22×D712yes—
352#117C22×D712yes—
353C2×C4⋊C4C22⋊D712yes—
354C2×C4⋊C4C22×D712yes—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4C22⋊D712yes—
361C2×C42—21no—
362C2×C42—142no—
363C2×C42C22×D711yescharacteristic
364C2×C42C22×D711yescharacteristic
365#107—78no—
366#106—78no—
367C4⋊C8—74no—
368C4⋊C8—74no—
369#103—78no—
370#102—78no—
371#102—78no—
372#102—78no—
373C22⋊C8—78no—
374#97—74no—
375C4×C8—74no—
376C22×C7—22no—
377C22×C7—24no—
378C22×C7—22no—
379C22×C7—28no—
380C22×C7—416no—
381C22×C7—44no—
382C22×C7—44no—
383C22×C7—44no—
384C22×C7—816no—
385C22×C7#52512yes—
386C22×C7C23×D411yescharacteristic
387C2×D7—44no—
388C2×D7—42no—
389C4×C7—22no—
390C4×C7—24no—
391C4×C7—22no—
392C4×C7—22no—
393C4×C7—44no—
394C4×C7#52512yes—
395C4×C7C22×#4112yes—
396Dic7—44no—
397Dic7—42no—
398C24—28no—
399C24—22no—
400C24—24no—
401C24—84no—
402C24C2×C22⋊D711yescharacteristic
403#41—148no—
404C2×Q8—72no—
405C2×Q8—142no—
406C2×D4—28no—
407C2×D4—216no—
408C2×D4—216no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—72no—
413C2×D4—142no—
414C2×D4—144no—
415C2×D4—142no—
416C2×D4#115718yes—
417C2×D4C23×D714yes—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—28no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—84no—
424C22×C4—84no—
425C22×C4—142no—
426C22×C4—144no—
427C22×C4C2×C22⋊D711yescharacteristic
428C22×C4C2×C22⋊D712yes—
429C22×C4C2×C22⋊D712yes—
430C22×C4C2×C22⋊D712yes—
431C22×C4C23×D712yes—
432C22×C4C23×D711yescharacteristic
433SD16—1416no—
434D8—1416no—
435M16—148no—
436C2×C8—78no—
437C4⋊C4—22no—
438C4⋊C4—74no—
439C4⋊C4—144no—
440C4⋊C4—144no—
441C4⋊C4—144no—
442C4⋊C4—142no—
443C4⋊C4—142no—
444C4⋊C4C2×C22⋊D714yes—
445C4⋊C4C2×C22⋊D714yes—
446C4⋊C4C23×D714yes—
447C22⋊C4—24no—
448C22⋊C4—28no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—142no—
452C22⋊C4—144no—
453C22⋊C4—144no—
454C22⋊C4—144no—
455C22⋊C4—144no—
456C22⋊C4C2×C22⋊D714yes—
457C22⋊C4C2×C22⋊D714yes—
458C42—24no—
459C42—142no—
460C42—144no—
461C42C2×C22⋊D712yes—
462C42C2×C22⋊D712yes—
463C42C23×D712yes—
464C42C23×D711yescharacteristic
465C42C23×D711yescharacteristic
466C2×C7—22no—
467C2×C7—42no—
468C2×C7—48no—
469C2×C7C2×#52511yescharacteristic
470C2×C7#358512yes—
471D7—82no—
472C23—216no—
473C23—22no—
474C23—28no—
475C23—24no—
476C23—42no—
477C23—44no—
478C23—44no—
479C23—88no—
480C23—816no—
481C23—142no—
482C23C22×C22⋊D712yes—
483C23C22×C22⋊D711yescharacteristic
484Q8—144no—
485Q8—562no—
486D4—216no—
487D4—28no—
488D4—24no—
489D4—144no—
490D4—284no—
491D4—562no—
492D4—564no—
493D4C2×#115718yes—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—88no—
502C2×C4—84no—
503C2×C4—84no—
504C2×C4—144no—
505C2×C4—142no—
506C2×C4—284no—
507C2×C4—564no—
508C2×C4C2×#115714yes—
509C2×C4C22×C22⋊D712yes—
510C2×C4C22×C22⋊D714yes—
511C2×C4C22×C22⋊D712yes—
512C2×C4C22×C22⋊D712yes—
513C2×C4C22×C22⋊D711yescharacteristic
514C2×C4C24×D711yescharacteristic
515C8—148no—
516C7#6056411yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—28no—
520C22—24no—
521C22—44no—
522C22—416no—
523C22—44no—
524C22—44no—
525C22—816no—
526C22—282no—
527C22—284no—
528C22#9048212yes—
529C22C23×C22⋊D711yescharacteristic
530C4—22no—
531C4—24no—
532C4—22no—
533C4—22no—
534C4—44no—
535C4—282no—
536C4—284no—
537C4#9048212yes—
538C4C22×#115712yes—
539C2—22no—
540C2—42no—
541C2—48no—
542C2—562no—
543C2C2×#9048211yescharacteristic
544C2#1174434512yes—
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#518C2
socleC22×C7C23×D4
hypercenterC2×#518D7
hypocenterC7#60564
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. C2×C7×#518C2semidirect
2. #11742806C2semidirect
3. #11741483C2semidirect
4. #11739990C2semidirect
5. #11739987C2semidirect
6. #11739986C2semidirect
7. #11739752C2semidirect
8. #11739741C2semidirect
9. C4×#6495C2semidirect
10. #11739661C2semidirect
11. #11739654C2semidirect
24. #90226C22semidirect
25. #90225C22semidirect
27. #90209C22semidirect
30. #90168C22semidirect
31. C4×#1157C22semidirect
32. #90161C22semidirect
37. #89791C22semidirect
38. #89790C22semidirect
39. C4×#1142C22semidirect
40. #89788C22semidirect
41. #89787C22semidirect
42. #89786C22semidirect
43. C4×#1141C22semidirect
44. #89781C22semidirect
45. #89780C22semidirect
46. #89779C22semidirect
47. #89775C22semidirect
48. #89772C22semidirect
49. #89772C22semidirect
50. #89768C22semidirect
51. #89738C22semidirect
52. #89736C22semidirect
53. #89696C22semidirect
54. C4×#1136C22semidirect
111. #6438C23semidirect
112. #6437C23semidirect
114. C4×D28C23semidirect
117. #6433C23semidirect
118. #6432C23semidirect
119. #6432C23semidirect
121. C4×Dic14C23semidirect
125. #6384C23semidirect
126. #6383C23semidirect
127. #6382C23semidirect
128. #6381C23semidirect
129. C4⋊(C7⋊C8)C23semidirect
130. C4⋊(C7⋊C8)C23semidirect
131. #6377C23semidirect
132. C4×C7⋊C8C23semidirect
134. C2×#518D7semidirect
516. C7#60564semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5182
#117428062
#117414832
#117399902
#117399872
#117399862
#117397522
#117397412
C4×#64952
#117396612
#117396542
#605647