Finite Group Databasebeta

← C2×#11744180 #14261560

Subgroups — C2×#11744180 #14261560

Order 1792.

6566 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#562C211yesmaximal, characteristic, complemented
2#11744180C2132yesmaximal, direct product factor
3C2×D7×#125C211yesmaximal, characteristic, complemented
4C2×C7⋊#564C211yesmaximal, characteristic, complemented
5C2×#90363C212yesmaximal, complemented
6C2×#90371C212yesmaximal, complemented
7C2×#90351C214yesmaximal, complemented
8C2×#90341C214yesmaximal, complemented
9C2×#90327C214yesmaximal, complemented
10C2×#90316C214yesmaximal, complemented
11C2×#90305C214yesmaximal, complemented
12C2×#90293C214yesmaximal, complemented
13C7×#562C22116yescomplemented
14C2×C7×#125C2211yescharacteristic
15C2×C7×#124C2212yes—
16C2×C7×#123C2214yes—
17C2×C7×C22⋊Q8C2214yes—
18C2×C7×#121C2214yes—
19C2×#6509C2212yes—
20C2×Q8×Dic7C2212yes—
21C2×#6507C2214yes—
22C2×#6501C2214yes—
23C2×#6501C2212yes—
24C2×#6498C2214yes—
25C2×#6498C2214yes—
26C2×#6498C2214yes—
27C2×D4×Dic7C2212yes—
28C2×D4×Dic7C2214yes—
29C2×C4×C22⋊D7C2214yes—
30C2×#6489C2214yes—
31C2×#6487C2214yes—
32C22×Dic7⋊C4C2214yes—
33D7×#125C22116yescomplemented
34C7⋊#564C22116yescomplemented
35#90371C22132yescomplemented
36#90363C22132yescomplemented
37#90351C22164yescomplemented
38#90341C22164yescomplemented
39#90327C22164yescomplemented
40#90316C22164yescomplemented
41#90305C22164yescomplemented
42#90293C22164yescomplemented
43C2×#6459C2214yes—
44C2×D7×C4⋊C4C2214yes—
45C2×D7×C4⋊C4C2212yes—
46C2×#6453C2214yes—
47C2×#6453C2214yes—
48C2×#6453C2212yes—
49C2×#6452C2214yes—
50C2×#6452C2214yes—
51C2×#6452C2214yes—
52C2×#6452C2214yes—
53C2×#6450C2214yes—
54C2×#6446C2214yes—
55C2×(C22⋊D7)⋊C4C2214yes—
56C2×(C22⋊D7)⋊C4C2214yes—
57C2×#6442C2214yes—
58C2×#6442C2214yes—
59C2×#6442C2214yes—
60C2×#6442C2214yes—
61C2×#6442C2214yes—
62C2×#6441C2214yes—
63C2×#6441C2214yes—
64C2×#6441C2214yes—
65C2×#6440C2214yes—
66C2×C42×D7C2211yescharacteristic
67C2×#6433C2212yes—
68C2×#6433C2211yescharacteristic
69C2×#3553—71nomaximal, Sylow
70C22×C7×Q8C2312yes—
71C22×C7×D4C2314yes—
72C22×C7×D4C2312yes—
73C23×C4×C7C2314yes—
74C22×C22⋊D7C2314yes—
75C23×Dic7C2314yes—
76C23×Dic7C2314yes—
77C22×C4×D7C2311yescharacteristic
78C22×C4×D7C2312yes—
79C22×C4×D7C2314yes—
80C22×Dic14C2314yes—
81C7×#125C2318yes—
82C7×#124C23116yes—
83C7×#123C23132yes—
84C7×C22⋊Q8C23132yes—
85C7×#121C23132yes—
86C2×C7×C4⋊C4C2314yes—
87C2×C7×C4⋊C4C2314yes—
88C2×C7×C4⋊C4C2312yes—
89C2×C7×C22⋊C4C2314yes—
90C2×C7×C22⋊C4C2314yes—
91C2×C7×C22⋊C4C2314yes—
92C2×C42×C7C2311yescharacteristic
93C2×C22⋊Dic7C2314yes—
94C2×C22⋊Dic7C2314yes—
95C2×C22⋊Dic7C2314yes—
96C2×C22⋊Dic7C2314yes—
97C2×C22⋊Dic7C2314yes—
98#6509C23116yes—
99Q8×Dic7C23116yes—
100#6507C23132yes—
101#6501C23116yes—
102#6501C23132yes—
103#6498C23132yes—
104#6498C23132yes—
105#6498C23132yes—
106D4×Dic7C23116yes—
107D4×Dic7C23132yes—
108C4×C22⋊D7C23132yes—
109C2×(C2×D7)⋊C4C2314yes—
110#6489C23132yes—
111C2×C4⋊Dic7C2312yes—
112C2×C4⋊Dic7C2312yes—
113C2×C4⋊Dic7C2312yes—
114C2×C4⋊Dic7C2314yes—
115C2×C4⋊Dic7C2314yes—
116C2×C4⋊Dic7C2314yes—
117#6487C23132yes—
118C2×Dic7⋊C4C2314yes—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C23132yes—
129C2×C4×Dic7C2311yescharacteristic
130C2×C4×Dic7C2312yes—
131C2×C4×Dic7C2314yes—
132C2×C4×Dic7C2314yes—
133C2×C4×Dic7C2314yes—
134#6459C23132yes—
135D7×C4⋊C4C23132yes—
136D7×C4⋊C4C23116yes—
137#6453C23132yes—
138#6453C23116yes—
139#6453C23132yes—
140#6452C23132yes—
141#6452C23132yes—
142#6452C23132yes—
143#6452C23132yes—
144#6450C23132yes—
145#6446C23132yes—
146(C22⋊D7)⋊C4C23132yes—
147(C22⋊D7)⋊C4C23132yes—
148#6442C23132yes—
149#6442C23132yes—
150#6442C23132yes—
151#6442C23132yes—
152#6442C23132yes—
153#6441C23132yes—
154#6441C23132yes—
155#6441C23132yes—
156#6440C23132yes—
157C42×D7C2318yes—
158#6433C23116yes—
159#6433C2318yes—
160#3553—732no—
161C2×#564—71no—
162C2×#563—72no—
163C2×#562D711yescharacteristic, complemented
164C2×#554—74no—
165C2×#553—74no—
166C2×#552—74no—
167C2×#541—74no—
168C2×#539—74no—
169C2×#539—74no—
170C2×#529—72no—
171C22×#125—71no—
172C24×C7C2414yes—
173C23×D7C2411yescharacteristic
174C2×C7×Q8—44no—
175C2×C7×Q8C2418yes—
176C2×C7×D4—48no—
177C2×C7×D4—44no—
178C2×C7×D4C24116yes—
179C2×C7×D4C2418yes—
180C22×C4×C7—48no—
181C22×C4×C7C2414yes—
182C22×C4×C7C2411yescharacteristic
183C22×C4×C7C2412yes—
184C22×C4×C7C2414yes—
185C22×C4×C7C24116yes—
186C2×C22⋊D7—216no—
187C2×C22⋊D7C24116yes—
188C22×Dic7—48no—
189C22×Dic7—48no—
190C22×Dic7C2412yes—
191C22×Dic7C2414yes—
192C22×Dic7C2411yescharacteristic
193C22×Dic7C2414yes—
194C22×Dic7C2414yes—
195C22×Dic7C24116yes—
196C22×Dic7C24116yes—
197C2×C4×D7—24no—
198C2×C4×D7—48no—
199C2×C4×D7—44no—
200C2×C4×D7C2414yes—
201C2×C4×D7C2418yes—
202C2×C4×D7C24116yes—
203C2×Dic14—48no—
204C2×Dic14C24116yes—
205C7×C4⋊C4C24116yes—
206C7×C4⋊C4C24116yes—
207C7×C4⋊C4C2418yes—
208C7×C22⋊C4C24116yes—
209C7×C22⋊C4C24116yes—
210C7×C22⋊C4C24116yes—
211C42×C7C2414yes—
212C22⋊Dic7C24116yes—
213C22⋊Dic7C24116yes—
214C22⋊Dic7C24116yes—
215C22⋊Dic7C24116yes—
216C22⋊Dic7C24116yes—
217(C2×D7)⋊C4C24116yes—
218C4⋊Dic7C2418yes—
219C4⋊Dic7C2418yes—
220C4⋊Dic7C2418yes—
221C4⋊Dic7C24116yes—
222C4⋊Dic7C24116yes—
223C4⋊Dic7C24116yes—
224Dic7⋊C4C24116yes—
225Dic7⋊C4C24116yes—
226Dic7⋊C4C24116yes—
227Dic7⋊C4C24116yes—
228Dic7⋊C4C24116yes—
229Dic7⋊C4C24116yes—
230Dic7⋊C4C24116yes—
231Dic7⋊C4C24116yes—
232Dic7⋊C4C24116yes—
233Dic7⋊C4C24116yes—
234C4×Dic7C2414yes—
235C4×Dic7C2418yes—
236C4×Dic7C24116yes—
237C4×Dic7C24116yes—
238C4×Dic7C24116yes—
239#564—716no—
240#563—732no—
241#562C2×D7116yescomplemented
242#554—764no—
243#553—764no—
244#552—764no—
245#541—764no—
246#539—764no—
247#539—764no—
248C2×C4⋊Q8—74no—
249#529—732no—
250C2×#126—74no—
251C2×#126—74no—
252C2×#126—74no—
253C2×#126—74no—
254C2×#126—74no—
255C2×#125—716no—
256C2×#125—74no—
257C2×#125—74no—
258C2×#125—74no—
259C2×#125—74no—
260C2×#125—72no—
261C2×#125—74no—
262C2×#125—74no—
263C2×#125—71no—
264C2×#125—72no—
265C2×#125C2×D711yescharacteristic
266C2×#124C2×D712yes—
267C2×#123—74no—
268C2×#123—74no—
269C2×#123—74no—
270C2×#123—74no—
271C2×#123C2×D714yes—
272C2×C22⋊Q8—72no—
273C2×C22⋊Q8—74no—
274C2×C22⋊Q8—74no—
275C2×C22⋊Q8—74no—
276C2×C22⋊Q8—74no—
277C2×C22⋊Q8—74no—
278C2×C22⋊Q8C2×D714yes—
279C2×#121—72no—
280C2×#121—74no—
281C2×#121C2×D714yes—
282C2×C4×Q8—72no—
283C2×C4×Q8—74no—
284C2×C4×D4—72no—
285C2×C4×D4—74no—
286C2×C4×D4—74no—
287C2×C4×D4—74no—
288C2×C4×D4—74no—
289C2×#117—74no—
290C2×#117—74no—
291C22×C4⋊C4—74no—
292C22×C4⋊C4—72no—
293C22×C4⋊C4—74no—
294C22×C42—71no—
295C23×C7—28no—
296C23×C7—28no—
297C23×C7—28no—
298C23×C7C2518yes—
299C23×C7C2511yescharacteristic
300C22×D7—24no—
301C22×D72−1+414yes—
302C22×D7C2512yes—
303C7×Q8—48no—
304C7×D4—416no—
305C7×D4—48no—
306C2×C4×C7—22no—
307C2×C4×C7—28no—
308C2×C4×C7—28no—
309C2×C4×C7—24no—
310C2×C4×C7—416no—
311C2×C4×C7C2518yes—
312C2×C4×C7C2512yes—
313C2×C4×C7C2514yes—
314C2×C4×C7C2518yes—
315C22⋊D7—232no—
316C2×Dic7—22no—
317C2×Dic7—28no—
318C2×Dic7—28no—
319C2×Dic7—28no—
320C2×Dic7—24no—
321C2×Dic7—416no—
322C2×Dic7—416no—
323C2×Dic7C2514yes—
324C2×Dic7C2518yes—
325C2×Dic7C2512yes—
326C2×Dic7C2518yes—
327C2×Dic7C2518yes—
328C4×D7—28no—
329C4×D7—416no—
330C4×D7—48no—
331Dic14—416no—
332C22×Q8—74no—
333C22×Q8C22×D712yes—
334C22×D4—74no—
335C22×D4C22×D714yes—
336C22×D4C22×D712yes—
337C23×C4—74no—
338C23×C4—74no—
339C23×C4—71no—
340C23×C4—74no—
341C23×C4—72no—
342C23×C4C22×D714yes—
343C4⋊Q8—732no—
344#126—732no—
345#126—732no—
346#126—732no—
347#126—732no—
348#126—732no—
349#125—732no—
350#125—716no—
351#125—732no—
352#125—732no—
353#125—732no—
354#125—732no—
355#125—732no—
356#125—78no—
357#125—716no—
358#125C22×D718yes—
359#124C22×D7116yes—
360#123—732no—
361#123—732no—
362#123—732no—
363#123—732no—
364#123C22×D7132yes—
365C22⋊Q8—716no—
366C22⋊Q8—732no—
367C22⋊Q8—732no—
368C22⋊Q8—732no—
369C22⋊Q8—732no—
370C22⋊Q8—732no—
371C22⋊Q8C22×D7132yes—
372#121—716no—
373#121—732no—
374#121C22×D7132yes—
375C4×Q8—716no—
376C4×Q8—732no—
377C4×D4—716no—
378C4×D4—732no—
379C4×D4—732no—
380C4×D4—732no—
381C4×D4—732no—
382#117—732no—
383#117—732no—
384C2×C4⋊C4—74no—
385C2×C4⋊C4—74no—
386C2×C4⋊C4—74no—
387C2×C4⋊C4—74no—
388C2×C4⋊C4—72no—
389C2×C4⋊C4—74no—
390C2×C4⋊C4—74no—
391C2×C4⋊C4—74no—
392C2×C4⋊C4—732no—
393C2×C4⋊C4—74no—
394C2×C4⋊C4—74no—
395C2×C4⋊C4—72no—
396C2×C4⋊C4—74no—
397C2×C4⋊C4—74no—
398C2×C4⋊C4—74no—
399C2×C4⋊C4—72no—
400C2×C4⋊C4—74no—
401C2×C4⋊C4—716no—
402C2×C4⋊C4—732no—
403C2×C4⋊C4C22×D714yes—
404C2×C4⋊C4C22×D712yes—
405C2×C4⋊C4C22×D714yes—
406C2×C22⋊C4—74no—
407C2×C22⋊C4—74no—
408C2×C22⋊C4—74no—
409C2×C22⋊C4—74no—
410C2×C22⋊C4—74no—
411C2×C22⋊C4—74no—
412C2×C22⋊C4C22×D714yes—
413C2×C22⋊C4C22×D714yes—
414C2×C22⋊C4C22×D714yes—
415C2×C42—71no—
416C2×C42—74no—
417C2×C42—74no—
418C2×C42—74no—
419C2×C42—72no—
420C2×C42—78no—
421C2×C42C22×D711yescharacteristic
422C22×C7—28no—
423C22×C7—28no—
424C22×C7—28no—
425C22×C7—416no—
426C22×C7C2×2−1+412yes—
427C22×C7#58514yes—
428C22×C7C2611yescharacteristic
429C2×D7—24no—
430C2×D7—28no—
431C2×D7C2×2−1+414yes—
432C4×C7—22no—
433C4×C7—28no—
434C4×C7—28no—
435C4×C7—24no—
436Dic7—22no—
437Dic7—28no—
438Dic7—28no—
439Dic7—28no—
440Dic7—24no—
441C24—71no—
442C24C23×D714yes—
443C2×Q8—44no—
444C2×Q8—716no—
445C2×Q8—288no—
446C2×Q8C23×D718yes—
447C2×D4—48no—
448C2×D4—44no—
449C2×D4—716no—
450C2×D4—1416no—
451C2×D4C23×D7116yes—
452C2×D4C23×D718yes—
453C22×C4—48no—
454C22×C4—72no—
455C22×C4—74no—
456C22×C4—71no—
457C22×C4—74no—
458C22×C4—74no—
459C22×C4—716no—
460C22×C4—716no—
461C22×C4—74no—
462C22×C4—78no—
463C22×C4—716no—
464C22×C4—144no—
465C22×C4—288no—
466C22×C4—284no—
467C22×C4—288no—
468C22×C4—288no—
469C22×C4C23×D714yes—
470C22×C4C23×D711yescharacteristic
471C22×C4C23×D712yes—
472C22×C4C23×D714yes—
473C22×C4C23×D7116yes—
474C4⋊C4—716no—
475C4⋊C4—716no—
476C4⋊C4—716no—
477C4⋊C4—716no—
478C4⋊C4—716no—
479C4⋊C4—716no—
480C4⋊C4—716no—
481C4⋊C4—716no—
482C4⋊C4—716no—
483C4⋊C4—716no—
484C4⋊C4—716no—
485C4⋊C4—78no—
486C4⋊C4—716no—
487C4⋊C4—78no—
488C4⋊C4—78no—
489C4⋊C4—716no—
490C4⋊C4C23×D7116yes—
491C4⋊C4C23×D718yes—
492C4⋊C4C23×D7116yes—
493C22⋊C4—716no—
494C22⋊C4—716no—
495C22⋊C4—716no—
496C22⋊C4—716no—
497C22⋊C4—716no—
498C22⋊C4—716no—
499C22⋊C4C23×D7116yes—
500C22⋊C4C23×D7116yes—
501C22⋊C4C23×D7116yes—
502C42—74no—
503C42—78no—
504C42—716no—
505C42—716no—
506C42—716no—
507C42C23×D714yes—
508C2×C7—48no—
509C2×C7#355314yescomplemented
510C2×C7C22×2−1+411yescharacteristic
511C2×C7C2×#58512yes—
512D7—24no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—72no—
517C23—74no—
518C23—144no—
519C23C24×D718yes—
520C23C24×D711yescharacteristic
521Q8—48no—
522Q8—2816no—
523D4—416no—
524D4—48no—
525D4—1432no—
526C2×C4—28no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—416no—
531C2×C4—74no—
532C2×C4—78no—
533C2×C4—72no—
534C2×C4—78no—
535C2×C4—78no—
536C2×C4—148no—
537C2×C4—144no—
538C2×C4—148no—
539C2×C4—148no—
540C2×C4—142no—
541C2×C4—148no—
542C2×C4—2816no—
543C2×C4—288no—
544C2×C4—2816no—
545C2×C4—2816no—
546C2×C4C24×D718yes—
547C2×C4C24×D712yes—
548C2×C4C24×D714yes—
549C2×C4C24×D718yes—
550C7C2×#355311yescharacteristic, complemented, Sylow
551C22—28no—
552C22—28no—
553C22—28no—
554C22—416no—
555C22—74no—
556C22—144no—
557C22—148no—
558C22#9061814yes—
559C22D7×2−1+412yes—
560C22C25×D711yescharacteristic
561C4—28no—
562C4—28no—
563C4—24no—
564C4—22no—
565C4—144no—
566C4—148no—
567C4—148no—
568C4—142no—
569C4—148no—
570C2—48no—
571C2—144no—
572C2#1174418014yesdirect product factor
573C2C2×#9061812yes—
574C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#562C2
socleC23×C7C25
hypercenterC2×#562D7
hypocenterC7C2×#3553
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. C2×C7×#562C2semidirect
2. #11744180C2direct (N × H)
3. C2×D7×#125C2semidirect
4. C2×C7⋊#564C2semidirect
5. C2×#90363C2semidirect
6. C2×#90371C2semidirect
7. C2×#90351C2semidirect
8. C2×#90341C2semidirect
9. C2×#90327C2semidirect
10. C2×#90316C2semidirect
11. C2×#90305C2semidirect
12. C2×#90293C2semidirect
13. C7×#562C22semidirect
33. D7×#125C22semidirect
34. C7⋊#564C22semidirect
35. #90371C22semidirect
36. #90363C22semidirect
37. #90351C22semidirect
38. #90341C22semidirect
39. #90327C22semidirect
40. #90316C22semidirect
41. #90305C22semidirect
42. #90293C22semidirect
163. C2×#562D7semidirect
241. #562C2×D7semidirect
509. C2×C7#3553semidirect
550. C7C2×#3553semidirect
572. C2#11744180direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5622
#117441802
C2×D7×#1252
C2×C7⋊#5642
C2×#903632
C2×#903712
C2×#903512
C2×#903412
C2×#903272
C2×#903162
C2×#903052
C2×#902932
C2×#35537