Finite Group Databasebeta

← C4×C7×#577 #13237388

Subgroups — C4×C7×#577 #13237388

Order 1792.

2742 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#577C211yesmaximal, characteristic
2C4×C7×2−1+4C211yesmaximal, characteristic, complemented
3C4×C7×H(5,𝔽2)C211yesmaximal, characteristic, complemented
4C7×#2952C213yesmaximal, complemented
5C7×#2949C213yesmaximal, complemented
6C7×#2947C213yesmaximal, complemented
7C7×#2946C213yesmaximal, complemented
8C4×C7×#137C213yesmaximal, complemented
9C4×C7×AGL(1,ℤ/8)C213yesmaximal, complemented
10C4×C7×#135C213yesmaximal, complemented
11C2×C4×C7×SD16C213yesmaximal, complemented
12C7×#2912C211yesmaximal, characteristic, complemented
13C7×#2898C211yesmaximal, characteristic, complemented
14C7×#2897C211yesmaximal, characteristic, complemented
15C4×C7×#131C211yesmaximal, characteristic, complemented
16C2×C7×2−1+4C2211yescharacteristic
17C2×C7×H(5,𝔽2)C2211yescharacteristic
18C7×#577C4116yesdirect product factor
19C2×C7×#137C2213yes—
20C2×C7×AGL(1,ℤ/8)C2213yes—
21C2×C7×#135C2213yes—
22C22×C7×SD16C2213yes—
23C2×C7×#131C2211yescharacteristic
24C2×C7×#131C2211yescharacteristic
25C7×#520—21no—
26C7×#520—23no—
27C7×#520C2213yes—
28C7×#520C2211yescharacteristic
29C7×#520C2211yescharacteristic
30C7×#520C2213yescomplemented
31C7×#519—21no—
32C7×#519C2213yescomplemented
33C7×#518—23no—
34C7×#518C2213yes—
35C4×C7×#41—21no—
36C4×C7×#41—23no—
37C4×C7×#41C2213yes—
38C4×C7×#41C2211yescharacteristic
39C4×C7×#41C2213yescomplemented
40C2×C4×C7×Q8—21no—
41C2×C4×C7×Q8C2213yescomplemented
42C2×C4×C7×D4—23no—
43C2×C4×C7×D4C2213yes—
44C7×#442C2216yescomplemented
45C7×#441C2216yescomplemented
46C7×#440C2216yescomplemented
47C7×#440C2216yescomplemented
48C4×C7×Q16C2213yescomplemented
49C4×C7×Q16C2213yescomplemented
50C4×C7×SD16C2213yescomplemented
51C4×C7×SD16C2216yescomplemented
52C4×C7×SD16C2216yescomplemented
53C4×C7×SD16C2216yescomplemented
54C4×C7×SD16C2211yescharacteristic, complemented
55C4×C7×SD16C2213yescomplemented
56C4×C7×SD16C2213yescomplemented
57C4×C7×D8C2213yescomplemented
58C4×C7×D8C2213yescomplemented
59C7×#428C2213yescomplemented
60C7×#428C2213yescomplemented
61C7×#427C2213yescomplemented
62C2×C7×#106C2213yescomplemented
63C7×#419C2213yescomplemented
64C7×#418C2213yes—
65C7×#417C2213yes—
66C7×#417C2213yescomplemented
67C7×#416C2213yes—
68C7×#416C2213yescomplemented
69C2×C7×#103C2213yescomplemented
70C2×C7×#102C2213yes—
71C7×#405C2213yescomplemented
72C7×#405C2213yescomplemented
73C4×C7×M16C2213yescomplemented
74C2×C4×C7×C8C2213yescomplemented
75C4×#577C711yesmaximal, characteristic, direct product factor, Sylow
76C7×2−1+4—24no—
77C7×2−1+4C2×C418yescomplemented
78C7×H(5,𝔽2)—24no—
79C7×H(5,𝔽2)C2×C418yescomplemented
80C2×C7×#41—21no—
81C2×C7×#41—23no—
82C2×C7×#41C2313yes—
83C2×C7×#41C2313yes—
84C2×C7×#41C2311yescharacteristic
85C22×C7×Q8—21no—
86C22×C7×Q8C2313yes—
87C22×C7×D4—23no—
88C22×C7×D4C2313yes—
89C23×C4×C7—23no—
90C7×#137C2×C4124yescomplemented
91C7×AGL(1,ℤ/8)C2×C4124yescomplemented
92C7×#135C2×C4124yescomplemented
93C2×C7×Q16C2313yes—
94C2×C7×SD16C2×C4124yescomplemented
95C2×C7×SD16C2313yes—
96C2×C7×SD16C2316yes—
97C2×C7×SD16C2311yescharacteristic
98C2×C7×D8C2313yes—
99C7×#131—24no—
100C7×#131C2×C418yescomplemented
101C2×C7×M16C2313yes—
102C2×C7×M16C2313yes—
103C22×C7×C8C2313yes—
104C22×C7×C8C2313yes—
105C4×C7×Q8—21no—
106C4×C7×Q8—21no—
107C4×C7×Q8—23no—
108C4×C7×Q8—23no—
109C4×C7×Q8—23no—
110C4×C7×Q8—23no—
111C4×C7×Q8D411yescharacteristic
112C4×C7×Q8D411yescharacteristic
113C4×C7×Q8C2313yes—
114C4×C7×Q8C2316yes—
115C4×C7×Q8C2311yescharacteristic
116C4×C7×Q8C2313yes—
117C4×C7×Q8C2313yes—
118C4×C7×D4—23no—
119C4×C7×D4—23no—
120C4×C7×D4—23no—
121C4×C7×D4—23no—
122C4×C7×D4—23no—
123C4×C7×D4—23no—
124C4×C7×D4—23no—
125C4×C7×D4—23no—
126C4×C7×D4—26no—
127C4×C7×D4—26no—
128C4×C7×D4—23no—
129C4×C7×D4—23no—
130C4×C7×D4D413yes—
131C4×C7×D4D413yes—
132C4×C7×D4C2313yes—
133C4×C7×D4C2316yes—
134C4×C7×D4C2313yes—
135C4×C7×D4C2311yescharacteristic
136C4×C7×D4C2313yes—
137C7×#117—23no—
138C7×#117—23no—
139C7×#117—26no—
140C7×#117—23no—
141C7×#117—23no—
142C7×#117C2313yes—
143C7×#117C2313yes—
144C7×#117C2313yes—
145C2×C7×C4⋊C4—23no—
146C2×C7×C4⋊C4—23no—
147C2×C7×C4⋊C4—23no—
148C2×C7×C4⋊C4C2313yes—
149C2×C7×C4⋊C4C2313yes—
150C2×C7×C22⋊C4—23no—
151C2×C7×C22⋊C4—26no—
152C2×C42×C7—23no—
153C2×C42×C7—23no—
154C2×C42×C7—23no—
155C2×C42×C7C2313yes—
156C7×#107C2313yes—
157C7×#107C2313yes—
158C7×#106C2313yes—
159C7×#106C2316yes—
160C7×#106C2311yescharacteristic
161C7×#103C2313yes—
162C7×#103C2316yes—
163C7×#103C2311yescharacteristic
164C7×#103C2313yes—
165C7×#103C2313yes—
166C7×#102C2313yes—
167C7×#102C2316yes—
168C7×#102C2313yes—
169C7×#102C2311yescharacteristic
170C7×#102C2313yes—
171C7×#97C2316yes—
172C4×C7×C8C2311yescharacteristic
173C4×C7×C8C2313yes—
174C4×C7×C8C2313yes—
175C4×C7×C8C2313yes—
176C2×#577C2×C711yescharacteristic
177C4×2−1+4C2×C711yescharacteristic, complemented
178C4×H(5,𝔽2)C2×C711yescharacteristic, complemented
179#2952C2×C713yescomplemented
180#2949C2×C713yescomplemented
181#2947C2×C713yescomplemented
182#2946C2×C713yescomplemented
183C4×#137C2×C713yescomplemented
184C4×AGL(1,ℤ/8)C2×C713yescomplemented
185C4×#135C2×C713yescomplemented
186C2×C4×SD16C2×C713yescomplemented
187#2912C2×C711yescharacteristic, complemented
188#2898C2×C711yescharacteristic, complemented
189#2897C2×C711yescharacteristic, complemented
190C4×#131C2×C711yescharacteristic, complemented
191C24×C7—23no—
192C7×#41—28no—
193C7×#41—224no—
194C7×#41—26no—
195C7×#41—26no—
196C7×#41C22×C4112yes—
197C7×#41C22×C414yes—
198C7×#41C22×C4112yescomplemented
199C7×#41#4114yes—
200C2×C7×Q8—28no—
201C2×C7×Q8—23no—
202C2×C7×Q8—26no—
203C2×C7×Q8C22×C4112yescomplemented
204C2×C7×Q8C2×D411yescharacteristic
205C2×C7×Q8C2413yes—
206C2×C7×Q8C2411yescharacteristic
207C2×C7×D4—23no—
208C2×C7×D4—23no—
209C2×C7×D4—224no—
210C2×C7×D4—23no—
211C2×C7×D4—26no—
212C2×C7×D4C22×C4112yes—
213C2×C7×D4C2×D413yes—
214C2×C7×D4C2411yescharacteristic
215C2×C7×D4C2413yes—
216C22×C4×C7—23no—
217C22×C4×C7—23no—
218C22×C4×C7—23no—
219C22×C4×C7—23no—
220C22×C4×C7—23no—
221C22×C4×C7—21no—
222C22×C4×C7—23no—
223C22×C4×C7—23no—
224C22×C4×C7—23no—
225C22×C4×C7—26no—
226C22×C4×C7—86no—
227C22×C4×C7C2×D413yes—
228C22×C4×C7C2×D413yes—
229C22×C4×C7C2413yes—
230C7×Q16C22×C4112yescomplemented
231C7×SD16C22×C4112yescomplemented
232C7×SD16C22×C4124yescomplemented
233C7×SD16C22×C414yescomplemented
234C7×D8C22×C4112yescomplemented
235C7×M16—26no—
236C7×M16C22×C4112yescomplemented
237C2×C7×C8—26no—
238C2×C7×C8C22×C4112yescomplemented
239C2×C7×C8C2411yescharacteristic
240C2×C7×C8C2413yes—
241C2×C7×C8C2411yescharacteristic
242C2×C7×C8C2413yes—
243C7×C4⋊C4—23no—
244C7×C4⋊C4—26no—
245C7×C4⋊C4—23no—
246C7×C4⋊C4—23no—
247C7×C4⋊C4—23no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—23no—
250C7×C4⋊C4C2×D413yes—
251C7×C4⋊C4C2×D413yes—
252C7×C4⋊C4C2413yes—
253C7×C4⋊C4C2411yescharacteristic
254C7×C4⋊C4C2413yes—
255C7×C4⋊C4C2411yescharacteristic
256C7×C22⋊C4—23no—
257C7×C22⋊C4—23no—
258C7×C22⋊C4—23no—
259C7×C22⋊C4—26no—
260C7×C22⋊C4—23no—
261C7×C22⋊C4—21no—
262C7×C22⋊C4—23no—
263C7×C22⋊C4C2×D416yes—
264C42×C7—23no—
265C42×C7—23no—
266C42×C7—26no—
267C42×C7—23no—
268C42×C7—23no—
269C42×C7—21no—
270C42×C7—23no—
271C42×C7C2×D413yes—
272C42×C7C2×D413yes—
273C42×C7C2413yes—
274C42×C7C2411yescharacteristic
275C2×2−1+4C22×C711yescharacteristic
276C2×H(5,𝔽2)C22×C711yescharacteristic
277#577C4×C7116yesdirect product factor
278C2×#137C22×C713yes—
279C2×AGL(1,ℤ/8)C22×C713yes—
280C2×#135C22×C713yes—
281C22×SD16C22×C713yes—
282C2×#131C22×C711yescharacteristic
283C2×#131C22×C711yescharacteristic
284#520—21no—
285#520—23no—
286#520C22×C713yes—
287#520C22×C711yescharacteristic
288#520C22×C711yescharacteristic
289#520C22×C713yescomplemented
290#519—21no—
291#519C22×C713yescomplemented
292#518—23no—
293#518C22×C713yes—
294C4×#41—21no—
295C4×#41—23no—
296C4×#41C22×C713yes—
297C4×#41C22×C711yescharacteristic
298C4×#41C22×C713yescomplemented
299C2×C4×Q8—21no—
300C2×C4×Q8C22×C713yescomplemented
301C2×C4×D4—23no—
302C2×C4×D4C22×C713yes—
303#442C22×C716yescomplemented
304#441C22×C716yescomplemented
305#440C22×C716yescomplemented
306#440C22×C716yescomplemented
307C4×Q16C22×C713yescomplemented
308C4×Q16C22×C713yescomplemented
309C4×SD16C22×C713yescomplemented
310C4×SD16C22×C716yescomplemented
311C4×SD16C22×C716yescomplemented
312C4×SD16C22×C716yescomplemented
313C4×SD16C22×C711yescharacteristic, complemented
314C4×SD16C22×C713yescomplemented
315C4×SD16C22×C713yescomplemented
316C4×D8C22×C713yescomplemented
317C4×D8C22×C713yescomplemented
318#428C22×C713yescomplemented
319#428C22×C713yescomplemented
320#427C22×C713yescomplemented
321C2×#106C22×C713yescomplemented
322#419C22×C713yescomplemented
323#418C22×C713yes—
324#417C22×C713yes—
325#417C22×C713yescomplemented
326#416C22×C713yes—
327#416C22×C713yescomplemented
328C2×#103C22×C713yescomplemented
329C2×#102C22×C713yes—
330#405C22×C713yescomplemented
331#405C22×C713yescomplemented
332C4×M16C22×C713yescomplemented
333C2×C4×C8C22×C713yescomplemented
334C23×C7—21no—
335C23×C7—23no—
336C23×C7—212no—
337C23×C7—83no—
338C23×C7—83no—
339C23×C7C22×D413yes—
340C7×Q8—212no—
341C7×Q8—23no—
342C7×Q8—21no—
343C7×Q8C4×D414yes—
344C7×Q8C23×C416yes—
345C7×Q8C23×C412yes—
346C7×D4—212no—
347C7×D4—212no—
348C7×D4—212no—
349C7×D4—23no—
350C7×D4—21no—
351C7×D4C4×D4112yes—
352C7×D4C23×C412yes—
353C7×D4C23×C416yes—
354C2×C4×C7—212no—
355C2×C4×C7—21no—
356C2×C4×C7—23no—
357C2×C4×C7—212no—
358C2×C4×C7—212no—
359C2×C4×C7—26no—
360C2×C4×C7—21no—
361C2×C4×C7—21no—
362C2×C4×C7—23no—
363C2×C4×C7—23no—
364C2×C4×C7—43no—
365C2×C4×C7—42no—
366C2×C4×C7—46no—
367C2×C4×C7—83no—
368C2×C4×C7—83no—
369C2×C4×C7—86no—
370C2×C4×C7—83no—
371C2×C4×C7—83no—
372C2×C4×C7C23×C416yes—
373C2×C4×C7C22×D413yes—
374C2×C4×C7C22×D413yes—
375C2×C4×C7C22×D411yescharacteristic
376C2×C4×C7C22×D413yes—
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C2×#4116yes—
379C2×C4×C7C2511yescharacteristic
380C7×C8—21no—
381C7×C8—23no—
382C7×C8C23×C412yes—
383C7×C8C23×C416yes—
3842−1+4—24no—
3852−1+4C2×C4×C718yescomplemented
386H(5,𝔽2)—24no—
387H(5,𝔽2)C2×C4×C718yescomplemented
388C2×#41—21no—
389C2×#41—23no—
390C2×#41C23×C713yes—
391C2×#41C23×C713yes—
392C2×#41C23×C711yescharacteristic
393C22×Q8—21no—
394C22×Q8C23×C713yes—
395C22×D4—23no—
396C22×D4C23×C713yes—
397C23×C4—23no—
398#137C2×C4×C7124yescomplemented
399AGL(1,ℤ/8)C2×C4×C7124yescomplemented
400#135C2×C4×C7124yescomplemented
401C2×Q16C23×C713yes—
402C2×SD16C2×C4×C7124yescomplemented
403C2×SD16C23×C713yes—
404C2×SD16C23×C716yes—
405C2×SD16C23×C711yescharacteristic
406C2×D8C23×C713yes—
407#131—24no—
408#131C2×C4×C718yescomplemented
409C2×M16C23×C713yes—
410C2×M16C23×C713yes—
411C22×C8C23×C713yes—
412C22×C8C23×C713yes—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—23no—
416C4×Q8—23no—
417C4×Q8—23no—
418C4×Q8—23no—
419C4×Q8C7×D411yescharacteristic
420C4×Q8C7×D411yescharacteristic
421C4×Q8C23×C713yes—
422C4×Q8C23×C716yes—
423C4×Q8C23×C711yescharacteristic
424C4×Q8C23×C713yes—
425C4×Q8C23×C713yes—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4—23no—
429C4×D4—23no—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—26no—
435C4×D4—26no—
436C4×D4—23no—
437C4×D4—23no—
438C4×D4C7×D413yes—
439C4×D4C7×D413yes—
440C4×D4C23×C713yes—
441C4×D4C23×C716yes—
442C4×D4C23×C713yes—
443C4×D4C23×C711yescharacteristic
444C4×D4C23×C713yes—
445#117—23no—
446#117—23no—
447#117—26no—
448#117—23no—
449#117—23no—
450#117C23×C713yes—
451#117C23×C713yes—
452#117C23×C713yes—
453C2×C4⋊C4—23no—
454C2×C4⋊C4—23no—
455C2×C4⋊C4—23no—
456C2×C4⋊C4C23×C713yes—
457C2×C4⋊C4C23×C713yes—
458C2×C22⋊C4—23no—
459C2×C22⋊C4—26no—
460C2×C42—23no—
461C2×C42—23no—
462C2×C42—23no—
463C2×C42C23×C713yes—
464#107C23×C713yes—
465#107C23×C713yes—
466#106C23×C713yes—
467#106C23×C716yes—
468#106C23×C711yescharacteristic
469#103C23×C713yes—
470#103C23×C716yes—
471#103C23×C711yescharacteristic
472#103C23×C713yes—
473#103C23×C713yes—
474#102C23×C713yes—
475#102C23×C716yes—
476#102C23×C713yes—
477#102C23×C711yescharacteristic
478#102C23×C713yes—
479#97C23×C716yes—
480C4×C8C23×C711yescharacteristic
481C4×C8C23×C713yes—
482C4×C8C23×C713yes—
483C4×C8C23×C713yes—
484C22×C7—23no—
485C22×C7—23no—
486C22×C7—22no—
487C22×C7—26no—
488C22×C7—41no—
489C22×C7—43no—
490C22×C7—43no—
491C22×C7—41no—
492C22×C7—812no—
493C22×C7C2×C4×D416yes—
494C22×C7C23×D411yescharacteristic
495C4×C7—21no—
496C4×C7—23no—
497C4×C7—22no—
498C4×C7—26no—
499C4×C7—23no—
500C4×C7—41no—
501C4×C7—43no—
502C4×C7—41no—
503C4×C7—43no—
504C4×C7C2×C4×D416yes—
505C4×C7#57712yesdirect product factor
506C4×C7C24×C411yescharacteristic
507C4×C7C22×#4111yescharacteristic
508C24—23no—
509#41—28no—
510#41—224no—
511#41—26no—
512#41—26no—
513#41C22×C4×C7112yes—
514#41C22×C4×C714yes—
515#41C22×C4×C7112yescomplemented
516#41C7×#4114yes—
517C2×Q8—28no—
518C2×Q8—23no—
519C2×Q8—26no—
520C2×Q8C22×C4×C7112yescomplemented
521C2×Q8C2×C7×D411yescharacteristic
522C2×Q8C24×C713yes—
523C2×Q8C24×C711yescharacteristic
524C2×D4—23no—
525C2×D4—23no—
526C2×D4—224no—
527C2×D4—23no—
528C2×D4—26no—
529C2×D4C22×C4×C7112yes—
530C2×D4C2×C7×D413yes—
531C2×D4C24×C711yescharacteristic
532C2×D4C24×C713yes—
533C22×C4—23no—
534C22×C4—23no—
535C22×C4—23no—
536C22×C4—23no—
537C22×C4—23no—
538C22×C4—21no—
539C22×C4—23no—
540C22×C4—23no—
541C22×C4—23no—
542C22×C4—26no—
543C22×C4—86no—
544C22×C4C2×C7×D413yes—
545C22×C4C2×C7×D413yes—
546C22×C4C24×C713yes—
547Q16C22×C4×C7112yescomplemented
548SD16C22×C4×C7112yescomplemented
549SD16C22×C4×C7124yescomplemented
550SD16C22×C4×C714yescomplemented
551D8C22×C4×C7112yescomplemented
552M16—26no—
553M16C22×C4×C7112yescomplemented
554C2×C8—26no—
555C2×C8C22×C4×C7112yescomplemented
556C2×C8C24×C711yescharacteristic
557C2×C8C24×C713yes—
558C2×C8C24×C711yescharacteristic
559C2×C8C24×C713yes—
560C4⋊C4—23no—
561C4⋊C4—26no—
562C4⋊C4—23no—
563C4⋊C4—23no—
564C4⋊C4—23no—
565C4⋊C4—21no—
566C4⋊C4—23no—
567C4⋊C4C2×C7×D413yes—
568C4⋊C4C2×C7×D413yes—
569C4⋊C4C24×C713yes—
570C4⋊C4C24×C711yescharacteristic
571C4⋊C4C24×C713yes—
572C4⋊C4C24×C711yescharacteristic
573C22⋊C4—23no—
574C22⋊C4—23no—
575C22⋊C4—23no—
576C22⋊C4—26no—
577C22⋊C4—23no—
578C22⋊C4—21no—
579C22⋊C4—23no—
580C22⋊C4C2×C7×D416yes—
581C42—21no—
582C42—23no—
583C42—23no—
584C42—23no—
585C42—26no—
586C42—23no—
587C42—23no—
588C42C2×C7×D413yes—
589C42C2×C7×D413yes—
590C42C24×C711yescharacteristic
591C42C24×C713yes—
592C2×C7—26no—
593C2×C7—42no—
594C2×C7—46no—
595C2×C7C22×C4×D411yescharacteristic
596C2×C7C2×#57711yescharacteristic
597C2×C7#358411yescharacteristic
598C23—21no—
599C23—23no—
600C23—212no—
601C23—83no—
602C23—83no—
603C23C22×C7×D413yes—
604Q8—23no—
605Q8—21no—
606Q8—212no—
607Q8C4×C7×D414yes—
608Q8C23×C4×C716yes—
609Q8C23×C4×C712yes—
610D4—212no—
611D4—212no—
612D4—23no—
613D4—21no—
614D4—212no—
615D4C4×C7×D4112yes—
616D4C23×C4×C712yes—
617D4C23×C4×C716yes—
618C2×C4—21no—
619C2×C4—23no—
620C2×C4—212no—
621C2×C4—212no—
622C2×C4—212no—
623C2×C4—26no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—23no—
627C2×C4—23no—
628C2×C4—43no—
629C2×C4—42no—
630C2×C4—46no—
631C2×C4—83no—
632C2×C4—83no—
633C2×C4—86no—
634C2×C4—83no—
635C2×C4—83no—
636C2×C4C23×C4×C716yes—
637C2×C4C22×C7×D413yes—
638C2×C4C22×C7×D413yes—
639C2×C4C22×C7×D411yescharacteristic
640C2×C4C22×C7×D413yes—
641C2×C4C22×C7×D411yescharacteristic
642C2×C4C2×C7×#4116yes—
643C2×C4C25×C711yescharacteristic
644C8—21no—
645C8—23no—
646C8C23×C4×C712yes—
647C8C23×C4×C716yes—
648C7C4×#57711yescharacteristic, direct product factor, Sylow
649C22—23no—
650C22—23no—
651C22—22no—
652C22—26no—
653C22—43no—
654C22—41no—
655C22—41no—
656C22—43no—
657C22—812no—
658C22C2×C4×C7×D416yes—
659C22C23×C7×D411yescharacteristic
660C4—23no—
661C4—21no—
662C4—23no—
663C4—22no—
664C4—26no—
665C4—43no—
666C4—41no—
667C4—41no—
668C4—43no—
669C4C2×C4×C7×D416yes—
670C4C7×#57712yesdirect product factor
671C4C24×C4×C711yescharacteristic
672C4C22×C7×#4111yescharacteristic
673C2—26no—
674C2—46no—
675C2—42no—
676C2C22×C4×C7×D411yescharacteristic
677C2C2×C7×#57711yescharacteristic
678C2C7×#358411yescharacteristic
subgroupG/H
centerC2×C4×C7C22×D4
commutatorC4C24×C4×C7
Frattini, cosocleC2×C4C25×C7
socleC22×C7C23×D4
prime radicalC2×C7×#577C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C7 ◁ C4×C7×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C7×2−1+4C2semidirect
3. C4×C7×H(5,𝔽2)C2semidirect
4. C7×#2952C2semidirect
5. C7×#2949C2semidirect
6. C7×#2947C2semidirect
7. C7×#2946C2semidirect
8. C4×C7×#137C2semidirect
9. C4×C7×AGL(1,ℤ/8)C2semidirect
10. C4×C7×#135C2semidirect
11. C2×C4×C7×SD16C2semidirect
12. C7×#2912C2semidirect
13. C7×#2898C2semidirect
14. C7×#2897C2semidirect
15. C4×C7×#131C2semidirect
18. C7×#577C4direct (N × H)
30. C7×#520C22semidirect
32. C7×#519C22semidirect
39. C4×C7×#41C22semidirect
41. C2×C4×C7×Q8C22semidirect
44. C7×#442C22semidirect
45. C7×#441C22semidirect
46. C7×#440C22semidirect
47. C7×#440C22semidirect
48. C4×C7×Q16C22semidirect
49. C4×C7×Q16C22semidirect
50. C4×C7×SD16C22semidirect
51. C4×C7×SD16C22semidirect
52. C4×C7×SD16C22semidirect
53. C4×C7×SD16C22semidirect
54. C4×C7×SD16C22semidirect
55. C4×C7×SD16C22semidirect
56. C4×C7×SD16C22semidirect
57. C4×C7×D8C22semidirect
58. C4×C7×D8C22semidirect
59. C7×#428C22semidirect
60. C7×#428C22semidirect
61. C7×#427C22semidirect
62. C2×C7×#106C22semidirect
63. C7×#419C22semidirect
66. C7×#417C22semidirect
68. C7×#416C22semidirect
69. C2×C7×#103C22semidirect
71. C7×#405C22semidirect
72. C7×#405C22semidirect
73. C4×C7×M16C22semidirect
74. C2×C4×C7×C8C22semidirect
75. C4×#577C7direct (N × H)
77. C7×2−1+4C2×C4semidirect
79. C7×H(5,𝔽2)C2×C4semidirect
90. C7×#137C2×C4semidirect
91. C7×AGL(1,ℤ/8)C2×C4semidirect
92. C7×#135C2×C4semidirect
94. C2×C7×SD16C2×C4semidirect
100. C7×#131C2×C4semidirect
177. C4×2−1+4C2×C7semidirect
178. C4×H(5,𝔽2)C2×C7semidirect
179. #2952C2×C7semidirect
180. #2949C2×C7semidirect
181. #2947C2×C7semidirect
182. #2946C2×C7semidirect
183. C4×#137C2×C7semidirect
184. C4×AGL(1,ℤ/8)C2×C7semidirect
185. C4×#135C2×C7semidirect
186. C2×C4×SD16C2×C7semidirect
187. #2912C2×C7semidirect
188. #2898C2×C7semidirect
189. #2897C2×C7semidirect
190. C4×#131C2×C7semidirect
198. C7×#41C22×C4semidirect
203. C2×C7×Q8C22×C4semidirect
230. C7×Q16C22×C4semidirect
231. C7×SD16C22×C4semidirect
232. C7×SD16C22×C4semidirect
233. C7×SD16C22×C4semidirect
234. C7×D8C22×C4semidirect
236. C7×M16C22×C4semidirect
238. C2×C7×C8C22×C4semidirect
277. #577C4×C7direct (N × H)
289. #520C22×C7semidirect
291. #519C22×C7semidirect
298. C4×#41C22×C7semidirect
300. C2×C4×Q8C22×C7semidirect
303. #442C22×C7semidirect
304. #441C22×C7semidirect
305. #440C22×C7semidirect
306. #440C22×C7semidirect
307. C4×Q16C22×C7semidirect
308. C4×Q16C22×C7semidirect
309. C4×SD16C22×C7semidirect
310. C4×SD16C22×C7semidirect
311. C4×SD16C22×C7semidirect
312. C4×SD16C22×C7semidirect
313. C4×SD16C22×C7semidirect
314. C4×SD16C22×C7semidirect
315. C4×SD16C22×C7semidirect
316. C4×D8C22×C7semidirect
317. C4×D8C22×C7semidirect
318. #428C22×C7semidirect
319. #428C22×C7semidirect
320. #427C22×C7semidirect
321. C2×#106C22×C7semidirect
322. #419C22×C7semidirect
325. #417C22×C7semidirect
327. #416C22×C7semidirect
328. C2×#103C22×C7semidirect
330. #405C22×C7semidirect
331. #405C22×C7semidirect
332. C4×M16C22×C7semidirect
333. C2×C4×C8C22×C7semidirect
385. 2−1+4C2×C4×C7semidirect
387. H(5,𝔽2)C2×C4×C7semidirect
398. #137C2×C4×C7semidirect
399. AGL(1,ℤ/8)C2×C4×C7semidirect
400. #135C2×C4×C7semidirect
402. C2×SD16C2×C4×C7semidirect
408. #131C2×C4×C7semidirect
505. C4×C7#577direct (N × H)
515. #41C22×C4×C7semidirect
520. C2×Q8C22×C4×C7semidirect
547. Q16C22×C4×C7semidirect
548. SD16C22×C4×C7semidirect
549. SD16C22×C4×C7semidirect
550. SD16C22×C4×C7semidirect
551. D8C22×C4×C7semidirect
553. M16C22×C4×C7semidirect
555. C2×C8C22×C4×C7semidirect
648. C7C4×#577direct (N × H)
670. C4C7×#577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5772
C4×C7×2−1+42
C4×C7×H(5,𝔽2)2
C7×#29522
C7×#29492
C7×#29472
C7×#29462
C4×C7×#1372
C4×C7×AGL(1,ℤ/8)2
C4×C7×#1352
C2×C4×C7×SD162
C7×#29122
C7×#28982
C7×#28972
C4×C7×#1312
C4×#5777