Finite Group Databasebeta

← C7×#13871 #13191087

Subgroups — C7×#13871 #13191087

Order 1792.

2590 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C22×C7×#117C211yesmaximal, characteristic, complemented
3C2×C7×#380C211yesmaximal, characteristic, complemented
4C2×C7×#380C212yesmaximal, complemented
5C7×#1440C212yesmaximal, complemented
6C7×#1438C212yesmaximal
7C7×#1437C212yesmaximal, complemented
8C7×#1436C212yesmaximal, complemented
9C7×C4⋊#95C212yesmaximal, complemented
10C23×C7×D4C2211yescharacteristic
11C24×C4×C7C2211yescharacteristic
12C24×C4×C7C2211yescharacteristic
13C2×C4×C7×D4—24no—
14C2×C4×C7×D4—24no—
15C2×C4×C7×D4C418yescomplemented
16C2×C7×#117—24no—
17C2×C7×#117—28no—
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2214yes—
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2212yes—
26C22×C42×C7C2212yes—
27C22×C42×C7C2211yescharacteristic
28C7×#380—24no—
29C7×#380—28no—
30C2×C7×#95C2212yes—
31C2×C7×#95C2214yes—
32C2×C7×#95C2214yes—
33C2×C7×#95C2214yes—
34#13871C711yesmaximal, characteristic, direct product factor, Sylow
35C25×C7C2311yescharacteristic
36C25×C7C2311yescharacteristic
37C22×C7×D4—22no—
38C22×C7×D4—22no—
39C22×C7×D4—24no—
40C22×C7×D4—24no—
41C22×C7×D4C2×C414yes—
42C23×C4×C7—24no—
43C23×C4×C7—24no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—24no—
47C23×C4×C7—24no—
48C23×C4×C7C2×C414yes—
49C23×C4×C7C2×C414yes—
50C23×C4×C7D414yes—
51C23×C4×C7D414yes—
52C23×C4×C7C2314yes—
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2314yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C4×C7×D4—232no—
60C7×#117—232no—
61C2×C7×C4⋊C4—24no—
62C2×C7×C4⋊C4—24no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—24no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4C2×C414yes—
69C2×C7×C4⋊C4D418yescomplemented
70C2×C7×C22⋊C4—24no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—28no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—28no—
78C2×C7×C22⋊C4—28no—
79C2×C7×C22⋊C4—44no—
80C2×C7×C22⋊C4—44no—
81C2×C7×C22⋊C4C2×C414yes—
82C2×C7×C22⋊C4C2×C414yes—
83C2×C42×C7—28no—
84C2×C42×C7—24no—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7C2×C414yes—
88C7×#95—28no—
89C7×#95—24no—
90C7×#95—28no—
91C7×#95—44no—
92C22×C4×D4C2×C711yescharacteristic
93C22×#117C2×C711yescharacteristic, complemented
94C2×#380C2×C712yescomplemented
95C2×#380C2×C711yescharacteristic, complemented
96#1440C2×C712yescomplemented
97#1438C2×C712yes—
98#1437C2×C712yescomplemented
99#1436C2×C712yescomplemented
100C4⋊#95C2×C712yescomplemented
101C24×C7—22no—
102C24×C7—22no—
103C24×C7—21no—
104C24×C7—21no—
105C24×C7—22no—
106C24×C7—22no—
107C24×C7—22no—
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7—22no—
113C24×C7—22no—
114C24×C7C22×C412yes—
115C24×C7C22×C412yes—
116C24×C7C2×D412yes—
117C24×C7C2×D412yes—
118C24×C7#4114yes—
119C24×C7C2411yescharacteristic
120C2×C7×D4—216no—
121C2×C7×D4—216no—
122C2×C7×D4—28no—
123C2×C7×D4—28no—
124C2×C7×D4—28no—
125C22×C4×C7—22no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—216no—
131C22×C4×C7—28no—
132C22×C4×C7—216no—
133C22×C4×C7—28no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—24no—
138C22×C4×C7—24no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—24no—
142C22×C4×C7—24no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—24no—
146C22×C4×C7—22no—
147C22×C4×C7—24no—
148C22×C4×C7—28no—
149C22×C4×C7—216no—
150C22×C4×C7—24no—
151C22×C4×C7—24no—
152C22×C4×C7—24no—
153C22×C4×C7—24no—
154C22×C4×C7—24no—
155C22×C4×C7—24no—
156C22×C4×C7—24no—
157C22×C4×C7—44no—
158C22×C4×C7—48no—
159C22×C4×C7—44no—
160C22×C4×C7C22⋊C4116yescomplemented
161C22×C4×C7C22×C412yes—
162C22×C4×C7C22×C412yes—
163C22×C4×C7C22×C412yes—
164C22×C4×C7C22×C412yes—
165C22×C4×C7C22×C412yes—
166C22×C4×C7C2×D418yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2×D412yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D414yes—
172C22×C4×C7#4114yes—
173C22×C4×C7#4114yes—
174C7×C4⋊C4—28no—
175C7×C4⋊C4—216no—
176C7×C4⋊C4—48no—
177C7×C22⋊C4—216no—
178C7×C22⋊C4—28no—
179C7×C22⋊C4—28no—
180C7×C22⋊C4—416no—
181C7×C22⋊C4—48no—
182C42×C7—216no—
183C42×C7—28no—
184C23×D4C22×C711yescharacteristic
185C24×C4C22×C711yescharacteristic
186C24×C4C22×C711yescharacteristic
187C2×C4×D4—24no—
188C2×C4×D4—24no—
189C2×C4×D4C4×C718yescomplemented
190C2×#117—24no—
191C2×#117—28no—
192C22×C4⋊C4C22×C712yes—
193C22×C4⋊C4C22×C711yescharacteristic
194C22×C4⋊C4C22×C712yes—
195C22×C22⋊C4C22×C712yes—
196C22×C22⋊C4C22×C714yes—
197C22×C22⋊C4C22×C711yescharacteristic
198C22×C22⋊C4C22×C711yescharacteristic
199C22×C22⋊C4C22×C712yes—
200C22×C42C22×C712yes—
201C22×C42C22×C711yescharacteristic
202#380—24no—
203#380—28no—
204C2×#95C22×C714yes—
205C2×#95C22×C712yes—
206C2×#95C22×C714yes—
207C2×#95C22×C714yes—
208C23×C7—22no—
209C23×C7—22no—
210C23×C7—22no—
211C23×C7—22no—
212C23×C7—24no—
213C23×C7—24no—
214C23×C7—24no—
215C23×C7—24no—
216C23×C7—22no—
217C23×C7—24no—
218C23×C7—22no—
219C23×C7—24no—
220C23×C7—24no—
221C23×C7—24no—
222C23×C7—24no—
223C23×C7—22no—
224C23×C7—22no—
225C23×C7—24no—
226C23×C7—24no—
227C23×C7—24no—
228C23×C7—24no—
229C23×C7—24no—
230C23×C7—41no—
231C23×C7—42no—
232C23×C7—41no—
233C23×C7—41no—
234C23×C7—41no—
235C23×C7—42no—
236C23×C7—42no—
237C23×C7—42no—
238C23×C7—42no—
239C23×C7—42no—
240C23×C7—42no—
241C23×C7—42no—
242C23×C7—42no—
243C23×C7—42no—
244C23×C7—42no—
245C23×C7—42no—
246C23×C7—42no—
247C23×C7—42no—
248C23×C7C2×C22⋊C414yes—
249C23×C7#11714yescomplemented
250C23×C7C23×C411yescharacteristic
251C23×C7C22×D411yescharacteristic
252C23×C7C22×D411yescharacteristic
253C23×C7C22×D412yes—
254C23×C7C2×#4112yes—
255C23×C7C2×#4112yes—
256C23×C7C2×#4112yes—
257C23×C7H(5,𝔽2)12yes—
258C23×C72−1+412yes—
259C7×D4—232no—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—24no—
263C2×C4×C7—22no—
264C2×C4×C7—24no—
265C2×C4×C7—22no—
266C2×C4×C7—24no—
267C2×C4×C7—24no—
268C2×C4×C7—232no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—28no—
274C2×C4×C7—28no—
275C2×C4×C7—28no—
276C2×C4×C7—41no—
277C2×C4×C7—42no—
278C2×C4×C7—41no—
279C2×C4×C7—44no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—42no—
283C2×C4×C7—44no—
284C2×C4×C7—44no—
285C2×C4×C7—44no—
286C2×C4×C7—416no—
287C2×C4×C7—44no—
288C2×C4×C7—44no—
289C2×C4×C7—44no—
290C2×C4×C7—44no—
291C2×C4×C7—44no—
292C2×C4×C7—44no—
293C2×C4×C7—44no—
294C2×C4×C7C2×C22⋊C414yes—
295C2×C4×C7C2×C22⋊C414yes—
296C2×C4×C7#11714yescomplemented
297C2×C4×C7C4×D418yes—
298C2×C4×C7#12014yes—
299C2×C4×C7#12118yes—
300C2×C4×C7#12314yes—
301C25C23×C711yescharacteristic
302C25C23×C711yescharacteristic
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4C2×C4×C714yes—
308C23×C4—24no—
309C23×C4—24no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—24no—
313C23×C4—24no—
314C23×C4C2×C4×C714yes—
315C23×C4C2×C4×C714yes—
316C23×C4C7×D414yes—
317C23×C4C7×D414yes—
318C23×C4C23×C714yes—
319C23×C4C23×C711yescharacteristic
320C23×C4C23×C711yescharacteristic
321C23×C4C23×C714yes—
322C23×C4C23×C711yescharacteristic
323C23×C4C23×C711yescharacteristic
324C23×C4C23×C711yescharacteristic
325C4×D4—232no—
326#117—232no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4C2×C4×C714yes—
335C2×C4⋊C4C7×D418yescomplemented
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4C2×C4×C714yes—
348C2×C22⋊C4C2×C4×C714yes—
349C2×C42—28no—
350C2×C42—24no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42C2×C4×C714yes—
354#95—28no—
355#95—24no—
356#95—28no—
357#95—44no—
358C22×C7—24no—
359C22×C7—28no—
360C22×C7—24no—
361C22×C7—24no—
362C22×C7—24no—
363C22×C7—42no—
364C22×C7—44no—
365C22×C7—44no—
366C22×C7—44no—
367C22×C7—44no—
368C22×C7—44no—
369C22×C7—44no—
370C22×C7—44no—
371C22×C7—44no—
372C22×C7—44no—
373C22×C7—44no—
374C22×C7—44no—
375C22×C7—42no—
376C22×C7C22×C22⋊C411yescharacteristic
377C22×C7C2×#11711yescharacteristic
378C22×C7C2×#11711yescharacteristic
379C22×C7C2×C4×D412yes—
380C22×C7#52012yes—
381C22×C7C2×#12011yescharacteristic
382C22×C7C2×#12112yes—
383C22×C7C2×#12311yescharacteristic
384C22×C7#52512yes—
385C22×C7#52512yes—
386C22×C7#53511yescharacteristic
387C22×C7#53611yescharacteristic
388C22×C7#53712yes—
389C22×C7#54612yes—
390C22×C7#54712yes—
391C22×C7#54812yes—
392C22×C7#55012yes—
393C22×C7#55212yes—
394C22×C7#55312yes—
395C22×C7#55512yes—
396C22×C7#55612yes—
397C4×C7—24no—
398C4×C7—24no—
399C4×C7—42no—
400C4×C7—48no—
401C4×C7—42no—
402C4×C7—84no—
403C4×C7#38618yes—
404C24—22no—
405C24—22no—
406C24—21no—
407C24—21no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24C22×C4×C712yes—
418C24C22×C4×C712yes—
419C24C2×C7×D412yes—
420C24C2×C7×D412yes—
421C24C7×#4114yes—
422C24C24×C711yescharacteristic
423C2×D4—216no—
424C2×D4—216no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—28no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—216no—
434C22×C4—28no—
435C22×C4—216no—
436C22×C4—28no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—28no—
452C22×C4—216no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—44no—
461C22×C4—48no—
462C22×C4—44no—
463C22×C4C7×C22⋊C4116yescomplemented
464C22×C4C22×C4×C712yes—
465C22×C4C22×C4×C712yes—
466C22×C4C22×C4×C712yes—
467C22×C4C22×C4×C712yes—
468C22×C4C22×C4×C712yes—
469C22×C4C2×C7×D418yes—
470C22×C4C2×C7×D412yes—
471C22×C4C2×C7×D412yes—
472C22×C4C2×C7×D412yes—
473C22×C4C2×C7×D412yes—
474C22×C4C2×C7×D414yes—
475C22×C4C7×#4114yes—
476C22×C4C7×#4114yes—
477C4⋊C4—28no—
478C4⋊C4—216no—
479C4⋊C4—48no—
480C22⋊C4—216no—
481C22⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—416no—
484C22⋊C4—48no—
485C42—216no—
486C42—28no—
487C2×C7—44no—
488C2×C7—44no—
489C2×C7#228011yescharacteristic
490C2×C7C2×#38611yescharacteristic
491C2×C7#231111yescharacteristic
492C2×C7#235212yes—
493C2×C7#235412yes—
494C2×C7#240712yes—
495C2×C7#241412yes—
496C2×C7#241512yes—
497C2×C7#248512yes—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—22no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—41no—
521C23—42no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23C2×C7×C22⋊C414yes—
539C23C7×#11714yescomplemented
540C23C23×C4×C711yescharacteristic
541C23C22×C7×D411yescharacteristic
542C23C22×C7×D411yescharacteristic
543C23C22×C7×D412yes—
544C23C2×C7×#4112yes—
545C23C2×C7×#4112yes—
546C23C2×C7×#4112yes—
547C23C7×H(5,𝔽2)12yes—
548C23C7×2−1+412yes—
549D4—232no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—232no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—28no—
564C2×C4—28no—
565C2×C4—28no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—44no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—416no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4C2×C7×C22⋊C414yes—
585C2×C4C2×C7×C22⋊C414yes—
586C2×C4C7×#11714yescomplemented
587C2×C4C4×C7×D418yes—
588C2×C4C7×#12014yes—
589C2×C4C7×#12118yes—
590C2×C4C7×#12314yes—
591C7#1387111yescharacteristic, direct product factor, Sylow
592C22—24no—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—28no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—42no—
606C22—42no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22C22×C7×C22⋊C411yescharacteristic
611C22C2×C7×#11711yescharacteristic
612C22C2×C7×#11711yescharacteristic
613C22C2×C4×C7×D412yes—
614C22C7×#52012yes—
615C22C2×C7×#12011yescharacteristic
616C22C2×C7×#12112yes—
617C22C2×C7×#12311yescharacteristic
618C22C7×#52512yes—
619C22C7×#52512yes—
620C22C7×#53511yescharacteristic
621C22C7×#53611yescharacteristic
622C22C7×#53712yes—
623C22C7×#54612yes—
624C22C7×#54712yes—
625C22C7×#54812yes—
626C22C7×#55012yes—
627C22C7×#55212yes—
628C22C7×#55312yes—
629C22C7×#55512yes—
630C22C7×#55612yes—
631C4—24no—
632C4—24no—
633C4—48no—
634C4—42no—
635C4—42no—
636C4—84no—
637C4C7×#38618yes—
638C2—44no—
639C2—44no—
640C2C7×#228011yescharacteristic
641C2C2×C7×#38611yescharacteristic
642C2C7×#231111yescharacteristic
643C2C7×#235212yes—
644C2C7×#235412yes—
645C2C7×#240712yes—
646C2C7×#241412yes—
647C2C7×#241512yes—
648C2C7×#248512yes—
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C7×#117C2semidirect
3. C2×C7×#380C2semidirect
4. C2×C7×#380C2semidirect
5. C7×#1440C2semidirect
7. C7×#1437C2semidirect
8. C7×#1436C2semidirect
9. C7×C4⋊#95C2semidirect
15. C2×C4×C7×D4C4semidirect
34. #13871C7direct (N × H)
69. C2×C7×C4⋊C4D4semidirect
93. C22×#117C2×C7semidirect
94. C2×#380C2×C7semidirect
95. C2×#380C2×C7semidirect
96. #1440C2×C7semidirect
98. #1437C2×C7semidirect
99. #1436C2×C7semidirect
100. C4⋊#95C2×C7semidirect
160. C22×C4×C7C22⋊C4semidirect
189. C2×C4×D4C4×C7semidirect
249. C23×C7#117semidirect
296. C2×C4×C7#117semidirect
335. C2×C4⋊C4C7×D4semidirect
463. C22×C4C7×C22⋊C4semidirect
539. C23C7×#117semidirect
586. C2×C4C7×#117semidirect
591. C7#13871direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C22×C7×#1172
C2×C7×#3802
C7×#14402
C7×#14382
C7×#14372
C7×#14362
C7×C4⋊#952
#138717