Finite Group Databasebeta

← C7×#14410 #13191626

Subgroups — C7×#14410 #13191626

Order 1792.

1866 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C212yesmaximal, complemented
2C2×C7×#386C211yesmaximal, characteristic
3C2×C7×#380C212yesmaximal, complemented
4C7×#1442C212yesmaximal, complemented
5C7×#1439C212yesmaximal, complemented
6C7×#1438C211yesmaximal, characteristic
7C7×#1438C211yesmaximal, characteristic
8C7×#1437C212yesmaximal, complemented
9C7×#1436C212yesmaximal, complemented
10C23×C7×D4C2211yescharacteristic
11C24×C4×C7C2211yescharacteristic
12C22×C7×C4⋊C4C2212yes—
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C22⋊C4C2212yes—
15C22×C7×C22⋊C4C2212yes—
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2212yes—
22C7×#388—28no—
23C7×#386C418yescomplemented
24C7×#380—28no—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34#14410C711yesmaximal, characteristic, direct product factor, Sylow
35C25×C7C2311yescharacteristic
36C25×C7C2311yescharacteristic
37C22×C7×D4—24no—
38C22×C7×D4—42no—
39C22×C7×D4—41no—
40C22×C7×D4—41no—
41C22×C7×D4C2×C414yes—
42C23×C4×C7—24no—
43C23×C4×C7—24no—
44C23×C4×C7—41no—
45C23×C4×C7—41no—
46C23×C4×C7C2×C414yes—
47C23×C4×C7C2312yes—
48C23×C4×C7C2312yes—
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2312yes—
51C23×C4×C7C2312yes—
52C23×C4×C7C2312yes—
53C23×C4×C7C2312yes—
54C2×C7×C4⋊C4—24no—
55C2×C7×C4⋊C4—24no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—24no—
58C2×C7×C4⋊C4—42no—
59C2×C7×C4⋊C4—42no—
60C2×C7×C22⋊C4—24no—
61C2×C7×C22⋊C4—24no—
62C2×C7×C22⋊C4—24no—
63C2×C7×C22⋊C4—24no—
64C2×C7×C22⋊C4—24no—
65C2×C7×C22⋊C4—24no—
66C2×C7×C22⋊C4—24no—
67C2×C7×C22⋊C4—24no—
68C2×C7×C22⋊C4—42no—
69C2×C7×C22⋊C4—41no—
70C2×C7×C22⋊C4—42no—
71C2×C7×C22⋊C4—42no—
72C2×C7×C22⋊C4—42no—
73C2×C7×C22⋊C4—42no—
74C2×C7×C22⋊C4—42no—
75C2×C7×C22⋊C4—41no—
76C2×C7×C22⋊C4C2×C418yes—
77C2×C7×C22⋊C4C2×C414yes—
78C2×C42×C7—24no—
79C2×C42×C7—42no—
80C2×C42×C7—42no—
81C7×#95—24no—
82C7×#95—24no—
83C7×#95—42no—
84C7×#95—42no—
85C7×#95—42no—
86C7×#95—41no—
87C7×#95—41no—
88C7×#95C2×C418yes—
89C7×#95D418yescomplemented
90C2×#388C2×C712yescomplemented
91C2×#386C2×C711yescharacteristic
92C2×#380C2×C712yescomplemented
93#1442C2×C712yescomplemented
94#1439C2×C712yescomplemented
95#1438C2×C711yescharacteristic
96#1438C2×C711yescharacteristic
97#1437C2×C712yescomplemented
98#1436C2×C712yescomplemented
99C24×C7—22no—
100C24×C7—22no—
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—21no—
112C24×C7—21no—
113C24×C7—22no—
114C24×C7C22×C412yes—
115C24×C7C22×C412yes—
116C24×C7#4114yes—
117C24×C7C2411yescharacteristic
118C2×C7×D4—28no—
119C2×C7×D4—44no—
120C2×C7×D4—44no—
121C2×C7×D4—48no—
122C2×C7×D4—48no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—216no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—44no—
165C22×C4×C7—44no—
166C22×C4×C7—48no—
167C22×C4×C7—44no—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C22×C414yes—
170C22×C4×C7C22×C414yes—
171C22×C4×C7C2×D414yes—
172C22×C4×C7C2×D414yes—
173C22×C4×C7C2×D414yes—
174C22×C4×C7#4114yes—
175C7×C4⋊C4—48no—
176C7×C4⋊C4—48no—
177C7×C22⋊C4—216no—
178C7×C22⋊C4—44no—
179C7×C22⋊C4—44no—
180C7×C22⋊C4—48no—
181C7×C22⋊C4—48no—
182C7×C22⋊C4—48no—
183C7×C22⋊C4—44no—
184C42×C7—48no—
185C23×D4C22×C711yescharacteristic
186C24×C4C22×C711yescharacteristic
187C22×C4⋊C4C22×C712yes—
188C22×C4⋊C4C22×C712yes—
189C22×C22⋊C4C22×C712yes—
190C22×C22⋊C4C22×C712yes—
191C22×C22⋊C4C22×C711yescharacteristic
192C22×C22⋊C4C22×C712yes—
193C22×C22⋊C4C22×C712yes—
194C22×C22⋊C4C22×C711yescharacteristic
195C22×C22⋊C4C22×C711yescharacteristic
196C22×C42C22×C712yes—
197#388—28no—
198#386C4×C718yescomplemented
199#380—28no—
200C2×#95C22×C712yes—
201C2×#95C22×C712yes—
202C2×#95C22×C711yescharacteristic
203C2×#95C22×C712yes—
204C2×#95C22×C712yes—
205C2×#95C22×C712yes—
206C2×#95C22×C711yescharacteristic
207C2×#95C22×C712yes—
208C2×#95C22×C712yes—
209C23×C7—24no—
210C23×C7—22no—
211C23×C7—22no—
212C23×C7—24no—
213C23×C7—24no—
214C23×C7—24no—
215C23×C7—24no—
216C23×C7—24no—
217C23×C7—24no—
218C23×C7—24no—
219C23×C7—22no—
220C23×C7—24no—
221C23×C7—22no—
222C23×C7—22no—
223C23×C7—24no—
224C23×C7—42no—
225C23×C7—42no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—41no—
229C23×C7—42no—
230C23×C7—41no—
231C23×C7—41no—
232C23×C7—42no—
233C23×C7—41no—
234C23×C7—42no—
235C23×C7—42no—
236C23×C7—42no—
237C23×C7—42no—
238C23×C7—42no—
239C23×C7—42no—
240C23×C7—41no—
241C23×C7—42no—
242C23×C7—42no—
243C23×C7—42no—
244C23×C7—41no—
245C23×C7—42no—
246C23×C7—42no—
247C23×C7—41no—
248C23×C7—42no—
249C23×C7—41no—
250C23×C7#11714yes—
251C23×C7C23×C411yescharacteristic
252C23×C7C22×D412yes—
253C23×C7C2×#4112yes—
254C23×C7C2×#4112yes—
255C23×C7H(5,𝔽2)12yes—
256C23×C7H(5,𝔽2)11yescharacteristic
257C23×C7H(5,𝔽2)11yescharacteristic
258C23×C7H(5,𝔽2)12yes—
259C23×C72−1+412yes—
260C7×D4—416no—
261C2×C4×C7—24no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—22no—
268C2×C4×C7—24no—
269C2×C4×C7—24no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—24no—
275C2×C4×C7—24no—
276C2×C4×C7—24no—
277C2×C4×C7—24no—
278C2×C4×C7—24no—
279C2×C4×C7—416no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—42no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
288C2×C4×C7—42no—
289C2×C4×C7—42no—
290C2×C4×C7—42no—
291C2×C4×C7—42no—
292C2×C4×C7—42no—
293C2×C4×C7—42no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7—42no—
297C2×C4×C7—42no—
298C2×C4×C7—42no—
299C2×C4×C7—42no—
300C2×C4×C7—42no—
301C2×C4×C7—42no—
302C2×C4×C7—42no—
303C2×C4×C7—42no—
304C2×C4×C7—42no—
305C2×C4×C7—42no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7C4×D418yes—
309C25C23×C711yescharacteristic
310C25C23×C711yescharacteristic
311C22×D4—24no—
312C22×D4—42no—
313C22×D4—41no—
314C22×D4—41no—
315C22×D4C2×C4×C714yes—
316C23×C4—24no—
317C23×C4—24no—
318C23×C4—41no—
319C23×C4—41no—
320C23×C4C2×C4×C714yes—
321C23×C4C23×C712yes—
322C23×C4C23×C712yes—
323C23×C4C23×C712yes—
324C23×C4C23×C711yescharacteristic
325C23×C4C23×C712yes—
326C23×C4C23×C712yes—
327C23×C4C23×C712yes—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4C2×C4×C718yes—
351C2×C22⋊C4C2×C4×C714yes—
352C2×C42—24no—
353C2×C42—42no—
354C2×C42—42no—
355#95—24no—
356#95—24no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—41no—
361#95—41no—
362#95C2×C4×C718yes—
363#95C7×D418yescomplemented
364C22×C7—24no—
365C22×C7—28no—
366C22×C7—44no—
367C22×C7—42no—
368C22×C7—42no—
369C22×C7—44no—
370C22×C7—44no—
371C22×C7—44no—
372C22×C7—44no—
373C22×C7—42no—
374C22×C7—44no—
375C22×C7—44no—
376C22×C7—42no—
377C22×C7—42no—
378C22×C7—82no—
379C22×C7—82no—
380C22×C7—82no—
381C22×C7—82no—
382C22×C7C2×#11711yescharacteristic
383C22×C7C2×C4×D412yes—
384C22×C7#51811yescharacteristic
385C22×C7#51811yescharacteristic
386C22×C7#52012yes—
387C22×C7#53512yes—
388C22×C7#53712yes—
389C22×C7#53812yes—
390C22×C7#53812yes—
391C22×C7#54012yes—
392C22×C7#54212yes—
393C22×C7D4211yescharacteristic
394C22×C7#54612yes—
395C22×C7#54612yes—
396C22×C7#54812yes—
397C22×C7#55111yescharacteristic
398C22×C7#55212yes—
399C22×C7#55312yes—
400C22×C7#56011yescharacteristic
401C22×C7#56212yes—
402C22×C7#56311yescharacteristic
403C4×C7—28no—
404C4×C7—42no—
405C4×C7—44no—
406C4×C7—44no—
407C4×C7—44no—
408C4×C7—82no—
409C4×C7—82no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24C22×C4×C712yes—
426C24C22×C4×C712yes—
427C24C7×#4114yes—
428C24C24×C711yescharacteristic
429C2×D4—28no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—48no—
433C2×D4—48no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—216no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—48no—
478C22×C4—44no—
479C22×C4C22×C4×C712yes—
480C22×C4C22×C4×C714yes—
481C22×C4C22×C4×C714yes—
482C22×C4C2×C7×D414yes—
483C22×C4C2×C7×D414yes—
484C22×C4C2×C7×D414yes—
485C22×C4C7×#4114yes—
486C4⋊C4—48no—
487C4⋊C4—48no—
488C22⋊C4—216no—
489C22⋊C4—44no—
490C22⋊C4—44no—
491C22⋊C4—48no—
492C22⋊C4—48no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C42—48no—
496C2×C7—44no—
497C2×C7—82no—
498C2×C7#231211yescharacteristic
499C2×C7#232412yes—
500C2×C7#235212yes—
501C2×C7#235811yescharacteristic
502C2×C7#237611yescharacteristic
503C2×C7#267612yes—
504C2×C7#270212yes—
505C2×C7#270312yes—
506C2×C7#274112yes—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—22no—
518C23—24no—
519C23—22no—
520C23—22no—
521C23—24no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—41no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23C7×#11714yes—
549C23C23×C4×C711yescharacteristic
550C23C22×C7×D412yes—
551C23C2×C7×#4112yes—
552C23C2×C7×#4112yes—
553C23C7×H(5,𝔽2)12yes—
554C23C7×H(5,𝔽2)11yescharacteristic
555C23C7×H(5,𝔽2)11yescharacteristic
556C23C7×H(5,𝔽2)12yes—
557C23C7×2−1+412yes—
558D4—416no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—416no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4C4×C7×D418yes—
607C7#1441011yescharacteristic, direct product factor, Sylow
608C22—24no—
609C22—28no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—42no—
621C22—42no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22C2×C7×#11711yescharacteristic
627C22C2×C4×C7×D412yes—
628C22C7×#51811yescharacteristic
629C22C7×#51811yescharacteristic
630C22C7×#52012yes—
631C22C7×#53512yes—
632C22C7×#53712yes—
633C22C7×#53812yes—
634C22C7×#53812yes—
635C22C7×#54012yes—
636C22C7×#54212yes—
637C22C7×D4211yescharacteristic
638C22C7×#54612yes—
639C22C7×#54612yes—
640C22C7×#54812yes—
641C22C7×#55111yescharacteristic
642C22C7×#55212yes—
643C22C7×#55312yes—
644C22C7×#56011yescharacteristic
645C22C7×#56212yes—
646C22C7×#56311yescharacteristic
647C4—28no—
648C4—44no—
649C4—44no—
650C4—42no—
651C4—44no—
652C4—82no—
653C4—82no—
654C2—44no—
655C2—82no—
656C2C7×#231211yescharacteristic
657C2C7×#232412yes—
658C2C7×#235212yes—
659C2C7×#235811yescharacteristic
660C2C7×#237611yescharacteristic
661C2C7×#267612yes—
662C2C7×#270212yes—
663C2C7×#270312yes—
664C2C7×#274112yes—
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
1. C2×C7×#388C2semidirect
3. C2×C7×#380C2semidirect
4. C7×#1442C2semidirect
5. C7×#1439C2semidirect
8. C7×#1437C2semidirect
9. C7×#1436C2semidirect
23. C7×#386C4semidirect
34. #14410C7direct (N × H)
89. C7×#95D4semidirect
90. C2×#388C2×C7semidirect
92. C2×#380C2×C7semidirect
93. #1442C2×C7semidirect
94. #1439C2×C7semidirect
97. #1437C2×C7semidirect
98. #1436C2×C7semidirect
198. #386C4×C7semidirect
363. #95C7×D4semidirect
607. C7#14410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C7×#3862
C2×C7×#3802
C7×#14422
C7×#14392
C7×#14382
C7×#14372
C7×#14362
#144107