Finite Group Databasebeta

← C7×#13943 #13191159

Subgroups — C7×#13943 #13191159

Order 1792.

1846 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#117C211yesmaximal, characteristic
2C2×C7×#388C212yesmaximal
3C7×#1441C212yesmaximal, complemented
4C7×#1440C212yesmaximal
5C7×#1436C212yesmaximal, complemented
6C7×C4⋊#95C211yesmaximal, characteristic, complemented
7C7×#1434C211yesmaximal, characteristic, complemented
8C7×#1434C211yesmaximal, characteristic, complemented
9C7×C22⋊#95C211yesmaximal, characteristic
10C7×C22⋊#95C211yesmaximal, characteristic
11C4×C7×#95C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C2×C7×#117—28no—
14C2×C7×#117C418yescomplemented
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C42×C7C2212yes—
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C7×#388—28no—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2212yes—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38#13943C711yesmaximal, characteristic, direct product factor, Sylow
39C25×C7C2311yescharacteristic
40C23×C4×C7—24no—
41C23×C4×C7—22no—
42C23×C4×C7—22no—
43C23×C4×C7—24no—
44C23×C4×C7C2×C414yes—
45C23×C4×C7C2312yes—
46C23×C4×C7C2312yes—
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C7×#117—232no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—24no—
58C2×C7×C4⋊C4—24no—
59C2×C7×C4⋊C4—24no—
60C2×C7×C4⋊C4—42no—
61C2×C7×C4⋊C4C2×C414yes—
62C2×C7×C4⋊C4C2×C414yes—
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—42no—
70C2×C7×C22⋊C4C2×C414yes—
71C2×C7×C22⋊C4C2×C414yes—
72C2×C7×C22⋊C4D418yes—
73C2×C42×C7—24no—
74C2×C42×C7—24no—
75C2×C42×C7—24no—
76C2×C42×C7—24no—
77C2×C42×C7—42no—
78C2×C42×C7C2×C414yes—
79C2×C42×C7C2×C414yes—
80C7×#95—24no—
81C7×#95—24no—
82C7×#95—24no—
83C7×#95—22no—
84C7×#95—22no—
85C7×#95—24no—
86C7×#95—24no—
87C7×#95—24no—
88C7×#95—22no—
89C7×#95—22no—
90C7×#95—42no—
91C7×#95—42no—
92C22×#117C2×C711yescharacteristic
93C2×#388C2×C712yes—
94#1441C2×C712yescomplemented
95#1440C2×C712yes—
96#1436C2×C712yescomplemented
97C4⋊#95C2×C711yescharacteristic, complemented
98#1434C2×C711yescharacteristic, complemented
99#1434C2×C711yescharacteristic, complemented
100C22⋊#95C2×C711yescharacteristic
101C22⋊#95C2×C711yescharacteristic
102C4×#95C2×C711yescharacteristic, complemented
103C24×C7—22no—
104C24×C7—22no—
105C24×C7—21no—
106C24×C7—21no—
107C24×C7—22no—
108C24×C7—21no—
109C24×C7—21no—
110C24×C7—21no—
111C24×C7—21no—
112C24×C7C22×C412yes—
113C24×C7C2×D414yes—
114C24×C7C2411yescharacteristic
115C22×C4×C7—216no—
116C22×C4×C7—216no—
117C22×C4×C7—28no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—22no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7—28no—
130C22×C4×C7—28no—
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—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
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—22no—
165C22×C4×C7C22×C412yes—
166C22×C4×C7C22×C412yes—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C22×C412yes—
170C22×C4×C7C22×C412yes—
171C22×C4×C7C2×D414yes—
172C22×C4×C7C2×D414yes—
173C22×C4×C7#4114yes—
174C22×C4×C7#4114yes—
175C22×C4×C7#4112yes—
176C22×C4×C7#4112yes—
177C22×C4×C7#4114yes—
178C7×C4⋊C4—28no—
179C7×C4⋊C4—28no—
180C7×C4⋊C4—48no—
181C7×C22⋊C4—28no—
182C7×C22⋊C4—48no—
183C7×C22⋊C4—48no—
184C7×C22⋊C4C22⋊C4116yes—
185C42×C7—28no—
186C42×C7—28no—
187C42×C7—48no—
188C24×C4C22×C711yescharacteristic
189C2×#117—28no—
190C2×#117C4×C718yescomplemented
191C22×C4⋊C4C22×C712yes—
192C22×C4⋊C4C22×C711yescharacteristic
193C22×C4⋊C4C22×C711yescharacteristic
194C22×C22⋊C4C22×C712yes—
195C22×C22⋊C4C22×C712yes—
196C22×C22⋊C4C22×C711yescharacteristic
197C22×C22⋊C4C22×C711yescharacteristic
198C22×C42C22×C712yes—
199C22×C42C22×C711yescharacteristic
200C22×C42C22×C711yescharacteristic
201#388—28no—
202C2×#95C22×C711yescharacteristic
203C2×#95C22×C711yescharacteristic
204C2×#95C22×C712yes—
205C2×#95C22×C711yescharacteristic
206C2×#95C22×C711yescharacteristic
207C2×#95C22×C712yes—
208C2×#95C22×C712yes—
209C2×#95C22×C712yes—
210C2×#95C22×C712yes—
211C2×#95C22×C712yes—
212C2×#95C22×C712yes—
213C2×#95C22×C712yes—
214C23×C7—22no—
215C23×C7—22no—
216C23×C7—22no—
217C23×C7—22no—
218C23×C7—22no—
219C23×C7—22no—
220C23×C7—24no—
221C23×C7—24no—
222C23×C7—24no—
223C23×C7—24no—
224C23×C7—24no—
225C23×C7—24no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—41no—
229C23×C7—41no—
230C23×C7—41no—
231C23×C7—41no—
232C23×C7—42no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7—42no—
236C23×C7C2×C22⋊C414yes—
237C23×C7C23×C411yescharacteristic
238C23×C7C22×D412yes—
239C23×C7C2×#4111yescharacteristic
240C23×C7C2×#4111yescharacteristic
241C23×C7C2×#4112yes—
242C23×C7C2×#4112yes—
243C23×C7C2×#4112yes—
244C23×C7H(5,𝔽2)11yescharacteristic
245C23×C7H(5,𝔽2)11yescharacteristic
246C23×C72−1+411yescharacteristic
247C23×C72−1+411yescharacteristic
248C2×C4×C7—232no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—24no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—24no—
275C2×C4×C7—24no—
276C2×C4×C7—24no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
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×C7C2×C22⋊C414yes—
304C2×C4×C7C2×C22⋊C414yes—
305C2×C4×C7#11714yes—
306C2×C4×C7#11714yes—
307C25C23×C711yescharacteristic
308C23×C4—24no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—24no—
312C23×C4C2×C4×C714yes—
313C23×C4C23×C712yes—
314C23×C4C23×C712yes—
315C23×C4C23×C711yescharacteristic
316C23×C4C23×C711yescharacteristic
317C23×C4C23×C712yes—
318C23×C4C23×C712yes—
319C23×C4C23×C711yescharacteristic
320C23×C4C23×C711yescharacteristic
321C23×C4C23×C711yescharacteristic
322C23×C4C23×C711yescharacteristic
323#117—232no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4C2×C4×C714yes—
330C2×C4⋊C4C2×C4×C714yes—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4C2×C4×C714yes—
339C2×C22⋊C4C2×C4×C714yes—
340C2×C22⋊C4C7×D418yes—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—42no—
346C2×C42C2×C4×C714yes—
347C2×C42C2×C4×C714yes—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—22no—
352#95—22no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—22no—
357#95—22no—
358#95—42no—
359#95—42no—
360C22×C7—24no—
361C22×C7—24no—
362C22×C7—24no—
363C22×C7—42no—
364C22×C7—42no—
365C22×C7—42no—
366C22×C7—44no—
367C22×C7—44no—
368C22×C7—44no—
369C22×C7—44no—
370C22×C7—42no—
371C22×C7C22×C22⋊C411yescharacteristic
372C22×C7C2×#11711yescharacteristic
373C22×C7C2×#11711yescharacteristic
374C22×C7C4×#4111yescharacteristic
375C22×C7C4×#4111yescharacteristic
376C22×C7#52011yescharacteristic
377C22×C7#52011yescharacteristic
378C22×C7#52512yes—
379C22×C7#52512yes—
380C22×C7#52912yes—
381C22×C7#52912yes—
382C22×C7#54011yescharacteristic
383C22×C7#54111yescharacteristic
384C22×C7#54211yescharacteristic
385C22×C7#54211yescharacteristic
386C22×C7#54612yes—
387C22×C7#54612yes—
388C22×C7#54712yes—
389C22×C7#54712yes—
390C22×C7#55212yes—
391C22×C7#55312yes—
392C22×C7#55512yes—
393C22×C7#55612yes—
394C4×C7—24no—
395C4×C7—24no—
396C4×C7—24no—
397C4×C7—24no—
398C4×C7—42no—
399C4×C7—42no—
400C4×C7—44no—
401C4×C7—44no—
402C4×C7—82no—
403C4×C7—82no—
404C24—22no—
405C24—22no—
406C24—21no—
407C24—21no—
408C24—22no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24C22×C4×C712yes—
414C24C2×C7×D414yes—
415C24C24×C711yescharacteristic
416C22×C4—216no—
417C22×C4—216no—
418C22×C4—28no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—28no—
431C22×C4—28no—
432C22×C4—22no—
433C22×C4—22no—
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—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4C22×C4×C712yes—
467C22×C4C22×C4×C712yes—
468C22×C4C22×C4×C712yes—
469C22×C4C22×C4×C712yes—
470C22×C4C22×C4×C712yes—
471C22×C4C22×C4×C712yes—
472C22×C4C2×C7×D414yes—
473C22×C4C2×C7×D414yes—
474C22×C4C7×#4114yes—
475C22×C4C7×#4114yes—
476C22×C4C7×#4112yes—
477C22×C4C7×#4112yes—
478C22×C4C7×#4114yes—
479C4⋊C4—28no—
480C4⋊C4—28no—
481C4⋊C4—48no—
482C22⋊C4—28no—
483C22⋊C4—48no—
484C22⋊C4—48no—
485C22⋊C4C7×C22⋊C4116yes—
486C42—28no—
487C42—28no—
488C42—48no—
489C2×C7—44no—
490C2×C7#228011yescharacteristic
491C2×C7#229811yescharacteristic
492C2×C7#231411yescharacteristic
493C2×C7#233911yescharacteristic
494C2×C7#233911yescharacteristic
495C2×C7#234611yescharacteristic
496C2×C7#234711yescharacteristic
497C2×C7#247012yes—
498C2×C7#247412yes—
499C2×C7#247612yes—
500C2×C7#247812yes—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—42no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23C2×C7×C22⋊C414yes—
524C23C23×C4×C711yescharacteristic
525C23C22×C7×D412yes—
526C23C2×C7×#4111yescharacteristic
527C23C2×C7×#4111yescharacteristic
528C23C2×C7×#4112yes—
529C23C2×C7×#4112yes—
530C23C2×C7×#4112yes—
531C23C7×H(5,𝔽2)11yescharacteristic
532C23C7×H(5,𝔽2)11yescharacteristic
533C23C7×2−1+411yescharacteristic
534C23C7×2−1+411yescharacteristic
535C2×C4—232no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
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×C4C2×C7×C22⋊C414yes—
591C2×C4C2×C7×C22⋊C414yes—
592C2×C4C7×#11714yes—
593C2×C4C7×#11714yes—
594C7#1394311yescharacteristic, direct product factor, Sylow
595C22—24no—
596C22—24no—
597C22—24no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22C22×C7×C22⋊C411yescharacteristic
607C22C2×C7×#11711yescharacteristic
608C22C2×C7×#11711yescharacteristic
609C22C4×C7×#4111yescharacteristic
610C22C4×C7×#4111yescharacteristic
611C22C7×#52011yescharacteristic
612C22C7×#52011yescharacteristic
613C22C7×#52512yes—
614C22C7×#52512yes—
615C22C7×#52912yes—
616C22C7×#52912yes—
617C22C7×#54011yescharacteristic
618C22C7×#54111yescharacteristic
619C22C7×#54211yescharacteristic
620C22C7×#54211yescharacteristic
621C22C7×#54612yes—
622C22C7×#54612yes—
623C22C7×#54712yes—
624C22C7×#54712yes—
625C22C7×#55212yes—
626C22C7×#55312yes—
627C22C7×#55512yes—
628C22C7×#55612yes—
629C4—24no—
630C4—24no—
631C4—24no—
632C4—24no—
633C4—44no—
634C4—44no—
635C4—42no—
636C4—42no—
637C4—82no—
638C4—82no—
639C2—44no—
640C2C7×#228011yescharacteristic
641C2C7×#229811yescharacteristic
642C2C7×#231411yescharacteristic
643C2C7×#233911yescharacteristic
644C2C7×#233911yescharacteristic
645C2C7×#234611yescharacteristic
646C2C7×#234711yescharacteristic
647C2C7×#247012yes—
648C2C7×#247412yes—
649C2C7×#247612yes—
650C2C7×#247812yes—
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1441C2semidirect
5. C7×#1436C2semidirect
6. C7×C4⋊#95C2semidirect
7. C7×#1434C2semidirect
8. C7×#1434C2semidirect
11. C4×C7×#95C2semidirect
14. C2×C7×#117C4semidirect
38. #13943C7direct (N × H)
94. #1441C2×C7semidirect
96. #1436C2×C7semidirect
97. C4⋊#95C2×C7semidirect
98. #1434C2×C7semidirect
99. #1434C2×C7semidirect
102. C4×#95C2×C7semidirect
190. C2×#117C4×C7semidirect
594. C7#13943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1172
C2×C7×#3882
C7×#14412
C7×#14402
C7×#14362
C7×C4⋊#952
C7×#14342
C7×C22⋊#952
C4×C7×#952
#139437