Finite Group Databasebeta

← C7×#14409 #13191625

Subgroups — C7×#14409 #13191625

Order 1792.

1606 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#387C212yesmaximal, complemented
2C2×C7×#385C211yesmaximal, characteristic
3C2×C7×#380C212yesmaximal
4C7×#1442C212yesmaximal, complemented
5C7×#1441C212yesmaximal, complemented
6C7×#1440C212yesmaximal
7C7×#1437C211yesmaximal, characteristic
8C7×#1437C211yesmaximal, characteristic
9C7×#1436C212yesmaximal, complemented
10C24×C4×C7C2211yescharacteristic
11C22×C7×C4⋊C4C2212yes—
12C22×C7×C4⋊C4C2212yes—
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C22⋊C4C2212yes—
15C22×C7×C22⋊C4C2212yes—
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C7×#387—28no—
21C7×#385C418yescomplemented
22C7×#380—28no—
23C2×C7×#95C2212yes—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34#14409C711yesmaximal, characteristic, direct product factor, Sylow
35C25×C7C2311yescharacteristic
36C23×C4×C7—24no—
37C23×C4×C7—24no—
38C23×C4×C7—41no—
39C23×C4×C7—41no—
40C23×C4×C7C2×C414yes—
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2312yes—
46C23×C4×C7C2312yes—
47C23×C4×C7C2312yes—
48C23×C4×C7C2312yes—
49C2×C7×C4⋊C4—24no—
50C2×C7×C4⋊C4—24no—
51C2×C7×C4⋊C4—24no—
52C2×C7×C4⋊C4—24no—
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—24no—
55C2×C7×C4⋊C4—42no—
56C2×C7×C4⋊C4—42no—
57C2×C7×C4⋊C4C2×C418yes—
58C2×C7×C22⋊C4—24no—
59C2×C7×C22⋊C4—24no—
60C2×C7×C22⋊C4—24no—
61C2×C7×C22⋊C4—24no—
62C2×C7×C22⋊C4—24no—
63C2×C7×C22⋊C4—41no—
64C2×C7×C22⋊C4—41no—
65C2×C7×C22⋊C4—42no—
66C2×C7×C22⋊C4—42no—
67C2×C7×C22⋊C4C2×C414yes—
68C2×C7×C22⋊C4C2×C414yes—
69C2×C42×C7—24no—
70C2×C42×C7—41no—
71C2×C42×C7—42no—
72C2×C42×C7—41no—
73C7×#95—24no—
74C7×#95—24no—
75C7×#95—24no—
76C7×#95—24no—
77C7×#95—42no—
78C7×#95—42no—
79C7×#95—42no—
80C7×#95—41no—
81C7×#95—41no—
82C7×#95C2×C418yes—
83C7×#95D418yes—
84C2×#387C2×C712yescomplemented
85C2×#385C2×C711yescharacteristic
86C2×#380C2×C712yes—
87#1442C2×C712yescomplemented
88#1441C2×C712yescomplemented
89#1440C2×C712yes—
90#1437C2×C711yescharacteristic
91#1437C2×C711yescharacteristic
92#1436C2×C712yescomplemented
93C24×C7—22no—
94C24×C7—22no—
95C24×C7—22no—
96C24×C7—21no—
97C24×C7—21no—
98C24×C7—22no—
99C24×C7—22no—
100C24×C7C22×C412yes—
101C24×C7#4114yes—
102C24×C7C2411yescharacteristic
103C22×C4×C7—22no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—22no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
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—216no—
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—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—44no—
149C22×C4×C7—44no—
150C22×C4×C7—48no—
151C22×C4×C7—44no—
152C22×C4×C7C22×C412yes—
153C22×C4×C7C22×C414yes—
154C22×C4×C7C22×C412yes—
155C22×C4×C7C22×C414yes—
156C22×C4×C7C2×D414yes—
157C22×C4×C7C2×D414yes—
158C22×C4×C7C2×D414yes—
159C22×C4×C7#4114yes—
160C7×C4⋊C4—216no—
161C7×C4⋊C4—48no—
162C7×C4⋊C4—48no—
163C7×C22⋊C4—28no—
164C7×C22⋊C4—44no—
165C7×C22⋊C4—48no—
166C7×C22⋊C4—48no—
167C42×C7—44no—
168C42×C7—44no—
169C24×C4C22×C711yescharacteristic
170C22×C4⋊C4C22×C712yes—
171C22×C4⋊C4C22×C712yes—
172C22×C4⋊C4C22×C712yes—
173C22×C22⋊C4C22×C712yes—
174C22×C22⋊C4C22×C712yes—
175C22×C22⋊C4C22×C711yescharacteristic
176C22×C22⋊C4C22×C711yescharacteristic
177C22×C42C22×C711yescharacteristic
178C22×C42C22×C711yescharacteristic
179#387—28no—
180#385C4×C718yescomplemented
181#380—28no—
182C2×#95C22×C712yes—
183C2×#95C22×C712yes—
184C2×#95C22×C712yes—
185C2×#95C22×C712yes—
186C2×#95C22×C712yes—
187C2×#95C22×C712yes—
188C2×#95C22×C711yescharacteristic
189C2×#95C22×C711yescharacteristic
190C2×#95C22×C712yes—
191C2×#95C22×C712yes—
192C2×#95C22×C712yes—
193C23×C7—24no—
194C23×C7—22no—
195C23×C7—22no—
196C23×C7—24no—
197C23×C7—24no—
198C23×C7—24no—
199C23×C7—24no—
200C23×C7—24no—
201C23×C7—24no—
202C23×C7—24no—
203C23×C7—42no—
204C23×C7—42no—
205C23×C7—42no—
206C23×C7—42no—
207C23×C7—41no—
208C23×C7—42no—
209C23×C7—41no—
210C23×C7—41no—
211C23×C7—42no—
212C23×C7—41no—
213C23×C7#11714yes—
214C23×C7C23×C411yescharacteristic
215C23×C7C22×D412yes—
216C23×C7C2×#4112yes—
217C23×C7C2×#4112yes—
218C23×C7H(5,𝔽2)11yescharacteristic
219C23×C7H(5,𝔽2)11yescharacteristic
220C23×C7H(5,𝔽2)12yes—
221C23×C72−1+412yes—
222C23×C72−1+412yes—
223C2×C4×C7—24no—
224C2×C4×C7—24no—
225C2×C4×C7—24no—
226C2×C4×C7—24no—
227C2×C4×C7—24no—
228C2×C4×C7—24no—
229C2×C4×C7—24no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—22no—
233C2×C4×C7—22no—
234C2×C4×C7—24no—
235C2×C4×C7—24no—
236C2×C4×C7—24no—
237C2×C4×C7—24no—
238C2×C4×C7—24no—
239C2×C4×C7—24no—
240C2×C4×C7—24no—
241C2×C4×C7—24no—
242C2×C4×C7—416no—
243C2×C4×C7—42no—
244C2×C4×C7—42no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—41no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—41no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7—41no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—41no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—42no—
270C2×C4×C7—42no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7C4×D418yes—
276C25C23×C711yescharacteristic
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—41no—
280C23×C4—41no—
281C23×C4C2×C4×C714yes—
282C23×C4C23×C712yes—
283C23×C4C23×C712yes—
284C23×C4C23×C711yescharacteristic
285C23×C4C23×C712yes—
286C23×C4C23×C711yescharacteristic
287C23×C4C23×C712yes—
288C23×C4C23×C712yes—
289C23×C4C23×C712yes—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C2×C4×C718yes—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4C2×C4×C714yes—
309C2×C22⋊C4C2×C4×C714yes—
310C2×C42—24no—
311C2×C42—41no—
312C2×C42—42no—
313C2×C42—41no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—42no—
319#95—42no—
320#95—42no—
321#95—41no—
322#95—41no—
323#95C2×C4×C718yes—
324#95C7×D418yes—
325C22×C7—24no—
326C22×C7—28no—
327C22×C7—44no—
328C22×C7—42no—
329C22×C7—42no—
330C22×C7—44no—
331C22×C7—44no—
332C22×C7—44no—
333C22×C7—44no—
334C22×C7C2×#11711yescharacteristic
335C22×C7C2×C4×D412yes—
336C22×C7#51811yescharacteristic
337C22×C7#51911yescharacteristic
338C22×C7#52012yes—
339C22×C7#53612yes—
340C22×C7#53712yes—
341C22×C7#53912yes—
342C22×C7#53912yes—
343C22×C7#54112yes—
344C22×C7#54212yes—
345C22×C7D4211yescharacteristic
346C22×C7#54612yes—
347C22×C7#54612yes—
348C22×C7#54812yes—
349C22×C7#55111yescharacteristic
350C22×C7#55212yes—
351C22×C7#55312yes—
352C22×C7#56011yescharacteristic
353C22×C7#56212yes—
354C22×C7#56311yescharacteristic
355C4×C7—28no—
356C4×C7—44no—
357C4×C7—42no—
358C4×C7—42no—
359C4×C7—44no—
360C4×C7—44no—
361C4×C7—82no—
362C4×C7—82no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—21no—
367C24—21no—
368C24—22no—
369C24—22no—
370C24C22×C4×C712yes—
371C24C7×#4114yes—
372C24C24×C711yescharacteristic
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—216no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—48no—
421C22×C4—44no—
422C22×C4C22×C4×C712yes—
423C22×C4C22×C4×C714yes—
424C22×C4C22×C4×C712yes—
425C22×C4C22×C4×C714yes—
426C22×C4C2×C7×D414yes—
427C22×C4C2×C7×D414yes—
428C22×C4C2×C7×D414yes—
429C22×C4C7×#4114yes—
430C4⋊C4—216no—
431C4⋊C4—48no—
432C4⋊C4—48no—
433C22⋊C4—28no—
434C22⋊C4—44no—
435C22⋊C4—48no—
436C22⋊C4—48no—
437C42—44no—
438C42—44no—
439C2×C7—44no—
440C2×C7#231311yescharacteristic
441C2×C7#232312yes—
442C2×C7#235212yes—
443C2×C7#235811yescharacteristic
444C2×C7#237611yescharacteristic
445C2×C7#268112yes—
446C2×C7#269012yes—
447C2×C7#269112yes—
448C2×C7#274712yes—
449C23—24no—
450C23—22no—
451C23—22no—
452C23—24no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—41no—
464C23—42no—
465C23—41no—
466C23—41no—
467C23—42no—
468C23—41no—
469C23C7×#11714yes—
470C23C23×C4×C711yescharacteristic
471C23C22×C7×D412yes—
472C23C2×C7×#4112yes—
473C23C2×C7×#4112yes—
474C23C7×H(5,𝔽2)11yescharacteristic
475C23C7×H(5,𝔽2)11yescharacteristic
476C23C7×H(5,𝔽2)12yes—
477C23C7×2−1+412yes—
478C23C7×2−1+412yes—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—416no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4C4×C7×D418yes—
532C7#1440911yescharacteristic, direct product factor, Sylow
533C22—24no—
534C22—28no—
535C22—44no—
536C22—44no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22—42no—
541C22—42no—
542C22C2×C7×#11711yescharacteristic
543C22C2×C4×C7×D412yes—
544C22C7×#51811yescharacteristic
545C22C7×#51911yescharacteristic
546C22C7×#52012yes—
547C22C7×#53612yes—
548C22C7×#53712yes—
549C22C7×#53912yes—
550C22C7×#53912yes—
551C22C7×#54112yes—
552C22C7×#54212yes—
553C22C7×D4211yescharacteristic
554C22C7×#54612yes—
555C22C7×#54612yes—
556C22C7×#54812yes—
557C22C7×#55111yescharacteristic
558C22C7×#55212yes—
559C22C7×#55312yes—
560C22C7×#56011yescharacteristic
561C22C7×#56212yes—
562C22C7×#56311yescharacteristic
563C4—28no—
564C4—44no—
565C4—44no—
566C4—44no—
567C4—42no—
568C4—42no—
569C4—82no—
570C4—82no—
571C2—44no—
572C2C7×#231311yescharacteristic
573C2C7×#232312yes—
574C2C7×#235212yes—
575C2C7×#235811yescharacteristic
576C2C7×#237611yescharacteristic
577C2C7×#268112yes—
578C2C7×#269012yes—
579C2C7×#269112yes—
580C2C7×#274712yes—
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
1. C2×C7×#387C2semidirect
4. C7×#1442C2semidirect
5. C7×#1441C2semidirect
9. C7×#1436C2semidirect
21. C7×#385C4semidirect
34. #14409C7direct (N × H)
84. C2×#387C2×C7semidirect
87. #1442C2×C7semidirect
88. #1441C2×C7semidirect
92. #1436C2×C7semidirect
180. #385C4×C7semidirect
532. C7#14409direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3872
C2×C7×#3852
C2×C7×#3802
C7×#14422
C7×#14412
C7×#14402
C7×#14372
C7×#14362
#144097