Finite Group Databasebeta

← C7×#13883 #13191099

Subgroups — C7×#13883 #13191099

Order 1792.

1862 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#380C211yesmaximal, characteristic
2C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
3C22×C7×#95C211yesmaximal, characteristic
4C7×#1443C212yesmaximal, complemented
5C7×#1442C212yesmaximal, complemented
6C7×#1436C212yesmaximal, complemented
7C7×#1434C212yesmaximal, complemented
8C7×C22⋊#95C211yesmaximal, characteristic
9C7×C22⋊#95C211yesmaximal, characteristic
10C7×C22⋊#95C211yesmaximal, characteristic
11C7×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C42×C7C2212yes—
21C7×#380—24no—
22C4×C7×C22⋊C4—24no—
23C2×C7×#95C418yescomplemented
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38#13883C711yesmaximal, characteristic, direct product factor, Sylow
39C25×C7C2311yescharacteristic
40C23×C4×C7—22no—
41C23×C4×C7—22no—
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—24no—
47C23×C4×C7—24no—
48C23×C4×C7—42no—
49C23×C4×C7—42no—
50C23×C4×C7—42no—
51C23×C4×C7—42no—
52C23×C4×C7C2×C414yes—
53C23×C4×C7C2×C414yes—
54C23×C4×C7C2×C414yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2312yes—
62C23×C4×C7C2312yes—
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C2×C7×C4⋊C4—24no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—42no—
68C2×C7×C22⋊C4—22no—
69C2×C7×C22⋊C4—22no—
70C2×C7×C22⋊C4—22no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4D414yes—
79C2×C7×C22⋊C4Q814yes—
80C2×C42×C7—24no—
81C2×C42×C7—24no—
82C2×C42×C7—42no—
83C7×#95—24no—
84C7×#95—24no—
85C7×#95—24no—
86C7×#95—24no—
87C7×#95—42no—
88C7×#95—42no—
89C7×#95—42no—
90C7×#95—42no—
91C7×#95—42no—
92C7×#95—42no—
93C7×#95C2×C414yes—
94C7×#95C2×C414yes—
95C7×#95C2×C414yes—
96C7×#95C2×C414yes—
97C2×#380C2×C711yescharacteristic
98C2×C4×C22⋊C4C2×C711yescharacteristic
99C22×#95C2×C711yescharacteristic
100#1443C2×C712yescomplemented
101#1442C2×C712yescomplemented
102#1436C2×C712yescomplemented
103#1434C2×C712yescomplemented
104C22⋊#95C2×C711yescharacteristic
105C22⋊#95C2×C711yescharacteristic
106C22⋊#95C2×C711yescharacteristic
107C22⋊#95C2×C711yescharacteristic
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7C22×C412yes—
113C24×C7C2×D412yes—
114C24×C7C2×Q812yes—
115C24×C7#4112yes—
116C24×C7#4112yes—
117C24×C7#4112yes—
118C24×C7#4112yes—
119C24×C7C2411yescharacteristic
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—28no—
127C22×C4×C7—28no—
128C22×C4×C7—28no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
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—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
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—28no—
158C22×C4×C7—28no—
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×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—44no—
174C22×C4×C7—44no—
175C22×C4×C7—44no—
176C22×C4×C7—44no—
177C22×C4×C7—48no—
178C22×C4×C7—48no—
179C22×C4×C7—48no—
180C22×C4×C7—48no—
181C22×C4×C7—48no—
182C22×C4×C7—48no—
183C22×C4×C7C22×C412yes—
184C22×C4×C7C22×C412yes—
185C22×C4×C7C22×C412yes—
186C22×C4×C7C22×C412yes—
187C22×C4×C7C22×C412yes—
188C22×C4×C7C22×C412yes—
189C22×C4×C7C2×D414yes—
190C22×C4×C7C2×Q814yes—
191C22×C4×C7#4114yes—
192C22×C4×C7#4114yes—
193C7×C4⋊C4—48no—
194C7×C22⋊C4—28no—
195C7×C22⋊C4—28no—
196C7×C22⋊C4—44no—
197C7×C22⋊C4—44no—
198C42×C7—48no—
199C24×C4C22×C711yescharacteristic
200C24×C4C22×C711yescharacteristic
201C24×C4C22×C711yescharacteristic
202C22×C4⋊C4C22×C712yes—
203C22×C22⋊C4C22×C711yescharacteristic
204C22×C22⋊C4C22×C711yescharacteristic
205C22×C22⋊C4C22×C711yescharacteristic
206C22×C22⋊C4C22×C711yescharacteristic
207C22×C42C22×C712yes—
208#380—24no—
209C4×C22⋊C4—24no—
210C2×#95C4×C718yescomplemented
211C2×#95C22×C712yes—
212C2×#95C22×C712yes—
213C2×#95C22×C712yes—
214C2×#95C22×C712yes—
215C2×#95C22×C712yes—
216C2×#95C22×C712yes—
217C2×#95C22×C712yes—
218C2×#95C22×C712yes—
219C2×#95C22×C712yes—
220C2×#95C22×C712yes—
221C2×#95C22×C711yescharacteristic
222C2×#95C22×C711yescharacteristic
223C2×#95C22×C711yescharacteristic
224C2×#95C22×C711yescharacteristic
225C23×C7—22no—
226C23×C7—22no—
227C23×C7—22no—
228C23×C7—22no—
229C23×C7—24no—
230C23×C7—24no—
231C23×C7—24no—
232C23×C7—24no—
233C23×C7—24no—
234C23×C7—24no—
235C23×C7—24no—
236C23×C7—24no—
237C23×C7—24no—
238C23×C7—24no—
239C23×C7—24no—
240C23×C7—24no—
241C23×C7#11714yes—
242C23×C7C4×D414yes—
243C23×C7C4×Q814yes—
244C23×C7C22⋊Q814yes—
245C23×C7#12314yes—
246C23×C7#12514yes—
247C23×C7#12614yes—
248C23×C7C23×C411yescharacteristic
249C23×C7C22×D411yescharacteristic
250C23×C7C22×Q811yescharacteristic
251C23×C7C2×#4111yescharacteristic
252C23×C7C2×#4111yescharacteristic
253C23×C7C2×#4112yes—
254C23×C7C2×#4112yes—
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4111yescharacteristic
257C23×C7H(5,𝔽2)12yes—
258C23×C7H(5,𝔽2)12yes—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—24no—
280C2×C4×C7—24no—
281C2×C4×C7—24no—
282C2×C4×C7—24no—
283C2×C4×C7—24no—
284C2×C4×C7—24no—
285C2×C4×C7—416no—
286C2×C4×C7—416no—
287C2×C4×C7—416no—
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×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7#11714yes—
319C2×C4×C7#11714yes—
320C25C23×C711yescharacteristic
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—24no—
328C23×C4—24no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4—42no—
332C23×C4—42no—
333C23×C4C2×C4×C714yes—
334C23×C4C2×C4×C714yes—
335C23×C4C2×C4×C714yes—
336C23×C4C23×C712yes—
337C23×C4C23×C712yes—
338C23×C4C23×C711yescharacteristic
339C23×C4C23×C711yescharacteristic
340C23×C4C23×C711yescharacteristic
341C23×C4C23×C711yescharacteristic
342C23×C4C23×C712yes—
343C23×C4C23×C712yes—
344C23×C4C23×C711yescharacteristic
345C23×C4C23×C711yescharacteristic
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—42no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4C7×D414yes—
360C2×C22⋊C4C7×Q814yes—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—42no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95C2×C4×C714yes—
375#95C2×C4×C714yes—
376#95C2×C4×C714yes—
377#95C2×C4×C714yes—
378C22×C7—24no—
379C22×C7—24no—
380C22×C7—24no—
381C22×C7—24no—
382C22×C7—24no—
383C22×C7—28no—
384C22×C7—28no—
385C22×C7—28no—
386C22×C7—28no—
387C22×C7—24no—
388C22×C7#38718yes—
389C22×C7C2×#11711yescharacteristic
390C22×C7C2×#11711yescharacteristic
391C22×C7C2×#11711yescharacteristic
392C22×C7C2×C4×D411yescharacteristic
393C22×C7C2×C4×Q811yescharacteristic
394C22×C7#51811yescharacteristic
395C22×C7#51811yescharacteristic
396C22×C7C2×C22⋊Q811yescharacteristic
397C22×C7C2×#12311yescharacteristic
398C22×C7C2×#12511yescharacteristic
399C22×C7C2×#12611yescharacteristic
400C22×C7#52912yes—
401C22×C7#52912yes—
402C22×C7#53812yes—
403C22×C7#53812yes—
404C22×C7#54612yes—
405C22×C7#54612yes—
406C22×C7#55112yes—
407C22×C7#55112yes—
408C22×C7#55312yes—
409C22×C7#55312yes—
410C22×C7#55412yes—
411C22×C7#55412yes—
412C4×C7—24no—
413C4×C7—24no—
414C4×C7—42no—
415C4×C7—42no—
416C4×C7—42no—
417C4×C7—42no—
418C4×C7—44no—
419C4×C7—44no—
420C4×C7—82no—
421C4×C7—82no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24C22×C4×C712yes—
427C24C2×C7×D412yes—
428C24C2×C7×Q812yes—
429C24C7×#4112yes—
430C24C7×#4112yes—
431C24C7×#4112yes—
432C24C7×#4112yes—
433C24C24×C711yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
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—28no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4C22×C4×C712yes—
498C22×C4C22×C4×C712yes—
499C22×C4C22×C4×C712yes—
500C22×C4C22×C4×C712yes—
501C22×C4C22×C4×C712yes—
502C22×C4C22×C4×C712yes—
503C22×C4C2×C7×D414yes—
504C22×C4C2×C7×Q814yes—
505C22×C4C7×#4114yes—
506C22×C4C7×#4114yes—
507C4⋊C4—48no—
508C22⋊C4—28no—
509C22⋊C4—28no—
510C22⋊C4—44no—
511C22⋊C4—44no—
512C42—48no—
513C2×C7—28no—
514C2×C7#228311yescharacteristic
515C2×C7C2×#38711yescharacteristic
516C2×C7#231211yescharacteristic
517C2×C7#234211yescharacteristic
518C2×C7#234211yescharacteristic
519C2×C7#234511yescharacteristic
520C2×C7#234511yescharacteristic
521C2×C7#244412yes—
522C2×C7#245012yes—
523C2×C7#250512yes—
524C2×C7#251012yes—
525C23—22no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23C7×#11714yes—
542C23C4×C7×D414yes—
543C23C4×C7×Q814yes—
544C23C7×C22⋊Q814yes—
545C23C7×#12314yes—
546C23C7×#12514yes—
547C23C7×#12614yes—
548C23C23×C4×C711yescharacteristic
549C23C22×C7×D411yescharacteristic
550C23C22×C7×Q811yescharacteristic
551C23C2×C7×#4111yescharacteristic
552C23C2×C7×#4111yescharacteristic
553C23C2×C7×#4112yes—
554C23C2×C7×#4112yes—
555C23C2×C7×#4111yescharacteristic
556C23C2×C7×#4111yescharacteristic
557C23C7×H(5,𝔽2)12yes—
558C23C7×H(5,𝔽2)12yes—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—416no—
586C2×C4—416no—
587C2×C4—416no—
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×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4C7×#11714yes—
619C2×C4C7×#11714yes—
620C7#1388311yescharacteristic, direct product factor, Sylow
621C22—28no—
622C22—28no—
623C22—28no—
624C22—28no—
625C22—24no—
626C22—24no—
627C22—24no—
628C22—24no—
629C22—24no—
630C22—24no—
631C22C7×#38718yes—
632C22C2×C7×#11711yescharacteristic
633C22C2×C7×#11711yescharacteristic
634C22C2×C7×#11711yescharacteristic
635C22C2×C4×C7×D411yescharacteristic
636C22C2×C4×C7×Q811yescharacteristic
637C22C7×#51811yescharacteristic
638C22C7×#51811yescharacteristic
639C22C2×C7×C22⋊Q811yescharacteristic
640C22C2×C7×#12311yescharacteristic
641C22C2×C7×#12511yescharacteristic
642C22C2×C7×#12611yescharacteristic
643C22C7×#52912yes—
644C22C7×#52912yes—
645C22C7×#53812yes—
646C22C7×#53812yes—
647C22C7×#54612yes—
648C22C7×#54612yes—
649C22C7×#55112yes—
650C22C7×#55112yes—
651C22C7×#55312yes—
652C22C7×#55312yes—
653C22C7×#55412yes—
654C22C7×#55412yes—
655C4—24no—
656C4—24no—
657C4—44no—
658C4—44no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—42no—
663C4—82no—
664C4—82no—
665C2—28no—
666C2C7×#228311yescharacteristic
667C2C2×C7×#38711yescharacteristic
668C2C7×#231211yescharacteristic
669C2C7×#234211yescharacteristic
670C2C7×#234211yescharacteristic
671C2C7×#234511yescharacteristic
672C2C7×#234511yescharacteristic
673C2C7×#244412yes—
674C2C7×#245012yes—
675C2C7×#250512yes—
676C2C7×#251012yes—
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
4. C7×#1443C2semidirect
5. C7×#1442C2semidirect
6. C7×#1436C2semidirect
7. C7×#1434C2semidirect
23. C2×C7×#95C4semidirect
38. #13883C7direct (N × H)
100. #1443C2×C7semidirect
101. #1442C2×C7semidirect
102. #1436C2×C7semidirect
103. #1434C2×C7semidirect
210. C2×#95C4×C7semidirect
620. C7#13883direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3802
C2×C4×C7×C22⋊C42
C22×C7×#952
C7×#14432
C7×#14422
C7×#14362
C7×#14342
C7×C22⋊#952
#138837