Finite Group Databasebeta

← C7×#15952 #13193168

Subgroups — C7×#15952 #13193168

Order 1792.

1862 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#386C212yesmaximal
2C2×C7×#381C212yesmaximal, complemented
3C7×#1445C211yesmaximal, characteristic, complemented
4C7×#1443C212yesmaximal, complemented
5C7×#1442C211yesmaximal, characteristic, complemented
6C7×#1439C212yesmaximal, complemented
7C7×#1439C212yesmaximal, complemented
8C7×#1438C211yesmaximal, characteristic
9C7×C22⋊#95C212yesmaximal, complemented
10C23×C7×D4C2211yescharacteristic
11C24×C4×C7C2212yes—
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2212yes—
15C22×C7×C22⋊C4C2212yes—
16C22×C7×C22⋊C4C2212yes—
17C22×C7×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2212yes—
19C7×#386—28no—
20C7×#381—28no—
21C2×C7×#95C2212yes—
22C2×C7×#95C2212yes—
23C2×C7×#95C2212yes—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7×#95C2212yes—
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2212yes—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2212yes—
32C2×C7×#95C2211yescharacteristic
33#15952C711yesmaximal, characteristic, direct product factor, Sylow
34C25×C7C2312yes—
35C22×C7×D4—24no—
36C22×C7×D4—24no—
37C22×C7×D4—41no—
38C22×C7×D4—41no—
39C22×C7×D4D414yes—
40C23×C4×C7—24no—
41C23×C4×C7—24no—
42C23×C4×C7—24no—
43C23×C4×C7—24no—
44C23×C4×C7—24no—
45C23×C4×C7—42no—
46C23×C4×C7—42no—
47C23×C4×C7C2312yes—
48C23×C4×C7C2312yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2312yes—
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—41no—
57C2×C7×C4⋊C4—41no—
58C2×C7×C4⋊C4—41no—
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—24no—
69C2×C7×C22⋊C4—42no—
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—
75C7×#95—24no—
76C7×#95—24no—
77C7×#95—24no—
78C7×#95—24no—
79C7×#95—24no—
80C7×#95—24no—
81C7×#95—42no—
82C7×#95—41no—
83C7×#95—41no—
84C7×#95—41no—
85C7×#95—42no—
86C7×#95D414yescomplemented
87C2×#386C2×C712yes—
88C2×#381C2×C712yescomplemented
89#1445C2×C711yescharacteristic, complemented
90#1443C2×C712yescomplemented
91#1442C2×C711yescharacteristic, complemented
92#1439C2×C712yescomplemented
93#1439C2×C712yescomplemented
94#1438C2×C711yescharacteristic
95C22⋊#95C2×C712yescomplemented
96C24×C7—22no—
97C24×C7—22no—
98C24×C7—22no—
99C24×C7—22no—
100C24×C7—22no—
101C24×C7—22no—
102C24×C7—22no—
103C24×C7—22no—
104C24×C7—22no—
105C24×C7—22no—
106C24×C7—22no—
107C24×C7—22no—
108C24×C7C2×D414yes—
109C24×C7#4114yes—
110C24×C7#4114yes—
111C24×C7C2411yescharacteristic
112C2×C7×D4—216no—
113C2×C7×D4—44no—
114C2×C7×D4—44no—
115C2×C7×D4—44no—
116C2×C7×D4—48no—
117C22×C4×C7—216no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
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—21no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
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—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—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—48no—
164C22×C4×C7—48no—
165C22×C4×C7—48no—
166C22×C4×C7—48no—
167C22×C4×C7—48no—
168C22×C4×C7—48no—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D414yes—
172C22×C4×C7#4114yes—
173C22×C4×C7#4112yes—
174C7×C4⋊C4—44no—
175C7×C4⋊C4—44no—
176C7×C22⋊C4—48no—
177C7×C22⋊C4—48no—
178C7×C22⋊C4—48no—
179C7×C22⋊C4—48no—
180C7×C22⋊C4—48no—
181C23×D4C22×C711yescharacteristic
182C24×C4C22×C712yes—
183C22×C4⋊C4C22×C711yescharacteristic
184C22×C4⋊C4C22×C711yescharacteristic
185C22×C22⋊C4C22×C712yes—
186C22×C22⋊C4C22×C712yes—
187C22×C22⋊C4C22×C712yes—
188C22×C22⋊C4C22×C712yes—
189C22×C22⋊C4C22×C712yes—
190#386—28no—
191#381—28no—
192C2×#95C22×C712yes—
193C2×#95C22×C712yes—
194C2×#95C22×C712yes—
195C2×#95C22×C712yes—
196C2×#95C22×C712yes—
197C2×#95C22×C712yes—
198C2×#95C22×C711yescharacteristic
199C2×#95C22×C712yes—
200C2×#95C22×C711yescharacteristic
201C2×#95C22×C711yescharacteristic
202C2×#95C22×C712yes—
203C2×#95C22×C711yescharacteristic
204C23×C7—24no—
205C23×C7—24no—
206C23×C7—24no—
207C23×C7—24no—
208C23×C7—24no—
209C23×C7—24no—
210C23×C7—24no—
211C23×C7—24no—
212C23×C7—24no—
213C23×C7—24no—
214C23×C7—24no—
215C23×C7—24no—
216C23×C7—24no—
217C23×C7—24no—
218C23×C7—24no—
219C23×C7—24no—
220C23×C7—24no—
221C23×C7—24no—
222C23×C7—42no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—42no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—42no—
229C23×C7—42no—
230C23×C7—42no—
231C23×C7—42no—
232C23×C7—42no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7—42no—
236C23×C7—42no—
237C23×C7—42no—
238C23×C7#12318yes—
239C23×C7C22×D411yescharacteristic
240C23×C7C22×D411yescharacteristic
241C23×C7C2×#4112yes—
242C23×C7C2×#4112yes—
243C23×C7C2×#4112yes—
244C23×C7C2×#4111yescharacteristic
245C23×C7H(5,𝔽2)11yescharacteristic
246C23×C7H(5,𝔽2)11yescharacteristic
247C23×C7H(5,𝔽2)11yescharacteristic
248C23×C7H(5,𝔽2)12yes—
249C23×C72−1+411yescharacteristic
250C7×D4—416no—
251C2×C4×C7—24no—
252C2×C4×C7—24no—
253C2×C4×C7—24no—
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—432no—
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—41no—
274C2×C4×C7—41no—
275C2×C4×C7—42no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—42no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
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—
302C25C23×C712yes—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—41no—
306C22×D4—41no—
307C22×D4C7×D414yes—
308C23×C4—24no—
309C23×C4—24no—
310C23×C4—24no—
311C23×C4—24no—
312C23×C4—24no—
313C23×C4—42no—
314C23×C4—42no—
315C23×C4C23×C712yes—
316C23×C4C23×C712yes—
317C23×C4C23×C712yes—
318C23×C4C23×C711yescharacteristic
319C23×C4C23×C712yes—
320C23×C4C23×C711yescharacteristic
321C23×C4C23×C711yescharacteristic
322C23×C4C23×C712yes—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—42no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343#95—24no—
344#95—24no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—42no—
350#95—41no—
351#95—41no—
352#95—41no—
353#95—42no—
354#95C7×D414yescomplemented
355C22×C7—28no—
356C22×C7—28no—
357C22×C7—28no—
358C22×C7—44no—
359C22×C7—44no—
360C22×C7—44no—
361C22×C7—44no—
362C22×C7—44no—
363C22×C7—44no—
364C22×C7—44no—
365C22×C7—44no—
366C22×C7—44no—
367C22×C7—44no—
368C22×C7—44no—
369C22×C7—44no—
370C22×C7C2×#12312yes—
371C22×C7#52512yes—
372C22×C7#52912yes—
373C22×C7#53411yescharacteristic
374C22×C7#53711yescharacteristic
375C22×C7#53811yescharacteristic
376C22×C7#53812yes—
377C22×C7#53912yes—
378C22×C7#54012yes—
379C22×C7D4211yescharacteristic
380C22×C7#54612yes—
381C22×C7#54612yes—
382C22×C7#54711yescharacteristic
383C22×C7#55011yescharacteristic
384C22×C7#55112yes—
385C22×C7#55111yescharacteristic
386C22×C7#55111yescharacteristic
387C22×C7#55112yes—
388C22×C7#55112yes—
389C22×C7#55212yes—
390C22×C7#55511yescharacteristic
391C22×C7#56011yescharacteristic
392C22×C7#56211yescharacteristic
393C4×C7—44no—
394C4×C7—44no—
395C4×C7—42no—
396C4×C7—42no—
397C4×C7—42no—
398C4×C7—82no—
399C4×C7—82no—
400C4×C7—82no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24C2×C7×D414yes—
414C24C7×#4114yes—
415C24C7×#4114yes—
416C24C24×C711yescharacteristic
417C2×D4—216no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—48no—
421C2×D4—44no—
422C22×C4—216no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
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×C4—22no—
467C22×C4—22no—
468C22×C4—48no—
469C22×C4—48no—
470C22×C4—48no—
471C22×C4—48no—
472C22×C4—48no—
473C22×C4—48no—
474C22×C4C2×C7×D412yes—
475C22×C4C2×C7×D412yes—
476C22×C4C2×C7×D414yes—
477C22×C4C7×#4114yes—
478C22×C4C7×#4112yes—
479C4⋊C4—44no—
480C4⋊C4—44no—
481C22⋊C4—48no—
482C22⋊C4—48no—
483C22⋊C4—48no—
484C22⋊C4—48no—
485C22⋊C4—48no—
486C2×C7—48no—
487C2×C7#241812yes—
488C2×C7#241912yes—
489C2×C7#247112yes—
490C2×C7#248311yescharacteristic
491C2×C7#257211yescharacteristic
492C2×C7#260911yescharacteristic
493C2×C7#268211yescharacteristic
494C2×C7#269311yescharacteristic
495C2×C7#269911yescharacteristic
496C2×C7#274312yes—
497C2×C7#276011yescharacteristic
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23C7×#12318yes—
533C23C22×C7×D411yescharacteristic
534C23C22×C7×D411yescharacteristic
535C23C2×C7×#4112yes—
536C23C2×C7×#4112yes—
537C23C2×C7×#4112yes—
538C23C2×C7×#4111yescharacteristic
539C23C7×H(5,𝔽2)11yescharacteristic
540C23C7×H(5,𝔽2)11yescharacteristic
541C23C7×H(5,𝔽2)11yescharacteristic
542C23C7×H(5,𝔽2)12yes—
543C23C7×2−1+411yescharacteristic
544D4—416no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—432no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
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×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C7#1595211yescharacteristic, direct product factor, Sylow
597C22—28no—
598C22—28no—
599C22—28no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22C2×C7×#12312yes—
613C22C7×#52512yes—
614C22C7×#52912yes—
615C22C7×#53411yescharacteristic
616C22C7×#53711yescharacteristic
617C22C7×#53812yes—
618C22C7×#53811yescharacteristic
619C22C7×#53912yes—
620C22C7×#54012yes—
621C22C7×D4211yescharacteristic
622C22C7×#54612yes—
623C22C7×#54612yes—
624C22C7×#54711yescharacteristic
625C22C7×#55011yescharacteristic
626C22C7×#55112yes—
627C22C7×#55112yes—
628C22C7×#55111yescharacteristic
629C22C7×#55112yes—
630C22C7×#55111yescharacteristic
631C22C7×#55212yes—
632C22C7×#55511yescharacteristic
633C22C7×#56011yescharacteristic
634C22C7×#56211yescharacteristic
635C4—44no—
636C4—44no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—82no—
641C4—82no—
642C4—82no—
643C2—48no—
644C2C7×#241812yes—
645C2C7×#241912yes—
646C2C7×#247112yes—
647C2C7×#248311yescharacteristic
648C2C7×#257211yescharacteristic
649C2C7×#260911yescharacteristic
650C2C7×#268211yescharacteristic
651C2C7×#269311yescharacteristic
652C2C7×#269911yescharacteristic
653C2C7×#274312yes—
654C2C7×#276011yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#381C2semidirect
3. C7×#1445C2semidirect
4. C7×#1443C2semidirect
5. C7×#1442C2semidirect
6. C7×#1439C2semidirect
7. C7×#1439C2semidirect
9. C7×C22⋊#95C2semidirect
33. #15952C7direct (N × H)
86. C7×#95D4semidirect
88. C2×#381C2×C7semidirect
89. #1445C2×C7semidirect
90. #1443C2×C7semidirect
91. #1442C2×C7semidirect
92. #1439C2×C7semidirect
93. #1439C2×C7semidirect
95. C22⋊#95C2×C7semidirect
354. #95C7×D4semidirect
596. C7#15952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3862
C2×C7×#3812
C7×#14452
C7×#14432
C7×#14422
C7×#14392
C7×#14382
C7×C22⋊#952
#159527