Finite Group Databasebeta

← C7×#14719 #13191935

Subgroups — C7×#14719 #13191935

Order 1792.

2982 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C23×C7×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#394C212yesmaximal, complemented
4C2×C7×#386C212yesmaximal, complemented
5C2×C7×#386C212yesmaximal, complemented
6C7×#1441C212yesmaximal, complemented
7C7×#1439C214yesmaximal, complemented
8C7×C22⋊#95C211yesmaximal, characteristic, complemented
9C23×C7×D4C2212yes—
10C23×C7×D4C2211yescharacteristic
11C24×C4×C7C2211yescharacteristic
12C24×C4×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C2×C7×#121—28no—
15C2×C7×#121—24no—
16C22×C7×C4⋊C4—24no—
17C22×C7×C4⋊C4—28no—
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2214yes—
24C22×C7×C22⋊C4C2214yes—
25C7×#394—28no—
26C7×#386—28no—
27C7×#386—28no—
28C2×C7×#95C2214yes—
29C2×C7×#95C2214yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32#14719C711yesmaximal, characteristic, direct product factor, Sylow
33C25×C7C2312yes—
34C25×C7C2311yescharacteristic
35C22×C7×D4—24no—
36C22×C7×D4—24no—
37C22×C7×D4—24no—
38C22×C7×D4—24no—
39C22×C7×D4—24no—
40C22×C7×D4—24no—
41C22×C7×D4—24no—
42C22×C7×D4—22no—
43C22×C7×D4—24no—
44C22×C7×D4—42no—
45C22×C7×D4D418yes—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—24no—
49C23×C4×C7—24no—
50C23×C4×C7—22no—
51C23×C4×C7—24no—
52C23×C4×C7—24no—
53C23×C4×C7—24no—
54C23×C4×C7—24no—
55C23×C4×C7—42no—
56C23×C4×C7—42no—
57C23×C4×C7D414yes—
58C23×C4×C7D414yescomplemented
59C23×C4×C7C2314yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2312yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2312yes—
65C7×#121—232no—
66C2×C7×C4⋊C4—232no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—24no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4D418yescomplemented
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—28no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—28no—
83C2×C7×C22⋊C4—28no—
84C2×C7×C22⋊C4—28no—
85C2×C7×C22⋊C4—28no—
86C2×C7×C22⋊C4—44no—
87C7×#95—28no—
88C7×#95—28no—
89C7×#95—24no—
90C7×#95—42no—
91C22×#121C2×C711yescharacteristic
92C23×C4⋊C4C2×C711yescharacteristic, complemented
93C2×#394C2×C712yescomplemented
94C2×#386C2×C712yescomplemented
95C2×#386C2×C712yescomplemented
96#1441C2×C712yescomplemented
97#1439C2×C714yescomplemented
98C22⋊#95C2×C711yescharacteristic, complemented
99C24×C7—22no—
100C24×C7—22no—
101C24×C7—22no—
102C24×C7—22no—
103C24×C7—22no—
104C24×C7—24no—
105C24×C7—22no—
106C24×C7—22no—
107C24×C7—24no—
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—24no—
112C24×C7—24no—
113C24×C7C2×D414yes—
114C24×C7C2×D414yes—
115C24×C7C2×D412yes—
116C24×C7C2×D412yes—
117C24×C7#4112yes—
118C24×C7#4114yes—
119C24×C7C2411yescharacteristic
120C2×C7×D4—28no—
121C2×C7×D4—216no—
122C2×C7×D4—216no—
123C2×C7×D4—216no—
124C2×C7×D4—416no—
125C2×C7×D4—44no—
126C2×C7×D4—48no—
127C2×C7×D4—48no—
128C2×C7×D4—48no—
129C2×C7×D4—48no—
130C2×C7×D4—44no—
131C22×C4×C7—28no—
132C22×C4×C7—216no—
133C22×C4×C7—28no—
134C22×C4×C7—28no—
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—216no—
142C22×C4×C7—28no—
143C22×C4×C7—28no—
144C22×C4×C7—22no—
145C22×C4×C7—24no—
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—24no—
157C22×C4×C7—28no—
158C22×C4×C7—24no—
159C22×C4×C7—24no—
160C22×C4×C7—24no—
161C22×C4×C7—24no—
162C22×C4×C7—24no—
163C22×C4×C7—24no—
164C22×C4×C7—24no—
165C22×C4×C7—44no—
166C22×C4×C7—416no—
167C22×C4×C7—416no—
168C22×C4×C7—44no—
169C22×C4×C7—44no—
170C22×C4×C7C2×D414yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D414yes—
173C22×C4×C7C2×D414yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7C2×D414yes—
176C22×C4×C7C2×D414yes—
177C22×C4×C7#4114yes—
178C7×C4⋊C4—216no—
179C7×C4⋊C4—28no—
180C7×C4⋊C4—216no—
181C7×C22⋊C4—216no—
182C7×C22⋊C4—416no—
183C7×C22⋊C4—48no—
184C7×C22⋊C4—416no—
185C23×D4C22×C712yes—
186C23×D4C22×C711yescharacteristic
187C24×C4C22×C711yescharacteristic
188C24×C4C22×C711yescharacteristic
189C24×C4C22×C711yescharacteristic
190C2×#121—28no—
191C2×#121—24no—
192C22×C4⋊C4—24no—
193C22×C4⋊C4—28no—
194C22×C4⋊C4C22×C712yes—
195C22×C4⋊C4C22×C711yescharacteristic
196C22×C4⋊C4C22×C712yes—
197C22×C22⋊C4C22×C714yes—
198C22×C22⋊C4C22×C712yes—
199C22×C22⋊C4C22×C712yes—
200C22×C22⋊C4C22×C714yes—
201#394—28no—
202#386—28no—
203#386—28no—
204C2×#95C22×C712yes—
205C2×#95C22×C714yes—
206C2×#95C22×C714yes—
207C2×#95C22×C712yes—
208C23×C7—22no—
209C23×C7—24no—
210C23×C7—22no—
211C23×C7—24no—
212C23×C7—22no—
213C23×C7—22no—
214C23×C7—24no—
215C23×C7—24no—
216C23×C7—28no—
217C23×C7—28no—
218C23×C7—28no—
219C23×C7—28no—
220C23×C7—24no—
221C23×C7—24no—
222C23×C7—24no—
223C23×C7—28no—
224C23×C7—28no—
225C23×C7—42no—
226C23×C7—44no—
227C23×C7—42no—
228C23×C7—42no—
229C23×C7—42no—
230C23×C7—42no—
231C23×C7—44no—
232C23×C7—42no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7—44no—
236C23×C7—44no—
237C23×C7—44no—
238C23×C7—44no—
239C23×C7—44no—
240C23×C7—44no—
241C23×C7—44no—
242C23×C7—44no—
243C23×C7#12014yes—
244C23×C7#12118yes—
245C23×C7#12114yes—
246C23×C7#12318yes—
247C23×C7#12414yes—
248C23×C7C22×D411yescharacteristic
249C23×C7C22×D412yes—
250C23×C7C22×D412yes—
251C23×C7C22×D411yescharacteristic
252C23×C7C2×#4111yescharacteristic
253C23×C7C2×#4112yes—
254C23×C7C2×#4112yes—
255C23×C7H(5,𝔽2)12yes—
256C23×C72−1+412yes—
257C7×D4—416no—
258C7×D4—432no—
259C2×C4×C7—232no—
260C2×C4×C7—24no—
261C2×C4×C7—22no—
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—28no—
269C2×C4×C7—22no—
270C2×C4×C7—24no—
271C2×C4×C7—22no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—24no—
275C2×C4×C7—22no—
276C2×C4×C7—28no—
277C2×C4×C7—416no—
278C2×C4×C7—416no—
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—44no—
286C2×C4×C7—44no—
287C2×C4×C7—44no—
288C2×C4×C7—44no—
289C2×C4×C7—44no—
290C2×C4×C7—44no—
291C2×C4×C7—44no—
292C2×C4×C7—44no—
293C2×C4×C7—44no—
294C2×C4×C7#12014yes—
295C2×C4×C7#12118yescomplemented
296C25C23×C712yes—
297C25C23×C711yescharacteristic
298C22×D4—24no—
299C22×D4—24no—
300C22×D4—24no—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—22no—
306C22×D4—24no—
307C22×D4—42no—
308C22×D4C7×D418yes—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—24no—
312C23×C4—24no—
313C23×C4—22no—
314C23×C4—24no—
315C23×C4—24no—
316C23×C4—24no—
317C23×C4—24no—
318C23×C4—42no—
319C23×C4—42no—
320C23×C4C7×D414yes—
321C23×C4C7×D414yescomplemented
322C23×C4C23×C714yes—
323C23×C4C23×C712yes—
324C23×C4C23×C711yescharacteristic
325C23×C4C23×C712yes—
326C23×C4C23×C711yescharacteristic
327C23×C4C23×C712yes—
328#121—232no—
329C2×C4⋊C4—232no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4C7×D418yescomplemented
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—44no—
350#95—28no—
351#95—28no—
352#95—24no—
353#95—42no—
354C22×C7—24no—
355C22×C7—24no—
356C22×C7—24no—
357C22×C7—24no—
358C22×C7—24no—
359C22×C7—216no—
360C22×C7—24no—
361C22×C7—216no—
362C22×C7—44no—
363C22×C7—44no—
364C22×C7—44no—
365C22×C7—48no—
366C22×C7—48no—
367C22×C7—82no—
368C22×C7—82no—
369C22×C7—82no—
370C22×C7—84no—
371C22×C7—82no—
372C22×C7—84no—
373C22×C7#39418yescomplemented
374C22×C7C2×#12011yescharacteristic
375C22×C7C2×#12011yescharacteristic
376C22×C7C2×#12111yescharacteristic
377C22×C7C2×#12112yes—
378C22×C7C2×#12112yes—
379C22×C7C2×#12312yes—
380C22×C7#52511yescharacteristic
381C22×C7#52512yes—
382C22×C7C2×#12411yescharacteristic
383C22×C7#53411yescharacteristic
384C22×C7#53611yescharacteristic
385C22×C7#53712yes—
386C22×C7#53912yes—
387C22×C7D4214yes—
388C22×C7#54714yes—
389C22×C7#54814yes—
390C22×C7#55314yes—
391C4×C7—28no—
392C4×C7—24no—
393C4×C7—44no—
394C4×C7—42no—
395C4×C7—44no—
396C4×C7—84no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24C2×C7×D414yes—
412C24C2×C7×D414yes—
413C24C2×C7×D412yes—
414C24C2×C7×D412yes—
415C24C7×#4112yes—
416C24C7×#4114yes—
417C24C24×C711yescharacteristic
418C2×D4—28no—
419C2×D4—216no—
420C2×D4—216no—
421C2×D4—216no—
422C2×D4—416no—
423C2×D4—44no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—44no—
429C22×C4—28no—
430C22×C4—216no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—216no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
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—22no—
454C22×C4—24no—
455C22×C4—28no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—44no—
464C22×C4—416no—
465C22×C4—416no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4C2×C7×D414yes—
469C22×C4C2×C7×D412yes—
470C22×C4C2×C7×D414yes—
471C22×C4C2×C7×D414yes—
472C22×C4C2×C7×D412yes—
473C22×C4C2×C7×D414yes—
474C22×C4C2×C7×D414yes—
475C22×C4C7×#4114yes—
476C4⋊C4—216no—
477C4⋊C4—28no—
478C4⋊C4—216no—
479C22⋊C4—216no—
480C22⋊C4—416no—
481C22⋊C4—48no—
482C22⋊C4—416no—
483C2×C7—28no—
484C2×C7—84no—
485C2×C7C2×#39411yescharacteristic
486C2×C7#240311yescharacteristic
487C2×C7#240611yescharacteristic
488C2×C7#241614yes—
489C2×C7#243611yescharacteristic
490C2×C7#244314yes—
491C2×C7#259111yescharacteristic
492C2×C7#261811yescharacteristic
493C2×C7#284711yescharacteristic
494C23—22no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—22no—
500C23—24no—
501C23—24no—
502C23—28no—
503C23—28no—
504C23—28no—
505C23—28no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—28no—
510C23—28no—
511C23—42no—
512C23—44no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—44no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23C7×#12014yes—
530C23C7×#12118yes—
531C23C7×#12114yes—
532C23C7×#12318yes—
533C23C7×#12414yes—
534C23C22×C7×D411yescharacteristic
535C23C22×C7×D412yes—
536C23C22×C7×D412yes—
537C23C22×C7×D411yescharacteristic
538C23C2×C7×#4111yescharacteristic
539C23C2×C7×#4112yes—
540C23C2×C7×#4112yes—
541C23C7×H(5,𝔽2)12yes—
542C23C7×2−1+412yes—
543D4—416no—
544D4—432no—
545C2×C4—232no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—28no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—28no—
563C2×C4—416no—
564C2×C4—416no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4C7×#12014yes—
581C2×C4C7×#12118yescomplemented
582C7#1471911yescharacteristic, direct product factor, Sylow
583C22—24no—
584C22—24no—
585C22—216no—
586C22—24no—
587C22—216no—
588C22—24no—
589C22—24no—
590C22—24no—
591C22—44no—
592C22—44no—
593C22—48no—
594C22—48no—
595C22—44no—
596C22—84no—
597C22—82no—
598C22—84no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22C7×#39418yescomplemented
603C22C2×C7×#12011yescharacteristic
604C22C2×C7×#12011yescharacteristic
605C22C2×C7×#12112yes—
606C22C2×C7×#12112yes—
607C22C2×C7×#12111yescharacteristic
608C22C2×C7×#12312yes—
609C22C7×#52511yescharacteristic
610C22C7×#52512yes—
611C22C2×C7×#12411yescharacteristic
612C22C7×#53411yescharacteristic
613C22C7×#53611yescharacteristic
614C22C7×#53712yes—
615C22C7×#53912yes—
616C22C7×D4214yes—
617C22C7×#54714yes—
618C22C7×#54814yes—
619C22C7×#55314yes—
620C4—24no—
621C4—28no—
622C4—42no—
623C4—44no—
624C4—44no—
625C4—84no—
626C2—28no—
627C2—84no—
628C2C2×C7×#39411yescharacteristic
629C2C7×#240311yescharacteristic
630C2C7×#240611yescharacteristic
631C2C7×#241614yes—
632C2C7×#243611yescharacteristic
633C2C7×#244314yes—
634C2C7×#259111yescharacteristic
635C2C7×#261811yescharacteristic
636C2C7×#284711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC22×C7×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C7×C4⋊C4C2semidirect
3. C2×C7×#394C2semidirect
4. C2×C7×#386C2semidirect
5. C2×C7×#386C2semidirect
6. C7×#1441C2semidirect
7. C7×#1439C2semidirect
8. C7×C22⋊#95C2semidirect
32. #14719C7direct (N × H)
58. C23×C4×C7D4semidirect
74. C2×C7×C4⋊C4D4semidirect
92. C23×C4⋊C4C2×C7semidirect
93. C2×#394C2×C7semidirect
94. C2×#386C2×C7semidirect
95. C2×#386C2×C7semidirect
96. #1441C2×C7semidirect
97. #1439C2×C7semidirect
98. C22⋊#95C2×C7semidirect
295. C2×C4×C7#121semidirect
321. C23×C4C7×D4semidirect
337. C2×C4⋊C4C7×D4semidirect
373. C22×C7#394semidirect
581. C2×C4C7×#121semidirect
582. C7#14719direct (N × H)
602. C22C7×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C23×C7×C4⋊C42
C2×C7×#3942
C2×C7×#3862
C7×#14412
C7×#14392
C7×C22⋊#952
#147197