Finite Group Databasebeta

← C7×#14729 #13191945

Subgroups — C7×#14729 #13191945

Order 1792.

2506 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C7×#396C212yesmaximal, complemented
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#386C211yesmaximal, characteristic
5C2×C7×#386C211yesmaximal, characteristic
6C2×C7×#385C211yesmaximal, characteristic, complemented
7C2×C7×#380C211yesmaximal, characteristic, complemented
8C7×#1441C212yesmaximal, complemented
9C7×#1441C212yesmaximal, complemented
10C7×#1439C212yesmaximal, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C22×C7×C4⋊C4—24no—
17C22×C7×C4⋊C4—28no—
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2212yes—
21C22×C7×C4⋊C4C2212yes—
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C7×#396—28no—
30C7×#386—24no—
31C7×#386—24no—
32C7×#386—24no—
33C7×#385—24no—
34C7×#380—24no—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2212yes—
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43#14729C711yesmaximal, characteristic, direct product factor, Sylow
44C25×C7C2311yescharacteristic
45C25×C7C2311yescharacteristic
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4Q814yes—
53C23×C4×C7—22no—
54C23×C4×C7—22no—
55C23×C4×C7—24no—
56C23×C4×C7—24no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—24no—
61C23×C4×C7—24no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—42no—
65C23×C4×C7—42no—
66C23×C4×C7D414yes—
67C23×C4×C7D414yes—
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2312yes—
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2312yes—
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2312yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2312yes—
77C2×C7×C4⋊C4—232no—
78C2×C7×C4⋊C4—24no—
79C2×C7×C4⋊C4—24no—
80C2×C7×C4⋊C4—24no—
81C2×C7×C4⋊C4—24no—
82C2×C7×C4⋊C4—24no—
83C2×C7×C4⋊C4—24no—
84C2×C7×C4⋊C4—24no—
85C2×C7×C4⋊C4—24no—
86C2×C7×C4⋊C4—24no—
87C2×C7×C4⋊C4—24no—
88C2×C7×C4⋊C4—42no—
89C2×C7×C4⋊C4D418yescomplemented
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4—42no—
108C2×C7×C22⋊C4D414yes—
109C7×#95—24no—
110C7×#95—24no—
111C7×#95—24no—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—24no—
115C7×#95—24no—
116C7×#95—42no—
117C23×C4⋊C4C2×C711yescharacteristic, complemented
118C2×#396C2×C712yescomplemented
119C2×#386C2×C711yescharacteristic
120C2×#386C2×C711yescharacteristic
121C2×#386C2×C711yescharacteristic
122C2×#385C2×C711yescharacteristic, complemented
123C2×#380C2×C711yescharacteristic, complemented
124#1441C2×C712yescomplemented
125#1441C2×C712yescomplemented
126#1439C2×C712yescomplemented
127C22⋊#95C2×C711yescharacteristic, complemented
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—22no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7C2×D412yes—
143C24×C7C2×D412yes—
144C24×C7C2×D412yes—
145C24×C7C2×Q812yes—
146C24×C7C2×Q812yes—
147C24×C7#4112yes—
148C24×C7#4112yes—
149C24×C7#4112yes—
150C24×C7C2411yescharacteristic
151C2×C7×D4—28no—
152C2×C7×D4—28no—
153C2×C7×D4—28no—
154C2×C7×D4—44no—
155C2×C7×D4—44no—
156C2×C7×D4—44no—
157C2×C7×D4—44no—
158C22×C4×C7—28no—
159C22×C4×C7—216no—
160C22×C4×C7—28no—
161C22×C4×C7—28no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—21no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—21no—
168C22×C4×C7—22no—
169C22×C4×C7—216no—
170C22×C4×C7—28no—
171C22×C4×C7—28no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—21no—
185C22×C4×C7—22no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—28no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—22no—
198C22×C4×C7—21no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—44no—
213C22×C4×C7—48no—
214C22×C4×C7—48no—
215C22×C4×C7—48no—
216C22×C4×C7—48no—
217C22×C4×C7—44no—
218C22×C4×C7—44no—
219C22×C4×C7C2×D414yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D414yes—
222C22×C4×C7C2×D412yes—
223C22×C4×C7C2×D414yes—
224C22×C4×C7C2×D414yes—
225C22×C4×C7C2×D414yes—
226C22×C4×C7C2×Q812yes—
227C22×C4×C7#4114yes—
228C7×C4⋊C4—216no—
229C7×C4⋊C4—216no—
230C7×C4⋊C4—48no—
231C7×C4⋊C4—48no—
232C7×C22⋊C4—28no—
233C7×C22⋊C4—48no—
234C7×C22⋊C4—44no—
235C7×C22⋊C4—44no—
236C7×C22⋊C4—44no—
237C7×C22⋊C4—44no—
238C7×C22⋊C4—48no—
239C23×D4C22×C711yescharacteristic
240C24×C4C22×C711yescharacteristic
241C24×C4C22×C711yescharacteristic
242C24×C4C22×C711yescharacteristic
243C22×C4⋊C4—24no—
244C22×C4⋊C4—28no—
245C22×C4⋊C4C22×C712yes—
246C22×C4⋊C4C22×C712yes—
247C22×C4⋊C4C22×C712yes—
248C22×C4⋊C4C22×C712yes—
249C22×C22⋊C4C22×C711yescharacteristic
250C22×C22⋊C4C22×C712yes—
251C22×C22⋊C4C22×C711yescharacteristic
252C22×C22⋊C4C22×C711yescharacteristic
253C22×C22⋊C4C22×C712yes—
254C22×C22⋊C4C22×C711yescharacteristic
255C22×C22⋊C4C22×C711yescharacteristic
256#396—28no—
257#386—24no—
258#386—24no—
259#386—24no—
260#385—24no—
261#380—24no—
262C2×#95C22×C712yes—
263C2×#95C22×C712yes—
264C2×#95C22×C712yes—
265C2×#95C22×C711yescharacteristic
266C2×#95C22×C712yes—
267C2×#95C22×C711yescharacteristic
268C2×#95C22×C712yes—
269C2×#95C22×C712yes—
270C23×C7—22no—
271C23×C7—24no—
272C23×C7—22no—
273C23×C7—24no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—24no—
277C23×C7—24no—
278C23×C7—24no—
279C23×C7—24no—
280C23×C7—24no—
281C23×C7—24no—
282C23×C7—24no—
283C23×C7—24no—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—24no—
290C23×C7—24no—
291C23×C7—41no—
292C23×C7—42no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—42no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7#12114yes—
310C23×C7#12114yes—
311C23×C7#12114yes—
312C23×C7C22⋊Q814yes—
313C23×C7C22⋊Q814yes—
314C23×C7C22⋊Q814yes—
315C23×C7#12614yes—
316C23×C7C22×D411yescharacteristic
317C23×C7C22×D412yes—
318C23×C7C22×D411yescharacteristic
319C23×C7C22×D411yescharacteristic
320C23×C7C22×Q811yescharacteristic
321C23×C7C2×#4111yescharacteristic
322C23×C7C2×#4111yescharacteristic
323C23×C7C2×#4111yescharacteristic
324C23×C7C2×#4112yes—
325C23×C7H(5,𝔽2)12yes—
326C23×C72−1+412yes—
327C7×D4—416no—
328C2×C4×C7—232no—
329C2×C4×C7—24no—
330C2×C4×C7—24no—
331C2×C4×C7—24no—
332C2×C4×C7—22no—
333C2×C4×C7—24no—
334C2×C4×C7—24no—
335C2×C4×C7—24no—
336C2×C4×C7—22no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—22no—
340C2×C4×C7—24no—
341C2×C4×C7—24no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—24no—
348C2×C4×C7—24no—
349C2×C4×C7—24no—
350C2×C4×C7—24no—
351C2×C4×C7—416no—
352C2×C4×C7—416no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—41no—
374C2×C4×C7—42no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7#12014yes—
385C2×C4×C7#12118yes—
386C25C23×C711yescharacteristic
387C25C23×C711yescharacteristic
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—22no—
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4C7×Q814yes—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4C7×D414yes—
409C23×C4C7×D414yes—
410C23×C4C23×C711yescharacteristic
411C23×C4C23×C712yes—
412C23×C4C23×C711yescharacteristic
413C23×C4C23×C712yes—
414C23×C4C23×C711yescharacteristic
415C23×C4C23×C712yes—
416C23×C4C23×C711yescharacteristic
417C23×C4C23×C711yescharacteristic
418C23×C4C23×C712yes—
419C2×C4⋊C4—232no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4C7×D418yescomplemented
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4C7×D414yes—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—22no—
455#95—22no—
456#95—24no—
457#95—24no—
458#95—42no—
459C22×C7—24no—
460C22×C7—24no—
461C22×C7—24no—
462C22×C7—24no—
463C22×C7—24no—
464C22×C7—24no—
465C22×C7—28no—
466C22×C7—28no—
467C22×C7—28no—
468C22×C7—28no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7—44no—
473C22×C7—44no—
474C22×C7—81no—
475C22×C7—81no—
476C22×C7—81no—
477C22×C7—81no—
478C22×C7—82no—
479C22×C7—82no—
480C22×C7#39618yescomplemented
481C22×C7C2×#12011yescharacteristic
482C22×C7C2×#12111yescharacteristic
483C22×C7C2×#12112yes—
484C22×C7C2×#12111yescharacteristic
485C22×C7C2×#12111yescharacteristic
486C22×C7C2×C22⋊Q811yescharacteristic
487C22×C7C2×C22⋊Q811yescharacteristic
488C22×C7C2×C22⋊Q811yescharacteristic
489C22×C7#52511yescharacteristic
490C22×C7#52512yes—
491C22×C7C2×#12611yescharacteristic
492C22×C7#53411yescharacteristic
493C22×C7#53611yescharacteristic
494C22×C7#53712yes—
495C22×C7#53912yes—
496C22×C7D4212yes—
497C22×C7#54612yes—
498C22×C7#54712yes—
499C22×C7#54812yes—
500C22×C7D4×Q812yes—
501C22×C7#55212yes—
502C22×C7#55312yes—
503C22×C7#55412yes—
504C4×C7—28no—
505C4×C7—24no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—44no—
509C4×C7—44no—
510C4×C7—81no—
511C4×C7—81no—
512C4×C7—82no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—22no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24C2×C7×D412yes—
528C24C2×C7×D412yes—
529C24C2×C7×D412yes—
530C24C2×C7×Q812yes—
531C24C2×C7×Q812yes—
532C24C7×#4112yes—
533C24C7×#4112yes—
534C24C7×#4112yes—
535C24C24×C711yescharacteristic
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C22×C4—28no—
544C22×C4—216no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—216no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4C2×C7×D414yes—
605C22×C4C2×C7×D412yes—
606C22×C4C2×C7×D414yes—
607C22×C4C2×C7×D412yes—
608C22×C4C2×C7×D414yes—
609C22×C4C2×C7×D414yes—
610C22×C4C2×C7×D414yes—
611C22×C4C2×C7×Q812yes—
612C22×C4C7×#4114yes—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—48no—
624C2×C7—28no—
625C2×C7—82no—
626C2×C7C2×#39611yescharacteristic
627C2×C7#240911yescharacteristic
628C2×C7#241011yescharacteristic
629C2×C7#241311yescharacteristic
630C2×C7#241612yes—
631C2×C7#241712yes—
632C2×C7#244912yes—
633C2×C7#248112yes—
634C2×C7#257911yescharacteristic
635C2×C7#261811yescharacteristic
636C2×C7#284711yescharacteristic
637C23—22no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—41no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—42no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23C7×#12114yes—
677C23C7×#12114yes—
678C23C7×#12114yes—
679C23C7×C22⋊Q814yes—
680C23C7×C22⋊Q814yes—
681C23C7×C22⋊Q814yes—
682C23C7×#12614yes—
683C23C22×C7×D411yescharacteristic
684C23C22×C7×D412yes—
685C23C22×C7×D411yescharacteristic
686C23C22×C7×D411yescharacteristic
687C23C22×C7×Q811yescharacteristic
688C23C2×C7×#4111yescharacteristic
689C23C2×C7×#4111yescharacteristic
690C23C2×C7×#4111yescharacteristic
691C23C2×C7×#4112yes—
692C23C7×H(5,𝔽2)12yes—
693C23C7×2−1+412yes—
694D4—416no—
695C2×C4—232no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4C7×#12014yes—
752C2×C4C7×#12118yes—
753C7#1472911yescharacteristic, direct product factor, Sylow
754C22—24no—
755C22—24no—
756C22—24no—
757C22—28no—
758C22—28no—
759C22—28no—
760C22—28no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—82no—
772C22—82no—
773C22—81no—
774C22—81no—
775C22C7×#39618yescomplemented
776C22C2×C7×#12011yescharacteristic
777C22C2×C7×#12111yescharacteristic
778C22C2×C7×#12111yescharacteristic
779C22C2×C7×#12111yescharacteristic
780C22C2×C7×#12112yes—
781C22C2×C7×C22⋊Q811yescharacteristic
782C22C2×C7×C22⋊Q811yescharacteristic
783C22C2×C7×C22⋊Q811yescharacteristic
784C22C7×#52511yescharacteristic
785C22C7×#52512yes—
786C22C2×C7×#12611yescharacteristic
787C22C7×#53411yescharacteristic
788C22C7×#53611yescharacteristic
789C22C7×#53712yes—
790C22C7×#53912yes—
791C22C7×D4212yes—
792C22C7×#54612yes—
793C22C7×#54712yes—
794C22C7×#54812yes—
795C22C7×D4×Q812yes—
796C22C7×#55212yes—
797C22C7×#55312yes—
798C22C7×#55412yes—
799C4—24no—
800C4—28no—
801C4—42no—
802C4—42no—
803C4—44no—
804C4—44no—
805C4—82no—
806C4—81no—
807C4—81no—
808C2—28no—
809C2—82no—
810C2C2×C7×#39611yescharacteristic
811C2C7×#240911yescharacteristic
812C2C7×#241011yescharacteristic
813C2C7×#241311yescharacteristic
814C2C7×#241612yes—
815C2C7×#241712yes—
816C2C7×#244912yes—
817C2C7×#248112yes—
818C2C7×#257911yescharacteristic
819C2C7×#261811yescharacteristic
820C2C7×#284711yescharacteristic
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
1. C23×C7×C4⋊C4C2semidirect
2. C2×C7×#396C2semidirect
6. C2×C7×#385C2semidirect
7. C2×C7×#380C2semidirect
8. C7×#1441C2semidirect
9. C7×#1441C2semidirect
10. C7×#1439C2semidirect
11. C7×C22⋊#95C2semidirect
43. #14729C7direct (N × H)
89. C2×C7×C4⋊C4D4semidirect
117. C23×C4⋊C4C2×C7semidirect
118. C2×#396C2×C7semidirect
122. C2×#385C2×C7semidirect
123. C2×#380C2×C7semidirect
124. #1441C2×C7semidirect
125. #1441C2×C7semidirect
126. #1439C2×C7semidirect
127. C22⋊#95C2×C7semidirect
431. C2×C4⋊C4C7×D4semidirect
480. C22×C7#396semidirect
753. C7#14729direct (N × H)
775. C22C7×#396semidirect

Maximal subgroups

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

subgroupindex
C23×C7×C4⋊C42
C2×C7×#3962
C2×C7×#3862
C2×C7×#3852
C2×C7×#3802
C7×#14412
C7×#14392
C7×C22⋊#952
#147297