Finite Group Databasebeta

← C7×#14727 #13191943

Subgroups — C7×#14727 #13191943

Order 1792.

3350 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C22⋊C4C211yesmaximal, characteristic
2C2×C7×#397C212yesmaximal, complemented
3C2×C7×#385C211yesmaximal, characteristic, complemented
4C2×C7×#379C211yesmaximal, characteristic
5C2×C7×#379C211yesmaximal, characteristic
6C7×#1440C212yesmaximal, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×C22⋊#95C211yesmaximal, characteristic, complemented
10C7×C22⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4C2212yescomplemented
16C22×C7×C22⋊C4—24no—
17C22×C7×C22⋊C4—28no—
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C7×#397—28no—
31C7×#385—24no—
32C7×#379—24no—
33C7×#379—24no—
34C2×C7×#95C2212yescomplemented
35C2×C7×#95C2212yescomplemented
36C2×C7×#95C2212yescomplemented
37C2×C7×#95C2212yescomplemented
38C2×C7×#95C2212yescomplemented
39C2×C7×#95C2212yescomplemented
40C2×C7×#95C2212yescomplemented
41#14727C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7—24no—
43C25×C7—24no—
44C25×C7—22no—
45C25×C7—22no—
46C25×C7—22no—
47C25×C7—22no—
48C25×C7—22no—
49C25×C7—22no—
50C25×C7—42no—
51C25×C7—42no—
52C25×C7D414yes—
53C25×C7C2311yescharacteristic
54C25×C7C2311yescharacteristic
55C25×C7C2311yescharacteristic
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—24no—
59C23×C4×C7—24no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—42no—
65C23×C4×C7—42no—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2312yes—
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2312yes—
72C23×C4×C7C2312yes—
73C23×C4×C7C2312yes—
74C2×C7×C4⋊C4—24no—
75C2×C7×C4⋊C4—24no—
76C2×C7×C4⋊C4—42no—
77C2×C7×C22⋊C4—232no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4—22no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—42no—
105C2×C7×C22⋊C4—42no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4—42no—
108C2×C7×C22⋊C4D418yes—
109C2×C7×C22⋊C4D414yes—
110C7×#95—24no—
111C7×#95—24no—
112C7×#95—24no—
113C7×#95—24no—
114C7×#95—42no—
115C7×#95—42no—
116C7×#95—42no—
117C23×C22⋊C4C2×C711yescharacteristic
118C2×#397C2×C712yescomplemented
119C2×#385C2×C711yescharacteristic, complemented
120C2×#379C2×C711yescharacteristic
121C2×#379C2×C711yescharacteristic
122#1440C2×C712yescomplemented
123#1440C2×C712yescomplemented
124#1439C2×C712yescomplemented
125C22⋊#95C2×C711yescharacteristic, complemented
126C22⋊#95C2×C711yescharacteristic, complemented
127C22⋊#95C2×C711yescharacteristic, complemented
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—216no—
133C24×C7—216no—
134C24×C7—28no—
135C24×C7—28no—
136C24×C7—28no—
137C24×C7—22no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7—21no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—21no—
144C24×C7—22no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—21no—
151C24×C7—22no—
152C24×C7—22no—
153C24×C7—22no—
154C24×C7—22no—
155C24×C7—28no—
156C24×C7—28no—
157C24×C7—44no—
158C24×C7—44no—
159C24×C7—48no—
160C24×C7—48no—
161C24×C7—48no—
162C24×C7—48no—
163C24×C7—48no—
164C24×C7—48no—
165C24×C7—48no—
166C24×C7—48no—
167C24×C7—48no—
168C24×C7—48no—
169C24×C7—44no—
170C24×C7—44no—
171C24×C7—44no—
172C24×C7—44no—
173C24×C7C2×D412yes—
174C24×C7C2×D414yes—
175C24×C7C2×D412yes—
176C24×C7C2×D412yes—
177C24×C7C2×D412yes—
178C24×C7#4114yes—
179C24×C7#4112yes—
180C24×C7#4112yes—
181C24×C7#4112yes—
182C24×C7#4112yes—
183C24×C7#4112yes—
184C24×C7C2411yescharacteristic
185C22×C4×C7—28no—
186C22×C4×C7—28no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—21no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—22no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—22no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—48no—
233C22×C4×C7—48no—
234C22×C4×C7—48no—
235C22×C4×C7—48no—
236C22×C4×C7—44no—
237C22×C4×C7—44no—
238C22×C4×C7—44no—
239C22×C4×C7—44no—
240C22×C4×C7C2×D414yes—
241C22×C4×C7C2×D414yes—
242C22×C4×C7C2×D414yes—
243C7×C4⋊C4—48no—
244C7×C22⋊C4—216no—
245C7×C22⋊C4—216no—
246C7×C22⋊C4—28no—
247C7×C22⋊C4—48no—
248C7×C22⋊C4—48no—
249C7×C22⋊C4—44no—
250C7×C22⋊C4—44no—
251C7×C22⋊C4—44no—
252C7×C22⋊C4—44no—
253C7×C22⋊C4—44no—
254C7×C22⋊C4—44no—
255C7×C22⋊C4—44no—
256C26C22×C711yescharacteristic
257C24×C4C22×C711yescharacteristic
258C24×C4C22×C711yescharacteristic
259C22×C4⋊C4C22×C712yescomplemented
260C22×C22⋊C4—24no—
261C22×C22⋊C4—28no—
262C22×C22⋊C4C22×C711yescharacteristic
263C22×C22⋊C4C22×C712yes—
264C22×C22⋊C4C22×C711yescharacteristic
265C22×C22⋊C4C22×C711yescharacteristic
266C22×C22⋊C4C22×C711yescharacteristic
267C22×C22⋊C4C22×C711yescharacteristic
268C22×C22⋊C4C22×C712yes—
269C22×C22⋊C4C22×C712yes—
270C22×C22⋊C4C22×C712yes—
271C22×C22⋊C4C22×C711yescharacteristic
272C22×C22⋊C4C22×C711yescharacteristic
273C22×C22⋊C4C22×C711yescharacteristic
274#397—28no—
275#385—24no—
276#379—24no—
277#379—24no—
278C2×#95C22×C712yescomplemented
279C2×#95C22×C712yescomplemented
280C2×#95C22×C712yescomplemented
281C2×#95C22×C712yescomplemented
282C2×#95C22×C712yescomplemented
283C2×#95C22×C712yescomplemented
284C2×#95C22×C712yescomplemented
285C23×C7—22no—
286C23×C7—22no—
287C23×C7—24no—
288C23×C7—24no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—24no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—24no—
295C23×C7—24no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—24no—
300C23×C7—24no—
301C23×C7—232no—
302C23×C7—22no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—24no—
311C23×C7—24no—
312C23×C7—24no—
313C23×C7—24no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—24no—
319C23×C7—24no—
320C23×C7—24no—
321C23×C7—24no—
322C23×C7—24no—
323C23×C7—24no—
324C23×C7—24no—
325C23×C7—24no—
326C23×C7—416no—
327C23×C7—416no—
328C23×C7—416no—
329C23×C7—416no—
330C23×C7—416no—
331C23×C7—432no—
332C23×C7—432no—
333C23×C7—432no—
334C23×C7—432no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—42no—
344C23×C7—42no—
345C23×C7—42no—
346C23×C7—42no—
347C23×C7—42no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—416no—
356C23×C7#12014yes—
357C23×C7#12114yes—
358C23×C7#12314yes—
359C23×C7#12314yes—
360C23×C7#12314yes—
361C23×C7#12314yes—
362C23×C7#12414yes—
363C23×C7#12614yes—
364C23×C7#12614yes—
365C23×C7C22×D411yescharacteristic
366C23×C7C22×D412yes—
367C23×C7C22×D411yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4112yes—
373C23×C7C2×#4111yescharacteristic
374C23×C7H(5,𝔽2)12yes—
375C23×C7H(5,𝔽2)12yes—
376C2×C4×C7—24no—
377C2×C4×C7—24no—
378C2×C4×C7—24no—
379C2×C4×C7—24no—
380C2×C4×C7—24no—
381C2×C4×C7—24no—
382C2×C4×C7—24no—
383C2×C4×C7—24no—
384C2×C4×C7—24no—
385C2×C4×C7—416no—
386C2×C4×C7—416no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—42no—
408C2×C4×C7—42no—
409C2×C4×C7—42no—
410C2×C4×C7—42no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—42no—
416C2×C4×C7—42no—
417C2×C4×C7—42no—
418C2×C4×C7—42no—
419C2×C4×C7—42no—
420C2×C4×C7—42no—
421C2×C4×C7—42no—
422C2×C4×C7—42no—
423C2×C4×C7—42no—
424C2×C4×C7—42no—
425C2×C4×C7—42no—
426C25—24no—
427C25—24no—
428C25—22no—
429C25—22no—
430C25—22no—
431C25—22no—
432C25—22no—
433C25—22no—
434C25—42no—
435C25—42no—
436C25C7×D414yes—
437C25C23×C711yescharacteristic
438C25C23×C711yescharacteristic
439C25C23×C711yescharacteristic
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4C23×C711yescharacteristic
451C23×C4C23×C711yescharacteristic
452C23×C4C23×C712yes—
453C23×C4C23×C711yescharacteristic
454C23×C4C23×C711yescharacteristic
455C23×C4C23×C712yes—
456C23×C4C23×C712yes—
457C23×C4C23×C712yes—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—42no—
461C2×C22⋊C4—232no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4C7×D418yes—
493C2×C22⋊C4C7×D414yes—
494#95—24no—
495#95—24no—
496#95—24no—
497#95—24no—
498#95—42no—
499#95—42no—
500#95—42no—
501C22×C7—24no—
502C22×C7—24no—
503C22×C7—24no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—28no—
507C22×C7—28no—
508C22×C7—28no—
509C22×C7—28no—
510C22×C7—24no—
511C22×C7—24no—
512C22×C7—24no—
513C22×C7—24no—
514C22×C7—24no—
515C22×C7—24no—
516C22×C7—24no—
517C22×C7—464no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—44no—
526C22×C7—44no—
527C22×C7—44no—
528C22×C7—44no—
529C22×C7—44no—
530C22×C7—44no—
531C22×C7—44no—
532C22×C7—44no—
533C22×C7—42no—
534C22×C7#39718yescomplemented
535C22×C7C2×#12011yescharacteristic
536C22×C7C2×#12111yescharacteristic
537C22×C7C2×#12311yescharacteristic
538C22×C7C2×#12311yescharacteristic
539C22×C7C2×#12311yescharacteristic
540C22×C7C2×#12311yescharacteristic
541C22×C7#52512yes—
542C22×C7#52512yes—
543C22×C7C2×#12411yescharacteristic
544C22×C7C2×#12611yescharacteristic
545C22×C7C2×#12611yescharacteristic
546C22×C7#53411yescharacteristic
547C22×C7#53411yescharacteristic
548C22×C7#53812yes—
549C22×C7#53812yes—
550C22×C7D4212yes—
551C22×C7#54612yes—
552C22×C7#54612yes—
553C22×C7#54612yes—
554C22×C7#54612yes—
555C22×C7#55112yes—
556C22×C7#55112yes—
557C22×C7#55112yes—
558C4×C7—44no—
559C4×C7—44no—
560C4×C7—44no—
561C4×C7—81no—
562C4×C7—81no—
563C4×C7—81no—
564C4×C7—81no—
565C4×C7—82no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—216no—
571C24—216no—
572C24—28no—
573C24—28no—
574C24—28no—
575C24—22no—
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C24—21no—
581C24—21no—
582C24—22no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—28no—
594C24—28no—
595C24—44no—
596C24—44no—
597C24—48no—
598C24—48no—
599C24—48no—
600C24—48no—
601C24—48no—
602C24—48no—
603C24—48no—
604C24—48no—
605C24—48no—
606C24—48no—
607C24—44no—
608C24—44no—
609C24—44no—
610C24—44no—
611C24C2×C7×D412yes—
612C24C2×C7×D414yes—
613C24C2×C7×D412yes—
614C24C2×C7×D412yes—
615C24C2×C7×D412yes—
616C24C7×#4114yes—
617C24C7×#4112yes—
618C24C7×#4112yes—
619C24C7×#4112yes—
620C24C7×#4112yes—
621C24C7×#4112yes—
622C24C24×C711yescharacteristic
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—48no—
671C22×C4—48no—
672C22×C4—48no—
673C22×C4—48no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4C2×C7×D414yes—
679C22×C4C2×C7×D414yes—
680C22×C4C2×C7×D414yes—
681C4⋊C4—48no—
682C22⋊C4—216no—
683C22⋊C4—216no—
684C22⋊C4—28no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C2×C7—28no—
695C2×C7—44no—
696C2×C7—44no—
697C2×C7C2×#39711yescharacteristic
698C2×C7#240511yescharacteristic
699C2×C7#241011yescharacteristic
700C2×C7#241211yescharacteristic
701C2×C7#241812yes—
702C2×C7#247212yes—
703C2×C7#248012yes—
704C2×C7#248012yes—
705C2×C7#248311yescharacteristic
706C2×C7#262211yescharacteristic
707C2×C7#284911yescharacteristic
708C23—22no—
709C23—22no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—232no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—416no—
750C23—416no—
751C23—416no—
752C23—416no—
753C23—432no—
754C23—432no—
755C23—432no—
756C23—432no—
757C23—416no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—416no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23C7×#12014yes—
780C23C7×#12114yes—
781C23C7×#12314yes—
782C23C7×#12314yes—
783C23C7×#12314yes—
784C23C7×#12314yes—
785C23C7×#12414yes—
786C23C7×#12614yes—
787C23C7×#12614yes—
788C23C22×C7×D411yescharacteristic
789C23C22×C7×D412yes—
790C23C22×C7×D411yescharacteristic
791C23C2×C7×#4111yescharacteristic
792C23C2×C7×#4111yescharacteristic
793C23C2×C7×#4111yescharacteristic
794C23C2×C7×#4111yescharacteristic
795C23C2×C7×#4112yes—
796C23C2×C7×#4111yescharacteristic
797C23C7×H(5,𝔽2)12yes—
798C23C7×H(5,𝔽2)12yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—416no—
809C2×C4—416no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C7#1472711yescharacteristic, direct product factor, Sylow
850C22—24no—
851C22—24no—
852C22—24no—
853C22—28no—
854C22—28no—
855C22—28no—
856C22—28no—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—464no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22C7×#39718yescomplemented
884C22C2×C7×#12011yescharacteristic
885C22C2×C7×#12111yescharacteristic
886C22C2×C7×#12311yescharacteristic
887C22C2×C7×#12311yescharacteristic
888C22C2×C7×#12311yescharacteristic
889C22C2×C7×#12311yescharacteristic
890C22C7×#52512yes—
891C22C7×#52512yes—
892C22C2×C7×#12411yescharacteristic
893C22C2×C7×#12611yescharacteristic
894C22C2×C7×#12611yescharacteristic
895C22C7×#53411yescharacteristic
896C22C7×#53411yescharacteristic
897C22C7×#53812yes—
898C22C7×#53812yes—
899C22C7×D4212yes—
900C22C7×#54612yes—
901C22C7×#54612yes—
902C22C7×#54612yes—
903C22C7×#54612yes—
904C22C7×#55112yes—
905C22C7×#55112yes—
906C22C7×#55112yes—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—81no—
911C4—81no—
912C4—82no—
913C4—81no—
914C4—81no—
915C2—28no—
916C2—44no—
917C2—44no—
918C2C2×C7×#39711yescharacteristic
919C2C7×#240511yescharacteristic
920C2C7×#241011yescharacteristic
921C2C7×#241211yescharacteristic
922C2C7×#241812yes—
923C2C7×#247212yes—
924C2C7×#248012yes—
925C2C7×#248012yes—
926C2C7×#248311yescharacteristic
927C2C7×#262211yescharacteristic
928C2C7×#284911yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC26×C7C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#397C2semidirect
3. C2×C7×#385C2semidirect
6. C7×#1440C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×C22⋊#95C2semidirect
10. C7×C22⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
15. C22×C7×C4⋊C4C22semidirect
34. C2×C7×#95C22semidirect
35. C2×C7×#95C22semidirect
36. C2×C7×#95C22semidirect
37. C2×C7×#95C22semidirect
38. C2×C7×#95C22semidirect
39. C2×C7×#95C22semidirect
40. C2×C7×#95C22semidirect
41. #14727C7direct (N × H)
118. C2×#397C2×C7semidirect
119. C2×#385C2×C7semidirect
122. #1440C2×C7semidirect
123. #1440C2×C7semidirect
124. #1439C2×C7semidirect
125. C22⋊#95C2×C7semidirect
126. C22⋊#95C2×C7semidirect
127. C22⋊#95C2×C7semidirect
259. C22×C4⋊C4C22×C7semidirect
278. C2×#95C22×C7semidirect
279. C2×#95C22×C7semidirect
280. C2×#95C22×C7semidirect
281. C2×#95C22×C7semidirect
282. C2×#95C22×C7semidirect
283. C2×#95C22×C7semidirect
284. C2×#95C22×C7semidirect
534. C22×C7#397semidirect
849. C7#14727direct (N × H)
883. C22C7×#397semidirect

Maximal subgroups

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

subgroupindex
C23×C7×C22⋊C42
C2×C7×#3972
C2×C7×#3852
C2×C7×#3792
C7×#14402
C7×#14392
C7×C22⋊#952
#147277