Finite Group Databasebeta

← C7×#23920 #13201136

Subgroups — C7×#23920 #13201136

Order 1792.

2272 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#525C211yesmaximal, characteristic, complemented
2C22×C7×#121C211yesmaximal, characteristic, complemented
3C2×C7×#449C212yesmaximal, complemented
4C2×C7×#450C211yesmaximal, characteristic, complemented
5C2×C7×#447C211yesmaximal, characteristic, complemented
6C7×#2000C212yesmaximal, complemented
7C7×#1999C212yesmaximal, complemented
8C7×#1875C212yesmaximal, complemented
9C7×#1874C211yesmaximal, characteristic, complemented
10C7×#1872C211yesmaximal, characteristic, complemented
11C7×#1779C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic, complemented
13C23×C7×D4—21no—
14C23×C7×D4C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C22×C7×SD16C2212yescomplemented
17C22×C7×D8C2212yescomplemented
18C7×#525—24no—
19C7×#525—24no—
20C2×C7×#123—21no—
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic, complemented
23C2×C7×#121—21no—
24C2×C7×#121—21no—
25C2×C7×#121—28no—
26C2×C7×#121C2212yes—
27C2×C7×#121C2211yescharacteristic
28C2×C7×#121C2212yes—
29C2×C7×#121C2211yescharacteristic, complemented
30C2×C7×#120—21no—
31C2×C4×C7×D4—21no—
32C2×C4×C7×D4—21no—
33C2×C7×#117C2211yescharacteristic, complemented
34C22×C7×C4⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4—21no—
36C7×#450—24no—
37C7×#449—28no—
38C7×#447—24no—
39C2×C7×#103C2212yescomplemented
40C2×C7×#102C2212yescomplemented
41C2×C7×#102C2212yescomplemented
42C2×C7×#102C2212yescomplemented
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×C22⋊C8C2211yescharacteristic
45C2×C7×C22⋊C8C2212yescomplemented
46C2×C7×C22⋊C8C2212yescomplemented
47C7×#340C2212yescomplemented
48C7×#340C2212yescomplemented
49#23920C711yesmaximal, characteristic, direct product factor, Sylow
50C25×C7—21no—
51C25×C7D411yescharacteristic
52C2×C7×#41—22no—
53C2×C7×#41—22no—
54C2×C7×#41—24no—
55C2×C7×#41—42no—
56C22×C7×Q8C2311yescharacteristic
57C22×C7×D4—28no—
58C22×C7×D4—22no—
59C22×C7×D4—22no—
60C22×C7×D4—21no—
61C22×C7×D4—21no—
62C22×C7×D4—21no—
63C22×C7×D4—24no—
64C22×C7×D4—21no—
65C22×C7×D4—22no—
66C22×C7×D4—22no—
67C22×C7×D4—42no—
68C22×C7×D4—44no—
69C22×C7×D4—44no—
70C22×C7×D4C2312yes—
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7—24no—
75C23×C4×C7—22no—
76C23×C4×C7—22no—
77C23×C4×C7—42no—
78C23×C4×C7D411yescharacteristic
79C23×C4×C7D411yescharacteristic
80C23×C4×C7D411yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C2×C7×SD16—24no—
85C2×C7×SD16—24no—
86C2×C7×SD16—42no—
87C2×C7×D8—24no—
88C2×C7×D8—24no—
89C2×C7×D8—42no—
90C22×C7×C8C2312yes—
91C22×C7×C8C2312yes—
92C7×#123—28no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8D414yescomplemented
97C7×#121—28no—
98C7×#121—28no—
99C7×#121—24no—
100C7×#121—22no—
101C7×#121—24no—
102C7×#121—22no—
103C7×#121—24no—
104C7×#121—22no—
105C7×#121D418yescomplemented
106C7×#121D414yescomplemented
107C7×#120—28no—
108C4×C7×D4—28no—
109C4×C7×D4—28no—
110C7×#117—22no—
111C7×#117—22no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—24no—
116C2×C7×C4⋊C4C2312yes—
117C2×C7×C4⋊C4C2311yescharacteristic
118C2×C7×C4⋊C4C2311yescharacteristic
119C2×C7×C22⋊C4—28no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—22no—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—21no—
126C2×C7×C22⋊C4—21no—
127C2×C42×C7—21no—
128C7×#103—24no—
129C7×#102—24no—
130C7×#102—24no—
131C7×#102—24no—
132C7×C22⋊C8—22no—
133C7×C22⋊C8—22no—
134C7×C22⋊C8—24no—
135C7×C22⋊C8—42no—
136C2×#525C2×C711yescharacteristic, complemented
137C22×#121C2×C711yescharacteristic, complemented
138C2×#449C2×C712yescomplemented
139C2×#450C2×C711yescharacteristic, complemented
140C2×#447C2×C711yescharacteristic, complemented
141#2000C2×C712yescomplemented
142#1999C2×C712yescomplemented
143#1875C2×C712yescomplemented
144#1874C2×C711yescharacteristic, complemented
145#1872C2×C711yescharacteristic, complemented
146#1779C2×C711yescharacteristic, complemented
147C24×C7—22no—
148C24×C7—22no—
149C24×C7—22no—
150C24×C7—24no—
151C24×C7—22no—
152C24×C7—22no—
153C24×C7—21no—
154C24×C7—22no—
155C24×C7—41no—
156C24×C7—41no—
157C24×C7—42no—
158C24×C7—42no—
159C24×C7—42no—
160C24×C7—42no—
161C24×C7—42no—
162C24×C7—42no—
163C24×C7C2×D411yescharacteristic
164C24×C7C2×D411yescharacteristic
165C24×C7C2×D411yescharacteristic
166C7×#41—48no—
167C7×#41—48no—
168C2×C7×Q8—21no—
169C2×C7×Q8—22no—
170C2×C7×Q8—22no—
171C2×C7×Q8C2×D412yescomplemented
172C2×C7×D4—24no—
173C2×C7×D4—24no—
174C2×C7×D4—24no—
175C2×C7×D4—28no—
176C2×C7×D4—24no—
177C2×C7×D4—28no—
178C2×C7×D4—22no—
179C2×C7×D4—22no—
180C2×C7×D4—22no—
181C2×C7×D4—22no—
182C2×C7×D4—21no—
183C2×C7×D4—22no—
184C2×C7×D4—22no—
185C2×C7×D4—22no—
186C2×C7×D4—48no—
187C2×C7×D4—48no—
188C2×C7×D4—42no—
189C2×C7×D4—42no—
190C2×C7×D4—432no—
191C2×C7×D4—44no—
192C2×C7×D4—44no—
193C2×C7×D4—44no—
194C2×C7×D4—42no—
195C2×C7×D4—42no—
196C2×C7×D4—42no—
197C2×C7×D4—42no—
198C2×C7×D4—42no—
199C2×C7×D4—44no—
200C2×C7×D4—42no—
201C2×C7×D4C2×D414yes—
202C2×C7×D4C2×D412yescomplemented
203C22×C4×C7—22no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—24no—
209C22×C4×C7—24no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—22no—
224C22×C4×C7—41no—
225C22×C4×C7—41no—
226C22×C4×C7—41no—
227C22×C4×C7—48no—
228C22×C4×C7—48no—
229C22×C4×C7—42no—
230C22×C4×C7—42no—
231C22×C4×C7—42no—
232C22×C4×C7—42no—
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D414yes—
237C22×C4×C7C2×D412yes—
238C22×C4×C7C2×D412yes—
239C22×C4×C7C2411yescharacteristic
240C7×SD16—48no—
241C7×D8—48no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8—22no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—22no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4C2×D414yes—
255C7×C4⋊C4C2×D412yescomplemented
256C7×C4⋊C4C2×D412yescomplemented
257C7×C22⋊C4—28no—
258C7×C22⋊C4—24no—
259C7×C22⋊C4—24no—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—28no—
263C7×C22⋊C4—24no—
264C42×C7—24no—
265C22×#41C22×C711yescharacteristic, complemented
266C23×D4—21no—
267C23×D4C22×C711yescharacteristic
268C24×C4C22×C711yescharacteristic
269C22×SD16C22×C712yescomplemented
270C22×D8C22×C712yescomplemented
271#525—24no—
272#525—24no—
273C2×#123—21no—
274C2×C22⋊Q8C22×C711yescharacteristic
275C2×C22⋊Q8C22×C711yescharacteristic, complemented
276C2×#121—21no—
277C2×#121—21no—
278C2×#121—28no—
279C2×#121C22×C712yes—
280C2×#121C22×C711yescharacteristic
281C2×#121C22×C712yes—
282C2×#121C22×C711yescharacteristic, complemented
283C2×#120—21no—
284C2×C4×D4—21no—
285C2×C4×D4—21no—
286C2×#117C22×C711yescharacteristic, complemented
287C22×C4⋊C4C22×C711yescharacteristic
288C22×C22⋊C4—21no—
289#450—24no—
290#449—28no—
291#447—24no—
292C2×#103C22×C712yescomplemented
293C2×#102C22×C712yescomplemented
294C2×#102C22×C712yescomplemented
295C2×#102C22×C712yescomplemented
296C2×C22⋊C8C22×C711yescharacteristic
297C2×C22⋊C8C22×C711yescharacteristic
298C2×C22⋊C8C22×C712yescomplemented
299C2×C22⋊C8C22×C712yescomplemented
300#340C22×C712yescomplemented
301#340C22×C712yescomplemented
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—28no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7—21no—
317C23×C7—21no—
318C23×C7—21no—
319C23×C7—22no—
320C23×C7—24no—
321C23×C7—44no—
322C23×C7—44no—
323C23×C7—44no—
324C23×C7—44no—
325C23×C7—44no—
326C23×C7—48no—
327C23×C7—48no—
328C23×C7—48no—
329C23×C7—44no—
330C23×C7—41no—
331C23×C7—42no—
332C23×C7—41no—
333C23×C7—42no—
334C23×C7—41no—
335C23×C7—42no—
336C23×C7—42no—
337C23×C7—42no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—42no—
342C23×C7—84no—
343C23×C7—84no—
344C23×C7—84no—
345C23×C7—84no—
346C23×C7#12012yes—
347C23×C7#12012yes—
348C23×C7#13512yes—
349C23×C7AGL(1,ℤ/8)12yes—
350C23×C7AGL(1,ℤ/8)12yes—
351C23×C7C22×D411yescharacteristic
352C7×Q8—24no—
353C7×Q8—42no—
354C7×D4—24no—
355C7×D4—24no—
356C7×D4—24no—
357C7×D4—48no—
358C7×D4—48no—
359C7×D4—416no—
360C7×D4—416no—
361C7×D4—48no—
362C7×D4—48no—
363C7×D4—42no—
364C7×D4—42no—
365C7×D4—42no—
366C2×C4×C7—21no—
367C2×C4×C7—21no—
368C2×C4×C7—21no—
369C2×C4×C7—21no—
370C2×C4×C7—24no—
371C2×C4×C7—24no—
372C2×C4×C7—24no—
373C2×C4×C7—24no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—21no—
377C2×C4×C7—21no—
378C2×C4×C7—22no—
379C2×C4×C7—24no—
380C2×C4×C7—21no—
381C2×C4×C7—44no—
382C2×C4×C7—44no—
383C2×C4×C7—44no—
384C2×C4×C7—48no—
385C2×C4×C7—48no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7#12012yes—
397C2×C4×C7#12012yes—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D411yescharacteristic
400C2×C4×C7C22×D411yescharacteristic
401C2×C4×C7H(5,𝔽2)12yes—
402C7×C8—42no—
403C7×C8—42no—
404C25—21no—
405C25C7×D411yescharacteristic
406C2×#41—22no—
407C2×#41—22no—
408C2×#41—24no—
409C2×#41—42no—
410C22×Q8C23×C711yescharacteristic
411C22×D4—28no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—24no—
418C22×D4—21no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—42no—
422C22×D4—44no—
423C22×D4—44no—
424C22×D4C23×C712yes—
425C22×D4C23×C711yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—24no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—42no—
432C23×C4C7×D411yescharacteristic
433C23×C4C7×D411yescharacteristic
434C23×C4C7×D411yescharacteristic
435C23×C4C23×C711yescharacteristic
436C23×C4C23×C711yescharacteristic
437C23×C4C23×C711yescharacteristic
438C2×SD16—24no—
439C2×SD16—24no—
440C2×SD16—42no—
441C2×D8—24no—
442C2×D8—24no—
443C2×D8—42no—
444C22×C8C23×C712yes—
445C22×C8C23×C712yes—
446#123—28no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8C7×D414yescomplemented
451#121—28no—
452#121—28no—
453#121—24no—
454#121—22no—
455#121—24no—
456#121—22no—
457#121—24no—
458#121—22no—
459#121C7×D418yescomplemented
460#121C7×D414yescomplemented
461#120—28no—
462C4×D4—28no—
463C4×D4—28no—
464#117—22no—
465#117—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4C23×C712yes—
471C2×C4⋊C4C23×C711yescharacteristic
472C2×C4⋊C4C23×C711yescharacteristic
473C2×C22⋊C4—28no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C42—21no—
482#103—24no—
483#102—24no—
484#102—24no—
485#102—24no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—24no—
489C22⋊C8—42no—
490C22×C7—22no—
491C22×C7—22no—
492C22×C7—22no—
493C22×C7—22no—
494C22×C7—22no—
495C22×C7—22no—
496C22×C7—22no—
497C22×C7—22no—
498C22×C7—22no—
499C22×C7—22no—
500C22×C7—22no—
501C22×C7—22no—
502C22×C7—416no—
503C22×C7—41no—
504C22×C7—41no—
505C22×C7—41no—
506C22×C7—41no—
507C22×C7—41no—
508C22×C7—41no—
509C22×C7—41no—
510C22×C7—41no—
511C22×C7—42no—
512C22×C7—44no—
513C22×C7—42no—
514C22×C7—44no—
515C22×C7—44no—
516C22×C7—42no—
517C22×C7—816no—
518C22×C7—81no—
519C22×C7—82no—
520C22×C7—81no—
521C22×C7—82no—
522C22×C7—82no—
523C22×C7—81no—
524C22×C7—81no—
525C22×C7—82no—
526C22×C7#44914yescomplemented
527C22×C7C2×#12011yescharacteristic
528C22×C7C2×#12011yescharacteristic
529C22×C7#53411yescharacteristic
530C22×C7C2×#13511yescharacteristic
531C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
532C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
533C22×C7#57511yescharacteristic
534C4×C7—22no—
535C4×C7—22no—
536C4×C7—41no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—44no—
540C4×C7—42no—
541C4×C7D4212yes—
542C4×C7D4212yes—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—24no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—22no—
551C24—41no—
552C24—41no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24C2×C7×D411yescharacteristic
560C24C2×C7×D411yescharacteristic
561C24C2×C7×D411yescharacteristic
562#41—48no—
563#41—48no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8C2×C7×D412yescomplemented
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—28no—
572C2×D4—24no—
573C2×D4—28no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—48no—
583C2×D4—48no—
584C2×D4—42no—
585C2×D4—432no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—44no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—44no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4C2×C7×D414yes—
598C2×D4C2×C7×D412yescomplemented
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4C2×C7×D411yescharacteristic
630C22×C4C2×C7×D411yescharacteristic
631C22×C4C2×C7×D411yescharacteristic
632C22×C4C2×C7×D414yes—
633C22×C4C2×C7×D412yes—
634C22×C4C2×C7×D412yes—
635C22×C4C24×C711yescharacteristic
636SD16—48no—
637D8—48no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C2×C7×D414yes—
651C4⋊C4C2×C7×D412yescomplemented
652C4⋊C4C2×C7×D412yescomplemented
653C22⋊C4—28no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—28no—
659C22⋊C4—24no—
660C42—24no—
661C2×C7—24no—
662C2×C7—42no—
663C2×C7—42no—
664C2×C7—82no—
665C2×C7—84no—
666C2×C7#240311yescharacteristic
667C2×C7C2×#44911yescharacteristic
668C2×C7#300211yescharacteristic
669C2×C7#300311yescharacteristic
670C2×C7#300611yescharacteristic
671C2×C7#318811yescharacteristic
672C2×C7#319411yescharacteristic
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—28no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—22no—
691C23—24no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—48no—
698C23—48no—
699C23—48no—
700C23—44no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—84no—
714C23—84no—
715C23—84no—
716C23—84no—
717C23C7×#12012yes—
718C23C7×#12012yes—
719C23C7×#13512yes—
720C23C7×AGL(1,ℤ/8)12yes—
721C23C7×AGL(1,ℤ/8)12yes—
722C23C22×C7×D411yescharacteristic
723Q8—24no—
724Q8—42no—
725D4—24no—
726D4—24no—
727D4—24no—
728D4—48no—
729D4—48no—
730D4—416no—
731D4—416no—
732D4—48no—
733D4—48no—
734D4—42no—
735D4—42no—
736D4—42no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—21no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—48no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4C7×#12012yes—
768C2×C4C7×#12012yes—
769C2×C4C22×C7×D412yes—
770C2×C4C22×C7×D411yescharacteristic
771C2×C4C22×C7×D411yescharacteristic
772C2×C4C7×H(5,𝔽2)12yes—
773C8—42no—
774C8—42no—
775C7#2392011yescharacteristic, direct product factor, Sylow
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—416no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—816no—
804C22—82no—
805C22—81no—
806C22—82no—
807C22—81no—
808C22—82no—
809C22—81no—
810C22—81no—
811C22—82no—
812C22C7×#44914yescomplemented
813C22C2×C7×#12011yescharacteristic
814C22C2×C7×#12011yescharacteristic
815C22C7×#53411yescharacteristic
816C22C2×C7×#13511yescharacteristic
817C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
818C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
819C22C7×#57511yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4C7×D4212yes—
828C4C7×D4212yes—
829C2—24no—
830C2—42no—
831C2—42no—
832C2—84no—
833C2—82no—
834C2C7×#240311yescharacteristic
835C2C2×C7×#44911yescharacteristic
836C2C7×#300211yescharacteristic
837C2C7×#300311yescharacteristic
838C2C7×#300611yescharacteristic
839C2C7×#318811yescharacteristic
840C2C7×#319411yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#525C2semidirect
2. C22×C7×#121C2semidirect
3. C2×C7×#449C2semidirect
4. C2×C7×#450C2semidirect
5. C2×C7×#447C2semidirect
6. C7×#2000C2semidirect
7. C7×#1999C2semidirect
8. C7×#1875C2semidirect
9. C7×#1874C2semidirect
10. C7×#1872C2semidirect
11. C7×#1779C2semidirect
12. C22×C7×#41C22semidirect
16. C22×C7×SD16C22semidirect
17. C22×C7×D8C22semidirect
22. C2×C7×C22⋊Q8C22semidirect
29. C2×C7×#121C22semidirect
33. C2×C7×#117C22semidirect
39. C2×C7×#103C22semidirect
40. C2×C7×#102C22semidirect
41. C2×C7×#102C22semidirect
42. C2×C7×#102C22semidirect
45. C2×C7×C22⋊C8C22semidirect
46. C2×C7×C22⋊C8C22semidirect
47. C7×#340C22semidirect
48. C7×#340C22semidirect
49. #23920C7direct (N × H)
96. C7×C22⋊Q8D4semidirect
105. C7×#121D4semidirect
106. C7×#121D4semidirect
136. C2×#525C2×C7semidirect
137. C22×#121C2×C7semidirect
138. C2×#449C2×C7semidirect
139. C2×#450C2×C7semidirect
140. C2×#447C2×C7semidirect
141. #2000C2×C7semidirect
142. #1999C2×C7semidirect
143. #1875C2×C7semidirect
144. #1874C2×C7semidirect
145. #1872C2×C7semidirect
146. #1779C2×C7semidirect
171. C2×C7×Q8C2×D4semidirect
202. C2×C7×D4C2×D4semidirect
255. C7×C4⋊C4C2×D4semidirect
256. C7×C4⋊C4C2×D4semidirect
265. C22×#41C22×C7semidirect
269. C22×SD16C22×C7semidirect
270. C22×D8C22×C7semidirect
275. C2×C22⋊Q8C22×C7semidirect
282. C2×#121C22×C7semidirect
286. C2×#117C22×C7semidirect
292. C2×#103C22×C7semidirect
293. C2×#102C22×C7semidirect
294. C2×#102C22×C7semidirect
295. C2×#102C22×C7semidirect
298. C2×C22⋊C8C22×C7semidirect
299. C2×C22⋊C8C22×C7semidirect
300. #340C22×C7semidirect
301. #340C22×C7semidirect
450. C22⋊Q8C7×D4semidirect
459. #121C7×D4semidirect
460. #121C7×D4semidirect
526. C22×C7#449semidirect
567. C2×Q8C2×C7×D4semidirect
598. C2×D4C2×C7×D4semidirect
651. C4⋊C4C2×C7×D4semidirect
652. C4⋊C4C2×C7×D4semidirect
775. C7#23920direct (N × H)
812. C22C7×#449semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5252
C22×C7×#1212
C2×C7×#4492
C2×C7×#4502
C2×C7×#4472
C7×#20002
C7×#19992
C7×#18752
C7×#18742
C7×#18722
C7×#17792
#239207