Finite Group Databasebeta

← C7×#23482 #13200698

Subgroups — C7×#23482 #13200698

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#525C211yesmaximal, characteristic
2C2×C7×#428C211yesmaximal, characteristic, complemented
3C2×C7×#417C211yesmaximal, characteristic, complemented
4C2×C7×#417C211yesmaximal, characteristic, complemented
5C2×C7×#407C211yesmaximal, characteristic, complemented
6C2×C7×#380C211yesmaximal, characteristic, complemented
7C7×#2036C212yesmaximal, complemented
8C7×#2035C212yesmaximal, complemented
9C7×#2034C212yesmaximal, complemented
10C7×#2033C212yesmaximal, complemented
11C7×#1736C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C22×C7×M16C2211yescharacteristic
15C22×C7×M16C2211yescharacteristic
16C7×#525—24no—
17C7×#525—24no—
18C2×C7×#123—21no—
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23C2×C7×#120—21no—
24C2×C4×C7×D4—21no—
25C2×C4×C7×D4—21no—
26C2×C7×#117C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4—21no—
30C7×#428—24no—
31C2×C7×#107C2212yescomplemented
32C2×C7×#106C2212yescomplemented
33C7×#417—24no—
34C7×#417—24no—
35C2×C7×#103C2212yescomplemented
36C2×C7×#103C2212yescomplemented
37C2×C7×#102C2212yescomplemented
38C2×C7×#102C2212yescomplemented
39C7×#407—24no—
40C2×C7×C22⋊C8C2212yes—
41C2×C7×C22⋊C8C2212yes—
42C7×#380—21no—
43C7×#380—21no—
44C7×#380C2212yes—
45C7×#380C2212yes—
46C2×C7×#95—21no—
47C7×#340C2212yescomplemented
48C7×#340C2212yescomplemented
49#23482C711yesmaximal, characteristic, direct product factor, Sylow
50C25×C7D411yescharacteristic
51C2×C7×#41—22no—
52C2×C7×#41—22no—
53C2×C7×#41—22no—
54C2×C7×#41—22no—
55C2×C7×#41—22no—
56C2×C7×#41D414yes—
57C22×C7×Q8C2311yescharacteristic
58C22×C7×D4—21no—
59C22×C7×D4—21no—
60C22×C7×D4—21no—
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—21no—
70C23×C4×C7—21no—
71C23×C4×C7D411yescharacteristic
72C23×C4×C7D411yescharacteristic
73C23×C4×C7D411yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C2×C7×M16—22no—
78C2×C7×M16—22no—
79C2×C7×M16—22no—
80C2×C7×M16—22no—
81C2×C7×M16—22no—
82C2×C7×M16D414yescomplemented
83C22×C7×C8C2312yes—
84C22×C7×C8C2312yes—
85C7×#123—28no—
86C7×C22⋊Q8—22no—
87C7×C22⋊Q8—22no—
88C7×C22⋊Q8—22no—
89C7×C22⋊Q8—22no—
90C7×#121—22no—
91C7×#121—22no—
92C7×#121—22no—
93C7×#121—22no—
94C7×#120—28no—
95C4×C7×D4—28no—
96C4×C7×D4—28no—
97C7×#117—22no—
98C7×#117D414yes—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—22no—
103C2×C7×C4⋊C4—22no—
104C2×C7×C4⋊C4—22no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4C2312yes—
108C2×C7×C4⋊C4C2312yes—
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4—44no—
119C2×C42×C7—21no—
120C7×#107—24no—
121C7×#106—24no—
122C7×#103—24no—
123C7×#103—24no—
124C7×#102—24no—
125C7×#102—24no—
126C7×C22⋊C8—24no—
127C7×C22⋊C8—24no—
128C7×#95—22no—
129C7×#95—22no—
130C2×#525C2×C711yescharacteristic
131C2×#428C2×C711yescharacteristic, complemented
132C2×#417C2×C711yescharacteristic, complemented
133C2×#417C2×C711yescharacteristic, complemented
134C2×#407C2×C711yescharacteristic, complemented
135C2×#380C2×C711yescharacteristic, complemented
136#2036C2×C712yescomplemented
137#2035C2×C712yescomplemented
138#2034C2×C712yescomplemented
139#2033C2×C712yescomplemented
140#1736C2×C711yescharacteristic, complemented
141C24×C7—22no—
142C24×C7—22no—
143C24×C7—22no—
144C24×C7—22no—
145C24×C7—22no—
146C24×C7—21no—
147C24×C7—41no—
148C24×C7—41no—
149C24×C7C2×D411yescharacteristic
150C24×C7C2×D411yescharacteristic
151C24×C7C2×D411yescharacteristic
152C7×#41—28no—
153C7×#41—28no—
154C7×#41—44no—
155C7×#41—44no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8C2×D412yes—
162C2×C7×D4—24no—
163C2×C7×D4—24no—
164C2×C7×D4—24no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4—42no—
171C2×C7×D4—42no—
172C2×C7×D4—42no—
173C2×C7×D4—42no—
174C2×C7×D4—42no—
175C2×C7×D4—42no—
176C2×C7×D4C2×D412yes—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—24no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—44no—
205C22×C4×C7—44no—
206C22×C4×C7—42no—
207C22×C4×C7—44no—
208C22×C4×C7—42no—
209C22×C4×C7—44no—
210C22×C4×C7—42no—
211C22×C4×C7—42no—
212C22×C4×C7—42no—
213C22×C4×C7—42no—
214C22×C4×C7—42no—
215C22×C4×C7—42no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7#4112yes—
223C22×C4×C7#4112yes—
224C22×C4×C7#4112yes—
225C22×C4×C7C2411yescharacteristic
226C7×M16—28no—
227C7×M16—44no—
228C2×C7×C8—22no—
229C2×C7×C8—22no—
230C2×C7×C8—22no—
231C2×C7×C8—22no—
232C2×C7×C8—22no—
233C2×C7×C8C2×D414yes—
234C7×C4⋊C4—24no—
235C7×C4⋊C4—24no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—22no—
239C7×C4⋊C4—22no—
240C7×C4⋊C4—22no—
241C7×C4⋊C4—22no—
242C7×C4⋊C4—42no—
243C7×C4⋊C4—42no—
244C7×C4⋊C4C2×D412yes—
245C7×C4⋊C4C2×D412yes—
246C7×C22⋊C4—24no—
247C7×C22⋊C4—24no—
248C7×C22⋊C4—24no—
249C7×C22⋊C4—24no—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—44no—
252C7×C22⋊C4—44no—
253C42×C7—24no—
254C22×#41C22×C711yescharacteristic
255C24×C4C22×C711yescharacteristic
256C22×M16C22×C711yescharacteristic
257C22×M16C22×C711yescharacteristic
258#525—24no—
259#525—24no—
260C2×#123—21no—
261C2×C22⋊Q8C22×C711yescharacteristic
262C2×C22⋊Q8C22×C711yescharacteristic
263C2×#121C22×C711yescharacteristic
264C2×#121C22×C711yescharacteristic
265C2×#120—21no—
266C2×C4×D4—21no—
267C2×C4×D4—21no—
268C2×#117C22×C711yescharacteristic
269C22×C4⋊C4C22×C711yescharacteristic
270C22×C4⋊C4C22×C711yescharacteristic
271C22×C22⋊C4—21no—
272#428—24no—
273C2×#107C22×C712yescomplemented
274C2×#106C22×C712yescomplemented
275#417—24no—
276#417—24no—
277C2×#103C22×C712yescomplemented
278C2×#103C22×C712yescomplemented
279C2×#102C22×C712yescomplemented
280C2×#102C22×C712yescomplemented
281#407—24no—
282C2×C22⋊C8C22×C712yes—
283C2×C22⋊C8C22×C712yes—
284#380—21no—
285#380—21no—
286#380C22×C712yes—
287#380C22×C712yes—
288C2×#95—21no—
289#340C22×C712yescomplemented
290#340C22×C712yescomplemented
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—28no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—22no—
309C23×C7—44no—
310C23×C7—44no—
311C23×C7—44no—
312C23×C7—44no—
313C23×C7—44no—
314C23×C7—44no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7#12012yes—
322C23×C7#12112yes—
323C23×C7#12312yes—
324C23×C7AGL(1,ℤ/8)12yes—
325C23×C7#13712yes—
326C23×C7C22×D411yescharacteristic
327C7×Q8—22no—
328C7×Q8—22no—
329C7×Q8—41no—
330C7×Q8—41no—
331C7×D4—22no—
332C7×D4—22no—
333C7×D4—48no—
334C7×D4—48no—
335C7×D4—48no—
336C7×D4—41no—
337C7×D4—41no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—22no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—44no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—44no—
363C2×C4×C7—44no—
364C2×C4×C7—48no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—84no—
372C2×C4×C7—84no—
373C2×C4×C7#12012yes—
374C2×C4×C7#12114yes—
375C2×C4×C7#12114yes—
376C2×C4×C7#12112yes—
377C2×C4×C7#12314yes—
378C2×C4×C7#12312yes—
379C2×C4×C7#12414yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C2×#4111yescharacteristic
384C2×C4×C7C2×#4111yescharacteristic
385C2×C4×C7C2×#4111yescharacteristic
386C7×C8—24no—
387C7×C8—42no—
388C25C7×D411yescharacteristic
389C2×#41—22no—
390C2×#41—22no—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—22no—
394C2×#41C7×D414yes—
395C22×Q8C23×C711yescharacteristic
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4C23×C711yescharacteristic
400C23×C4—21no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4C7×D411yescharacteristic
410C23×C4C7×D411yescharacteristic
411C23×C4C7×D411yescharacteristic
412C23×C4C23×C711yescharacteristic
413C23×C4C23×C711yescharacteristic
414C23×C4C23×C711yescharacteristic
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—22no—
418C2×M16—22no—
419C2×M16—22no—
420C2×M16C7×D414yescomplemented
421C22×C8C23×C712yes—
422C22×C8C23×C712yes—
423#123—28no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428#121—22no—
429#121—22no—
430#121—22no—
431#121—22no—
432#120—28no—
433C4×D4—28no—
434C4×D4—28no—
435#117—22no—
436#117C7×D414yes—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C712yes—
446C2×C4⋊C4C23×C712yes—
447C2×C4⋊C4C23×C711yescharacteristic
448C2×C4⋊C4C23×C711yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—44no—
457C2×C42—21no—
458#107—24no—
459#106—24no—
460#103—24no—
461#103—24no—
462#102—24no—
463#102—24no—
464C22⋊C8—24no—
465C22⋊C8—24no—
466#95—22no—
467#95—22no—
468C22×C7—22no—
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—22no—
477C22×C7—22no—
478C22×C7—22no—
479C22×C7—22no—
480C22×C7—416no—
481C22×C7—41no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—41no—
487C22×C7—41no—
488C22×C7—41no—
489C22×C7—42no—
490C22×C7—42no—
491C22×C7—42no—
492C22×C7—81no—
493C22×C7—81no—
494C22×C7—81no—
495C22×C7—81no—
496C22×C7#39414yes—
497C22×C7C2×#12011yescharacteristic
498C22×C7C2×#12111yescharacteristic
499C22×C7C2×#12311yescharacteristic
500C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
501C22×C7C2×#13711yescharacteristic
502C22×C7#57511yescharacteristic
503C22×C7#57511yescharacteristic
504C4×C7—41no—
505C4×C7—41no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—42no—
509C4×C7—82no—
510C4×C7—82no—
511C4×C7#39414yes—
512C4×C7C2×#12111yescharacteristic
513C4×C7C2×#12111yescharacteristic
514C4×C7C2×#12311yescharacteristic
515C4×C7C2×#12411yescharacteristic
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—41no—
523C24—41no—
524C24C2×C7×D411yescharacteristic
525C24C2×C7×D411yescharacteristic
526C24C2×C7×D411yescharacteristic
527#41—28no—
528#41—28no—
529#41—44no—
530#41—44no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8C2×C7×D412yes—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4C2×C7×D412yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4C2×C7×D411yescharacteristic
592C22×C4C2×C7×D411yescharacteristic
593C22×C4C2×C7×D411yescharacteristic
594C22×C4C2×C7×D412yes—
595C22×C4C2×C7×D412yes—
596C22×C4C2×C7×D412yes—
597C22×C4C7×#4112yes—
598C22×C4C7×#4112yes—
599C22×C4C7×#4112yes—
600C22×C4C24×C711yescharacteristic
601M16—28no—
602M16—44no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8C2×C7×D414yes—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4C2×C7×D412yes—
620C4⋊C4C2×C7×D412yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C42—24no—
629C2×C7—24no—
630C2×C7—42no—
631C2×C7—42no—
632C2×C7—82no—
633C2×C7C2×#39411yescharacteristic
634C2×C7#300611yescharacteristic
635C2×C7#300711yescharacteristic
636C2×C7#305511yescharacteristic
637C2×C7#305611yescharacteristic
638C2×C7#309211yescharacteristic
639C2×C7#309311yescharacteristic
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—28no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23C7×#12012yes—
671C23C7×#12112yes—
672C23C7×#12312yes—
673C23C7×AGL(1,ℤ/8)12yes—
674C23C7×#13712yes—
675C23C22×C7×D411yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—41no—
679Q8—41no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—48no—
684D4—48no—
685D4—41no—
686D4—41no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4C7×#12012yes—
723C2×C4C7×#12114yes—
724C2×C4C7×#12114yes—
725C2×C4C7×#12112yes—
726C2×C4C7×#12314yes—
727C2×C4C7×#12312yes—
728C2×C4C7×#12414yes—
729C2×C4C22×C7×D411yescharacteristic
730C2×C4C22×C7×D411yescharacteristic
731C2×C4C22×C7×D411yescharacteristic
732C2×C4C2×C7×#4111yescharacteristic
733C2×C4C2×C7×#4111yescharacteristic
734C2×C4C2×C7×#4111yescharacteristic
735C8—24no—
736C8—42no—
737C7#2348211yescharacteristic, direct product factor, Sylow
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22C7×#39414yes—
767C22C2×C7×#12011yescharacteristic
768C22C2×C7×#12111yescharacteristic
769C22C2×C7×#12311yescharacteristic
770C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
771C22C2×C7×#13711yescharacteristic
772C22C7×#57511yescharacteristic
773C22C7×#57511yescharacteristic
774C4—42no—
775C4—42no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4C7×#39414yes—
782C4C2×C7×#12111yescharacteristic
783C4C2×C7×#12111yescharacteristic
784C4C2×C7×#12311yescharacteristic
785C4C2×C7×#12411yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×C7×#39411yescharacteristic
791C2C7×#300611yescharacteristic
792C2C7×#300711yescharacteristic
793C2C7×#305511yescharacteristic
794C2C7×#305611yescharacteristic
795C2C7×#309211yescharacteristic
796C2C7×#309311yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#525C2
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
2. C2×C7×#428C2semidirect
3. C2×C7×#417C2semidirect
4. C2×C7×#417C2semidirect
5. C2×C7×#407C2semidirect
6. C2×C7×#380C2semidirect
7. C7×#2036C2semidirect
8. C7×#2035C2semidirect
9. C7×#2034C2semidirect
10. C7×#2033C2semidirect
11. C7×#1736C2semidirect
31. C2×C7×#107C22semidirect
32. C2×C7×#106C22semidirect
35. C2×C7×#103C22semidirect
36. C2×C7×#103C22semidirect
37. C2×C7×#102C22semidirect
38. C2×C7×#102C22semidirect
47. C7×#340C22semidirect
48. C7×#340C22semidirect
49. #23482C7direct (N × H)
82. C2×C7×M16D4semidirect
131. C2×#428C2×C7semidirect
132. C2×#417C2×C7semidirect
133. C2×#417C2×C7semidirect
134. C2×#407C2×C7semidirect
135. C2×#380C2×C7semidirect
136. #2036C2×C7semidirect
137. #2035C2×C7semidirect
138. #2034C2×C7semidirect
139. #2033C2×C7semidirect
140. #1736C2×C7semidirect
273. C2×#107C22×C7semidirect
274. C2×#106C22×C7semidirect
277. C2×#103C22×C7semidirect
278. C2×#103C22×C7semidirect
279. C2×#102C22×C7semidirect
280. C2×#102C22×C7semidirect
289. #340C22×C7semidirect
290. #340C22×C7semidirect
420. C2×M16C7×D4semidirect
737. C7#23482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5252
C2×C7×#4282
C2×C7×#4172
C2×C7×#4072
C2×C7×#3802
C7×#20362
C7×#20352
C7×#20342
C7×#20332
C7×#17362
#234827