Finite Group Databasebeta

← C7×#24029 #13201245

Subgroups — C7×#24029 #13201245

Order 1792.

1264 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3489C211yesmaximal, characteristic
2C7×#3092C211yesmaximal, characteristic, complemented
3C2×C7×#417C211yesmaximal, characteristic, complemented
4C7×#2503C211yesmaximal, characteristic, complemented
5C7×#2040C212yesmaximal, complemented
6C7×#2038C212yesmaximal, complemented
7C7×#1901C211yesmaximal, characteristic, complemented
8C7×#1871C211yesmaximal, characteristic, complemented
9C7×#1860C212yesmaximal, complemented
10C7×#1793C212yesmaximal, complemented
11C7×#1789C211yesmaximal, characteristic, complemented
12C2×C7×2−1+4C2211yescharacteristic
13C22×C7×#41C2211yescharacteristic
14C22×C7×M16C2211yescharacteristic
15C7×D4×Q8—21no—
16C7×#548—21no—
17C7×#547—21no—
18C7×#547—22no—
19C7×#546—21no—
20C7×#546—22no—
21C7×#537—21no—
22C7×#537C2211yescharacteristic
23C7×#536—21no—
24C7×#536C2211yescharacteristic
25C7×#525—21no—
26C7×#525C2211yescharacteristic
27C2×C7×C22⋊Q8—21no—
28C2×C7×C22⋊Q8C2211yescharacteristic
29C7×#520C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic
31C7×#484—21no—
32C7×#483—21no—
33C7×#481—21no—
34C7×#480—21no—
35C7×#428C2212yescomplemented
36C2×C7×#104C2212yes—
37C2×C7×#104C2212yes—
38C2×C7×#104C2212yescomplemented
39C7×#417—21no—
40C7×#417—21no—
41C7×#417C2212yes—
42C7×#417C2212yes—
43C7×#417C2212yescomplemented
44C2×C7×#103—21no—
45C2×C7×#102—21no—
46C2×C7×#101C2212yescomplemented
47C7×#407C2211yescharacteristic
48C7×#400—22no—
49C7×#391C2212yescomplemented
50C7×#382C2212yescomplemented
51C7×#381—22no—
52C4×C7×C22⋊C4C2211yescharacteristic
53C7×#343C2212yescomplemented
54C7×#339C2212yescomplemented
55#24029C711yesmaximal, characteristic, direct product factor, Sylow
56C7×2−1+4—24no—
57C7×2−1+4—42no—
58C2×C7×#41—21no—
59C2×C7×#41—21no—
60C2×C7×#41—21no—
61C2×C7×#41—21no—
62C2×C7×#41—22no—
63C2×C7×#41—24no—
64C2×C7×#41—42no—
65C2×C7×#41D411yescharacteristic
66C2×C7×#41D411yescharacteristic
67C2×C7×#41C2311yescharacteristic
68C2×C7×#41C2311yescharacteristic
69C2×C7×#41C2311yescharacteristic
70C22×C7×Q8—21no—
71C22×C7×Q8—21no—
72C22×C7×Q8D411yescharacteristic
73C22×C7×Q8C2311yescharacteristic
74C22×C7×D4—21no—
75C22×C7×D4D411yescharacteristic
76C23×C4×C7—21no—
77C23×C4×C7—21no—
78C23×C4×C7C2311yescharacteristic
79C2×C7×M16—21no—
80C2×C7×M16—42no—
81C2×C7×M16C2312yes—
82C2×C7×M16C2312yes—
83C22×C7×C8—21no—
84C7×C4⋊Q8—22no—
85C7×C4⋊Q8—21no—
86C7×#124—22no—
87C7×#124—21no—
88C7×#123—22no—
89C7×#123—22no—
90C7×#123—22no—
91C7×#123—21no—
92C7×#123—22no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8—21no—
97C7×C22⋊Q8—21no—
98C7×C22⋊Q8—21no—
99C7×C22⋊Q8—21no—
100C7×C22⋊Q8—21no—
101C7×C22⋊Q8—21no—
102C7×C22⋊Q8—21no—
103C7×C22⋊Q8—21no—
104C7×C22⋊Q8D411yescharacteristic
105C7×C22⋊Q8D411yescharacteristic
106C7×#121—22no—
107C7×#121—22no—
108C7×#121—22no—
109C7×#121—21no—
110C7×#121—21no—
111C7×#121—22no—
112C7×#121D411yescharacteristic
113C7×#121D411yescharacteristic
114C7×#120—22no—
115C7×#120—21no—
116C4×C7×Q8—21no—
117C4×C7×D4—22no—
118C4×C7×D4—22no—
119C4×C7×D4—21no—
120C4×C7×D4—22no—
121C4×C7×D4—21no—
122C4×C7×D4—21no—
123C7×#117—21no—
124C7×#117C2311yescharacteristic
125C2×C7×C4⋊C4—22no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—21no—
128C2×C7×C4⋊C4—21no—
129C2×C7×C4⋊C4—21no—
130C2×C7×C4⋊C4—21no—
131C2×C7×C4⋊C4—21no—
132C2×C7×C4⋊C4D412yes—
133C2×C7×C4⋊C4C2312yes—
134C2×C7×C4⋊C4C2311yescharacteristic
135C2×C7×C22⋊C4—22no—
136C2×C7×C22⋊C4—21no—
137C2×C7×C22⋊C4D412yes—
138C2×C42×C7C2312yes—
139C7×#107—22no—
140C7×#106—22no—
141C7×#104—24no—
142C7×#104—42no—
143C7×#104—42no—
144C7×#103—22no—
145C7×#103—22no—
146C7×#103—22no—
147C7×#102—22no—
148C7×#102—22no—
149C7×#102—22no—
150C7×#101—42no—
151C7×C22⋊C8—21no—
152C7×C22⋊C8—21no—
153C7×#95—21no—
154C7×#95—24no—
155C7×#95—24no—
156#3489C2×C711yescharacteristic
157#3092C2×C711yescharacteristic, complemented
158C2×#417C2×C711yescharacteristic, complemented
159#2503C2×C711yescharacteristic, complemented
160#2040C2×C712yescomplemented
161#2038C2×C712yescomplemented
162#1901C2×C711yescharacteristic, complemented
163#1871C2×C711yescharacteristic, complemented
164#1860C2×C712yescomplemented
165#1793C2×C712yescomplemented
166#1789C2×C711yescharacteristic, complemented
167C24×C7—21no—
168C24×C7C2×D411yescharacteristic
169C7×#41—22no—
170C7×#41—22no—
171C7×#41—22no—
172C7×#41—22no—
173C7×#41—22no—
174C7×#41—22no—
175C7×#41—22no—
176C7×#41—44no—
177C7×#41—41no—
178C7×#41—41no—
179C7×#41—44no—
180C7×#41—44no—
181C7×#41—48no—
182C7×#41—42no—
183C7×#41—42no—
184C7×#41#4114yes—
185C2×C7×Q8—22no—
186C2×C7×Q8—21no—
187C2×C7×Q8—21no—
188C2×C7×Q8—21no—
189C2×C7×Q8—22no—
190C2×C7×Q8—22no—
191C2×C7×Q8—22no—
192C2×C7×Q8—41no—
193C2×C7×Q8—44no—
194C2×C7×Q8—42no—
195C2×C7×Q8—42no—
196C2×C7×Q8C2×D411yescharacteristic
197C2×C7×Q8C2×D411yescharacteristic
198C2×C7×Q8C2×D411yescharacteristic
199C2×C7×D4—21no—
200C2×C7×D4—22no—
201C2×C7×D4—22no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—21no—
206C2×C7×D4—21no—
207C2×C7×D4—22no—
208C2×C7×D4—21no—
209C2×C7×D4—21no—
210C2×C7×D4—41no—
211C2×C7×D4—44no—
212C2×C7×D4C2×D411yescharacteristic
213C2×C7×D4C2×D411yescharacteristic
214C2×C7×D4C2×D411yescharacteristic
215C22×C4×C7—21no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—21no—
221C22×C4×C7—22no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—44no—
229C22×C4×C7—44no—
230C22×C4×C7—41no—
231C22×C4×C7—41no—
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2×D412yes—
239C22×C4×C7C2411yescharacteristic
240C7×M16—22no—
241C7×M16—22no—
242C7×M16—22no—
243C7×M16—22no—
244C7×M16—42no—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8—42no—
248C7×C4⋊C4—22no—
249C7×C4⋊C4—22no—
250C7×C4⋊C4—22no—
251C7×C4⋊C4—22no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—22no—
254C7×C4⋊C4—22no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—22no—
259C7×C4⋊C4—22no—
260C7×C4⋊C4—41no—
261C7×C4⋊C4—41no—
262C7×C4⋊C4C2×D411yescharacteristic
263C7×C4⋊C4C2×D411yescharacteristic
264C7×C22⋊C4—22no—
265C7×C22⋊C4—22no—
266C7×C22⋊C4—22no—
267C7×C22⋊C4—22no—
268C7×C22⋊C4—22no—
269C7×C22⋊C4—21no—
270C7×C22⋊C4—22no—
271C7×C22⋊C4—22no—
272C7×C22⋊C4—21no—
273C7×C22⋊C4—21no—
274C7×C22⋊C4—21no—
275C7×C22⋊C4—21no—
276C7×C22⋊C4—42no—
277C42×C7—22no—
278C42×C7—21no—
279C42×C7—22no—
280C42×C7—22no—
281C2×2−1+4C22×C711yescharacteristic
282C22×#41C22×C711yescharacteristic
283C22×M16C22×C711yescharacteristic
284D4×Q8—21no—
285#548—21no—
286#547—21no—
287#547—22no—
288#546—21no—
289#546—22no—
290#537—21no—
291#537C22×C711yescharacteristic
292#536—21no—
293#536C22×C711yescharacteristic
294#525—21no—
295#525C22×C711yescharacteristic
296C2×C22⋊Q8—21no—
297C2×C22⋊Q8C22×C711yescharacteristic
298#520C22×C711yescharacteristic
299C22×C4⋊C4C22×C711yescharacteristic
300#484—21no—
301#483—21no—
302#481—21no—
303#480—21no—
304#428C22×C712yescomplemented
305C2×#104C22×C712yes—
306C2×#104C22×C712yes—
307C2×#104C22×C712yescomplemented
308#417—21no—
309#417—21no—
310#417C22×C712yes—
311#417C22×C712yes—
312#417C22×C712yescomplemented
313C2×#103—21no—
314C2×#102—21no—
315C2×#101C22×C712yescomplemented
316#407C22×C711yescharacteristic
317#400—22no—
318#391C22×C712yescomplemented
319#382C22×C712yescomplemented
320#381—22no—
321C4×C22⋊C4C22×C711yescharacteristic
322#343C22×C712yescomplemented
323#339C22×C712yescomplemented
324C23×C7—21no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—21no—
328C23×C7—21no—
329C23×C7—41no—
330C23×C7—42no—
331C23×C7—42no—
332C23×C7—81no—
333C23×C7#12011yescharacteristic
334C23×C7#12011yescharacteristic
335C23×C7C22×D411yescharacteristic
336C7×Q8—21no—
337C7×Q8—21no—
338C7×Q8—21no—
339C7×Q8—22no—
340C7×Q8—42no—
341C7×Q8—44no—
342C7×Q8—41no—
343C7×Q8—41no—
344C7×Q8—42no—
345C7×Q8#12312yes—
346C7×D4—24no—
347C7×D4—21no—
348C7×D4—21no—
349C7×D4—21no—
350C7×D4—22no—
351C7×D4—42no—
352C7×D4—42no—
353C7×D4—42no—
354C7×D4—44no—
355C7×D4—42no—
356C7×D4—42no—
357C7×D4—42no—
358C7×D4—81no—
359C7×D4—82no—
360C7×D4#12312yes—
361C2×C4×C7—21no—
362C2×C4×C7—22no—
363C2×C4×C7—21no—
364C2×C4×C7—21no—
365C2×C4×C7—21no—
366C2×C4×C7—21no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—24no—
370C2×C4×C7—21no—
371C2×C4×C7—22no—
372C2×C4×C7—21no—
373C2×C4×C7—21no—
374C2×C4×C7—22no—
375C2×C4×C7—21no—
376C2×C4×C7—24no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—44no—
381C2×C4×C7—44no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—44no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—82no—
392C2×C4×C7—82no—
393C2×C4×C7—82no—
394C2×C4×C7#12011yescharacteristic
395C2×C4×C7#12011yescharacteristic
396C2×C4×C7C22×D411yescharacteristic
397C2×C4×C7C22×D411yescharacteristic
398C2×C4×C7C2×#4112yes—
399C2×C4×C7H(5,𝔽2)12yes—
400C7×C8—42no—
401C7×C8—42no—
4022−1+4—24no—
4032−1+4—42no—
404C2×#41—21no—
405C2×#41—21no—
406C2×#41—21no—
407C2×#41—22no—
408C2×#41—21no—
409C2×#41—24no—
410C2×#41—42no—
411C2×#41C7×D411yescharacteristic
412C2×#41C7×D411yescharacteristic
413C2×#41C23×C711yescharacteristic
414C2×#41C23×C711yescharacteristic
415C2×#41C23×C711yescharacteristic
416C22×Q8—21no—
417C22×Q8—21no—
418C22×Q8C7×D411yescharacteristic
419C22×Q8C23×C711yescharacteristic
420C22×D4—21no—
421C22×D4C7×D411yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4C23×C711yescharacteristic
425C2×M16—21no—
426C2×M16—42no—
427C2×M16C23×C712yes—
428C2×M16C23×C712yes—
429C22×C8—21no—
430C4⋊Q8—22no—
431C4⋊Q8—21no—
432#124—22no—
433#124—21no—
434#123—22no—
435#123—22no—
436#123—22no—
437#123—21no—
438#123—22no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—21no—
443C22⋊Q8—21no—
444C22⋊Q8—21no—
445C22⋊Q8—21no—
446C22⋊Q8—21no—
447C22⋊Q8—21no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8C7×D411yescharacteristic
451C22⋊Q8C7×D411yescharacteristic
452#121—22no—
453#121—22no—
454#121—22no—
455#121—21no—
456#121—21no—
457#121—22no—
458#121C7×D411yescharacteristic
459#121C7×D411yescharacteristic
460#120—22no—
461#120—21no—
462C4×Q8—21no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—21no—
466C4×D4—22no—
467C4×D4—21no—
468C4×D4—21no—
469#117—21no—
470#117C23×C711yescharacteristic
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4C7×D412yes—
479C2×C4⋊C4C23×C712yes—
480C2×C4⋊C4C23×C711yescharacteristic
481C2×C22⋊C4—22no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4C7×D412yes—
484C2×C42C23×C712yes—
485#107—22no—
486#106—22no—
487#104—24no—
488#104—42no—
489#104—42no—
490#103—22no—
491#103—22no—
492#103—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#101—42no—
497C22⋊C8—21no—
498C22⋊C8—21no—
499#95—21no—
500#95—24no—
501#95—24no—
502C22×C7—21no—
503C22×C7—21no—
504C22×C7—21no—
505C22×C7—21no—
506C22×C7—21no—
507C22×C7—22no—
508C22×C7—21no—
509C22×C7—21no—
510C22×C7—44no—
511C22×C7—41no—
512C22×C7—41no—
513C22×C7—41no—
514C22×C7—41no—
515C22×C7—41no—
516C22×C7—41no—
517C22×C7—41no—
518C22×C7—41no—
519C22×C7—84no—
520C22×C7#45412yes—
521C22×C7C2×#12011yescharacteristic
522C22×C7#54612yes—
523C4×C7—21no—
524C4×C7—21no—
525C4×C7—22no—
526C4×C7—42no—
527C4×C7—41no—
528C4×C7—41no—
529C4×C7—41no—
530C4×C7—42no—
531C4×C7—41no—
532C4×C7—82no—
533C4×C7—82no—
534C4×C7C2×#12311yescharacteristic
535C4×C7#53411yescharacteristic
536C4×C7#54612yes—
537C24—21no—
538C24C2×C7×D411yescharacteristic
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—44no—
547#41—41no—
548#41—41no—
549#41—44no—
550#41—44no—
551#41—48no—
552#41—42no—
553#41—42no—
554#41C7×#4114yes—
555C2×Q8—22no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—41no—
563C2×Q8—44no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8C2×C7×D411yescharacteristic
567C2×Q8C2×C7×D411yescharacteristic
568C2×Q8C2×C7×D411yescharacteristic
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—44no—
582C2×D4C2×C7×D411yescharacteristic
583C2×D4C2×C7×D411yescharacteristic
584C2×D4C2×C7×D411yescharacteristic
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4C2×C7×D412yes—
603C22×C4C2×C7×D411yescharacteristic
604C22×C4C2×C7×D411yescharacteristic
605C22×C4C2×C7×D411yescharacteristic
606C22×C4C2×C7×D411yescharacteristic
607C22×C4C2×C7×D411yescharacteristic
608C22×C4C2×C7×D412yes—
609C22×C4C24×C711yescharacteristic
610M16—22no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—42no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—42no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—21no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4C2×C7×D411yescharacteristic
633C4⋊C4C2×C7×D411yescharacteristic
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—21no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—42no—
647C42—22no—
648C42—21no—
649C42—22no—
650C42—22no—
651C2×C7—22no—
652C2×C7—22no—
653C2×C7—41no—
654C2×C7—42no—
655C2×C7—81no—
656C2×C7—81no—
657C2×C7#240511yescharacteristic
658C2×C7C2×#45411yescharacteristic
659C2×C7#302211yescharacteristic
660C23—21no—
661C23—22no—
662C23—22no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—81no—
669C23C7×#12011yescharacteristic
670C23C7×#12011yescharacteristic
671C23C22×C7×D411yescharacteristic
672Q8—21no—
673Q8—21no—
674Q8—21no—
675Q8—22no—
676Q8—42no—
677Q8—44no—
678Q8—41no—
679Q8—41no—
680Q8—42no—
681Q8C7×#12312yes—
682D4—24no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—22no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—81no—
695D4—82no—
696D4C7×#12312yes—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—24no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4C7×#12011yescharacteristic
731C2×C4C7×#12011yescharacteristic
732C2×C4C22×C7×D411yescharacteristic
733C2×C4C22×C7×D411yescharacteristic
734C2×C4C2×C7×#4112yes—
735C2×C4C7×H(5,𝔽2)12yes—
736C8—42no—
737C8—42no—
738C7#2402911yescharacteristic, direct product factor, Sylow
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—22no—
745C22—21no—
746C22—21no—
747C22—44no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—84no—
757C22C7×#45412yes—
758C22C2×C7×#12011yescharacteristic
759C22C7×#54612yes—
760C4—21no—
761C4—21no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—82no—
770C4—82no—
771C4C2×C7×#12311yescharacteristic
772C4C7×#53411yescharacteristic
773C4C7×#54612yes—
774C2—22no—
775C2—22no—
776C2—41no—
777C2—42no—
778C2—81no—
779C2—81no—
780C2C7×#240511yescharacteristic
781C2C2×C7×#45411yescharacteristic
782C2C7×#302211yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#3092C2semidirect
3. C2×C7×#417C2semidirect
4. C7×#2503C2semidirect
5. C7×#2040C2semidirect
6. C7×#2038C2semidirect
7. C7×#1901C2semidirect
8. C7×#1871C2semidirect
9. C7×#1860C2semidirect
10. C7×#1793C2semidirect
11. C7×#1789C2semidirect
35. C7×#428C22semidirect
38. C2×C7×#104C22semidirect
43. C7×#417C22semidirect
46. C2×C7×#101C22semidirect
49. C7×#391C22semidirect
50. C7×#382C22semidirect
53. C7×#343C22semidirect
54. C7×#339C22semidirect
55. #24029C7direct (N × H)
157. #3092C2×C7semidirect
158. C2×#417C2×C7semidirect
159. #2503C2×C7semidirect
160. #2040C2×C7semidirect
161. #2038C2×C7semidirect
162. #1901C2×C7semidirect
163. #1871C2×C7semidirect
164. #1860C2×C7semidirect
165. #1793C2×C7semidirect
166. #1789C2×C7semidirect
304. #428C22×C7semidirect
307. C2×#104C22×C7semidirect
312. #417C22×C7semidirect
315. C2×#101C22×C7semidirect
318. #391C22×C7semidirect
319. #382C22×C7semidirect
322. #343C22×C7semidirect
323. #339C22×C7semidirect
738. C7#24029direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34892
C7×#30922
C2×C7×#4172
C7×#25032
C7×#20402
C7×#20382
C7×#19012
C7×#18712
C7×#18602
C7×#17932
C7×#17892
#240297