Finite Group Databasebeta

← C7×#23880 #13201096

Subgroups — C7×#23880 #13201096

Order 1792.

1696 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#137C211yesmaximal, characteristic, complemented
2C7×#3489C211yesmaximal, characteristic
3C2×C7×#456C212yesmaximal, complemented
4C7×#3004C211yesmaximal, characteristic, complemented
5C7×#2434C211yesmaximal, characteristic, complemented
6C7×#2007C212yesmaximal, complemented
7C7×#2005C212yesmaximal, complemented
8C7×#1901C211yesmaximal, characteristic, complemented
9C7×#1882C212yesmaximal, complemented
10C7×#1871C211yesmaximal, characteristic, complemented
11C7×#1789C211yesmaximal, characteristic, complemented
12C2×C7×2−1+4C2211yescharacteristic
13C22×C7×#41C2211yescharacteristic
14C23×C7×Q8C2211yescharacteristic
15C2×C7×#137—21no—
16C2×C7×#137—21no—
17C2×C7×#137—28no—
18C2×C7×#137C2212yes—
19C2×C7×#137C2212yes—
20C2×C7×#137C2212yescomplemented
21C22×C7×Q16—21no—
22C22×C7×SD16—21no—
23C22×C7×M16C2211yescharacteristic
24C7×D4×Q8—21no—
25C7×#548—21no—
26C7×#547—21no—
27C7×#547—22no—
28C7×#546—21no—
29C7×#546—22no—
30C7×#537—21no—
31C7×#537C2211yescharacteristic
32C7×#536—21no—
33C7×#536C2211yescharacteristic
34C2×C7×C4⋊Q8C2212yescomplemented
35C7×#525—21no—
36C7×#525C2211yescharacteristic
37C2×C7×C22⋊Q8—21no—
38C2×C7×C22⋊Q8C2211yescharacteristic
39C7×#520C2211yescharacteristic
40C7×#456—28no—
41C7×#451—21no—
42C7×#451—21no—
43C7×#448—21no—
44C7×#448—21no—
45C2×C7×#104C2212yes—
46C2×C7×#104C2212yes—
47C2×C7×#104C2212yescomplemented
48C7×#419C2212yescomplemented
49C2×C7×#101C2212yescomplemented
50C7×#407C2211yescharacteristic
51C7×#395—22no—
52C7×#391C2212yescomplemented
53C7×#385—22no—
54C4×C7×C22⋊C4C2211yescharacteristic
55C7×#343C2212yescomplemented
56C7×#339C2212yescomplemented
57#23880C711yesmaximal, characteristic, direct product factor, Sylow
58C7×2−1+4—24no—
59C7×2−1+4—42no—
60C2×C7×#41—21no—
61C2×C7×#41—21no—
62C2×C7×#41—21no—
63C2×C7×#41—21no—
64C2×C7×#41—22no—
65C2×C7×#41—24no—
66C2×C7×#41—42no—
67C2×C7×#41D411yescharacteristic
68C2×C7×#41D411yescharacteristic
69C2×C7×#41C2311yescharacteristic
70C2×C7×#41C2311yescharacteristic
71C2×C7×#41C2311yescharacteristic
72C22×C7×Q8—21no—
73C22×C7×Q8—21no—
74C22×C7×Q8—21no—
75C22×C7×Q8—24no—
76C22×C7×Q8—21no—
77C22×C7×Q8—21no—
78C22×C7×Q8—21no—
79C22×C7×Q8—21no—
80C22×C7×Q8—42no—
81C22×C7×Q8D411yescharacteristic
82C22×C7×Q8C2312yes—
83C22×C7×Q8C2311yescharacteristic
84C22×C7×D4—21no—
85C22×C7×D4D411yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C23×C4×C7C2311yescharacteristic
89C7×#137—28no—
90C7×#137—28no—
91C7×#137—24no—
92C7×#137—24no—
93C7×#137—24no—
94C7×#137—24no—
95C7×#137—42no—
96C7×#137D418yescomplemented
97C2×C7×Q16—28no—
98C2×C7×Q16—22no—
99C2×C7×Q16—22no—
100C2×C7×Q16—22no—
101C2×C7×SD16—28no—
102C2×C7×SD16—22no—
103C2×C7×SD16—22no—
104C2×C7×SD16—22no—
105C2×C7×M16—21no—
106C2×C7×M16—24no—
107C2×C7×M16C2312yes—
108C2×C7×M16C2312yes—
109C22×C7×C8—21no—
110C7×C4⋊Q8—22no—
111C7×C4⋊Q8—21no—
112C7×C4⋊Q8—24no—
113C7×C4⋊Q8—42no—
114C7×#124—22no—
115C7×#124—21no—
116C7×#123—22no—
117C7×#123—22no—
118C7×#123—22no—
119C7×#123—21no—
120C7×#123—22no—
121C7×C22⋊Q8—22no—
122C7×C22⋊Q8—22no—
123C7×C22⋊Q8—22no—
124C7×C22⋊Q8—21no—
125C7×C22⋊Q8—21no—
126C7×C22⋊Q8—21no—
127C7×C22⋊Q8—21no—
128C7×C22⋊Q8—21no—
129C7×C22⋊Q8—21no—
130C7×C22⋊Q8—21no—
131C7×C22⋊Q8—21no—
132C7×C22⋊Q8D411yescharacteristic
133C7×C22⋊Q8D411yescharacteristic
134C7×#121—22no—
135C7×#121—22no—
136C7×#121—22no—
137C7×#121—21no—
138C7×#121—21no—
139C7×#121—22no—
140C7×#121D411yescharacteristic
141C7×#121D411yescharacteristic
142C7×#120—22no—
143C7×#120—21no—
144C4×C7×Q8—21no—
145C4×C7×D4—22no—
146C4×C7×D4—22no—
147C4×C7×D4—21no—
148C4×C7×D4—22no—
149C4×C7×D4—21no—
150C4×C7×D4—21no—
151C7×#117—21no—
152C7×#117C2311yescharacteristic
153C2×C7×C4⋊C4—22no—
154C2×C7×C4⋊C4—21no—
155C2×C7×C4⋊C4—24no—
156C2×C7×C4⋊C4D412yes—
157C2×C7×C4⋊C4C2311yescharacteristic
158C2×C7×C22⋊C4—22no—
159C2×C7×C22⋊C4—21no—
160C2×C7×C22⋊C4D412yes—
161C2×C42×C7C2312yes—
162C7×#104—24no—
163C7×#104—24no—
164C7×#104—42no—
165C7×#103—22no—
166C7×#103—22no—
167C7×#101—24no—
168C7×C22⋊C8—21no—
169C7×C22⋊C8—21no—
170C7×#95—21no—
171C7×#95—24no—
172C22×#137C2×C711yescharacteristic, complemented
173#3489C2×C711yescharacteristic
174C2×#456C2×C712yescomplemented
175#3004C2×C711yescharacteristic, complemented
176#2434C2×C711yescharacteristic, complemented
177#2007C2×C712yescomplemented
178#2005C2×C712yescomplemented
179#1901C2×C711yescharacteristic, complemented
180#1882C2×C712yescomplemented
181#1871C2×C711yescharacteristic, complemented
182#1789C2×C711yescharacteristic, complemented
183C24×C7—21no—
184C24×C7C2×D411yescharacteristic
185C7×#41—22no—
186C7×#41—22no—
187C7×#41—22no—
188C7×#41—22no—
189C7×#41—22no—
190C7×#41—22no—
191C7×#41—22no—
192C7×#41—44no—
193C7×#41—41no—
194C7×#41—41no—
195C7×#41—44no—
196C7×#41—44no—
197C7×#41—48no—
198C7×#41—42no—
199C7×#41—42no—
200C7×#41C2×D414yes—
201C2×C7×Q8—22no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—22no—
207C2×C7×Q8—22no—
208C2×C7×Q8—24no—
209C2×C7×Q8—24no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—22no—
213C2×C7×Q8—22no—
214C2×C7×Q8—22no—
215C2×C7×Q8—44no—
216C2×C7×Q8—41no—
217C2×C7×Q8—44no—
218C2×C7×Q8—44no—
219C2×C7×Q8—44no—
220C2×C7×Q8—42no—
221C2×C7×Q8—42no—
222C2×C7×Q8—42no—
223C2×C7×Q8—42no—
224C2×C7×Q8—41no—
225C2×C7×Q8—41no—
226C2×C7×Q8C2×D411yescharacteristic
227C2×C7×Q8C2×D411yescharacteristic
228C2×C7×Q8C2×D414yes—
229C2×C7×Q8C2×D411yescharacteristic
230C2×C7×D4—21no—
231C2×C7×D4—22no—
232C2×C7×D4—22no—
233C2×C7×D4—21no—
234C2×C7×D4—21no—
235C2×C7×D4—21no—
236C2×C7×D4—21no—
237C2×C7×D4—21no—
238C2×C7×D4—22no—
239C2×C7×D4—21no—
240C2×C7×D4—21no—
241C2×C7×D4—41no—
242C2×C7×D4—44no—
243C2×C7×D4C2×D411yescharacteristic
244C2×C7×D4C2×D411yescharacteristic
245C2×C7×D4C2×D411yescharacteristic
246C22×C4×C7—21no—
247C22×C4×C7—22no—
248C22×C4×C7—22no—
249C22×C4×C7—22no—
250C22×C4×C7—22no—
251C22×C4×C7—21no—
252C22×C4×C7—22no—
253C22×C4×C7—22no—
254C22×C4×C7—22no—
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—44no—
260C22×C4×C7—44no—
261C22×C4×C7—41no—
262C22×C4×C7—41no—
263C22×C4×C7C2×D412yes—
264C22×C4×C7C2×D411yescharacteristic
265C22×C4×C7C2×D411yescharacteristic
266C22×C4×C7C2×D411yescharacteristic
267C22×C4×C7C2×D411yescharacteristic
268C22×C4×C7C2×D411yescharacteristic
269C22×C4×C7C2×D412yes—
270C22×C4×C7C2411yescharacteristic
271C7×Q16—28no—
272C7×Q16—28no—
273C7×Q16—44no—
274C7×SD16—28no—
275C7×SD16—28no—
276C7×SD16—44no—
277C7×M16—24no—
278C7×M16—22no—
279C7×M16—22no—
280C7×M16—22no—
281C7×M16C2×D414yes—
282C2×C7×C8—24no—
283C2×C7×C8—22no—
284C2×C7×C8—22no—
285C7×C4⋊C4—22no—
286C7×C4⋊C4—22no—
287C7×C4⋊C4—22no—
288C7×C4⋊C4—22no—
289C7×C4⋊C4—21no—
290C7×C4⋊C4—22no—
291C7×C4⋊C4—22no—
292C7×C4⋊C4—21no—
293C7×C4⋊C4—21no—
294C7×C4⋊C4—21no—
295C7×C4⋊C4—48no—
296C7×C4⋊C4C2×D411yescharacteristic
297C7×C4⋊C4C2×D411yescharacteristic
298C7×C22⋊C4—24no—
299C7×C22⋊C4—22no—
300C7×C22⋊C4—22no—
301C7×C22⋊C4—22no—
302C7×C22⋊C4—22no—
303C7×C22⋊C4—22no—
304C7×C22⋊C4—21no—
305C7×C22⋊C4—22no—
306C7×C22⋊C4—22no—
307C7×C22⋊C4—21no—
308C7×C22⋊C4—21no—
309C7×C22⋊C4—21no—
310C7×C22⋊C4—21no—
311C42×C7—22no—
312C42×C7—21no—
313C42×C7—22no—
314C42×C7—22no—
315C2×2−1+4C22×C711yescharacteristic
316C22×#41C22×C711yescharacteristic
317C23×Q8C22×C711yescharacteristic
318C2×#137—21no—
319C2×#137—21no—
320C2×#137—28no—
321C2×#137C22×C712yes—
322C2×#137C22×C712yes—
323C2×#137C22×C712yescomplemented
324C22×Q16—21no—
325C22×SD16—21no—
326C22×M16C22×C711yescharacteristic
327D4×Q8—21no—
328#548—21no—
329#547—21no—
330#547—22no—
331#546—21no—
332#546—22no—
333#537—21no—
334#537C22×C711yescharacteristic
335#536—21no—
336#536C22×C711yescharacteristic
337C2×C4⋊Q8C22×C712yescomplemented
338#525—21no—
339#525C22×C711yescharacteristic
340C2×C22⋊Q8—21no—
341C2×C22⋊Q8C22×C711yescharacteristic
342#520C22×C711yescharacteristic
343#456—28no—
344#451—21no—
345#451—21no—
346#448—21no—
347#448—21no—
348C2×#104C22×C712yes—
349C2×#104C22×C712yes—
350C2×#104C22×C712yescomplemented
351#419C22×C712yescomplemented
352C2×#101C22×C712yescomplemented
353#407C22×C711yescharacteristic
354#395—22no—
355#391C22×C712yescomplemented
356#385—22no—
357C4×C22⋊C4C22×C711yescharacteristic
358#343C22×C712yescomplemented
359#339C22×C712yescomplemented
360C23×C7—21no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—21no—
364C23×C7—21no—
365C23×C7—41no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7—81no—
369C23×C7#12011yescharacteristic
370C23×C7#12011yescharacteristic
371C23×C7C22×D411yescharacteristic
372C7×Q8—21no—
373C7×Q8—24no—
374C7×Q8—21no—
375C7×Q8—21no—
376C7×Q8—24no—
377C7×Q8—22no—
378C7×Q8—42no—
379C7×Q8—44no—
380C7×Q8—44no—
381C7×Q8—44no—
382C7×Q8—41no—
383C7×Q8—42no—
384C7×Q8—41no—
385C7×Q8—42no—
386C7×Q8—42no—
387C7×Q8#12012yes—
388C7×D4—24no—
389C7×D4—21no—
390C7×D4—21no—
391C7×D4—21no—
392C7×D4—22no—
393C7×D4—42no—
394C7×D4—42no—
395C7×D4—42no—
396C7×D4—44no—
397C7×D4—42no—
398C7×D4—42no—
399C7×D4—42no—
400C7×D4—81no—
401C7×D4—82no—
402C7×D4#12012yes—
403C2×C4×C7—21no—
404C2×C4×C7—22no—
405C2×C4×C7—21no—
406C2×C4×C7—21no—
407C2×C4×C7—21no—
408C2×C4×C7—21no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—24no—
412C2×C4×C7—24no—
413C2×C4×C7—21no—
414C2×C4×C7—22no—
415C2×C4×C7—21no—
416C2×C4×C7—21no—
417C2×C4×C7—22no—
418C2×C4×C7—21no—
419C2×C4×C7—24no—
420C2×C4×C7—24no—
421C2×C4×C7—42no—
422C2×C4×C7—42no—
423C2×C4×C7—42no—
424C2×C4×C7—44no—
425C2×C4×C7—42no—
426C2×C4×C7—44no—
427C2×C4×C7—44no—
428C2×C4×C7—44no—
429C2×C4×C7—42no—
430C2×C4×C7—42no—
431C2×C4×C7—42no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—42no—
435C2×C4×C7—42no—
436C2×C4×C7—82no—
437C2×C4×C7#12011yescharacteristic
438C2×C4×C7#12011yescharacteristic
439C2×C4×C7C22×D411yescharacteristic
440C2×C4×C7C22×D412yes—
441C2×C4×C7C22×D411yescharacteristic
442C2×C4×C7H(5,𝔽2)12yes—
443C7×C8—24no—
444C7×C8—42no—
4452−1+4—24no—
4462−1+4—42no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—22no—
451C2×#41—21no—
452C2×#41—24no—
453C2×#41—42no—
454C2×#41C7×D411yescharacteristic
455C2×#41C7×D411yescharacteristic
456C2×#41C23×C711yescharacteristic
457C2×#41C23×C711yescharacteristic
458C2×#41C23×C711yescharacteristic
459C22×Q8—21no—
460C22×Q8—21no—
461C22×Q8—21no—
462C22×Q8—24no—
463C22×Q8—21no—
464C22×Q8—21no—
465C22×Q8—21no—
466C22×Q8—21no—
467C22×Q8—42no—
468C22×Q8C7×D411yescharacteristic
469C22×Q8C23×C712yes—
470C22×Q8C23×C711yescharacteristic
471C22×D4—21no—
472C22×D4C7×D411yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4C23×C711yescharacteristic
476#137—28no—
477#137—28no—
478#137—24no—
479#137—24no—
480#137—24no—
481#137—24no—
482#137—42no—
483#137C7×D418yescomplemented
484C2×Q16—28no—
485C2×Q16—22no—
486C2×Q16—22no—
487C2×Q16—22no—
488C2×SD16—28no—
489C2×SD16—22no—
490C2×SD16—22no—
491C2×SD16—22no—
492C2×M16—21no—
493C2×M16—24no—
494C2×M16C23×C712yes—
495C2×M16C23×C712yes—
496C22×C8—21no—
497C4⋊Q8—22no—
498C4⋊Q8—21no—
499C4⋊Q8—24no—
500C4⋊Q8—42no—
501#124—22no—
502#124—21no—
503#123—22no—
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8C7×D411yescharacteristic
520C22⋊Q8C7×D411yescharacteristic
521#121—22no—
522#121—22no—
523#121—22no—
524#121—21no—
525#121—21no—
526#121—22no—
527#121C7×D411yescharacteristic
528#121C7×D411yescharacteristic
529#120—22no—
530#120—21no—
531C4×Q8—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—22no—
536C4×D4—21no—
537C4×D4—21no—
538#117—21no—
539#117C23×C711yescharacteristic
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4C7×D412yes—
544C2×C4⋊C4C23×C711yescharacteristic
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4C7×D412yes—
548C2×C42C23×C712yes—
549#104—24no—
550#104—24no—
551#104—42no—
552#103—22no—
553#103—22no—
554#101—24no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557#95—21no—
558#95—24no—
559C22×C7—21no—
560C22×C7—21no—
561C22×C7—21no—
562C22×C7—21no—
563C22×C7—21no—
564C22×C7—22no—
565C22×C7—21no—
566C22×C7—21no—
567C22×C7—44no—
568C22×C7—41no—
569C22×C7—41no—
570C22×C7—41no—
571C22×C7—41no—
572C22×C7—41no—
573C22×C7—41no—
574C22×C7—41no—
575C22×C7—41no—
576C22×C7—84no—
577C22×C7#45612yescomplemented
578C22×C7C2×#12011yescharacteristic
579C22×C7D4212yes—
580C4×C7—21no—
581C4×C7—21no—
582C4×C7—22no—
583C4×C7—44no—
584C4×C7—42no—
585C4×C7—41no—
586C4×C7—41no—
587C4×C7—44no—
588C4×C7—41no—
589C4×C7—42no—
590C4×C7—41no—
591C4×C7C2×#12011yescharacteristic
592C4×C7#53411yescharacteristic
593C4×C7D4212yes—
594C24—21no—
595C24C2×C7×D411yescharacteristic
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—44no—
604#41—41no—
605#41—41no—
606#41—44no—
607#41—44no—
608#41—48no—
609#41—42no—
610#41—42no—
611#41C2×C7×D414yes—
612C2×Q8—22no—
613C2×Q8—21no—
614C2×Q8—22no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—24no—
620C2×Q8—24no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—44no—
627C2×Q8—41no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—42no—
632C2×Q8—42no—
633C2×Q8—42no—
634C2×Q8—42no—
635C2×Q8—41no—
636C2×Q8—41no—
637C2×Q8C2×C7×D411yescharacteristic
638C2×Q8C2×C7×D411yescharacteristic
639C2×Q8C2×C7×D414yes—
640C2×Q8C2×C7×D411yescharacteristic
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—41no—
653C2×D4—44no—
654C2×D4C2×C7×D411yescharacteristic
655C2×D4C2×C7×D411yescharacteristic
656C2×D4C2×C7×D411yescharacteristic
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4C2×C7×D412yes—
675C22×C4C2×C7×D411yescharacteristic
676C22×C4C2×C7×D411yescharacteristic
677C22×C4C2×C7×D411yescharacteristic
678C22×C4C2×C7×D411yescharacteristic
679C22×C4C2×C7×D411yescharacteristic
680C22×C4C2×C7×D412yes—
681C22×C4C24×C711yescharacteristic
682Q16—28no—
683Q16—28no—
684Q16—44no—
685SD16—28no—
686SD16—28no—
687SD16—44no—
688M16—24no—
689M16—22no—
690M16—22no—
691M16—22no—
692M16C2×C7×D414yes—
693C2×C8—24no—
694C2×C8—22no—
695C2×C8—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—48no—
707C4⋊C4C2×C7×D411yescharacteristic
708C4⋊C4C2×C7×D411yescharacteristic
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—24no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—21no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C42—22no—
723C42—21no—
724C42—22no—
725C42—22no—
726C2×C7—22no—
727C2×C7—22no—
728C2×C7—41no—
729C2×C7—42no—
730C2×C7—81no—
731C2×C7—81no—
732C2×C7#240311yescharacteristic
733C2×C7C2×#45611yescharacteristic
734C2×C7#302211yescharacteristic
735C23—21no—
736C23—22no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—41no—
741C23—42no—
742C23—42no—
743C23—81no—
744C23C7×#12011yescharacteristic
745C23C7×#12011yescharacteristic
746C23C22×C7×D411yescharacteristic
747Q8—21no—
748Q8—24no—
749Q8—21no—
750Q8—21no—
751Q8—24no—
752Q8—22no—
753Q8—42no—
754Q8—44no—
755Q8—44no—
756Q8—44no—
757Q8—41no—
758Q8—42no—
759Q8—41no—
760Q8—42no—
761Q8—42no—
762Q8C7×#12012yes—
763D4—24no—
764D4—21no—
765D4—21no—
766D4—21no—
767D4—22no—
768D4—42no—
769D4—42no—
770D4—42no—
771D4—44no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—81no—
776D4—82no—
777D4C7×#12012yes—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—82no—
812C2×C4C7×#12011yescharacteristic
813C2×C4C7×#12011yescharacteristic
814C2×C4C22×C7×D411yescharacteristic
815C2×C4C22×C7×D412yes—
816C2×C4C22×C7×D411yescharacteristic
817C2×C4C7×H(5,𝔽2)12yes—
818C8—24no—
819C8—42no—
820C7#2388011yescharacteristic, direct product factor, Sylow
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—44no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—84no—
839C22C7×#45612yescomplemented
840C22C2×C7×#12011yescharacteristic
841C22C7×D4212yes—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—44no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—44no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4C2×C7×#12011yescharacteristic
854C4C7×#53411yescharacteristic
855C4C7×D4212yes—
856C2—22no—
857C2—22no—
858C2—41no—
859C2—42no—
860C2—81no—
861C2—81no—
862C2C7×#240311yescharacteristic
863C2C2×C7×#45611yescharacteristic
864C2C7×#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
1. C22×C7×#137C2semidirect
3. C2×C7×#456C2semidirect
4. C7×#3004C2semidirect
5. C7×#2434C2semidirect
6. C7×#2007C2semidirect
7. C7×#2005C2semidirect
8. C7×#1901C2semidirect
9. C7×#1882C2semidirect
10. C7×#1871C2semidirect
11. C7×#1789C2semidirect
20. C2×C7×#137C22semidirect
34. C2×C7×C4⋊Q8C22semidirect
47. C2×C7×#104C22semidirect
48. C7×#419C22semidirect
49. C2×C7×#101C22semidirect
52. C7×#391C22semidirect
55. C7×#343C22semidirect
56. C7×#339C22semidirect
57. #23880C7direct (N × H)
96. C7×#137D4semidirect
172. C22×#137C2×C7semidirect
174. C2×#456C2×C7semidirect
175. #3004C2×C7semidirect
176. #2434C2×C7semidirect
177. #2007C2×C7semidirect
178. #2005C2×C7semidirect
179. #1901C2×C7semidirect
180. #1882C2×C7semidirect
181. #1871C2×C7semidirect
182. #1789C2×C7semidirect
323. C2×#137C22×C7semidirect
337. C2×C4⋊Q8C22×C7semidirect
350. C2×#104C22×C7semidirect
351. #419C22×C7semidirect
352. C2×#101C22×C7semidirect
355. #391C22×C7semidirect
358. #343C22×C7semidirect
359. #339C22×C7semidirect
483. #137C7×D4semidirect
577. C22×C7#456semidirect
820. C7#23880direct (N × H)
839. C22C7×#456semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1372
C7×#34892
C2×C7×#4562
C7×#30042
C7×#24342
C7×#20072
C7×#20052
C7×#19012
C7×#18822
C7×#18712
C7×#17892
#238807