Finite Group Databasebeta

← C7×#14020 #13191236

Subgroups — C7×#14020 #13191236

Order 1792.

2178 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#386C211yesmaximal, characteristic
2C2×C7×#386C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
5C22×C7×#95C211yesmaximal, characteristic, complemented
6C7×#1443C212yesmaximal, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1437C212yesmaximal, complemented
9C7×#1434C212yesmaximal, complemented
10C7×C22⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C42×C7C2212yes—
24C7×#386—24no—
25C7×#386—24no—
26C7×#386C418yescomplemented
27C4×C7×C22⋊C4—24no—
28C2×C7×#95—24no—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40#14020C711yesmaximal, characteristic, direct product factor, Sylow
41C25×C7C2311yescharacteristic
42C25×C7C2311yescharacteristic
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4C2×C414yes—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7—22no—
53C23×C4×C7—22no—
54C23×C4×C7—22no—
55C23×C4×C7—24no—
56C23×C4×C7—24no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—42no—
60C23×C4×C7—42no—
61C23×C4×C7—42no—
62C23×C4×C7—42no—
63C23×C4×C7C2×C414yes—
64C23×C4×C7D414yes—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2312yes—
69C23×C4×C7C2312yes—
70C23×C4×C7C2312yes—
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2312yes—
73C23×C4×C7C2311yescharacteristic
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C7×C22⋊C4—42no—
90C2×C7×C22⋊C4C2×C414yes—
91C2×C7×C22⋊C4C2×C418yescomplemented
92C2×C7×C22⋊C4D414yes—
93C2×C42×C7—24no—
94C2×C42×C7—24no—
95C2×C42×C7—42no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—24no—
99C7×#95—24no—
100C7×#95—22no—
101C7×#95—22no—
102C7×#95—24no—
103C7×#95—42no—
104C7×#95—42no—
105C7×#95—42no—
106C7×#95C2×C418yescomplemented
107C2×#386C2×C711yescharacteristic
108C2×#386C2×C711yescharacteristic
109C2×#386C2×C711yescharacteristic
110C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
111C22×#95C2×C711yescharacteristic, complemented
112#1443C2×C712yescomplemented
113#1440C2×C712yescomplemented
114#1437C2×C712yescomplemented
115#1434C2×C712yescomplemented
116C22⋊#95C2×C711yescharacteristic, complemented
117C22⋊#95C2×C711yescharacteristic, complemented
118C24×C7—22no—
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7C22×C412yes—
133C24×C7C22×C412yes—
134C24×C7C2×D412yes—
135C24×C7C2×D412yes—
136C24×C7#4112yes—
137C24×C7#4112yes—
138C24×C7#4112yes—
139C24×C7#4112yes—
140C24×C7C2411yescharacteristic
141C2×C7×D4—28no—
142C2×C7×D4—28no—
143C2×C7×D4—28no—
144C2×C7×D4—44no—
145C2×C7×D4—44no—
146C2×C7×D4—44no—
147C2×C7×D4—44no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—28no—
152C22×C4×C7—28no—
153C22×C4×C7—28no—
154C22×C4×C7—22no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—21no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—28no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—48no—
200C22×C4×C7—44no—
201C22×C4×C7—48no—
202C22×C4×C7—48no—
203C22×C4×C7—48no—
204C22×C4×C7—48no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7—44no—
208C22×C4×C7—48no—
209C22×C4×C7—44no—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C22×C414yes—
212C22×C4×C7C22×C414yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×D414yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7#4114yes—
217C22×C4×C7#4114yes—
218C7×C22⋊C4—28no—
219C7×C22⋊C4—28no—
220C7×C22⋊C4—48no—
221C7×C22⋊C4—48no—
222C7×C22⋊C4—44no—
223C7×C22⋊C4—44no—
224C7×C22⋊C4—44no—
225C42×C7—48no—
226C23×D4C22×C711yescharacteristic
227C24×C4C22×C711yescharacteristic
228C24×C4C22×C711yescharacteristic
229C24×C4C22×C711yescharacteristic
230C22×C22⋊C4C22×C711yescharacteristic
231C22×C22⋊C4C22×C711yescharacteristic
232C22×C22⋊C4C22×C712yes—
233C22×C22⋊C4C22×C711yescharacteristic
234C22×C22⋊C4C22×C711yescharacteristic
235C22×C22⋊C4C22×C711yescharacteristic
236C22×C22⋊C4C22×C712yes—
237C22×C42C22×C712yes—
238#386—24no—
239#386—24no—
240#386C4×C718yescomplemented
241C4×C22⋊C4—24no—
242C2×#95—24no—
243C2×#95C22×C712yes—
244C2×#95C22×C711yescharacteristic
245C2×#95C22×C712yes—
246C2×#95C22×C712yes—
247C2×#95C22×C712yes—
248C2×#95C22×C712yes—
249C2×#95C22×C711yescharacteristic
250C2×#95C22×C712yes—
251C2×#95C22×C712yes—
252C2×#95C22×C712yes—
253C2×#95C22×C712yes—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—24no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—24no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—22no—
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—42no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—42no—
285C23×C7—42no—
286C23×C7—42no—
287C23×C7—42no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7#11714yes—
294C23×C7C4×D414yes—
295C23×C7C4×D414yes—
296C23×C7#12114yes—
297C23×C7#12314yes—
298C23×C7#12414yes—
299C23×C7#12614yes—
300C23×C7C23×C411yescharacteristic
301C23×C7C22×D411yescharacteristic
302C23×C7C22×D411yescharacteristic
303C23×C7C2×#4111yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C23×C7C2×#4111yescharacteristic
306C23×C7C2×#4111yescharacteristic
307C23×C7C2×#4112yes—
308C23×C7C2×#4112yes—
309C23×C7H(5,𝔽2)12yes—
310C23×C7H(5,𝔽2)12yes—
311C7×D4—416no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—22no—
317C2×C4×C7—24no—
318C2×C4×C7—24no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—24no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—22no—
326C2×C4×C7—24no—
327C2×C4×C7—22no—
328C2×C4×C7—24no—
329C2×C4×C7—22no—
330C2×C4×C7—24no—
331C2×C4×C7—24no—
332C2×C4×C7—24no—
333C2×C4×C7—24no—
334C2×C4×C7—416no—
335C2×C4×C7—416no—
336C2×C4×C7—416no—
337C2×C4×C7—42no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7#12314yes—
370C25C23×C711yescharacteristic
371C25C23×C711yescharacteristic
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4C2×C4×C714yes—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4C2×C4×C714yes—
393C23×C4C7×D414yes—
394C23×C4C23×C711yescharacteristic
395C23×C4C23×C711yescharacteristic
396C23×C4C23×C712yes—
397C23×C4C23×C712yes—
398C23×C4C23×C711yescharacteristic
399C23×C4C23×C712yes—
400C23×C4C23×C711yescharacteristic
401C23×C4C23×C712yes—
402C23×C4C23×C711yescharacteristic
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4C2×C4×C714yes—
420C2×C22⋊C4C2×C4×C718yescomplemented
421C2×C22⋊C4C7×D414yes—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—42no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—22no—
430#95—22no—
431#95—24no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95C2×C4×C718yescomplemented
436C22×C7—24no—
437C22×C7—24no—
438C22×C7—28no—
439C22×C7—28no—
440C22×C7—24no—
441C22×C7—24no—
442C22×C7—28no—
443C22×C7—24no—
444C22×C7—28no—
445C22×C7—24no—
446C22×C7—42no—
447C22×C7—44no—
448C22×C7—44no—
449C22×C7—42no—
450C22×C7—42no—
451C22×C7—81no—
452C22×C7—81no—
453C22×C7—81no—
454C22×C7—82no—
455C22×C7—81no—
456C22×C7—82no—
457C22×C7#38818yes—
458C22×C7C2×#11711yescharacteristic
459C22×C7C2×C4×D411yescharacteristic
460C22×C7C2×C4×D411yescharacteristic
461C22×C7C4×#4112yes—
462C22×C7#51812yes—
463C22×C7C2×#12111yescharacteristic
464C22×C7C2×#12311yescharacteristic
465C22×C7C2×#12311yescharacteristic
466C22×C7#52511yescharacteristic
467C22×C7C2×#12411yescharacteristic
468C22×C7C2×#12611yescharacteristic
469C22×C7#52912yes—
470C22×C7#53411yescharacteristic
471C22×C7#53511yescharacteristic
472C22×C7#53812yes—
473C22×C7#54612yes—
474C22×C7#54612yes—
475C22×C7#55112yes—
476C22×C7#55112yes—
477C22×C7#55312yes—
478C22×C7#55312yes—
479C22×C7#55312yes—
480C22×C7#55312yes—
481C4×C7—24no—
482C4×C7—44no—
483C4×C7—44no—
484C4×C7—44no—
485C4×C7—42no—
486C4×C7—44no—
487C4×C7—42no—
488C4×C7—81no—
489C4×C7—81no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—22no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24C22×C4×C712yes—
505C24C22×C4×C712yes—
506C24C2×C7×D412yes—
507C24C2×C7×D412yes—
508C24C7×#4112yes—
509C24C7×#4112yes—
510C24C7×#4112yes—
511C24C7×#4112yes—
512C24C24×C711yescharacteristic
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—28no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—48no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—44no—
582C22×C4C22×C4×C712yes—
583C22×C4C22×C4×C714yes—
584C22×C4C22×C4×C714yes—
585C22×C4C2×C7×D412yes—
586C22×C4C2×C7×D414yes—
587C22×C4C2×C7×D412yes—
588C22×C4C7×#4114yes—
589C22×C4C7×#4114yes—
590C22⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C42—48no—
598C2×C7—28no—
599C2×C7—82no—
600C2×C7C2×#38811yescharacteristic
601C2×C7C4×#12311yescharacteristic
602C2×C7#232111yescharacteristic
603C2×C7#235312yes—
604C2×C7#236412yes—
605C2×C7#241111yescharacteristic
606C2×C7#241211yescharacteristic
607C2×C7#244412yes—
608C2×C7#250411yescharacteristic
609C2×C7#251012yes—
610C2×C7#259111yescharacteristic
611C23—24no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23C7×#11714yes—
651C23C4×C7×D414yes—
652C23C4×C7×D414yes—
653C23C7×#12114yes—
654C23C7×#12314yes—
655C23C7×#12414yes—
656C23C7×#12614yes—
657C23C23×C4×C711yescharacteristic
658C23C22×C7×D411yescharacteristic
659C23C22×C7×D411yescharacteristic
660C23C2×C7×#4111yescharacteristic
661C23C2×C7×#4111yescharacteristic
662C23C2×C7×#4111yescharacteristic
663C23C2×C7×#4111yescharacteristic
664C23C2×C7×#4112yes—
665C23C2×C7×#4112yes—
666C23C7×H(5,𝔽2)12yes—
667C23C7×H(5,𝔽2)12yes—
668D4—416no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—416no—
692C2×C4—416no—
693C2×C4—416no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4C7×#12314yes—
727C7#1402011yescharacteristic, direct product factor, Sylow
728C22—24no—
729C22—24no—
730C22—28no—
731C22—24no—
732C22—28no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—28no—
737C22—28no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—44no—
743C22—81no—
744C22—81no—
745C22—82no—
746C22—81no—
747C22—82no—
748C22—81no—
749C22C7×#38818yes—
750C22C2×C7×#11711yescharacteristic
751C22C2×C4×C7×D411yescharacteristic
752C22C2×C4×C7×D411yescharacteristic
753C22C4×C7×#4112yes—
754C22C7×#51812yes—
755C22C2×C7×#12111yescharacteristic
756C22C2×C7×#12311yescharacteristic
757C22C2×C7×#12311yescharacteristic
758C22C7×#52511yescharacteristic
759C22C2×C7×#12411yescharacteristic
760C22C2×C7×#12611yescharacteristic
761C22C7×#52912yes—
762C22C7×#53411yescharacteristic
763C22C7×#53511yescharacteristic
764C22C7×#53812yes—
765C22C7×#54612yes—
766C22C7×#54612yes—
767C22C7×#55112yes—
768C22C7×#55112yes—
769C22C7×#55312yes—
770C22C7×#55312yes—
771C22C7×#55312yes—
772C22C7×#55312yes—
773C4—24no—
774C4—44no—
775C4—42no—
776C4—44no—
777C4—42no—
778C4—44no—
779C4—44no—
780C4—81no—
781C4—81no—
782C2—28no—
783C2—82no—
784C2C2×C7×#38811yescharacteristic
785C2C4×C7×#12311yescharacteristic
786C2C7×#232111yescharacteristic
787C2C7×#235312yes—
788C2C7×#236412yes—
789C2C7×#241111yescharacteristic
790C2C7×#241211yescharacteristic
791C2C7×#244412yes—
792C2C7×#250411yescharacteristic
793C2C7×#251012yes—
794C2C7×#259111yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4×C7×C22⋊C4C2semidirect
5. C22×C7×#95C2semidirect
6. C7×#1443C2semidirect
7. C7×#1440C2semidirect
8. C7×#1437C2semidirect
9. C7×#1434C2semidirect
10. C7×C22⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
26. C7×#386C4semidirect
40. #14020C7direct (N × H)
91. C2×C7×C22⋊C4C2×C4semidirect
106. C7×#95C2×C4semidirect
110. C2×C4×C22⋊C4C2×C7semidirect
111. C22×#95C2×C7semidirect
112. #1443C2×C7semidirect
113. #1440C2×C7semidirect
114. #1437C2×C7semidirect
115. #1434C2×C7semidirect
116. C22⋊#95C2×C7semidirect
117. C22⋊#95C2×C7semidirect
240. #386C4×C7semidirect
420. C2×C22⋊C4C2×C4×C7semidirect
435. #95C2×C4×C7semidirect
727. C7#14020direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3862
C2×C4×C7×C22⋊C42
C22×C7×#952
C7×#14432
C7×#14402
C7×#14372
C7×#14342
C7×C22⋊#952
#140207