Finite Group Databasebeta

← C7×#16516 #13193732

Subgroups — C7×#16516 #13193732

Order 1792.

2014 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#394C212yesmaximal, complemented
2C2×C7×#392C211yesmaximal, characteristic
3C2×C7×#390C211yesmaximal, characteristic, complemented
4C2×C7×#388C211yesmaximal, characteristic, complemented
5C2×C7×#382C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1439C212yesmaximal, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1438C211yesmaximal, characteristic, complemented
11C7×#1438C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C23×C7×D4C2212yes—
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C42×C7C2211yescharacteristic
27C7×#394—28no—
28C7×#392—24no—
29C7×#390—24no—
30C7×#388—24no—
31C7×#382—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2211yescharacteristic
40#16516C711yesmaximal, characteristic, direct product factor, Sylow
41C25×C7C2311yescharacteristic
42C25×C7C2312yes—
43C22×C7×D4—24no—
44C22×C7×D4—24no—
45C22×C7×D4—24no—
46C22×C7×D4—22no—
47C22×C7×D4—24no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—42no—
51C22×C7×D4—42no—
52C22×C7×D4—42no—
53C22×C7×D4—42no—
54C22×C7×D4—42no—
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2312yes—
57C23×C4×C7C2312yes—
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2312yes—
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—42no—
69C2×C7×C4⋊C4—42no—
70C2×C7×C4⋊C4—42no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C7×C22⋊C4—42no—
90C2×C7×C22⋊C4—42no—
91C2×C7×C22⋊C4—42no—
92C2×C7×C22⋊C4—42no—
93C2×C7×C22⋊C4—42no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4D414yescomplemented
97C2×C42×C7—22no—
98C2×C42×C7—22no—
99C2×C42×C7D414yescomplemented
100C7×#95—24no—
101C7×#95—22no—
102C7×#95—22no—
103C7×#95—22no—
104C7×#95—24no—
105C7×#95—42no—
106C7×#95—42no—
107C7×#95D414yes—
108C2×#394C2×C712yescomplemented
109C2×#392C2×C711yescharacteristic
110C2×#390C2×C711yescharacteristic, complemented
111C2×#388C2×C711yescharacteristic, complemented
112C2×#382C2×C711yescharacteristic, complemented
113#1442C2×C711yescharacteristic, complemented
114#1439C2×C711yescharacteristic, complemented
115#1439C2×C712yescomplemented
116#1439C2×C712yescomplemented
117#1438C2×C711yescharacteristic, complemented
118#1438C2×C712yescomplemented
119C24×C7—21no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—21no—
123C24×C7—22no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—21no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7—21no—
143C24×C7C2×D412yes—
144C24×C7#4114yes—
145C24×C7C2411yescharacteristic
146C2×C7×D4—28no—
147C2×C7×D4—48no—
148C2×C7×D4—48no—
149C2×C7×D4—48no—
150C2×C7×D4—48no—
151C2×C7×D4—44no—
152C2×C7×D4—48no—
153C2×C7×D4—48no—
154C2×C7×D4—48no—
155C2×C7×D4—48no—
156C2×C7×D4—48no—
157C2×C7×D4—44no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—21no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—21no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—21no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—21no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—21no—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D414yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D412yes—
206C22×C4×C7C2×D412yes—
207C22×C4×C7C2×D412yes—
208C22×C4×C7C2×D412yes—
209C22×C4×C7#4112yes—
210C22×C4×C7#4112yes—
211C7×C4⋊C4—48no—
212C7×C4⋊C4—44no—
213C7×C4⋊C4—44no—
214C7×C22⋊C4—28no—
215C7×C22⋊C4—48no—
216C7×C22⋊C4—48no—
217C7×C22⋊C4—44no—
218C7×C22⋊C4—48no—
219C7×C22⋊C4—48no—
220C7×C22⋊C4—48no—
221C7×C22⋊C4—44no—
222C7×C22⋊C4—48no—
223C42×C7—28no—
224C23×D4C22×C711yescharacteristic
225C23×D4C22×C712yes—
226C22×C4⋊C4C22×C712yes—
227C22×C4⋊C4C22×C711yescharacteristic
228C22×C4⋊C4C22×C711yescharacteristic
229C22×C22⋊C4C22×C711yescharacteristic
230C22×C22⋊C4C22×C712yes—
231C22×C22⋊C4C22×C712yes—
232C22×C22⋊C4C22×C711yescharacteristic
233C22×C22⋊C4C22×C712yes—
234C22×C22⋊C4C22×C712yes—
235C22×C22⋊C4C22×C711yescharacteristic
236C22×C22⋊C4C22×C712yes—
237C22×C22⋊C4C22×C712yes—
238C22×C42C22×C711yescharacteristic
239#394—28no—
240#392—24no—
241#390—24no—
242#388—24no—
243#382—24no—
244C2×#95C22×C712yes—
245C2×#95C22×C711yescharacteristic
246C2×#95C22×C712yes—
247C2×#95C22×C711yescharacteristic
248C2×#95C22×C711yescharacteristic
249C2×#95C22×C712yes—
250C2×#95C22×C712yes—
251C2×#95C22×C711yescharacteristic
252C23×C7—22no—
253C23×C7—24no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—22no—
258C23×C7—24no—
259C23×C7—24no—
260C23×C7—24no—
261C23×C7—22no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—41no—
265C23×C7—42no—
266C23×C7—42no—
267C23×C7—41no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—41no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—41no—
281C23×C7—42no—
282C23×C7—42no—
283C23×C7—42no—
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—42no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7—41no—
297C23×C7—42no—
298C23×C7—42no—
299C23×C7—42no—
300C23×C7—41no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7C22×D411yescharacteristic
311C23×C7C22×D411yescharacteristic
312C23×C7C22×D411yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C23×C7C2×#4112yes—
316C23×C7H(5,𝔽2)12yes—
317C23×C7H(5,𝔽2)12yes—
318C23×C7H(5,𝔽2)12yes—
319C23×C7H(5,𝔽2)11yescharacteristic
320C23×C72−1+411yescharacteristic
321C7×D4—416no—
322C7×D4—432no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—24no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—24no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
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—41no—
351C2×C4×C7—42no—
352C2×C4×C7—41no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—41no—
364C2×C4×C7—42no—
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—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7#12114yes—
375C2×C4×C7#12114yes—
376C25C23×C711yescharacteristic
377C25C23×C712yes—
378C22×D4—24no—
379C22×D4—24no—
380C22×D4—24no—
381C22×D4—22no—
382C22×D4—24no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C23×C4C23×C712yes—
391C23×C4C23×C712yes—
392C23×C4C23×C711yescharacteristic
393C23×C4C23×C711yescharacteristic
394C23×C4C23×C711yescharacteristic
395C23×C4C23×C711yescharacteristic
396C23×C4C23×C712yes—
397C23×C4C23×C711yescharacteristic
398C23×C4C23×C711yescharacteristic
399C2×C4⋊C4—24no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4C7×D414yescomplemented
432C2×C42—22no—
433C2×C42—22no—
434C2×C42C7×D414yescomplemented
435#95—24no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—24no—
440#95—42no—
441#95—42no—
442#95C7×D414yes—
443C22×C7—42no—
444C22×C7—44no—
445C22×C7—44no—
446C22×C7—44no—
447C22×C7—44no—
448C22×C7—42no—
449C22×C7—44no—
450C22×C7—44no—
451C22×C7—44no—
452C22×C7—44no—
453C22×C7—42no—
454C22×C7—44no—
455C22×C7—81no—
456C22×C7—82no—
457C22×C7—81no—
458C22×C7—82no—
459C22×C7—82no—
460C22×C7—81no—
461C22×C7—81no—
462C22×C7—82no—
463C22×C7—82no—
464C22×C7—82no—
465C22×C7—82no—
466C22×C7—82no—
467C22×C7—82no—
468C22×C7—82no—
469C22×C7C2×#12111yescharacteristic
470C22×C7C2×#12111yescharacteristic
471C22×C7#52511yescharacteristic
472C22×C7#53511yescharacteristic
473C22×C7#53511yescharacteristic
474C22×C7#53511yescharacteristic
475C22×C7#53512yes—
476C22×C7#53512yes—
477C22×C7#53711yescharacteristic
478C22×C7#53812yes—
479C22×C7#53912yes—
480C22×C7#54012yes—
481C22×C7#54012yes—
482C22×C7D4211yescharacteristic
483C22×C7#54612yes—
484C22×C7#54612yes—
485C22×C7#54711yescharacteristic
486C22×C7#54811yescharacteristic
487C22×C7#55112yes—
488C22×C7#55311yescharacteristic
489C22×C7#55312yes—
490C22×C7H(3,𝔽4)12yes—
491C22×C7#56212yes—
492C4×C7—24no—
493C4×C7—24no—
494C4×C7—42no—
495C4×C7—44no—
496C4×C7—42no—
497C4×C7—81no—
498C4×C7—81no—
499C4×C7—82no—
500C4×C7—82no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—22no—
506C24—21no—
507C24—21no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24C2×C7×D412yes—
526C24C7×#4114yes—
527C24C24×C711yescharacteristic
528C2×D4—28no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—44no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—48no—
537C2×D4—48no—
538C2×D4—48no—
539C2×D4—44no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
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—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4C2×C7×D412yes—
585C22×C4C2×C7×D414yes—
586C22×C4C2×C7×D412yes—
587C22×C4C2×C7×D412yes—
588C22×C4C2×C7×D412yes—
589C22×C4C2×C7×D412yes—
590C22×C4C2×C7×D412yes—
591C22×C4C7×#4112yes—
592C22×C4C7×#4112yes—
593C4⋊C4—48no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C22⋊C4—28no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—44no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—44no—
604C22⋊C4—48no—
605C42—28no—
606C2×C7—82no—
607C2×C7—84no—
608C2×C7#241111yescharacteristic
609C2×C7#241611yescharacteristic
610C2×C7#253511yescharacteristic
611C2×C7#261911yescharacteristic
612C2×C7#261911yescharacteristic
613C2×C7#263611yescharacteristic
614C2×C7#267012yes—
615C2×C7#270612yes—
616C2×C7#271112yes—
617C2×C7#275312yes—
618C2×C7#281911yescharacteristic
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—24no—
630C23—24no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—42no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C22×C7×D411yescharacteristic
678C23C22×C7×D411yescharacteristic
679C23C22×C7×D411yescharacteristic
680C23C2×C7×#4111yescharacteristic
681C23C2×C7×#4111yescharacteristic
682C23C2×C7×#4112yes—
683C23C7×H(5,𝔽2)12yes—
684C23C7×H(5,𝔽2)12yes—
685C23C7×H(5,𝔽2)12yes—
686C23C7×H(5,𝔽2)11yescharacteristic
687C23C7×2−1+411yescharacteristic
688D4—416no—
689D4—432no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4C7×#12114yes—
742C2×C4C7×#12114yes—
743C7#1651611yescharacteristic, direct product factor, Sylow
744C22—44no—
745C22—44no—
746C22—44no—
747C22—42no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—81no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—81no—
765C22—82no—
766C22—81no—
767C22—82no—
768C22—82no—
769C22—81no—
770C22C2×C7×#12111yescharacteristic
771C22C2×C7×#12111yescharacteristic
772C22C7×#52511yescharacteristic
773C22C7×#53511yescharacteristic
774C22C7×#53512yes—
775C22C7×#53512yes—
776C22C7×#53511yescharacteristic
777C22C7×#53511yescharacteristic
778C22C7×#53711yescharacteristic
779C22C7×#53812yes—
780C22C7×#53912yes—
781C22C7×#54012yes—
782C22C7×#54012yes—
783C22C7×D4211yescharacteristic
784C22C7×#54612yes—
785C22C7×#54612yes—
786C22C7×#54711yescharacteristic
787C22C7×#54811yescharacteristic
788C22C7×#55112yes—
789C22C7×#55311yescharacteristic
790C22C7×#55312yes—
791C22C7×H(3,𝔽4)12yes—
792C22C7×#56212yes—
793C4—24no—
794C4—24no—
795C4—44no—
796C4—42no—
797C4—42no—
798C4—82no—
799C4—81no—
800C4—81no—
801C4—82no—
802C2—84no—
803C2—82no—
804C2C7×#241111yescharacteristic
805C2C7×#241611yescharacteristic
806C2C7×#253511yescharacteristic
807C2C7×#261911yescharacteristic
808C2C7×#261911yescharacteristic
809C2C7×#263611yescharacteristic
810C2C7×#267012yes—
811C2C7×#270612yes—
812C2C7×#271112yes—
813C2C7×#275312yes—
814C2C7×#281911yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC2×C7×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#394C2semidirect
3. C2×C7×#390C2semidirect
4. C2×C7×#388C2semidirect
5. C2×C7×#382C2semidirect
6. C7×#1442C2semidirect
7. C7×#1439C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
10. C7×#1438C2semidirect
11. C7×#1438C2semidirect
40. #16516C7direct (N × H)
96. C2×C7×C22⋊C4D4semidirect
99. C2×C42×C7D4semidirect
108. C2×#394C2×C7semidirect
110. C2×#390C2×C7semidirect
111. C2×#388C2×C7semidirect
112. C2×#382C2×C7semidirect
113. #1442C2×C7semidirect
114. #1439C2×C7semidirect
115. #1439C2×C7semidirect
116. #1439C2×C7semidirect
117. #1438C2×C7semidirect
118. #1438C2×C7semidirect
431. C2×C22⋊C4C7×D4semidirect
434. C2×C42C7×D4semidirect
743. C7#16516direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3942
C2×C7×#3922
C2×C7×#3902
C2×C7×#3882
C2×C7×#3822
C7×#14422
C7×#14392
C7×#14382
#165167