Finite Group Databasebeta

← C7×#15159 #13192375

Subgroups — C7×#15159 #13192375

Order 1792.

2578 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic, complemented
2C2×C7×#394C211yesmaximal, characteristic, complemented
3C2×C7×#392C211yesmaximal, characteristic
4C2×C7×#388C211yesmaximal, characteristic, complemented
5C2×C7×#386C212yesmaximal, complemented
6C7×#1441C211yesmaximal, characteristic, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1438C212yesmaximal, complemented
10C7×#1434C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C23×C7×D4C2212yes—
14C24×C4×C7C2212yes—
15C2×C4×C7×D4—28no—
16C2×C4×C7×D4—24no—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2212yes—
27C22×C42×C7C2211yescharacteristic
28C7×#394—24no—
29C7×#392—24no—
30C7×#388—24no—
31C7×#386—28no—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2212yes—
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41#15159C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2311yescharacteristic
43C25×C7C2312yes—
44C22×C7×D4—24no—
45C22×C7×D4—24no—
46C22×C7×D4—24no—
47C22×C7×D4—24no—
48C22×C7×D4—24no—
49C22×C7×D4—24no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—24no—
53C22×C7×D4—42no—
54C22×C7×D4—42no—
55C22×C7×D4D414yes—
56C23×C4×C7—24no—
57C23×C4×C7—24no—
58C23×C4×C7—42no—
59C23×C4×C7—42no—
60C23×C4×C7—42no—
61C23×C4×C7—42no—
62C23×C4×C7D418yescomplemented
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2312yes—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2312yes—
68C23×C4×C7C2312yes—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C4×C7×D4—232no—
73C2×C7×C4⋊C4—24no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—24no—
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—24no—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—24no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4—42no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4—42no—
101C2×C42×C7—24no—
102C2×C42×C7D414yescomplemented
103C7×#95—24no—
104C7×#95—24no—
105C7×#95—22no—
106C7×#95—22no—
107C7×#95—22no—
108C7×#95—22no—
109C7×#95—24no—
110C7×#95—42no—
111C7×#95—42no—
112C22×C4×D4C2×C711yescharacteristic, complemented
113C2×#394C2×C711yescharacteristic, complemented
114C2×#392C2×C711yescharacteristic
115C2×#388C2×C711yescharacteristic, complemented
116C2×#386C2×C712yescomplemented
117#1441C2×C711yescharacteristic, complemented
118#1440C2×C712yescomplemented
119#1439C2×C711yescharacteristic, complemented
120#1438C2×C712yescomplemented
121#1434C2×C711yescharacteristic, complemented
122C22⋊#95C2×C712yescomplemented
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
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—21no—
136C24×C7—22no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7—21no—
143C24×C7—22no—
144C24×C7—21no—
145C24×C7C2×D414yes—
146C24×C7C2×D414yes—
147C24×C7#4112yes—
148C24×C7#4114yes—
149C24×C7C2411yescharacteristic
150C2×C7×D4—28no—
151C2×C7×D4—28no—
152C2×C7×D4—216no—
153C2×C7×D4—216no—
154C2×C7×D4—216no—
155C2×C7×D4—28no—
156C2×C7×D4—48no—
157C2×C7×D4—48no—
158C2×C7×D4—48no—
159C2×C7×D4—48no—
160C2×C7×D4—48no—
161C2×C7×D4—48no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—21no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—22no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—21no—
182C22×C4×C7—22no—
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—216no—
190C22×C4×C7—21no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—21no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—21no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—48no—
208C22×C4×C7—48no—
209C22×C4×C7—48no—
210C22×C4×C7—48no—
211C22×C4×C7—48no—
212C22×C4×C7—48no—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×D414yes—
215C22×C4×C7C2×D414yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7#4114yes—
220C22×C4×C7#4112yes—
221C22×C4×C7#4112yes—
222C7×C4⋊C4—28no—
223C7×C4⋊C4—44no—
224C7×C22⋊C4—28no—
225C7×C22⋊C4—216no—
226C7×C22⋊C4—48no—
227C7×C22⋊C4—48no—
228C7×C22⋊C4—48no—
229C7×C22⋊C4—48no—
230C7×C22⋊C4—44no—
231C7×C22⋊C4—44no—
232C42×C7—28no—
233C23×D4C22×C711yescharacteristic
234C23×D4C22×C712yes—
235C24×C4C22×C712yes—
236C2×C4×D4—28no—
237C2×C4×D4—24no—
238C22×C4⋊C4C22×C711yescharacteristic
239C22×C4⋊C4C22×C711yescharacteristic
240C22×C22⋊C4C22×C711yescharacteristic
241C22×C22⋊C4C22×C712yes—
242C22×C22⋊C4C22×C712yes—
243C22×C22⋊C4C22×C711yescharacteristic
244C22×C22⋊C4C22×C711yescharacteristic
245C22×C22⋊C4C22×C712yes—
246C22×C22⋊C4C22×C712yes—
247C22×C22⋊C4C22×C712yes—
248C22×C42C22×C711yescharacteristic
249#394—24no—
250#392—24no—
251#388—24no—
252#386—28no—
253C2×#95C22×C711yescharacteristic
254C2×#95C22×C711yescharacteristic
255C2×#95C22×C711yescharacteristic
256C2×#95C22×C712yes—
257C2×#95C22×C712yes—
258C2×#95C22×C711yescharacteristic
259C2×#95C22×C712yes—
260C2×#95C22×C712yes—
261C2×#95C22×C712yes—
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—24no—
271C23×C7—24no—
272C23×C7—24no—
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—24no—
276C23×C7—24no—
277C23×C7—24no—
278C23×C7—24no—
279C23×C7—24no—
280C23×C7—22no—
281C23×C7—24no—
282C23×C7—22no—
283C23×C7—24no—
284C23×C7—22no—
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—42no—
297C23×C7—42no—
298C23×C7—42no—
299C23×C7—42no—
300C23×C7—42no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—42no—
304C23×C7—41no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—41no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—42no—
313C23×C7—41no—
314C23×C7—42no—
315C23×C7—42no—
316C23×C7—42no—
317C23×C7—41no—
318C23×C7—42no—
319C23×C7#12118yes—
320C23×C7C22×D412yes—
321C23×C7C22×D411yescharacteristic
322C23×C7C22×D411yescharacteristic
323C23×C7C2×#4112yes—
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4112yes—
327C23×C7C2×#4111yescharacteristic
328C23×C7H(5,𝔽2)11yescharacteristic
329C23×C7H(5,𝔽2)12yes—
330C23×C7H(5,𝔽2)11yescharacteristic
331C7×D4—232no—
332C7×D4—432no—
333C2×C4×C7—22no—
334C2×C4×C7—24no—
335C2×C4×C7—22no—
336C2×C4×C7—24no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—24no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—24no—
346C2×C4×C7—22no—
347C2×C4×C7—24no—
348C2×C4×C7—24no—
349C2×C4×C7—22no—
350C2×C4×C7—24no—
351C2×C4×C7—24no—
352C2×C4×C7—22no—
353C2×C4×C7—432no—
354C2×C4×C7—41no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—41no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—41no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—41no—
377C2×C4×C7—42no—
378C2×C4×C7—41no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7#12014yes—
386C2×C4×C7#12114yes—
387C25C23×C711yescharacteristic
388C25C23×C712yes—
389C22×D4—24no—
390C22×D4—24no—
391C22×D4—24no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—24no—
398C22×D4—42no—
399C22×D4—42no—
400C22×D4C7×D414yes—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4C7×D418yescomplemented
408C23×C4C23×C711yescharacteristic
409C23×C4C23×C711yescharacteristic
410C23×C4C23×C712yes—
411C23×C4C23×C711yescharacteristic
412C23×C4C23×C712yes—
413C23×C4C23×C711yescharacteristic
414C23×C4C23×C712yes—
415C23×C4C23×C711yescharacteristic
416C23×C4C23×C711yescharacteristic
417C4×D4—232no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C42—24no—
447C2×C42C7×D414yescomplemented
448#95—24no—
449#95—24no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—24no—
455#95—42no—
456#95—42no—
457C22×C7—28no—
458C22×C7—28no—
459C22×C7—28no—
460C22×C7—44no—
461C22×C7—44no—
462C22×C7—44no—
463C22×C7—44no—
464C22×C7—44no—
465C22×C7—44no—
466C22×C7—44no—
467C22×C7—44no—
468C22×C7—44no—
469C22×C7—44no—
470C22×C7—44no—
471C22×C7—44no—
472C22×C7—42no—
473C22×C7—44no—
474C22×C7—42no—
475C22×C7—44no—
476C22×C7—42no—
477C22×C7—81no—
478C22×C7—82no—
479C22×C7—81no—
480C22×C7—81no—
481C22×C7—82no—
482C22×C7—81no—
483C22×C7C2×#12011yescharacteristic
484C22×C7C2×#12112yes—
485C22×C7C2×#12111yescharacteristic
486C22×C7#52511yescharacteristic
487C22×C7#52512yes—
488C22×C7#52511yescharacteristic
489C22×C7#52512yes—
490C22×C7#53212yes—
491C22×C7#53211yescharacteristic
492C22×C7#53412yes—
493C22×C7#53412yes—
494C22×C7#53511yescharacteristic
495C22×C7#53511yescharacteristic
496C22×C7#54611yescharacteristic
497C22×C7#54612yes—
498C22×C7#54611yescharacteristic
499C22×C7#55112yes—
500C22×C7#55112yes—
501C22×C7#55312yes—
502C22×C7#55311yescharacteristic
503C22×C7#55312yes—
504C22×C7#55311yescharacteristic
505C22×C7#55912yes—
506C4×C7—24no—
507C4×C7—24no—
508C4×C7—44no—
509C4×C7—42no—
510C4×C7—44no—
511C4×C7—42no—
512C4×C7—81no—
513C4×C7—82no—
514C4×C7—81no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—21no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—22no—
536C24—21no—
537C24C2×C7×D414yes—
538C24C2×C7×D414yes—
539C24C7×#4112yes—
540C24C7×#4114yes—
541C24C24×C711yescharacteristic
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—216no—
545C2×D4—216no—
546C2×D4—216no—
547C2×D4—28no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—48no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—216no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4C2×C7×D412yes—
606C22×C4C2×C7×D414yes—
607C22×C4C2×C7×D414yes—
608C22×C4C2×C7×D412yes—
609C22×C4C2×C7×D412yes—
610C22×C4C2×C7×D412yes—
611C22×C4C7×#4114yes—
612C22×C4C7×#4112yes—
613C22×C4C7×#4112yes—
614C4⋊C4—28no—
615C4⋊C4—44no—
616C22⋊C4—216no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C42—28no—
625C2×C7—48no—
626C2×C7—82no—
627C2×C7#238811yescharacteristic
628C2×C7#253412yes—
629C2×C7#253511yescharacteristic
630C2×C7#254312yes—
631C2×C7#254411yescharacteristic
632C2×C7#259811yescharacteristic
633C2×C7#260012yes—
634C2×C7#260212yes—
635C2×C7#260311yescharacteristic
636C2×C7#261311yescharacteristic
637C2×C7#284711yescharacteristic
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23C7×#12118yes—
696C23C22×C7×D412yes—
697C23C22×C7×D411yescharacteristic
698C23C22×C7×D411yescharacteristic
699C23C2×C7×#4112yes—
700C23C2×C7×#4111yescharacteristic
701C23C2×C7×#4111yescharacteristic
702C23C2×C7×#4112yes—
703C23C2×C7×#4111yescharacteristic
704C23C7×H(5,𝔽2)11yescharacteristic
705C23C7×H(5,𝔽2)12yes—
706C23C7×H(5,𝔽2)11yescharacteristic
707D4—232no—
708D4—432no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—432no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4C7×#12014yes—
762C2×C4C7×#12114yes—
763C7#1515911yescharacteristic, direct product factor, Sylow
764C22—28no—
765C22—28no—
766C22—28no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—42no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—82no—
785C22—81no—
786C22—81no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22C2×C7×#12011yescharacteristic
791C22C2×C7×#12112yes—
792C22C2×C7×#12111yescharacteristic
793C22C7×#52512yes—
794C22C7×#52511yescharacteristic
795C22C7×#52511yescharacteristic
796C22C7×#52512yes—
797C22C7×#53212yes—
798C22C7×#53211yescharacteristic
799C22C7×#53412yes—
800C22C7×#53412yes—
801C22C7×#53511yescharacteristic
802C22C7×#53511yescharacteristic
803C22C7×#54611yescharacteristic
804C22C7×#54612yes—
805C22C7×#54611yescharacteristic
806C22C7×#55112yes—
807C22C7×#55112yes—
808C22C7×#55311yescharacteristic
809C22C7×#55311yescharacteristic
810C22C7×#55312yes—
811C22C7×#55312yes—
812C22C7×#55912yes—
813C4—24no—
814C4—24no—
815C4—42no—
816C4—44no—
817C4—42no—
818C4—44no—
819C4—82no—
820C4—81no—
821C4—81no—
822C2—48no—
823C2—82no—
824C2C7×#238811yescharacteristic
825C2C7×#253412yes—
826C2C7×#253511yescharacteristic
827C2C7×#254312yes—
828C2C7×#254411yescharacteristic
829C2C7×#259811yescharacteristic
830C2C7×#260012yes—
831C2C7×#260212yes—
832C2C7×#260311yescharacteristic
833C2C7×#261311yescharacteristic
834C2C7×#284711yescharacteristic
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. C22×C4×C7×D4C2semidirect
2. C2×C7×#394C2semidirect
4. C2×C7×#388C2semidirect
5. C2×C7×#386C2semidirect
6. C7×#1441C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×#1438C2semidirect
10. C7×#1434C2semidirect
11. C7×C22⋊#95C2semidirect
41. #15159C7direct (N × H)
62. C23×C4×C7D4semidirect
102. C2×C42×C7D4semidirect
112. C22×C4×D4C2×C7semidirect
113. C2×#394C2×C7semidirect
115. C2×#388C2×C7semidirect
116. C2×#386C2×C7semidirect
117. #1441C2×C7semidirect
118. #1440C2×C7semidirect
119. #1439C2×C7semidirect
120. #1438C2×C7semidirect
121. #1434C2×C7semidirect
122. C22⋊#95C2×C7semidirect
407. C23×C4C7×D4semidirect
447. C2×C42C7×D4semidirect
763. C7#15159direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C2×C7×#3942
C2×C7×#3922
C2×C7×#3882
C2×C7×#3862
C7×#14412
C7×#14402
C7×#14392
C7×#14382
C7×#14342
C7×C22⋊#952
#151597