Finite Group Databasebeta

← C7×#15160 #13192376

Subgroups — C7×#15160 #13192376

Order 1792.

2294 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#397C211yesmaximal, characteristic, complemented
2C2×C7×#394C212yesmaximal, complemented
3C2×C7×#392C211yesmaximal, characteristic
4C2×C7×#390C211yesmaximal, characteristic, complemented
5C2×C7×#386C212yesmaximal, complemented
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
7C7×#1445C211yesmaximal, characteristic, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1438C211yesmaximal, characteristic, complemented
10C7×#1437C212yesmaximal, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2212yes—
13C23×C7×D4C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2212yes—
25C22×C42×C7C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C7×#397—24no—
28C7×#394—28no—
29C7×#392—24no—
30C7×#390—24no—
31C7×#386—28no—
32C4×C7×C22⋊C4—24no—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2212yes—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2212yes—
41#15160C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2312yes—
43C25×C7C2311yescharacteristic
44C22×C7×D4—24no—
45C22×C7×D4—24no—
46C22×C7×D4—24no—
47C22×C7×D4—24no—
48C22×C7×D4—24no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—24no—
52C22×C7×D4—22no—
53C22×C7×D4—42no—
54C22×C7×D4—42no—
55C22×C7×D4—42no—
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—42no—
59C23×C4×C7—42no—
60C23×C4×C7D414yescomplemented
61C23×C4×C7C2312yes—
62C23×C4×C7C2312yes—
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2312yes—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—24no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—42no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—24no—
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—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4—42no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4D414yes—
99C2×C7×C22⋊C4D414yescomplemented
100C2×C42×C7—22no—
101C2×C42×C7—42no—
102C2×C42×C7—42no—
103C2×C42×C7D414yescomplemented
104C7×#95—22no—
105C7×#95—22no—
106C7×#95—24no—
107C7×#95—24no—
108C7×#95—22no—
109C7×#95—24no—
110C7×#95—22no—
111C7×#95—24no—
112C2×#397C2×C711yescharacteristic, complemented
113C2×#394C2×C712yescomplemented
114C2×#392C2×C711yescharacteristic
115C2×#390C2×C711yescharacteristic, complemented
116C2×#386C2×C712yescomplemented
117C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
118#1445C2×C711yescharacteristic, complemented
119#1439C2×C712yescomplemented
120#1438C2×C711yescharacteristic, complemented
121#1437C2×C712yescomplemented
122C4⋊#95C2×C711yescharacteristic, complemented
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
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—22no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7—22no—
143C24×C7—22no—
144C24×C7—22no—
145C24×C7C2×D412yes—
146C24×C7C2×D412yes—
147C24×C7C2×D412yes—
148C24×C7#4114yes—
149C24×C7C2411yescharacteristic
150C2×C7×D4—28no—
151C2×C7×D4—216no—
152C2×C7×D4—48no—
153C2×C7×D4—48no—
154C2×C7×D4—48no—
155C2×C7×D4—48no—
156C2×C7×D4—44no—
157C2×C7×D4—48no—
158C2×C7×D4—48no—
159C2×C7×D4—48no—
160C2×C7×D4—48no—
161C2×C7×D4—44no—
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—21no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—21no—
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—28no—
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—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—48no—
202C22×C4×C7—44no—
203C22×C4×C7—44no—
204C22×C4×C7—48no—
205C22×C4×C7C2×D412yes—
206C22×C4×C7C2×D412yes—
207C22×C4×C7C2×D412yes—
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7#4114yes—
215C22×C4×C7#4112yes—
216C22×C4×C7#4112yes—
217C22×C4×C7#4112yes—
218C7×C4⋊C4—48no—
219C7×C4⋊C4—44no—
220C7×C22⋊C4—28no—
221C7×C22⋊C4—28no—
222C7×C22⋊C4—48no—
223C7×C22⋊C4—48no—
224C7×C22⋊C4—48no—
225C7×C22⋊C4—48no—
226C7×C22⋊C4—48no—
227C7×C22⋊C4—48no—
228C42×C7—44no—
229C42×C7—44no—
230C23×D4C22×C712yes—
231C23×D4C22×C711yescharacteristic
232C24×C4C22×C711yescharacteristic
233C22×C4⋊C4C22×C711yescharacteristic
234C22×C4⋊C4C22×C712yes—
235C22×C22⋊C4C22×C712yes—
236C22×C22⋊C4C22×C712yes—
237C22×C22⋊C4C22×C712yes—
238C22×C22⋊C4C22×C712yes—
239C22×C22⋊C4C22×C712yes—
240C22×C22⋊C4C22×C711yescharacteristic
241C22×C22⋊C4C22×C711yescharacteristic
242C22×C22⋊C4C22×C712yes—
243C22×C42C22×C711yescharacteristic
244C22×C42C22×C711yescharacteristic
245#397—24no—
246#394—28no—
247#392—24no—
248#390—24no—
249#386—28no—
250C4×C22⋊C4—24no—
251C2×#95C22×C711yescharacteristic
252C2×#95C22×C712yes—
253C2×#95C22×C711yescharacteristic
254C2×#95C22×C712yes—
255C2×#95C22×C712yes—
256C2×#95C22×C711yescharacteristic
257C2×#95C22×C711yescharacteristic
258C2×#95C22×C712yes—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—24no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
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—41no—
279C23×C7—42no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
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—42no—
297C23×C7—42no—
298C23×C7—42no—
299C23×C7—42no—
300C23×C7—42no—
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×C7—42no—
311C23×C7—42no—
312C23×C7—42no—
313C23×C7—42no—
314C23×C7—42no—
315C23×C7—42no—
316C23×C7#12714yes—
317C23×C7C22×D411yescharacteristic
318C23×C7C22×D411yescharacteristic
319C23×C7C22×D411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C2×#4111yescharacteristic
322C23×C7C2×#4111yescharacteristic
323C23×C7C2×#4111yescharacteristic
324C23×C7C2×#4112yes—
325C23×C7C2×#4112yes—
326C23×C7H(5,𝔽2)12yes—
327C23×C7H(5,𝔽2)12yes—
328C7×D4—416no—
329C7×D4—432no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—24no—
336C2×C4×C7—22no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—24no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—24no—
346C2×C4×C7—24no—
347C2×C4×C7—24no—
348C2×C4×C7—24no—
349C2×C4×C7—24no—
350C2×C4×C7—24no—
351C2×C4×C7—416no—
352C2×C4×C7—41no—
353C2×C4×C7—42no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—42no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
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—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7#12114yes—
380C2×C4×C7#12114yes—
381C2×C4×C7#12114yes—
382C25C23×C712yes—
383C25C23×C711yescharacteristic
384C22×D4—24no—
385C22×D4—24no—
386C22×D4—24no—
387C22×D4—24no—
388C22×D4—24no—
389C22×D4—22no—
390C22×D4—22no—
391C22×D4—24no—
392C22×D4—22no—
393C22×D4—42no—
394C22×D4—42no—
395C22×D4—42no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4C7×D414yescomplemented
401C23×C4C23×C712yes—
402C23×C4C23×C712yes—
403C23×C4C23×C711yescharacteristic
404C23×C4C23×C711yescharacteristic
405C23×C4C23×C711yescharacteristic
406C23×C4C23×C712yes—
407C23×C4C23×C711yescharacteristic
408C23×C4C23×C711yescharacteristic
409C23×C4C23×C711yescharacteristic
410C2×C4⋊C4—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—42no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4C7×D414yes—
439C2×C22⋊C4C7×D414yescomplemented
440C2×C42—22no—
441C2×C42—42no—
442C2×C42—42no—
443C2×C42C7×D414yescomplemented
444#95—22no—
445#95—22no—
446#95—24no—
447#95—24no—
448#95—22no—
449#95—24no—
450#95—22no—
451#95—24no—
452C22×C7—24no—
453C22×C7—28no—
454C22×C7—44no—
455C22×C7—42no—
456C22×C7—42no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—42no—
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—82no—
471C22×C7—82no—
472C22×C7—82no—
473C22×C7—82no—
474C22×C7—82no—
475C22×C7—82no—
476C22×C7—82no—
477C22×C7—82no—
478C22×C7C2×#12111yescharacteristic
479C22×C7C2×#12111yescharacteristic
480C22×C7C2×#12111yescharacteristic
481C22×C7#52512yes—
482C22×C7#52511yescharacteristic
483C22×C7#52912yes—
484C22×C7C2×#12711yescharacteristic
485C22×C7#53211yescharacteristic
486C22×C7#53211yescharacteristic
487C22×C7#53211yescharacteristic
488C22×C7#53211yescharacteristic
489C22×C7#53412yes—
490C22×C7#53411yescharacteristic
491C22×C7#53511yescharacteristic
492C22×C7#53812yes—
493C22×C7#54612yes—
494C22×C7#54612yes—
495C22×C7#54612yes—
496C22×C7#54612yes—
497C22×C7#55112yes—
498C22×C7#55312yes—
499C22×C7#55312yes—
500C22×C7#55912yes—
501C4×C7—24no—
502C4×C7—24no—
503C4×C7—24no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—44no—
507C4×C7—42no—
508C4×C7—82no—
509C4×C7—82no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—22no—
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—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24C2×C7×D412yes—
533C24C2×C7×D412yes—
534C24C2×C7×D412yes—
535C24C7×#4114yes—
536C24C24×C711yescharacteristic
537C2×D4—28no—
538C2×D4—216no—
539C2×D4—48no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—44no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—44no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4C2×C7×D412yes—
593C22×C4C2×C7×D412yes—
594C22×C4C2×C7×D412yes—
595C22×C4C2×C7×D412yes—
596C22×C4C2×C7×D412yes—
597C22×C4C2×C7×D412yes—
598C22×C4C2×C7×D412yes—
599C22×C4C2×C7×D412yes—
600C22×C4C2×C7×D412yes—
601C22×C4C7×#4114yes—
602C22×C4C7×#4112yes—
603C22×C4C7×#4112yes—
604C22×C4C7×#4112yes—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C22⋊C4—28no—
608C22⋊C4—28no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C42—44no—
616C42—44no—
617C2×C7—44no—
618C2×C7—84no—
619C2×C7#239211yescharacteristic
620C2×C7#253411yescharacteristic
621C2×C7#253511yescharacteristic
622C2×C7#253912yes—
623C2×C7#254311yescharacteristic
624C2×C7#254411yescharacteristic
625C2×C7#255712yes—
626C2×C7#255912yes—
627C2×C7#260212yes—
628C2×C7#261711yescharacteristic
629C2×C7#285611yescharacteristic
630C23—22no—
631C23—22no—
632C23—22no—
633C23—24no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—41no—
650C23—42no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
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—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23C7×#12714yes—
688C23C22×C7×D411yescharacteristic
689C23C22×C7×D411yescharacteristic
690C23C22×C7×D411yescharacteristic
691C23C22×C7×D411yescharacteristic
692C23C2×C7×#4111yescharacteristic
693C23C2×C7×#4111yescharacteristic
694C23C2×C7×#4111yescharacteristic
695C23C2×C7×#4112yes—
696C23C2×C7×#4112yes—
697C23C7×H(5,𝔽2)12yes—
698C23C7×H(5,𝔽2)12yes—
699D4—416no—
700D4—432no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—416no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
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×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4C7×#12114yes—
751C2×C4C7×#12114yes—
752C2×C4C7×#12114yes—
753C7#1516011yescharacteristic, direct product factor, Sylow
754C22—28no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22C2×C7×#12111yescharacteristic
781C22C2×C7×#12111yescharacteristic
782C22C2×C7×#12111yescharacteristic
783C22C7×#52511yescharacteristic
784C22C7×#52512yes—
785C22C7×#52912yes—
786C22C2×C7×#12711yescharacteristic
787C22C7×#53211yescharacteristic
788C22C7×#53211yescharacteristic
789C22C7×#53211yescharacteristic
790C22C7×#53211yescharacteristic
791C22C7×#53411yescharacteristic
792C22C7×#53412yes—
793C22C7×#53511yescharacteristic
794C22C7×#53812yes—
795C22C7×#54612yes—
796C22C7×#54612yes—
797C22C7×#54612yes—
798C22C7×#54612yes—
799C22C7×#55112yes—
800C22C7×#55312yes—
801C22C7×#55312yes—
802C22C7×#55912yes—
803C4—24no—
804C4—24no—
805C4—24no—
806C4—42no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—82no—
811C4—82no—
812C2—44no—
813C2—84no—
814C2C7×#239211yescharacteristic
815C2C7×#253411yescharacteristic
816C2C7×#253511yescharacteristic
817C2C7×#253912yes—
818C2C7×#254311yescharacteristic
819C2C7×#254411yescharacteristic
820C2C7×#255712yes—
821C2C7×#255912yes—
822C2C7×#260212yes—
823C2C7×#261711yescharacteristic
824C2C7×#285611yescharacteristic
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×#397C2semidirect
2. C2×C7×#394C2semidirect
4. C2×C7×#390C2semidirect
5. C2×C7×#386C2semidirect
6. C2×C4×C7×C22⋊C4C2semidirect
7. C7×#1445C2semidirect
8. C7×#1439C2semidirect
9. C7×#1438C2semidirect
10. C7×#1437C2semidirect
11. C7×C4⋊#95C2semidirect
41. #15160C7direct (N × H)
60. C23×C4×C7D4semidirect
99. C2×C7×C22⋊C4D4semidirect
103. C2×C42×C7D4semidirect
112. C2×#397C2×C7semidirect
113. C2×#394C2×C7semidirect
115. C2×#390C2×C7semidirect
116. C2×#386C2×C7semidirect
117. C2×C4×C22⋊C4C2×C7semidirect
118. #1445C2×C7semidirect
119. #1439C2×C7semidirect
120. #1438C2×C7semidirect
121. #1437C2×C7semidirect
122. C4⋊#95C2×C7semidirect
400. C23×C4C7×D4semidirect
439. C2×C22⋊C4C7×D4semidirect
443. C2×C42C7×D4semidirect
753. C7#15160direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3972
C2×C7×#3942
C2×C7×#3922
C2×C7×#3902
C2×C7×#3862
C2×C4×C7×C22⋊C42
C7×#14452
C7×#14392
C7×#14382
C7×#14372
C7×C4⋊#952
#151607