Finite Group Databasebeta

← C7×#16551 #13193767

Subgroups — C7×#16551 #13193767

Order 1792.

2470 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#394C212yesmaximal, complemented
2C2×C7×#394C211yesmaximal, characteristic, complemented
3C2×C7×#392C212yesmaximal, complemented
4C2×C7×#392C212yesmaximal, complemented
5C2×C7×#390C211yesmaximal, characteristic, complemented
6C7×#1441C211yesmaximal, characteristic, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1438C212yesmaximal, complemented
9C7×#1437C212yesmaximal, complemented
10C23×C7×D4C2212yes—
11C23×C7×D4C2211yescharacteristic
12C23×C7×D4C2212yes—
13C23×C7×D4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C22⋊C4C2212yes—
17C22×C7×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C42×C7C2211yescharacteristic
25C7×#394—24no—
26C7×#394—28no—
27C7×#392—28no—
28C7×#392—28no—
29C7×#390—24no—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2211yescharacteristic
36#16551C711yesmaximal, characteristic, direct product factor, Sylow
37C25×C7C2312yes—
38C25×C7C2312yes—
39C22×C7×D4—24no—
40C22×C7×D4—24no—
41C22×C7×D4—24no—
42C22×C7×D4—24no—
43C22×C7×D4—24no—
44C22×C7×D4—22no—
45C22×C7×D4—24no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—24no—
49C22×C7×D4—41no—
50C22×C7×D4—41no—
51C22×C7×D4—41no—
52C22×C7×D4—41no—
53C22×C7×D4—42no—
54C22×C7×D4—42no—
55C22×C7×D4—42no—
56C22×C7×D4—42no—
57C22×C7×D4—42no—
58C22×C7×D4—42no—
59C22×C7×D4—42no—
60C22×C7×D4—42no—
61C22×C7×D4—42no—
62C22×C7×D4—41no—
63C22×C7×D4—41no—
64C22×C7×D4D414yescomplemented
65C23×C4×C7C2312yes—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2312yes—
68C23×C4×C7C2312yes—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2312yes—
71C23×C4×C7C2311yescharacteristic
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—41no—
74C2×C7×C4⋊C4—41no—
75C2×C7×C4⋊C4—41no—
76C2×C7×C4⋊C4D414yescomplemented
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
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—42no—
93C2×C7×C22⋊C4—42no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4—42no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4—42no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4D418yescomplemented
101C2×C42×C7—22no—
102C2×C42×C7—41no—
103C2×C42×C7—41no—
104C7×#95—24no—
105C7×#95—24no—
106C7×#95—24no—
107C7×#95—22no—
108C7×#95—42no—
109C7×#95—41no—
110C2×#394C2×C711yescharacteristic, complemented
111C2×#394C2×C712yescomplemented
112C2×#392C2×C712yescomplemented
113C2×#392C2×C712yescomplemented
114C2×#390C2×C711yescharacteristic, complemented
115#1441C2×C711yescharacteristic, complemented
116#1440C2×C712yescomplemented
117#1438C2×C712yescomplemented
118#1437C2×C712yescomplemented
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—22no—
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—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×C7—22no—
146C24×C7—22no—
147C24×C7C2×D414yes—
148C24×C7C2×D414yes—
149C24×C7C2411yescharacteristic
150C2×C7×D4—28no—
151C2×C7×D4—44no—
152C2×C7×D4—44no—
153C2×C7×D4—48no—
154C2×C7×D4—48no—
155C2×C7×D4—48no—
156C2×C7×D4—48no—
157C2×C7×D4—48no—
158C2×C7×D4—44no—
159C2×C7×D4—44no—
160C2×C7×D4—44no—
161C2×C7×D4—44no—
162C2×C7×D4—48no—
163C2×C7×D4—44no—
164C2×C7×D4—48no—
165C2×C7×D4—48no—
166C2×C7×D4—44no—
167C2×C7×D4—48no—
168C2×C7×D4—48no—
169C2×C7×D4—48no—
170C2×C7×D4—48no—
171C2×C7×D4—48no—
172C2×C7×D4—48no—
173C2×C7×D4—44no—
174C2×C7×D4—48no—
175C2×C7×D4—48no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
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—22no—
189C22×C4×C7—21no—
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—22no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7C2×D414yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D414yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7#4114yes—
220C22×C4×C7#4112yes—
221C7×C4⋊C4—44no—
222C7×C4⋊C4—44no—
223C7×C22⋊C4—48no—
224C7×C22⋊C4—48no—
225C7×C22⋊C4—48no—
226C7×C22⋊C4—48no—
227C7×C22⋊C4—48no—
228C7×C22⋊C4—48no—
229C7×C22⋊C4—48no—
230C7×C22⋊C4—48no—
231C42×C7—44no—
232C23×D4C22×C711yescharacteristic
233C23×D4C22×C712yes—
234C23×D4C22×C712yes—
235C23×D4C22×C711yescharacteristic
236C22×C4⋊C4C22×C711yescharacteristic
237C22×C4⋊C4C22×C711yescharacteristic
238C22×C22⋊C4C22×C712yes—
239C22×C22⋊C4C22×C712yes—
240C22×C22⋊C4C22×C712yes—
241C22×C22⋊C4C22×C712yes—
242C22×C22⋊C4C22×C712yes—
243C22×C22⋊C4C22×C712yes—
244C22×C22⋊C4C22×C712yes—
245C22×C22⋊C4C22×C712yes—
246C22×C42C22×C711yescharacteristic
247#394—24no—
248#394—28no—
249#392—28no—
250#392—28no—
251#390—24no—
252C2×#95C22×C712yes—
253C2×#95C22×C712yes—
254C2×#95C22×C712yes—
255C2×#95C22×C711yescharacteristic
256C2×#95C22×C712yes—
257C2×#95C22×C711yescharacteristic
258C23×C7—24no—
259C23×C7—24no—
260C23×C7—24no—
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—24no—
271C23×C7—24no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—42no—
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—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—42no—
317C23×C7—42no—
318C23×C7—42no—
319C23×C7—42no—
320C23×C7—42no—
321C23×C7—42no—
322C23×C7—42no—
323C23×C7—42no—
324C23×C7—42no—
325C23×C7—42no—
326C23×C7—42no—
327C23×C7—42no—
328C23×C7C22×D411yescharacteristic
329C23×C7C22×D411yescharacteristic
330C23×C7C22×D412yes—
331C23×C7C2×#4111yescharacteristic
332C23×C7C2×#4112yes—
333C23×C7H(5,𝔽2)11yescharacteristic
334C23×C7H(5,𝔽2)11yescharacteristic
335C23×C7H(5,𝔽2)11yescharacteristic
336C23×C7H(5,𝔽2)11yescharacteristic
337C23×C7H(5,𝔽2)12yes—
338C23×C7H(5,𝔽2)12yes—
339C7×D4—416no—
340C7×D4—416no—
341C7×D4—432no—
342C7×D4—432no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—24no—
350C2×C4×C7—24no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—24no—
354C2×C4×C7—24no—
355C2×C4×C7—24no—
356C2×C4×C7—24no—
357C2×C4×C7—24no—
358C2×C4×C7—24no—
359C2×C4×C7—24no—
360C2×C4×C7—24no—
361C2×C4×C7—24no—
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—41no—
371C2×C4×C7—41no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—41no—
376C2×C4×C7—42no—
377C2×C4×C7—41no—
378C2×C4×C7—42no—
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—42no—
386C2×C4×C7—42no—
387C2×C4×C7#12114yes—
388C25C23×C712yes—
389C25C23×C712yes—
390C22×D4—24no—
391C22×D4—24no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4—22no—
396C22×D4—24no—
397C22×D4—22no—
398C22×D4—22no—
399C22×D4—24no—
400C22×D4—41no—
401C22×D4—41no—
402C22×D4—41no—
403C22×D4—41no—
404C22×D4—42no—
405C22×D4—42no—
406C22×D4—42no—
407C22×D4—42no—
408C22×D4—42no—
409C22×D4—42no—
410C22×D4—42no—
411C22×D4—42no—
412C22×D4—42no—
413C22×D4—41no—
414C22×D4—41no—
415C22×D4C7×D414yescomplemented
416C23×C4C23×C712yes—
417C23×C4C23×C711yescharacteristic
418C23×C4C23×C712yes—
419C23×C4C23×C711yescharacteristic
420C23×C4C23×C712yes—
421C23×C4C23×C712yes—
422C23×C4C23×C711yescharacteristic
423C2×C4⋊C4—24no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4C7×D414yescomplemented
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—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4C7×D418yescomplemented
452C2×C42—22no—
453C2×C42—41no—
454C2×C42—41no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—22no—
459#95—42no—
460#95—41no—
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—44no—
473C22×C7—44no—
474C22×C7—44no—
475C22×C7—82no—
476C22×C7—82no—
477C22×C7—82no—
478C22×C7—82no—
479C22×C7—82no—
480C22×C7—82no—
481C22×C7—82no—
482C22×C7—82no—
483C22×C7—82no—
484C22×C7—82no—
485C22×C7—82no—
486C22×C7—82no—
487C22×C7—82no—
488C22×C7—82no—
489C22×C7—82no—
490C22×C7—82no—
491C22×C7C2×#12111yescharacteristic
492C22×C7#53212yes—
493C22×C7#53411yescharacteristic
494C22×C7#53411yescharacteristic
495C22×C7#53411yescharacteristic
496C22×C7#53412yes—
497C22×C7#53511yescharacteristic
498C22×C7#53512yes—
499C22×C7#53811yescharacteristic
500C22×C7#53811yescharacteristic
501C22×C7#53812yes—
502C22×C7#54012yes—
503C22×C7#54012yes—
504C22×C7D4212yes—
505C22×C7D4211yescharacteristic
506C22×C7D4212yes—
507C22×C7#54612yes—
508C22×C7#54612yes—
509C22×C7#55012yes—
510C22×C7#55511yescharacteristic
511C22×C7#56011yescharacteristic
512C22×C7#56012yes—
513C22×C7H(3,𝔽4)11yescharacteristic
514C4×C7—24no—
515C4×C7—42no—
516C4×C7—42no—
517C4×C7—44no—
518C4×C7—44no—
519C4×C7—44no—
520C4×C7—82no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24C2×C7×D414yes—
550C24C2×C7×D414yes—
551C24C24×C711yescharacteristic
552C2×D4—28no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—48no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—48no—
565C2×D4—44no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—44no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—44no—
576C2×D4—48no—
577C2×D4—48no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4C2×C7×D414yes—
616C22×C4C2×C7×D412yes—
617C22×C4C2×C7×D414yes—
618C22×C4C2×C7×D412yes—
619C22×C4C2×C7×D412yes—
620C22×C4C2×C7×D412yes—
621C22×C4C7×#4114yes—
622C22×C4C7×#4112yes—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C42—44no—
634C2×C7—84no—
635C2×C7—84no—
636C2×C7#242812yes—
637C2×C7#255511yescharacteristic
638C2×C7#261711yescharacteristic
639C2×C7#266112yes—
640C2×C7#266911yescharacteristic
641C2×C7#267312yes—
642C2×C7#267812yes—
643C2×C7#267911yescharacteristic
644C2×C7#269911yescharacteristic
645C2×C7#273311yescharacteristic
646C2×C7#282811yescharacteristic
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
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—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23C22×C7×D411yescharacteristic
718C23C22×C7×D411yescharacteristic
719C23C22×C7×D412yes—
720C23C2×C7×#4111yescharacteristic
721C23C2×C7×#4112yes—
722C23C7×H(5,𝔽2)11yescharacteristic
723C23C7×H(5,𝔽2)11yescharacteristic
724C23C7×H(5,𝔽2)11yescharacteristic
725C23C7×H(5,𝔽2)11yescharacteristic
726C23C7×H(5,𝔽2)12yes—
727C23C7×H(5,𝔽2)12yes—
728D4—416no—
729D4—416no—
730D4—432no—
731D4—432no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4C7×#12114yes—
777C7#1655111yescharacteristic, direct product factor, Sylow
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22C2×C7×#12111yescharacteristic
809C22C7×#53212yes—
810C22C7×#53412yes—
811C22C7×#53411yescharacteristic
812C22C7×#53411yescharacteristic
813C22C7×#53411yescharacteristic
814C22C7×#53512yes—
815C22C7×#53511yescharacteristic
816C22C7×#53811yescharacteristic
817C22C7×#53812yes—
818C22C7×#53811yescharacteristic
819C22C7×#54012yes—
820C22C7×#54012yes—
821C22C7×D4212yes—
822C22C7×D4211yescharacteristic
823C22C7×D4212yes—
824C22C7×#54612yes—
825C22C7×#54612yes—
826C22C7×#55012yes—
827C22C7×#55511yescharacteristic
828C22C7×#56011yescharacteristic
829C22C7×#56012yes—
830C22C7×H(3,𝔽4)11yescharacteristic
831C4—24no—
832C4—42no—
833C4—42no—
834C4—44no—
835C4—44no—
836C4—44no—
837C4—82no—
838C2—84no—
839C2—84no—
840C2C7×#242812yes—
841C2C7×#255511yescharacteristic
842C2C7×#261711yescharacteristic
843C2C7×#266112yes—
844C2C7×#266911yescharacteristic
845C2C7×#267312yes—
846C2C7×#267812yes—
847C2C7×#267911yescharacteristic
848C2C7×#269911yescharacteristic
849C2C7×#273311yescharacteristic
850C2C7×#282811yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
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
2. C2×C7×#394C2semidirect
3. C2×C7×#392C2semidirect
4. C2×C7×#392C2semidirect
5. C2×C7×#390C2semidirect
6. C7×#1441C2semidirect
7. C7×#1440C2semidirect
8. C7×#1438C2semidirect
9. C7×#1437C2semidirect
36. #16551C7direct (N × H)
64. C22×C7×D4D4semidirect
76. C2×C7×C4⋊C4D4semidirect
100. C2×C7×C22⋊C4D4semidirect
110. C2×#394C2×C7semidirect
111. C2×#394C2×C7semidirect
112. C2×#392C2×C7semidirect
113. C2×#392C2×C7semidirect
114. C2×#390C2×C7semidirect
115. #1441C2×C7semidirect
116. #1440C2×C7semidirect
117. #1438C2×C7semidirect
118. #1437C2×C7semidirect
415. C22×D4C7×D4semidirect
427. C2×C4⋊C4C7×D4semidirect
451. C2×C22⋊C4C7×D4semidirect
777. C7#16551direct (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
C7×#14412
C7×#14402
C7×#14382
C7×#14372
#165517