Finite Group Databasebeta

← C7×#16500 #13193716

Subgroups — C7×#16500 #13193716

Order 1792.

2698 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic, complemented
2C2×C7×#397C211yesmaximal, characteristic, complemented
3C2×C7×#392C212yesmaximal, complemented
4C2×C7×#392C211yesmaximal, characteristic, complemented
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C7×#1445C211yesmaximal, characteristic, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1438C212yesmaximal, complemented
9C7×#1438C212yesmaximal, complemented
10C7×#1438C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2212yes—
13C23×C7×D4C2212yes—
14C23×C7×D4C2211yescharacteristic
15C23×C7×D4C2211yescharacteristic
16C24×C4×C7C2211yescharacteristic
17C2×C7×#121—24no—
18C2×C7×#121—24no—
19C2×C7×#121—24no—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2212yes—
30C7×#397—24no—
31C7×#392—24no—
32C7×#392—28no—
33C7×#386—24no—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42#16500C711yesmaximal, characteristic, direct product factor, Sylow
43C25×C7C2311yescharacteristic
44C25×C7C2312yes—
45C25×C7C2311yescharacteristic
46C22×C7×D4—24no—
47C22×C7×D4—24no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—24no—
51C22×C7×D4—24no—
52C22×C7×D4—24no—
53C22×C7×D4—24no—
54C22×C7×D4—24no—
55C22×C7×D4—22no—
56C22×C7×D4—22no—
57C22×C7×D4—24no—
58C22×C7×D4—42no—
59C22×C7×D4—42no—
60C22×C7×D4—42no—
61C22×C7×D4—42no—
62C22×C7×D4—42no—
63C22×C7×D4—42no—
64C22×C7×D4—42no—
65C22×C7×D4—42no—
66C22×C7×D4—42no—
67C22×C7×D4—42no—
68C22×C7×D4D414yescomplemented
69C22×C7×D4D414yescomplemented
70C23×C4×C7—22no—
71C23×C4×C7—22no—
72C23×C4×C7—42no—
73C23×C4×C7—42no—
74C23×C4×C7D414yescomplemented
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2312yes—
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2312yes—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2312yes—
82C23×C4×C7C2311yescharacteristic
83C7×#121—232no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4D414yescomplemented
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—24no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—42no—
103C2×C7×C22⋊C4—42no—
104C2×C7×C22⋊C4—42no—
105C2×C7×C22⋊C4—42no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4—42no—
108C2×C7×C22⋊C4—42no—
109C2×C7×C22⋊C4—42no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4—42no—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—24no—
115C7×#95—22no—
116C7×#95—24no—
117C7×#95—22no—
118C7×#95—42no—
119C7×#95—42no—
120C22×#121C2×C711yescharacteristic, complemented
121C2×#397C2×C711yescharacteristic, complemented
122C2×#392C2×C711yescharacteristic, complemented
123C2×#392C2×C712yescomplemented
124C2×#386C2×C711yescharacteristic, complemented
125#1445C2×C711yescharacteristic, complemented
126#1440C2×C712yescomplemented
127#1438C2×C712yescomplemented
128#1438C2×C712yescomplemented
129#1438C2×C711yescharacteristic, complemented
130C22⋊#95C2×C711yescharacteristic, complemented
131C24×C7—21no—
132C24×C7—21no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7—21no—
141C24×C7—22no—
142C24×C7—22no—
143C24×C7—21no—
144C24×C7—22no—
145C24×C7—22no—
146C24×C7—21no—
147C24×C7—22no—
148C24×C7—22no—
149C24×C7—22no—
150C24×C7—21no—
151C24×C7—22no—
152C24×C7—22no—
153C24×C7—22no—
154C24×C7—22no—
155C24×C7—22no—
156C24×C7—22no—
157C24×C7—22no—
158C24×C7—22no—
159C24×C7—22no—
160C24×C7—22no—
161C24×C7—22no—
162C24×C7—21no—
163C24×C7C2×D414yes—
164C24×C7C2×D412yes—
165C24×C7C2×D412yes—
166C24×C7C2×D412yes—
167C24×C7#4112yes—
168C24×C7C2411yescharacteristic
169C2×C7×D4—216no—
170C2×C7×D4—28no—
171C2×C7×D4—28no—
172C2×C7×D4—48no—
173C2×C7×D4—48no—
174C2×C7×D4—48no—
175C2×C7×D4—48no—
176C2×C7×D4—48no—
177C2×C7×D4—48no—
178C2×C7×D4—44no—
179C2×C7×D4—44no—
180C2×C7×D4—48no—
181C2×C7×D4—48no—
182C2×C7×D4—48no—
183C2×C7×D4—48no—
184C2×C7×D4—48no—
185C2×C7×D4—44no—
186C2×C7×D4—48no—
187C2×C7×D4—48no—
188C2×C7×D4—44no—
189C2×C7×D4—48no—
190C2×C7×D4—48no—
191C2×C7×D4—48no—
192C2×C7×D4—48no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—21no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—21no—
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—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—28no—
216C22×C4×C7—21no—
217C22×C4×C7—22no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—21no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—21no—
232C22×C4×C7—22no—
233C22×C4×C7—44no—
234C22×C4×C7—44no—
235C22×C4×C7—48no—
236C22×C4×C7—48no—
237C22×C4×C7C2×D412yes—
238C22×C4×C7C2×D412yes—
239C22×C4×C7C2×D414yes—
240C22×C4×C7C2×D412yes—
241C22×C4×C7C2×D412yes—
242C22×C4×C7C2×D412yes—
243C22×C4×C7#4114yes—
244C7×C4⋊C4—28no—
245C7×C22⋊C4—216no—
246C7×C22⋊C4—48no—
247C7×C22⋊C4—48no—
248C7×C22⋊C4—48no—
249C7×C22⋊C4—44no—
250C7×C22⋊C4—48no—
251C7×C22⋊C4—44no—
252C7×C22⋊C4—48no—
253C7×C22⋊C4—44no—
254C23×D4C22×C712yes—
255C23×D4C22×C712yes—
256C23×D4C22×C711yescharacteristic
257C23×D4C22×C711yescharacteristic
258C24×C4C22×C711yescharacteristic
259C2×#121—24no—
260C2×#121—24no—
261C2×#121—24no—
262C22×C4⋊C4C22×C711yescharacteristic
263C22×C22⋊C4C22×C711yescharacteristic
264C22×C22⋊C4C22×C712yes—
265C22×C22⋊C4C22×C712yes—
266C22×C22⋊C4C22×C712yes—
267C22×C22⋊C4C22×C712yes—
268C22×C22⋊C4C22×C712yes—
269C22×C22⋊C4C22×C711yescharacteristic
270C22×C22⋊C4C22×C711yescharacteristic
271C22×C22⋊C4C22×C712yes—
272#397—24no—
273#392—24no—
274#392—28no—
275#386—24no—
276C2×#95C22×C711yescharacteristic
277C2×#95C22×C712yes—
278C2×#95C22×C711yescharacteristic
279C2×#95C22×C712yes—
280C2×#95C22×C711yescharacteristic
281C2×#95C22×C711yescharacteristic
282C2×#95C22×C712yes—
283C2×#95C22×C712yes—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—24no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—24no—
292C23×C7—22no—
293C23×C7—22no—
294C23×C7—24no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—22no—
300C23×C7—24no—
301C23×C7—24no—
302C23×C7—24no—
303C23×C7—22no—
304C23×C7—24no—
305C23×C7—22no—
306C23×C7—24no—
307C23×C7—24no—
308C23×C7—24no—
309C23×C7—24no—
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—41no—
319C23×C7—42no—
320C23×C7—42no—
321C23×C7—41no—
322C23×C7—42no—
323C23×C7—41no—
324C23×C7—42no—
325C23×C7—42no—
326C23×C7—41no—
327C23×C7—42no—
328C23×C7—42no—
329C23×C7—42no—
330C23×C7—42no—
331C23×C7—41no—
332C23×C7—42no—
333C23×C7—41no—
334C23×C7—42no—
335C23×C7—42no—
336C23×C7—42no—
337C23×C7—42no—
338C23×C7—42no—
339C23×C7—42no—
340C23×C7—42no—
341C23×C7—42no—
342C23×C7—42no—
343C23×C7—42no—
344C23×C7—42no—
345C23×C7—42no—
346C23×C7—42no—
347C23×C7—42no—
348C23×C7—42no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7#12114yes—
365C23×C7C22×D411yescharacteristic
366C23×C7C22×D411yescharacteristic
367C23×C7C22×D411yescharacteristic
368C23×C7C22×D411yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4112yes—
371C23×C7H(5,𝔽2)12yes—
372C23×C7H(5,𝔽2)12yes—
373C23×C7H(5,𝔽2)12yes—
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C7H(5,𝔽2)11yescharacteristic
376C7×D4—416no—
377C7×D4—416no—
378C7×D4—432no—
379C7×D4—432no—
380C2×C4×C7—22no—
381C2×C4×C7—24no—
382C2×C4×C7—22no—
383C2×C4×C7—24no—
384C2×C4×C7—22no—
385C2×C4×C7—24no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—24no—
389C2×C4×C7—22no—
390C2×C4×C7—24no—
391C2×C4×C7—24no—
392C2×C4×C7—24no—
393C2×C4×C7—24no—
394C2×C4×C7—24no—
395C2×C4×C7—416no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—41no—
399C2×C4×C7—42no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—41no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
407C2×C4×C7—42no—
408C2×C4×C7—42no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—42no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—42no—
416C2×C4×C7—41no—
417C2×C4×C7—42no—
418C2×C4×C7—42no—
419C2×C4×C7—42no—
420C2×C4×C7—42no—
421C2×C4×C7—42no—
422C2×C4×C7—42no—
423C2×C4×C7—42no—
424C2×C4×C7—42no—
425C2×C4×C7—42no—
426C2×C4×C7#12014yes—
427C25C23×C711yescharacteristic
428C25C23×C712yes—
429C25C23×C711yescharacteristic
430C22×D4—24no—
431C22×D4—24no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—24no—
435C22×D4—24no—
436C22×D4—24no—
437C22×D4—24no—
438C22×D4—24no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—24no—
442C22×D4—42no—
443C22×D4—42no—
444C22×D4—42no—
445C22×D4—42no—
446C22×D4—42no—
447C22×D4—42no—
448C22×D4—42no—
449C22×D4—42no—
450C22×D4—42no—
451C22×D4—42no—
452C22×D4C7×D414yescomplemented
453C22×D4C7×D414yescomplemented
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4C7×D414yescomplemented
459C23×C4C23×C711yescharacteristic
460C23×C4C23×C712yes—
461C23×C4C23×C711yescharacteristic
462C23×C4C23×C711yescharacteristic
463C23×C4C23×C712yes—
464C23×C4C23×C711yescharacteristic
465C23×C4C23×C712yes—
466C23×C4C23×C711yescharacteristic
467#121—232no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4C7×D414yescomplemented
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496#95—22no—
497#95—22no—
498#95—24no—
499#95—22no—
500#95—24no—
501#95—22no—
502#95—42no—
503#95—42no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—24no—
507C22×C7—42no—
508C22×C7—42no—
509C22×C7—44no—
510C22×C7—44no—
511C22×C7—42no—
512C22×C7—44no—
513C22×C7—44no—
514C22×C7—42no—
515C22×C7—44no—
516C22×C7—42no—
517C22×C7—44no—
518C22×C7—42no—
519C22×C7—44no—
520C22×C7—44no—
521C22×C7—44no—
522C22×C7—44no—
523C22×C7—44no—
524C22×C7—44no—
525C22×C7—44no—
526C22×C7—42no—
527C22×C7—81no—
528C22×C7—82no—
529C22×C7—82no—
530C22×C7—81no—
531C22×C7—82no—
532C22×C7—82no—
533C22×C7—81no—
534C22×C7—82no—
535C22×C7—82no—
536C22×C7—82no—
537C22×C7—82no—
538C22×C7—82no—
539C22×C7—81no—
540C22×C7—82no—
541C22×C7C2×#12011yescharacteristic
542C22×C7C2×#12111yescharacteristic
543C22×C7#53211yescharacteristic
544C22×C7#53411yescharacteristic
545C22×C7#53412yes—
546C22×C7#53411yescharacteristic
547C22×C7#53412yes—
548C22×C7#53512yes—
549C22×C7#53511yescharacteristic
550C22×C7#53511yescharacteristic
551C22×C7#53812yes—
552C22×C7#53812yes—
553C22×C7#54012yes—
554C22×C7D4211yescharacteristic
555C22×C7D4211yescharacteristic
556C22×C7#54611yescharacteristic
557C22×C7#54611yescharacteristic
558C22×C7#54612yes—
559C22×C7#54612yes—
560C22×C7#55012yes—
561C22×C7#55312yes—
562C22×C7#56012yes—
563C22×C7#56012yes—
564C4×C7—24no—
565C4×C7—42no—
566C4×C7—42no—
567C4×C7—44no—
568C4×C7—44no—
569C4×C7—82no—
570C4×C7—81no—
571C4×C7—81no—
572C24—21no—
573C24—21no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—21no—
579C24—21no—
580C24—21no—
581C24—21no—
582C24—22no—
583C24—22no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—21no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—21no—
604C24C2×C7×D414yes—
605C24C2×C7×D412yes—
606C24C2×C7×D412yes—
607C24C2×C7×D412yes—
608C24C7×#4112yes—
609C24C24×C711yescharacteristic
610C2×D4—216no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—48no—
614C2×D4—48no—
615C2×D4—48no—
616C2×D4—48no—
617C2×D4—48no—
618C2×D4—48no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—48no—
622C2×D4—48no—
623C2×D4—48no—
624C2×D4—48no—
625C2×D4—48no—
626C2×D4—44no—
627C2×D4—48no—
628C2×D4—48no—
629C2×D4—44no—
630C2×D4—48no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—48no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—28no—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—48no—
677C22×C4—48no—
678C22×C4C2×C7×D412yes—
679C22×C4C2×C7×D412yes—
680C22×C4C2×C7×D414yes—
681C22×C4C2×C7×D412yes—
682C22×C4C2×C7×D412yes—
683C22×C4C2×C7×D412yes—
684C22×C4C7×#4114yes—
685C4⋊C4—28no—
686C22⋊C4—216no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—44no—
691C22⋊C4—48no—
692C22⋊C4—44no—
693C22⋊C4—48no—
694C22⋊C4—44no—
695C2×C7—44no—
696C2×C7—84no—
697C2×C7—82no—
698C2×C7#240811yescharacteristic
699C2×C7#243111yescharacteristic
700C2×C7#254311yescharacteristic
701C2×C7#261311yescharacteristic
702C2×C7#261711yescharacteristic
703C2×C7#266111yescharacteristic
704C2×C7#266812yes—
705C2×C7#267312yes—
706C2×C7#268812yes—
707C2×C7#271412yes—
708C2×C7#281511yescharacteristic
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—24no—
720C23—22no—
721C23—22no—
722C23—24no—
723C23—24no—
724C23—22no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—22no—
729C23—24no—
730C23—22no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—41no—
744C23—42no—
745C23—42no—
746C23—41no—
747C23—42no—
748C23—41no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—41no—
758C23—41no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—41no—
775C23—41no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23C7×#12114yes—
790C23C22×C7×D411yescharacteristic
791C23C22×C7×D411yescharacteristic
792C23C22×C7×D411yescharacteristic
793C23C22×C7×D411yescharacteristic
794C23C2×C7×#4111yescharacteristic
795C23C2×C7×#4112yes—
796C23C7×H(5,𝔽2)12yes—
797C23C7×H(5,𝔽2)12yes—
798C23C7×H(5,𝔽2)12yes—
799C23C7×H(5,𝔽2)11yescharacteristic
800C23C7×H(5,𝔽2)11yescharacteristic
801D4—416no—
802D4—432no—
803D4—416no—
804D4—432no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—416no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4C7×#12014yes—
852C7#1650011yescharacteristic, direct product factor, Sylow
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—44no—
858C22—44no—
859C22—42no—
860C22—44no—
861C22—44no—
862C22—42no—
863C22—42no—
864C22—44no—
865C22—42no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—42no—
874C22—44no—
875C22—42no—
876C22—82no—
877C22—81no—
878C22—82no—
879C22—82no—
880C22—81no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—81no—
887C22—82no—
888C22—81no—
889C22—82no—
890C22C2×C7×#12011yescharacteristic
891C22C2×C7×#12111yescharacteristic
892C22C7×#53211yescharacteristic
893C22C7×#53411yescharacteristic
894C22C7×#53412yes—
895C22C7×#53412yes—
896C22C7×#53411yescharacteristic
897C22C7×#53511yescharacteristic
898C22C7×#53512yes—
899C22C7×#53511yescharacteristic
900C22C7×#53812yes—
901C22C7×#53812yes—
902C22C7×#54012yes—
903C22C7×D4211yescharacteristic
904C22C7×D4211yescharacteristic
905C22C7×#54611yescharacteristic
906C22C7×#54611yescharacteristic
907C22C7×#54612yes—
908C22C7×#54612yes—
909C22C7×#55012yes—
910C22C7×#55312yes—
911C22C7×#56012yes—
912C22C7×#56012yes—
913C4—24no—
914C4—44no—
915C4—44no—
916C4—42no—
917C4—42no—
918C4—82no—
919C4—81no—
920C4—81no—
921C2—44no—
922C2—84no—
923C2—82no—
924C2C7×#240811yescharacteristic
925C2C7×#243111yescharacteristic
926C2C7×#254311yescharacteristic
927C2C7×#261311yescharacteristic
928C2C7×#261711yescharacteristic
929C2C7×#266111yescharacteristic
930C2C7×#266812yes—
931C2C7×#267312yes—
932C2C7×#268812yes—
933C2C7×#271412yes—
934C2C7×#281511yescharacteristic
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. C22×C7×#121C2semidirect
2. C2×C7×#397C2semidirect
3. C2×C7×#392C2semidirect
4. C2×C7×#392C2semidirect
5. C2×C7×#386C2semidirect
6. C7×#1445C2semidirect
7. C7×#1440C2semidirect
8. C7×#1438C2semidirect
9. C7×#1438C2semidirect
10. C7×#1438C2semidirect
11. C7×C22⋊#95C2semidirect
42. #16500C7direct (N × H)
68. C22×C7×D4D4semidirect
69. C22×C7×D4D4semidirect
74. C23×C4×C7D4semidirect
86. C2×C7×C4⋊C4D4semidirect
120. C22×#121C2×C7semidirect
121. C2×#397C2×C7semidirect
122. C2×#392C2×C7semidirect
123. C2×#392C2×C7semidirect
124. C2×#386C2×C7semidirect
125. #1445C2×C7semidirect
126. #1440C2×C7semidirect
127. #1438C2×C7semidirect
128. #1438C2×C7semidirect
129. #1438C2×C7semidirect
130. C22⋊#95C2×C7semidirect
452. C22×D4C7×D4semidirect
453. C22×D4C7×D4semidirect
458. C23×C4C7×D4semidirect
470. C2×C4⋊C4C7×D4semidirect
852. C7#16500direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C2×C7×#3972
C2×C7×#3922
C2×C7×#3862
C7×#14452
C7×#14402
C7×#14382
C7×C22⋊#952
#165007