Finite Group Databasebeta

← C7×#15183 #13192399

Subgroups — C7×#15183 #13192399

Order 1792.

1586 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic, complemented
2C2×C7×#380C211yesmaximal, characteristic
3C2×C7×#380C211yesmaximal, characteristic
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
5C7×#1445C212yesmaximal, complemented
6C7×#1443C212yesmaximal, complemented
7C7×#1440C212yesmaximal
8C7×#1439C212yesmaximal
9C7×C4⋊#95C211yesmaximal, characteristic, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2212yes—
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C7×#389—24no—
25C7×#380—24no—
26C7×#380—24no—
27C4×C7×C22⋊C4—24no—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39#15183C711yesmaximal, characteristic, direct product factor, Sylow
40C25×C7C2311yescharacteristic
41C23×C4×C7—22no—
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7D414yes—
48C23×C4×C7C2312yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C2×C7×C4⋊C4—22no—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—24no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—42no—
72C2×C7×C4⋊C4D414yes—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—42no—
82C2×C7×C22⋊C4—42no—
83C2×C7×C22⋊C4—42no—
84C2×C7×C22⋊C4Q814yes—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C7×#95—22no—
92C7×#95—22no—
93C7×#95—24no—
94C7×#95—24no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—42no—
98C7×#95—42no—
99C7×#95—42no—
100C7×#95—42no—
101C7×#95—42no—
102C2×#389C2×C711yescharacteristic, complemented
103C2×#380C2×C711yescharacteristic
104C2×#380C2×C711yescharacteristic
105C2×C4×C22⋊C4C2×C711yescharacteristic
106#1445C2×C712yescomplemented
107#1443C2×C712yescomplemented
108#1440C2×C712yes—
109#1439C2×C712yes—
110C4⋊#95C2×C711yescharacteristic, complemented
111C4⋊#95C2×C711yescharacteristic, complemented
112C4⋊#95C2×C711yescharacteristic, complemented
113C24×C7—21no—
114C24×C7—21no—
115C24×C7—21no—
116C24×C7—21no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7C2×D412yes—
126C24×C7C2×Q812yes—
127C24×C7#4112yes—
128C24×C7C2411yescharacteristic
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—28no—
166C22×C4×C7—28no—
167C22×C4×C7—28no—
168C22×C4×C7—22no—
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—22no—
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—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—44no—
190C22×C4×C7—44no—
191C22×C4×C7—44no—
192C22×C4×C7—44no—
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2×D414yes—
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2×D412yes—
197C22×C4×C7C2×Q812yes—
198C22×C4×C7C2×Q812yes—
199C22×C4×C7#4112yes—
200C22×C4×C7#4112yes—
201C22×C4×C7#4112yes—
202C22×C4×C7#4112yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C7×C4⋊C4—28no—
207C7×C4⋊C4—48no—
208C7×C4⋊C4—44no—
209C7×C4⋊C4—44no—
210C7×C4⋊C4—44no—
211C7×C22⋊C4—28no—
212C7×C22⋊C4—28no—
213C7×C22⋊C4—48no—
214C7×C22⋊C4—48no—
215C42×C7—44no—
216C42×C7—44no—
217C24×C4C22×C711yescharacteristic
218C22×C4⋊C4C22×C711yescharacteristic
219C22×C4⋊C4C22×C711yescharacteristic
220C22×C4⋊C4C22×C711yescharacteristic
221C22×C4⋊C4C22×C712yes—
222C22×C4⋊C4C22×C711yescharacteristic
223C22×C22⋊C4C22×C711yescharacteristic
224C22×C22⋊C4C22×C712yes—
225C22×C22⋊C4C22×C711yescharacteristic
226C22×C22⋊C4C22×C712yes—
227C22×C42C22×C711yescharacteristic
228C22×C42C22×C711yescharacteristic
229#389—24no—
230#380—24no—
231#380—24no—
232C4×C22⋊C4—24no—
233C2×#95C22×C712yes—
234C2×#95C22×C712yes—
235C2×#95C22×C711yescharacteristic
236C2×#95C22×C712yes—
237C2×#95C22×C712yes—
238C2×#95C22×C711yescharacteristic
239C2×#95C22×C712yes—
240C2×#95C22×C712yes—
241C2×#95C22×C712yes—
242C2×#95C22×C712yes—
243C2×#95C22×C712yes—
244C23×C7—22no—
245C23×C7—22no—
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—41no—
263C23×C7—41no—
264C23×C7—41no—
265C23×C7—41no—
266C23×C7—41no—
267C23×C7—41no—
268C23×C7—41no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7C22⋊Q814yes—
279C23×C7C22×D411yescharacteristic
280C23×C7C22×D411yescharacteristic
281C23×C7C22×Q811yescharacteristic
282C23×C7C2×#4111yescharacteristic
283C23×C7C2×#4111yescharacteristic
284C23×C7C2×#4111yescharacteristic
285C23×C7C2×#4111yescharacteristic
286C23×C7C2×#4111yescharacteristic
287C23×C7C2×#4111yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7H(5,𝔽2)11yescharacteristic
291C23×C7H(5,𝔽2)11yescharacteristic
292C23×C7H(5,𝔽2)11yescharacteristic
293C23×C72−1+411yescharacteristic
294C2×C4×C7—22no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—24no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—24no—
303C2×C4×C7—22no—
304C2×C4×C7—24no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—42no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—42no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—42no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—42no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—416no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
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—42no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7#12114yes—
359C2×C4×C7#12314yes—
360C2×C4×C7#12314yes—
361C2×C4×C7#12314yes—
362C2×C4×C7#12414yes—
363C2×C4×C7#12614yes—
364C2×C4×C7#12614yes—
365C25C23×C711yescharacteristic
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4C7×D414yes—
373C23×C4C23×C712yes—
374C23×C4C23×C712yes—
375C23×C4C23×C712yes—
376C23×C4C23×C712yes—
377C23×C4C23×C711yescharacteristic
378C23×C4C23×C711yescharacteristic
379C23×C4C23×C711yescharacteristic
380C23×C4C23×C711yescharacteristic
381C23×C4C23×C711yescharacteristic
382C23×C4C23×C711yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4C7×D414yes—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C7×Q814yes—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416#95—22no—
417#95—22no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427C22×C7—24no—
428C22×C7—24no—
429C22×C7—24no—
430C22×C7—42no—
431C22×C7—42no—
432C22×C7—42no—
433C22×C7—42no—
434C22×C7—42no—
435C22×C7—42no—
436C22×C7—42no—
437C22×C7—42no—
438C22×C7—42no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7C2×#12111yescharacteristic
443C22×C7C2×C22⋊Q811yescharacteristic
444C22×C7C2×#12311yescharacteristic
445C22×C7C2×#12311yescharacteristic
446C22×C7C2×#12311yescharacteristic
447C22×C7#52511yescharacteristic
448C22×C7C2×#12411yescharacteristic
449C22×C7C2×#12611yescharacteristic
450C22×C7C2×#12611yescharacteristic
451C22×C7#52911yescharacteristic
452C22×C7#52911yescharacteristic
453C22×C7#53311yescharacteristic
454C22×C7#53311yescharacteristic
455C22×C7#53511yescharacteristic
456C22×C7#53711yescharacteristic
457C22×C7#54011yescharacteristic
458C22×C7#54011yescharacteristic
459C22×C7#54211yescharacteristic
460C22×C7#54211yescharacteristic
461C22×C7#54611yescharacteristic
462C22×C7#54611yescharacteristic
463C22×C7D4×Q811yescharacteristic
464C22×C7#55011yescharacteristic
465C22×C7#55211yescharacteristic
466C22×C7#55211yescharacteristic
467C22×C7#55311yescharacteristic
468C22×C7#55311yescharacteristic
469C22×C7#55311yescharacteristic
470C22×C7#55311yescharacteristic
471C22×C7#55411yescharacteristic
472C22×C7#55411yescharacteristic
473C22×C7#55411yescharacteristic
474C22×C7#55511yescharacteristic
475C22×C7#55511yescharacteristic
476C22×C7#55611yescharacteristic
477C4×C7—42no—
478C4×C7—42no—
479C4×C7—42no—
480C4×C7—44no—
481C4×C7—42no—
482C4×C7—42no—
483C4×C7—82no—
484C4×C7—82no—
485C4×C7—82no—
486C4×C7#39718yes—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24C2×C7×D412yes—
500C24C2×C7×Q812yes—
501C24C7×#4112yes—
502C24C24×C711yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
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—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4C2×C7×D412yes—
568C22×C4C2×C7×D414yes—
569C22×C4C2×C7×D412yes—
570C22×C4C2×C7×D412yes—
571C22×C4C2×C7×Q812yes—
572C22×C4C2×C7×Q812yes—
573C22×C4C7×#4112yes—
574C22×C4C7×#4112yes—
575C22×C4C7×#4112yes—
576C22×C4C7×#4112yes—
577C22×C4C7×#4112yes—
578C22×C4C7×#4112yes—
579C22×C4C7×#4112yes—
580C4⋊C4—28no—
581C4⋊C4—48no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C42—44no—
590C42—44no—
591C2×C7—44no—
592C2×C7C2×#39711yescharacteristic
593C2×C7#241411yescharacteristic
594C2×C7#241711yescharacteristic
595C2×C7#242011yescharacteristic
596C2×C7#242311yescharacteristic
597C2×C7#248511yescharacteristic
598C2×C7#248711yescharacteristic
599C2×C7#249011yescharacteristic
600C2×C7#249211yescharacteristic
601C2×C7#249411yescharacteristic
602C2×C7#249511yescharacteristic
603C2×C7#249711yescharacteristic
604C2×C7#249711yescharacteristic
605C2×C7#262411yescharacteristic
606C2×C7#285511yescharacteristic
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23C7×C22⋊Q814yes—
642C23C22×C7×D411yescharacteristic
643C23C22×C7×D411yescharacteristic
644C23C22×C7×Q811yescharacteristic
645C23C2×C7×#4111yescharacteristic
646C23C2×C7×#4111yescharacteristic
647C23C2×C7×#4111yescharacteristic
648C23C2×C7×#4111yescharacteristic
649C23C2×C7×#4111yescharacteristic
650C23C2×C7×#4111yescharacteristic
651C23C2×C7×#4111yescharacteristic
652C23C2×C7×#4111yescharacteristic
653C23C7×H(5,𝔽2)11yescharacteristic
654C23C7×H(5,𝔽2)11yescharacteristic
655C23C7×H(5,𝔽2)11yescharacteristic
656C23C7×2−1+411yescharacteristic
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—416no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4C7×#12114yes—
722C2×C4C7×#12314yes—
723C2×C4C7×#12314yes—
724C2×C4C7×#12314yes—
725C2×C4C7×#12414yes—
726C2×C4C7×#12614yes—
727C2×C4C7×#12614yes—
728C7#1518311yescharacteristic, direct product factor, Sylow
729C22—24no—
730C22—24no—
731C22—24no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22C2×C7×#12111yescharacteristic
745C22C2×C7×C22⋊Q811yescharacteristic
746C22C2×C7×#12311yescharacteristic
747C22C2×C7×#12311yescharacteristic
748C22C2×C7×#12311yescharacteristic
749C22C7×#52511yescharacteristic
750C22C2×C7×#12411yescharacteristic
751C22C2×C7×#12611yescharacteristic
752C22C2×C7×#12611yescharacteristic
753C22C7×#52911yescharacteristic
754C22C7×#52911yescharacteristic
755C22C7×#53311yescharacteristic
756C22C7×#53311yescharacteristic
757C22C7×#53511yescharacteristic
758C22C7×#53711yescharacteristic
759C22C7×#54011yescharacteristic
760C22C7×#54011yescharacteristic
761C22C7×#54211yescharacteristic
762C22C7×#54211yescharacteristic
763C22C7×#54611yescharacteristic
764C22C7×#54611yescharacteristic
765C22C7×D4×Q811yescharacteristic
766C22C7×#55011yescharacteristic
767C22C7×#55211yescharacteristic
768C22C7×#55211yescharacteristic
769C22C7×#55311yescharacteristic
770C22C7×#55311yescharacteristic
771C22C7×#55311yescharacteristic
772C22C7×#55311yescharacteristic
773C22C7×#55411yescharacteristic
774C22C7×#55411yescharacteristic
775C22C7×#55411yescharacteristic
776C22C7×#55511yescharacteristic
777C22C7×#55511yescharacteristic
778C22C7×#55611yescharacteristic
779C4—42no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—42no—
784C4—42no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4C7×#39718yes—
789C2—44no—
790C2C2×C7×#39711yescharacteristic
791C2C7×#241411yescharacteristic
792C2C7×#241711yescharacteristic
793C2C7×#242011yescharacteristic
794C2C7×#242311yescharacteristic
795C2C7×#248511yescharacteristic
796C2C7×#248711yescharacteristic
797C2C7×#249011yescharacteristic
798C2C7×#249211yescharacteristic
799C2C7×#249411yescharacteristic
800C2C7×#249511yescharacteristic
801C2C7×#249711yescharacteristic
802C2C7×#249711yescharacteristic
803C2C7×#262411yescharacteristic
804C2C7×#285511yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#389C2semidirect
5. C7×#1445C2semidirect
6. C7×#1443C2semidirect
9. C7×C4⋊#95C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×C4⋊#95C2semidirect
39. #15183C7direct (N × H)
102. C2×#389C2×C7semidirect
106. #1445C2×C7semidirect
107. #1443C2×C7semidirect
110. C4⋊#95C2×C7semidirect
111. C4⋊#95C2×C7semidirect
112. C4⋊#95C2×C7semidirect
728. C7#15183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×C7×#3802
C2×C4×C7×C22⋊C42
C7×#14452
C7×#14432
C7×#14402
C7×#14392
C7×C4⋊#952
#151837