Finite Group Databasebeta

← C7×#15132 #13192348

Subgroups — C7×#15132 #13192348

Order 1792.

1626 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#397C212yesmaximal
2C2×C7×#389C211yesmaximal, characteristic, complemented
3C2×C7×#380C211yesmaximal, characteristic
4C2×C7×#380C211yesmaximal, characteristic
5C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
6C7×#1443C212yesmaximal, complemented
7C7×#1442C212yesmaximal, complemented
8C7×#1440C212yesmaximal
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⋊C4C2212yes—
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C7×#397—28no—
25C7×#389—24no—
26C7×#380—24no—
27C7×#380—24no—
28C4×C7×C22⋊C4—24no—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40#15132C711yesmaximal, characteristic, direct product factor, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7D414yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2312yes—
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—42no—
73C2×C7×C4⋊C4D414yes—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
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—42no—
85C2×C7×C22⋊C4D414yes—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C42×C7—22no—
92C7×#95—22no—
93C7×#95—22no—
94C7×#95—24no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—24no—
99C7×#95—24no—
100C7×#95—24no—
101C7×#95—24no—
102C7×#95—42no—
103C2×#397C2×C712yes—
104C2×#389C2×C711yescharacteristic, complemented
105C2×#380C2×C711yescharacteristic
106C2×#380C2×C711yescharacteristic
107C2×C4×C22⋊C4C2×C711yescharacteristic
108#1443C2×C712yescomplemented
109#1442C2×C712yescomplemented
110#1440C2×C712yes—
111C4⋊#95C2×C711yescharacteristic, complemented
112C4⋊#95C2×C711yescharacteristic, complemented
113C4⋊#95C2×C711yescharacteristic, complemented
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×C7—21no—
126C24×C7C2×D412yes—
127C24×C7C2×D412yes—
128C24×C7#4112yes—
129C24×C7C2411yescharacteristic
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—22no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
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—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
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—22no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—28no—
167C22×C4×C7—28no—
168C22×C4×C7—28no—
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—22no—
190C22×C4×C7—44no—
191C22×C4×C7—44no—
192C22×C4×C7—44no—
193C22×C4×C7—44no—
194C22×C4×C7C2×D412yes—
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2×D414yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D412yes—
200C22×C4×C7#4112yes—
201C22×C4×C7#4112yes—
202C22×C4×C7#4112yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C22×C4×C7#4112yes—
207C7×C4⋊C4—28no—
208C7×C4⋊C4—48no—
209C7×C4⋊C4—44no—
210C7×C4⋊C4—44no—
211C7×C4⋊C4—44no—
212C7×C22⋊C4—28no—
213C7×C22⋊C4—28no—
214C7×C22⋊C4—48no—
215C7×C22⋊C4—48no—
216C42×C7—44no—
217C42×C7—44no—
218C24×C4C22×C711yescharacteristic
219C22×C4⋊C4C22×C711yescharacteristic
220C22×C4⋊C4C22×C711yescharacteristic
221C22×C4⋊C4C22×C711yescharacteristic
222C22×C4⋊C4C22×C712yes—
223C22×C4⋊C4C22×C711yescharacteristic
224C22×C22⋊C4C22×C712yes—
225C22×C22⋊C4C22×C711yescharacteristic
226C22×C22⋊C4C22×C712yes—
227C22×C22⋊C4C22×C711yescharacteristic
228C22×C42C22×C711yescharacteristic
229C22×C42C22×C711yescharacteristic
230#397—28no—
231#389—24no—
232#380—24no—
233#380—24no—
234C4×C22⋊C4—24no—
235C2×#95C22×C712yes—
236C2×#95C22×C712yes—
237C2×#95C22×C712yes—
238C2×#95C22×C712yes—
239C2×#95C22×C712yes—
240C2×#95C22×C712yes—
241C2×#95C22×C711yescharacteristic
242C2×#95C22×C712yes—
243C2×#95C22×C712yes—
244C2×#95C22×C711yescharacteristic
245C2×#95C22×C712yes—
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—22no—
263C23×C7—22no—
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×C7—41no—
279C23×C7—41no—
280C23×C7#12114yes—
281C23×C7C22×D411yescharacteristic
282C23×C7C22×D411yescharacteristic
283C23×C7C22×D411yescharacteristic
284C23×C7C2×#4111yescharacteristic
285C23×C7C2×#4111yescharacteristic
286C23×C7C2×#4111yescharacteristic
287C23×C7C2×#4111yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7H(5,𝔽2)11yescharacteristic
293C23×C72−1+411yescharacteristic
294C23×C72−1+411yescharacteristic
295C23×C72−1+411yescharacteristic
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—24no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—24no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
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—41no—
321C2×C4×C7—41no—
322C2×C4×C7—42no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—42no—
328C2×C4×C7—41no—
329C2×C4×C7—42no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—42no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—416no—
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—42no—
359C2×C4×C7—42no—
360C2×C4×C7#12114yes—
361C2×C4×C7#12314yes—
362C2×C4×C7#12314yes—
363C2×C4×C7#12314yes—
364C2×C4×C7#12414yes—
365C2×C4×C7#12614yes—
366C2×C4×C7#12614yes—
367C25C23×C711yescharacteristic
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4C7×D414yes—
375C23×C4C23×C712yes—
376C23×C4C23×C712yes—
377C23×C4C23×C712yes—
378C23×C4C23×C712yes—
379C23×C4C23×C711yescharacteristic
380C23×C4C23×C711yescharacteristic
381C23×C4C23×C711yescharacteristic
382C23×C4C23×C711yescharacteristic
383C23×C4C23×C711yescharacteristic
384C23×C4C23×C711yescharacteristic
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4C7×D414yes—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4C7×D414yes—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418#95—22no—
419#95—22no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—42no—
429C22×C7—24no—
430C22×C7—24no—
431C22×C7—24no—
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×C7—42no—
443C22×C7—42no—
444C22×C7C2×#12111yescharacteristic
445C22×C7C2×#12111yescharacteristic
446C22×C7C2×#12311yescharacteristic
447C22×C7C2×#12311yescharacteristic
448C22×C7C2×#12311yescharacteristic
449C22×C7#52511yescharacteristic
450C22×C7C2×#12411yescharacteristic
451C22×C7C2×#12611yescharacteristic
452C22×C7C2×#12611yescharacteristic
453C22×C7#52911yescharacteristic
454C22×C7#52911yescharacteristic
455C22×C7#53211yescharacteristic
456C22×C7#53211yescharacteristic
457C22×C7#53611yescharacteristic
458C22×C7#53711yescharacteristic
459C22×C7#54111yescharacteristic
460C22×C7#54111yescharacteristic
461C22×C7#54211yescharacteristic
462C22×C7#54211yescharacteristic
463C22×C7D4211yescharacteristic
464C22×C7#54711yescharacteristic
465C22×C7#54711yescharacteristic
466C22×C7#54711yescharacteristic
467C22×C7#54711yescharacteristic
468C22×C7#54811yescharacteristic
469C22×C7#54811yescharacteristic
470C22×C7#55211yescharacteristic
471C22×C7#55211yescharacteristic
472C22×C7#55211yescharacteristic
473C22×C7#55211yescharacteristic
474C22×C7#55311yescharacteristic
475C22×C7#55311yescharacteristic
476C22×C7#55511yescharacteristic
477C22×C7#55611yescharacteristic
478C22×C7#55611yescharacteristic
479C4×C7—42no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—44no—
483C4×C7—42no—
484C4×C7—42no—
485C4×C7—82no—
486C4×C7—82no—
487C4×C7—82no—
488C4×C7#39718yescomplemented
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24C2×C7×D412yes—
502C24C2×C7×D412yes—
503C24C7×#4112yes—
504C24C24×C711yescharacteristic
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
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—22no—
564C22×C4—22no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4C2×C7×D412yes—
570C22×C4C2×C7×D412yes—
571C22×C4C2×C7×D414yes—
572C22×C4C2×C7×D412yes—
573C22×C4C2×C7×D412yes—
574C22×C4C2×C7×D412yes—
575C22×C4C7×#4112yes—
576C22×C4C7×#4112yes—
577C22×C4C7×#4112yes—
578C22×C4C7×#4112yes—
579C22×C4C7×#4112yes—
580C22×C4C7×#4112yes—
581C22×C4C7×#4112yes—
582C4⋊C4—28no—
583C4⋊C4—48no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C22⋊C4—28no—
588C22⋊C4—28no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C42—44no—
592C42—44no—
593C2×C7—44no—
594C2×C7C2×#39711yescharacteristic
595C2×C7#241511yescharacteristic
596C2×C7#241611yescharacteristic
597C2×C7#242111yescharacteristic
598C2×C7#242211yescharacteristic
599C2×C7#248511yescharacteristic
600C2×C7#248611yescharacteristic
601C2×C7#248911yescharacteristic
602C2×C7#249111yescharacteristic
603C2×C7#249411yescharacteristic
604C2×C7#249511yescharacteristic
605C2×C7#249611yescharacteristic
606C2×C7#249611yescharacteristic
607C2×C7#262511yescharacteristic
608C2×C7#285411yescharacteristic
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—22no—
626C23—22no—
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—
641C23—41no—
642C23—41no—
643C23C7×#12114yes—
644C23C22×C7×D411yescharacteristic
645C23C22×C7×D411yescharacteristic
646C23C22×C7×D411yescharacteristic
647C23C2×C7×#4111yescharacteristic
648C23C2×C7×#4111yescharacteristic
649C23C2×C7×#4111yescharacteristic
650C23C2×C7×#4111yescharacteristic
651C23C2×C7×#4111yescharacteristic
652C23C2×C7×#4111yescharacteristic
653C23C2×C7×#4111yescharacteristic
654C23C2×C7×#4111yescharacteristic
655C23C7×H(5,𝔽2)11yescharacteristic
656C23C7×2−1+411yescharacteristic
657C23C7×2−1+411yescharacteristic
658C23C7×2−1+411yescharacteristic
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—416no—
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×C4—42no—
722C2×C4—42no—
723C2×C4C7×#12114yes—
724C2×C4C7×#12314yes—
725C2×C4C7×#12314yes—
726C2×C4C7×#12314yes—
727C2×C4C7×#12414yes—
728C2×C4C7×#12614yes—
729C2×C4C7×#12614yes—
730C7#1513211yescharacteristic, direct product factor, Sylow
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×C7×#12111yescharacteristic
747C22C2×C7×#12111yescharacteristic
748C22C2×C7×#12311yescharacteristic
749C22C2×C7×#12311yescharacteristic
750C22C2×C7×#12311yescharacteristic
751C22C7×#52511yescharacteristic
752C22C2×C7×#12411yescharacteristic
753C22C2×C7×#12611yescharacteristic
754C22C2×C7×#12611yescharacteristic
755C22C7×#52911yescharacteristic
756C22C7×#52911yescharacteristic
757C22C7×#53211yescharacteristic
758C22C7×#53211yescharacteristic
759C22C7×#53611yescharacteristic
760C22C7×#53711yescharacteristic
761C22C7×#54111yescharacteristic
762C22C7×#54111yescharacteristic
763C22C7×#54211yescharacteristic
764C22C7×#54211yescharacteristic
765C22C7×D4211yescharacteristic
766C22C7×#54711yescharacteristic
767C22C7×#54711yescharacteristic
768C22C7×#54711yescharacteristic
769C22C7×#54711yescharacteristic
770C22C7×#54811yescharacteristic
771C22C7×#54811yescharacteristic
772C22C7×#55211yescharacteristic
773C22C7×#55211yescharacteristic
774C22C7×#55211yescharacteristic
775C22C7×#55211yescharacteristic
776C22C7×#55311yescharacteristic
777C22C7×#55311yescharacteristic
778C22C7×#55511yescharacteristic
779C22C7×#55611yescharacteristic
780C22C7×#55611yescharacteristic
781C4—42no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—42no—
786C4—42no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4C7×#39718yescomplemented
791C2—44no—
792C2C2×C7×#39711yescharacteristic
793C2C7×#241511yescharacteristic
794C2C7×#241611yescharacteristic
795C2C7×#242111yescharacteristic
796C2C7×#242211yescharacteristic
797C2C7×#248511yescharacteristic
798C2C7×#248611yescharacteristic
799C2C7×#248911yescharacteristic
800C2C7×#249111yescharacteristic
801C2C7×#249411yescharacteristic
802C2C7×#249511yescharacteristic
803C2C7×#249611yescharacteristic
804C2C7×#249611yescharacteristic
805C2C7×#262511yescharacteristic
806C2C7×#285411yescharacteristic
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
2. C2×C7×#389C2semidirect
6. C7×#1443C2semidirect
7. C7×#1442C2semidirect
9. C7×C4⋊#95C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×C4⋊#95C2semidirect
40. #15132C7direct (N × H)
104. C2×#389C2×C7semidirect
108. #1443C2×C7semidirect
109. #1442C2×C7semidirect
111. C4⋊#95C2×C7semidirect
112. C4⋊#95C2×C7semidirect
113. C4⋊#95C2×C7semidirect
488. C4×C7#397semidirect
730. C7#15132direct (N × H)
790. C4C7×#397semidirect

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×#3892
C2×C7×#3802
C2×C4×C7×C22⋊C42
C7×#14432
C7×#14422
C7×#14402
C7×C4⋊#952
#151327