Finite Group Databasebeta

← C7×#15138 #13192354

Subgroups — C7×#15138 #13192354

Order 1792.

1762 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#397C212yesmaximal, complemented
2C2×C7×#390C211yesmaximal, characteristic
3C2×C7×#390C211yesmaximal, characteristic
4C2×C7×#390C211yesmaximal, characteristic
5C2×C7×#389C211yesmaximal, characteristic, complemented
6C7×#1440C212yesmaximal, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×C4⋊#95C211yesmaximal, characteristic, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C4×C7×#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C4⋊C4C2211yescharacteristic
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×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C7×#397—28no—
27C7×#390—24no—
28C7×#390—24no—
29C7×#390—24no—
30C7×#389—24no—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2211yescharacteristic
40#15138C711yesmaximal, characteristic, direct product factor, Sylow
41C25×C7C2312yes—
42C22×C7×D4—22no—
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4D414yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2312yes—
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—24no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
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—42no—
70C2×C7×C4⋊C4D414yes—
71C2×C7×C22⋊C4—24no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
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—42no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×C42×C7—22no—
95C2×C42×C7—22no—
96C2×C42×C7—22no—
97C2×C42×C7—22no—
98C7×#95—24no—
99C7×#95—24no—
100C7×#95—24no—
101C7×#95—22no—
102C7×#95—22no—
103C7×#95—22no—
104C7×#95—42no—
105C7×#95—42no—
106C7×#95D414yescomplemented
107C2×#397C2×C712yescomplemented
108C2×#390C2×C711yescharacteristic
109C2×#390C2×C711yescharacteristic
110C2×#390C2×C711yescharacteristic
111C2×#389C2×C711yescharacteristic, complemented
112#1440C2×C712yescomplemented
113#1440C2×C712yescomplemented
114#1439C2×C712yescomplemented
115C4⋊#95C2×C711yescharacteristic, complemented
116C4⋊#95C2×C711yescharacteristic, complemented
117C4×#95C2×C711yescharacteristic, complemented
118C24×C7—22no—
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×C7C2×D414yes—
133C24×C7C2411yescharacteristic
134C2×C7×D4—28no—
135C2×C7×D4—28no—
136C2×C7×D4—28no—
137C2×C7×D4—44no—
138C2×C7×D4—44no—
139C2×C7×D4—44no—
140C2×C7×D4—44no—
141C22×C4×C7—21no—
142C22×C4×C7—22no—
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—21no—
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—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—22no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—22no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
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—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×C7C2×D412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D414yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C22×C4×C7#4112yes—
207C22×C4×C7#4112yes—
208C22×C4×C7#4112yes—
209C22×C4×C7#4112yes—
210C22×C4×C7#4112yes—
211C7×C4⋊C4—28no—
212C7×C4⋊C4—48no—
213C7×C4⋊C4—44no—
214C7×C4⋊C4—44no—
215C7×C22⋊C4—48no—
216C7×C22⋊C4—48no—
217C7×C22⋊C4—48no—
218C7×C22⋊C4—48no—
219C7×C22⋊C4—48no—
220C7×C22⋊C4—48no—
221C42×C7—44no—
222C42×C7—44no—
223C42×C7—44no—
224C23×D4C22×C711yescharacteristic
225C22×C4⋊C4C22×C711yescharacteristic
226C22×C4⋊C4C22×C711yescharacteristic
227C22×C4⋊C4C22×C712yes—
228C22×C4⋊C4C22×C711yescharacteristic
229C22×C22⋊C4C22×C712yes—
230C22×C22⋊C4C22×C712yes—
231C22×C22⋊C4C22×C712yes—
232C22×C22⋊C4C22×C712yes—
233C22×C22⋊C4C22×C712yes—
234C22×C22⋊C4C22×C712yes—
235C22×C42C22×C711yescharacteristic
236C22×C42C22×C711yescharacteristic
237C22×C42C22×C711yescharacteristic
238#397—28no—
239#390—24no—
240#390—24no—
241#390—24no—
242#389—24no—
243C2×#95C22×C712yes—
244C2×#95C22×C712yes—
245C2×#95C22×C711yescharacteristic
246C2×#95C22×C711yescharacteristic
247C2×#95C22×C711yescharacteristic
248C2×#95C22×C712yes—
249C2×#95C22×C712yes—
250C2×#95C22×C712yes—
251C2×#95C22×C711yescharacteristic
252C23×C7—24no—
253C23×C7—24no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—24no—
258C23×C7—24no—
259C23×C7—42no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—42no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—42no—
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×C7C22×D411yescharacteristic
288C23×C7C22×D411yescharacteristic
289C23×C7C22×D411yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4111yescharacteristic
293C23×C7C2×#4111yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7C2×#4111yescharacteristic
296C23×C7C2×#4111yescharacteristic
297C23×C7C2×#4111yescharacteristic
298C23×C7H(5,𝔽2)11yescharacteristic
299C23×C7H(5,𝔽2)11yescharacteristic
300C23×C7H(5,𝔽2)11yescharacteristic
301C23×C72−1+411yescharacteristic
302C7×D4—416no—
303C2×C4×C7—24no—
304C2×C4×C7—22no—
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—22no—
313C2×C4×C7—24no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—24no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—42no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—42no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—42no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
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—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7#12114yes—
367C2×C4×C7#12314yes—
368C2×C4×C7#12314yes—
369C2×C4×C7#12314yes—
370C2×C4×C7#12414yes—
371C2×C4×C7#12614yes—
372C2×C4×C7#12614yes—
373C25C23×C712yes—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4C7×D414yes—
381C23×C4C23×C712yes—
382C23×C4C23×C712yes—
383C23×C4C23×C712yes—
384C23×C4C23×C711yescharacteristic
385C23×C4C23×C711yescharacteristic
386C23×C4C23×C711yescharacteristic
387C23×C4C23×C711yescharacteristic
388C23×C4C23×C711yescharacteristic
389C23×C4C23×C711yescharacteristic
390C23×C4C23×C711yescharacteristic
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4C7×D414yes—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—42no—
437#95—42no—
438#95C7×D414yescomplemented
439C22×C7—44no—
440C22×C7—44no—
441C22×C7—44no—
442C22×C7—44no—
443C22×C7—44no—
444C22×C7—44no—
445C22×C7—44no—
446C22×C7—82no—
447C22×C7—82no—
448C22×C7—82no—
449C22×C7—82no—
450C22×C7—82no—
451C22×C7—82no—
452C22×C7—82no—
453C22×C7—82no—
454C22×C7C2×#12111yescharacteristic
455C22×C7C2×#12311yescharacteristic
456C22×C7C2×#12311yescharacteristic
457C22×C7C2×#12311yescharacteristic
458C22×C7C2×#12411yescharacteristic
459C22×C7C2×#12611yescharacteristic
460C22×C7C2×#12611yescharacteristic
461C22×C7#52911yescharacteristic
462C22×C7#52911yescharacteristic
463C22×C7#52911yescharacteristic
464C22×C7#53211yescharacteristic
465C22×C7#53211yescharacteristic
466C22×C7#53211yescharacteristic
467C22×C7#54011yescharacteristic
468C22×C7#54011yescharacteristic
469C22×C7#54011yescharacteristic
470C22×C7#54211yescharacteristic
471C22×C7#54211yescharacteristic
472C22×C7#54211yescharacteristic
473C22×C7D4211yescharacteristic
474C22×C7D4211yescharacteristic
475C22×C7#54611yescharacteristic
476C22×C7#54611yescharacteristic
477C22×C7#54611yescharacteristic
478C22×C7#54711yescharacteristic
479C22×C7#54711yescharacteristic
480C22×C7#54811yescharacteristic
481C22×C7#55011yescharacteristic
482C22×C7#55011yescharacteristic
483C22×C7#55311yescharacteristic
484C22×C7#55311yescharacteristic
485C22×C7#55511yescharacteristic
486C22×C7#55611yescharacteristic
487C22×C7#55911yescharacteristic
488C22×C7#55911yescharacteristic
489C4×C7—42no—
490C4×C7—42no—
491C4×C7—42no—
492C4×C7—42no—
493C4×C7—44no—
494C4×C7—42no—
495C4×C7—42no—
496C4×C7—82no—
497C4×C7—82no—
498C4×C7#39718yescomplemented
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24C2×C7×D414yes—
514C24C24×C711yescharacteristic
515C2×D4—28no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C22×C4—21no—
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—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4C2×C7×D412yes—
579C22×C4C2×C7×D412yes—
580C22×C4C2×C7×D414yes—
581C22×C4C2×C7×D412yes—
582C22×C4C2×C7×D412yes—
583C22×C4C2×C7×D412yes—
584C22×C4C7×#4112yes—
585C22×C4C7×#4112yes—
586C22×C4C7×#4112yes—
587C22×C4C7×#4112yes—
588C22×C4C7×#4112yes—
589C22×C4C7×#4112yes—
590C22×C4C7×#4112yes—
591C22×C4C7×#4112yes—
592C4⋊C4—28no—
593C4⋊C4—48no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C42—44no—
603C42—44no—
604C42—44no—
605C2×C7—84no—
606C2×C7C2×#39711yescharacteristic
607C2×C7#242011yescharacteristic
608C2×C7#242211yescharacteristic
609C2×C7#242711yescharacteristic
610C2×C7#242811yescharacteristic
611C2×C7#244511yescharacteristic
612C2×C7#244511yescharacteristic
613C2×C7#244711yescharacteristic
614C2×C7#244811yescharacteristic
615C2×C7#249011yescharacteristic
616C2×C7#249111yescharacteristic
617C2×C7#251211yescharacteristic
618C2×C7#251311yescharacteristic
619C2×C7#264411yescharacteristic
620C2×C7#286011yescharacteristic
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C22×C7×D411yescharacteristic
657C23C22×C7×D411yescharacteristic
658C23C22×C7×D411yescharacteristic
659C23C2×C7×#4111yescharacteristic
660C23C2×C7×#4111yescharacteristic
661C23C2×C7×#4111yescharacteristic
662C23C2×C7×#4111yescharacteristic
663C23C2×C7×#4111yescharacteristic
664C23C2×C7×#4111yescharacteristic
665C23C2×C7×#4111yescharacteristic
666C23C2×C7×#4111yescharacteristic
667C23C7×H(5,𝔽2)11yescharacteristic
668C23C7×H(5,𝔽2)11yescharacteristic
669C23C7×H(5,𝔽2)11yescharacteristic
670C23C7×2−1+411yescharacteristic
671D4—416no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4C7×#12114yes—
736C2×C4C7×#12314yes—
737C2×C4C7×#12314yes—
738C2×C4C7×#12314yes—
739C2×C4C7×#12414yes—
740C2×C4C7×#12614yes—
741C2×C4C7×#12614yes—
742C7#1513811yescharacteristic, direct product factor, Sylow
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22C2×C7×#12111yescharacteristic
759C22C2×C7×#12311yescharacteristic
760C22C2×C7×#12311yescharacteristic
761C22C2×C7×#12311yescharacteristic
762C22C2×C7×#12411yescharacteristic
763C22C2×C7×#12611yescharacteristic
764C22C2×C7×#12611yescharacteristic
765C22C7×#52911yescharacteristic
766C22C7×#52911yescharacteristic
767C22C7×#52911yescharacteristic
768C22C7×#53211yescharacteristic
769C22C7×#53211yescharacteristic
770C22C7×#53211yescharacteristic
771C22C7×#54011yescharacteristic
772C22C7×#54011yescharacteristic
773C22C7×#54011yescharacteristic
774C22C7×#54211yescharacteristic
775C22C7×#54211yescharacteristic
776C22C7×#54211yescharacteristic
777C22C7×D4211yescharacteristic
778C22C7×D4211yescharacteristic
779C22C7×#54611yescharacteristic
780C22C7×#54611yescharacteristic
781C22C7×#54611yescharacteristic
782C22C7×#54711yescharacteristic
783C22C7×#54711yescharacteristic
784C22C7×#54811yescharacteristic
785C22C7×#55011yescharacteristic
786C22C7×#55011yescharacteristic
787C22C7×#55311yescharacteristic
788C22C7×#55311yescharacteristic
789C22C7×#55511yescharacteristic
790C22C7×#55611yescharacteristic
791C22C7×#55911yescharacteristic
792C22C7×#55911yescharacteristic
793C4—42no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—44no—
798C4—42no—
799C4—42no—
800C4—82no—
801C4—82no—
802C4C7×#39718yescomplemented
803C2—84no—
804C2C2×C7×#39711yescharacteristic
805C2C7×#242011yescharacteristic
806C2C7×#242211yescharacteristic
807C2C7×#242711yescharacteristic
808C2C7×#242811yescharacteristic
809C2C7×#244511yescharacteristic
810C2C7×#244511yescharacteristic
811C2C7×#244711yescharacteristic
812C2C7×#244811yescharacteristic
813C2C7×#249011yescharacteristic
814C2C7×#249111yescharacteristic
815C2C7×#251211yescharacteristic
816C2C7×#251311yescharacteristic
817C2C7×#264411yescharacteristic
818C2C7×#286011yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
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
5. C2×C7×#389C2semidirect
6. C7×#1440C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×C4⋊#95C2semidirect
10. C7×C4⋊#95C2semidirect
11. C4×C7×#95C2semidirect
40. #15138C7direct (N × H)
106. C7×#95D4semidirect
107. C2×#397C2×C7semidirect
111. C2×#389C2×C7semidirect
112. #1440C2×C7semidirect
113. #1440C2×C7semidirect
114. #1439C2×C7semidirect
115. C4⋊#95C2×C7semidirect
116. C4⋊#95C2×C7semidirect
117. C4×#95C2×C7semidirect
438. #95C7×D4semidirect
498. C4×C7#397semidirect
742. C7#15138direct (N × H)
802. 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×#3902
C2×C7×#3892
C7×#14402
C7×#14392
C7×C4⋊#952
C4×C7×#952
#151387