Finite Group Databasebeta

← C7×#23981 #13201197

Subgroups — C7×#23981 #13201197

Order 1792.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic, complemented
2C2×C7×#452C211yesmaximal, characteristic, complemented
3C2×C7×#417C211yesmaximal, characteristic, complemented
4C7×#2407C211yesmaximal, characteristic
5C7×#2024C211yesmaximal, characteristic, complemented
6C7×#2023C211yesmaximal, characteristic, complemented
7C7×#2001C211yesmaximal, characteristic, complemented
8C7×#2000C211yesmaximal, characteristic, complemented
9C7×#1894C211yesmaximal, characteristic, complemented
10C7×#1880C211yesmaximal, characteristic, complemented
11C7×#1878C211yesmaximal, characteristic, complemented
12C7×#1874C211yesmaximal, characteristic, complemented
13C7×#1872C211yesmaximal, characteristic, complemented
14C7×#1870C211yesmaximal, characteristic, complemented
15C7×#1823C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C7×#554—24no—
21C7×#554—24no—
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C7×#125—21no—
24C2×C7×C22⋊Q8—21no—
25C2×C7×C22⋊Q8—21no—
26C2×C7×C22⋊Q8C2211yescharacteristic
27C2×C7×C22⋊Q8C2211yescharacteristic
28C2×C7×C22⋊Q8C2211yescharacteristic
29C2×C7×#121C2211yescharacteristic
30C2×C4×C7×Q8C2211yescharacteristic
31C2×C4×C7×D4—21no—
32C2×C4×C7×D4C2211yescharacteristic
33C22×C7×C4⋊C4C2211yescharacteristic
34C22×C7×C4⋊C4C2211yescharacteristic
35C7×#452—24no—
36C7×#417—24no—
37C2×C7×#103C2211yescharacteristic
38C2×C7×#103C2211yescharacteristic
39C2×C7×#103C2211yescharacteristic
40C2×C7×#103C2211yescharacteristic
41C2×C7×#103C2211yescharacteristic
42C2×C7×#102C2211yescharacteristic
43C2×C7×#102C2211yescharacteristic
44C2×C7×#102C2211yescharacteristic
45C2×C7×C22⋊C8C2211yescharacteristic
46C2×C7×C22⋊C8C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C7×#394—21no—
49C7×#392—21no—
50C7×#391C2211yescharacteristic
51C7×#390C2211yescharacteristic
52C7×#386—21no—
53C7×#385—21no—
54C7×#380C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#23981C711yesmaximal, characteristic, direct product factor, Sylow
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—41no—
69C2×C7×#41—41no—
70C22×C7×Q8—21no—
71C22×C7×Q8C2311yescharacteristic
72C22×C7×Q8C2311yescharacteristic
73C22×C7×D4—21no—
74C22×C7×D4—21no—
75C22×C7×D4D411yescharacteristic
76C22×C7×D4C2311yescharacteristic
77C23×C4×C7—21no—
78C23×C4×C7—21no—
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C2×C7×Q16—22no—
83C2×C7×Q16—22no—
84C2×C7×Q16—41no—
85C2×C7×SD16—22no—
86C2×C7×SD16—22no—
87C2×C7×SD16—41no—
88C2×C7×M16—22no—
89C2×C7×M16—41no—
90C2×C7×M16—41no—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×C4⋊Q8—22no—
96C7×C4⋊Q8—22no—
97C7×#125—28no—
98C7×C22⋊Q8—28no—
99C7×C22⋊Q8—28no—
100C7×C22⋊Q8—22no—
101C7×C22⋊Q8—22no—
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8—22no—
104C7×C22⋊Q8—41no—
105C7×C22⋊Q8D414yescomplemented
106C7×#121—22no—
107C7×#121—41no—
108C4×C7×Q8—22no—
109C4×C7×Q8—22no—
110C4×C7×D4—28no—
111C4×C7×D4—22no—
112C4×C7×D4—22no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—22no—
116C2×C7×C4⋊C4—21no—
117C2×C7×C4⋊C4—21no—
118C2×C7×C4⋊C4—21no—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4—22no—
121C2×C7×C4⋊C4—22no—
122C2×C7×C4⋊C4—21no—
123C2×C7×C4⋊C4D411yescharacteristic
124C2×C7×C4⋊C4D414yescomplemented
125C2×C7×C4⋊C4C2311yescharacteristic
126C2×C7×C4⋊C4C2311yescharacteristic
127C2×C7×C4⋊C4C2311yescharacteristic
128C2×C7×C4⋊C4C2311yescharacteristic
129C2×C7×C4⋊C4C2311yescharacteristic
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4—21no—
132C2×C7×C22⋊C4—21no—
133C2×C7×C22⋊C4—21no—
134C2×C7×C22⋊C4—21no—
135C2×C7×C22⋊C4—21no—
136C2×C7×C22⋊C4—21no—
137C2×C7×C22⋊C4D411yescharacteristic
138C2×C7×C22⋊C4D411yescharacteristic
139C2×C42×C7—21no—
140C2×C42×C7C2311yescharacteristic
141C7×#103—22no—
142C7×#103—22no—
143C7×#103—22no—
144C7×#103—41no—
145C7×#103—41no—
146C7×#102—22no—
147C7×#102—22no—
148C7×#102—22no—
149C7×C22⋊C8—22no—
150C7×C22⋊C8—41no—
151C7×C22⋊C8—41no—
152C7×#95—21no—
153C7×#95—21no—
154C7×#95—21no—
155C2×#554C2×C711yescharacteristic, complemented
156C2×#452C2×C711yescharacteristic, complemented
157C2×#417C2×C711yescharacteristic, complemented
158#2407C2×C711yescharacteristic
159#2024C2×C711yescharacteristic, complemented
160#2023C2×C711yescharacteristic, complemented
161#2001C2×C711yescharacteristic, complemented
162#2000C2×C711yescharacteristic, complemented
163#1894C2×C711yescharacteristic, complemented
164#1880C2×C711yescharacteristic, complemented
165#1878C2×C711yescharacteristic, complemented
166#1874C2×C711yescharacteristic, complemented
167#1872C2×C711yescharacteristic, complemented
168#1870C2×C711yescharacteristic, complemented
169#1823C2×C711yescharacteristic, complemented
170C24×C7—21no—
171C24×C7C2×D411yescharacteristic
172C24×C7C2×D411yescharacteristic
173C7×#41—28no—
174C7×#41—44no—
175C7×#41—44no—
176C7×#41—44no—
177C2×C7×Q8—24no—
178C2×C7×Q8—21no—
179C2×C7×Q8—21no—
180C2×C7×Q8—21no—
181C2×C7×Q8—21no—
182C2×C7×Q8—21no—
183C2×C7×Q8—21no—
184C2×C7×Q8—21no—
185C2×C7×Q8—21no—
186C2×C7×Q8—21no—
187C2×C7×Q8—21no—
188C2×C7×Q8—81no—
189C2×C7×Q8—81no—
190C2×C7×Q8C2×D412yes—
191C2×C7×Q8#4112yes—
192C2×C7×D4—22no—
193C2×C7×D4—22no—
194C2×C7×D4—22no—
195C2×C7×D4—21no—
196C2×C7×D4—21no—
197C2×C7×D4—21no—
198C2×C7×D4—21no—
199C2×C7×D4—21no—
200C2×C7×D4—42no—
201C2×C7×D4—42no—
202C2×C7×D4—42no—
203C2×C7×D4—42no—
204C2×C7×D4—42no—
205C2×C7×D4—81no—
206C2×C7×D4#4112yes—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—24no—
217C22×C4×C7—24no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—42no—
227C22×C4×C7—42no—
228C22×C4×C7—42no—
229C22×C4×C7—81no—
230C22×C4×C7—81no—
231C22×C4×C7—81no—
232C22×C4×C7—81no—
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D412yes—
237C22×C4×C7C2×D412yes—
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2411yescharacteristic
240C7×Q16—44no—
241C7×SD16—44no—
242C7×M16—44no—
243C2×C7×C8—21no—
244C2×C7×C8—21no—
245C2×C7×C8—21no—
246C2×C7×C8—21no—
247C2×C7×C8—21no—
248C2×C7×C8—21no—
249C2×C7×C8—21no—
250C2×C7×C8—21no—
251C2×C7×C8—21no—
252C2×C7×C8—21no—
253C2×C7×C8—21no—
254C2×C7×C8—21no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—24no—
257C7×C4⋊C4—24no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—24no—
260C7×C4⋊C4—24no—
261C7×C4⋊C4—22no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—21no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4—21no—
269C7×C4⋊C4—42no—
270C7×C4⋊C4C2×D412yes—
271C7×C4⋊C4C2×D412yes—
272C7×C4⋊C4C2×D412yes—
273C7×C22⋊C4—24no—
274C7×C22⋊C4—24no—
275C7×C22⋊C4—22no—
276C7×C22⋊C4—22no—
277C7×C22⋊C4—42no—
278C7×C22⋊C4—42no—
279C7×C22⋊C4—42no—
280C7×C22⋊C4—81no—
281C7×C22⋊C4—81no—
282C42×C7—24no—
283C42×C7—21no—
284C42×C7—21no—
285C22×#41C22×C711yescharacteristic
286C22×Q16C22×C711yescharacteristic
287C22×SD16C22×C711yescharacteristic
288C22×M16C22×C711yescharacteristic
289#554—24no—
290#554—24no—
291C2×C4⋊Q8C22×C711yescharacteristic
292C2×#125—21no—
293C2×C22⋊Q8—21no—
294C2×C22⋊Q8—21no—
295C2×C22⋊Q8C22×C711yescharacteristic
296C2×C22⋊Q8C22×C711yescharacteristic
297C2×C22⋊Q8C22×C711yescharacteristic
298C2×#121C22×C711yescharacteristic
299C2×C4×Q8C22×C711yescharacteristic
300C2×C4×D4—21no—
301C2×C4×D4C22×C711yescharacteristic
302C22×C4⋊C4C22×C711yescharacteristic
303C22×C4⋊C4C22×C711yescharacteristic
304#452—24no—
305#417—24no—
306C2×#103C22×C711yescharacteristic
307C2×#103C22×C711yescharacteristic
308C2×#103C22×C711yescharacteristic
309C2×#103C22×C711yescharacteristic
310C2×#103C22×C711yescharacteristic
311C2×#102C22×C711yescharacteristic
312C2×#102C22×C711yescharacteristic
313C2×#102C22×C711yescharacteristic
314C2×C22⋊C8C22×C711yescharacteristic
315C2×C22⋊C8C22×C711yescharacteristic
316C2×C22⋊C8C22×C711yescharacteristic
317#394—21no—
318#392—21no—
319#391C22×C711yescharacteristic
320#390C22×C711yescharacteristic
321#386—21no—
322#385—21no—
323#380C22×C711yescharacteristic
324#340C22×C711yescharacteristic
325#340C22×C711yescharacteristic
326#340C22×C711yescharacteristic
327#340C22×C711yescharacteristic
328#340C22×C711yescharacteristic
329#340C22×C711yescharacteristic
330#336C22×C711yescharacteristic
331#336C22×C711yescharacteristic
332C23×C7—21no—
333C23×C7—21no—
334C23×C7—21no—
335C23×C7—21no—
336C23×C7—21no—
337C23×C7—21no—
338C23×C7—21no—
339C23×C7—21no—
340C23×C7—21no—
341C23×C7—21no—
342C23×C7—21no—
343C23×C7—21no—
344C23×C7—22no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7#12012yes—
352C23×C7#13712yes—
353C23×C7C22×D411yescharacteristic
354C7×Q8—22no—
355C7×Q8—22no—
356C7×Q8—22no—
357C7×Q8—22no—
358C7×Q8—41no—
359C7×Q8—41no—
360C7×Q8—41no—
361C7×Q8—41no—
362C7×Q8—84no—
363C7×D4—28no—
364C7×D4—22no—
365C7×D4—22no—
366C7×D4—48no—
367C7×D4—41no—
368C7×D4—41no—
369C7×D4—84no—
370C2×C4×C7—21no—
371C2×C4×C7—21no—
372C2×C4×C7—21no—
373C2×C4×C7—21no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—21no—
380C2×C4×C7—22no—
381C2×C4×C7—21no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—21no—
385C2×C4×C7—22no—
386C2×C4×C7—21no—
387C2×C4×C7—21no—
388C2×C4×C7—21no—
389C2×C4×C7—48no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—84no—
411C2×C4×C7—84no—
412C2×C4×C7#12012yes—
413C2×C4×C7#13712yes—
414C2×C4×C7C22×D411yescharacteristic
415C2×C4×C7C22×D411yescharacteristic
416C2×C4×C7C2×#4111yescharacteristic
417C2×C4×C7C2×#4111yescharacteristic
418C2×C4×C7H(5,𝔽2)11yescharacteristic
419C2×C4×C7H(5,𝔽2)11yescharacteristic
420C7×C8—41no—
421C7×C8—41no—
422C7×C8—41no—
423C7×C8—41no—
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41—41no—
429C2×#41—41no—
430C22×Q8—21no—
431C22×Q8C23×C711yescharacteristic
432C22×Q8C23×C711yescharacteristic
433C22×D4—21no—
434C22×D4—21no—
435C22×D4C7×D411yescharacteristic
436C22×D4C23×C711yescharacteristic
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4C23×C711yescharacteristic
441C23×C4C23×C711yescharacteristic
442C2×Q16—22no—
443C2×Q16—22no—
444C2×Q16—41no—
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16—41no—
448C2×M16—22no—
449C2×M16—41no—
450C2×M16—41no—
451C22×C8C23×C711yescharacteristic
452C22×C8C23×C711yescharacteristic
453C22×C8C23×C711yescharacteristic
454C22×C8C23×C711yescharacteristic
455C4⋊Q8—22no—
456C4⋊Q8—22no—
457#125—28no—
458C22⋊Q8—28no—
459C22⋊Q8—28no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—41no—
465C22⋊Q8C7×D414yescomplemented
466#121—22no—
467#121—41no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×D4—28no—
471C4×D4—22no—
472C4×D4—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4C7×D411yescharacteristic
484C2×C4⋊C4C7×D414yescomplemented
485C2×C4⋊C4C23×C711yescharacteristic
486C2×C4⋊C4C23×C711yescharacteristic
487C2×C4⋊C4C23×C711yescharacteristic
488C2×C4⋊C4C23×C711yescharacteristic
489C2×C4⋊C4C23×C711yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4C7×D411yescharacteristic
498C2×C22⋊C4C7×D411yescharacteristic
499C2×C42—21no—
500C2×C42C23×C711yescharacteristic
501#103—22no—
502#103—22no—
503#103—22no—
504#103—41no—
505#103—41no—
506#102—22no—
507#102—22no—
508#102—22no—
509C22⋊C8—22no—
510C22⋊C8—41no—
511C22⋊C8—41no—
512#95—21no—
513#95—21no—
514#95—21no—
515C22×C7—22no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—22no—
521C22×C7—41no—
522C22×C7—41no—
523C22×C7—41no—
524C22×C7—41no—
525C22×C7—41no—
526C22×C7—41no—
527C22×C7—41no—
528C22×C7—41no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—42no—
532C22×C7—81no—
533C22×C7—81no—
534C22×C7—81no—
535C22×C7—81no—
536C22×C7C2×#12011yescharacteristic
537C22×C7#54611yescharacteristic
538C22×C7#54611yescharacteristic
539C22×C7C2×#13711yescharacteristic
540C22×C7C2×#13711yescharacteristic
541C22×C7#57611yescharacteristic
542C22×C7#57711yescharacteristic
543C4×C7—22no—
544C4×C7—22no—
545C4×C7—41no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7—41no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7—81no—
553C4×C7—81no—
554C4×C7#52511yescharacteristic
555C4×C7#53511yescharacteristic
556C4×C7#54611yescharacteristic
557C4×C7#54611yescharacteristic
558C24—21no—
559C24C2×C7×D411yescharacteristic
560C24C2×C7×D411yescharacteristic
561#41—28no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—24no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—81no—
577C2×Q8—81no—
578C2×Q8C2×C7×D412yes—
579C2×Q8C7×#4112yes—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—81no—
594C2×D4C7×#4112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4C2×C7×D411yescharacteristic
622C22×C4C2×C7×D411yescharacteristic
623C22×C4C2×C7×D411yescharacteristic
624C22×C4C2×C7×D412yes—
625C22×C4C2×C7×D412yes—
626C22×C4C2×C7×D411yescharacteristic
627C22×C4C24×C711yescharacteristic
628Q16—44no—
629SD16—44no—
630M16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—42no—
658C4⋊C4C2×C7×D412yes—
659C4⋊C4C2×C7×D412yes—
660C4⋊C4C2×C7×D412yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C42—24no—
671C42—21no—
672C42—21no—
673C2×C7—42no—
674C2×C7—42no—
675C2×C7—82no—
676C2×C7#240411yescharacteristic
677C2×C7#300411yescharacteristic
678C2×C7#301211yescharacteristic
679C2×C7#331411yescharacteristic
680C2×C7#331611yescharacteristic
681C2×C7#333111yescharacteristic
682C2×C7#333311yescharacteristic
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23C7×#12012yes—
703C23C7×#13712yes—
704C23C22×C7×D411yescharacteristic
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8—84no—
714D4—28no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—84no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—48no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4C7×#12012yes—
764C2×C4C7×#13712yes—
765C2×C4C22×C7×D411yescharacteristic
766C2×C4C22×C7×D411yescharacteristic
767C2×C4C2×C7×#4111yescharacteristic
768C2×C4C2×C7×#4111yescharacteristic
769C2×C4C7×H(5,𝔽2)11yescharacteristic
770C2×C4C7×H(5,𝔽2)11yescharacteristic
771C8—41no—
772C8—41no—
773C8—41no—
774C8—41no—
775C7#2398111yescharacteristic, direct product factor, Sylow
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22C2×C7×#12011yescharacteristic
798C22C7×#54611yescharacteristic
799C22C7×#54611yescharacteristic
800C22C2×C7×#13711yescharacteristic
801C22C2×C7×#13711yescharacteristic
802C22C7×#57611yescharacteristic
803C22C7×#57711yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—42no—
808C4—42no—
809C4—41no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—81no—
814C4—81no—
815C4C7×#52511yescharacteristic
816C4C7×#53511yescharacteristic
817C4C7×#54611yescharacteristic
818C4C7×#54611yescharacteristic
819C2—42no—
820C2—42no—
821C2—82no—
822C2C7×#240411yescharacteristic
823C2C7×#300411yescharacteristic
824C2C7×#301211yescharacteristic
825C2C7×#331411yescharacteristic
826C2C7×#331611yescharacteristic
827C2C7×#333111yescharacteristic
828C2C7×#333311yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#2407C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#554C2semidirect
2. C2×C7×#452C2semidirect
3. C2×C7×#417C2semidirect
5. C7×#2024C2semidirect
6. C7×#2023C2semidirect
7. C7×#2001C2semidirect
8. C7×#2000C2semidirect
9. C7×#1894C2semidirect
10. C7×#1880C2semidirect
11. C7×#1878C2semidirect
12. C7×#1874C2semidirect
13. C7×#1872C2semidirect
14. C7×#1870C2semidirect
15. C7×#1823C2semidirect
63. #23981C7direct (N × H)
105. C7×C22⋊Q8D4semidirect
124. C2×C7×C4⋊C4D4semidirect
155. C2×#554C2×C7semidirect
156. C2×#452C2×C7semidirect
157. C2×#417C2×C7semidirect
159. #2024C2×C7semidirect
160. #2023C2×C7semidirect
161. #2001C2×C7semidirect
162. #2000C2×C7semidirect
163. #1894C2×C7semidirect
164. #1880C2×C7semidirect
165. #1878C2×C7semidirect
166. #1874C2×C7semidirect
167. #1872C2×C7semidirect
168. #1870C2×C7semidirect
169. #1823C2×C7semidirect
465. C22⋊Q8C7×D4semidirect
484. C2×C4⋊C4C7×D4semidirect
775. C7#23981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×C7×#4522
C2×C7×#4172
C7×#24072
C7×#20242
C7×#20232
C7×#20012
C7×#20002
C7×#18942
C7×#18802
C7×#18782
C7×#18742
C7×#18722
C7×#18702
C7×#18232
#239817