Finite Group Databasebeta

← C7×#24381 #13201597

Subgroups — C7×#24381 #13201597

Order 1792.

1658 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C7×#465C212yesmaximal, complemented
3C2×C7×#448C211yesmaximal, characteristic, complemented
4C22×C7×C22⋊C8C211yesmaximal, characteristic, complemented
5C7×#2847C211yesmaximal, characteristic
6C7×#2035C212yesmaximal, complemented
7C7×#2000C212yesmaximal, complemented
8C7×#1892C212yesmaximal, complemented
9C7×#1874C211yesmaximal, characteristic, complemented
10C7×#1853C211yesmaximal, characteristic, complemented
11C7×#1787C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C22×C7×SD16C2212yescomplemented
15C23×C7×C8C2212yes—
16C2×C7×C22⋊Q8—21no—
17C2×C7×C22⋊Q8—21no—
18C2×C7×C22⋊Q8—28no—
19C2×C7×C22⋊Q8C2212yes—
20C2×C7×C22⋊Q8C2212yes—
21C2×C7×#121C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C7×#120—21no—
25C22×C7×C4⋊C4—21no—
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4—21no—
28C7×#465—28no—
29C7×#448—24no—
30C2×C7×#106C2212yescomplemented
31C2×C7×#103C2212yescomplemented
32C2×C7×#103C2212yescomplemented
33C2×C7×#103C2212yescomplemented
34C2×C7×#102C2212yescomplemented
35C2×C7×C22⋊C8—24no—
36C2×C7×C22⋊C8C2212yes—
37C2×C7×C22⋊C8C2211yescharacteristic
38C2×C7×C22⋊C8C2211yescharacteristic
39C7×#386—21no—
40C7×#386—21no—
41C7×#386—21no—
42C7×#380C2211yescharacteristic
43C7×#380C2211yescharacteristic
44C7×#380C2211yescharacteristic
45C7×#340C2212yescomplemented
46C7×#340C2212yescomplemented
47#24381C711yesmaximal, characteristic, direct product factor, Sylow
48C25×C7D411yescharacteristic
49C22×C7×Q8—24no—
50C22×C7×Q8—21no—
51C22×C7×Q8—22no—
52C22×C7×Q8—22no—
53C22×C7×Q8—42no—
54C22×C7×Q8C2312yes—
55C22×C7×D4—21no—
56C22×C7×D4—21no—
57C22×C7×D4—21no—
58C22×C7×D4C2311yescharacteristic
59C23×C4×C7—21no—
60C23×C4×C7—21no—
61C23×C4×C7—24no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—42no—
65C23×C4×C7D411yescharacteristic
66C23×C4×C7D411yescharacteristic
67C23×C4×C7D411yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C2×C7×SD16—24no—
72C2×C7×SD16—24no—
73C2×C7×SD16—42no—
74C22×C7×C8—24no—
75C22×C7×C8—24no—
76C22×C7×C8—42no—
77C22×C7×C8C2312yes—
78C22×C7×C8C2312yes—
79C7×C22⋊Q8—28no—
80C7×C22⋊Q8—28no—
81C7×C22⋊Q8—24no—
82C7×C22⋊Q8—24no—
83C7×C22⋊Q8—24no—
84C7×C22⋊Q8D418yescomplemented
85C7×#121—22no—
86C7×#121—24no—
87C7×#121—22no—
88C7×#121—42no—
89C7×#120—44no—
90C2×C7×C4⋊C4—28no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4C2311yescharacteristic
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2312yes—
99C2×C7×C22⋊C4—28no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4—21no—
108C7×#106—24no—
109C7×#103—24no—
110C7×#103—24no—
111C7×#103—42no—
112C7×#102—24no—
113C7×C22⋊C8—22no—
114C7×C22⋊C8—24no—
115C7×C22⋊C8D414yescomplemented
116C7×#95—21no—
117C7×#95—21no—
118C7×#95—21no—
119C22×C22⋊Q8C2×C711yescharacteristic, complemented
120C2×#465C2×C712yescomplemented
121C2×#448C2×C711yescharacteristic, complemented
122C22×C22⋊C8C2×C711yescharacteristic, complemented
123#2847C2×C711yescharacteristic
124#2035C2×C712yescomplemented
125#2000C2×C712yescomplemented
126#1892C2×C712yescomplemented
127#1874C2×C711yescharacteristic, complemented
128#1853C2×C711yescharacteristic, complemented
129#1787C2×C711yescharacteristic, complemented
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—21no—
135C24×C7—41no—
136C24×C7—41no—
137C24×C7SD1614yescomplemented
138C24×C7C2×D411yescharacteristic
139C24×C7C2×D411yescharacteristic
140C24×C7C2×D411yescharacteristic
141C2×C7×Q8—24no—
142C2×C7×Q8—22no—
143C2×C7×Q8—22no—
144C2×C7×Q8—22no—
145C2×C7×Q8—22no—
146C2×C7×Q8—22no—
147C2×C7×Q8—48no—
148C2×C7×Q8—48no—
149C2×C7×Q8—42no—
150C2×C7×Q8—42no—
151C2×C7×Q8C2×D414yes—
152C2×C7×D4—22no—
153C2×C7×D4—21no—
154C2×C7×D4—21no—
155C2×C7×D4—22no—
156C2×C7×D4—42no—
157C2×C7×D4—42no—
158C2×C7×D4—42no—
159C2×C7×D4—42no—
160C2×C7×D4—42no—
161C2×C7×D4—42no—
162C2×C7×D4—42no—
163C2×C7×D4—42no—
164C2×C7×D4—42no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—24no—
171C22×C4×C7—24no—
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—21no—
181C22×C4×C7—22no—
182C22×C4×C7—21no—
183C22×C4×C7—22no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—41no—
188C22×C4×C7—41no—
189C22×C4×C7—41no—
190C22×C4×C7—48no—
191C22×C4×C7—48no—
192C22×C4×C7—42no—
193C22×C4×C7—42no—
194C22×C4×C7—42no—
195C22×C4×C7—42no—
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D414yes—
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D412yes—
201C22×C4×C7#4112yes—
202C22×C4×C7C2411yescharacteristic
203C7×SD16—48no—
204C2×C7×C8—22no—
205C2×C7×C8—22no—
206C2×C7×C8—22no—
207C2×C7×C8—22no—
208C2×C7×C8—22no—
209C2×C7×C8—48no—
210C2×C7×C8C2×D414yes—
211C7×C4⋊C4—24no—
212C7×C4⋊C4—28no—
213C7×C4⋊C4—28no—
214C7×C4⋊C4—22no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—22no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—22no—
219C7×C4⋊C4C2×D414yes—
220C7×C22⋊C4—28no—
221C7×C22⋊C4—28no—
222C7×C22⋊C4—42no—
223C7×C22⋊C4—42no—
224C7×C22⋊C4—42no—
225C7×C22⋊C4—42no—
226C7×C22⋊C4—42no—
227C7×C22⋊C4—42no—
228C23×Q8C22×C711yescharacteristic
229C24×C4C22×C711yescharacteristic
230C22×SD16C22×C712yescomplemented
231C23×C8C22×C712yes—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—28no—
235C2×C22⋊Q8C22×C712yes—
236C2×C22⋊Q8C22×C712yes—
237C2×#121C22×C711yescharacteristic
238C2×#121C22×C711yescharacteristic
239C2×#121C22×C711yescharacteristic
240C2×#120—21no—
241C22×C4⋊C4—21no—
242C22×C4⋊C4C22×C711yescharacteristic
243C22×C22⋊C4—21no—
244#465—28no—
245#448—24no—
246C2×#106C22×C712yescomplemented
247C2×#103C22×C712yescomplemented
248C2×#103C22×C712yescomplemented
249C2×#103C22×C712yescomplemented
250C2×#102C22×C712yescomplemented
251C2×C22⋊C8—24no—
252C2×C22⋊C8C22×C711yescharacteristic
253C2×C22⋊C8C22×C712yes—
254C2×C22⋊C8C22×C711yescharacteristic
255#386—21no—
256#386—21no—
257#386—21no—
258#380C22×C711yescharacteristic
259#380C22×C711yescharacteristic
260#380C22×C711yescharacteristic
261#340C22×C712yescomplemented
262#340C22×C712yescomplemented
263C23×C7—21no—
264C23×C7—21no—
265C23×C7—21no—
266C23×C7—21no—
267C23×C7—21no—
268C23×C7—21no—
269C23×C7—21no—
270C23×C7—21no—
271C23×C7—21no—
272C23×C7—21no—
273C23×C7—21no—
274C23×C7—21no—
275C23×C7—21no—
276C23×C7—21no—
277C23×C7—28no—
278C23×C7—28no—
279C23×C7—44no—
280C23×C7—44no—
281C23×C7—44no—
282C23×C7—44no—
283C23×C7—44no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7—41no—
289C23×C7—41no—
290C23×C7—41no—
291C23×C7#12012yes—
292C23×C7#12112yes—
293C23×C7C2×SD1612yes—
294C23×C7C2×SD1612yes—
295C23×C7C2×SD1612yes—
296C23×C7#13512yes—
297C23×C7#13712yes—
298C23×C7C22×D411yescharacteristic
299C7×Q8—24no—
300C7×Q8—24no—
301C7×Q8—48no—
302C7×Q8—42no—
303C7×Q8—42no—
304C7×D4—42no—
305C7×D4—42no—
306C7×D4—84no—
307C7×D4—84no—
308C7×D4—84no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—21no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—24no—
317C2×C4×C7—24no—
318C2×C4×C7—24no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—44no—
323C2×C4×C7—44no—
324C2×C4×C7—44no—
325C2×C4×C7—48no—
326C2×C4×C7—48no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—41no—
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#12012yes—
343C2×C4×C7#12112yes—
344C2×C4×C7C22×D411yescharacteristic
345C2×C4×C7C22×D412yes—
346C2×C4×C7C2×#4111yescharacteristic
347C2×C4×C7H(5,𝔽2)12yes—
348C7×C8—24no—
349C7×C8—42no—
350C25C7×D411yescharacteristic
351C22×Q8—24no—
352C22×Q8—21no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—42no—
356C22×Q8C23×C712yes—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4C23×C711yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—24no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—42no—
367C23×C4C7×D411yescharacteristic
368C23×C4C7×D411yescharacteristic
369C23×C4C7×D411yescharacteristic
370C23×C4C23×C711yescharacteristic
371C23×C4C23×C711yescharacteristic
372C23×C4C23×C711yescharacteristic
373C2×SD16—24no—
374C2×SD16—24no—
375C2×SD16—42no—
376C22×C8—24no—
377C22×C8—24no—
378C22×C8—42no—
379C22×C8C23×C712yes—
380C22×C8C23×C712yes—
381C22⋊Q8—28no—
382C22⋊Q8—28no—
383C22⋊Q8—24no—
384C22⋊Q8—24no—
385C22⋊Q8—24no—
386C22⋊Q8C7×D418yescomplemented
387#121—22no—
388#121—24no—
389#121—22no—
390#121—42no—
391#120—44no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4C23×C711yescharacteristic
398C2×C4⋊C4C23×C711yescharacteristic
399C2×C4⋊C4C23×C711yescharacteristic
400C2×C4⋊C4C23×C712yes—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410#106—24no—
411#103—24no—
412#103—24no—
413#103—42no—
414#102—24no—
415C22⋊C8—22no—
416C22⋊C8—24no—
417C22⋊C8C7×D414yescomplemented
418#95—21no—
419#95—21no—
420#95—21no—
421C22×C7—22no—
422C22×C7—22no—
423C22×C7—22no—
424C22×C7—22no—
425C22×C7—22no—
426C22×C7—22no—
427C22×C7—22no—
428C22×C7—22no—
429C22×C7—22no—
430C22×C7—22no—
431C22×C7—22no—
432C22×C7—22no—
433C22×C7—22no—
434C22×C7—22no—
435C22×C7—22no—
436C22×C7—416no—
437C22×C7—41no—
438C22×C7—41no—
439C22×C7—41no—
440C22×C7—41no—
441C22×C7—81no—
442C22×C7—81no—
443C22×C7—81no—
444C22×C7—81no—
445C22×C7—81no—
446C22×C7—81no—
447C22×C7—81no—
448C22×C7#44814yescomplemented
449C22×C7#46514yescomplemented
450C22×C7C2×#12011yescharacteristic
451C22×C7C2×#12111yescharacteristic
452C22×C7#53411yescharacteristic
453C22×C7C22×SD1611yescharacteristic
454C22×C7C2×#13511yescharacteristic
455C22×C7C2×#13711yescharacteristic
456C22×C7#57511yescharacteristic
457C4×C7—22no—
458C4×C7—22no—
459C4×C7—41no—
460C4×C7—44no—
461C4×C7—44no—
462C4×C7—81no—
463C4×C7—81no—
464C4×C7—81no—
465C4×C7D4212yes—
466C4×C7#54612yes—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—21no—
472C24—41no—
473C24—41no—
474C24C7×SD1614yescomplemented
475C24C2×C7×D411yescharacteristic
476C24C2×C7×D411yescharacteristic
477C24C2×C7×D411yescharacteristic
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8C2×C7×D414yes—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—22no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4C2×C7×D411yescharacteristic
534C22×C4C2×C7×D411yescharacteristic
535C22×C4C2×C7×D414yes—
536C22×C4C2×C7×D411yescharacteristic
537C22×C4C2×C7×D412yes—
538C22×C4C7×#4112yes—
539C22×C4C24×C711yescharacteristic
540SD16—48no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—48no—
547C2×C8C2×C7×D414yes—
548C4⋊C4—24no—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—22no—
556C4⋊C4C2×C7×D414yes—
557C22⋊C4—28no—
558C22⋊C4—28no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C2×C7—24no—
566C2×C7—24no—
567C2×C7—42no—
568C2×C7—161no—
569C2×C7#241011yescharacteristic
570C2×C7C2×#44811yescharacteristic
571C2×C7#300211yescharacteristic
572C2×C7C2×#46511yescharacteristic
573C2×C7#305611yescharacteristic
574C2×C7#318711yescharacteristic
575C2×C7#319011yescharacteristic
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—28no—
591C23—28no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C7×#12012yes—
605C23C7×#12112yes—
606C23C2×C7×SD1612yes—
607C23C2×C7×SD1612yes—
608C23C2×C7×SD1612yes—
609C23C7×#13512yes—
610C23C7×#13712yes—
611C23C22×C7×D411yescharacteristic
612Q8—24no—
613Q8—24no—
614Q8—48no—
615Q8—42no—
616Q8—42no—
617D4—42no—
618D4—42no—
619D4—84no—
620D4—84no—
621D4—84no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—48no—
639C2×C4—48no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4C7×#12012yes—
656C2×C4C7×#12112yes—
657C2×C4C22×C7×D411yescharacteristic
658C2×C4C22×C7×D412yes—
659C2×C4C2×C7×#4111yescharacteristic
660C2×C4C7×H(5,𝔽2)12yes—
661C8—24no—
662C8—42no—
663C7#2438111yescharacteristic, direct product factor, Sylow
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—416no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C7×#44814yescomplemented
692C22C7×#46514yescomplemented
693C22C2×C7×#12011yescharacteristic
694C22C2×C7×#12111yescharacteristic
695C22C7×#53411yescharacteristic
696C22C22×C7×SD1611yescharacteristic
697C22C2×C7×#13511yescharacteristic
698C22C2×C7×#13711yescharacteristic
699C22C7×#57511yescharacteristic
700C4—22no—
701C4—22no—
702C4—41no—
703C4—44no—
704C4—44no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C7×D4212yes—
709C4C7×#54612yes—
710C2—24no—
711C2—24no—
712C2—42no—
713C2—161no—
714C2C7×#241011yescharacteristic
715C2C2×C7×#44811yescharacteristic
716C2C7×#300211yescharacteristic
717C2C2×C7×#46511yescharacteristic
718C2C7×#305611yescharacteristic
719C2C7×#318711yescharacteristic
720C2C7×#319011yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×C22⋊Q8C2semidirect
2. C2×C7×#465C2semidirect
3. C2×C7×#448C2semidirect
4. C22×C7×C22⋊C8C2semidirect
6. C7×#2035C2semidirect
7. C7×#2000C2semidirect
8. C7×#1892C2semidirect
9. C7×#1874C2semidirect
10. C7×#1853C2semidirect
11. C7×#1787C2semidirect
14. C22×C7×SD16C22semidirect
30. C2×C7×#106C22semidirect
31. C2×C7×#103C22semidirect
32. C2×C7×#103C22semidirect
33. C2×C7×#103C22semidirect
34. C2×C7×#102C22semidirect
45. C7×#340C22semidirect
46. C7×#340C22semidirect
47. #24381C7direct (N × H)
84. C7×C22⋊Q8D4semidirect
115. C7×C22⋊C8D4semidirect
119. C22×C22⋊Q8C2×C7semidirect
120. C2×#465C2×C7semidirect
121. C2×#448C2×C7semidirect
122. C22×C22⋊C8C2×C7semidirect
124. #2035C2×C7semidirect
125. #2000C2×C7semidirect
126. #1892C2×C7semidirect
127. #1874C2×C7semidirect
128. #1853C2×C7semidirect
129. #1787C2×C7semidirect
137. C24×C7SD16semidirect
230. C22×SD16C22×C7semidirect
246. C2×#106C22×C7semidirect
247. C2×#103C22×C7semidirect
248. C2×#103C22×C7semidirect
249. C2×#103C22×C7semidirect
250. C2×#102C22×C7semidirect
261. #340C22×C7semidirect
262. #340C22×C7semidirect
386. C22⋊Q8C7×D4semidirect
417. C22⋊C8C7×D4semidirect
448. C22×C7#448semidirect
449. C22×C7#465semidirect
474. C24C7×SD16semidirect
663. C7#24381direct (N × H)
691. C22C7×#448semidirect
692. C22C7×#465semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×C7×#4652
C2×C7×#4482
C22×C7×C22⋊C82
C7×#28472
C7×#20352
C7×#20002
C7×#18922
C7×#18742
C7×#18532
C7×#17872
#243817