Finite Group Databasebeta

← Dic7×#465 #13360278

Subgroups — Dic7×#465 #13360278

Order 1792.

1138 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#465C211yesmaximal, characteristic
2C2×SD16×Dic7C211yesmaximal, characteristic, complemented
3C22×C8×Dic7C211yesmaximal, characteristic, complemented
4Dic7×C22⋊Q8C211yesmaximal, characteristic, complemented
5Dic7×#121C211yesmaximal, characteristic
6#11729803C211yesmaximal, characteristic, complemented
7#11729724C211yesmaximal, characteristic, complemented
8#11729450C211yesmaximal, characteristic, complemented
9#11729435C211yesmaximal, characteristic
10#11728314C211yesmaximal, characteristic, complemented
11Dic7×#106C211yesmaximal, characteristic, complemented
12#11728007C211yesmaximal, characteristic, complemented
13Dic7×#103C211yesmaximal, characteristic, complemented
14#11727939C211yesmaximal, characteristic, complemented
15Dic7×#102C211yesmaximal, characteristic, complemented
16C22×C7×SD16C2211yescharacteristic
17C23×C7×C8C2211yescharacteristic
18C2×C7×C22⋊Q8C2211yescharacteristic
19C2×C7×#121C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C2×D4×Dic7—21no—
22C2×D4×Dic7C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C23×C7⋊C8C2211yescharacteristic
25C7×#465C418yescomplemented
26C2×C7×#106C2211yescharacteristic
27C2×C7×#103C2211yescharacteristic
28C2×C7×#102C2211yescharacteristic
29#90002C2211yescharacteristic
30C2×#6409C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32#89993C2211yescharacteristic
33#89992—21no—
34C2×#6406C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36#89984C2211yescharacteristic
37#89984C2211yescharacteristic
38SD16×Dic7—24no—
39C2×#6391C2211yescharacteristic
40C2×#6391C2211yescharacteristic
41C2×C8×Dic7—24no—
42C2×C8×Dic7C2211yescharacteristic
43C2×C8×Dic7C2211yescharacteristic
44C2×C8×Dic7C2211yescharacteristic
45C2×C8×Dic7C2211yescharacteristic
46#89757C2211yescharacteristic
47#89757C2211yescharacteristic
48#89753—21no—
49C4⋊C4×Dic7—21no—
50C4⋊C4×Dic7C2211yescharacteristic
51C4⋊C4×Dic7C2211yescharacteristic
52#89723—21no—
53#89722—21no—
54C22⋊C4×Dic7—21no—
55C22⋊C4×Dic7—21no—
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62C4×#465—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×C7×D4—21no—
65C22×C7×D4C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7—21no—
68C23×Dic7D411yescharacteristic
69C23×Dic7D411yescharacteristic
70C2×C7×SD16—22no—
71C2×C7×SD16—22no—
72C2×C7×SD16C2×C414yescomplemented
73C22×C7×C8—22no—
74C22×C7×C8—22no—
75C22×C7×C8C2×C414yescomplemented
76C22×C7×C8C2311yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C7×C22⋊Q8—22no—
79C7×C22⋊Q8C2×C414yescomplemented
80C7×#121—22no—
81C7×#121C2×C414yes—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—21no—
87C2×C22⋊Dic7—21no—
88C2×C22⋊Dic7—21no—
89C2×C22⋊Dic7—21no—
90C2×C22⋊Dic7—21no—
91C2×C22⋊Dic7—21no—
92Q8×Dic7—22no—
93Q8×Dic7—22no—
94D4×Dic7—22no—
95D4×Dic7—22no—
96D4×Dic7—44no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4⋊Dic7C2311yescharacteristic
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—21no—
107C2×C4×Dic7—21no—
108C2×C4×Dic7—21no—
109C2×C4×Dic7D411yescharacteristic
110C2×C4×Dic7D411yescharacteristic
111C2×C4×Dic7C2311yescharacteristic
112C2×C4×Dic7C2311yescharacteristic
113C22×C7⋊C8—22no—
114C22×C7⋊C8—22no—
115C22×C7⋊C8—22no—
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C7×#106C2×C414yescomplemented
119C7×#103C2×C414yescomplemented
120C7×#102C2×C414yescomplemented
121#6409—22no—
122#6409—22no—
123#6406—22no—
124#6406—22no—
125C7⋊#95—21no—
126C7⋊#95—21no—
127C7⋊#95—21no—
128C7⋊#95—21no—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C7⋊#95—21no—
132C7⋊#95—21no—
133#6391—22no—
134#6391—22no—
135C8×Dic7—22no—
136C8×Dic7—22no—
137C8×Dic7—22no—
138C8×Dic7D414yescomplemented
139C2×#465D711yescharacteristic
140C2×C4×SD16—71no—
141C22×C4×C8—71no—
142C4×C22⋊Q8—71no—
143C4×#121—71no—
144#1968—71no—
145#1941—71no—
146#1934—71no—
147#1933—71no—
148#1893—71no—
149#1892—71no—
150#1807—71no—
151C4×#106—71no—
152C4×#103—71no—
153C4×#102—71no—
154C24×C7—21no—
155C24×C7C2×D411yescharacteristic
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8C22×C412yes—
162C2×C7×D4—24no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—42no—
169C2×C7×D4—42no—
170C2×C7×D4C22×C412yes—
171C22×C4×C7—21no—
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×C7C22×C412yes—
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7#4112yes—
181C22×C4×C7C2411yescharacteristic
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—42no—
192C22×Dic7—42no—
193C22×Dic7—42no—
194C22×Dic7SD1614yescomplemented
195C22×Dic7C2×D411yescharacteristic
196C22×Dic7C2×D411yescharacteristic
197C22×Dic7C2×D411yescharacteristic
198C22×Dic7C2×D411yescharacteristic
199C7×SD16—28no—
200C2×C7×C8—21no—
201C2×C7×C8—21no—
202C2×C7×C8—28no—
203C2×C7×C8C22×C412yes—
204C2×C7×C8C22×C412yes—
205C2×C7×C8C2×D412yes—
206C2×C7×C8#4112yes—
207C7×C4⋊C4—24no—
208C7×C4⋊C4—21no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4C22×C412yes—
211C7×C4⋊C4C22×C412yes—
212C7×C22⋊C4—24no—
213C7×C22⋊C4—24no—
214C22⋊Dic7—42no—
215C22⋊Dic7—42no—
216C22⋊Dic7—42no—
217C22⋊Dic7—42no—
218C22⋊Dic7—42no—
219C4⋊Dic7—21no—
220C4⋊Dic7—21no—
221C4⋊Dic7—21no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7—21no—
225C4⋊Dic7—21no—
226C4⋊Dic7—21no—
227C4⋊Dic7—42no—
228C4⋊Dic7—42no—
229C4⋊Dic7—42no—
230C4×Dic7—21no—
231C4×Dic7—21no—
232C4×Dic7—22no—
233C4×Dic7—22no—
234C4×Dic7—42no—
235C4×Dic7—42no—
236C4×Dic7—42no—
237C4×Dic7C2×D412yes—
238C4×Dic7#4112yes—
239C2×C7⋊C8—28no—
240C2×C7⋊C8—21no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8C2×D412yes—
245C2×C7⋊C8#4112yes—
246C22×SD16C2×D711yescharacteristic
247C23×C8—71no—
248C23×C8C2×D711yescharacteristic
249C2×C22⋊Q8C2×D711yescharacteristic
250C2×#121C2×D711yescharacteristic
251C2×C4×Q8—71no—
252C2×C4×D4—71no—
253C2×C4×D4—141no—
254C22×C42—71no—
255#465Dic718yesdirect product factor
256C4×SD16—144no—
257C2×#106—71no—
258C2×#106—71no—
259C2×#106C2×D711yescharacteristic
260C2×#103—71no—
261C2×#103—71no—
262C2×#103C2×D711yescharacteristic
263C2×#102—71no—
264C2×#102—71no—
265C2×#102C2×D711yescharacteristic
266C2×C4×C8—71no—
267C2×C4×C8—71no—
268C2×C4×C8—71no—
269C2×C4×C8—71no—
270C2×C4×C8—144no—
271#391—71no—
272#390—71no—
273#389—71no—
274#389—71no—
275#388—141no—
276#387—141no—
277#386—141no—
278#385—141no—
279#380—71no—
280#380—71no—
281C4×C4⋊C4—71no—
282C4×C4⋊C4—71no—
283C4×C4⋊C4—141no—
284C4×C22⋊C4—141no—
285C4×C22⋊C4—141no—
286#340—71no—
287#340—71no—
288#340—71no—
289#340—71no—
290#340—71no—
291#340—71no—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—21no—
296C23×C7—22no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7C4×D412yes—
304C23×C7C2×SD1612yes—
305C23×C7#13512yes—
306C23×C7C22×D411yescharacteristic
307C7×Q8—22no—
308C7×Q8—22no—
309C7×Q8—41no—
310C7×Q8—41no—
311C7×D4—22no—
312C7×D4—22no—
313C7×D4—48no—
314C7×D4—41no—
315C7×D4—41no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7C4×D412yes—
332C2×C4×C7C23×C411yescharacteristic
333C2×C4×C7C22×D411yescharacteristic
334C2×C4×C7C2×#4111yescharacteristic
335C2×C4×C7C2×#4111yescharacteristic
336C2×C4×C7C2×#4111yescharacteristic
337C2×C4×C7C2×#4111yescharacteristic
338C2×Dic7—28no—
339C2×Dic7—21no—
340C2×Dic7—21no—
341C2×Dic7—21no—
342C2×Dic7—21no—
343C2×Dic7—21no—
344C2×Dic7—21no—
345C2×Dic7—28no—
346C2×Dic7—41no—
347C2×Dic7—41no—
348C2×Dic7—41no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—84no—
359C2×Dic7#12112yes—
360C2×Dic7#12112yes—
361C2×Dic7C2×SD1612yes—
362C2×Dic7C2×SD1612yes—
363C2×Dic7#13512yes—
364C2×Dic7#13512yes—
365C7×C8—22no—
366C7×C8C4×D414yescomplemented
367C7⋊C8—22no—
368C7⋊C8—22no—
369C22×Q8C22×D711yescharacteristic
370C22×D4—21no—
371C22×D4C22×D711yescharacteristic
372C23×C4—71no—
373C23×C4—71no—
374C23×C4—141no—
375C23×C4C22×D711yescharacteristic
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16C2×Dic714yescomplemented
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—71no—
382C22×C8—71no—
383C22×C8—142no—
384C22×C8—142no—
385C22×C8—142no—
386C22×C8C2×Dic714yescomplemented
387C22×C8C22×D711yescharacteristic
388C22×C8C22×D711yescharacteristic
389C22⋊Q8—22no—
390C22⋊Q8C2×Dic714yescomplemented
391#121—22no—
392#121C2×Dic714yes—
393C4×Q8—142no—
394C4×Q8—142no—
395C4×D4—142no—
396C4×D4—142no—
397C4×D4—284no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—71no—
400C2×C4⋊C4—71no—
401C2×C4⋊C4—71no—
402C2×C4⋊C4—71no—
403C2×C4⋊C4—141no—
404C2×C4⋊C4—141no—
405C2×C4⋊C4—141no—
406C2×C4⋊C4C22×D711yescharacteristic
407C2×C4⋊C4C22×D711yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—141no—
411C2×C22⋊C4—141no—
412C2×C22⋊C4—141no—
413C2×C22⋊C4—141no—
414C2×C22⋊C4—141no—
415C2×C42—71no—
416C2×C42—71no—
417C2×C42—71no—
418C2×C42—71no—
419C2×C42—142no—
420C2×C42—142no—
421C2×C42—141no—
422C2×C42—141no—
423C2×C42—141no—
424#106—142no—
425#106—142no—
426#106C2×Dic714yescomplemented
427#103—142no—
428#103—142no—
429#103C2×Dic714yescomplemented
430#102—142no—
431#102—142no—
432#102C2×Dic714yescomplemented
433C4×C8—74no—
434C4×C8—142no—
435C4×C8—142no—
436C4×C8—142no—
437#95—141no—
438#95—141no—
439#95—141no—
440#95—141no—
441#95—141no—
442#95—141no—
443#95—141no—
444#95—141no—
445C22×C7—22no—
446C22×C7—22no—
447C22×C7—22no—
448C22×C7—22no—
449C22×C7—22no—
450C22×C7—22no—
451C22×C7—42no—
452C22×C7—42no—
453C22×C7—42no—
454C22×C7—81no—
455C22×C7—81no—
456C22×C7—81no—
457C22×C7—81no—
458C22×C7C4×SD1614yescomplemented
459C22×C7C2×C4×D411yescharacteristic
460C22×C7C2×#12111yescharacteristic
461C22×C7#53211yescharacteristic
462C22×C7C22×SD1611yescharacteristic
463C22×C7C2×#13511yescharacteristic
464C22×C7C2×#13511yescharacteristic
465C22×C7C2×#13511yescharacteristic
466C4×C7—22no—
467C4×C7—42no—
468C4×C7—42no—
469C4×C7—42no—
470C4×C7C2×C4×D411yescharacteristic
471C4×C7C4×#4111yescharacteristic
472C4×C7#52511yescharacteristic
473C4×C7#52911yescharacteristic
474Dic7—22no—
475Dic7—22no—
476Dic7—22no—
477Dic7—81no—
478Dic7—81no—
479Dic7—81no—
480Dic7—81no—
481Dic7#46514yesdirect product factor
482C24—21no—
483C24D4×D711yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C22×Dic712yes—
490C2×D4—24no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4C22×Dic712yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—71no—
507C22×C4—74no—
508C22×C4—71no—
509C22×C4—71no—
510C22×C4—71no—
511C22×C4—142no—
512C22×C4—142no—
513C22×C4—142no—
514C22×C4—142no—
515C22×C4—142no—
516C22×C4—141no—
517C22×C4—141no—
518C22×C4—141no—
519C22×C4—141no—
520C22×C4—282no—
521C22×C4—282no—
522C22×C4—282no—
523C22×C4D4×D711yescharacteristic
524C22×C4#115912yes—
525C22×C4C22×Dic712yes—
526C22×C4C23×D711yescharacteristic
527SD16—28no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—28no—
531C2×C8—72no—
532C2×C8—72no—
533C2×C8—148no—
534C2×C8—141no—
535C2×C8—141no—
536C2×C8—141no—
537C2×C8—141no—
538C2×C8D4×D712yes—
539C2×C8#115912yes—
540C2×C8C22×Dic712yes—
541C2×C8C22×Dic712yes—
542C4⋊C4—24no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—141no—
546C4⋊C4—141no—
547C4⋊C4—141no—
548C4⋊C4—141no—
549C4⋊C4—141no—
550C4⋊C4—141no—
551C4⋊C4—141no—
552C4⋊C4—141no—
553C4⋊C4—282no—
554C4⋊C4—282no—
555C4⋊C4—282no—
556C4⋊C4C22×Dic712yes—
557C4⋊C4C22×Dic712yes—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—282no—
561C22⋊C4—282no—
562C22⋊C4—282no—
563C22⋊C4—282no—
564C22⋊C4—282no—
565C42—72no—
566C42—72no—
567C42—142no—
568C42—142no—
569C42—141no—
570C42—141no—
571C42—282no—
572C42—282no—
573C42—282no—
574C2×C7—24no—
575C2×C7—82no—
576C2×C7C4×#12111yescharacteristic
577C2×C7C2×C4×SD1611yescharacteristic
578C2×C7C4×#13511yescharacteristic
579C2×C7C2×#46511yescharacteristic
580C2×C7#305011yescharacteristic
581C2×C7#316711yescharacteristic
582C2×C7#316811yescharacteristic
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23D7×SD1612yes—
595C23#647912yes—
596C23D4×Dic712yes—
597C23C2×D4×D711yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—41no—
601Q8—41no—
602D4—22no—
603D4—22no—
604D4—48no—
605D4—41no—
606D4—41no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—72no—
623C2×C4—72no—
624C2×C4—72no—
625C2×C4—72no—
626C2×C4—72no—
627C2×C4—72no—
628C2×C4—148no—
629C2×C4—148no—
630C2×C4—141no—
631C2×C4—141no—
632C2×C4—141no—
633C2×C4—141no—
634C2×C4—141no—
635C2×C4—141no—
636C2×C4—281no—
637C2×C4—281no—
638C2×C4—281no—
639C2×C4—281no—
640C2×C4—281no—
641C2×C4—281no—
642C2×C4—281no—
643C2×C4—281no—
644C2×C4—281no—
645C2×C4—281no—
646C2×C4—281no—
647C2×C4—281no—
648C2×C4—564no—
649C2×C4D4×Dic712yes—
650C2×C4C2×D4×D711yescharacteristic
651C2×C4C2×#115911yescharacteristic
652C2×C4C2×#115911yescharacteristic
653C2×C4D7×#4111yescharacteristic
654C2×C4D7×#4111yescharacteristic
655C2×C4C23×Dic711yescharacteristic
656C8—22no—
657C8—142no—
658C8—142no—
659C8D4×Dic714yescomplemented
660C7C4×#46511yescharacteristic, complemented, Sylow
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22SD16×Dic714yescomplemented
675C22#9028711yescharacteristic
676C22D7×#12111yescharacteristic
677C22C2×D7×SD1611yescharacteristic
678C22C2×#647911yescharacteristic
679C22D7×#13511yescharacteristic
680C22D7×#13511yescharacteristic
681C22C2×D4×Dic711yescharacteristic
682C4—22no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—74no—
687C4—142no—
688C4—142no—
689C4—142no—
690C4—561no—
691C4—561no—
692C4—561no—
693C4—561no—
694C4#9029111yescharacteristic
695C4#9029711yescharacteristic
696C4C2×D4×Dic711yescharacteristic
697C4#41×Dic711yescharacteristic
698C2—24no—
699C2—82no—
700C2#1173807711yescharacteristic
701C2#1173807811yescharacteristic
702C2D7×#46511yescharacteristic
703C2#1173810111yescharacteristic
704C2Dic7×#12111yescharacteristic
705C2C2×SD16×Dic711yescharacteristic
706C2Dic7×#13511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#465C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
cosocleC22×C4×C7C24
hypercenterC2×#465D7
hypocenterC7C4×#465
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic7C2semidirect
3. C22×C8×Dic7C2semidirect
4. Dic7×C22⋊Q8C2semidirect
6. #11729803C2semidirect
7. #11729724C2semidirect
8. #11729450C2semidirect
10. #11728314C2semidirect
11. Dic7×#106C2semidirect
12. #11728007C2semidirect
13. Dic7×#103C2semidirect
14. #11727939C2semidirect
15. Dic7×#102C2semidirect
25. C7×#465C4semidirect
72. C2×C7×SD16C2×C4semidirect
75. C22×C7×C8C2×C4semidirect
79. C7×C22⋊Q8C2×C4semidirect
118. C7×#106C2×C4semidirect
119. C7×#103C2×C4semidirect
120. C7×#102C2×C4semidirect
138. C8×Dic7D4semidirect
194. C22×Dic7SD16semidirect
255. #465Dic7direct (N × H)
366. C7×C8C4×D4semidirect
378. C2×SD16C2×Dic7semidirect
386. C22×C8C2×Dic7semidirect
390. C22⋊Q8C2×Dic7semidirect
426. #106C2×Dic7semidirect
429. #103C2×Dic7semidirect
432. #102C2×Dic7semidirect
458. C22×C7C4×SD16semidirect
481. Dic7#465direct (N × H)
659. C8D4×Dic7semidirect
660. C7C4×#465semidirect
674. C22SD16×Dic7semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4652
C2×SD16×Dic72
C22×C8×Dic72
Dic7×C22⋊Q82
Dic7×#1212
#117298032
#117297242
#117294502
#117294352
#117283142
Dic7×#1062
#117280072
Dic7×#1032
#117279392
Dic7×#1022
C4×#4657