Finite Group Databasebeta

← C4×#89813 #13360273

Subgroups — C4×#89813 #13360273

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
1C4×C7×#121C211yesmaximal, characteristic
2C2×#89813C211yesmaximal, characteristic
3C2×C4×#1142C211yesmaximal, characteristic, complemented
4C4×#6487C211yesmaximal, characteristic, complemented
5C22×C4×C7⋊C8C211yesmaximal, characteristic, complemented
6#11729435C211yesmaximal, characteristic
7C4×#6406C211yesmaximal, characteristic, complemented
8#11727400C211yesmaximal, characteristic, complemented
9#11727398C211yesmaximal, characteristic, complemented
10#11727372C211yesmaximal, characteristic, complemented
11#11727368C211yesmaximal, characteristic, complemented
12#11727268C211yesmaximal, characteristic, complemented
13#11727265C211yesmaximal, characteristic, complemented
14C4×#6382C211yesmaximal, characteristic, complemented
15C4×#6384C211yesmaximal, characteristic, complemented
16C2×C7×#121C2211yescharacteristic
17C2×C4×C7×D4—21no—
18C2×C4×C7×D4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×#1142C2211yescharacteristic
21C2×#6487C2211yescharacteristic
22C23×C7⋊C8C2211yescharacteristic
23C23×C7⋊C8C2211yescharacteristic
24C2×C4×Dic14C2211yescharacteristic
25C7×#390C2211yescharacteristic
26C7×#389C2211yescharacteristic
27C7×#388—21no—
28C7×#386—21no—
29C7×#380C2211yescharacteristic
30C4×C7×C4⋊C4C2211yescharacteristic
31C4×C7×C22⋊C4—21no—
32C2×#6406C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35#89984C2211yescharacteristic
36#89982—21no—
37C4×C22⋊Dic7—21no—
38#89813C418yesdirect product factor
39C4×#1142—24no—
40C2×#6384C2211yescharacteristic
41C2×#6384C2211yescharacteristic
42C2×#6384C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C2×#6382C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C4×C4⋊Dic7C2211yescharacteristic
47#89705—21no—
48C4×Dic7⋊C4—21no—
49#89701C2211yescharacteristic
50#89700C2211yescharacteristic
51C2×C4×C7⋊C8—24no—
52C2×C4×C7⋊C8C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×C4×C7⋊C8C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62C4×#465—71nomaximal, Sylow
63C22×C7×D4—21no—
64C22×C7×D4C2311yescharacteristic
65C23×C4×C7—21no—
66C23×C4×C7D411yescharacteristic
67C23×C4×C7D411yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C22×Dic14C2311yescharacteristic
70C7×#121—22no—
71C7×#121C2×C414yes—
72C4×C7×D4—22no—
73C4×C7×D4—22no—
74C4×C7×D4—44no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C7×C4⋊C4C2311yescharacteristic
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C22⋊C4—21no—
80C2×C7×C22⋊C4—21no—
81C2×C7×C22⋊C4—21no—
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—21no—
87C2×C42×C7D411yescharacteristic
88C2×C42×C7D411yescharacteristic
89C2×C42×C7C2311yescharacteristic
90C2×C42×C7C2311yescharacteristic
91C2×C22⋊Dic7—21no—
92C2×C22⋊Dic7—21no—
93C2×#1142—22no—
94C2×#1142—22no—
95C2×#1142C2×C414yescomplemented
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2311yescharacteristic
99#6487—22no—
100#6487C2×C414yescomplemented
101C2×Dic7⋊C4—21no—
102C2×Dic7⋊C4—21no—
103C2×Dic7⋊C4—21no—
104C2×C4×Dic7—21no—
105C2×C4×Dic7—21no—
106C22×C7⋊C8—22no—
107C22×C7⋊C8—22no—
108C22×C7⋊C8—22no—
109C22×C7⋊C8—22no—
110C22×C7⋊C8—22no—
111C22×C7⋊C8C2×C414yescomplemented
112C22×C7⋊C8C2311yescharacteristic
113C22×C7⋊C8C2311yescharacteristic
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C4×Dic14—22no—
117C4×Dic14—22no—
118C7×#95—21no—
119C7×#95—21no—
120C7×#95—21no—
121#6406—22no—
122#6406—22no—
123#6406C2×C414yescomplemented
124C7⋊#95—21no—
125C7⋊#95—21no—
126C7⋊#95—21no—
127C7⋊#95—21no—
128C7⋊#95—21no—
129#6384—22no—
130#6384—22no—
131#6384C2×C414yescomplemented
132#6382—22no—
133#6382—22no—
134#6382C2×C414yescomplemented
135C4×C7⋊C8—22no—
136C4×C7⋊C8—22no—
137C4×C7⋊C8—22no—
138C4×C7⋊C8D414yescomplemented
139C2×#465—71no—
140C2×C4×SD16—71no—
141C22×C4×C8—71no—
142C4×C22⋊Q8—71no—
143C4×#121D711yescharacteristic
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×D4—24no—
157C2×C7×D4—21no—
158C2×C7×D4—21no—
159C2×C7×D4—21no—
160C2×C7×D4—21no—
161C2×C7×D4—21no—
162C2×C7×D4—42no—
163C2×C7×D4—42no—
164C2×C7×D4C22×C412yes—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
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—42no—
178C22×C4×C7—42no—
179C22×C4×C7—42no—
180C22×C4×C7SD1614yescomplemented
181C22×C4×C7C22×C412yes—
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7#4112yes—
188C22×C4×C7C2411yescharacteristic
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C2×Dic14—21no—
194C2×Dic14—21no—
195C2×Dic14—21no—
196C2×Dic14—21no—
197C2×Dic14—21no—
198C2×Dic14C22×C412yes—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—21no—
201C7×C4⋊C4—21no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—42no—
205C7×C4⋊C4C22×C412yes—
206C7×C22⋊C4—24no—
207C7×C22⋊C4—42no—
208C7×C22⋊C4—42no—
209C7×C22⋊C4—42no—
210C7×C22⋊C4—42no—
211C42×C7—22no—
212C42×C7—22no—
213C42×C7—21no—
214C42×C7—21no—
215C42×C7—42no—
216C42×C7C2×D412yes—
217C42×C7#4112yes—
218C22⋊Dic7—24no—
219C22⋊Dic7—42no—
220#1142—28no—
221C4⋊Dic7—21no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7—21no—
225C4⋊Dic7—21no—
226C4⋊Dic7C22×C412yes—
227Dic7⋊C4—24no—
228Dic7⋊C4—42no—
229Dic7⋊C4—42no—
230C4×Dic7—42no—
231C4×Dic7—42no—
232C2×C7⋊C8—28no—
233C2×C7⋊C8—21no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8—21no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8—21no—
238C2×C7⋊C8—21no—
239C2×C7⋊C8—28no—
240C2×C7⋊C8C22×C412yes—
241C2×C7⋊C8C22×C412yes—
242C2×C7⋊C8C2×D412yes—
243C2×C7⋊C8C2×D412yes—
244C2×C7⋊C8#4112yes—
245C2×C7⋊C8#4112yes—
246C22×SD16—71no—
247C23×C8—71no—
248C23×C8—71no—
249C2×C22⋊Q8—71no—
250C2×#121C2×D711yescharacteristic
251C2×C4×Q8—71no—
252C2×C4×D4—21no—
253C2×C4×D4C2×D711yescharacteristic
254C22×C42C2×D711yescharacteristic
255#465—78no—
256C4×SD16—144no—
257C2×#106—71no—
258C2×#106—71no—
259C2×#106—71no—
260C2×#103—71no—
261C2×#103—71no—
262C2×#103—71no—
263C2×#102—71no—
264C2×#102—71no—
265C2×#102—71no—
266C2×C4×C8—71no—
267C2×C4×C8—71no—
268C2×C4×C8—71no—
269C2×C4×C8—71no—
270C2×C4×C8—144no—
271#391—71no—
272#390C2×D711yescharacteristic
273#389—71no—
274#389C2×D711yescharacteristic
275#388—21no—
276#387—141no—
277#386—21no—
278#385—141no—
279#380—71no—
280#380C2×D711yescharacteristic
281C4×C4⋊C4—71no—
282C4×C4⋊C4—141no—
283C4×C4⋊C4C2×D711yescharacteristic
284C4×C22⋊C4—21no—
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×D4—22no—
308C7×D4—22no—
309C7×D4—48no—
310C7×D4—41no—
311C7×D4—41no—
312C2×C4×C7—28no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—28no—
326C2×C4×C7—22no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—84no—
336C2×C4×C7C4×D412yes—
337C2×C4×C7#12112yes—
338C2×C4×C7#12112yes—
339C2×C4×C7C2×SD1612yes—
340C2×C4×C7C2×SD1612yes—
341C2×C4×C7#13512yes—
342C2×C4×C7#13512yes—
343C2×C4×C7C23×C411yescharacteristic
344C2×C4×C7C22×D411yescharacteristic
345C2×C4×C7C2×#4111yescharacteristic
346C2×C4×C7C2×#4111yescharacteristic
347C2×C4×C7C2×#4111yescharacteristic
348C2×C4×C7C2×#4111yescharacteristic
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361Dic14—22no—
362Dic14—22no—
363Dic14—41no—
364Dic14—41no—
365C7⋊C8—22no—
366C7⋊C8—22no—
367C7⋊C8—22no—
368C7⋊C8C4×D414yescomplemented
369C22×Q8—71no—
370C22×D4—21no—
371C22×D4C22×D711yescharacteristic
372C23×C4—21no—
373C23×C4C22⋊D711yescharacteristic
374C23×C4C22⋊D711yescharacteristic
375C23×C4C22×D711yescharacteristic
376C2×SD16—74no—
377C2×SD16—142no—
378C2×SD16—142no—
379C22×C8—71no—
380C22×C8—74no—
381C22×C8—71no—
382C22×C8—71no—
383C22×C8—71no—
384C22×C8—142no—
385C22×C8—142no—
386C22×C8—142no—
387C22×C8—142no—
388C22×C8—142no—
389C22⋊Q8—74no—
390C22⋊Q8—142no—
391#121—22no—
392#121C4×D714yes—
393C4×Q8—142no—
394C4×Q8—142no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—44no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—71no—
400C2×C4⋊C4—71no—
401C2×C4⋊C4—71no—
402C2×C4⋊C4—141no—
403C2×C4⋊C4—141no—
404C2×C4⋊C4—141no—
405C2×C4⋊C4C22×D711yescharacteristic
406C2×C4⋊C4C22×D711yescharacteristic
407C2×C4⋊C4C22×D711yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—141no—
414C2×C22⋊C4—141no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—21no—
418C2×C42—141no—
419C2×C42—141no—
420C2×C42C22⋊D711yescharacteristic
421C2×C42C22⋊D711yescharacteristic
422C2×C42C22×D711yescharacteristic
423C2×C42C22×D711yescharacteristic
424#106—74no—
425#106—142no—
426#106—142no—
427#103—74no—
428#103—142no—
429#103—142no—
430#102—74no—
431#102—142no—
432#102—142no—
433C4×C8—74no—
434C4×C8—142no—
435C4×C8—142no—
436C4×C8—142no—
437#95—21no—
438#95—21no—
439#95—21no—
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—22no—
468C4×C7—22no—
469C4×C7—22no—
470C4×C7—42no—
471C4×C7—81no—
472C4×C7—81no—
473C4×C7#46514yescomplemented
474C4×C7C2×C4×D411yescharacteristic
475C4×C7C4×#4111yescharacteristic
476C4×C7#52511yescharacteristic
477C4×C7#52911yescharacteristic
478Dic7—42no—
479Dic7—42no—
480Dic7—81no—
481Dic7—81no—
482C24—21no—
483C24C2×C22⋊D711yescharacteristic
484C2×Q8—72no—
485C2×Q8—141no—
486C2×Q8—141no—
487C2×Q8—141no—
488C2×Q8—141no—
489C2×Q8—141no—
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×D4C2×C4×D712yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—141no—
515C22×C4—141no—
516C22×C4—141no—
517C22×C4—141no—
518C22×C4#114214yescomplemented
519C22×C4C2×C4×D712yes—
520C22×C4#115712yes—
521C22×C4C2×C22⋊D711yescharacteristic
522C22×C4C2×C22⋊D711yescharacteristic
523C22×C4C2×C22⋊D711yescharacteristic
524C22×C4C2×C22⋊D711yescharacteristic
525C22×C4C2×C22⋊D711yescharacteristic
526C22×C4C23×D711yescharacteristic
527SD16—148no—
528C2×C8—72no—
529C2×C8—72no—
530C2×C8—72no—
531C2×C8—72no—
532C2×C8—72no—
533C2×C8—72no—
534C2×C8—148no—
535C2×C8—148no—
536C2×C8—141no—
537C2×C8—141no—
538C2×C8—141no—
539C2×C8—141no—
540C2×C8—141no—
541C2×C8—141no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—72no—
549C4⋊C4—144no—
550C4⋊C4—141no—
551C4⋊C4—141no—
552C4⋊C4—141no—
553C4⋊C4—141no—
554C4⋊C4—141no—
555C4⋊C4—282no—
556C4⋊C4—282no—
557C4⋊C4C2×C4×D712yes—
558C22⋊C4—24no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—144no—
564C22⋊C4—282no—
565C42—22no—
566C42—22no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—282no—
571C42—282no—
572C42D4×D712yes—
573C42#115912yes—
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—
594C23C4×C22⋊D712yes—
595C23C2×#114212yes—
596C23#651312yes—
597C23C22×C22⋊D711yescharacteristic
598Q8—142no—
599Q8—142no—
600Q8—281no—
601Q8—281no—
602D4—22no—
603D4—22no—
604D4—48no—
605D4—41no—
606D4—41no—
607C2×C4—28no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—28no—
621C2×C4—22no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—84no—
631C2×C4—142no—
632C2×C4—142no—
633C2×C4—281no—
634C2×C4—281no—
635C2×C4—281no—
636C2×C4—281no—
637C2×C4—281no—
638C2×C4—281no—
639C2×C4—281no—
640C2×C4—281no—
641C2×C4—281no—
642C2×C4—281no—
643C2×C4C4×C22⋊D712yes—
644C2×C4C2×#114212yes—
645C2×C4C2×#114212yes—
646C2×C4#650212yes—
647C2×C4#650212yes—
648C2×C4#651312yes—
649C2×C4#651312yes—
650C2×C4C22×C4×D711yescharacteristic
651C2×C4C2×#115711yescharacteristic
652C2×C4C2×D4×D711yescharacteristic
653C2×C4C2×#115911yescharacteristic
654C2×C4D7×#4111yescharacteristic
655C2×C4D7×#4111yescharacteristic
656C8—74no—
657C8—142no—
658C8—142no—
659C8—142no—
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—
674C22C4×#114214yescomplemented
675C22C2×C4×C22⋊D711yescharacteristic
676C22C22×#114211yescharacteristic
677C22C2×#650211yescharacteristic
678C22C2×#651311yescharacteristic
679C22C2×#651311yescharacteristic
680C22C2×#651311yescharacteristic
681C22#9052311yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—282no—
690C4—282no—
691C4—561no—
692C4—561no—
693C4#8981314yesdirect product factor
694C4C4×#115911yescharacteristic
695C4#9022911yescharacteristic
696C4C4×D4×D711yescharacteristic
697C4#9023811yescharacteristic
698C2—24no—
699C2—82no—
700C2C2×C4×#114211yescharacteristic
701C2C4×#650211yescharacteristic
702C2C4×#651311yescharacteristic
703C2C2×#8981311yescharacteristic
704C2#1174036711yescharacteristic
705C2#1174057911yescharacteristic
706C2#1174073511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#121C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
cosocleC22×C4×C7C24
hypercenterC4×#121D7
hypocenterC7C4×#465
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
3. C2×C4×#1142C2semidirect
4. C4×#6487C2semidirect
5. C22×C4×C7⋊C8C2semidirect
7. C4×#6406C2semidirect
8. #11727400C2semidirect
9. #11727398C2semidirect
10. #11727372C2semidirect
11. #11727368C2semidirect
12. #11727268C2semidirect
13. #11727265C2semidirect
14. C4×#6382C2semidirect
15. C4×#6384C2semidirect
38. #89813C4direct (N × H)
95. C2×#1142C2×C4semidirect
100. #6487C2×C4semidirect
111. C22×C7⋊C8C2×C4semidirect
123. #6406C2×C4semidirect
131. #6384C2×C4semidirect
134. #6382C2×C4semidirect
138. C4×C7⋊C8D4semidirect
180. C22×C4×C7SD16semidirect
368. C7⋊C8C4×D4semidirect
458. C22×C7C4×SD16semidirect
473. C4×C7#465semidirect
518. C22×C4#1142semidirect
660. C7C4×#465semidirect
674. C22C4×#1142semidirect
693. C4#89813direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C7×#1212
C2×#898132
C2×C4×#11422
C4×#64872
C22×C4×C7⋊C82
#117294352
C4×#64062
#117274002
#117273982
#117273722
#117273682
#117272682
#117272652
C4×#63822
C4×#63842
C4×#4657