Finite Group Databasebeta

← C4×#89775 #13360949

Subgroups — C4×#89775 #13360949

Order 1792.

972 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×#117C211yesmaximal, characteristic, complemented
2C2×#89775C211yesmaximal, characteristic
3C4×#6493C211yesmaximal, characteristic
4#11729340C211yesmaximal, characteristic
5#11729330C211yesmaximal, characteristic, complemented
6#11729329C211yesmaximal, characteristic, complemented
7C4×C22⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
8C4×#6381C211yesmaximal, characteristic, complemented
9C4×#6382C211yesmaximal, characteristic, complemented
10C4×#6383C211yesmaximal, characteristic, complemented
11C4×#6383C211yesmaximal, characteristic, complemented
12#11727217C211yesmaximal, characteristic, complemented
13#11727216C211yesmaximal, characteristic, complemented
14#11727215C211yesmaximal, characteristic, complemented
15#11727214C211yesmaximal, characteristic, complemented
16C2×C7×#117C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C2×#6493C2211yescharacteristic
20C2×C4×C22⋊D7—21no—
21C2×C4×D28C2211yescharacteristic
22C4×C7×C4⋊C4C2211yescharacteristic
23C4×C7×C4⋊C4C2211yescharacteristic
24C4×C7×C4⋊C4C2211yescharacteristic
25C4×C7×C4⋊C4C2211yescharacteristic
26C4×C7×C22⋊C4—21no—
27C4×C7×C22⋊C4—21no—
28C7×#376—21no—
29C43×C7—21no—
30#89985—21no—
31#89984C2211yescharacteristic
32C2×C22⋊(C7⋊C8)C2211yescharacteristic
33C2×C22⋊(C7⋊C8)C2211yescharacteristic
34#89775C418yesdirect product factor
35C2×#6383C2211yescharacteristic
36C2×#6383C2211yescharacteristic
37C2×#6383C2211yescharacteristic
38C2×#6383C2211yescharacteristic
39C2×#6382C2211yescharacteristic
40C2×#6382C2211yescharacteristic
41C2×#6381C2211yescharacteristic
42C2×#6381C2211yescharacteristic
43#89712—21no—
44#89711C2211yescharacteristic
45C4×(C2×D7)⋊C4—21no—
46C4×C4⋊Dic7C2211yescharacteristic
47#89700C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49C2×C4×C7⋊C8C2211yescharacteristic
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60C4×#482—71nomaximal, Sylow
61C23×C4×C7D411yescharacteristic
62C23×C4×C7D411yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C22×C22⋊D7—21no—
65C22×D28C2311yescharacteristic
66C22×C4×D7—21no—
67C7×#117—22no—
68C7×#117—22no—
69C7×#117—22no—
70C7×#117C2×C414yescomplemented
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C22⋊C4—21no—
76C2×C7×C22⋊C4—21no—
77C2×C42×C7—21no—
78C2×C42×C7—21no—
79C2×C42×C7—22no—
80C2×C42×C7—22no—
81C2×C42×C7—21no—
82C2×C42×C7—21no—
83C2×C42×C7—21no—
84C2×C42×C7—21no—
85C2×C42×C7D411yescharacteristic
86C2×C42×C7D411yescharacteristic
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—21no—
90#6493—22no—
91#6493C2×C414yes—
92C4×C22⋊D7—44no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100C2×Dic7⋊C4—21no—
101C2×C4×Dic7—21no—
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106C4×D28—22no—
107C4×D28—22no—
108C7×#95—21no—
109C7×#95—21no—
110C7×#95—21no—
111C7×#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C22⋊(C7⋊C8)—22no—
116C22⋊(C7⋊C8)C2×C414yescomplemented
117#6383—22no—
118#6383—22no—
119#6383C2×C414yescomplemented
120#6383C2×C414yescomplemented
121#6382—22no—
122#6382C2×C414yescomplemented
123#6381—22no—
124#6381C2×C414yescomplemented
125C4×C7⋊C8—22no—
126C4×C7⋊C8—22no—
127C2×#482—71no—
128C4×#121—71no—
129C4×#117D711yescharacteristic, complemented
130#1926—71no—
131#1925—71no—
132#1921—71no—
133#1920—71no—
134#1875—71no—
135#1854—71no—
136#1825—71no—
137C4×#107—71no—
138C4×#106—71no—
139C4×#102—71no—
140C4×#102—71no—
141C4×C22⋊C8—71no—
142C24×C7C2×D411yescharacteristic
143C23×D7—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—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—41no—
158C22×C4×C7C22×C412yes—
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7#4112yes—
165C22×C4×C7C2411yescharacteristic
166C2×C22⋊D7—24no—
167C2×C22⋊D7—42no—
168C2×C22⋊D7—42no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C2×D28—21no—
173C2×D28—21no—
174C2×D28—21no—
175C2×D28—21no—
176C2×D28—21no—
177C2×D28C22×C412yes—
178C2×C4×D7—42no—
179C2×C4×D7—42no—
180C2×C4×D7—42no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4C22×C412yes—
186C7×C4⋊C4C22×C412yes—
187C7×C4⋊C4#4112yes—
188C7×C4⋊C4#4112yes—
189C7×C22⋊C4—24no—
190C7×C22⋊C4—24no—
191C42×C7—24no—
192C42×C7—24no—
193C42×C7—22no—
194C42×C7—22no—
195C42×C7—21no—
196C42×C7—21no—
197C42×C7—42no—
198C42×C7—42no—
199C42×C7—42no—
200C42×C7—42no—
201C42×C7#4112yes—
202C42×C7#4112yes—
203C22⋊Dic7—42no—
204(C2×D7)⋊C4—24no—
205(C2×D7)⋊C4—42no—
206(C2×D7)⋊C4—42no—
207(C2×D7)⋊C4—42no—
208C4⋊Dic7—21no—
209C4⋊Dic7—21no—
210C4⋊Dic7—21no—
211C4⋊Dic7—21no—
212C4⋊Dic7—21no—
213C4⋊Dic7C22×C412yes—
214Dic7⋊C4—42no—
215C4×Dic7—42no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8—21no—
221C2×C7⋊C8—21no—
222C2×C7⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8—21no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8C22×C412yes—
227C2×C7⋊C8C22×C412yes—
228C2×#121—71no—
229C2×C4×D4—71no—
230C2×C4×D4—141no—
231C2×#117C2×D711yescharacteristic
232C2×#117C2×D711yescharacteristic
233C22×C42C2×D711yescharacteristic
234#482—78no—
235C2×#107—71no—
236C2×#107—71no—
237C2×#106—71no—
238C2×#106—71no—
239C2×#102—71no—
240C2×#102—71no—
241C2×#102—71no—
242C2×#102—71no—
243C2×C22⋊C8—71no—
244C2×C22⋊C8—71no—
245C2×C4×C8—71no—
246C2×C4×C8—71no—
247#390—71no—
248#389—71no—
249#388—141no—
250#386—141no—
251#380—71no—
252C4×C4⋊C4—71no—
253C4×C4⋊C4C2×D711yescharacteristic
254C4×C4⋊C4C2×D711yescharacteristic
255C4×C4⋊C4C2×D711yescharacteristic
256C4×C4⋊C4C2×D711yescharacteristic
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—141no—
260#376—21no—
261C43—21no—
262#340—71no—
263#340—71no—
264#340—71no—
265#340—71no—
266#340—71no—
267#340—71no—
268#340—71no—
269#340—71no—
270#336—71no—
271#336—71no—
272C23×C7—21no—
273C23×C7—21no—
274C23×C7—21no—
275C23×C7—21no—
276C23×C7—21no—
277C23×C7—21no—
278C23×C7C4×D412yes—
279C23×C7C22×D411yescharacteristic
280C22×D7—22no—
281C22×D7—41no—
282C22×D7—41no—
283C22×D7—41no—
284C22×D7—41no—
285C22×D7—41no—
286C22×D7—41no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—21no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—21no—
303C2×C4×C7—21no—
304C2×C4×C7—44no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—41no—
312C2×C4×C7—41no—
313C2×C4×C7—44no—
314C2×C4×C7C4×D412yes—
315C2×C4×C7#12312yes—
316C2×C4×C7#12312yes—
317C2×C4×C7#13512yes—
318C2×C4×C7#13512yes—
319C2×C4×C7AGL(1,ℤ/8)12yes—
320C2×C4×C7C23×C411yescharacteristic
321C2×C4×C7C2×#4111yescharacteristic
322C2×C4×C7C2×#4111yescharacteristic
323C2×C4×C7C2×#4111yescharacteristic
324C2×C4×C7C2×#4111yescharacteristic
325C2×C4×C7C2×#4111yescharacteristic
326C22⋊D7—48no—
327C2×Dic7—22no—
328C2×Dic7—41no—
329C2×Dic7—41no—
330C2×Dic7—41no—
331C2×Dic7—41no—
332C2×Dic7—41no—
333C2×Dic7—41no—
334C2×Dic7—41no—
335C2×Dic7—41no—
336D28—22no—
337D28—22no—
338D28—41no—
339D28—41no—
340C4×D7—84no—
341C7⋊C8—22no—
342C7⋊C8—22no—
343C7⋊C8—41no—
344C7⋊C8—41no—
345C22×D4—71no—
346C22×D4—141no—
347C23×C4—141no—
348C23×C4C22⋊D711yescharacteristic
349C23×C4C22⋊D711yescharacteristic
350C23×C4C22×D711yescharacteristic
351C22×C8—71no—
352C22×C8—71no—
353C22×C8—71no—
354C22×C8—71no—
355#121—74no—
356#121—142no—
357C4×D4—142no—
358C4×D4—142no—
359C4×D4—284no—
360#117—22no—
361#117—22no—
362#117—22no—
363#117C4×D714yescomplemented
364C2×C4⋊C4—71no—
365C2×C4⋊C4—71no—
366C2×C4⋊C4—71no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4C22×D711yescharacteristic
369C2×C4⋊C4C22×D711yescharacteristic
370C2×C4⋊C4C22×D711yescharacteristic
371C2×C4⋊C4C22×D711yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—141no—
375C2×C22⋊C4—141no—
376C2×C22⋊C4—141no—
377C2×C22⋊C4—141no—
378C2×C22⋊C4—141no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—141no—
388C2×C42C22⋊D711yescharacteristic
389C2×C42C22⋊D711yescharacteristic
390C2×C42C22×D711yescharacteristic
391C2×C42C22×D711yescharacteristic
392#107—74no—
393#107—142no—
394#106—74no—
395#106—142no—
396#102—74no—
397#102—74no—
398#102—142no—
399#102—142no—
400C22⋊C8—74no—
401C22⋊C8—142no—
402C4×C8—142no—
403C4×C8—142no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—141no—
409#95—141no—
410#95—141no—
411C22×C7—22no—
412C22×C7—22no—
413C22×C7—22no—
414C22×C7—41no—
415C22×C7—41no—
416C22×C7—41no—
417C22×C7—41no—
418C22×C7C2×C4×D411yescharacteristic
419C22×C7C2×#12311yescharacteristic
420C22×C7#52511yescharacteristic
421C22×C7C2×#13511yescharacteristic
422C22×C7C2×#13511yescharacteristic
423C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C7#57511yescharacteristic
425C2×D7—42no—
426C2×D7—42no—
427C2×D7—42no—
428C2×D7—81no—
429C2×D7—81no—
430C2×D7—81no—
431C2×D7—81no—
432C4×C7—22no—
433C4×C7—22no—
434C4×C7—22no—
435C4×C7—41no—
436C4×C7—42no—
437C4×C7—42no—
438C4×C7—42no—
439C4×C7—42no—
440C4×C7#48214yescomplemented
441C4×C7C4×#4111yescharacteristic
442C4×C7C4×#4111yescharacteristic
443C4×C7#52911yescharacteristic
444C4×C7#52911yescharacteristic
445Dic7—42no—
446Dic7—81no—
447Dic7—81no—
448C24—141no—
449C24C2×C22⋊D711yescharacteristic
450C2×D4—72no—
451C2×D4—144no—
452C2×D4—141no—
453C2×D4—141no—
454C2×D4—141no—
455C2×D4—141no—
456C2×D4—141no—
457C2×D4—282no—
458C2×D4—282no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—41no—
473C22×C4—141no—
474C22×C4—141no—
475C22×C4—141no—
476C22×C4—282no—
477C22×C4—282no—
478C22×C4—282no—
479C22×C4C2×C4×D712yes—
480C22×C4#115712yes—
481C22×C4C2×C22⋊D711yescharacteristic
482C22×C4C2×C22⋊D711yescharacteristic
483C22×C4C2×C22⋊D711yescharacteristic
484C22×C4C2×C22⋊D711yescharacteristic
485C22×C4C2×C22⋊D711yescharacteristic
486C22×C4C23×D711yescharacteristic
487C2×C8—72no—
488C2×C8—72no—
489C2×C8—141no—
490C2×C8—141no—
491C2×C8—141no—
492C2×C8—141no—
493C2×C8—141no—
494C2×C8—141no—
495C2×C8—141no—
496C2×C8—141no—
497C2×C8—141no—
498C2×C8—141no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—72no—
504C4⋊C4—141no—
505C4⋊C4—141no—
506C4⋊C4—141no—
507C4⋊C4—141no—
508C4⋊C4—141no—
509C4⋊C4—282no—
510C4⋊C4C2×C4×D712yes—
511C4⋊C4C2×C4×D712yes—
512C4⋊C4#115712yes—
513C4⋊C4#115712yes—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—144no—
517C22⋊C4—282no—
518C22⋊C4—282no—
519C22⋊C4—282no—
520C22⋊C4—282no—
521C42—24no—
522C42—24no—
523C42—22no—
524C42—22no—
525C42—21no—
526C42—21no—
527C42—42no—
528C42—42no—
529C42—42no—
530C42—42no—
531C42—282no—
532C42#115712yes—
533C42#115712yes—
534C2×C7—42no—
535C2×C7C4×#12311yescharacteristic
536C2×C7C4×#13511yescharacteristic
537C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
538C2×C7C2×#48211yescharacteristic
539C2×C7#309111yescharacteristic
540C2×C7#310211yescharacteristic
541C2×C7#310611yescharacteristic
542D7—82no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—142no—
550C23—281no—
551C23—281no—
552C23—281no—
553C23—281no—
554C23—281no—
555C23—281no—
556C23C4×C22⋊D712yes—
557C23C22×C22⋊D711yescharacteristic
558D4—142no—
559D4—142no—
560D4—288no—
561D4—281no—
562D4—281no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—44no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—44no—
590C2×C4—142no—
591C2×C4—281no—
592C2×C4—281no—
593C2×C4—281no—
594C2×C4—281no—
595C2×C4—281no—
596C2×C4—281no—
597C2×C4—281no—
598C2×C4—281no—
599C2×C4—564no—
600C2×C4C4×C22⋊D712yes—
601C2×C4#649212yes—
602C2×C4#649212yes—
603C2×C4#651212yes—
604C2×C4#651312yes—
605C2×C4#651312yes—
606C2×C4C22×C4×D711yescharacteristic
607C2×C4C2×#115711yescharacteristic
608C2×C4C2×#115711yescharacteristic
609C2×C4C2×#115711yescharacteristic
610C2×C4C2×#115711yescharacteristic
611C2×C4C2×#115711yescharacteristic
612C8—142no—
613C8—142no—
614C8—281no—
615C8—281no—
616C7C4×#48211yescharacteristic, complemented, Sylow
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—282no—
625C22—282no—
626C22—282no—
627C22—561no—
628C22—561no—
629C22—561no—
630C22—561no—
631C22C2×C4×C22⋊D711yescharacteristic
632C22C2×#649211yescharacteristic
633C22#9048211yescharacteristic
634C22C2×#651211yescharacteristic
635C22C2×#651311yescharacteristic
636C22C2×#651311yescharacteristic
637C22#9051311yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—282no—
647C4—561no—
648C4—561no—
649C4#8977514yesdirect product factor
650C4C4×#115711yescharacteristic
651C4C4×#115711yescharacteristic
652C4#9017011yescharacteristic
653C4#9017011yescharacteristic
654C2—42no—
655C2—562no—
656C2C4×#649211yescharacteristic
657C2C2×#8977511yescharacteristic
658C2#1173966011yescharacteristic
659C2C4×#651311yescharacteristic
660C2C4×#651211yescharacteristic
661C2#1173997311yescharacteristic
662C2#1173997411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#117C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenterC4×#117D7
hypocenterC7C4×#482
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
1. C4×C7×#117C2semidirect
5. #11729330C2semidirect
6. #11729329C2semidirect
7. C4×C22⋊(C7⋊C8)C2semidirect
8. C4×#6381C2semidirect
9. C4×#6382C2semidirect
10. C4×#6383C2semidirect
11. C4×#6383C2semidirect
12. #11727217C2semidirect
13. #11727216C2semidirect
14. #11727215C2semidirect
15. #11727214C2semidirect
34. #89775C4direct (N × H)
70. C7×#117C2×C4semidirect
116. C22⋊(C7⋊C8)C2×C4semidirect
119. #6383C2×C4semidirect
120. #6383C2×C4semidirect
122. #6382C2×C4semidirect
124. #6381C2×C4semidirect
129. C4×#117D7semidirect
363. #117C4×D7semidirect
440. C4×C7#482semidirect
616. C7C4×#482semidirect
649. C4#89775direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C7×#1172
C2×#897752
C4×#64932
#117293402
#117293302
#117293292
C4×C22⋊(C7⋊C8)2
C4×#63812
C4×#63822
C4×#63832
#117272172
#117272162
#117272152
#117272142
C4×#4827