Finite Group Databasebeta

← C4×#89638 #13360953

Subgroups — C4×#89638 #13360953

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
1C2×#89638C211yesmaximal, characteristic
2C4×#6458C211yesmaximal, characteristic
3C4×#6455C211yesmaximal, characteristic, complemented
4C4×C7×#106C211yesmaximal, characteristic, complemented
5#11728334C211yesmaximal, characteristic, complemented
6#11728323C211yesmaximal, characteristic, complemented
7#11728312C211yesmaximal, characteristic, complemented
8C4×#6395C211yesmaximal, characteristic, complemented
9C4×(C2×D7)⋊C8C211yesmaximal, characteristic, complemented
10C4×#6381C211yesmaximal, characteristic, complemented
11C4×#6383C211yesmaximal, characteristic, complemented
12#11726635C211yesmaximal, characteristic
13#11726627C211yesmaximal, characteristic, complemented
14#11726575C211yesmaximal, characteristic, complemented
15#11726545C211yesmaximal, characteristic, complemented
16C2×#6458C2211yescharacteristic
17C2×#6455C2211yescharacteristic
18C2×#6455C2211yescharacteristic
19C2×C4×D28—21no—
20C2×C4×D28C2211yescharacteristic
21C2×C42×D7C2211yescharacteristic
22C2×C7×#106C2211yescharacteristic
23C2×C7×#106C2211yescharacteristic
24C2×C4×C7×C8C2211yescharacteristic
25C4×C7×C4⋊C4C2211yescharacteristic
26C4×C7×C4⋊C4C2211yescharacteristic
27C2×#6395C2211yescharacteristic
28C2×#6395C2211yescharacteristic
29C2×(C2×D7)⋊C8C2211yescharacteristic
30C2×(C2×D7)⋊C8C2211yescharacteristic
31#89760C2211yescharacteristic
32#89759C2211yescharacteristic
33#89757C2211yescharacteristic
34C4⋊C4×Dic7C2211yescharacteristic
35C4⋊C4×Dic7C2211yescharacteristic
36C2×#6383C2211yescharacteristic
37C2×#6383C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39C2×#6381C2211yescharacteristic
40C4×(C2×D7)⋊C4—21no—
41C4×(C2×D7)⋊C4—21no—
42C4×C4⋊Dic7C2211yescharacteristic
43C42×Dic7—21no—
44C2×C4×C7⋊C8C2211yescharacteristic
45#89638C418yesdirect product factor
46#89442—21no—
47#89438—21no—
48#89437—21no—
49#89420—21no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60C4×#482—71nomaximal, Sylow
61C22×D28—21no—
62C22×D28C2311yescharacteristic
63C22×C4×D7—21no—
64C22×C4×D7D411yescharacteristic
65C22×C4×D7D411yescharacteristic
66C22×C4×D7C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C42×C7—21no—
74C2×C42×C7—21no—
75C2×C42×C7C2311yescharacteristic
76C2×(C2×D7)⋊C4—21no—
77C2×(C2×D7)⋊C4—21no—
78C2×(C2×D7)⋊C4—21no—
79C2×(C2×D7)⋊C4—21no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4—21no—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4×Dic7—21no—
88C2×C4×Dic7—21no—
89C2×C4×Dic7—21no—
90C2×C4×Dic7—21no—
91C2×C4×Dic7—21no—
92C2×C4×Dic7D411yescharacteristic
93C2×C4×Dic7D411yescharacteristic
94C2×C4×Dic7C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97#6458—22no—
98#6458C2×C414yes—
99#6455—22no—
100#6455—22no—
101#6455—22no—
102#6455C2×C414yescomplemented
103C4×D28—22no—
104C4×D28—22no—
105C4×D28—44no—
106C42×D7—22no—
107C42×D7—22no—
108C7×#106—22no—
109C7×#106C2×C414yescomplemented
110C4×C7×C8—22no—
111C7×#95—21no—
112C7×#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118#6395—22no—
119#6395C2×C414yescomplemented
120(C2×D7)⋊C8—22no—
121(C2×D7)⋊C8C2×C414yescomplemented
122#6383—22no—
123#6383C2×C414yescomplemented
124#6381—22no—
125#6381C2×C414yescomplemented
126C4×C7⋊C8—22no—
127C2×#482—71no—
128C4×#121—71no—
129C4×#117—71no—
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×#106D711yescharacteristic, complemented
139C4×#102—71no—
140C4×#102—71no—
141C4×C22⋊C8—71no—
142C23×D7—21no—
143C23×D7C2×D411yescharacteristic
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2411yescharacteristic
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7C2×D411yescharacteristic
155C22×Dic7C2×D411yescharacteristic
156C22×Dic7C2×D411yescharacteristic
157C2×D28—21no—
158C2×D28—21no—
159C2×D28—21no—
160C2×D28—21no—
161C2×D28—24no—
162C2×D28—21no—
163C2×D28—42no—
164C2×D28—42no—
165C2×D28C22×C412yes—
166C2×C4×D7—21no—
167C2×C4×D7—21no—
168C2×C4×D7—21no—
169C2×C4×D7—21no—
170C2×C4×D7—22no—
171C2×C4×D7—22no—
172C2×C4×D7—22no—
173C2×C4×D7—22no—
174C2×C4×D7—22no—
175C2×C4×D7—41no—
176C2×C4×D7—42no—
177C2×C4×D7—42no—
178C2×C4×D7—42no—
179C2×C4×D7C22×C412yes—
180C2×C4×D7#4112yes—
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8C22×C412yes—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—21no—
190C7×C4⋊C4—21no—
191C7×C4⋊C4—21no—
192C7×C4⋊C4C22×C412yes—
193C7×C4⋊C4C22×C412yes—
194C7×C4⋊C4#4112yes—
195C42×C7—42no—
196C42×C7—42no—
197C42×C7#4112yes—
198C42×C7#4112yes—
199(C2×D7)⋊C4—24no—
200(C2×D7)⋊C4—24no—
201(C2×D7)⋊C4—24no—
202(C2×D7)⋊C4—42no—
203(C2×D7)⋊C4—42no—
204(C2×D7)⋊C4—42no—
205(C2×D7)⋊C4—42no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—21no—
209C4⋊Dic7—21no—
210C4⋊Dic7—42no—
211C4⋊Dic7C22×C412yes—
212C4⋊Dic7#4112yes—
213C4×Dic7—24no—
214C4×Dic7—22no—
215C4×Dic7—22no—
216C4×Dic7—21no—
217C4×Dic7—21no—
218C4×Dic7—24no—
219C4×Dic7—42no—
220C4×Dic7—42no—
221C4×Dic7—42no—
222C2×C7⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8—21no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8C22×C412yes—
228C2×#121—71no—
229C2×C4×D4—71no—
230C2×C4×D4—141no—
231C2×#117—71no—
232C2×#117—71no—
233C22×C42—71no—
234#482—78no—
235C2×#107—71no—
236C2×#107—71no—
237C2×#106C2×D711yescharacteristic
238C2×#106C2×D711yescharacteristic
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×C8C2×D711yescharacteristic
247#390—71no—
248#389—71no—
249#388—141no—
250#386—141no—
251#380—71no—
252C4×C4⋊C4—71no—
253C4×C4⋊C4—71no—
254C4×C4⋊C4—71no—
255C4×C4⋊C4C2×D711yescharacteristic
256C4×C4⋊C4C2×D711yescharacteristic
257C4×C22⋊C4—141no—
258C4×C22⋊C4—141no—
259C4×C22⋊C4—141no—
260#376—141no—
261C43—141no—
262#340—71no—
263#340—71no—
264#340—71no—
265#340—71no—
266#340—71no—
267#340—71no—
268#340C2×D711yescharacteristic
269#340C2×D711yescharacteristic
270#336—71no—
271#336—71no—
272C23×C7C22×D411yescharacteristic
273C22×D7—21no—
274C22×D7—21no—
275C22×D7—21no—
276C22×D7—21no—
277C22×D7—21no—
278C22×D7—21no—
279C22×D7—22no—
280C22×D7—41no—
281C22×D7—41no—
282C22×D7—41no—
283C22×D7—41no—
284C22×D7—41no—
285C22×D7—41no—
286C22×D7C4×D412yes—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—22no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7#12312yes—
302C2×C4×C7#12312yes—
303C2×C4×C7#13512yes—
304C2×C4×C7AGL(1,ℤ/8)12yes—
305C2×C4×C7C23×C411yescharacteristic
306C2×C4×C7C2×#4111yescharacteristic
307C2×C4×C7C2×#4111yescharacteristic
308C2×C4×C7C2×#4111yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
310C2×C4×C7C2×#4111yescharacteristic
311C2×Dic7—21no—
312C2×Dic7—21no—
313C2×Dic7—21no—
314C2×Dic7—21no—
315C2×Dic7—22no—
316C2×Dic7—21no—
317C2×Dic7—22no—
318C2×Dic7—21no—
319C2×Dic7—21no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7C4×D412yes—
328C2×Dic7#13512yes—
329D28—22no—
330D28—22no—
331D28—48no—
332D28—41no—
333D28—41no—
334C4×D7—22no—
335C4×D7—22no—
336C4×D7—22no—
337C4×D7—22no—
338C4×D7—44no—
339C4×D7—44no—
340C4×D7—84no—
341C7×C8—22no—
342C7×C8—41no—
343C7⋊C8—22no—
344C7⋊C8—41no—
345C22×D4—71no—
346C22×D4—141no—
347C23×C4—71no—
348C23×C4—71no—
349C23×C4—71no—
350C23×C4—141no—
351C22×C8—71no—
352C22×C8—71no—
353C22×C8C22×D711yescharacteristic
354C22×C8C22×D711yescharacteristic
355#121—74no—
356#121—142no—
357C4×D4—142no—
358C4×D4—142no—
359C4×D4—284no—
360#117—74no—
361#117—142no—
362#117—142no—
363#117—142no—
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—141no—
373C2×C22⋊C4—141no—
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—71no—
382C2×C42—71no—
383C2×C42—71no—
384C2×C42—141no—
385C2×C42—141no—
386C2×C42—142no—
387C2×C42—142no—
388C2×C42—141no—
389C2×C42—141no—
390C2×C42—141no—
391C2×C42C22×D711yescharacteristic
392#107—74no—
393#107—142no—
394#106—22no—
395#106C4×D714yescomplemented
396#102—74no—
397#102—74no—
398#102—142no—
399#102—142no—
400C22⋊C8—74no—
401C22⋊C8—142no—
402C4×C8—22no—
403C4×C8—142no—
404#95—21no—
405#95—21no—
406#95—141no—
407#95—141no—
408#95—141no—
409#95—141no—
410#95—141no—
411C22×C7C2×C4×D411yescharacteristic
412C22×C7C2×#12311yescharacteristic
413C22×C7#52511yescharacteristic
414C22×C7C2×#13511yescharacteristic
415C22×C7C2×#13511yescharacteristic
416C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C7#57511yescharacteristic
418C2×D7—22no—
419C2×D7—22no—
420C2×D7—22no—
421C2×D7—41no—
422C2×D7—41no—
423C2×D7—41no—
424C2×D7—41no—
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—42no—
434C4×C7—42no—
435C4×C7—42no—
436C4×C7—81no—
437C4×C7#48214yescomplemented
438C4×C7C4×#4111yescharacteristic
439C4×C7C4×#4111yescharacteristic
440C4×C7#52911yescharacteristic
441C4×C7#52911yescharacteristic
442Dic7—22no—
443Dic7—22no—
444Dic7—41no—
445Dic7—42no—
446Dic7—42no—
447Dic7—81no—
448C24—71no—
449C24—141no—
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—71no—
464C22×C4—71no—
465C22×C4—72no—
466C22×C4—72no—
467C22×C4—71no—
468C22×C4—142no—
469C22×C4—141no—
470C22×C4—141no—
471C22×C4—141no—
472C22×C4—141no—
473C22×C4—141no—
474C22×C4—141no—
475C22×C4—142no—
476C22×C4—142no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—141no—
480C22×C4—281no—
481C22×C4—282no—
482C22×C4—282no—
483C22×C4—282no—
484C22×C4D4×D711yescharacteristic
485C22×C4D4×D711yescharacteristic
486C22×C4C23×D711yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—72no—
493C2×C8—141no—
494C2×C8—141no—
495C2×C8—141no—
496C2×C8—141no—
497C2×C8—141no—
498C2×C8C2×C4×D712yes—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—72no—
505C4⋊C4—72no—
506C4⋊C4—141no—
507C4⋊C4—141no—
508C4⋊C4—141no—
509C4⋊C4—141no—
510C4⋊C4—282no—
511C4⋊C4C2×C4×D712yes—
512C4⋊C4C2×C4×D712yes—
513C4⋊C4#115712yes—
514C22⋊C4—144no—
515C22⋊C4—144no—
516C22⋊C4—144no—
517C22⋊C4—282no—
518C22⋊C4—282no—
519C22⋊C4—282no—
520C22⋊C4—282no—
521C42—42no—
522C42—42no—
523C42—144no—
524C42—144no—
525C42—142no—
526C42—142no—
527C42—141no—
528C42—141no—
529C42—282no—
530C42—282no—
531C42—282no—
532C42#115712yes—
533C42#116112yes—
534C2×C7C4×#12311yescharacteristic
535C2×C7C4×#13511yescharacteristic
536C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
537C2×C7C2×#48211yescharacteristic
538C2×C7#309111yescharacteristic
539C2×C7#310211yescharacteristic
540C2×C7#310611yescharacteristic
541D7—42no—
542D7—82no—
543C23—72no—
544C23—141no—
545C23—141no—
546C23—141no—
547C23—141no—
548C23—141no—
549C23—141no—
550C23—142no—
551C23—281no—
552C23—281no—
553C23—281no—
554C23—281no—
555C23—281no—
556C23—281no—
557C23C2×D4×D711yescharacteristic
558D4—142no—
559D4—142no—
560D4—288no—
561D4—281no—
562D4—281no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—72no—
578C2×C4—72no—
579C2×C4—141no—
580C2×C4—141no—
581C2×C4—141no—
582C2×C4—141no—
583C2×C4—142no—
584C2×C4—142no—
585C2×C4—142no—
586C2×C4—142no—
587C2×C4—141no—
588C2×C4—141no—
589C2×C4—141no—
590C2×C4—142no—
591C2×C4—142no—
592C2×C4—284no—
593C2×C4—281no—
594C2×C4—281no—
595C2×C4—281no—
596C2×C4—281no—
597C2×C4—284no—
598C2×C4—281no—
599C2×C4—281no—
600C2×C4—281no—
601C2×C4—564no—
602C2×C4#645712yes—
603C2×C4#645712yes—
604C2×C4#647712yes—
605C2×C4#647912yes—
606C2×C4C22×C4×D711yescharacteristic
607C2×C4C2×#115711yescharacteristic
608C2×C4C2×#115711yescharacteristic
609C2×C4C2×#116111yescharacteristic
610C2×C4D7×#4111yescharacteristic
611C2×C4D7×#4111yescharacteristic
612C8—22no—
613C8—41no—
614C8—142no—
615C8—281no—
616C7C4×#48211yescharacteristic, complemented, Sylow
617C22—142no—
618C22—142no—
619C22—142no—
620C22—281no—
621C22—281no—
622C22—281no—
623C22—281no—
624C22—282no—
625C22—282no—
626C22—282no—
627C22—561no—
628C22—561no—
629C22—561no—
630C22—561no—
631C22C2×#645711yescharacteristic
632C22C4×D4×D711yescharacteristic
633C22#9023811yescharacteristic
634C22C2×#647711yescharacteristic
635C22C2×#647911yescharacteristic
636C22D7×#13511yescharacteristic
637C22#9045911yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—142no—
644C4—142no—
645C4—282no—
646C4—282no—
647C4—281no—
648C4—561no—
649C4#8963814yesdirect product factor
650C4C4×#115711yescharacteristic
651C4#9021911yescharacteristic
652C4C4×#116111yescharacteristic
653C4#9027111yescharacteristic
654C2—282no—
655C2—562no—
656C2C4×#645711yescharacteristic
657C2C2×#8963811yescharacteristic
658C2#1173663011yescharacteristic
659C2C4×#647911yescharacteristic
660C2C4×#647711yescharacteristic
661C2#1173709711yescharacteristic
662C2#1173714011yescharacteristic
subgroupG/H
centerC22×C4D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#106C2
socleC23×C7C22×D4
prime radicalC2×#6458C22
cosocleC22×C4×C7C24
hypercenterC4×#106D7
hypocenterC7C4×#482
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
3. C4×#6455C2semidirect
4. C4×C7×#106C2semidirect
5. #11728334C2semidirect
6. #11728323C2semidirect
7. #11728312C2semidirect
8. C4×#6395C2semidirect
9. C4×(C2×D7)⋊C8C2semidirect
10. C4×#6381C2semidirect
11. C4×#6383C2semidirect
13. #11726627C2semidirect
14. #11726575C2semidirect
15. #11726545C2semidirect
45. #89638C4direct (N × H)
102. #6455C2×C4semidirect
109. C7×#106C2×C4semidirect
119. #6395C2×C4semidirect
121. (C2×D7)⋊C8C2×C4semidirect
123. #6383C2×C4semidirect
125. #6381C2×C4semidirect
138. C4×#106D7semidirect
395. #106C4×D7semidirect
437. C4×C7#482semidirect
616. C7C4×#482semidirect
649. C4#89638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#896382
C4×#64582
C4×#64552
C4×C7×#1062
#117283342
#117283232
#117283122
C4×#63952
C4×(C2×D7)⋊C82
C4×#63812
C4×#63832
#117266352
#117266272
#117265752
#117265452
C4×#4827