Finite Group Databasebeta

← C4×#89509 #13360951

Subgroups — C4×#89509 #13360951

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×#6493C211yesmaximal, characteristic
2C4×#6489C211yesmaximal, characteristic, complemented
3C2×#89509C211yesmaximal, characteristic
4C4×C7×C22⋊C8C211yesmaximal, characteristic, complemented
5#11727687C211yesmaximal, characteristic
6#11727683C211yesmaximal, characteristic, complemented
7#11727680C211yesmaximal, characteristic, complemented
8C4×#6392C211yesmaximal, characteristic, complemented
9C4×#6391C211yesmaximal, characteristic, complemented
10C4×#6395C211yesmaximal, characteristic, complemented
11C4×#6395C211yesmaximal, characteristic, complemented
12#11726380C211yesmaximal, characteristic, complemented
13#11726379C211yesmaximal, characteristic, complemented
14#11726378C211yesmaximal, characteristic, complemented
15#11726377C211yesmaximal, characteristic, complemented
16C22×C42×C7C2211yescharacteristic
17C2×#6493C2211yescharacteristic
18C2×C4×C22⋊D7—21no—
19C2×#6489C2211yescharacteristic
20C2×#6489C2211yescharacteristic
21C2×C4×D28C2211yescharacteristic
22C2×C7×C22⋊C8C2211yescharacteristic
23C2×C7×C22⋊C8C2211yescharacteristic
24C2×C4×C7×C8C2211yescharacteristic
25C2×C4×C7×C8C2211yescharacteristic
26#89985—21no—
27#89984C2211yescharacteristic
28C4×C22⋊Dic7—21no—
29C4×C22⋊Dic7—21no—
30C2×#6395C2211yescharacteristic
31C2×#6395C2211yescharacteristic
32C2×#6395C2211yescharacteristic
33C2×#6395C2211yescharacteristic
34C2×#6392C2211yescharacteristic
35C2×#6392C2211yescharacteristic
36C2×#6391C2211yescharacteristic
37C2×#6391C2211yescharacteristic
38#89712—21no—
39#89711C2211yescharacteristic
40C4×(C2×D7)⋊C4—21no—
41C4×C4⋊Dic7C2211yescharacteristic
42C4×C4⋊Dic7C2211yescharacteristic
43C4×C4⋊Dic7C2211yescharacteristic
44C4×C4⋊Dic7C2211yescharacteristic
45C4×C4⋊Dic7C2211yescharacteristic
46#89704—21no—
47C42×Dic7—21no—
48#89700C2211yescharacteristic
49#89509C418yesdirect product factor
50C7×#336C2211yescharacteristic
51C7×#336C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60C4×#482—71nomaximal, Sylow
61C23×C4×C7D411yescharacteristic
62C23×C4×C7D411yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C22×C22⋊D7—21no—
65C22×D28C2311yescharacteristic
66C22×C4×D7—21no—
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C22×C7×C8C2311yescharacteristic
71C2×C42×C7—22no—
72C2×C42×C7—22no—
73C2×C42×C7D411yescharacteristic
74C2×C42×C7D411yescharacteristic
75C2×C42×C7C2311yescharacteristic
76C2×C42×C7C2311yescharacteristic
77C2×C22⋊Dic7—21no—
78C2×C22⋊Dic7—21no—
79C2×C22⋊Dic7—21no—
80#6493—22no—
81#6493C2×C414yes—
82C4×C22⋊D7—44no—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4—21no—
85C2×(C2×D7)⋊C4—21no—
86C2×(C2×D7)⋊C4—21no—
87#6489—22no—
88#6489—22no—
89#6489—22no—
90#6489C2×C414yescomplemented
91C2×C4⋊Dic7C2311yescharacteristic
92C2×C4⋊Dic7C2311yescharacteristic
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2311yescharacteristic
95C2×C4⋊Dic7C2311yescharacteristic
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2311yescharacteristic
98C2×Dic7⋊C4—21no—
99C2×C4×Dic7—21no—
100C2×C4×Dic7—21no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7—21no—
104C2×C4×Dic7—21no—
105C2×C4×Dic7—21no—
106C4×D28—22no—
107C4×D28—22no—
108C7×C22⋊C8—22no—
109C7×C22⋊C8C2×C414yescomplemented
110C4×C7×C8—22no—
111C4×C7×C8—22no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119#6395—22no—
120#6395—22no—
121#6395C2×C414yescomplemented
122#6395C2×C414yescomplemented
123#6392—22no—
124#6392C2×C414yescomplemented
125#6391—22no—
126#6391C2×C414yescomplemented
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×#106—71no—
139C4×#102—71no—
140C4×#102—71no—
141C4×C22⋊C8D711yescharacteristic, complemented
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—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—41no—
154C22×C4×C7C22×C412yes—
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7#4112yes—
161C22×C4×C7C2411yescharacteristic
162C2×C22⋊D7—24no—
163C2×C22⋊D7—42no—
164C2×C22⋊D7—42no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
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—
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8C22×C412yes—
192C2×C7×C8C22×C412yes—
193C42×C7—22no—
194C42×C7—22no—
195C42×C7—21no—
196C42×C7—21no—
197C42×C7#4112yes—
198C42×C7#4112yes—
199C22⋊Dic7—24no—
200C22⋊Dic7—24no—
201C22⋊Dic7—42no—
202(C2×D7)⋊C4—24no—
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—21no—
211C4⋊Dic7—21no—
212C4⋊Dic7—21no—
213C4⋊Dic7—21no—
214C4⋊Dic7—21no—
215C4⋊Dic7C22×C412yes—
216C4⋊Dic7C22×C412yes—
217C4⋊Dic7C22×C412yes—
218C4⋊Dic7#4112yes—
219C4⋊Dic7#4112yes—
220Dic7⋊C4—42no—
221C4×Dic7—24no—
222C4×Dic7—24no—
223C4×Dic7—42no—
224C4×Dic7—42no—
225C4×Dic7—42no—
226C4×Dic7—42no—
227C4×Dic7—42no—
228C2×#121—71no—
229C2×C4×D4—71no—
230C2×C4×D4—141no—
231C2×#117—71no—
232C2×#117—71no—
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⋊C8C2×D711yescharacteristic
244C2×C22⋊C8C2×D711yescharacteristic
245C2×C4×C8C2×D711yescharacteristic
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⋊C4—71no—
256C4×C4⋊C4—71no—
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#340—71no—
269#340—71no—
270#336C2×D711yescharacteristic
271#336C2×D711yescharacteristic
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—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—44no—
301C2×C4×C7—44no—
302C2×C4×C7C4×D412yes—
303C2×C4×C7#12312yes—
304C2×C4×C7#12312yes—
305C2×C4×C7#13512yes—
306C2×C4×C7#13512yes—
307C2×C4×C7AGL(1,ℤ/8)12yes—
308C2×C4×C7C23×C411yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
310C2×C4×C7C2×#4111yescharacteristic
311C2×C4×C7C2×#4111yescharacteristic
312C2×C4×C7C2×#4111yescharacteristic
313C2×C4×C7C2×#4111yescharacteristic
314C22⋊D7—48no—
315C2×Dic7—22no—
316C2×Dic7—22no—
317C2×Dic7—22no—
318C2×Dic7—22no—
319C2×Dic7—22no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
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×C4D2811yescharacteristic
349C23×C4D2811yescharacteristic
350C23×C4C22×D711yescharacteristic
351C22×C8C22×D711yescharacteristic
352C22×C8C22×D711yescharacteristic
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—71no—
368C2×C4⋊C4—71no—
369C2×C4⋊C4—71no—
370C2×C4⋊C4—71no—
371C2×C4⋊C4—141no—
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—22no—
380C2×C42—22no—
381C2×C42—141no—
382C2×C42—141no—
383C2×C42—141no—
384C2×C42—141no—
385C2×C42—141no—
386C2×C42—141no—
387C2×C42—141no—
388C2×C42D2811yescharacteristic
389C2×C42D2811yescharacteristic
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—22no—
401C22⋊C8C4×D714yescomplemented
402C4×C8—22no—
403C4×C8—22no—
404#95—141no—
405#95—141no—
406#95—141no—
407#95—141no—
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#48214yescomplemented
437C4×C7C4×#4111yescharacteristic
438C4×C7C4×#4111yescharacteristic
439C4×C7#52911yescharacteristic
440C4×C7#52911yescharacteristic
441Dic7—42no—
442Dic7—42no—
443Dic7—42no—
444Dic7—42no—
445Dic7—42no—
446Dic7—81no—
447Dic7—81no—
448C24—141no—
449C24C2×D2811yescharacteristic
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—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—41no—
469C22×C4—141no—
470C22×C4—141no—
471C22×C4—141no—
472C22×C4—141no—
473C22×C4—141no—
474C22×C4—141no—
475C22×C4—141no—
476C22×C4—282no—
477C22×C4—282no—
478C22×C4—282no—
479C22×C4C2×C4×D712yes—
480C22×C4C2×D2811yescharacteristic
481C22×C4C2×D2811yescharacteristic
482C22×C4C2×D2811yescharacteristic
483C22×C4C2×D2811yescharacteristic
484C22×C4C2×D2811yescharacteristic
485C22×C4#115712yes—
486C22×C4C23×D711yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8C2×C4×D712yes—
498C2×C8C2×C4×D712yes—
499C4⋊C4—72no—
500C4⋊C4—72no—
501C4⋊C4—72no—
502C4⋊C4—72no—
503C4⋊C4—72no—
504C4⋊C4—141no—
505C4⋊C4—141no—
506C4⋊C4—141no—
507C4⋊C4—141no—
508C4⋊C4—141no—
509C4⋊C4—141no—
510C4⋊C4—141no—
511C4⋊C4—141no—
512C4⋊C4—141no—
513C4⋊C4—282no—
514C22⋊C4—144no—
515C22⋊C4—144no—
516C22⋊C4—144no—
517C22⋊C4—282no—
518C22⋊C4—282no—
519C22⋊C4—282no—
520C22⋊C4—282no—
521C42—22no—
522C42—22no—
523C42—21no—
524C42—21no—
525C42—144no—
526C42—144no—
527C42—282no—
528C42—282no—
529C42—282no—
530C42—282no—
531C42—282no—
532C42#115912yes—
533C42#115912yes—
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×D2812yes—
557C23C22×D2811yescharacteristic
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—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—142no—
579C2×C4—142no—
580C2×C4—142no—
581C2×C4—142no—
582C2×C4—142no—
583C2×C4—281no—
584C2×C4—281no—
585C2×C4—281no—
586C2×C4—281no—
587C2×C4—281no—
588C2×C4—281no—
589C2×C4—281no—
590C2×C4—281no—
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×D2812yes—
601C2×C4#644912yes—
602C2×C4#644912yes—
603C2×C4#646712yes—
604C2×C4#646712yes—
605C2×C4#647112yes—
606C2×C4C22×C4×D711yescharacteristic
607C2×C4C2×#115711yescharacteristic
608C2×C4C2×#115911yescharacteristic
609C2×C4C2×#115911yescharacteristic
610C2×C4D7×#4111yescharacteristic
611C2×C4D7×#4111yescharacteristic
612C8—22no—
613C8—22no—
614C8—41no—
615C8—41no—
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×D2811yescharacteristic
632C22C2×#644911yescharacteristic
633C22#9021511yescharacteristic
634C22C2×#646711yescharacteristic
635C22C2×#646711yescharacteristic
636C22C2×#647111yescharacteristic
637C22#9043911yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—282no—
643C4—282no—
644C4—282no—
645C4—282no—
646C4—282no—
647C4—561no—
648C4—561no—
649C4#8950914yesdirect product factor
650C4C4×#115911yescharacteristic
651C4C4×#115911yescharacteristic
652C4#9022911yescharacteristic
653C4#9022911yescharacteristic
654C2—42no—
655C2—562no—
656C2C4×#644911yescharacteristic
657C2C4×#646711yescharacteristic
658C2C4×#647111yescharacteristic
659C2C2×#8950911yescharacteristic
660C2#1173603611yescharacteristic
661C2#1173674411yescharacteristic
662C2#1173674611yescharacteristic
subgroupG/H
centerC22×C4C2×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×C22⋊C8C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenterC4×C22⋊C8D7
hypocenterC7C4×#482
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#6489C2semidirect
4. C4×C7×C22⋊C8C2semidirect
6. #11727683C2semidirect
7. #11727680C2semidirect
8. C4×#6392C2semidirect
9. C4×#6391C2semidirect
10. C4×#6395C2semidirect
11. C4×#6395C2semidirect
12. #11726380C2semidirect
13. #11726379C2semidirect
14. #11726378C2semidirect
15. #11726377C2semidirect
49. #89509C4direct (N × H)
90. #6489C2×C4semidirect
109. C7×C22⋊C8C2×C4semidirect
121. #6395C2×C4semidirect
122. #6395C2×C4semidirect
124. #6392C2×C4semidirect
126. #6391C2×C4semidirect
141. C4×C22⋊C8D7semidirect
401. C22⋊C8C4×D7semidirect
436. C4×C7#482semidirect
616. C7C4×#482semidirect
649. C4#89509direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#64932
C4×#64892
C2×#895092
C4×C7×C22⋊C82
#117276872
#117276832
#117276802
C4×#63922
C4×#63912
C4×#63952
#117263802
#117263792
#117263782
#117263772
C4×#4827