Finite Group Databasebeta

← C4×#89725 #13275614

Subgroups — C4×#89725 #13275614

Order 1792.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×C4×C22⋊Dic7C212yesmaximal
3C2×#89725C211yesmaximal, characteristic
4C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
5#11729303C212yesmaximal
6#11729300C211yesmaximal, characteristic
7C4×C7⋊#95C212yesmaximal, complemented
8C4×C7⋊#95C211yesmaximal, characteristic, complemented
9#11727176C211yesmaximal, characteristic, complemented
10#11727172C212yesmaximal, complemented
11#11727169C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C22⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2212yes—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C22×C4×Dic7C2212yes—
23C4×C7×C22⋊C4—24no—
24C2×C7×#95C2211yescharacteristic
25C2×C7×#95C2211yescharacteristic
26C4×C22⋊Dic7—28no—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2212yes—
37#89725C418yesdirect product factor
38C4×C4⋊Dic7—24no—
39C4×#397—71nomaximal, Sylow
40C25×C7C2311yescharacteristic
41C23×C4×C7—22no—
42C23×C4×C7—22no—
43C23×C4×C7—24no—
44C23×C4×C7—24no—
45C23×C4×C7D414yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×Dic7C2312yes—
53C23×Dic7C2312yes—
54C23×Dic7C2312yes—
55C23×Dic7C2312yes—
56C2×C7×C22⋊C4—22no—
57C2×C7×C22⋊C4—22no—
58C2×C7×C22⋊C4—22no—
59C2×C7×C22⋊C4—22no—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4C2×C414yes—
62C2×C42×C7—24no—
63C2×C42×C7—22no—
64C2×C42×C7—24no—
65C2×C42×C7D414yes—
66C2×C22⋊Dic7—24no—
67C2×C22⋊Dic7—24no—
68C2×C22⋊Dic7—24no—
69C2×C22⋊Dic7—24no—
70C2×C22⋊Dic7—24no—
71C2×C22⋊Dic7C2×C418yes—
72C2×C4⋊Dic7—22no—
73C2×C4⋊Dic7—22no—
74C2×C4⋊Dic7—22no—
75C2×C4⋊Dic7—24no—
76C2×C4⋊Dic7C2×C414yescomplemented
77C2×C4×Dic7—24no—
78C2×C4×Dic7—24no—
79C2×C4×Dic7—24no—
80C2×C4×Dic7—24no—
81C2×C4×Dic7—24no—
82C2×C4×Dic7—24no—
83C7×#95—22no—
84C7×#95—22no—
85C7⋊#95—24no—
86C7⋊#95—24no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—22no—
90C7⋊#95—24no—
91C7⋊#95—24no—
92C7⋊#95—24no—
93C7⋊#95C2×C414yescomplemented
94C7⋊#95C2×C418yescomplemented
95C2×#397—71no—
96C2×C4×C4⋊C4—71no—
97C2×C4×C22⋊C4—72no—
98C2×C4×C22⋊C4D711yescharacteristic
99#1445—71no—
100#1443—72no—
101#1442—71no—
102#1440—72no—
103#1439—71no—
104C4×#95—71no—
105C4×#95—72no—
106C24×C7—21no—
107C24×C7—22no—
108C24×C7—22no—
109C24×C7—21no—
110C24×C7—21no—
111C24×C7—21no—
112C24×C7—22no—
113C24×C7—22no—
114C24×C7C22×C412yes—
115C24×C7C2×D412yes—
116C24×C7#4112yes—
117C24×C7C2411yescharacteristic
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—28no—
137C22×C4×C7—216no—
138C22×C4×C7—44no—
139C22×C4×C7—44no—
140C22×C4×C7—48no—
141C22×C4×C7C22×C412yes—
142C22×C4×C7C22×C412yes—
143C22×C4×C7C2×D412yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7C2×D412yes—
146C22×C4×C7C2×D412yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7#4112yes—
149C22×C4×C7#4112yes—
150C22×C4×C7#4112yes—
151C22×C4×C7#4114yes—
152C22×C4×C7#4114yes—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7C22×C414yes—
178C22×Dic7C22×C414yes—
179C22×Dic7#4114yes—
180C22×Dic7#4114yes—
181C7×C22⋊C4—28no—
182C7×C22⋊C4—28no—
183C42×C7—28no—
184C42×C7—44no—
185C22⋊Dic7—216no—
186C22⋊Dic7—216no—
187C4⋊Dic7—28no—
188C4⋊Dic7—28no—
189C4×Dic7—48no—
190C4×Dic7—48no—
191C24×C4C2×D711yescharacteristic
192C22×C4⋊C4—71no—
193C22×C4⋊C4—71no—
194C22×C22⋊C4—72no—
195C22×C22⋊C4—72no—
196C22×C22⋊C4C2×D711yescharacteristic
197C22×C22⋊C4C2×D711yescharacteristic
198C22×C42—72no—
199C22×C42—72no—
200C22×C42C2×D711yescharacteristic
201C22×C42C2×D711yescharacteristic
202#397—78no—
203C4×C4⋊C4—144no—
204C4×C22⋊C4—24no—
205C4×C22⋊C4—148no—
206C2×#95—71no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95—71no—
210C2×#95—72no—
211C2×#95—72no—
212C2×#95—72no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95C2×D711yescharacteristic
217C2×#95C2×D711yescharacteristic
218C23×C7—22no—
219C23×C7—22no—
220C23×C7—24no—
221C23×C7—24no—
222C23×C7—22no—
223C23×C7—24no—
224C23×C7—24no—
225C23×C7—22no—
226C23×C7—22no—
227C23×C7—24no—
228C23×C7—24no—
229C23×C7—22no—
230C23×C7—41no—
231C23×C7—41no—
232C23×C7—41no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7—42no—
236C23×C7—42no—
237C23×C7—42no—
238C23×C7—42no—
239C23×C7—41no—
240C23×C7C4×D414yes—
241C23×C7C23×C411yescharacteristic
242C23×C7C22×D411yescharacteristic
243C23×C7C22×D411yescharacteristic
244C23×C7C2×#4111yescharacteristic
245C23×C7C2×#4111yescharacteristic
246C23×C7C2×#4111yescharacteristic
247C23×C7C2×#4111yescharacteristic
248C23×C7C2×#4112yes—
249C23×C7C2×#4112yes—
250C23×C7C2×#4112yes—
251C23×C7C2×#4112yes—
252C2×C4×C7—24no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—24no—
256C2×C4×C7—22no—
257C2×C4×C7—24no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—24no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—24no—
264C2×C4×C7—22no—
265C2×C4×C7—41no—
266C2×C4×C7—41no—
267C2×C4×C7—41no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
270C2×C4×C7—42no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—41no—
276C2×C4×C7—416no—
277C2×C4×C7C4×D414yes—
278C2×C4×C7#12114yes—
279C2×C4×C7#12318yes—
280C2×C4×C7#12314yes—
281C2×C4×C7#12414yes—
282C2×C4×C7#12618yes—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—24no—
286C2×Dic7—24no—
287C2×Dic7—24no—
288C2×Dic7—24no—
289C2×Dic7—24no—
290C2×Dic7—24no—
291C2×Dic7—24no—
292C2×Dic7—24no—
293C2×Dic7—24no—
294C2×Dic7—24no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—42no—
303C2×Dic7—42no—
304C2×Dic7—42no—
305C2×Dic7—42no—
306C2×Dic7—42no—
307C2×Dic7—42no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C25C22×D711yescharacteristic
312C23×C4—22no—
313C23×C4—24no—
314C23×C4—24no—
315C23×C4—22no—
316C23×C4—72no—
317C23×C4—72no—
318C23×C4—72no—
319C23×C4—72no—
320C23×C4D2814yes—
321C23×C4C22×D711yescharacteristic
322C23×C4C22×D711yescharacteristic
323C23×C4C22×D711yescharacteristic
324C23×C4C22×D711yescharacteristic
325C23×C4C22×D711yescharacteristic
326C23×C4C22×D711yescharacteristic
327C2×C4⋊C4—74no—
328C2×C4⋊C4—144no—
329C2×C4⋊C4—142no—
330C2×C4⋊C4—142no—
331C2×C4⋊C4—142no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—78no—
338C2×C22⋊C4—144no—
339C2×C22⋊C4—144no—
340C2×C22⋊C4—144no—
341C2×C22⋊C4—144no—
342C2×C22⋊C4—144no—
343C2×C22⋊C4C4×D714yes—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—22no—
347C2×C42—144no—
348C2×C42—144no—
349C2×C42—144no—
350C2×C42—144no—
351C2×C42—144no—
352C2×C42—144no—
353C2×C42C22⋊D714yes—
354#95—22no—
355#95—22no—
356#95—74no—
357#95—78no—
358#95—144no—
359#95—144no—
360#95—144no—
361#95—144no—
362#95—144no—
363#95—144no—
364#95—142no—
365#95—144no—
366C22×C7—24no—
367C22×C7—28no—
368C22×C7—44no—
369C22×C7—42no—
370C22×C7—42no—
371C22×C7—44no—
372C22×C7—42no—
373C22×C7—42no—
374C22×C7—44no—
375C22×C7—42no—
376C22×C7—42no—
377C22×C7C2×C4×D411yescharacteristic
378C22×C7C2×C4×D411yescharacteristic
379C22×C7C4×#4111yescharacteristic
380C22×C7C4×#4112yes—
381C22×C7C4×#4112yes—
382C22×C7C2×#12111yescharacteristic
383C22×C7C2×#12312yes—
384C22×C7C2×#12311yescharacteristic
385C22×C7#52512yes—
386C22×C7#52511yescharacteristic
387C22×C7#52511yescharacteristic
388C22×C7C2×#12411yescharacteristic
389C22×C7C2×#12612yes—
390C22×C7#52911yescharacteristic
391C22×C7#52912yes—
392C22×C7#52912yes—
393C22×C7#52912yes—
394C22×C7#52912yes—
395C22×C7#52912yes—
396C22×C7#52912yes—
397C22×C7#52912yes—
398C22×C7#53211yescharacteristic
399C22×C7#53211yescharacteristic
400C4×C7—24no—
401C4×C7—42no—
402C4×C7—42no—
403C4×C7—42no—
404C4×C7—42no—
405C4×C7#39718yescomplemented
406Dic7—44no—
407Dic7—44no—
408Dic7—44no—
409Dic7—44no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—21no—
418C24C2×C4×D712yes—
419C24C2×D2812yes—
420C24#115712yes—
421C24C23×D711yescharacteristic
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—216no—
441C22×C4—28no—
442C22×C4—48no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—74no—
446C22×C4—74no—
447C22×C4—74no—
448C22×C4—74no—
449C22×C4—142no—
450C22×C4—142no—
451C22×C4—142no—
452C22×C4—142no—
453C22×C4—142no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—142no—
463C22×C4—142no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4—142no—
467C22×C4—142no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4C2×C4×D712yes—
474C22×C4C2×C4×D712yes—
475C22×C4C2×D2812yes—
476C22×C4C2×D2812yes—
477C22×C4#115712yes—
478C22×C4#115712yes—
479C22×C4#115712yes—
480C22×C4#115914yes—
481C22×C4#115914yes—
482C22×C4C2×C22⋊D712yes—
483C22×C4C2×C22⋊D712yes—
484C22×C4C2×C22⋊D712yes—
485C4⋊C4—148no—
486C4⋊C4—148no—
487C22⋊C4—28no—
488C22⋊C4—28no—
489C22⋊C4—1416no—
490C22⋊C4—1416no—
491C42—28no—
492C42—44no—
493C42—288no—
494C42—288no—
495C2×C7—44no—
496C2×C7C4×#12111yescharacteristic
497C2×C7C4×#12311yescharacteristic
498C2×C7C4×#12312yes—
499C2×C7C4×#12411yescharacteristic
500C2×C7C4×#12612yes—
501C2×C7C2×#39711yescharacteristic
502C2×C7#239211yescharacteristic
503C2×C7#239512yes—
504C2×C7#239511yescharacteristic
505C2×C7#239811yescharacteristic
506C2×C7#240112yes—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23C4×D2814yes—
530C23C22×C4×D711yescharacteristic
531C23C22×D2811yescharacteristic
532C23C2×#115711yescharacteristic
533C23C2×#115711yescharacteristic
534C23C2×#115711yescharacteristic
535C23C2×#115711yescharacteristic
536C23C2×#115912yes—
537C23C2×#115912yes—
538C23D7×#4112yes—
539C23D7×#4112yes—
540C23C22×C22⋊D711yescharacteristic
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—416no—
566C2×C4—144no—
567C2×C4—144no—
568C2×C4—144no—
569C2×C4—144no—
570C2×C4—144no—
571C2×C4—144no—
572C2×C4—144no—
573C2×C4—144no—
574C2×C4—144no—
575C2×C4—144no—
576C2×C4—144no—
577C2×C4—144no—
578C2×C4—282no—
579C2×C4—282no—
580C2×C4—282no—
581C2×C4—282no—
582C2×C4—282no—
583C2×C4—282no—
584C2×C4—282no—
585C2×C4—282no—
586C2×C4—282no—
587C2×C4—282no—
588C2×C4—282no—
589C2×C4—282no—
590C2×C4—282no—
591C2×C4—282no—
592C2×C4—282no—
593C2×C4—282no—
594C2×C4#644218yes—
595C2×C4#644918yes—
596C2×C4C4×C22⋊D714yes—
597C2×C4#649314yes—
598C2×C4#649814yes—
599C2×C4#649914yes—
600C7C4×#39711yescharacteristic, complemented, Sylow
601C22—24no—
602C22—28no—
603C22—42no—
604C22—44no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—44no—
611C22—44no—
612C22C2×C4×D2811yescharacteristic
613C22C4×#115711yescharacteristic
614C22#9016811yescharacteristic
615C22#9017011yescharacteristic
616C22C2×#644212yes—
617C22C2×#644912yes—
618C22#9021512yes—
619C22#9021912yes—
620C22C4×#115912yes—
621C22C4×#115912yes—
622C22#9022912yes—
623C22#9022912yes—
624C22#9022912yes—
625C22#9022912yes—
626C22#9024812yes—
627C22#9024812yes—
628C22C2×C4×C22⋊D711yescharacteristic
629C22C2×#649311yescharacteristic
630C22#9048211yescharacteristic
631C22C2×#649811yescharacteristic
632C22C2×#649911yescharacteristic
633C22#9051911yescharacteristic
634C22#9052311yescharacteristic
635C4—24no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—284no—
641C4—284no—
642C4—284no—
643C4—284no—
644C4#8972518yesdirect product factor
645C2—44no—
646C2C4×#644912yes—
647C2C4×#644212yes—
648C2#1173092712yes—
649C2#1173102812yes—
650C2C4×#649311yescharacteristic
651C2C2×#8972511yescharacteristic
652C2#1173971811yescharacteristic
653C2C4×#649811yescharacteristic
654C2C4×#649911yescharacteristic
655C2#1173979111yescharacteristic
656C2#1173979311yescharacteristic
subgroupG/H
centerC23×C4C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C4×#397
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊Dic7C2semidirect
7. C4×C7⋊#95C2semidirect
8. C4×C7⋊#95C2semidirect
9. #11727176C2semidirect
10. #11727172C2semidirect
11. #11727169C2semidirect
37. #89725C4direct (N × H)
76. C2×C4⋊Dic7C2×C4semidirect
93. C7⋊#95C2×C4semidirect
94. C7⋊#95C2×C4semidirect
405. C4×C7#397semidirect
600. C7C4×#397semidirect
644. C4#89725direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×C4×C22⋊Dic72
C2×#897252
C2×C4×C4⋊Dic72
#117293032
#117293002
C4×C7⋊#952
#117271762
#117271722
#117271692
C4×#3977