Finite Group Databasebeta

← C4×#89975 #13360665

Subgroups — C4×#89975 #13360665

Order 1792.

914 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×#137C211yesmaximal, characteristic, complemented
2C2×#89975C211yesmaximal, characteristic
3C4×#6512C211yesmaximal, characteristic
4C4×#6511C211yesmaximal, characteristic, complemented
5C2×C4×#1143C211yesmaximal, characteristic, complemented
6#11729857C211yesmaximal, characteristic, complemented
7C4×#6410C211yesmaximal, characteristic, complemented
8#11728427C211yesmaximal, characteristic, complemented
9#11728422C211yesmaximal, characteristic, complemented
10#11728092C211yesmaximal, characteristic, complemented
11#11728089C211yesmaximal, characteristic, complemented
12#11728057C211yesmaximal, characteristic
13#11728053C211yesmaximal, characteristic, complemented
14C4×#6396C211yesmaximal, characteristic, complemented
15C4×#6397C211yesmaximal, characteristic, complemented
16C2×C7×#137C2211yescharacteristic
17C4×C7×#41C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×#6512C2211yescharacteristic
20C2×#6511C2211yescharacteristic
21C2×#6511C2211yescharacteristic
22C22×#1143C2211yescharacteristic
23C2×C4×D28C2211yescharacteristic
24C7×#441—21no—
25C7×#440—21no—
26C4×C7×Q16—21no—
27C4×C7×SD16—21no—
28C7×#428C2211yescharacteristic
29C7×#419C2211yescharacteristic
30C7×#417C2211yescharacteristic
31C4×C7×M16C2211yescharacteristic
32#90004C2211yescharacteristic
33C2×#6410C2211yescharacteristic
34C2×#6410C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36#89975C418yesdirect product factor
37C2×#6397C2211yescharacteristic
38C2×#6397C2211yescharacteristic
39C2×#6396C2211yescharacteristic
40C2×#6396C2211yescharacteristic
41#89798—21no—
42C4×#1143—21no—
43C4×#1143—21no—
44C4×#1143—21no—
45C4×#1143—21no—
46C4×#1143—21no—
47#89786—21no—
48C4×#1141—21no—
49#89773C2211yescharacteristic
50#89769—21no—
51#89769—21no—
52#89769C2211yescharacteristic
53#89769C2211yescharacteristic
54#89767C2211yescharacteristic
55C2×#6383C2211yescharacteristic
56C2×#6382C2211yescharacteristic
57C4×#1136—21no—
58C4×#1136C2211yescharacteristic
59C4×#1136C2211yescharacteristic
60C2×C4×C7⋊C8—21no—
61C2×C4×C7⋊C8C2211yescharacteristic
62#89353C2211yescharacteristic
63#89353C2211yescharacteristic
64#89349C2211yescharacteristic
65#89349C2211yescharacteristic
66#89325C2211yescharacteristic
67#89325C2211yescharacteristic
68C4×#471—71nomaximal, Sylow
69C2×C7×#41C2311yescharacteristic
70C22×C7×Q8C2311yescharacteristic
71C22×D28C2311yescharacteristic
72C22×C4×D7—21no—
73C7×#137—22no—
74C7×#137C2×C414yescomplemented
75C2×C7×Q16—21no—
76C2×C7×SD16—21no—
77C2×C7×M16C2311yescharacteristic
78C2×C7×M16C2311yescharacteristic
79C4×C7×Q8—21no—
80C4×C7×Q8—21no—
81C4×C7×Q8—21no—
82C4×C7×Q8—21no—
83C4×C7×Q8D411yescharacteristic
84C4×C7×Q8D411yescharacteristic
85C4×C7×D4—21no—
86C4×C7×D4—21no—
87C4×C7×D4D411yescharacteristic
88C4×C7×D4D411yescharacteristic
89C7×#117—21no—
90C7×#117C2311yescharacteristic
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4C2311yescharacteristic
93C2×C42×C7—21no—
94C2×C42×C7—21no—
95C2×C42×C7C2311yescharacteristic
96#6512—22no—
97#6512C2×C414yes—
98#6511—22no—
99#6511—22no—
100#6511—22no—
101#6511C2×C414yescomplemented
102C2×#1143—21no—
103C2×#1143—21no—
104C2×#1143—21no—
105C2×#1143—22no—
106C2×#1143C2×C414yescomplemented
107C2×#1141—21no—
108C2×(C2×D7)⋊C4—21no—
109C2×C4⋊Dic7C2311yescharacteristic
110C2×#1136—21no—
111C2×#1136—21no—
112C2×#1136C2311yescharacteristic
113C2×#1136C2311yescharacteristic
114C2×#1136C2311yescharacteristic
115C2×#1136C2311yescharacteristic
116C22×C7⋊C8—21no—
117C22×C7⋊C8—21no—
118C22×C7⋊C8C2311yescharacteristic
119C22×C7⋊C8C2311yescharacteristic
120C4×D28—21no—
121C4×D28—21no—
122C4×D28—21no—
123C4×D28—21no—
124C7×#107—21no—
125C7×#106—21no—
126C7×#103—21no—
127C7×#103—21no—
128C7×#103—21no—
129C7×#102—21no—
130C7×#97—21no—
131C4×C7×C8—21no—
132#6410—22no—
133#6410C2×C414yescomplemented
134#6409—21no—
135#6409—21no—
136#6409—21no—
137#6406—21no—
138#6397—22no—
139#6397C2×C414yescomplemented
140#6396—22no—
141#6396C2×C414yescomplemented
142#6383—21no—
143#6383—21no—
144#6383—21no—
145#6383—21no—
146#6382—21no—
147#6382—21no—
148#6382—21no—
149#6381—21no—
150#6377—21no—
151#6377—21no—
152#6377—21no—
153#6377—21no—
154C4×C7⋊C8—21no—
155C4×C7⋊C8—21no—
156C4×C7⋊C8—21no—
157C4×C7⋊C8—21no—
158C4×C7⋊C8D411yescharacteristic
159C4×C7⋊C8D411yescharacteristic
160C4×C7⋊C8D411yescharacteristic
161C4×C7⋊C8D411yescharacteristic
162C2×#471—71no—
163C4×#137D711yescharacteristic, complemented
164C4×AGL(1,ℤ/8)—71no—
165C2×C4×SD16—71no—
166C4×#131—71no—
167#1977—71no—
168#1951—71no—
169#1931—71no—
170#1930—71no—
171#1908—71no—
172#1907—71no—
173#1815—71no—
174C4×#108—71no—
175C4×#101—71no—
176C4×#100—71no—
177C23×D7—21no—
178C7×#41—21no—
179C7×#41—21no—
180C7×#41C22×C412yes—
181C7×#41#4112yes—
182C2×C7×Q8—21no—
183C2×C7×Q8—21no—
184C2×C7×Q8—21no—
185C2×C7×Q8—21no—
186C2×C7×Q8—21no—
187C2×C7×Q8C22×C412yes—
188C2×C7×Q8C2×D411yescharacteristic
189C2×C7×D4—21no—
190C2×C7×D4C2×D411yescharacteristic
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7#4111yescharacteristic
197C22×C4×C7#4111yescharacteristic
198C22×C4×C7C2411yescharacteristic
199C22×Dic7—21no—
200C2×D28—21no—
201C2×D28—21no—
202C2×D28—21no—
203C2×D28—21no—
204C2×D28—21no—
205C2×D28C22×C412yes—
206C2×C4×D7—41no—
207C2×C4×D7—41no—
208C2×C4×D7—82no—
209C7×Q16—24no—
210C7×SD16—24no—
211C7×M16—21no—
212C7×M16—21no—
213C7×M16—21no—
214C7×M16C22×C412yes—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—41no—
222C7×C4⋊C4—41no—
223C7×C4⋊C4C2×D411yescharacteristic
224C7×C4⋊C4C2×D411yescharacteristic
225C7×C22⋊C4—21no—
226C7×C22⋊C4—21no—
227C7×C22⋊C4—21no—
228C42×C7—21no—
229C42×C7—21no—
230C42×C7—21no—
231C42×C7—41no—
232C42×C7—41no—
233C42×C7C2×D411yescharacteristic
234C42×C7C2×D411yescharacteristic
235C42×C7C2×D411yescharacteristic
236C42×C7C2×D411yescharacteristic
237#1143—24no—
238#1143—24no—
239#1143—24no—
240#1141—24no—
241(C2×D7)⋊C4—41no—
242(C2×D7)⋊C4—41no—
243C4⋊Dic7—21no—
244C4⋊Dic7—21no—
245#1136—24no—
246#1136—21no—
247#1136—21no—
248#1136—21no—
249#1136—24no—
250#1136—21no—
251#1136—21no—
252#1136C22×C412yes—
253#1136C22×C412yes—
254#1136#4112yes—
255C2×C7⋊C8—24no—
256C2×C7⋊C8—21no—
257C2×C7⋊C8—21no—
258C2×C7⋊C8—21no—
259C2×C7⋊C8—21no—
260C2×C7⋊C8—21no—
261C2×C7⋊C8—24no—
262C2×C7⋊C8—21no—
263C2×C7⋊C8C22×C412yes—
264C2×C7⋊C8C2×D411yescharacteristic
265C2×C7⋊C8C2×D411yescharacteristic
266C2×C7⋊C8C2×D411yescharacteristic
267C2×C7⋊C8C2×D411yescharacteristic
268C2×C7⋊C8#4112yes—
269C2×#137C2×D711yescharacteristic
270C2×AGL(1,ℤ/8)—71no—
271C22×SD16—71no—
272C2×#131—71no—
273C2×#131—71no—
274C4×#41C2×D711yescharacteristic
275C2×C4×Q8C2×D711yescharacteristic
276C2×C4×D4—71no—
277#471—78no—
278#442—141no—
279#441—21no—
280#440—21no—
281#440—141no—
282C4×Q16—21no—
283C4×SD16—21no—
284C4×SD16—141no—
285C4×SD16—141no—
286C4×SD16—141no—
287C4×SD16—141no—
288C4×SD16—141no—
289C4×D8—141no—
290C2×#108—71no—
291C2×#108—71no—
292#428—71no—
293#428C2×D711yescharacteristic
294C2×#106—71no—
295#419C2×D711yescharacteristic
296#418—71no—
297#417—71no—
298#417C2×D711yescharacteristic
299C2×#103—71no—
300C2×#102—71no—
301C2×#101—71no—
302C2×#101—71no—
303C2×#100—71no—
304C2×#100—71no—
305#405—71no—
306#405—71no—
307#405—141no—
308#405—141no—
309C4×M16—71no—
310C4×M16—71no—
311C4×M16—141no—
312C4×M16C2×D711yescharacteristic
313C2×C4×C8—71no—
314C2×C4×C8—141no—
315#343—71no—
316#343—71no—
317#343—71no—
318#343—71no—
319#341—71no—
320#341—71no—
321C23×C7—21no—
322C23×C7C2×#4111yescharacteristic
323C22×D7—22no—
324C22×D7—41no—
325C22×D7—41no—
326C22×D7—81no—
327C22×D7—81no—
328C7×Q8—21no—
329C7×Q8—22no—
330C7×Q8—22no—
331C7×Q8—41no—
332C7×Q8—41no—
333C7×Q8C4×D412yes—
334C7×D4—22no—
335C7×D4—22no—
336C7×D4—21no—
337C7×D4C4×D412yes—
338C2×C4×C7—21no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—41no—
346C2×C4×C7—42no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—42no—
350C2×C4×C7—41no—
351C2×C4×C7—81no—
352C2×C4×C7#12111yescharacteristic
353C2×C4×C7#12111yescharacteristic
354C2×C4×C7#12111yescharacteristic
355C2×C4×C7#12111yescharacteristic
356C2×C4×C7C23×C411yescharacteristic
357C2×C4×C7C22×D411yescharacteristic
358C2×C4×C7C22×D411yescharacteristic
359C2×C4×C7C2×#4111yescharacteristic
360C2×C4×C7C2×#4111yescharacteristic
361C2×C4×C7C2×#4111yescharacteristic
362C2×Dic7—41no—
363C2×Dic7—81no—
364D28—22no—
365D28—22no—
366D28—41no—
367D28—41no—
368C4×D7—82no—
369C4×D7—82no—
370C7×C8—22no—
371C7×C8—41no—
372C7⋊C8—22no—
373C7⋊C8—22no—
374C7⋊C8—21no—
375C7⋊C8—22no—
376C7⋊C8—21no—
377C7⋊C8—41no—
378C7⋊C8C4×D412yes—
379C7⋊C8C4×D412yes—
380C2×#41C22×D711yescharacteristic
381C22×Q8C22×D711yescharacteristic
382C22×D4—71no—
383C23×C4—141no—
384#137—22no—
385#137C4×D714yescomplemented
386AGL(1,ℤ/8)—74no—
387AGL(1,ℤ/8)—142no—
388C2×Q16—21no—
389C2×SD16—21no—
390C2×SD16—74no—
391C2×SD16—142no—
392C2×SD16—141no—
393C2×SD16—141no—
394C2×SD16—141no—
395C2×D8—141no—
396#131—74no—
397#131—142no—
398#131—142no—
399#131—142no—
400C2×M16—71no—
401C2×M16—71no—
402C2×M16—71no—
403C2×M16—71no—
404C2×M16—141no—
405C2×M16—141no—
406C2×M16C22×D711yescharacteristic
407C2×M16C22×D711yescharacteristic
408C22×C8—71no—
409C22×C8—71no—
410C22×C8—141no—
411C22×C8—141no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C22⋊D711yescharacteristic
417C4×Q8C22⋊D711yescharacteristic
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—141no—
421C4×D4—141no—
422C4×D4—141no—
423C4×D4—141no—
424C4×D4C22⋊D711yescharacteristic
425C4×D4C22⋊D711yescharacteristic
426#117—21no—
427#117C22×D711yescharacteristic
428C2×C4⋊C4—21no—
429C2×C4⋊C4—71no—
430C2×C4⋊C4C22×D711yescharacteristic
431C2×C22⋊C4—141no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C22×D711yescharacteristic
435#108—74no—
436#108—142no—
437#107—21no—
438#107—141no—
439#106—21no—
440#106—141no—
441#106—141no—
442#106—141no—
443#103—21no—
444#103—21no—
445#103—21no—
446#103—141no—
447#103—141no—
448#103—141no—
449#102—21no—
450#102—141no—
451#102—141no—
452#102—141no—
453#102—141no—
454#102—141no—
455#101—74no—
456#101—142no—
457#100—74no—
458#100—142no—
459#97—21no—
460#97—141no—
461#97—141no—
462#97—141no—
463#97—141no—
464C4×C8—21no—
465C4×C8—71no—
466C4×C8—71no—
467C4×C8—71no—
468C4×C8—71no—
469C4×C8—141no—
470C4×C8—141no—
471C4×C8—141no—
472C4×C8—141no—
473C22×C7—21no—
474C22×C7—21no—
475C22×C7—22no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7C4×#4111yescharacteristic
479C22×C7C2×#12111yescharacteristic
480C22×C7#52911yescharacteristic
481C2×D7—42no—
482C2×D7—82no—
483C2×D7—81no—
484C2×D7—81no—
485C2×D7—82no—
486C4×C7—21no—
487C4×C7—21no—
488C4×C7—21no—
489C4×C7—22no—
490C4×C7—41no—
491C4×C7—41no—
492C4×C7—42no—
493C4×C7—81no—
494C4×C7#47112yescomplemented
495C4×C7C2×C4×D411yescharacteristic
496C4×C7C2×C4×D411yescharacteristic
497C4×C7#52511yescharacteristic
498C4×C7#53211yescharacteristic
499Dic7—81no—
500C24—141no—
501#41—21no—
502#41—21no—
503#41C2×C4×D712yes—
504#41#115712yes—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8C2×C4×D712yes—
511C2×Q8C2×C22⋊D711yescharacteristic
512C2×D4—21no—
513C2×D4—72no—
514C2×D4—141no—
515C2×D4—141no—
516C2×D4—141no—
517C2×D4—141no—
518C2×D4—141no—
519C2×D4C2×C22⋊D711yescharacteristic
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—141no—
526C22×C4—281no—
527C22×C4—281no—
528C22×C4—562no—
529C22×C4#115911yescharacteristic
530C22×C4#115911yescharacteristic
531C22×C4C23×D711yescharacteristic
532Q16—24no—
533SD16—24no—
534SD16—144no—
535SD16—144no—
536SD16—144no—
537D8—144no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—72no—
542M16—72no—
543M16—72no—
544M16—144no—
545M16—144no—
546M16—141no—
547M16—141no—
548M16—141no—
549M16—141no—
550M16—141no—
551M16C2×C4×D712yes—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—72no—
555C2×C8—71no—
556C2×C8—71no—
557C2×C8—72no—
558C2×C8—71no—
559C2×C8—71no—
560C2×C8—144no—
561C2×C8—144no—
562C2×C8—141no—
563C2×C8—141no—
564C2×C8—141no—
565C2×C8—141no—
566C2×C8—141no—
567C2×C8—141no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—141no—
575C4⋊C4—141no—
576C4⋊C4C2×C22⋊D711yescharacteristic
577C4⋊C4C2×C22⋊D711yescharacteristic
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—281no—
582C22⋊C4—281no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—41no—
587C42—41no—
588C42D4×D711yescharacteristic
589C42D4×D711yescharacteristic
590C42C2×C22⋊D711yescharacteristic
591C42C2×C22⋊D711yescharacteristic
592C2×C7—21no—
593C2×C7—21no—
594C2×C7—42no—
595C2×C7C4×#12111yescharacteristic
596C2×C7C2×#47111yescharacteristic
597C2×C7#306711yescharacteristic
598D7—82no—
599C23—21no—
600C23—142no—
601C23—281no—
602C23—281no—
603C23—561no—
604C23—561no—
605C23C2×#115911yescharacteristic
606Q8—21no—
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8C4×C22⋊D712yes—
612D4—22no—
613D4—22no—
614D4—21no—
615D4—142no—
616D4—142no—
617D4—281no—
618D4—281no—
619D4C4×C22⋊D712yes—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—81no—
634C2×C4—281no—
635C2×C4—562no—
636C2×C4—562no—
637C2×C4—561no—
638C2×C4#650211yescharacteristic
639C2×C4#650211yescharacteristic
640C2×C4#650211yescharacteristic
641C2×C4#650211yescharacteristic
642C2×C4C22×C4×D711yescharacteristic
643C2×C4C2×#115711yescharacteristic
644C2×C4C2×D4×D711yescharacteristic
645C2×C4D7×#4111yescharacteristic
646C2×C4D7×#4111yescharacteristic
647C2×C4C22×C22⋊D711yescharacteristic
648C8—22no—
649C8—41no—
650C8—72no—
651C8—72no—
652C8—142no—
653C8—142no—
654C8—141no—
655C8—141no—
656C8—142no—
657C8—281no—
658C7C4×#47111yescharacteristic, complemented, Sylow
659C22—21no—
660C22—21no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—282no—
665C22—562no—
666C22—562no—
667C22—561no—
668C22—561no—
669C22C4×#115911yescharacteristic
670C22#9022911yescharacteristic
671C22C2×#650211yescharacteristic
672C4—21no—
673C4—21no—
674C4—22no—
675C4—21no—
676C4—41no—
677C4—42no—
678C4—41no—
679C4—81no—
680C4—561no—
681C4#8997512yesdirect product factor
682C4C4×D4×D711yescharacteristic
683C4#9023811yescharacteristic
684C4C2×C4×C22⋊D711yescharacteristic
685C4#9052311yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—562no—
690C2C4×#650211yescharacteristic
691C2C2×#8997511yescharacteristic
692C2#1174144611yescharacteristic
subgroupG/H
centerC2×C4#6502
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#137C2
socleC22×C7C2×#121
prime radicalC2×#6512C22
cosocleC22×C4×C7C24
hypercenterC4×#137D7
hypocenterC7C4×#471
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
1. C4×C7×#137C2semidirect
4. C4×#6511C2semidirect
5. C2×C4×#1143C2semidirect
6. #11729857C2semidirect
7. C4×#6410C2semidirect
8. #11728427C2semidirect
9. #11728422C2semidirect
10. #11728092C2semidirect
11. #11728089C2semidirect
13. #11728053C2semidirect
14. C4×#6396C2semidirect
15. C4×#6397C2semidirect
36. #89975C4direct (N × H)
74. C7×#137C2×C4semidirect
101. #6511C2×C4semidirect
106. C2×#1143C2×C4semidirect
133. #6410C2×C4semidirect
139. #6397C2×C4semidirect
141. #6396C2×C4semidirect
163. C4×#137D7semidirect
385. #137C4×D7semidirect
494. C4×C7#471semidirect
658. C7C4×#471semidirect
681. C4#89975direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C7×#1372
C2×#899752
C4×#65122
C4×#65112
C2×C4×#11432
#117298572
C4×#64102
#117284272
#117284222
#117280922
#117280892
#117280572
#117280532
C4×#63962
C4×#63972
C4×#4717