Finite Group Databasebeta

← C2×#11729485 #13380680

Subgroups — C2×#11729485 #13380680

Order 1792.

2190 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#124C211yesmaximal, characteristic, complemented
2C22×#6505C211yesmaximal, characteristic, complemented
3C2×#90496C211yesmaximal, characteristic
4C2×#89997C211yesmaximal, characteristic, complemented
5C22×#6407C211yesmaximal, characteristic, complemented
6C22×#6379C211yesmaximal, characteristic, complemented
7#11729485C218yesmaximal, direct product factor
8C2×#89318C211yesmaximal, characteristic, complemented
9C23×C7×Q8C2211yescharacteristic
10C23×C7×D4C2211yescharacteristic
11C22×#1157C2211yescharacteristic
12C2×C7×#124—24no—
13C2×C7×#124—22no—
14C2×C7×#124—24no—
15C2×C7×#124C2214yescomplemented
16C22×C7×C22⋊C4—22no—
17C22×C42×C7C2211yescharacteristic
18C2×#6516—22no—
19C22×#1144—21no—
20C2×#6505—24no—
21C2×#6505—22no—
22C2×#6505—24no—
23C2×#6505C2214yescomplemented
24C22×#1143—21no—
25#90496—22no—
26#90496—22no—
27#90496—22no—
28#90496C2214yes—
29C2×#6503—21no—
30C2×#6501—22no—
31C2×#6499—21no—
32C2×#6489C2211yescharacteristic
33C22×#1136C2211yescharacteristic
34C22×#1136C2211yescharacteristic
35#89997—22no—
36#89997C2214yescomplemented
37C2×#6409—22no—
38C2×#6407—24no—
39C2×#6407C2214yescomplemented
40C2×#6379—24no—
41C2×#6379C2214yescomplemented
42#89318C2214yescomplemented
43C2×#2004—71nomaximal, Sylow
44C25×C7D412yes—
45C22×C7×Q8—22no—
46C22×C7×Q8—21no—
47C22×C7×Q8—21no—
48C22×C7×Q8—21no—
49C22×C7×Q8—22no—
50C22×C7×Q8—21no—
51C22×C7×Q8—21no—
52C22×C7×Q8—22no—
53C22×C7×Q8D414yescomplemented
54C22×C7×Q8C2312yes—
55C22×C7×D4—21no—
56C22×C7×D4—21no—
57C22×C7×D4—21no—
58C22×C7×D4—21no—
59C22×C7×D4—22no—
60C22×C7×D4—22no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4D412yes—
64C22×C7×D4C2312yes—
65C23×C4×C7—21no—
66C23×C4×C7—21no—
67C23×C4×C7C2311yescharacteristic
68C22×C22⋊D7—21no—
69C22×C22⋊D7—24no—
70C2×#1157—21no—
71C2×#1157—21no—
72C2×#1157—22no—
73C2×#1157—22no—
74C2×#1157—22no—
75C2×#1157—22no—
76C2×#1157D412yes—
77C2×#1157C2312yes—
78C22×D28D411yescharacteristic
79C22×C4×D7—21no—
80C22×Dic14D411yescharacteristic
81C7×#124—216no—
82C7×#124—28no—
83C7×#124—28no—
84C2×C7×C22⋊C4—216no—
85C2×C7×C22⋊C4—28no—
86C2×C42×C7—21no—
87C2×C42×C7—22no—
88C2×C42×C7D414yescomplemented
89C2×C42×C7C2312yes—
90#6516—28no—
91#6516—28no—
92C2×C22⋊Dic7—24no—
93C2×C22⋊Dic7—21no—
94C2×#1144—28no—
95C2×#1144—24no—
96#6505—216no—
97#6505—28no—
98#6505—28no—
99C2×#1143—28no—
100C2×#1143—24no—
101#6503—24no—
102#6503—24no—
103#6501—28no—
104#6501—28no—
105#6499—24no—
106#6499—24no—
107#6489—21no—
108#6489—21no—
109#6489D412yes—
110#6489C2312yes—
111C2×C4⋊Dic7D412yes—
112C2×C4×Dic7—21no—
113C2×#1136—22no—
114C2×#1136—21no—
115C2×#1136—21no—
116C2×#1136—22no—
117C2×#1136—22no—
118C2×#1136D414yescomplemented
119C2×#1136C2312yes—
120C2×#1136C2312yes—
121C22×C7⋊C8—21no—
122C22×C7⋊C8—21no—
123#6409—28no—
124#6407—28no—
125#6379—28no—
126C22×#137—71no—
127C2×#535—71no—
128C22×#124D711yescharacteristic, complemented
129C22×#104—71no—
130C2×#419—71no—
131C22×#100—71no—
132#2004—78no—
133C2×#339—71no—
134C24×C7—22no—
135C24×C7—24no—
136C24×C7—22no—
137C24×C7—24no—
138C24×C7—48no—
139C24×C7C2×D411yescharacteristic
140C24×C7C2×D414yes—
141C23×D7—21no—
142C2×C7×Q8—24no—
143C2×C7×Q8—22no—
144C2×C7×Q8—24no—
145C2×C7×Q8—24no—
146C2×C7×Q8—24no—
147C2×C7×Q8—24no—
148C2×C7×Q8—22no—
149C2×C7×Q8—22no—
150C2×C7×Q8—22no—
151C2×C7×Q8—22no—
152C2×C7×Q8—41no—
153C2×C7×Q8—41no—
154C2×C7×Q8—42no—
155C2×C7×Q8—42no—
156C2×C7×Q8—42no—
157C2×C7×Q8—42no—
158C2×C7×Q8—42no—
159C2×C7×Q8C2×D414yescomplemented
160C2×C7×D4—22no—
161C2×C7×D4—22no—
162C2×C7×D4—24no—
163C2×C7×D4—24no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—22no—
167C2×C7×D4—22no—
168C2×C7×D4—22no—
169C2×C7×D4—22no—
170C2×C7×D4—42no—
171C2×C7×D4—42no—
172C2×C7×D4—42no—
173C2×C7×D4—42no—
174C2×C7×D4—42no—
175C2×C7×D4—42no—
176C2×C7×D4—42no—
177C2×C7×D4—42no—
178C22×C4×C7—24no—
179C22×C4×C7—24no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—44no—
183C22×C4×C7—41no—
184C22×C4×C7—41no—
185C22×C4×C7—42no—
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D412yes—
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D412yes—
194C22×C4×C7#4112yes—
195C22×C4×C7C2411yescharacteristic
196C2×C22⋊D7—22no—
197C2×C22⋊D7—22no—
198C2×C22⋊D7—216no—
199C2×C22⋊D7—42no—
200C2×C22⋊D7—42no—
201C2×C22⋊D7—88no—
202C22×Dic7—22no—
203C22×Dic7—21no—
204#1157—24no—
205#1157—24no—
206#1157—22no—
207#1157—22no—
208#1157—22no—
209#1157—22no—
210#1157—42no—
211#1157—42no—
212#1157—42no—
213#1157—42no—
214C2×D28—22no—
215C2×D28—22no—
216C2×D28—21no—
217C2×D28C2×D412yes—
218C2×C4×D7—22no—
219C2×C4×D7—22no—
220C2×C4×D7—42no—
221C2×C4×D7—42no—
222C2×Dic14—22no—
223C2×Dic14—22no—
224C2×Dic14—21no—
225C2×Dic14C2×D412yes—
226C7×C22⋊C4—232no—
227C42×C7—24no—
228C42×C7—22no—
229C42×C7C2×D414yescomplemented
230C22⋊Dic7—216no—
231C22⋊Dic7—22no—
232C22⋊Dic7—22no—
233#1144—216no—
234#1143—216no—
235C4⋊Dic7—22no—
236C4⋊Dic7C2×D414yes—
237C4×Dic7—22no—
238C4×Dic7—22no—
239#1136—24no—
240#1136—22no—
241#1136—22no—
242#1136—22no—
243#1136—42no—
244#1136C2×D414yescomplemented
245C2×C7⋊C8—24no—
246C2×C7⋊C8—22no—
247C2×C7⋊C8—22no—
248C2×C7⋊C8—42no—
249C22×#41—71no—
250C23×Q8C2×D711yescharacteristic
251C23×D4C2×D711yescharacteristic
252C2×#137—74no—
253C2×#137—144no—
254C2×#137—142no—
255C2×#137—144no—
256C22×Q16—141no—
257C22×SD16—141no—
258C22×M16—71no—
259C22×M16—71no—
260#535—74no—
261#535—142no—
262#535—142no—
263#535—142no—
264C2×#127—141no—
265C2×#124—24no—
266C2×#124—22no—
267C2×#124—24no—
268C2×#124—141no—
269C2×#124C2×D714yescomplemented
270C2×#121—142no—
271C2×#120—142no—
272C2×#117—71no—
273C22×C22⋊C4—22no—
274C22×C42C2×D711yescharacteristic
275C2×#104—74no—
276C2×#104—144no—
277#419—74no—
278#419—142no—
279C2×#103—142no—
280C2×#100—74no—
281C2×#100—144no—
282#339—74no—
283C23×C7—24no—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—48no—
288C23×C7—416no—
289C23×C7—44no—
290C23×C7—44no—
291C23×C7—48no—
292C23×C7—84no—
293C23×C7—88no—
294C23×C7#12011yescharacteristic
295C23×C7#12011yescharacteristic
296C23×C7#12012yes—
297C23×C7#12112yes—
298C23×C7C22×D411yescharacteristic
299C22×D7—22no—
300C22×D7—42no—
301C22×D7—44no—
302C7×Q8—24no—
303C7×Q8—24no—
304C7×Q8—42no—
305C7×Q8—42no—
306C7×Q8—44no—
307C7×Q8—44no—
308C7×D4—42no—
309C7×D4—42no—
310C7×D4—42no—
311C7×D4—42no—
312C7×D4—44no—
313C7×D4—44no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—44no—
317C2×C4×C7—48no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—44no—
321C2×C4×C7—44no—
322C2×C4×C7#12012yes—
323C2×C4×C7#12012yes—
324C2×C4×C7#12011yescharacteristic
325C2×C4×C7#12011yescharacteristic
326C2×C4×C7#12012yes—
327C2×C4×C7#12112yes—
328C2×C4×C7#12112yes—
329C2×C4×C7#12112yes—
330C2×C4×C7#12112yes—
331C2×C4×C7#12112yes—
332C2×C4×C7#12712yes—
333C2×C4×C7#12712yes—
334C2×C4×C7C22×D411yescharacteristic
335C2×C4×C7C22×D411yescharacteristic
336C2×C4×C7C22×D411yescharacteristic
337C2×C4×C7C22×D411yescharacteristic
338C2×C4×C7C22×D411yescharacteristic
339C2×C4×C7C2×#4111yescharacteristic
340C22⋊D7—42no—
341C22⋊D7—42no—
342C22⋊D7—44no—
343C22⋊D7—816no—
344C2×Dic7—24no—
345C2×Dic7—22no—
346C2×Dic7—42no—
347C2×Dic7—44no—
348D28—22no—
349D28—22no—
350D28—42no—
351C4×D7—42no—
352C4×D7—42no—
353C4×D7—44no—
354Dic14—22no—
355Dic14—22no—
356Dic14—42no—
357C7⋊C8—24no—
358C7⋊C8—42no—
359C25C22⋊D712yes—
360C2×#41—72no—
361C2×#41—72no—
362C2×#41—141no—
363C2×#41—141no—
364C2×#41—142no—
365C2×#41—142no—
366C2×#41—142no—
367C2×#41—142no—
368C22×Q8—22no—
369C22×Q8—21no—
370C22×Q8—21no—
371C22×Q8—21no—
372C22×Q8—22no—
373C22×Q8—21no—
374C22×Q8—21no—
375C22×Q8—22no—
376C22×Q8—71no—
377C22×Q8C22⋊D714yescomplemented
378C22×Q8C22×D712yes—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—71no—
388C22×D4—141no—
389C22×D4—144no—
390C22×D4C22⋊D712yes—
391C22×D4C22×D712yes—
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—141no—
395C23×C4C22×D711yescharacteristic
396#137—148no—
397#137—1416no—
398#137—148no—
399C2×Q16—144no—
400C2×Q16—148no—
401C2×SD16—144no—
402C2×SD16—148no—
403C2×M16—74no—
404C2×M16—72no—
405C2×M16—72no—
406C2×M16—141no—
407C2×M16—142no—
408C2×M16—141no—
409C2×M16—142no—
410C2×M16—142no—
411C22×C8—141no—
412C22×C8—141no—
413#127—144no—
414#127—144no—
415#124—216no—
416#124—28no—
417#124—28no—
418#124—144no—
419#124—144no—
420#121—148no—
421#121—148no—
422#120—148no—
423#120—148no—
424#117—72no—
425#117—72no—
426#117—141no—
427#117—141no—
428C2×C4⋊C4—72no—
429C2×C22⋊C4—216no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—144no—
432C2×C22⋊C4—141no—
433C2×C42—21no—
434C2×C42—22no—
435C2×C42—141no—
436C2×C42C22⋊D714yescomplemented
437C2×C42C22×D712yes—
438#104—148no—
439#103—148no—
440#100—148no—
441C22×C7—22no—
442C22×C7—22no—
443C22×C7—24no—
444C22×C7—24no—
445C22×C7—48no—
446C22×C7—44no—
447C22×C7—48no—
448C22×C7—84no—
449C22×C7—88no—
450C22×C7—88no—
451C22×C7#39212yes—
452C22×C7#39212yes—
453C22×C7#45514yes—
454C22×C7C2×#12011yescharacteristic
455C22×C7C2×#12011yescharacteristic
456C22×C7C2×#12111yescharacteristic
457C2×D7—42no—
458C2×D7—44no—
459C2×D7—84no—
460C4×C7—44no—
461C4×C7—44no—
462C4×C7#39212yes—
463C4×C7#39212yes—
464C4×C7C2×#12011yescharacteristic
465C4×C7C2×#12111yescharacteristic
466C4×C7C2×#12111yescharacteristic
467C4×C7C2×#12711yescharacteristic
468Dic7—42no—
469Dic7—44no—
470C24—22no—
471C24—24no—
472C24—22no—
473C24—24no—
474C24—48no—
475C24—141no—
476C24C2×C22⋊D711yescharacteristic
477C24C2×C22⋊D714yes—
478#41—144no—
479#41—144no—
480#41—142no—
481#41—142no—
482#41—142no—
483#41—142no—
484#41—282no—
485#41—282no—
486#41—282no—
487#41—282no—
488C2×Q8—24no—
489C2×Q8—22no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—24no—
493C2×Q8—24no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—72no—
506C2×Q8—141no—
507C2×Q8—142no—
508C2×Q8—142no—
509C2×Q8C2×C22⋊D714yescomplemented
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—72no—
529C2×D4—142no—
530C2×D4—142no—
531C2×D4—1416no—
532C2×D4—142no—
533C2×D4—141no—
534C2×D4—142no—
535C2×D4—282no—
536C2×D4—282no—
537C2×D4—568no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—44no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—42no—
546C22×C4—142no—
547C22×C4—141no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—282no—
551C22×C4—282no—
552C22×C4D4×D711yescharacteristic
553C22×C4D4×D711yescharacteristic
554C22×C4D4×D712yes—
555C22×C4D4×D711yescharacteristic
556C22×C4D4×D711yescharacteristic
557C22×C4#115912yes—
558C22×C4C2×C22⋊D711yescharacteristic
559C22×C4C2×C22⋊D712yes—
560C22×C4C2×C22⋊D712yes—
561C22×C4C23×D711yescharacteristic
562Q16—1416no—
563SD16—1416no—
564M16—74no—
565M16—144no—
566M16—142no—
567M16—142no—
568M16—142no—
569M16—282no—
570C2×C8—144no—
571C2×C8—142no—
572C2×C8—142no—
573C2×C8—282no—
574C4⋊C4—74no—
575C4⋊C4—142no—
576C22⋊C4—232no—
577C22⋊C4—1416no—
578C22⋊C4—142no—
579C22⋊C4—142no—
580C42—24no—
581C42—22no—
582C42—142no—
583C42—142no—
584C42C2×C22⋊D714yescomplemented
585C2×C7—21no—
586C2×C7—21no—
587C2×C7—22no—
588C2×C7—84no—
589C2×C7#200414yescomplemented
590C2×C7C2×#39211yescharacteristic
591C2×C7C2×#45512yes—
592D7—82no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—48no—
598C23—416no—
599C23—44no—
600C23—44no—
601C23—48no—
602C23—84no—
603C23—88no—
604C23—142no—
605C23—282no—
606C23—284no—
607C23#650011yescharacteristic
608C23#650011yescharacteristic
609C23#650212yes—
610C23#651612yes—
611C23C22×C22⋊D711yescharacteristic
612Q8—24no—
613Q8—24no—
614Q8—42no—
615Q8—42no—
616Q8—44no—
617Q8—44no—
618Q8—142no—
619Q8—142no—
620Q8—282no—
621D4—42no—
622D4—42no—
623D4—42no—
624D4—42no—
625D4—44no—
626D4—44no—
627D4—142no—
628D4—142no—
629D4—282no—
630D4—284no—
631D4—282no—
632D4—282no—
633D4—5616no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—48no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—144no—
643C2×C4—142no—
644C2×C4—282no—
645C2×C4—284no—
646C2×C4—282no—
647C2×C4—282no—
648C2×C4—284no—
649C2×C4#650012yes—
650C2×C4#650012yes—
651C2×C4#650011yescharacteristic
652C2×C4#650011yescharacteristic
653C2×C4#650112yes—
654C2×C4#650112yes—
655C2×C4#650212yes—
656C2×C4#650212yes—
657C2×C4#650212yes—
658C2×C4#650312yes—
659C2×C4#650312yes—
660C2×C4#651612yes—
661C2×C4C2×D4×D711yescharacteristic
662C2×C4C2×D4×D711yescharacteristic
663C2×C4C2×D4×D711yescharacteristic
664C2×C4C2×#115911yescharacteristic
665C2×C4C22×C22⋊D711yescharacteristic
666C2×C4C22×C22⋊D711yescharacteristic
667C8—144no—
668C8—282no—
669C7C2×#200411yescharacteristic, complemented, Sylow
670C22—24no—
671C22—24no—
672C22—22no—
673C22—22no—
674C22—48no—
675C22—44no—
676C22—48no—
677C22—84no—
678C22—88no—
679C22—88no—
680C22—282no—
681C22—284no—
682C22—564no—
683C22#8983314yes—
684C22#8999512yes—
685C22#8999512yes—
686C22C2×#650011yescharacteristic
687C22C2×#650211yescharacteristic
688C22C2×#651611yescharacteristic
689C4—44no—
690C4—44no—
691C4—282no—
692C4—284no—
693C4#8999512yes—
694C4#8999512yes—
695C4C2×#650011yescharacteristic
696C4C2×#650111yescharacteristic
697C4C2×#650211yescharacteristic
698C4C2×#650311yescharacteristic
699C2—21no—
700C2—21no—
701C2—22no—
702C2—84no—
703C2—562no—
704C2#1172948514yesdirect product factor
705C2C2×#8983312yes—
706C2C2×#8999511yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC22×C7×#124C2
socleC23×C7#120
prime radicalC2×#90496C2
hypercenterC22×#124D7
hypocenterC7C2×#2004
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×C7×#124C2semidirect
2. C22×#6505C2semidirect
4. C2×#89997C2semidirect
5. C22×#6407C2semidirect
6. C22×#6379C2semidirect
7. #11729485C2direct (N × H)
8. C2×#89318C2semidirect
15. C2×C7×#124C22semidirect
23. C2×#6505C22semidirect
36. #89997C22semidirect
39. C2×#6407C22semidirect
41. C2×#6379C22semidirect
42. #89318C22semidirect
53. C22×C7×Q8D4semidirect
88. C2×C42×C7D4semidirect
118. C2×#1136D4semidirect
128. C22×#124D7semidirect
159. C2×C7×Q8C2×D4semidirect
229. C42×C7C2×D4semidirect
244. #1136C2×D4semidirect
269. C2×#124C2×D7semidirect
377. C22×Q8C22⋊D7semidirect
436. C2×C42C22⋊D7semidirect
509. C2×Q8C2×C22⋊D7semidirect
584. C42C2×C22⋊D7semidirect
589. C2×C7#2004semidirect
669. C7C2×#2004semidirect
704. C2#11729485direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1242
C22×#65052
C2×#904962
C2×#899972
C22×#64072
C22×#63792
#117294852
C2×#893182
C2×#20047