Finite Group Databasebeta

← C2×#11727957 #13355481

Subgroups — C2×#11727957 #13355481

Order 1792.

2310 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6501C211yesmaximal, characteristic
2C23×#1131C211yesmaximal, characteristic, complemented
3C22×C7×#102C211yesmaximal, characteristic, complemented
4C22×#6406C211yesmaximal, characteristic, complemented
5C2×#89759C211yesmaximal, characteristic, complemented
6C2×#89346C211yesmaximal, characteristic, complemented
7C2×#89324C211yesmaximal, characteristic, complemented
8#11727957C218yesmaximal, direct product factor
9C23×C7×D4C2211yescharacteristic
10C23×C22⋊D7—21no—
11C23×C4×D7C2211yescharacteristic
12C23×C7×C8C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C22⋊Dic7—21no—
15C2×#6501—22no—
16C2×#6501—24no—
17C2×#6501C418yescomplemented
18C2×#6501C2214yes—
19C22×(C2×D7)⋊C4—21no—
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C23×C7⋊C8C2211yescharacteristic
23C22×#1131—24no—
24C22×#1131—24no—
25C22×#1131—24no—
26C22×#1131C2214yescomplemented
27C2×C7×#102—24no—
28C2×C7×#102C2214yescomplemented
29C2×#6406—24no—
30C2×#6406C2214yescomplemented
31C2×C7⋊#95—21no—
32#89759—22no—
33#89759C2214yescomplemented
34#89346C2214yescomplemented
35#89324C2214yescomplemented
36C2×#1895—71nomaximal, Sylow
37C25×C7—21no—
38C24×D7D411yescharacteristic
39C22×C7×D4—22no—
40C22×C7×D4—22no—
41C22×C7×D4—21no—
42C22×C7×D4—22no—
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4C2×C414yes—
46C22×C7×D4C2312yes—
47C23×C4×C7—21no—
48C23×C4×C7C2311yescharacteristic
49C22×C22⋊D7—28no—
50C22×C22⋊D7—24no—
51C22×C22⋊D7—44no—
52C22×C22⋊D7—44no—
53C23×Dic7—21no—
54C23×Dic7—21no—
55C23×Dic7D411yescharacteristic
56C22×C4×D7—22no—
57C22×C4×D7—22no—
58C22×C4×D7—22no—
59C22×C4×D7—22no—
60C22×C4×D7C2×C414yes—
61C22×C4×D7D412yes—
62C22×C4×D7D414yes—
63C22×C4×D7C2312yes—
64C22×C7×C8—22no—
65C22×C7×C8—22no—
66C22×C7×C8D414yescomplemented
67C22×C7×C8C2312yes—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4C2312yes—
72C2×C22⋊Dic7—28no—
73C2×C22⋊Dic7—24no—
74#6501—216no—
75#6501—28no—
76#6501C2×C4116yescomplemented
77C2×(C2×D7)⋊C4—24no—
78C2×(C2×D7)⋊C4—44no—
79C2×C4⋊Dic7—21no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7C2×C414yes—
85C2×C4⋊Dic7C2312yes—
86C2×C4⋊Dic7C2312yes—
87C22×C7⋊C8—22no—
88C22×C7⋊C8—22no—
89C22×C7⋊C8D414yescomplemented
90C22×C7⋊C8C2312yes—
91C2×#1131—232no—
92C2×#1131—28no—
93C2×#1131—28no—
94C2×#1131—28no—
95C7×#102—28no—
96#6406—28no—
97C7⋊#95—24no—
98C23×M16—71no—
99C22×#121—71no—
100C22×#102—71no—
101C22×#102D711yescharacteristic, complemented
102C2×#380—71no—
103#1895—78no—
104C2×#340—71no—
105C2×#340—71no—
106C24×C7—24no—
107C24×C7—22no—
108C24×C7—42no—
109C24×C7—42no—
110C24×C7—42no—
111C24×C7—42no—
112C24×C7—42no—
113C24×C7—42no—
114C24×C7C2×D411yescharacteristic
115C23×D7—22no—
116C23×D7—22no—
117C23×D7—22no—
118C23×D7—22no—
119C23×D7—22no—
120C23×D7—22no—
121C23×D7C22⋊C414yes—
122C23×D7C2×D412yes—
123C2×C7×D4—24no—
124C2×C7×D4—28no—
125C2×C7×D4—28no—
126C2×C7×D4—22no—
127C2×C7×D4—22no—
128C2×C7×D4—22no—
129C2×C7×D4—22no—
130C2×C7×D4—22no—
131C2×C7×D4—44no—
132C2×C7×D4—42no—
133C2×C7×D4—42no—
134C2×C7×D4—44no—
135C2×C7×D4C22×C414yes—
136C22×C4×C7—22no—
137C22×C4×C7—42no—
138C22×C4×C7—42no—
139C22×C4×C7—42no—
140C22×C4×C7C22×C412yes—
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2×D412yes—
143C22×C4×C7C2×D412yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7#4112yes—
146C22×C4×C7#4112yes—
147C22×C4×C7C2411yescharacteristic
148C2×C22⋊D7—216no—
149C2×C22⋊D7—48no—
150C2×C22⋊D7—48no—
151C2×C22⋊D7—432no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—24no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—42no—
158C22×Dic7—42no—
159C22×Dic7—42no—
160C22×Dic7—42no—
161C22×Dic7—42no—
162C22×Dic7C22⋊C414yes—
163C22×Dic7C2×D412yes—
164C2×C4×D7—28no—
165C2×C4×D7—28no—
166C2×C4×D7—28no—
167C2×C4×D7—24no—
168C2×C4×D7—24no—
169C2×C4×D7—28no—
170C2×C4×D7—22no—
171C2×C4×D7—22no—
172C2×C4×D7—22no—
173C2×C4×D7—22no—
174C2×C4×D7C22⋊C418yes—
175C2×C4×D7C22×C414yes—
176C2×C4×D7C2×D414yes—
177C2×C7×C8—28no—
178C2×C7×C8—22no—
179C2×C7×C8—22no—
180C2×C7×C8C2×D414yescomplemented
181C7×C4⋊C4—22no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—42no—
184C22⋊Dic7—216no—
185(C2×D7)⋊C4—48no—
186C4⋊Dic7—24no—
187C4⋊Dic7—22no—
188C4⋊Dic7—22no—
189C4⋊Dic7—22no—
190C4⋊Dic7—42no—
191C4⋊Dic7C22×C414yes—
192C2×C7⋊C8—28no—
193C2×C7⋊C8—22no—
194C2×C7⋊C8—22no—
195C2×C7⋊C8C2×D414yescomplemented
196#1131—232no—
197C23×D4—141no—
198C23×D4C2×D711yescharacteristic
199C24×C4—71no—
200C22×M16—74no—
201C22×M16—144no—
202C22×M16—144no—
203C22×M16—144no—
204C23×C8—71no—
205C23×C8C2×D711yescharacteristic
206C2×#121—78no—
207C2×#121—74no—
208C2×#121—144no—
209C2×#121—142no—
210C22×C4⋊C4—71no—
211C22×C4⋊C4—71no—
212C22×C4⋊C4C2×D711yescharacteristic
213C22×C22⋊C4—141no—
214C22×C22⋊C4—141no—
215C2×#102—24no—
216C2×#102—74no—
217C2×#102—144no—
218C2×#102C2×D714yescomplemented
219#380—74no—
220#380—142no—
221C2×#95—141no—
222#340—74no—
223#340—74no—
224C23×C7—24no—
225C23×C7—42no—
226C23×C7—42no—
227C23×C7—42no—
228C23×C7—42no—
229C23×C7—42no—
230C23×C7—42no—
231C23×C7—48no—
232C23×C7—48no—
233C23×C7—48no—
234C23×C7—84no—
235C23×C7—84no—
236C23×C7—84no—
237C23×C7—84no—
238C23×C7C2×C22⋊C412yes—
239C23×C7#12112yes—
240C23×C7#12112yes—
241C23×C7AGL(1,ℤ/8)12yes—
242C23×C7AGL(1,ℤ/8)12yes—
243C23×C7AGL(1,ℤ/8)12yes—
244C23×C7#13712yes—
245C23×C7C22×D411yescharacteristic
246C22×D7—22no—
247C22×D7—22no—
248C22×D7—22no—
249C22×D7—22no—
250C22×D7—22no—
251C22×D7—22no—
252C22×D7—28no—
253C22×D7—28no—
254C22×D7—28no—
255C22×D7—44no—
256C22×D7—44no—
257C22×D7—44no—
258C22×D7—44no—
259C22×D7C2×C22⋊C414yes—
260C7×D4—24no—
261C7×D4—24no—
262C7×D4—42no—
263C7×D4—42no—
264C7×D4—48no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—84no—
269C2×C4×C7C2×C22⋊C412yes—
270C2×C4×C7C4×D414yes—
271C2×C4×C7C4×D414yes—
272C2×C4×C7#12014yes—
273C2×C4×C7#12112yes—
274C2×C4×C7#12112yes—
275C2×C4×C7#12314yes—
276C2×C4×C7C23×C411yescharacteristic
277C2×C4×C7C22×D411yescharacteristic
278C2×C4×C7C22×D411yescharacteristic
279C2×C4×C7C22×D411yescharacteristic
280C2×C4×C7C2×#4111yescharacteristic
281C2×C4×C7C2×#4111yescharacteristic
282C22⋊D7—432no—
283C2×Dic7—22no—
284C2×Dic7—22no—
285C2×Dic7—28no—
286C2×Dic7—24no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—48no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—84no—
294C2×Dic7C2×C22⋊C414yes—
295C4×D7—24no—
296C4×D7—24no—
297C4×D7—24no—
298C4×D7—24no—
299C4×D7—216no—
300C7×C8—24no—
301C7⋊C8—24no—
302C25—21no—
303C25—71no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—21no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—148no—
311C22×D4—144no—
312C22×D4—284no—
313C22×D4—284no—
314C22×D4C4×D714yes—
315C22×D4C22×D712yes—
316C23×C4—21no—
317C23×C4—71no—
318C23×C4—74no—
319C23×C4—74no—
320C23×C4—72no—
321C23×C4—72no—
322C23×C4—142no—
323C23×C4—142no—
324C23×C4—142no—
325C23×C4—142no—
326C23×C4—141no—
327C23×C4—141no—
328C23×C4C22×D711yescharacteristic
329C2×M16—148no—
330C2×M16—148no—
331C2×M16—1432no—
332C2×M16—148no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—74no—
336C22×C8—72no—
337C22×C8—142no—
338C22×C8—142no—
339C22×C8C22⋊D714yescomplemented
340C22×C8C22×D712yes—
341#121—716no—
342#121—1416no—
343#121—148no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—74no—
348C2×C4⋊C4—72no—
349C2×C4⋊C4—72no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4—142no—
352C2×C4⋊C4—142no—
353C2×C4⋊C4—142no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4C22×D712yes—
356C2×C22⋊C4—148no—
357C2×C22⋊C4—144no—
358C2×C22⋊C4—144no—
359C2×C22⋊C4—284no—
360#102—28no—
361#102—148no—
362#95—144no—
363C22×C7—44no—
364C22×C7—44no—
365C22×C7—44no—
366C22×C7—816no—
367C22×C7—82no—
368C22×C7—82no—
369C22×C7—82no—
370C22×C7—82no—
371C22×C7#38614yes—
372C22×C7#41714yes—
373C22×C7#41814yes—
374C22×C7#46814yes—
375C22×C7#46814yes—
376C22×C7#46914yes—
377C22×C7#46914yes—
378C22×C7C22×C22⋊C411yescharacteristic
379C22×C7C2×#12111yescharacteristic
380C22×C7C2×#12111yescharacteristic
381C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C7C2×#13711yescharacteristic
385C2×D7—24no—
386C2×D7—24no—
387C2×D7—24no—
388C2×D7—416no—
389C2×D7—42no—
390C2×D7—42no—
391C2×D7—42no—
392C2×D7—42no—
393C4×C7—82no—
394C4×C7#38614yes—
395C4×C7C2×C4×D411yescharacteristic
396C4×C7C2×C4×D411yescharacteristic
397C4×C7C2×#12011yescharacteristic
398C4×C7C2×#12311yescharacteristic
399Dic7—24no—
400Dic7—44no—
401Dic7—82no—
402C24—24no—
403C24—22no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—74no—
411C24—72no—
412C24—142no—
413C24—142no—
414C24—142no—
415C24—142no—
416C24—142no—
417C24—142no—
418C24D4×D711yescharacteristic
419C2×D4—24no—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—44no—
428C2×D4—42no—
429C2×D4—44no—
430C2×D4—42no—
431C2×D4—1416no—
432C2×D4—288no—
433C2×D4—288no—
434C2×D4—2832no—
435C2×D4C2×C4×D714yes—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—74no—
441C22×C4—72no—
442C22×C4—78no—
443C22×C4—74no—
444C22×C4—74no—
445C22×C4—142no—
446C22×C4—142no—
447C22×C4—148no—
448C22×C4—148no—
449C22×C4—144no—
450C22×C4—148no—
451C22×C4—148no—
452C22×C4—144no—
453C22×C4—142no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—144no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—282no—
461C22×C4—282no—
462C22×C4—282no—
463C22×C4—282no—
464C22×C4—282no—
465C22×C4C2×C4×D712yes—
466C22×C4#115712yes—
467C22×C4D4×D711yescharacteristic
468C22×C4D4×D712yes—
469C22×C4D4×D712yes—
470C22×C4#115912yes—
471C22×C4C2×C22⋊D712yes—
472C22×C4C23×D711yescharacteristic
473M16—1432no—
474C2×C8—28no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—74no—
478C2×C8—148no—
479C2×C8—142no—
480C2×C8—142no—
481C2×C8C2×C22⋊D714yescomplemented
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—42no—
485C4⋊C4—74no—
486C4⋊C4—144no—
487C4⋊C4—142no—
488C4⋊C4—142no—
489C4⋊C4—142no—
490C4⋊C4—282no—
491C22⋊C4—1416no—
492C22⋊C4—288no—
493C2×C7—84no—
494C2×C7#189518yescomplemented
495C2×C7C2×#38611yescharacteristic
496C2×C7C2×#41811yescharacteristic
497C2×C7C2×#41711yescharacteristic
498C2×C7C2×#46811yescharacteristic
499C2×C7C2×#46811yescharacteristic
500C2×C7C2×#46911yescharacteristic
501C2×C7C2×#46911yescharacteristic
502D7—44no—
503C23—24no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—48no—
511C23—48no—
512C23—48no—
513C23—74no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23—84no—
518C23—142no—
519C23—142no—
520C23—142no—
521C23—142no—
522C23—142no—
523C23—142no—
524C23—148no—
525C23—148no—
526C23—148no—
527C23—284no—
528C23—284no—
529C23—284no—
530C23—284no—
531C23D7×C22⋊C412yes—
532C23#644712yes—
533C23#647412yes—
534C23#647412yes—
535C23#647712yes—
536C23#647812yes—
537C23#650112yes—
538C23C2×D4×D711yescharacteristic
539D4—24no—
540D4—24no—
541D4—42no—
542D4—42no—
543D4—48no—
544D4—2832no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—74no—
549C2×C4—84no—
550C2×C4—142no—
551C2×C4—142no—
552C2×C4—148no—
553C2×C4—144no—
554C2×C4—144no—
555C2×C4—144no—
556C2×C4—144no—
557C2×C4—1416no—
558C2×C4—144no—
559C2×C4—282no—
560C2×C4—282no—
561C2×C4—288no—
562C2×C4—282no—
563C2×C4—282no—
564C2×C4—282no—
565C2×C4—564no—
566C2×C4D7×C22⋊C412yes—
567C2×C4(C22⋊D7)⋊C414yes—
568C2×C4#644614yes—
569C2×C4#644712yes—
570C2×C4C4×C22⋊D714yes—
571C2×C4#650014yes—
572C2×C4#650112yes—
573C2×C4C22×C4×D711yescharacteristic
574C2×C4C2×#115711yescharacteristic
575C2×C4C2×D4×D711yescharacteristic
576C2×C4C2×D4×D711yescharacteristic
577C2×C4C2×#115911yescharacteristic
578C2×C4C22×C22⋊D711yescharacteristic
579C8—24no—
580C8—144no—
581C7C2×#189511yescharacteristic, complemented, Sylow
582C22—44no—
583C22—44no—
584C22—44no—
585C22—816no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22—144no—
591C22—144no—
592C22—144no—
593C22—2816no—
594C22—282no—
595C22—282no—
596C22—282no—
597C22—282no—
598C22#8954214yes—
599C22#8954314yes—
600C22#8955214yes—
601C22#8955414yes—
602C22#8972814yes—
603C22#8993114yes—
604C22#8994614yes—
605C22C2×D7×C22⋊C411yescharacteristic
606C22C2×#644711yescharacteristic
607C22C2×#647411yescharacteristic
608C22C2×#647411yescharacteristic
609C22C2×#647711yescharacteristic
610C22C2×#647811yescharacteristic
611C22C2×#650111yescharacteristic
612C4—82no—
613C4—144no—
614C4—284no—
615C4—562no—
616C4#8972814yes—
617C4C2×(C22⋊D7)⋊C411yescharacteristic
618C4C2×#644611yescharacteristic
619C4C2×C4×C22⋊D711yescharacteristic
620C4C2×#650011yescharacteristic
621C2—84no—
622C2—284no—
623C2#1172795718yesdirect product factor
624C2C2×#8954211yescharacteristic
625C2C2×#8954311yescharacteristic
626C2C2×#8955211yescharacteristic
627C2C2×#8955411yescharacteristic
628C2C2×#8972811yescharacteristic
629C2C2×#8993111yescharacteristic
630C2C2×#8994611yescharacteristic
subgroupG/H
centerC24D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC22×C7×#102C2
socleC24×C7C2×D4
prime radicalC22×#6501C2
cosocleC22×C4×C7C24
hypercenterC22×#102D7
hypocenterC7C2×#1895
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C23×#1131C2semidirect
3. C22×C7×#102C2semidirect
4. C22×#6406C2semidirect
5. C2×#89759C2semidirect
6. C2×#89346C2semidirect
7. C2×#89324C2semidirect
8. #11727957C2direct (N × H)
17. C2×#6501C4semidirect
26. C22×#1131C22semidirect
28. C2×C7×#102C22semidirect
30. C2×#6406C22semidirect
33. #89759C22semidirect
34. #89346C22semidirect
35. #89324C22semidirect
66. C22×C7×C8D4semidirect
76. #6501C2×C4semidirect
89. C22×C7⋊C8D4semidirect
101. C22×#102D7semidirect
180. C2×C7×C8C2×D4semidirect
195. C2×C7⋊C8C2×D4semidirect
218. C2×#102C2×D7semidirect
339. C22×C8C22⋊D7semidirect
481. C2×C8C2×C22⋊D7semidirect
494. C2×C7#1895semidirect
581. C7C2×#1895semidirect
623. C2#11727957direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65012
C23×#11312
C22×C7×#1022
C22×#64062
C2×#897592
C2×#893462
C2×#893242
#117279572
C2×#18957