Finite Group Databasebeta

← C2×#11726639 #13355483

Subgroups — C2×#11726639 #13355483

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
1C23×#1131C211yesmaximal, characteristic, complemented
2C22×#6458C211yesmaximal, characteristic
3C22×#6395C211yesmaximal, characteristic, complemented
4C2×#89759C211yesmaximal, characteristic, complemented
5C22×#6383C211yesmaximal, characteristic, complemented
6C2×C7×#340C211yesmaximal, characteristic, complemented
7C2×#89324C211yesmaximal, characteristic, complemented
8#11726639C218yesmaximal, direct product factor
9C23×D28—21no—
10C23×D28C2211yescharacteristic
11C23×C4×D7C2211yescharacteristic
12C23×C7×C8C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×(C2×D7)⋊C4—21no—
16C22×(C2×D7)⋊C4—21no—
17C22×C4⋊Dic7C2211yescharacteristic
18C23×C7⋊C8C2211yescharacteristic
19C22×#1131—24no—
20C22×#1131—24no—
21C22×#1131—24no—
22C22×#1131C2214yescomplemented
23C2×#6458—22no—
24C2×#6458—24no—
25C2×#6458C418yescomplemented
26C2×#6458C2214yes—
27C2×C7⋊#95—21no—
28C2×#6395—24no—
29C2×#6395C2214yescomplemented
30#89759—22no—
31#89759C2214yescomplemented
32C2×#6383—24no—
33C2×#6383C2214yescomplemented
34C7×#340C2214yescomplemented
35#89324C2214yescomplemented
36C2×#1895—71nomaximal, Sylow
37C24×D7—21no—
38C24×D7D411yescharacteristic
39C23×C4×C7—21no—
40C23×C4×C7—21no—
41C23×C4×C7C2311yescharacteristic
42C23×Dic7—21no—
43C23×Dic7D411yescharacteristic
44C22×D28—22no—
45C22×D28—22no—
46C22×D28—22no—
47C22×D28—22no—
48C22×D28—28no—
49C22×D28—24no—
50C22×D28—21no—
51C22×D28—22no—
52C22×D28—44no—
53C22×D28—44no—
54C22×D28C2×C414yes—
55C22×D28C2312yes—
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—21no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4C2×C414yes—
74C2×C7×C4⋊C4C2312yes—
75C2×C7×C4⋊C4C2312yes—
76C2×(C2×D7)⋊C4—28no—
77C2×(C2×D7)⋊C4—24no—
78C2×(C2×D7)⋊C4—24no—
79C2×(C2×D7)⋊C4—44no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—21no—
83C2×C4⋊Dic7C2312yes—
84C22×C7⋊C8—22no—
85C22×C7⋊C8—22no—
86C22×C7⋊C8D414yescomplemented
87C22×C7⋊C8C2312yes—
88C2×#1131—232no—
89C2×#1131—28no—
90C2×#1131—28no—
91C2×#1131—28no—
92#6458—216no—
93#6458—28no—
94#6458C2×C4116yescomplemented
95C7⋊#95—24no—
96#6395—28no—
97#6383—28no—
98C23×M16—71no—
99C22×#121—71no—
100C22×#102—71no—
101C22×#102—71no—
102C2×#380—71no—
103#1895—78no—
104C2×#340—71no—
105C2×#340D711yescharacteristic, complemented
106C24×C7C2×D411yescharacteristic
107C23×D7—22no—
108C23×D7—22no—
109C23×D7—22no—
110C23×D7—22no—
111C23×D7—22no—
112C23×D7—22no—
113C23×D7—24no—
114C23×D7—22no—
115C23×D7—42no—
116C23×D7—42no—
117C23×D7—42no—
118C23×D7—42no—
119C23×D7—42no—
120C23×D7—42no—
121C23×D7C22⋊C414yes—
122C23×D7C2×D412yes—
123C22×C4×C7—24no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—42no—
127C22×C4×C7—42no—
128C22×C4×C7—42no—
129C22×C4×C7—42no—
130C22×C4×C7—42no—
131C22×C4×C7C22×C412yes—
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2×D412yes—
134C22×C4×C7C2×D412yes—
135C22×C4×C7C2×D412yes—
136C22×C4×C7#4112yes—
137C22×C4×C7#4112yes—
138C22×C4×C7C2411yescharacteristic
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—42no—
143C22×Dic7—42no—
144C22×Dic7—42no—
145C22×Dic7C22⋊C414yes—
146C22×Dic7C2×D412yes—
147C2×D28—28no—
148C2×D28—28no—
149C2×D28—22no—
150C2×D28—22no—
151C2×D28—22no—
152C2×D28—22no—
153C2×D28—216no—
154C2×D28—24no—
155C2×D28—22no—
156C2×D28—48no—
157C2×D28—48no—
158C2×D28—432no—
159C2×D28—44no—
160C2×D28—42no—
161C2×D28—42no—
162C2×D28—44no—
163C2×D28C22×C414yes—
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—24no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—22no—
184C7×C4⋊C4—22no—
185C7×C4⋊C4—42no—
186C7×C4⋊C4C22×C414yes—
187(C2×D7)⋊C4—216no—
188(C2×D7)⋊C4—48no—
189C4⋊Dic7—22no—
190C4⋊Dic7—22no—
191C4⋊Dic7—42no—
192C2×C7⋊C8—28no—
193C2×C7⋊C8—22no—
194C2×C7⋊C8—22no—
195C2×C7⋊C8C2×D414yescomplemented
196#1131—232no—
197C23×D4—71no—
198C23×D4—141no—
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⋊C4C2×D711yescharacteristic
212C22×C4⋊C4C2×D711yescharacteristic
213C22×C22⋊C4—141no—
214C22×C22⋊C4—141no—
215C2×#102—74no—
216C2×#102—74no—
217C2×#102—144no—
218C2×#102—144no—
219#380—74no—
220#380—142no—
221C2×#95—141no—
222#340—74no—
223#340C2×D714yescomplemented
224C23×C7C2×C22⋊C412yes—
225C23×C7#12112yes—
226C23×C7#12112yes—
227C23×C7AGL(1,ℤ/8)12yes—
228C23×C7AGL(1,ℤ/8)12yes—
229C23×C7AGL(1,ℤ/8)12yes—
230C23×C7#13712yes—
231C23×C7C22×D411yescharacteristic
232C22×D7—22no—
233C22×D7—22no—
234C22×D7—22no—
235C22×D7—22no—
236C22×D7—22no—
237C22×D7—22no—
238C22×D7—28no—
239C22×D7—28no—
240C22×D7—28no—
241C22×D7—24no—
242C22×D7—44no—
243C22×D7—44no—
244C22×D7—44no—
245C22×D7—44no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—42no—
250C22×D7—42no—
251C22×D7—42no—
252C22×D7—48no—
253C22×D7—48no—
254C22×D7—48no—
255C22×D7—84no—
256C22×D7—84no—
257C22×D7—84no—
258C22×D7—84no—
259C22×D7C2×C22⋊C414yes—
260C2×C4×C7—24no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—48no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—84no—
268C2×C4×C7C2×C22⋊C412yes—
269C2×C4×C7C4×D414yes—
270C2×C4×C7C4×D414yes—
271C2×C4×C7#12014yes—
272C2×C4×C7#12112yes—
273C2×C4×C7#12112yes—
274C2×C4×C7#12314yes—
275C2×C4×C7C23×C411yescharacteristic
276C2×C4×C7C22×D411yescharacteristic
277C2×C4×C7C22×D411yescharacteristic
278C2×C4×C7C22×D411yescharacteristic
279C2×C4×C7C2×#4111yescharacteristic
280C2×C4×C7C2×#4111yescharacteristic
281C2×Dic7—22no—
282C2×Dic7—22no—
283C2×Dic7—28no—
284C2×Dic7—42no—
285C2×Dic7—42no—
286C2×Dic7—42no—
287C2×Dic7—84no—
288C2×Dic7C2×C22⋊C414yes—
289D28—24no—
290D28—24no—
291D28—432no—
292D28—42no—
293D28—42no—
294D28—48no—
295C4×D7—24no—
296C4×D7—24no—
297C4×D7—24no—
298C4×D7—24no—
299C4×D7—216no—
300C7×C8—24no—
301C7⋊C8—24no—
302C25—71no—
303C25—141no—
304C22×D4—74no—
305C22×D4—72no—
306C22×D4—148no—
307C22×D4—144no—
308C22×D4—142no—
309C22×D4—142no—
310C22×D4—142no—
311C22×D4—141no—
312C22×D4—142no—
313C22×D4—142no—
314C22×D4—284no—
315C22×D4—284no—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—71no—
319C23×C4—74no—
320C23×C4—74no—
321C23×C4—72no—
322C23×C4—72no—
323C23×C4—142no—
324C23×C4—142no—
325C23×C4—142no—
326C23×C4—142no—
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×C8D2814yescomplemented
340C22×C8C22×D712yes—
341#121—716no—
342#121—1416no—
343#121—148no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—72no—
350C2×C4⋊C4—142no—
351C2×C4⋊C4—142no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4C4×D714yes—
354C2×C4⋊C4C22×D712yes—
355C2×C4⋊C4C22×D712yes—
356C2×C22⋊C4—148no—
357C2×C22⋊C4—144no—
358C2×C22⋊C4—144no—
359C2×C22⋊C4—284no—
360#102—148no—
361#102—148no—
362#95—144no—
363C22×C7#38614yes—
364C22×C7#41714yes—
365C22×C7#41814yes—
366C22×C7#46814yes—
367C22×C7#46814yes—
368C22×C7#46914yes—
369C22×C7#46914yes—
370C22×C7C22×C22⋊C411yescharacteristic
371C22×C7C2×#12111yescharacteristic
372C22×C7C2×#12111yescharacteristic
373C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C7C2×#13711yescharacteristic
377C2×D7—24no—
378C2×D7—24no—
379C2×D7—24no—
380C2×D7—416no—
381C2×D7—42no—
382C2×D7—42no—
383C2×D7—42no—
384C2×D7—42no—
385C2×D7—44no—
386C2×D7—44no—
387C2×D7—44no—
388C2×D7—816no—
389C2×D7—82no—
390C2×D7—82no—
391C2×D7—82no—
392C2×D7—82no—
393C4×C7—44no—
394C4×C7—82no—
395C4×C7#38614yes—
396C4×C7C2×C4×D411yescharacteristic
397C4×C7C2×C4×D411yescharacteristic
398C4×C7C2×#12011yescharacteristic
399C4×C7C2×#12311yescharacteristic
400Dic7—24no—
401Dic7—82no—
402C24—74no—
403C24—72no—
404C24—142no—
405C24—142no—
406C24—142no—
407C24—142no—
408C24—142no—
409C24—142no—
410C24—144no—
411C24—142no—
412C24—282no—
413C24—282no—
414C24—282no—
415C24—282no—
416C24—282no—
417C24—282no—
418C24D4×D711yescharacteristic
419C2×D4—74no—
420C2×D4—1416no—
421C2×D4—148no—
422C2×D4—144no—
423C2×D4—148no—
424C2×D4—142no—
425C2×D4—142no—
426C2×D4—142no—
427C2×D4—142no—
428C2×D4—142no—
429C2×D4—288no—
430C2×D4—288no—
431C2×D4—2832no—
432C2×D4—284no—
433C2×D4—282no—
434C2×D4—284no—
435C2×D4—282no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—74no—
445C22×C4—72no—
446C22×C4—78no—
447C22×C4—74no—
448C22×C4—74no—
449C22×C4—142no—
450C22×C4—142no—
451C22×C4—148no—
452C22×C4—148no—
453C22×C4—144no—
454C22×C4—148no—
455C22×C4—148no—
456C22×C4—144no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—282no—
463C22×C4—282no—
464C22×C4—282no—
465C22×C4C2×C4×D712yes—
466C22×C4C2×D2812yes—
467C22×C4#115712yes—
468C22×C4D4×D711yescharacteristic
469C22×C4D4×D712yes—
470C22×C4D4×D712yes—
471C22×C4#116112yes—
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×D2814yescomplemented
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—42no—
487C4⋊C4—142no—
488C4⋊C4—142no—
489C4⋊C4—282no—
490C4⋊C4C2×C4×D714yes—
491C22⋊C4—1416no—
492C22⋊C4—288no—
493C2×C7#189518yescomplemented
494C2×C7C2×#38611yescharacteristic
495C2×C7C2×#41811yescharacteristic
496C2×C7C2×#41711yescharacteristic
497C2×C7C2×#46811yescharacteristic
498C2×C7C2×#46811yescharacteristic
499C2×C7C2×#46911yescharacteristic
500C2×C7C2×#46911yescharacteristic
501D7—44no—
502D7—84no—
503C23—74no—
504C23—142no—
505C23—142no—
506C23—142no—
507C23—142no—
508C23—142no—
509C23—142no—
510C23—148no—
511C23—148no—
512C23—148no—
513C23—144no—
514C23—284no—
515C23—284no—
516C23—284no—
517C23—284no—
518C23—282no—
519C23—282no—
520C23—282no—
521C23—282no—
522C23—282no—
523C23—282no—
524C23—288no—
525C23—288no—
526C23—288no—
527C23—564no—
528C23—564no—
529C23—564no—
530C23—564no—
531C23D7×C22⋊C412yes—
532C23#644712yes—
533C23#645812yes—
534C23#647412yes—
535C23#647712yes—
536C23#647712yes—
537C23#648112yes—
538C23C2×D4×D711yescharacteristic
539D4—144no—
540D4—144no—
541D4—2832no—
542D4—282no—
543D4—282no—
544D4—288no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—48no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—74no—
553C2×C4—84no—
554C2×C4—142no—
555C2×C4—142no—
556C2×C4—148no—
557C2×C4—144no—
558C2×C4—144no—
559C2×C4—144no—
560C2×C4—144no—
561C2×C4—1416no—
562C2×C4—282no—
563C2×C4—282no—
564C2×C4—282no—
565C2×C4—564no—
566C2×C4C4×D2814yes—
567C2×C4D7×C22⋊C412yes—
568C2×C4#644514yes—
569C2×C4#644712yes—
570C2×C4#645614yes—
571C2×C4#645714yes—
572C2×C4#645812yes—
573C2×C4C22×C4×D711yescharacteristic
574C2×C4C22×D2811yescharacteristic
575C2×C4C2×#115711yescharacteristic
576C2×C4C2×D4×D711yescharacteristic
577C2×C4C2×D4×D711yescharacteristic
578C2×C4C2×#116111yescharacteristic
579C8—24no—
580C8—144no—
581C7C2×#189511yescharacteristic, complemented, Sylow
582C22—144no—
583C22—144no—
584C22—144no—
585C22—282no—
586C22—2816no—
587C22—282no—
588C22—282no—
589C22—282no—
590C22—284no—
591C22—284no—
592C22—284no—
593C22—562no—
594C22—5616no—
595C22—562no—
596C22—562no—
597C22—562no—
598C22#8943714yes—
599C22#8954214yes—
600C22#8955414yes—
601C22#8957514yes—
602C22#8958414yes—
603C22#8963714yes—
604C22#8965814yes—
605C22C2×D7×C22⋊C411yescharacteristic
606C22C2×#644711yescharacteristic
607C22C2×#645811yescharacteristic
608C22C2×#647411yescharacteristic
609C22C2×#647711yescharacteristic
610C22C2×#647711yescharacteristic
611C22C2×#648111yescharacteristic
612C4—44no—
613C4—82no—
614C4—144no—
615C4—562no—
616C4#8943714yes—
617C4C2×C4×D2811yescharacteristic
618C4C2×#644511yescharacteristic
619C4C2×#645611yescharacteristic
620C4C2×#645711yescharacteristic
621C2—284no—
622C2—564no—
623C2#1172663918yesdirect product factor
624C2C2×#8943711yescharacteristic
625C2C2×#8954211yescharacteristic
626C2C2×#8955411yescharacteristic
627C2C2×#8957511yescharacteristic
628C2C2×#8958411yescharacteristic
629C2C2×#8963711yescharacteristic
630C2C2×#8965811yescharacteristic
subgroupG/H
centerC24D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#340C2
socleC24×C7C2×D4
prime radicalC22×#6458C2
cosocleC22×C4×C7C24
hypercenterC2×#340D7
hypocenterC7C2×#1895
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C23×#1131C2semidirect
3. C22×#6395C2semidirect
4. C2×#89759C2semidirect
5. C22×#6383C2semidirect
6. C2×C7×#340C2semidirect
7. C2×#89324C2semidirect
8. #11726639C2direct (N × H)
22. C22×#1131C22semidirect
25. C2×#6458C4semidirect
29. C2×#6395C22semidirect
31. #89759C22semidirect
33. C2×#6383C22semidirect
34. C7×#340C22semidirect
35. #89324C22semidirect
66. C22×C7×C8D4semidirect
86. C22×C7⋊C8D4semidirect
94. #6458C2×C4semidirect
105. C2×#340D7semidirect
180. C2×C7×C8C2×D4semidirect
195. C2×C7⋊C8C2×D4semidirect
223. #340C2×D7semidirect
339. C22×C8D28semidirect
481. C2×C8C2×D28semidirect
493. C2×C7#1895semidirect
581. C7C2×#1895semidirect
623. C2#11726639direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#11312
C22×#64582
C22×#63952
C2×#897592
C22×#63832
C2×C7×#3402
C2×#893242
#117266392
C2×#18957