Finite Group Databasebeta

← #13385943

Subgroups — #13385943

Order 1792.

1690 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic, complemented
2C2×#89808C211yesmaximal, characteristic, complemented
3#11739848C211yesmaximal, characteristic, complemented
4C22×#6383C211yesmaximal, characteristic, complemented
5#11729546C212yesmaximal, complemented
6#11729438C212yesmaximal, complemented
7#11729435C211yesmaximal, characteristic, complemented
8#11729367C212yesmaximal, complemented
9#11729364C211yesmaximal, characteristic, complemented
10#11729314C212yesmaximal, complemented
11#11729307C211yesmaximal, characteristic, complemented
12C22×C7×#41—21no—
13C23×D28C2211yescharacteristic
14C7×#547—24no—
15C7×#547—24no—
16C2×C7×C4⋊Q8C2211yescharacteristic, complemented
17C2×C7×#123—21no—
18C2×C7×#123—21no—
19C2×C7×C22⋊Q8—21no—
20C2×C7×#121C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic, complemented
22C2×C4×C7×D4C2211yescharacteristic
23C2×C4×C7×D4C2211yescharacteristic, complemented
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic, complemented
26C2×#6500—21no—
27C22×#1141C2212yes—
28C2×#6493C2212yes—
29C23×C7⋊C8C2211yescharacteristic
30C2×#6406C2212yescomplemented
31#89984C2211yescharacteristic
32C2×C22⋊(C7⋊C8)C2211yescharacteristic
33C2×C22⋊(C7⋊C8)C2212yescomplemented
34#89808—24no—
35#89763—21no—
36C2×#6383—24no—
37C2×#6383C2212yes—
38C2×#6383C2212yes—
39C2×#6383C2212yes—
40#89732—21no—
41#89727—21no—
42#89711C2212yes—
43#89324C2212yescomplemented
44#89324C2212yescomplemented
45#89324C2212yescomplemented
46#89319C2212yescomplemented
47#23960—71nomaximal, Sylow
48C24×D7—21no—
49C2×C7×#41—28no—
50C2×C7×#41—44no—
51C2×C7×#41—44no—
52C22×C7×Q8—21no—
53C22×C7×D4—21no—
54C22×C7×D4—21no—
55C22×C7×D4D411yescharacteristic
56C22×C7×D4C2311yescharacteristic
57C23×C4×C7—21no—
58C23×C4×C7—21no—
59C23×C4×C7—21no—
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C22×C22⋊D7—22no—
63C22×D28—22no—
64C22×D28—24no—
65C22×D28—22no—
66C22×D28—21no—
67C22×D28—42no—
68C22×D28C2312yes—
69C7×C4⋊Q8—22no—
70C7×C4⋊Q8—22no—
71C7×#123—28no—
72C7×#123—28no—
73C7×C22⋊Q8—28no—
74C7×#121—22no—
75C7×#121—22no—
76C7×#121—22no—
77C7×#121D414yescomplemented
78C4×C7×D4—22no—
79C4×C7×D4—22no—
80C4×C7×D4—22no—
81C4×C7×D4—22no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4D411yescharacteristic
89C2×C7×C4⋊C4D414yescomplemented
90C2×C7×C4⋊C4C2311yescharacteristic
91C2×C7×C4⋊C4C2311yescharacteristic
92C2×C7×C4⋊C4C2311yescharacteristic
93C2×C7×C22⋊C4—21no—
94C2×C7×C22⋊C4—21no—
95C2×C7×C22⋊C4—21no—
96C2×C7×C22⋊C4D411yescharacteristic
97C2×C7×C22⋊C4D411yescharacteristic
98C2×C42×C7C2311yescharacteristic
99C2×C22⋊Dic7—21no—
100#6500—44no—
101C2×#1141—24no—
102C2×#1141—24no—
103C2×#1141—42no—
104#6493—24no—
105#6493—42no—
106C2×(C2×D7)⋊C4—22no—
107C2×(C2×D7)⋊C4—22no—
108C2×(C2×D7)⋊C4—22no—
109C2×C4⋊Dic7C2312yes—
110C22×C7⋊C8—22no—
111C22×C7⋊C8—42no—
112C22×C7⋊C8C2312yes—
113C22×C7⋊C8C2312yes—
114#6406—42no—
115C7⋊#95—21no—
116C22⋊(C7⋊C8)—22no—
117C22⋊(C7⋊C8)—42no—
118#6383—24no—
119#6383—24no—
120#6383—24no—
121C2×#547D711yescharacteristic, complemented
122C2×#447—71no—
123C22×#102—71no—
124#2408—71no—
125#2023—72no—
126#1999—72no—
127#1893—71no—
128#1879—72no—
129#1874—72no—
130#1869—71no—
131#1823—71no—
132C24×C7—21no—
133C24×C7C2×D411yescharacteristic
134C24×C7C2×D411yescharacteristic
135C23×D7—22no—
136C23×D7—44no—
137C23×D7—42no—
138C23×D7—42no—
139C23×D7—42no—
140C23×D7—82no—
141C7×#41—432no—
142C2×C7×Q8—24no—
143C2×C7×Q8—42no—
144C2×C7×Q8—42no—
145C2×C7×D4—22no—
146C2×C7×D4—22no—
147C2×C7×D4—24no—
148C2×C7×D4—24no—
149C2×C7×D4—21no—
150C2×C7×D4—22no—
151C2×C7×D4—22no—
152C2×C7×D4—42no—
153C2×C7×D4—42no—
154C2×C7×D4—42no—
155C2×C7×D4—42no—
156C2×C7×D4D814yescomplemented
157C2×C7×D4C2×D412yes—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—24no—
161C22×C4×C7—24no—
162C22×C4×C7—24no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—42no—
171C22×C4×C7—42no—
172C22×C4×C7—42no—
173C22×C4×C7—42no—
174C22×C4×C7—42no—
175C22×C4×C7—42no—
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2411yescharacteristic
183C2×C22⋊D7—44no—
184C2×C22⋊D7—44no—
185C2×C22⋊D7—82no—
186C22×Dic7—22no—
187C2×D28—28no—
188C2×D28—22no—
189C2×D28—22no—
190C2×D28—22no—
191C2×D28—22no—
192C2×D28—22no—
193C2×D28—48no—
194C2×D28—44no—
195C2×D28—44no—
196C2×D28—42no—
197C2×D28#4114yescomplemented
198C7×C4⋊C4—24no—
199C7×C4⋊C4—24no—
200C7×C4⋊C4—24no—
201C7×C4⋊C4—22no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4C2×D412yes—
206C7×C4⋊C4C2×D412yes—
207C7×C4⋊C4C2×D412yes—
208C7×C22⋊C4—24no—
209C7×C22⋊C4—24no—
210C7×C22⋊C4—22no—
211C7×C22⋊C4—24no—
212C7×C22⋊C4—22no—
213C42×C7—21no—
214C42×C7—21no—
215C22⋊Dic7—42no—
216#1141—48no—
217(C2×D7)⋊C4—44no—
218(C2×D7)⋊C4—44no—
219(C2×D7)⋊C4—82no—
220C4⋊Dic7—22no—
221C4⋊Dic7—22no—
222C2×C7⋊C8—22no—
223C2×C7⋊C8—22no—
224C2×C7⋊C8—22no—
225C2×C7⋊C8—22no—
226C2×C7⋊C8—22no—
227C2×C7⋊C8—22no—
228C2×C7⋊C8—44no—
229C22×#41—21no—
230C23×D4—71no—
231C22×D8—72no—
232C23×C8—71no—
233#547—24no—
234#547—24no—
235C2×C4⋊Q8C2×D711yescharacteristic, complemented
236C2×#123—21no—
237C2×#123—21no—
238C2×C22⋊Q8—21no—
239C2×#121—72no—
240C2×#121C2×D711yescharacteristic
241C2×#121C2×D711yescharacteristic, complemented
242C2×#120—141no—
243C2×C4×D4C2×D711yescharacteristic
244C2×C4×D4C2×D711yescharacteristic, complemented
245C22×C4⋊C4C2×D711yescharacteristic
246C22×C4⋊C4C2×D711yescharacteristic, complemented
247#447—144no—
248C2×#102—72no—
249C2×#102—72no—
250C2×#102—72no—
251C2×#102—72no—
252C2×#102—144no—
253C2×C22⋊C8—71no—
254C2×C22⋊C8—72no—
255#394—141no—
256#392—141no—
257#390—72no—
258#380—71no—
259#379—141no—
260#340—72no—
261#340—72no—
262#340—72no—
263#336—72no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—21no—
267C23×C7—22no—
268C23×C7—21no—
269C23×C7—22no—
270C23×C7—22no—
271C23×C7—42no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—42no—
275C23×C7#12012yes—
276C23×C7C2×D812yes—
277C23×C7C2×D812yes—
278C23×C7AGL(1,ℤ/8)12yes—
279C23×C7C22×D411yescharacteristic
280C22×D7—24no—
281C22×D7—48no—
282C22×D7—42no—
283C22×D7—42no—
284C22×D7—42no—
285C22×D7—42no—
286C22×D7—42no—
287C22×D7—42no—
288C22×D7—88no—
289C22×D7—88no—
290C22×D7—84no—
291C22×D7—84no—
292C7×Q8—48no—
293C7×D4—28no—
294C7×D4—24no—
295C7×D4—48no—
296C7×D4—48no—
297C7×D4—41no—
298C7×D4—41no—
299C2×C4×C7—21no—
300C2×C4×C7—22no—
301C2×C4×C7—21no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—24no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—48no—
313C2×C4×C7—48no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—48no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—42no—
324C2×C4×C7#12012yes—
325C2×C4×C7C2×D812yes—
326C2×C4×C7C22×D411yescharacteristic
327C2×C4×C7C22×D411yescharacteristic
328C2×C4×C7C2×#4112yes—
329C2×C4×C7H(5,𝔽2)12yes—
330C22⋊D7—88no—
331C2×Dic7—42no—
332C2×Dic7—42no—
333C2×Dic7—42no—
334D28—24no—
335D28—24no—
336D28—48no—
337D28—42no—
338D28—42no—
339C7⋊C8—42no—
340C7⋊C8—42no—
341C25—141no—
342C2×#41—28no—
343C2×#41—44no—
344C2×#41—44no—
345C22×Q8—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—72no—
349C22×D4—144no—
350C22×D4—142no—
351C22×D4—142no—
352C22×D4—142no—
353C22×D4—141no—
354C22×D4—282no—
355C22×D4C22⋊D711yescharacteristic
356C22×D4C22×D711yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4C22×D711yescharacteristic
361C23×C4C22×D711yescharacteristic
362C2×D8—144no—
363C2×D8—144no—
364C2×D8—282no—
365C22×C8—72no—
366C22×C8—72no—
367C22×C8—142no—
368C22×C8—282no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371#123—28no—
372#123—28no—
373C22⋊Q8—28no—
374#121—22no—
375#121—22no—
376#121—22no—
377#121—144no—
378#121—282no—
379#121C22⋊D714yescomplemented
380#120—284no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—72no—
392C2×C4⋊C4C22⋊D711yescharacteristic
393C2×C4⋊C4C22⋊D714yescomplemented
394C2×C4⋊C4C22×D711yescharacteristic
395C2×C4⋊C4C22×D711yescharacteristic
396C2×C4⋊C4C22×D711yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—141no—
401C2×C22⋊C4—142no—
402C2×C22⋊C4—142no—
403C2×C22⋊C4—142no—
404C2×C22⋊C4C22⋊D711yescharacteristic
405C2×C22⋊C4C22⋊D711yescharacteristic
406C2×C42C22×D711yescharacteristic
407#102—144no—
408#102—144no—
409#102—144no—
410#102—282no—
411C22⋊C8—142no—
412C22⋊C8—282no—
413#95—141no—
414C22×C7—22no—
415C22×C7—22no—
416C22×C7—24no—
417C22×C7—24no—
418C22×C7—22no—
419C22×C7—24no—
420C22×C7—41no—
421C22×C7—41no—
422C22×C7—42no—
423C22×C7—42no—
424C22×C7—42no—
425C22×C7—42no—
426C22×C7—82no—
427C22×C7—82no—
428C22×C7#44714yes—
429C22×C7C2×#12011yescharacteristic
430C22×C7#54612yes—
431C22×C7C22×D811yescharacteristic
432C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
433C22×C7#57712yes—
434C2×D7—44no—
435C2×D7—44no—
436C2×D7—44no—
437C2×D7—816no—
438C2×D7—82no—
439C2×D7—82no—
440C2×D7—82no—
441C2×D7—82no—
442C4×C7—22no—
443C4×C7—22no—
444C4×C7—41no—
445C4×C7—42no—
446C4×C7—42no—
447C4×C7—42no—
448C4×C7—41no—
449C4×C7#52511yescharacteristic
450C4×C7#53511yescharacteristic
451C4×C7#54612yes—
452Dic7—82no—
453C24—21no—
454C24—142no—
455C24—284no—
456C24—282no—
457C24—282no—
458C24—282no—
459C24—562no—
460C24C2×C22⋊D711yescharacteristic
461C24C2×C22⋊D711yescharacteristic
462#41—432no—
463C2×Q8—24no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—74no—
478C2×D4—148no—
479C2×D4—142no—
480C2×D4—142no—
481C2×D4—142no—
482C2×D4—142no—
483C2×D4—142no—
484C2×D4—288no—
485C2×D4—284no—
486C2×D4—284no—
487C2×D4—284no—
488C2×D4—284no—
489C2×D4—282no—
490C2×D4—562no—
491C2×D4#114114yescomplemented
492C2×D4C2×C22⋊D712yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—142no—
512C22×C4C2×C22⋊D711yescharacteristic
513C22×C4C2×C22⋊D711yescharacteristic
514C22×C4C2×C22⋊D711yescharacteristic
515C22×C4C2×C22⋊D711yescharacteristic
516C22×C4C2×C22⋊D712yes—
517C22×C4C2×C22⋊D712yes—
518C22×C4C23×D711yescharacteristic
519D8—288no—
520C2×C8—142no—
521C2×C8—142no—
522C2×C8—142no—
523C2×C8—142no—
524C2×C8—142no—
525C2×C8—142no—
526C2×C8—284no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—142no—
535C4⋊C4—142no—
536C4⋊C4C2×C22⋊D712yes—
537C4⋊C4C2×C22⋊D712yes—
538C4⋊C4C2×C22⋊D712yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—22no—
542C22⋊C4—24no—
543C22⋊C4—22no—
544C22⋊C4—284no—
545C22⋊C4—282no—
546C22⋊C4—284no—
547C22⋊C4—562no—
548C42—21no—
549C42—21no—
550C2×C7—24no—
551C2×C7—42no—
552C2×C7—82no—
553C2×C7#240411yescharacteristic
554C2×C7C2×#44711yescharacteristic
555C2×C7#301011yescharacteristic
556C2×C7#329412yes—
557C2×C7#330612yes—
558D7—84no—
559C23—22no—
560C23—22no—
561C23—21no—
562C23—22no—
563C23—22no—
564C23—21no—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—42no—
569C23—42no—
570C23—144no—
571C23—288no—
572C23—282no—
573C23—282no—
574C23—282no—
575C23—282no—
576C23—282no—
577C23—282no—
578C23—568no—
579C23—568no—
580C23—564no—
581C23—564no—
582C23C2×#114112yes—
583C23C2×#114112yes—
584C23#649512yes—
585C23#651612yes—
586C23C22×C22⋊D711yescharacteristic
587Q8—48no—
588D4—28no—
589D4—24no—
590D4—48no—
591D4—48no—
592D4—41no—
593D4—41no—
594D4—144no—
595D4—144no—
596D4—288no—
597D4—282no—
598D4—282no—
599D4—568no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—48no—
614C2×C4—48no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—48no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—282no—
628C2×C4C2×#114112yes—
629C2×C4#651612yes—
630C2×C4D7×#4112yes—
631C2×C4#655312yes—
632C2×C4C22×C22⋊D711yescharacteristic
633C2×C4C22×C22⋊D711yescharacteristic
634C8—282no—
635C8—282no—
636C7#2396011yescharacteristic, complemented, Sylow
637C22—24no—
638C22—24no—
639C22—22no—
640C22—22no—
641C22—24no—
642C22—22no—
643C22—42no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—82no—
650C22—82no—
651C22—284no—
652C22—284no—
653C22—284no—
654C22—5616no—
655C22—562no—
656C22—562no—
657C22—562no—
658C22—562no—
659C22#8998914yes—
660C22C22×#114111yescharacteristic
661C22C2×#649511yescharacteristic
662C22#9052012yes—
663C22#9052812yes—
664C22C2×#651611yescharacteristic
665C4—22no—
666C4—22no—
667C4—42no—
668C4—42no—
669C4—42no—
670C4—41no—
671C4—41no—
672C4—562no—
673C4#9051911yescharacteristic
674C4#9052012yes—
675C4#9052111yescharacteristic
676C2—24no—
677C2—42no—
678C2—82no—
679C2—564no—
680C2#1174097012yes—
681C2#1174097112yes—
682C2C2×#8998911yescharacteristic
683C2#1174154111yescharacteristic
684C2#1174155811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7#23960
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C7×#547C2semidirect
2. C2×#89808C2semidirect
3. #11739848C2semidirect
4. C22×#6383C2semidirect
5. #11729546C2semidirect
6. #11729438C2semidirect
7. #11729435C2semidirect
8. #11729367C2semidirect
9. #11729364C2semidirect
10. #11729314C2semidirect
11. #11729307C2semidirect
16. C2×C7×C4⋊Q8C22semidirect
21. C2×C7×#121C22semidirect
23. C2×C4×C7×D4C22semidirect
25. C22×C7×C4⋊C4C22semidirect
30. C2×#6406C22semidirect
33. C2×C22⋊(C7⋊C8)C22semidirect
43. #89324C22semidirect
44. #89324C22semidirect
45. #89324C22semidirect
46. #89319C22semidirect
77. C7×#121D4semidirect
89. C2×C7×C4⋊C4D4semidirect
121. C2×#547D7semidirect
156. C2×C7×D4D8semidirect
197. C2×D28#41semidirect
235. C2×C4⋊Q8C2×D7semidirect
241. C2×#121C2×D7semidirect
244. C2×C4×D4C2×D7semidirect
246. C22×C4⋊C4C2×D7semidirect
379. #121C22⋊D7semidirect
393. C2×C4⋊C4C22⋊D7semidirect
491. C2×D4#1141semidirect
636. C7#23960semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5472
C2×#898082
#117398482
C22×#63832
#117295462
#117294382
#117294352
#117293672
#117293642
#117293142
#117293072
#239607