Finite Group Databasebeta

← #13386768

Subgroups — #13386768

Order 1792.

1364 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#548C211yesmaximal, characteristic
2C22×#6409C211yesmaximal, characteristic, complemented
3C2×#89805C211yesmaximal, characteristic, complemented
4#11739818C211yesmaximal, characteristic, complemented
5#11729889C212yesmaximal, complemented
6#11729886C211yesmaximal, characteristic, complemented
7#11729476C212yesmaximal, complemented
8#11729449C212yesmaximal, complemented
9#11729435C211yesmaximal, characteristic, complemented
10#11729382C212yesmaximal, complemented
11#11729364C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic
13C23×C7×Q8C2211yescharacteristic
14C7×#548—24no—
15C7×#548—24no—
16C2×C7×#124—21no—
17C2×C7×#124C2211yescharacteristic
18C2×C7×C22⋊Q8—21no—
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#121—21no—
21C2×C7×#121C2211yescharacteristic
22C2×C4×C7×Q8C2211yescharacteristic
23C2×C4×C7×D4—21no—
24C2×C4×C7×D4C2211yescharacteristic
25C2×#6498—21no—
26C22×C4⋊Dic7C2211yescharacteristic
27C23×C7⋊C8C2211yescharacteristic
28C2×#6409—24no—
29C2×#6409C2212yes—
30C2×#6409C2212yes—
31C2×#6409C2212yes—
32C2×#6409C2212yes—
33C2×#6406C2212yes—
34C2×#6406C2212yes—
35#89984C2211yescharacteristic
36#89984C2212yes—
37C2×C22⋊(C7⋊C8)C2211yescharacteristic
38C2×C22⋊(C7⋊C8)C2212yes—
39#89805—24no—
40#89755—21no—
41C2×#6381C2212yes—
42#89725—21no—
43#89715—21no—
44#89700C2212yes—
45#89324C2212yes—
46#89319C2212yes—
47#24035—71nomaximal, Sylow
48C2×C7×#41—22no—
49C2×C7×#41—22no—
50C2×C7×#41—24no—
51C2×C7×#41—42no—
52C22×C7×Q8—21no—
53C22×C7×Q8—22no—
54C22×C7×Q8—24no—
55C22×C7×Q8—42no—
56C22×C7×Q8D414yes—
57C22×C7×Q8C2311yescharacteristic
58C22×C7×Q8C2311yescharacteristic
59C22×C7×D4—21no—
60C22×C7×D4—21no—
61C22×C7×D4D411yescharacteristic
62C22×C7×D4C2311yescharacteristic
63C23×C4×C7—21no—
64C23×C4×C7—21no—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7—21no—
68C7×#124—28no—
69C7×#124—22no—
70C7×#124—22no—
71C7×C22⋊Q8—28no—
72C7×C22⋊Q8—22no—
73C7×C22⋊Q8—22no—
74C7×#121—28no—
75C7×#121—22no—
76C7×#121D414yes—
77C4×C7×Q8—22no—
78C4×C7×Q8—22no—
79C4×C7×D4—28no—
80C4×C7×D4—22no—
81C4×C7×D4—22no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4D411yescharacteristic
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C7×C22⋊C4D411yescharacteristic
91C2×C7×C22⋊C4D411yescharacteristic
92C2×C42×C7—21no—
93C2×C42×C7C2311yescharacteristic
94C2×C22⋊Dic7—21no—
95C2×C22⋊Dic7—22no—
96#6498—44no—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7C2312yes—
101C2×C4⋊Dic7C2312yes—
102C2×Dic7⋊C4—22no—
103C22×C7⋊C8—22no—
104C22×C7⋊C8—42no—
105C22×C7⋊C8C2312yes—
106C22×C7⋊C8C2312yes—
107#6409—24no—
108#6409—24no—
109#6409—24no—
110#6409—42no—
111#6406—24no—
112#6406—42no—
113C7⋊#95—22no—
114C7⋊#95—22no—
115C7⋊#95—21no—
116C22⋊(C7⋊C8)—22no—
117C22⋊(C7⋊C8)—42no—
118#6381—24no—
119C2×#548D711yescharacteristic
120C2×#480—71no—
121C22×#103—71no—
122#2486—71no—
123#2042—72no—
124#2036—72no—
125#1893—71no—
126#1869—71no—
127#1863—72no—
128#1788—72no—
129#1787—71no—
130C24×C7—21no—
131C24×C7C2×D411yescharacteristic
132C24×C7C2×D411yescharacteristic
133C7×#41—48no—
134C7×#41—44no—
135C7×#41—44no—
136C2×C7×Q8—24no—
137C2×C7×Q8—21no—
138C2×C7×Q8—21no—
139C2×C7×Q8—22no—
140C2×C7×Q8—28no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—44no—
144C2×C7×Q8—44no—
145C2×C7×Q8—48no—
146C2×C7×Q8C2×D412yes—
147C2×C7×Q8C2×D412yes—
148C2×C7×Q8#4114yes—
149C2×C7×D4—24no—
150C2×C7×D4—22no—
151C2×C7×D4—24no—
152C2×C7×D4—22no—
153C2×C7×D4—22no—
154C2×C7×D4—21no—
155C2×C7×D4—22no—
156C2×C7×D4—22no—
157C2×C7×D4—44no—
158C2×C7×D4—42no—
159C2×C7×D4—42no—
160C2×C7×D4C2×D412yes—
161C22×C4×C7—21no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—24no—
165C22×C4×C7—24no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—44no—
173C22×C4×C7—44no—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2×D412yes—
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2411yescharacteristic
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—42no—
184C22×Dic7—42no—
185C22×Dic7—42no—
186C7×C4⋊C4—24no—
187C7×C4⋊C4—24no—
188C7×C4⋊C4—22no—
189C7×C4⋊C4—21no—
190C7×C4⋊C4C2×D412yes—
191C7×C22⋊C4—24no—
192C7×C22⋊C4—24no—
193C7×C22⋊C4—24no—
194C7×C22⋊C4—22no—
195C7×C22⋊C4—24no—
196C7×C22⋊C4—22no—
197C42×C7—24no—
198C42×C7—21no—
199C42×C7—21no—
200C22⋊Dic7—44no—
201C22⋊Dic7—42no—
202C4⋊Dic7—22no—
203C4⋊Dic7—22no—
204C4⋊Dic7—22no—
205C4⋊Dic7—22no—
206C4⋊Dic7—42no—
207Dic7⋊C4—44no—
208C2×C7⋊C8—22no—
209C2×C7⋊C8—22no—
210C2×C7⋊C8—22no—
211C2×C7⋊C8—22no—
212C2×C7⋊C8—22no—
213C2×C7⋊C8—22no—
214C2×C7⋊C8—44no—
215C22×#41C2×D711yescharacteristic
216C23×Q8C2×D711yescharacteristic
217C23×C8—71no—
218#548—24no—
219#548—24no—
220C2×#124—21no—
221C2×#124C2×D711yescharacteristic
222C2×#123—141no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2×D711yescharacteristic
225C2×#121—21no—
226C2×#121C2×D711yescharacteristic
227C2×C4×Q8C2×D711yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4C2×D711yescharacteristic
230C22×C4⋊C4—71no—
231#480—144no—
232C2×#107—72no—
233C2×#103—72no—
234C2×#103—72no—
235C2×#103—72no—
236C2×#103—72no—
237C2×#103—144no—
238C2×#102—72no—
239C2×#102—72no—
240C2×C22⋊C8—71no—
241C2×C22⋊C8—72no—
242#398—141no—
243#397—141no—
244#389—72no—
245#381—141no—
246#380—71no—
247#380—72no—
248#340—72no—
249#336—72no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—21no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—21no—
256C23×C7—21no—
257C23×C7—22no—
258C23×C7—42no—
259C23×C7—41no—
260C23×C7—41no—
261C23×C7—42no—
262C23×C7#12012yes—
263C23×C7#13512yes—
264C23×C7AGL(1,ℤ/8)12yes—
265C23×C7C22×D411yescharacteristic
266C7×Q8—22no—
267C7×Q8—24no—
268C7×Q8—22no—
269C7×Q8—22no—
270C7×Q8—48no—
271C7×Q8—42no—
272C7×Q8#12314yescomplemented
273C7×D4—24no—
274C7×D4—48no—
275C7×D4—44no—
276C7×D4—48no—
277C7×D4—41no—
278C7×D4—41no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—24no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—24no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—21no—
290C2×C4×C7—22no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—22no—
294C2×C4×C7—48no—
295C2×C4×C7—48no—
296C2×C4×C7—42no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—42no—
302C2×C4×C7#12012yes—
303C2×C4×C7C22×D411yescharacteristic
304C2×C4×C7C22×D411yescharacteristic
305C2×C4×C7C2×#4112yes—
306C2×C4×C7H(5,𝔽2)12yes—
307C2×Dic7—42no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7—84no—
314C7⋊C8—42no—
315C7⋊C8—42no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—24no—
319C2×#41—42no—
320C22×Q8—21no—
321C22×Q8—22no—
322C22×Q8—24no—
323C22×Q8—42no—
324C22×Q8C22⋊D714yes—
325C22×Q8C22×D711yescharacteristic
326C22×Q8C22×D711yescharacteristic
327C22×D4—21no—
328C22×D4—21no—
329C22×D4C22⋊D711yescharacteristic
330C22×D4C22×D711yescharacteristic
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—141no—
334C23×C4C22×D711yescharacteristic
335C23×C4C22×D711yescharacteristic
336C22×C8—72no—
337C22×C8—72no—
338C22×C8—142no—
339C22×C8—282no—
340#124—28no—
341#124—22no—
342#124—22no—
343#123—284no—
344C22⋊Q8—28no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347#121—28no—
348#121—22no—
349#121C22⋊D714yes—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×D4—28no—
353C4×D4—22no—
354C4×D4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—72no—
358C2×C4⋊C4—72no—
359C2×C4⋊C4—142no—
360C2×C4⋊C4—142no—
361C2×C4⋊C4—141no—
362C2×C4⋊C4—142no—
363C2×C4⋊C4C22⋊D711yescharacteristic
364C2×C4⋊C4C22×D711yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—141no—
370C2×C22⋊C4—142no—
371C2×C22⋊C4C22⋊D711yescharacteristic
372C2×C22⋊C4C22⋊D711yescharacteristic
373C2×C42—21no—
374C2×C42C22×D711yescharacteristic
375#107—144no—
376#103—144no—
377#103—144no—
378#103—144no—
379#103—282no—
380#102—144no—
381#102—282no—
382C22⋊C8—142no—
383C22⋊C8—282no—
384#95—142no—
385#95—141no—
386#95—142no—
387C22×C7—22no—
388C22×C7—22no—
389C22×C7—24no—
390C22×C7—24no—
391C22×C7—42no—
392C22×C7—41no—
393C22×C7—41no—
394C22×C7—42no—
395C22×C7—41no—
396C22×C7—42no—
397C22×C7—42no—
398C22×C7—42no—
399C22×C7—82no—
400C22×C7—82no—
401C22×C7#44914yes—
402C22×C7C2×#12011yescharacteristic
403C22×C7#54612yes—
404C22×C7C2×#13511yescharacteristic
405C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
406C22×C7#57812yes—
407C4×C7—22no—
408C4×C7—24no—
409C4×C7—41no—
410C4×C7—42no—
411C4×C7—41no—
412C4×C7—42no—
413C4×C7—41no—
414C4×C7C2×#12311yescharacteristic
415C4×C7#53411yescharacteristic
416C4×C7#54612yes—
417Dic7—82no—
418Dic7—82no—
419C24—21no—
420C24C2×C22⋊D711yescharacteristic
421C24C2×C22⋊D711yescharacteristic
422#41—48no—
423#41—44no—
424#41—44no—
425C2×Q8—24no—
426C2×Q8—22no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—28no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×Q8—48no—
435C2×Q8#115914yes—
436C2×Q8C2×C22⋊D712yes—
437C2×Q8C2×C22⋊D712yes—
438C2×D4—24no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—24no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—44no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4C2×C22⋊D712yes—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—142no—
464C22×C4—142no—
465C22×C4—282no—
466C22×C4—282no—
467C22×C4—282no—
468C22×C4C2×C22⋊D711yescharacteristic
469C22×C4C2×C22⋊D711yescharacteristic
470C22×C4C2×C22⋊D711yescharacteristic
471C22×C4C2×C22⋊D711yescharacteristic
472C22×C4C2×C22⋊D712yes—
473C22×C4C2×C22⋊D712yes—
474C22×C4C23×D711yescharacteristic
475C2×C8—142no—
476C2×C8—142no—
477C2×C8—142no—
478C2×C8—142no—
479C2×C8—142no—
480C2×C8—142no—
481C2×C8—284no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—142no—
487C4⋊C4—142no—
488C4⋊C4—142no—
489C4⋊C4—142no—
490C4⋊C4—284no—
491C4⋊C4—282no—
492C4⋊C4C2×C22⋊D712yes—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4—22no—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—284no—
500C22⋊C4—282no—
501C42—24no—
502C42—21no—
503C42—21no—
504C2×C7—24no—
505C2×C7—81no—
506C2×C7—82no—
507C2×C7#240511yescharacteristic
508C2×C7C2×#44911yescharacteristic
509C2×C7#301111yescharacteristic
510C2×C7#330012yes—
511C2×C7#330812yes—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—21no—
516C23—21no—
517C23—22no—
518C23—21no—
519C23—22no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—42no—
524C23#651212yes—
525C23#651312yes—
526C23#651612yes—
527C23C22×C22⋊D711yescharacteristic
528Q8—22no—
529Q8—24no—
530Q8—22no—
531Q8—22no—
532Q8—48no—
533Q8—42no—
534Q8#649814yescomplemented
535D4—24no—
536D4—48no—
537D4—44no—
538D4—48no—
539D4—41no—
540D4—41no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—48no—
557C2×C4—48no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—282no—
565C2×C4—282no—
566C2×C4—282no—
567C2×C4—282no—
568C2×C4—282no—
569C2×C4—282no—
570C2×C4—564no—
571C2×C4#651612yes—
572C2×C4C2×#115912yes—
573C2×C4#654812yes—
574C2×C4C22×C22⋊D711yescharacteristic
575C2×C4C22×C22⋊D711yescharacteristic
576C8—282no—
577C8—282no—
578C7#2403511yescharacteristic, complemented, Sylow
579C22—24no—
580C22—22no—
581C22—24no—
582C22—22no—
583C22—42no—
584C22—42no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—41no—
590C22—42no—
591C22—82no—
592C22—82no—
593C22#9001014yes—
594C22#9049712yes—
595C22C2×#651211yescharacteristic
596C22C2×#651311yescharacteristic
597C22#9052912yes—
598C22C2×#651611yescharacteristic
599C4—22no—
600C4—24no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—41no—
606C4—562no—
607C4—562no—
608C4C2×#649811yescharacteristic
609C4#9049511yescharacteristic
610C4#9049712yes—
611C2—24no—
612C2—81no—
613C2—82no—
614C2#1174097912yes—
615C2#1174098112yes—
616C2#1174149211yescharacteristic
617C2C2×#9001011yescharacteristic
618C2#1174156211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#548C2
socleC23×C7C22×D4
hypercenterC2×#548D7
hypocenterC7#24035
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
2. C22×#6409C2semidirect
3. C2×#89805C2semidirect
4. #11739818C2semidirect
5. #11729889C2semidirect
6. #11729886C2semidirect
7. #11729476C2semidirect
8. #11729449C2semidirect
9. #11729435C2semidirect
10. #11729382C2semidirect
11. #11729364C2semidirect
272. C7×Q8#123semidirect
534. Q8#6498semidirect
578. C7#24035semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5482
C22×#64092
C2×#898052
#117398182
#117298892
#117298862
#117294762
#117294492
#117294352
#117293822
#117293642
#240357