Finite Group Databasebeta

← #13360975

Subgroups — #13360975

Order 1792.

1048 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6501C211yesmaximal, characteristic
2C2×#89546C211yesmaximal, characteristic
3C4×D7×C4⋊C4C211yesmaximal, characteristic, complemented
4C7×#1762C211yesmaximal, characteristic, complemented
5#11729363C211yesmaximal, characteristic, complemented
6#11727954C211yesmaximal, characteristic
7#11727928C211yesmaximal, characteristic, complemented
8#11727910C211yesmaximal, characteristic, complemented
9#11727568C211yesmaximal, characteristic, complemented
10#11727561C211yesmaximal, characteristic, complemented
11#11727235C211yesmaximal, characteristic, complemented
12#11726629C211yesmaximal, characteristic, complemented
13#11726625C211yesmaximal, characteristic, complemented
14#11726574C211yesmaximal, characteristic, complemented
15#11726544C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×#6501C2211yescharacteristic
18C2×C4×C22⋊D7—21no—
19C2×D7×C4⋊C4C2211yescharacteristic
20C2×D7×C4⋊C4C2211yescharacteristic
21C2×C42×D7—21no—
22C2×C42×D7C2211yescharacteristic
23C2×C7×#102C2211yescharacteristic
24C2×C7×#102C2211yescharacteristic
25C2×C7×#97C2211yescharacteristic
26C4×C7×C4⋊C4C2211yescharacteristic
27#89993C2211yescharacteristic
28C2×#6406C2211yescharacteristic
29C2×#6406C2211yescharacteristic
30C4×C22⋊Dic7—21no—
31C2×(C2×D7)⋊C8C2211yescharacteristic
32C2×(C2×D7)⋊C8C2211yescharacteristic
33C2×#6392C2211yescharacteristic
34C2×#6391C2211yescharacteristic
35#89759C2211yescharacteristic
36C4⋊C4×Dic7C2211yescharacteristic
37C4⋊C4×Dic7C2211yescharacteristic
38#89745C2211yescharacteristic
39C2×#6382C2211yescharacteristic
40C2×#6381C2211yescharacteristic
41#89728—21no—
42#89716—21no—
43C4×C4⋊Dic7C2211yescharacteristic
44C4×C4⋊Dic7C2211yescharacteristic
45C4×Dic7⋊C4—21no—
46C2×#6377C2211yescharacteristic
47#89546C418yescomplemented
48D7×#95—21no—
49#89421—21no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#21578—71nomaximal, Sylow
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C22×C22⋊D7—21no—
64C22×C4×D7—21no—
65C22×C4×D7—21no—
66C22×C4×D7D411yescharacteristic
67C22×C4×D7D411yescharacteristic
68C22×C4×D7C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C22×C7×C8C2311yescharacteristic
71C4×C7×D4—22no—
72C4×C7×D4—22no—
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C22⋊C4—21no—
77C2×C42×C7—21no—
78C2×C42×C7C2311yescharacteristic
79C2×C22⋊Dic7—21no—
80C2×C22⋊Dic7—21no—
81C2×C22⋊Dic7—21no—
82#6501—22no—
83#6501C2×C414yes—
84C4×C22⋊D7—44no—
85C2×(C2×D7)⋊C4—21no—
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×C4×Dic7—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7—21no—
97C2×C4×Dic7D411yescharacteristic
98C2×C4×Dic7D411yescharacteristic
99C2×C4×Dic7C2311yescharacteristic
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102D7×C4⋊C4—22no—
103D7×C4⋊C4—22no—
104D7×C4⋊C4—22no—
105D7×C4⋊C4C2×C414yescomplemented
106C42×D7—22no—
107C42×D7—22no—
108C42×D7—44no—
109C7×#102—22no—
110C7×#102C2×C414yescomplemented
111C7×#97—22no—
112C7×#95—21no—
113#6406—22no—
114#6406C2×C414yescomplemented
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119C7⋊#95—21no—
120C7⋊#95—21no—
121(C2×D7)⋊C8—22no—
122(C2×D7)⋊C8C2×C414yescomplemented
123#6392C2×C414yescomplemented
124#6391—22no—
125#6382—22no—
126#6381C2×C414yescomplemented
127#6377—22no—
128C2×#480—71no—
129C4×#121—71no—
130C2×C4×C4⋊C4—71no—
131#1926—71no—
132#1926—71no—
133#1921—71no—
134#1921—71no—
135#1874—71no—
136#1853—71no—
137#1823—71no—
138#1776—71no—
139#1776—71no—
140#1762—71no—
141#1762D711yescharacteristic, complemented
142#1749—71no—
143C24×C7—21no—
144C23×D7C2×D411yescharacteristic
145C2×C7×D4—21no—
146C2×C7×D4—21no—
147C2×C7×D4—21no—
148C2×C7×D4—21no—
149C2×C7×D4—21no—
150C2×C7×D4C22×C412yes—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—42no—
155C22×C4×C7—42no—
156C22×C4×C7—42no—
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2411yescharacteristic
160C2×C22⋊D7—24no—
161C2×C22⋊D7—42no—
162C2×C22⋊D7—42no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7C2×D411yescharacteristic
168C22×Dic7C2×D411yescharacteristic
169C22×Dic7C2×D411yescharacteristic
170C2×C4×D7—22no—
171C2×C4×D7—22no—
172C2×C4×D7—21no—
173C2×C4×D7—21no—
174C2×C4×D7—21no—
175C2×C4×D7—21no—
176C2×C4×D7—22no—
177C2×C4×D7—24no—
178C2×C4×D7—24no—
179C2×C4×D7—22no—
180C2×C4×D7—22no—
181C2×C4×D7—41no—
182C2×C4×D7—42no—
183C2×C4×D7—42no—
184C2×C4×D7—42no—
185C2×C4×D7—42no—
186C2×C4×D7C22×C412yes—
187C2×C4×D7#4112yes—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8—21no—
192C2×C7×C8—21no—
193C2×C7×C8C22×C412yes—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4C22×C412yes—
199C7×C4⋊C4#4112yes—
200C7×C22⋊C4—42no—
201C42×C7—42no—
202C42×C7#4112yes—
203C42×C7#4112yes—
204C22⋊Dic7—24no—
205C22⋊Dic7—42no—
206C22⋊Dic7—42no—
207(C2×D7)⋊C4—42no—
208C4⋊Dic7—21no—
209C4⋊Dic7—21no—
210C4⋊Dic7—21no—
211C4⋊Dic7—21no—
212C4⋊Dic7—21no—
213C4⋊Dic7C22×C412yes—
214C4⋊Dic7C22×C412yes—
215C4⋊Dic7#4112yes—
216Dic7⋊C4—24no—
217Dic7⋊C4—24no—
218Dic7⋊C4—42no—
219C4×Dic7—22no—
220C4×Dic7—22no—
221C4×Dic7—21no—
222C4×Dic7—21no—
223C4×Dic7—42no—
224C4×Dic7—42no—
225C4×Dic7—42no—
226C4×Dic7—42no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8—21no—
232C2×C7⋊C8C22×C412yes—
233C2×#121—71no—
234C2×C4×D4—141no—
235C2×C4×D4C2×D711yescharacteristic
236C22×C4⋊C4—71no—
237C22×C4⋊C4—71no—
238C22×C42—71no—
239C22×C42—141no—
240#480—78no—
241C2×#107—71no—
242C2×#107—71no—
243C2×#106—71no—
244C2×#106—71no—
245C2×#102—71no—
246C2×#102—71no—
247C2×#102C2×D711yescharacteristic
248C2×#102C2×D711yescharacteristic
249C2×C22⋊C8—71no—
250C2×C22⋊C8—71no—
251C2×#97—71no—
252C2×#97C2×D711yescharacteristic
253#390—71no—
254#389—71no—
255#388—141no—
256#386—141no—
257#380—71no—
258C4×C4⋊C4—71no—
259C4×C4⋊C4—71no—
260C4×C4⋊C4—71no—
261C4×C4⋊C4—71no—
262C4×C4⋊C4—141no—
263C4×C4⋊C4—141no—
264C4×C4⋊C4C2×D711yescharacteristic
265C4×C22⋊C4—141no—
266C2×#95—141no—
267#340—71no—
268#340—71no—
269#340—71no—
270#340—71no—
271#340—71no—
272#340—71no—
273#340C2×D711yescharacteristic
274#340C2×D711yescharacteristic
275#336—71no—
276#336—71no—
277C23×C7—22no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7C22×D411yescharacteristic
285C22×D7—21no—
286C22×D7—21no—
287C22×D7—21no—
288C22×D7—21no—
289C22×D7C4×D412yes—
290C22×D7AGL(1,ℤ/8)12yes—
291C22×D7AGL(1,ℤ/8)12yes—
292C7×D4—22no—
293C7×D4—22no—
294C7×D4—41no—
295C7×D4—41no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—84no—
310C2×C4×C7#12312yes—
311C2×C4×C7#12312yes—
312C2×C4×C7C23×C411yescharacteristic
313C2×C4×C7C2×#4111yescharacteristic
314C2×C4×C7C2×#4111yescharacteristic
315C2×C4×C7C2×#4111yescharacteristic
316C2×C4×C7C2×#4111yescharacteristic
317C2×C4×C7C2×#4111yescharacteristic
318C22⋊D7—48no—
319C2×Dic7—21no—
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7—21no—
323C2×Dic7—22no—
324C2×Dic7—22no—
325C2×Dic7—21no—
326C2×Dic7—22no—
327C2×Dic7—21no—
328C2×Dic7—21no—
329C2×Dic7—41no—
330C2×Dic7—41no—
331C2×Dic7—41no—
332C2×Dic7—41no—
333C2×Dic7—41no—
334C2×Dic7—41no—
335C2×Dic7—41no—
336C2×Dic7—41no—
337C2×Dic7—41no—
338C2×Dic7C4×D412yes—
339C2×Dic7#13712yes—
340C4×D7—28no—
341C4×D7—22no—
342C4×D7—22no—
343C4×D7—22no—
344C4×D7—22no—
345C4×D7—44no—
346C4×D7—48no—
347C4×D7—48no—
348C7×C8—22no—
349C7×C8—41no—
350C7⋊C8—22no—
351C7⋊C8—41no—
352C22×D4—141no—
353C22×D4C22×D711yescharacteristic
354C23×C4—21no—
355C23×C4—71no—
356C23×C4—71no—
357C23×C4—71no—
358C23×C4—141no—
359C23×C4—141no—
360C22×C8—71no—
361C22×C8—71no—
362C22×C8C22×D711yescharacteristic
363C22×C8C22×D711yescharacteristic
364#121—74no—
365#121—142no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—284no—
369C2×C4⋊C4—71no—
370C2×C4⋊C4—71no—
371C2×C4⋊C4—71no—
372C2×C4⋊C4—74no—
373C2×C4⋊C4—71no—
374C2×C4⋊C4—142no—
375C2×C4⋊C4—142no—
376C2×C4⋊C4—141no—
377C2×C4⋊C4—141no—
378C2×C4⋊C4—142no—
379C2×C4⋊C4—141no—
380C2×C4⋊C4C22×D711yescharacteristic
381C2×C4⋊C4C22×D711yescharacteristic
382C2×C4⋊C4C22×D711yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—141no—
385C2×C22⋊C4—141no—
386C2×C22⋊C4—141no—
387C2×C22⋊C4—141no—
388C2×C42—21no—
389C2×C42—71no—
390C2×C42—71no—
391C2×C42—71no—
392C2×C42—142no—
393C2×C42—142no—
394C2×C42—141no—
395C2×C42—141no—
396C2×C42—141no—
397C2×C42—141no—
398C2×C42—284no—
399C2×C42C22×D711yescharacteristic
400#107—74no—
401#107—74no—
402#106—142no—
403#106—142no—
404#102—22no—
405#102—74no—
406#102—142no—
407#102C4×D714yescomplemented
408C22⋊C8—74no—
409C22⋊C8—142no—
410#97—22no—
411#97—142no—
412#95—21no—
413#95—141no—
414#95—141no—
415#95—141no—
416#95—141no—
417#95—141no—
418#95—141no—
419C22×C7—42no—
420C22×C7—42no—
421C22×C7—42no—
422C22×C7—81no—
423C22×C7—81no—
424C22×C7—81no—
425C22×C7—81no—
426C22×C7C2×C4×D411yescharacteristic
427C22×C7C2×#12311yescharacteristic
428C22×C7#52511yescharacteristic
429C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C7C2×#13711yescharacteristic
432C22×C7#57511yescharacteristic
433C2×D7—22no—
434C2×D7—22no—
435C2×D7—22no—
436C2×D7—22no—
437C2×D7—22no—
438C2×D7—22no—
439C2×D7#44214yes—
440C4×C7—22no—
441C4×C7—22no—
442C4×C7—42no—
443C4×C7—42no—
444C4×C7—81no—
445C4×C7C4×#4111yescharacteristic
446C4×C7C4×#4111yescharacteristic
447C4×C7#52911yescharacteristic
448C4×C7#52911yescharacteristic
449Dic7—22no—
450Dic7—22no—
451Dic7—41no—
452Dic7—42no—
453Dic7—42no—
454Dic7—42no—
455Dic7—81no—
456C24—21no—
457C24—71no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—144no—
464C2×D4—282no—
465C2×D4—282no—
466C2×D4C2×C4×D712yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—71no—
474C22×C4—71no—
475C22×C4—72no—
476C22×C4—72no—
477C22×C4—71no—
478C22×C4—142no—
479C22×C4—142no—
480C22×C4—144no—
481C22×C4—142no—
482C22×C4—144no—
483C22×C4—142no—
484C22×C4—141no—
485C22×C4—141no—
486C22×C4—141no—
487C22×C4—141no—
488C22×C4—141no—
489C22×C4—141no—
490C22×C4—141no—
491C22×C4—142no—
492C22×C4—141no—
493C22×C4—281no—
494C22×C4—282no—
495C22×C4—282no—
496C22×C4—282no—
497C22×C4—282no—
498C22×C4D4×D711yescharacteristic
499C22×C4D4×D711yescharacteristic
500C22×C4C23×D711yescharacteristic
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—72no—
507C2×C8—141no—
508C2×C8—141no—
509C2×C8—141no—
510C2×C8—141no—
511C2×C8—141no—
512C2×C8C2×C4×D712yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—72no—
518C4⋊C4—72no—
519C4⋊C4—72no—
520C4⋊C4—144no—
521C4⋊C4—144no—
522C4⋊C4—141no—
523C4⋊C4—141no—
524C4⋊C4—141no—
525C4⋊C4—141no—
526C4⋊C4—141no—
527C4⋊C4—282no—
528C4⋊C4C2×C4×D712yes—
529C4⋊C4#115712yes—
530C22⋊C4—42no—
531C22⋊C4—144no—
532C22⋊C4—282no—
533C22⋊C4—282no—
534C22⋊C4—282no—
535C42—42no—
536C42—142no—
537C42—142no—
538C42—141no—
539C42—141no—
540C42—282no—
541C42—282no—
542C42—282no—
543C42—282no—
544C42#115712yes—
545C42#115912yes—
546C2×C7—82no—
547C2×C7C4×#12311yescharacteristic
548C2×C7C2×#44211yescharacteristic
549C2×C7C4×#13711yescharacteristic
550C2×C7#309211yescharacteristic
551C2×C7#309411yescharacteristic
552C2×C7#311211yescharacteristic
553C2×C7#311411yescharacteristic
554D7—24no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—72no—
563C23—72no—
564C23—72no—
565C23—141no—
566C23—141no—
567C23—141no—
568C23—141no—
569C23C2×D4×D711yescharacteristic
570D4—22no—
571D4—22no—
572D4—41no—
573D4—41no—
574D4—288no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—72no—
589C2×C4—72no—
590C2×C4—84no—
591C2×C4—148no—
592C2×C4—141no—
593C2×C4—141no—
594C2×C4—141no—
595C2×C4—141no—
596C2×C4—142no—
597C2×C4—142no—
598C2×C4—142no—
599C2×C4—142no—
600C2×C4—141no—
601C2×C4—141no—
602C2×C4—141no—
603C2×C4—142no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—284no—
607C2×C4—288no—
608C2×C4—288no—
609C2×C4—281no—
610C2×C4—281no—
611C2×C4—281no—
612C2×C4—281no—
613C2×C4—281no—
614C2×C4—281no—
615C2×C4—281no—
616C2×C4—281no—
617C2×C4—281no—
618C2×C4#644612yes—
619C2×C4#644612yes—
620C2×C4C22×C4×D711yescharacteristic
621C2×C4C2×#115711yescharacteristic
622C2×C4C2×#115711yescharacteristic
623C2×C4C2×#115911yescharacteristic
624C2×C4D7×#4111yescharacteristic
625C2×C4D7×#4111yescharacteristic
626C8—22no—
627C8—41no—
628C8—142no—
629C8—281no—
630C7#2157811yescharacteristic, complemented, Sylow
631C22—42no—
632C22—42no—
633C22—42no—
634C22—74no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—142no—
640C22—142no—
641C22—142no—
642C22—142no—
643C22—142no—
644C22—142no—
645C22C2×#644611yescharacteristic
646C22C4×D4×D711yescharacteristic
647C22#9023811yescharacteristic
648C22D7×AGL(1,ℤ/8)11yescharacteristic
649C22D7×AGL(1,ℤ/8)11yescharacteristic
650C22#9046411yescharacteristic
651C22D7×#13711yescharacteristic
652C4—22no—
653C4—22no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—142no—
658C4—142no—
659C4—281no—
660C4—282no—
661C4—282no—
662C4—282no—
663C4—561no—
664C4C4×#115711yescharacteristic
665C4#9021911yescharacteristic
666C4C4×#115911yescharacteristic
667C4#9024811yescharacteristic
668C2—82no—
669C2—144no—
670C2C4×#644611yescharacteristic
671C2#1173633711yescharacteristic
672C2#1173637811yescharacteristic
673C2#1173721911yescharacteristic
674C2#1173722611yescharacteristic
675C2D7×#44211yescharacteristic
676C2#1173731611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1762C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
cosocleC22×C4×C7C24
hypercenter#1762D7
hypocenterC7#21578
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. C4×D7×C4⋊C4C2semidirect
4. C7×#1762C2semidirect
5. #11729363C2semidirect
7. #11727928C2semidirect
8. #11727910C2semidirect
9. #11727568C2semidirect
10. #11727561C2semidirect
11. #11727235C2semidirect
12. #11726629C2semidirect
13. #11726625C2semidirect
14. #11726574C2semidirect
15. #11726544C2semidirect
47. #89546C4semidirect
105. D7×C4⋊C4C2×C4semidirect
110. C7×#102C2×C4semidirect
114. #6406C2×C4semidirect
122. (C2×D7)⋊C8C2×C4semidirect
123. #6392C2×C4semidirect
126. #6381C2×C4semidirect
141. #1762D7semidirect
407. #102C4×D7semidirect
630. C7#21578semidirect

Maximal subgroups

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

subgroupindex
C4×#65012
C2×#895462
C4×D7×C4⋊C42
C7×#17622
#117293632
#117279542
#117279282
#117279102
#117275682
#117275612
#117272352
#117266292
#117266252
#117265742
#117265442
#215787