Finite Group Databasebeta

← #13392138

Subgroups — #13392138

Order 1792.

1260 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#480C211yesmaximal, characteristic, complemented
2#11740098C211yesmaximal, characteristic
3#11739604C211yesmaximal, characteristic, complemented
4C22×#6383C211yesmaximal, characteristic, complemented
5#11729435C211yesmaximal, characteristic, complemented
6#11728393C212yesmaximal, complemented
7#11728377C212yesmaximal, complemented
8#11727931C212yesmaximal, complemented
9#11727915C212yesmaximal, complemented
10#11727713C211yesmaximal, characteristic, complemented
11#11727704C211yesmaximal, characteristic, complemented
12C23×D28C2211yescharacteristic
13C2×C7×#121C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C2×#6503C2212yes—
16C2×#6500—21no—
17C2×#6500—21no—
18C2×#6489—21no—
19C23×C7⋊C8C2211yescharacteristic
20C7×#480—24no—
21C2×C7×#107C2211yescharacteristic, complemented
22C2×C7×#107C2211yescharacteristic, complemented
23C2×C7×#102C2211yescharacteristic, complemented
24C2×C7×#102C2211yescharacteristic, complemented
25C2×C7×C22⋊C8C2211yescharacteristic
26C2×#6406C2212yescomplemented
27#89984C2211yescharacteristic
28#89983—21no—
29C4×C22⋊Dic7C2211yescharacteristic
30C2×#6395C2212yes—
31C2×#6395C2212yes—
32C2×Dic7⋊C8C2212yescomplemented
33#89760C2212yes—
34#89757C2212yescomplemented
35#89753—22no—
36C4⋊C4×Dic7C2212yescomplemented
37C2×#6383—24no—
38C2×#6383C2212yes—
39C2×#6383C2212yes—
40#89732—22no—
41#89345C2212yescomplemented
42#89324C2212yescomplemented
43#24476—71nomaximal, Sylow
44C24×D7—21no—
45C22×C7×D4—21no—
46C22×C7×D4C2311yescharacteristic
47C23×C4×C7—21no—
48C23×C4×C7C2311yescharacteristic
49C22×C22⋊D7—22no—
50C22×C22⋊D7—22no—
51C22×D28—22no—
52C22×D28—24no—
53C22×D28—22no—
54C22×D28—21no—
55C22×D28—42no—
56C22×D28C2312yes—
57C22×C7×C8C2311yescharacteristic
58C22×C7×C8C2311yescharacteristic
59C7×#121—22no—
60C7×#121—22no—
61C2×C7×C4⋊C4—21no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4D414yescomplemented
64C2×C7×C4⋊C4C2311yescharacteristic
65C2×C7×C4⋊C4C2311yescharacteristic
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C7×C22⋊C4—21no—
68C2×C22⋊Dic7—21no—
69C2×C22⋊Dic7D411yescharacteristic
70C2×C22⋊Dic7D411yescharacteristic
71#6503—24no—
72#6503—42no—
73#6500—44no—
74#6500—44no—
75C2×(C2×D7)⋊C4—22no—
76C2×(C2×D7)⋊C4—22no—
77#6489—44no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7C2312yes—
80C2×C4×Dic7—22no—
81C2×C4×Dic7C2312yes—
82C22×C7⋊C8—22no—
83C22×C7⋊C8—42no—
84C22×C7⋊C8C2312yes—
85C7×#107—22no—
86C7×#107—22no—
87C7×#102—22no—
88C7×#102—22no—
89C7×C22⋊C8—22no—
90#6406—42no—
91C7⋊#95—21no—
92C7⋊#95—22no—
93C7⋊#95—22no—
94C7⋊#95D412yes—
95#6395—24no—
96#6395—42no—
97Dic7⋊C8—42no—
98#6383—24no—
99#6383—24no—
100C2×#480D711yescharacteristic, complemented
101C22×#102—71no—
102#2433—71no—
103#2344—71no—
104#2067—72no—
105#2041—72no—
106#1982—72no—
107#1925—72no—
108#1893—71no—
109#1850—71no—
110#1786—71no—
111C24×C7—21no—
112C24×C7C2×D411yescharacteristic
113C23×D7—22no—
114C23×D7—44no—
115C23×D7—42no—
116C23×D7—42no—
117C23×D7—42no—
118C23×D7—82no—
119C2×C7×D4—21no—
120C2×C7×D4—22no—
121C2×C7×D4—21no—
122C2×C7×D4—22no—
123C2×C7×D4—42no—
124C2×C7×D4—42no—
125C2×C7×D4—42no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—24no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—42no—
133C22×C4×C7—42no—
134C22×C4×C7C2×D411yescharacteristic
135C22×C4×C7C2×D412yes—
136C22×C4×C7#4112yes—
137C22×C4×C7C2411yescharacteristic
138C2×C22⋊D7—44no—
139C2×C22⋊D7—44no—
140C2×C22⋊D7—44no—
141C2×C22⋊D7—44no—
142C2×C22⋊D7—82no—
143C2×C22⋊D7—82no—
144C22×Dic7—22no—
145C22×Dic7C2×D412yes—
146C22×Dic7C2×D412yes—
147C2×D28—28no—
148C2×D28—22no—
149C2×D28—22no—
150C2×D28—22no—
151C2×D28—22no—
152C2×D28—22no—
153C2×D28—48no—
154C2×D28—44no—
155C2×D28—44no—
156C2×D28—42no—
157C2×D28#4114yes—
158C2×C7×C8—21no—
159C2×C7×C8—21no—
160C2×C7×C8—22no—
161C2×C7×C8—22no—
162C7×C4⋊C4—24no—
163C7×C4⋊C4—21no—
164C7×C4⋊C4—21no—
165C7×C4⋊C4—21no—
166C7×C4⋊C4—21no—
167C7×C4⋊C4C2×D412yes—
168C7×C4⋊C4C2×D412yes—
169C7×C22⋊C4—42no—
170C22⋊Dic7—22no—
171C22⋊Dic7—42no—
172C22⋊Dic7D814yes—
173(C2×D7)⋊C4—44no—
174(C2×D7)⋊C4—44no—
175C4⋊Dic7—22no—
176C4⋊Dic7—22no—
177C4⋊Dic7—44no—
178C4×Dic7—22no—
179C4×Dic7—22no—
180C4×Dic7—44no—
181C2×C7⋊C8—22no—
182C2×C7⋊C8—22no—
183C2×C7⋊C8—22no—
184C2×C7⋊C8—44no—
185C23×D4—71no—
186C23×C8—71no—
187C2×#127—72no—
188C2×#121C2×D711yescharacteristic
189C2×#120—141no—
190C2×#120—141no—
191C2×#117—141no—
192C22×C4⋊C4C2×D711yescharacteristic
193#480—24no—
194C2×#107C2×D711yescharacteristic, complemented
195C2×#107C2×D711yescharacteristic, complemented
196C2×C4⋊C8—72no—
197C2×#102—72no—
198C2×#102—72no—
199C2×#102—72no—
200C2×#102—72no—
201C2×#102—72no—
202C2×#102—144no—
203C2×#102C2×D711yescharacteristic, complemented
204C2×#102C2×D711yescharacteristic, complemented
205C2×C22⋊C8C2×D711yescharacteristic
206#392—142no—
207#390—72no—
208#389—72no—
209#387—142no—
210#381—141no—
211#380—71no—
212C4×C4⋊C4—72no—
213C4×C22⋊C4—71no—
214#340—72no—
215#336—72no—
216C23×C7—22no—
217C23×C7—22no—
218C23×C7—41no—
219C23×C7—42no—
220C23×C7—41no—
221C23×C7—41no—
222C23×C7—42no—
223C23×C7#12112yes—
224C23×C7C2×D812yes—
225C23×C7AGL(1,ℤ/8)12yes—
226C23×C7C22×D411yescharacteristic
227C22×D7—24no—
228C22×D7—48no—
229C22×D7—42no—
230C22×D7—42no—
231C22×D7—42no—
232C22×D7—42no—
233C22×D7—42no—
234C22×D7—42no—
235C22×D7—88no—
236C22×D7—88no—
237C22×D7—84no—
238C22×D7—84no—
239C7×D4—41no—
240C7×D4—41no—
241C7×D4—42no—
242C7×D4—84no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—22no—
246C2×C4×C7—24no—
247C2×C4×C7—22no—
248C2×C4×C7—22no—
249C2×C4×C7—41no—
250C2×C4×C7—41no—
251C2×C4×C7—41no—
252C2×C4×C7—41no—
253C2×C4×C7—48no—
254C2×C4×C7—41no—
255C2×C4×C7—41no—
256C2×C4×C7—41no—
257C2×C4×C7#12112yes—
258C2×C4×C7C22×D411yescharacteristic
259C2×C4×C7C2×#4111yescharacteristic
260C2×C4×C7C2×#4112yes—
261C2×C4×C7H(5,𝔽2)12yes—
262C22⋊D7—88no—
263C22⋊D7—88no—
264C2×Dic7—22no—
265C2×Dic7—22no—
266C2×Dic7—22no—
267C2×Dic7—22no—
268C2×Dic7—22no—
269C2×Dic7—42no—
270C2×Dic7—42no—
271C2×Dic7—42no—
272C2×Dic7C2×D814yes—
273D28—24no—
274D28—24no—
275D28—48no—
276D28—42no—
277D28—42no—
278C7×C8—41no—
279C7×C8—41no—
280C7⋊C8—42no—
281C25—141no—
282C22×D4—21no—
283C22×D4—72no—
284C22×D4—144no—
285C22×D4—142no—
286C22×D4—142no—
287C22×D4—141no—
288C22×D4—142no—
289C22×D4—142no—
290C22×D4—282no—
291C22×D4C22×D711yescharacteristic
292C23×C4—21no—
293C23×C4C22×D711yescharacteristic
294C22×C8—72no—
295C22×C8—142no—
296C22×C8—282no—
297C22×C8C22×D711yescharacteristic
298C22×C8C22×D711yescharacteristic
299#127—144no—
300#127—282no—
301#121—22no—
302#121—22no—
303#120—284no—
304#120—284no—
305#117—284no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—72no—
309C2×C4⋊C4—142no—
310C2×C4⋊C4C22⋊D714yescomplemented
311C2×C4⋊C4C22×D711yescharacteristic
312C2×C4⋊C4C22×D711yescharacteristic
313C2×C4⋊C4C22×D711yescharacteristic
314C2×C22⋊C4—21no—
315C2×C22⋊C4—71no—
316C2×C22⋊C4—71no—
317C2×C22⋊C4—142no—
318C2×C22⋊C4—142no—
319C2×C22⋊C4—141no—
320C2×C42—72no—
321C2×C42—142no—
322#107—22no—
323#107—22no—
324C4⋊C8—282no—
325#102—22no—
326#102—22no—
327#102—144no—
328#102—144no—
329#102—144no—
330#102—282no—
331#102—282no—
332C22⋊C8—22no—
333#95—72no—
334#95—142no—
335#95—142no—
336#95—141no—
337C22×C7—22no—
338C22×C7—24no—
339C22×C7—22no—
340C22×C7—24no—
341C22×C7—81no—
342C22×C7—81no—
343C22×C7—82no—
344C22×C7—81no—
345C22×C7—82no—
346C22×C7#45914yes—
347C22×C7C2×#12111yescharacteristic
348C22×C7#54612yes—
349C22×C7C22×D811yescharacteristic
350C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C7#57712yes—
352C2×D7—44no—
353C2×D7—44no—
354C2×D7—44no—
355C2×D7—816no—
356C2×D7—82no—
357C2×D7—82no—
358C2×D7—82no—
359C2×D7—82no—
360C4×C7—22no—
361C4×C7—42no—
362C4×C7—42no—
363C4×C7—81no—
364C4×C7#52511yescharacteristic
365C4×C7#53511yescharacteristic
366C4×C7#55112yes—
367Dic7—24no—
368Dic7—42no—
369Dic7—82no—
370C24—21no—
371C24—142no—
372C24—284no—
373C24—282no—
374C24—282no—
375C24—282no—
376C24—562no—
377C24D4×D711yescharacteristic
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—74no—
386C2×D4—148no—
387C2×D4—142no—
388C2×D4—142no—
389C2×D4—142no—
390C2×D4—142no—
391C2×D4—142no—
392C2×D4—288no—
393C2×D4—284no—
394C2×D4—284no—
395C2×D4—284no—
396C2×D4—284no—
397C2×D4—284no—
398C2×D4—284no—
399C2×D4—282no—
400C2×D4—562no—
401C2×D4—562no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—72no—
411C22×C4—72no—
412C22×C4—142no—
413C22×C4D4×D711yescharacteristic
414C22×C4#115912yes—
415C22×C4C2×C22⋊D712yes—
416C22×C4C23×D711yescharacteristic
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—142no—
422C2×C8—142no—
423C2×C8—142no—
424C2×C8—284no—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—142no—
431C4⋊C4—142no—
432C4⋊C4—284no—
433C4⋊C4C2×C22⋊D712yes—
434C4⋊C4C2×C22⋊D712yes—
435C22⋊C4—42no—
436C22⋊C4—74no—
437C22⋊C4—142no—
438C22⋊C4—284no—
439C22⋊C4—284no—
440C22⋊C4—282no—
441C42—142no—
442C42—142no—
443C42—284no—
444C2×C7—24no—
445C2×C7—161no—
446C2×C7#241111yescharacteristic
447C2×C7C2×#45911yescharacteristic
448C2×C7#304311yescharacteristic
449C2×C7#329412yes—
450C2×C7#331012yes—
451D7—84no—
452C23—22no—
453C23—22no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—42no—
459C23—144no—
460C23—288no—
461C23—282no—
462C23—282no—
463C23—282no—
464C23—282no—
465C23—282no—
466C23—282no—
467C23—568no—
468C23—568no—
469C23—564no—
470C23—564no—
471C23D7×D812yes—
472C23#647412yes—
473C23#650212yes—
474C23C2×D4×D711yescharacteristic
475D4—41no—
476D4—41no—
477D4—42no—
478D4—84no—
479D4—144no—
480D4—144no—
481D4—288no—
482D4—282no—
483D4—282no—
484D4—568no—
485D4—568no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—48no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—74no—
501C2×C4—142no—
502C2×C4—142no—
503C2×C4—142no—
504C2×C4—142no—
505C2×C4—142no—
506C2×C4—282no—
507C2×C4—282no—
508C2×C4—282no—
509C2×C4#650212yes—
510C2×C4C2×#115911yescharacteristic
511C2×C4D7×#4112yes—
512C2×C4#655312yes—
513C2×C4C22×C22⋊D711yescharacteristic
514C8—41no—
515C8—41no—
516C8—282no—
517C7#2447611yescharacteristic, complemented, Sylow
518C22—24no—
519C22—24no—
520C22—22no—
521C22—22no—
522C22—81no—
523C22—82no—
524C22—82no—
525C22—81no—
526C22—81no—
527C22—284no—
528C22—284no—
529C22—284no—
530C22—5616no—
531C22—562no—
532C22—562no—
533C22—562no—
534C22—562no—
535C22#8992214yes—
536C22#9034512yes—
537C22C2×D7×D811yescharacteristic
538C22C2×#647411yescharacteristic
539C22#9046912yes—
540C22C2×#650211yescharacteristic
541C4—22no—
542C4—42no—
543C4—42no—
544C4—81no—
545C4—144no—
546C4—282no—
547C4—562no—
548C4#9034912yes—
549C4#9051911yescharacteristic
550C4#9052111yescharacteristic
551C2—24no—
552C2—161no—
553C2—564no—
554C2#1173874712yes—
555C2#1173874812yes—
556C2#1174033911yescharacteristic
557C2C2×#8992211yescharacteristic
558C2#1174141411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#480C2
socleC23×C7C22×D4
prime radical#11740098C2
hypercenterC2×#480D7
hypocenterC7#24476
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×C7×#480C2semidirect
3. #11739604C2semidirect
4. C22×#6383C2semidirect
5. #11729435C2semidirect
6. #11728393C2semidirect
7. #11728377C2semidirect
8. #11727931C2semidirect
9. #11727915C2semidirect
10. #11727713C2semidirect
11. #11727704C2semidirect
21. C2×C7×#107C22semidirect
22. C2×C7×#107C22semidirect
23. C2×C7×#102C22semidirect
24. C2×C7×#102C22semidirect
26. C2×#6406C22semidirect
32. C2×Dic7⋊C8C22semidirect
34. #89757C22semidirect
36. C4⋊C4×Dic7C22semidirect
41. #89345C22semidirect
42. #89324C22semidirect
63. C2×C7×C4⋊C4D4semidirect
100. C2×#480D7semidirect
194. C2×#107C2×D7semidirect
195. C2×#107C2×D7semidirect
203. C2×#102C2×D7semidirect
204. C2×#102C2×D7semidirect
310. C2×C4⋊C4C22⋊D7semidirect
517. C7#24476semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4802
#117400982
#117396042
C22×#63832
#117294352
#117283932
#117283772
#117279312
#117279152
#117277132
#117277042
#244767