Finite Group Databasebeta

← #13410062

Subgroups — #13410062

Order 1792.

1422 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#535C211yesmaximal, characteristic
2C2×#89843C211yesmaximal, characteristic, complemented
3C2×#89828C211yesmaximal, characteristic, complemented
4#11739710C211yesmaximal, characteristic, complemented
5#11729889C212yesmaximal, complemented
6#11729882C212yesmaximal, complemented
7#11729518C211yesmaximal, characteristic, complemented
8#11729516C212yesmaximal, complemented
9#11729480C211yesmaximal, characteristic, complemented
10#11729476C212yesmaximal, complemented
11#11729336C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C7×#535—24no—
15C7×#535—24no—
16C2×C7×#127C2211yescharacteristic
17C2×C7×#127C2211yescharacteristic
18C2×C7×#124C2211yescharacteristic
19C2×C7×#124C2211yescharacteristic
20C2×C7×#121—22no—
21C2×C7×#120—22no—
22C2×C7×#117C2211yescharacteristic
23C2×#6433C2211yescharacteristic, complemented
24C2×#6409C2212yescomplemented
25C2×#6409C2212yescomplemented
26C2×#6406C2212yes—
27C2×#6406C2212yes—
28C2×#6406C2212yes—
29C2×#6406C2212yes—
30C2×#6406C2212yescomplemented
31C2×#6406C2212yescomplemented
32#89984C2212yes—
33C2×C22⋊(C7⋊C8)C2212yes—
34#89843—24no—
35#89828—24no—
36#89756—22no—
37#89720—22no—
38#89707C2211yescharacteristic, complemented
39#89700C2212yescomplemented
40C2×#6377C2211yescharacteristic, complemented
41C2×C4×C7⋊C8C2211yescharacteristic, complemented
42#89319C2212yescomplemented
43#25867—71nomaximal, Sylow
44C25×C7—21no—
45C2×C7×#41—22no—
46C2×C7×#41—22no—
47C2×C7×#41—24no—
48C2×C7×#41—42no—
49C22×C7×Q8C2311yescharacteristic
50C22×C7×D4—21no—
51C22×C7×D4—22no—
52C22×C7×D4—22no—
53C22×C7×D4—21no—
54C22×C7×D4—22no—
55C22×C7×D4—22no—
56C22×C7×D4—24no—
57C22×C7×D4—42no—
58C22×C7×D4C2311yescharacteristic
59C22×C7×D4C2311yescharacteristic
60C22×C7×D4C2311yescharacteristic
61C23×C4×C7—21no—
62C23×C4×C7C2311yescharacteristic
63C7×#127—22no—
64C7×#127—22no—
65C7×#127—22no—
66C7×#127D414yes—
67C7×#124—22no—
68C7×#124—22no—
69C7×#124—22no—
70C7×#124D414yes—
71C7×#121—216no—
72C7×#120—216no—
73C7×#117—22no—
74C7×#117—22no—
75C2×C7×C4⋊C4D412yes—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4D412yes—
79C2×C42×C7C2311yescharacteristic
80C2×C42×C7C2311yescharacteristic
81C2×C22⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7C2312yes—
84C2×C4⋊Dic7C2312yes—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C22×C7⋊C8C2312yes—
88C22×C7⋊C8C2312yes—
89#6433—22no—
90#6433—22no—
91#6409—24no—
92#6409—42no—
93#6406—24no—
94#6406—24no—
95#6406—24no—
96#6406—42no—
97#6406—42no—
98#6406—42no—
99C7⋊#95—22no—
100C7⋊#95—22no—
101C22⋊(C7⋊C8)—24no—
102#6377—22no—
103C4×C7⋊C8—22no—
104C2×#535D711yescharacteristic
105C2×#490—71no—
106C2×#488—71no—
107#2629—71no—
108#2042—72no—
109#2041—72no—
110#1959—71no—
111#1957—71no—
112#1788—72no—
113#1786—72no—
114#1750—71no—
115C24×C7—24no—
116C24×C7—21no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—42no—
120C24×C7—42no—
121C24×C7—82no—
122C24×C7—82no—
123C24×C7C2×D411yescharacteristic
124C7×#41—48no—
125C7×#41—48no—
126C2×C7×Q8—21no—
127C2×C7×Q8—22no—
128C2×C7×Q8—22no—
129C2×C7×Q8C2×D412yes—
130C2×C7×D4—24no—
131C2×C7×D4—24no—
132C2×C7×D4—28no—
133C2×C7×D4—28no—
134C2×C7×D4—21no—
135C2×C7×D4—21no—
136C2×C7×D4—21no—
137C2×C7×D4—22no—
138C2×C7×D4—22no—
139C2×C7×D4—22no—
140C2×C7×D4—22no—
141C2×C7×D4—22no—
142C2×C7×D4—22no—
143C2×C7×D4—48no—
144C2×C7×D4—48no—
145C2×C7×D4—42no—
146C2×C7×D4—42no—
147C2×C7×D4—42no—
148C2×C7×D4—42no—
149C2×C7×D4—82no—
150C2×C7×D4—82no—
151C2×C7×D4—82no—
152C2×C7×D4—82no—
153C2×C7×D4C2×D412yes—
154C2×C7×D4C2×D412yes—
155C2×C7×D4C2×D412yes—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—22no—
159C22×C4×C7—24no—
160C22×C4×C7—21no—
161C22×C4×C7—42no—
162C22×C4×C7—42no—
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D412yes—
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7#4114yes—
167C22×C4×C7C2411yescharacteristic
168C22×Dic7—22no—
169C22×Dic7—22no—
170C7×C4⋊C4—24no—
171C7×C22⋊C4—28no—
172C7×C22⋊C4—28no—
173C7×C22⋊C4—24no—
174C42×C7—21no—
175C42×C7—21no—
176C42×C7C2×D412yes—
177C42×C7C2×D412yes—
178C22⋊Dic7—82no—
179C4⋊Dic7—22no—
180C4⋊Dic7—22no—
181C4⋊Dic7—22no—
182C4⋊Dic7—22no—
183C4⋊Dic7—82no—
184Dic7⋊C4—44no—
185Dic7⋊C4—82no—
186C2×C7⋊C8—22no—
187C2×C7⋊C8—22no—
188C2×C7⋊C8—22no—
189C2×C7⋊C8—22no—
190C2×C7⋊C8—22no—
191C2×C7⋊C8—22no—
192C22×#41C2×D711yescharacteristic
193C23×D4C2×D711yescharacteristic
194#535—24no—
195#535—24no—
196C2×#127C2×D711yescharacteristic
197C2×#127C2×D711yescharacteristic
198C2×#125—71no—
199C2×#124C2×D711yescharacteristic
200C2×#124C2×D711yescharacteristic
201C2×#121—22no—
202C2×#120—22no—
203C2×#117C2×D711yescharacteristic
204#490—144no—
205#488—144no—
206C2×#103—72no—
207C2×#103—72no—
208C2×#102—72no—
209C2×#102—72no—
210C2×#102—72no—
211C2×#102—72no—
212C2×#102—72no—
213C2×#102—72no—
214C2×C22⋊C8—72no—
215C2×#97—71no—
216C2×C4×C8—71no—
217#398—142no—
218#396—142no—
219#389—72no—
220#384—71no—
221#380—72no—
222#336—72no—
223C23×C7—21no—
224C23×C7—21no—
225C23×C7—22no—
226C23×C7—22no—
227C23×C7—22no—
228C23×C7—22no—
229C23×C7—22no—
230C23×C7—48no—
231C23×C7—41no—
232C23×C7—41no—
233C23×C7—41no—
234C23×C7—41no—
235C23×C7—41no—
236C23×C7—41no—
237C23×C7—42no—
238C23×C7—42no—
239C23×C7—42no—
240C23×C7—42no—
241C23×C7—42no—
242C23×C7—42no—
243C23×C7—88no—
244C23×C7—88no—
245C23×C7—84no—
246C23×C7—84no—
247C23×C7#12412yes—
248C23×C7C22×D411yescharacteristic
249C7×Q8—24no—
250C7×Q8—42no—
251C7×D4—24no—
252C7×D4—24no—
253C7×D4—24no—
254C7×D4—48no—
255C7×D4—48no—
256C7×D4—42no—
257C7×D4—42no—
258C7×D4—42no—
259C7×D4—88no—
260C7×D4—88no—
261C2×C4×C7—21no—
262C2×C4×C7—21no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—48no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7#12014yes—
275C2×C4×C7#12412yes—
276C2×C4×C7C22×D411yescharacteristic
277C2×C4×C7C22×D411yescharacteristic
278C2×C4×C7C2×#4112yes—
279C2×C4×C7H(5,𝔽2)12yes—
280C2×Dic7—42no—
281C2×Dic7—42no—
282C2×Dic7—42no—
283C2×Dic7—42no—
284C2×Dic7—42no—
285C2×Dic7—42no—
286C7⋊C8—42no—
287C7⋊C8—42no—
288C25—21no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—24no—
292C2×#41—42no—
293C22×Q8C22×D711yescharacteristic
294C22×D4—21no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—24no—
298C22×D4—21no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—42no—
302C22×D4C22×D711yescharacteristic
303C22×D4C22×D711yescharacteristic
304C22×D4C22×D711yescharacteristic
305C23×C4—21no—
306C23×C4C22×D711yescharacteristic
307C22×C8—72no—
308C22×C8—72no—
309#127—22no—
310#127—22no—
311#127—22no—
312#127C22⋊D714yes—
313#125—142no—
314#125—142no—
315#124—22no—
316#124—22no—
317#124—22no—
318#124C22⋊D714yes—
319#121—216no—
320#120—216no—
321#117—22no—
322#117—22no—
323C2×C4⋊C4—72no—
324C2×C4⋊C4—72no—
325C2×C4⋊C4—142no—
326C2×C4⋊C4—142no—
327C2×C4⋊C4—142no—
328C2×C4⋊C4C22⋊D712yes—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—142no—
332C2×C22⋊C4C22⋊D712yes—
333C2×C42C22×D711yescharacteristic
334C2×C42C22×D711yescharacteristic
335#103—144no—
336#103—282no—
337#102—144no—
338#102—144no—
339#102—144no—
340#102—282no—
341#102—282no—
342#102—282no—
343C22⋊C8—144no—
344#97—142no—
345C4×C8—142no—
346#95—142no—
347#95—142no—
348C22×C7—24no—
349C22×C7—22no—
350C22×C7—41no—
351C22×C7—41no—
352C22×C7—42no—
353C22×C7—42no—
354C22×C7—42no—
355C22×C7—42no—
356C22×C7—44no—
357C22×C7—44no—
358C22×C7—44no—
359C22×C7—816no—
360C22×C7—82no—
361C22×C7—82no—
362C22×C7—82no—
363C22×C7—81no—
364C22×C7—81no—
365C22×C7—81no—
366C22×C7—81no—
367C22×C7—81no—
368C22×C7—81no—
369C22×C7C2×#12011yescharacteristic
370C22×C7C2×#12411yescharacteristic
371C22×C7#53511yescharacteristic
372C22×C7#57612yes—
373C22×C7#57712yes—
374C4×C7—22no—
375C4×C7—24no—
376C4×C7—42no—
377C4×C7—42no—
378C4×C7#54612yes—
379C4×C7#54612yes—
380Dic7—82no—
381Dic7—82no—
382C24—24no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—42no—
387C24—42no—
388C24—82no—
389C24—82no—
390C24C2×C22⋊D711yescharacteristic
391#41—48no—
392#41—48no—
393C2×Q8—21no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8C2×C22⋊D712yes—
397C2×D4—24no—
398C2×D4—24no—
399C2×D4—28no—
400C2×D4—28no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—48no—
411C2×D4—48no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—82no—
417C2×D4—82no—
418C2×D4—82no—
419C2×D4—82no—
420C2×D4C2×C22⋊D712yes—
421C2×D4C2×C22⋊D712yes—
422C2×D4C2×C22⋊D712yes—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—21no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—142no—
431C22×C4—142no—
432C22×C4#115914yes—
433C22×C4C2×C22⋊D712yes—
434C22×C4C2×C22⋊D711yescharacteristic
435C22×C4C2×C22⋊D712yes—
436C22×C4C23×D711yescharacteristic
437C2×C8—142no—
438C2×C8—142no—
439C2×C8—142no—
440C2×C8—142no—
441C2×C8—142no—
442C2×C8—142no—
443C4⋊C4—24no—
444C4⋊C4—142no—
445C4⋊C4—142no—
446C4⋊C4—142no—
447C4⋊C4—142no—
448C4⋊C4—284no—
449C4⋊C4—562no—
450C4⋊C4—562no—
451C22⋊C4—28no—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—562no—
455C42—21no—
456C42—21no—
457C42C2×C22⋊D712yes—
458C42C2×C22⋊D712yes—
459C2×C7—42no—
460C2×C7—82no—
461C2×C7—82no—
462C2×C7—82no—
463C2×C7#243511yescharacteristic
464C2×C7#301212yes—
465C2×C7#313612yes—
466C2×C7#322011yescharacteristic
467C2×C7#322211yescharacteristic
468C23—21no—
469C23—22no—
470C23—22no—
471C23—21no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—48no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—88no—
489C23—88no—
490C23—84no—
491C23—84no—
492C23#649912yes—
493C23C22×C22⋊D711yescharacteristic
494Q8—24no—
495Q8—42no—
496D4—24no—
497D4—24no—
498D4—24no—
499D4—48no—
500D4—48no—
501D4—42no—
502D4—42no—
503D4—42no—
504D4—88no—
505D4—88no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—48no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—282no—
520C2×C4—282no—
521C2×C4—282no—
522C2×C4—282no—
523C2×C4—282no—
524C2×C4—282no—
525C2×C4#649912yes—
526C2×C4#651614yes—
527C2×C4C2×#115912yes—
528C2×C4#654812yes—
529C2×C4C22×C22⋊D711yescharacteristic
530C2×C4C22×C22⋊D711yescharacteristic
531C8—282no—
532C8—282no—
533C7#2586711yescharacteristic, complemented, Sylow
534C22—22no—
535C22—24no—
536C22—42no—
537C22—41no—
538C22—41no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—816no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×#649911yescharacteristic
556C22#9049611yescharacteristic
557C22#9052612yes—
558C22#9052712yes—
559C22C2×#651611yescharacteristic
560C4—22no—
561C4—24no—
562C4—42no—
563C4—42no—
564C4—562no—
565C4—562no—
566C4#9049712yes—
567C4#9049712yes—
568C2—42no—
569C2—82no—
570C2—82no—
571C2—82no—
572C2#1174082512yes—
573C2#1174083311yescharacteristic
574C2#1174083811yescharacteristic
575C2#1174149511yescharacteristic
576C2#1174154712yes—
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#535C2
socleC23×C7C22×D4
hypercenterC2×#535D7
hypocenterC7#25867
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
2. C2×#89843C2semidirect
3. C2×#89828C2semidirect
4. #11739710C2semidirect
5. #11729889C2semidirect
6. #11729882C2semidirect
7. #11729518C2semidirect
8. #11729516C2semidirect
9. #11729480C2semidirect
10. #11729476C2semidirect
11. #11729336C2semidirect
23. C2×#6433C22semidirect
24. C2×#6409C22semidirect
25. C2×#6409C22semidirect
30. C2×#6406C22semidirect
31. C2×#6406C22semidirect
38. #89707C22semidirect
39. #89700C22semidirect
40. C2×#6377C22semidirect
41. C2×C4×C7⋊C8C22semidirect
42. #89319C22semidirect
533. C7#25867semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5352
C2×#898432
C2×#898282
#117397102
#117298892
#117298822
#117295182
#117295162
#117294802
#117294762
#117293362
#258677