Finite Group Databasebeta

← #13395094

Subgroups — #13395094

Order 1792.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#432C211yesmaximal, characteristic, complemented
2#11739521C211yesmaximal, characteristic, complemented
3C4×#6493C211yesmaximal, characteristic
4C2×#89618C211yesmaximal, characteristic, complemented
5#11728233C211yesmaximal, characteristic, complemented
6#11728214C211yesmaximal, characteristic, complemented
7#11728208C211yesmaximal, characteristic, complemented
8#11727693C212yesmaximal, complemented
9#11727689C212yesmaximal
10#11727574C212yesmaximal, complemented
11#11727572C212yesmaximal, complemented
12C22×C42×C7C2211yescharacteristic
13C2×#6493C2211yescharacteristic
14C2×C4×C22⋊D7—21no—
15C2×#6487—21no—
16C2×C4×D28C2211yescharacteristic
17C2×#6432C2211yescharacteristic
18C7×#432—24no—
19C2×C7×C4⋊C8C2211yescharacteristic
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C7×C22⋊C8C2212yes—
22C2×C7×#97C2212yes—
23#89985—21no—
24#89984—21no—
25#89984C2212yes—
26#89984C2211yescharacteristic
27C2×#6395C2212yes—
28C2×#6395C2212yes—
29C2×#6392C2212yes—
30C2×#6391C2212yes—
31#89712—21no—
32#89711C2211yescharacteristic
33C4×(C2×D7)⋊C4—21no—
34#89707C2211yescharacteristic
35C4×C4⋊Dic7C2211yescharacteristic
36#89701—21no—
37#89700—21no—
38#89700C2211yescharacteristic
39#89700C2212yes—
40#89618—24no—
41#89346C2212yes—
42#89346C2212yes—
43#89346C2212yes—
44#89346C2212yes—
45#24709—71nomaximal, Sylow
46C23×C4×C7D411yescharacteristic
47C23×C4×C7D411yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C22×C22⋊D7—21no—
50C22×D28C2311yescharacteristic
51C22×C4×D7—21no—
52C22×Dic14—21no—
53C22×C7×C8C2312yes—
54C22×C7×C8C2312yes—
55C2×C42×C7—22no—
56C2×C42×C7—22no—
57C2×C42×C7D411yescharacteristic
58C2×C42×C7D411yescharacteristic
59C2×C42×C7C2311yescharacteristic
60C2×C42×C7C2311yescharacteristic
61C2×C22⋊Dic7—22no—
62C2×C22⋊Dic7—21no—
63#6493—22no—
64#6493—22no—
65C4×C22⋊D7—44no—
66C2×(C2×D7)⋊C4—21no—
67C2×(C2×D7)⋊C4—21no—
68C2×(C2×D7)⋊C4—21no—
69C2×(C2×D7)⋊C4—21no—
70C2×C4⋊Dic7—21no—
71C2×C4⋊Dic7—21no—
72C2×C4⋊Dic7—21no—
73C2×C4⋊Dic7C2311yescharacteristic
74C2×C4⋊Dic7C2312yes—
75C2×C4⋊Dic7C2311yescharacteristic
76C2×C4⋊Dic7C2312yes—
77C2×C4⋊Dic7C2311yescharacteristic
78#6487—44no—
79C2×Dic7⋊C4—22no—
80C2×Dic7⋊C4—21no—
81C2×C4×Dic7—21no—
82C4×D28—22no—
83C4×D28—22no—
84#6432—22no—
85#6432—22no—
86C7×C4⋊C8—22no—
87C7×C4⋊C8D414yescomplemented
88C7×C22⋊C8—24no—
89C7×#97—24no—
90C7⋊#95—22no—
91C7⋊#95—22no—
92C7⋊#95—21no—
93C7⋊#95—21no—
94C7⋊#95—21no—
95#6395—24no—
96#6395—24no—
97#6392—24no—
98#6391—24no—
99C2×#474—71no—
100C2×#432D711yescharacteristic, complemented
101#2857—71no—
102C4×#121—71no—
103#2076—72no—
104#2034—72no—
105#1988—71no—
106#1948—71no—
107#1944—72no—
108#1936—72no—
109#1802—71no—
110C24×C7C2×D411yescharacteristic
111C23×D7—21no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—41no—
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7C2411yescharacteristic
130C2×C22⋊D7—24no—
131C2×C22⋊D7—42no—
132C2×C22⋊D7—42no—
133C22×Dic7—21no—
134C22×Dic7—21no—
135C22×Dic7—22no—
136C22×Dic7—22no—
137C22×Dic7—21no—
138C2×D28—21no—
139C2×D28—21no—
140C2×D28—21no—
141C2×D28—21no—
142C2×D28—21no—
143C2×D28#4112yes—
144C2×C4×D7—42no—
145C2×C4×D7—42no—
146C2×C4×D7—42no—
147C2×Dic14—42no—
148C2×Dic14—42no—
149C2×Dic14—42no—
150C2×C7×C8—22no—
151C2×C7×C8—22no—
152C2×C7×C8—22no—
153C2×C7×C8—22no—
154C2×C7×C8—22no—
155C2×C7×C8C2×D414yes—
156C42×C7—22no—
157C42×C7—22no—
158C42×C7—21no—
159C42×C7—21no—
160C42×C7C2×D412yes—
161C42×C7#4112yes—
162C22⋊Dic7—44no—
163C22⋊Dic7—42no—
164(C2×D7)⋊C4—24no—
165(C2×D7)⋊C4—42no—
166(C2×D7)⋊C4—42no—
167(C2×D7)⋊C4—42no—
168C4⋊Dic7—21no—
169C4⋊Dic7—22no—
170C4⋊Dic7—21no—
171C4⋊Dic7—22no—
172C4⋊Dic7—21no—
173C4⋊Dic7—22no—
174C4⋊Dic7—22no—
175C4⋊Dic7—21no—
176C4⋊Dic7—21no—
177C4⋊Dic7—42no—
178C4⋊Dic7—42no—
179C4⋊Dic7—42no—
180C4⋊Dic7#4112yes—
181Dic7⋊C4—44no—
182Dic7⋊C4—42no—
183C4×Dic7—42no—
184C2×C4⋊Q8—71no—
185C2×C22⋊Q8—141no—
186C2×#121—71no—
187C2×C4×D4—71no—
188C2×C4×D4—141no—
189C22×C42C2×D711yescharacteristic
190#474—144no—
191#432—24no—
192C2×#107—72no—
193C2×#106—72no—
194C2×C4⋊C8C2×D711yescharacteristic
195C2×C4⋊C8C2×D711yescharacteristic
196C2×#102—72no—
197C2×#102—72no—
198C2×C22⋊C8C2×D712yes—
199C2×#97C2×D712yes—
200#391—141no—
201#390—71no—
202#389—72no—
203#389—71no—
204#389—141no—
205#388—141no—
206#386—141no—
207#384—71no—
208#380—71no—
209#380—72no—
210#380—141no—
211C4×C4⋊C4—71no—
212C4×C22⋊C4—141no—
213#340—72no—
214#340—72no—
215#340—72no—
216#340—72no—
217C23×C7—21no—
218C23×C7—21no—
219C23×C7—21no—
220C23×C7—21no—
221C23×C7—21no—
222C23×C7—21no—
223C23×C7#13712yes—
224C23×C7C22×D411yescharacteristic
225C22×D7—22no—
226C22×D7—41no—
227C22×D7—41no—
228C22×D7—41no—
229C22×D7—41no—
230C22×D7—41no—
231C22×D7—41no—
232C2×C4×C7—21no—
233C2×C4×C7—21no—
234C2×C4×C7—21no—
235C2×C4×C7—21no—
236C2×C4×C7—21no—
237C2×C4×C7—21no—
238C2×C4×C7—21no—
239C2×C4×C7—21no—
240C2×C4×C7—21no—
241C2×C4×C7—21no—
242C2×C4×C7—21no—
243C2×C4×C7—44no—
244C2×C4×C7—41no—
245C2×C4×C7—41no—
246C2×C4×C7—41no—
247C2×C4×C7—41no—
248C2×C4×C7—44no—
249C2×C4×C7#12112yes—
250C2×C4×C7#12112yes—
251C2×C4×C7AGL(1,ℤ/8)12yes—
252C2×C4×C7AGL(1,ℤ/8)12yes—
253C2×C4×C7C22×D411yescharacteristic
254C2×C4×C7C2×#4111yescharacteristic
255C2×C4×C7C2×#4111yescharacteristic
256C2×C4×C7C2×#4111yescharacteristic
257C2×C4×C72−1+411yescharacteristic
258C2×C4×C72−1+411yescharacteristic
259C22⋊D7—48no—
260C2×Dic7—22no—
261C2×Dic7—41no—
262C2×Dic7—41no—
263C2×Dic7—42no—
264C2×Dic7—41no—
265C2×Dic7—42no—
266C2×Dic7—41no—
267C2×Dic7—41no—
268C2×Dic7—42no—
269C2×Dic7—42no—
270C2×Dic7—41no—
271C2×Dic7—42no—
272C2×Dic7—41no—
273C2×Dic7—42no—
274C2×Dic7—41no—
275D28—22no—
276D28—22no—
277D28—41no—
278D28—41no—
279C4×D7—84no—
280Dic14—84no—
281C7×C8—24no—
282C7×C8—42no—
283C22×Q8—141no—
284C22×D4—71no—
285C22×D4—141no—
286C23×C4—141no—
287C23×C4D2811yescharacteristic
288C23×C4D2811yescharacteristic
289C23×C4C22×D711yescharacteristic
290C22×C8C22×D712yes—
291C22×C8C22×D712yes—
292C4⋊Q8—142no—
293C4⋊Q8—142no—
294C22⋊Q8—284no—
295#121—142no—
296#121—142no—
297C4×D4—142no—
298C4×D4—142no—
299C4×D4—284no—
300C2×C4⋊C4—71no—
301C2×C4⋊C4—71no—
302C2×C4⋊C4—72no—
303C2×C4⋊C4—71no—
304C2×C4⋊C4—72no—
305C2×C4⋊C4—141no—
306C2×C4⋊C4—142no—
307C2×C4⋊C4—141no—
308C2×C4⋊C4—141no—
309C2×C4⋊C4—141no—
310C2×C22⋊C4—141no—
311C2×C22⋊C4—141no—
312C2×C22⋊C4—142no—
313C2×C22⋊C4—141no—
314C2×C22⋊C4—141no—
315C2×C22⋊C4—141no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—141no—
319C2×C42D2811yescharacteristic
320C2×C42D2811yescharacteristic
321C2×C42C22×D711yescharacteristic
322C2×C42C22×D711yescharacteristic
323#107—144no—
324#106—144no—
325C4⋊C8—22no—
326C4⋊C8C22⋊D714yescomplemented
327#102—144no—
328#102—144no—
329C22⋊C8—24no—
330#97—24no—
331#95—141no—
332#95—141no—
333#95—141no—
334#95—142no—
335#95—142no—
336C22×C7—22no—
337C22×C7—22no—
338C22×C7—22no—
339C22×C7—41no—
340C22×C7—41no—
341C22×C7—41no—
342C22×C7—41no—
343C22×C7C2×#12111yescharacteristic
344C22×C7#52511yescharacteristic
345C22×C7#53611yescharacteristic
346C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C7C2×#13711yescharacteristic
349C22×C7#57511yescharacteristic
350C2×D7—42no—
351C2×D7—42no—
352C2×D7—42no—
353C2×D7—81no—
354C2×D7—81no—
355C2×D7—81no—
356C2×D7—81no—
357C4×C7—22no—
358C4×C7—41no—
359C4×C7—41no—
360C4×C7—41no—
361C4×C7#46914yes—
362C4×C7#54711yescharacteristic
363C4×C7#54811yescharacteristic
364C4×C7#55211yescharacteristic
365C4×C7#55611yescharacteristic
366Dic7—42no—
367Dic7—82no—
368Dic7—81no—
369Dic7—82no—
370Dic7—81no—
371C24—141no—
372C24C2×D2811yescharacteristic
373C2×Q8—282no—
374C2×Q8—282no—
375C2×Q8—282no—
376C2×D4—72no—
377C2×D4—144no—
378C2×D4—141no—
379C2×D4—141no—
380C2×D4—141no—
381C2×D4—141no—
382C2×D4—141no—
383C2×D4—282no—
384C2×D4—282no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4—141no—
398C22×C4—141no—
399C22×C4—141no—
400C22×C4—142no—
401C22×C4—142no—
402C22×C4—282no—
403C22×C4—282no—
404C22×C4—282no—
405C22×C4C2×D2811yescharacteristic
406C22×C4C2×D2811yescharacteristic
407C22×C4C2×D2811yescharacteristic
408C22×C4C2×D2811yescharacteristic
409C22×C4C2×D2811yescharacteristic
410C22×C4C23×D711yescharacteristic
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8C2×C22⋊D714yes—
417C4⋊C4—72no—
418C4⋊C4—141no—
419C4⋊C4—141no—
420C4⋊C4—142no—
421C4⋊C4—142no—
422C4⋊C4—142no—
423C4⋊C4—141no—
424C4⋊C4—141no—
425C4⋊C4—142no—
426C4⋊C4—141no—
427C4⋊C4—282no—
428C4⋊C4—284no—
429C4⋊C4—282no—
430C4⋊C4—282no—
431C4⋊C4—282no—
432C22⋊C4—144no—
433C22⋊C4—282no—
434C22⋊C4—282no—
435C22⋊C4—282no—
436C22⋊C4—284no—
437C22⋊C4—282no—
438C42—22no—
439C42—22no—
440C42—21no—
441C42—21no—
442C42—282no—
443C42#115712yes—
444C42C2×C22⋊D712yes—
445C2×C7—42no—
446C2×C7#241511yescharacteristic
447C2×C7C2×#46911yescharacteristic
448C2×C7#305611yescharacteristic
449C2×C7#311011yescharacteristic
450C2×C7#311511yescharacteristic
451C2×C7#323511yescharacteristic
452C2×C7#323911yescharacteristic
453D7—82no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—142no—
461C23—281no—
462C23—281no—
463C23—281no—
464C23—281no—
465C23—281no—
466C23—281no—
467C23#647212yes—
468C23C22×D2811yescharacteristic
469Q8—564no—
470D4—142no—
471D4—142no—
472D4—288no—
473D4—281no—
474D4—281no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—142no—
493C2×C4—281no—
494C2×C4—281no—
495C2×C4—281no—
496C2×C4—282no—
497C2×C4—281no—
498C2×C4—282no—
499C2×C4—281no—
500C2×C4—282no—
501C2×C4—281no—
502C2×C4—282no—
503C2×C4—282no—
504C2×C4—281no—
505C2×C4—281no—
506C2×C4—282no—
507C2×C4—564no—
508C2×C4#647112yes—
509C2×C4#647112yes—
510C2×C4#649312yes—
511C2×C4#649312yes—
512C2×C4C2×#115711yescharacteristic
513C2×C4D7×#4111yescharacteristic
514C2×C4D7×#4111yescharacteristic
515C2×C4#655411yescharacteristic
516C2×C4#655411yescharacteristic
517C2×C4C22×C22⋊D711yescharacteristic
518C8—24no—
519C8—42no—
520C7#2470911yescharacteristic, complemented, Sylow
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—282no—
529C22—282no—
530C22—282no—
531C22—561no—
532C22—561no—
533C22—561no—
534C22—561no—
535C22#9021511yescharacteristic
536C22#9021711yescharacteristic
537C22C2×#647111yescharacteristic
538C22C2×#647111yescharacteristic
539C22C2×#647211yescharacteristic
540C22#9043911yescharacteristic
541C22C2×#649311yescharacteristic
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—282no—
547C4—561no—
548C4—562no—
549C4—561no—
550C4—562no—
551C4#8990714yes—
552C4#9022011yescharacteristic
553C4#9022411yescharacteristic
554C4#9051511yescharacteristic
555C4#9052211yescharacteristic
556C2—42no—
557C2—562no—
558C2#1173676411yescharacteristic
559C2#1173676811yescharacteristic
560C2#1173678911yescharacteristic
561C2#1173679211yescharacteristic
562C2#1173972211yescharacteristic
563C2C2×#8990711yescharacteristic
564C2#1174122111yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#432C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenterC2×#432D7
hypocenterC7#24709
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×C7×#432C2semidirect
2. #11739521C2semidirect
4. C2×#89618C2semidirect
5. #11728233C2semidirect
6. #11728214C2semidirect
7. #11728208C2semidirect
8. #11727693C2semidirect
10. #11727574C2semidirect
11. #11727572C2semidirect
87. C7×C4⋊C8D4semidirect
100. C2×#432D7semidirect
326. C4⋊C8C22⋊D7semidirect
520. C7#24709semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4322
#117395212
C4×#64932
C2×#896182
#117282332
#117282142
#117282082
#117276932
#117276892
#117275742
#117275722
#247097