Finite Group Databasebeta

← #13559881

Subgroups — #13559881

Order 1792.

2130 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2852C211yesmaximal, characteristic, complemented
2#11740549C211yesmaximal, characteristic, complemented
3Dic7×#126C211yesmaximal, characteristic, complemented
4#11739523C211yesmaximal, characteristic, complemented
5C2×C42×Dic7C211yesmaximal, characteristic, complemented
6#11733265C213yesmaximal, complemented
7#11732900C213yesmaximal, complemented
8#11732736C213yesmaximal, complemented
9#11732387C213yesmaximal, complemented
10#11732315C213yesmaximal, complemented
11#11732103C213yesmaximal
12#11732032C213yesmaximal, complemented
13#11731823C213yesmaximal, complemented
14#11731738C211yesmaximal, characteristic, complemented
15#11731704C211yesmaximal, characteristic, complemented
16C22×#1159C2211yescharacteristic
17C2×C7×#126C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×C4×Dic7C2213yes—
20C22×C4×Dic7C2213yes—
21C2×#6461C2213yes—
22C2×#6442C2213yes—
23C2×#6440C2213yes—
24C2×#6439C2211yescharacteristic
25C7×#388C2213yes—
26C7×#387C2213yes—
27C7×#386C2213yes—
28C7×#385C2213yes—
29C7×#383C2211yescharacteristic
30#89992C2213yes—
31#89985C2213yes—
32#89982C2213yes—
33#89762C2213yes—
34#89753C2213yes—
35#89750C2213yes—
36C4⋊C4×Dic7C2213yes—
37C4⋊C4×Dic7C2213yes—
38#89744C2213yes—
39#89744C2213yes—
40#89730C2213yes—
41#89729C2213yes—
42#89729C2213yes—
43#89723C2213yes—
44#89722C2213yes—
45#89718C2213yes—
46#89717C2213yes—
47#89716C2213yes—
48C22⋊C4×Dic7C2213yes—
49C22⋊C4×Dic7C2213yes—
50#89712C2213yes—
51#89709C2211yescharacteristic
52#89705C2213yes—
53C42×Dic7C2213yes—
54C42×Dic7C2211yescharacteristic
55C42×Dic7C2211yescharacteristic
56C42×Dic7C2213yes—
57#89442C2213yes—
58#89441C2213yes—
59#89438C2213yes—
60#89438C2213yes—
61#89427C2213yes—
62#89426C2213yes—
63#89425C2213yes—
64#89424C2213yes—
65#89423C2213yes—
66#89423C2213yes—
67#89421C2213yes—
68#89421C2213yes—
69#89419C2213yes—
70#89419C2213yes—
71#89418C2213yes—
72#89418C2213yes—
73#36641—71nomaximal, Sylow
74C22×C7×D4C2311yescharacteristic
75C23×C4×C7C2313yes—
76C22×C22⋊D7C2311yescharacteristic
77C22×C22⋊D7C2311yescharacteristic
78C23×Dic7C2313yes—
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C2×#1159—212no—
82C22×C4×D7C2311yescharacteristic
83C22×Dic14C2311yescharacteristic
84C7×#126—24no—
85C2×C7×C4⋊C4C2313yes—
86C2×C7×C4⋊C4C2313yes—
87C2×C7×C22⋊C4C2313yes—
88C2×C7×C22⋊C4C2313yes—
89C2×C7×C22⋊C4C2313yes—
90C2×C42×C7—24no—
91C2×C42×C7C2313yes—
92C2×C42×C7C2311yescharacteristic
93C2×C22⋊Dic7C2313yes—
94C2×C22⋊Dic7C2313yes—
95C2×C22⋊Dic7C2313yes—
96C2×(C2×D7)⋊C4C2313yes—
97C2×(C2×D7)⋊C4C2313yes—
98C2×(C2×D7)⋊C4C2313yes—
99C2×(C2×D7)⋊C4C2313yes—
100C2×C4⋊Dic7C2313yes—
101C2×C4⋊Dic7C2313yes—
102C2×Dic7⋊C4C2313yes—
103C2×Dic7⋊C4C2313yes—
104C2×Dic7⋊C4C2313yes—
105C2×Dic7⋊C4C2313yes—
106C2×Dic7⋊C4C2313yes—
107C2×Dic7⋊C4C2313yes—
108C2×C4×Dic7—212no—
109C2×C4×Dic7—212no—
110C2×C4×Dic7C2313yes—
111C2×C4×Dic7C2313yes—
112C2×C4×Dic7C2313yes—
113C2×C4×Dic7C2313yes—
114C2×C4×Dic7C2313yes—
115C2×C4×Dic7C2313yes—
116C2×C4×Dic7C2313yes—
117C2×C4×Dic7C2313yes—
118C2×C4×Dic7C2313yes—
119C2×C4×Dic7C2313yes—
120#6461—212no—
121#6442—212no—
122#6440—212no—
123#6439—24no—
124C7×#95C2313yes—
125C7×#95C2313yes—
126C7×#95C2313yes—
127C7×#95C2313yes—
128C7⋊#95C2313yes—
129C7⋊#95C2313yes—
130C7⋊#95C2313yes—
131C7⋊#95C2313yes—
132C7⋊#95C2313yes—
133C7⋊#95C2313yes—
134C7⋊#95C2313yes—
135C7⋊#95C2313yes—
136C7⋊#95C2313yes—
137C7⋊#95C2313yes—
138C7⋊#95C2313yes—
139C7⋊#95C2313yes—
140#2863—73no—
141#2863—71no—
142#2860—73no—
143#2860—71no—
144#2852—71no—
145#2852—73no—
146#2852—73no—
147#2852D711yescharacteristic, complemented
148C4×#126—73no—
149C4×#126—73no—
150C4×#126—71no—
151C4×#126—71no—
152#2297—73no—
153#2296—73no—
154C2×C43—71no—
155C24×C7C2411yescharacteristic
156C24×C7C2411yescharacteristic
157C23×D7C2411yescharacteristic
158C2×C7×D4—26no—
159C22×C4×C7—26no—
160C22×C4×C7—26no—
161C22×C4×C7—26no—
162C22×C4×C7C2411yescharacteristic
163C22×C4×C7C2413yes—
164C22×C4×C7C2413yes—
165C22×C4×C7C2413yes—
166C22×C4×C7C2413yes—
167C2×C22⋊D7—26no—
168C2×C22⋊D7—26no—
169C22×Dic7—26no—
170C22×Dic7—26no—
171C22×Dic7—26no—
172C22×Dic7—26no—
173C22×Dic7#41112yes—
174C22×Dic7C2411yescharacteristic
175C22×Dic7C2413yes—
176C22×Dic7C2413yes—
177C22×Dic7C2413yes—
178C22×Dic7C2413yes—
179C22×Dic7C2411yescharacteristic
180C22×Dic7C2411yescharacteristic
181#1159—416no—
182C2×C4×D7—26no—
183C2×Dic14—26no—
184C7×C4⋊C4—26no—
185C7×C4⋊C4—26no—
186C7×C22⋊C4—26no—
187C7×C22⋊C4—26no—
188C7×C22⋊C4—26no—
189C42×C7—26no—
190C42×C7#4114yescomplemented
191C22⋊Dic7—26no—
192C22⋊Dic7—26no—
193C22⋊Dic7—26no—
194(C2×D7)⋊C4—26no—
195(C2×D7)⋊C4—26no—
196(C2×D7)⋊C4—26no—
197(C2×D7)⋊C4—26no—
198C4⋊Dic7—26no—
199C4⋊Dic7—26no—
200Dic7⋊C4—26no—
201Dic7⋊C4—26no—
202Dic7⋊C4—26no—
203Dic7⋊C4—26no—
204Dic7⋊C4—26no—
205Dic7⋊C4—26no—
206C4×Dic7—26no—
207C4×Dic7—26no—
208C4×Dic7—26no—
209C4×Dic7—26no—
210C4×Dic7—26no—
211C4×Dic7—26no—
212C4×Dic7—26no—
213C4×Dic7—26no—
214C4×Dic7—26no—
215C4×Dic7#41112yescomplemented
216C22×#41—71no—
217C2×#126—73no—
218C2×#126—73no—
219C2×#126—71no—
220C2×#126C2×D711yescharacteristic
221C2×#117—73no—
222C22×C42—73no—
223C22×C42—73no—
224C22×C42C2×D711yescharacteristic
225#391—73no—
226#391—73no—
227#390—73no—
228#390—73no—
229#389—73no—
230#389—73no—
231#389—73no—
232#389—73no—
233#388—73no—
234#388—73no—
235#388—73no—
236#388—73no—
237#388—73no—
238#388—73no—
239#388—73no—
240#388C2×D713yes—
241#387—73no—
242#387—73no—
243#387—73no—
244#387—73no—
245#387—73no—
246#387—73no—
247#387—73no—
248#387C2×D713yes—
249#386—73no—
250#386—73no—
251#386—73no—
252#386C2×D713yes—
253#385—73no—
254#385—73no—
255#385—73no—
256#385C2×D713yes—
257#383—71no—
258#383—73no—
259#383—73no—
260#383C2×D711yescharacteristic
261C4×C4⋊C4—73no—
262C4×C4⋊C4—73no—
263C4×C4⋊C4—73no—
264C4×C4⋊C4—73no—
265C4×C22⋊C4—73no—
266C4×C22⋊C4—73no—
267C4×C22⋊C4—73no—
268C4×C22⋊C4—73no—
269C43—73no—
270C43—71no—
271C43—73no—
272C43—71no—
273C23×C7—23no—
274C23×C7—21no—
275C23×C7—23no—
276C23×C7—21no—
277C23×C7—23no—
278C23×C7C2×#4116yes—
279C23×C7C2511yescharacteristic
280C22×D7—21no—
281C22×D7—23no—
282C22×D7—23no—
283C7×D4—44no—
284C2×C4×C7—224no—
285C2×C4×C7—23no—
286C2×C4×C7—23no—
287C2×C4×C7—23no—
288C2×C4×C7—23no—
289C2×C4×C7—23no—
290C2×C4×C7—23no—
291C2×C4×C7—23no—
292C2×C4×C7—23no—
293C2×C4×C7—23no—
294C2×C4×C7—23no—
295C2×C4×C7—23no—
296C2×C4×C7C2×#4116yes—
297C2×C4×C7C2×#4116yes—
298C22⋊D7—44no—
299C22⋊D7—44no—
300C2×Dic7—224no—
301C2×Dic7—23no—
302C2×Dic7—23no—
303C2×Dic7—23no—
304C2×Dic7—23no—
305C2×Dic7—23no—
306C2×Dic7—23no—
307C2×Dic7—23no—
308C2×Dic7—23no—
309C2×Dic7—23no—
310C2×Dic7—23no—
311C2×Dic7—23no—
312C2×Dic7—44no—
313C2×Dic7#126116yescomplemented
314C2×Dic7C2×#4116yes—
315C2×Dic7C2×#4116yes—
316C2×Dic7C2×#4116yes—
317C2×Dic7C2×#4116yes—
318C4×D7—44no—
319Dic14—44no—
320C2×#41—1412no—
321C22×Q8—71no—
322C22×D4—71no—
323C22×D4—71no—
324C22×D4C22×D711yescharacteristic
325C23×C4—71no—
326C23×C4—71no—
327C23×C4—73no—
328C23×C4—71no—
329C23×C4C22×D713yes—
330#126—24no—
331#126—1412no—
332#126—1412no—
333#126—144no—
334#117—1412no—
335C2×C4⋊C4—73no—
336C2×C4⋊C4—73no—
337C2×C4⋊C4—73no—
338C2×C4⋊C4—73no—
339C2×C4⋊C4—73no—
340C2×C4⋊C4—73no—
341C2×C4⋊C4—73no—
342C2×C4⋊C4—73no—
343C2×C4⋊C4C22×D713yes—
344C2×C4⋊C4C22×D713yes—
345C2×C22⋊C4—73no—
346C2×C22⋊C4—73no—
347C2×C22⋊C4—73no—
348C2×C22⋊C4—73no—
349C2×C22⋊C4—73no—
350C2×C22⋊C4—73no—
351C2×C22⋊C4—73no—
352C2×C22⋊C4C22×D713yes—
353C2×C22⋊C4C22×D713yes—
354C2×C22⋊C4C22×D713yes—
355C2×C42—24no—
356C2×C42—73no—
357C2×C42—73no—
358C2×C42—73no—
359C2×C42—73no—
360C2×C42—73no—
361C2×C42—73no—
362C2×C42—73no—
363C2×C42—73no—
364C2×C42—73no—
365C2×C42—73no—
366C2×C42—1412no—
367C2×C42—1412no—
368C2×C42C22×D713yes—
369C2×C42C22×D711yescharacteristic
370#95—73no—
371#95—73no—
372#95—73no—
373#95—73no—
374#95—73no—
375#95—73no—
376#95—73no—
377#95—73no—
378#95—73no—
379#95—73no—
380#95—73no—
381#95—73no—
382#95C22×D713yes—
383#95C22×D713yes—
384#95C22×D713yes—
385#95C22×D713yes—
386C22×C7—26no—
387C22×C7—26no—
388C22×C7—41no—
389C22×C7—43no—
390C22×C7—43no—
391C22×C7C2×#12614yes—
392C22×C7C22×#4111yescharacteristic
393C22×C7C22×#4113yes—
394C22×C7C22×#4113yes—
395C2×D7—41no—
396C2×D7—43no—
397C2×D7—43no—
398C4×C7—26no—
399C4×C7—26no—
400C4×C7—41no—
401C4×C7—43no—
402C4×C7—43no—
403Dic7—26no—
404Dic7—26no—
405Dic7—41no—
406Dic7—43no—
407Dic7—43no—
408Dic7C2×#12614yes—
409Dic7C2×#12614yes—
410C24—71no—
411C24C23×D711yescharacteristic
412C24C23×D711yescharacteristic
413#41—2816no—
414C2×Q8—146no—
415C2×D4—26no—
416C2×D4—146no—
417C2×D4—146no—
418C22×C4—26no—
419C22×C4—26no—
420C22×C4—26no—
421C22×C4—712no—
422C22×C4—71no—
423C22×C4—71no—
424C22×C4—73no—
425C22×C4—73no—
426C22×C4—71no—
427C22×C4—73no—
428C22×C4—73no—
429C22×C4—146no—
430C22×C4—146no—
431C22×C4—146no—
432C22×C4—146no—
433C22×C4—146no—
434C22×C4C23×D711yescharacteristic
435C22×C4C23×D713yes—
436C22×C4C23×D713yes—
437C22×C4C23×D713yes—
438C22×C4C23×D713yes—
439C4⋊C4—26no—
440C4⋊C4—26no—
441C4⋊C4—146no—
442C4⋊C4—146no—
443C4⋊C4—146no—
444C4⋊C4—146no—
445C4⋊C4—146no—
446C4⋊C4—146no—
447C4⋊C4—146no—
448C4⋊C4—146no—
449C22⋊C4—26no—
450C22⋊C4—26no—
451C22⋊C4—26no—
452C22⋊C4—146no—
453C22⋊C4—146no—
454C22⋊C4—146no—
455C22⋊C4—146no—
456C22⋊C4—146no—
457C22⋊C4—146no—
458C22⋊C4—146no—
459C42—26no—
460C42—712no—
461C42—146no—
462C42—146no—
463C42—146no—
464C42—146no—
465C42—146no—
466C42—146no—
467C42—146no—
468C42—146no—
469C42—146no—
470C42#115914yescomplemented
471C2×C7—24no—
472C2×C7—81no—
473C2×C7C22×#12611yescharacteristic
474C2×C7#344413yes—
475C2×C7#344413yes—
476D7—81no—
477C23—21no—
478C23—23no—
479C23—21no—
480C23—23no—
481C23—23no—
482C23—141no—
483C23—143no—
484C23—143no—
485C23D7×#4116yes—
486C23C24×D711yescharacteristic
487Q8—284no—
488D4—44no—
489D4—284no—
490D4—284no—
491C2×C4—224no—
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—716no—
504C2×C4—76no—
505C2×C4—76no—
506C2×C4—76no—
507C2×C4—76no—
508C2×C4—1424no—
509C2×C4—143no—
510C2×C4—143no—
511C2×C4—143no—
512C2×C4—143no—
513C2×C4—143no—
514C2×C4—143no—
515C2×C4—143no—
516C2×C4—143no—
517C2×C4—143no—
518C2×C4—143no—
519C2×C4—143no—
520C2×C4—284no—
521C2×C4—284no—
522C2×C4C2×#115916yes—
523C2×C4D7×#4116yes—
524C7#3664111yescharacteristic, complemented, Sylow
525C22—26no—
526C22—26no—
527C22—43no—
528C22—41no—
529C22—43no—
530C22—283no—
531C22—281no—
532C22—283no—
533C22D7×#12614yes—
534C22C22×#115911yescharacteristic
535C22C2×D7×#4113yes—
536C22C2×D7×#4113yes—
537C4—26no—
538C4—26no—
539C4—43no—
540C4—41no—
541C4—43no—
542C4—74no—
543C4—74no—
544C4—146no—
545C4—146no—
546C4—283no—
547C4—281no—
548C4—283no—
549C2—24no—
550C2—81no—
551C2—561no—
552C2#1174308613yes—
553C2C2×D7×#12611yescharacteristic
554C2#1174318713yes—
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2852C2
prime radicalC22×#1159C22
hypercenter#2852D7
hypocenterC7#36641
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2852

Complements

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

NH ≅ G/Ntype
1. C7×#2852C2semidirect
2. #11740549C2semidirect
3. Dic7×#126C2semidirect
4. #11739523C2semidirect
5. C2×C42×Dic7C2semidirect
6. #11733265C2semidirect
7. #11732900C2semidirect
8. #11732736C2semidirect
9. #11732387C2semidirect
10. #11732315C2semidirect
12. #11732032C2semidirect
13. #11731823C2semidirect
14. #11731738C2semidirect
15. #11731704C2semidirect
147. #2852D7semidirect
190. C42×C7#41semidirect
215. C4×Dic7#41semidirect
313. C2×Dic7#126semidirect
470. C42#1159semidirect
524. C7#36641semidirect

Maximal subgroups

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

subgroupindex
C7×#28522
#117405492
Dic7×#1262
#117395232
C2×C42×Dic72
#117332652
#117329002
#117327362
#117323872
#117323152
#117321032
#117320322
#117318232
#117317382
#117317042
#366417