Finite Group Databasebeta

← #13559883

Subgroups — #13559883

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
1C4×C7×#126C211yesmaximal, characteristic, complemented
2#11740565C211yesmaximal, characteristic, complemented
3#11740549C211yesmaximal, characteristic, complemented
4#11733403C213yesmaximal, complemented
5#11733265C213yesmaximal, complemented
6#11732891C213yesmaximal, complemented
7#11732736C213yesmaximal, complemented
8#11731762C211yesmaximal, characteristic, complemented
9#11731738C211yesmaximal, characteristic, complemented
10#11731200C213yesmaximal, complemented
11C4×#6461C213yesmaximal, complemented
12#11731008C213yesmaximal
13C4×#6442C213yesmaximal, complemented
14C43×D7C211yesmaximal, characteristic, complemented
15C4×#6439C211yesmaximal, characteristic, complemented
16C22×#1157C2211yescharacteristic
17C2×C7×#126C2211yescharacteristic
18C2×#6461C2213yes—
19C2×#6442C2213yes—
20C2×#6439C2211yescharacteristic
21C2×#6435C2213yes—
22C2×C42×D7C2213yes—
23C2×C42×D7C2211yescharacteristic
24C2×C42×D7C2213yes—
25C7×#388C2213yes—
26C7×#387C2213yes—
27C7×#383C2211yescharacteristic
28C4×C7×C4⋊C4C2213yes—
29C4×C7×C22⋊C4C2213yes—
30C43×C7C2211yescharacteristic
31C4×C22⋊Dic7C2213yes—
32#89762C2213yes—
33#89761C2213yes—
34#89761C2213yes—
35#89753C2213yes—
36#89750C2213yes—
37#89744C2213yes—
38#89744C2213yes—
39#89729C2213yes—
40#89729C2213yes—
41#89728C2213yes—
42#89728C2213yes—
43#89723C2213yes—
44#89717C2213yes—
45#89716C2213yes—
46#89712C2213yes—
47C4×(C2×D7)⋊C4C2213yes—
48C4×(C2×D7)⋊C4C2213yes—
49#89709C2211yescharacteristic
50C4×C4⋊Dic7C2213yes—
51#89705C2213yes—
52C4×Dic7⋊C4C2213yes—
53C4×Dic7⋊C4C2213yes—
54C42×Dic7C2213yes—
55C42×Dic7C2211yescharacteristic
56C42×Dic7C2213yes—
57#89442C2213yes—
58#89441C2213yes—
59#89440C2213yes—
60#89440C2213yes—
61#89437C2213yes—
62#89437C2213yes—
63#89427C2213yes—
64#89426C2213yes—
65#89425C2213yes—
66#89424C2213yes—
67#89423C2213yes—
68#89423C2213yes—
69#89419C2213yes—
70#89419C2213yes—
71#89418C2213yes—
72#89418C2213yes—
73#36641—71nomaximal, Sylow
74C23×C4×C7C2311yescharacteristic
75C22×C22⋊D7C2311yescharacteristic
76C22×C22⋊D7C2311yescharacteristic
77C2×#1157—212no—
78C22×D28C2311yescharacteristic
79C22×C4×D7C2313yes—
80C22×C4×D7C2313yes—
81C22×C4×D7C2311yescharacteristic
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×C42×C7C2313yes—
90C2×C42×C7C2313yes—
91C2×C42×C7C2313yes—
92C2×C42×C7C2311yescharacteristic
93C2×C22⋊Dic7C2313yes—
94C2×C22⋊Dic7C2313yes—
95C2×(C2×D7)⋊C4C2313yes—
96C2×(C2×D7)⋊C4C2313yes—
97C2×(C2×D7)⋊C4C2313yes—
98C2×(C2×D7)⋊C4C2313yes—
99C2×(C2×D7)⋊C4C2313yes—
100C2×(C2×D7)⋊C4C2313yes—
101C2×C4⋊Dic7C2313yes—
102C2×C4⋊Dic7C2313yes—
103C2×Dic7⋊C4C2313yes—
104C2×Dic7⋊C4C2313yes—
105C2×Dic7⋊C4C2313yes—
106C2×Dic7⋊C4C2313yes—
107C2×Dic7⋊C4C2313yes—
108C2×Dic7⋊C4C2313yes—
109C2×C4×Dic7C2313yes—
110C2×C4×Dic7C2313yes—
111C2×C4×Dic7C2313yes—
112C2×C4×Dic7C2313yes—
113C2×C4×Dic7C2313yes—
114C2×C4×Dic7C2313yes—
115C2×C4×Dic7C2313yes—
116C2×C4×Dic7C2313yes—
117#6461—212no—
118#6442—212no—
119#6439—24no—
120#6435—212no—
121C42×D7—212no—
122C42×D7—24no—
123C42×D7—212no—
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—73no—
145#2852—73no—
146#2852—71no—
147#2852—71no—
148C4×#126—73no—
149C4×#126—73no—
150C4×#126—71no—
151C4×#126D711yescharacteristic, complemented
152#2297—73no—
153#2296—73no—
154C2×C43—71no—
155C24×C7C2411yescharacteristic
156C23×D7C2411yescharacteristic
157C23×D7C2411yescharacteristic
158C22×C4×C7—26no—
159C22×C4×C7C2411yescharacteristic
160C22×C4×C7C2413yes—
161C22×C4×C7C2413yes—
162C22×C4×C7C2413yes—
163C22×C4×C7C2413yes—
164C22×C4×C7C2411yescharacteristic
165C2×C22⋊D7—26no—
166C2×C22⋊D7—26no—
167C22×Dic7C2411yescharacteristic
168C22×Dic7C2413yes—
169C22×Dic7C2413yes—
170C22×Dic7C2413yes—
171C22×Dic7C2413yes—
172C22×Dic7C2411yescharacteristic
173#1157—416no—
174C2×D28—26no—
175C2×C4×D7—26no—
176C2×C4×D7—26no—
177C2×C4×D7—26no—
178C2×C4×D7—26no—
179C2×C4×D7—26no—
180C2×C4×D7—26no—
181C2×C4×D7—26no—
182C2×C4×D7#41112yes—
183C2×Dic14—26no—
184C7×C4⋊C4—26no—
185C7×C4⋊C4—26no—
186C7×C22⋊C4—26no—
187C7×C22⋊C4—26no—
188C42×C7—26no—
189C42×C7—26no—
190C42×C7—26no—
191C42×C7#4114yescomplemented
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—
198(C2×D7)⋊C4—26no—
199(C2×D7)⋊C4—26no—
200C4⋊Dic7—26no—
201C4⋊Dic7—26no—
202Dic7⋊C4—26no—
203Dic7⋊C4—26no—
204Dic7⋊C4—26no—
205Dic7⋊C4—26no—
206Dic7⋊C4—26no—
207Dic7⋊C4—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—71no—
224C22×C42—73no—
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#386—73no—
253#385—73no—
254#385—73no—
255#385—73no—
256#385—73no—
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⋊C4C2×D713yes—
265C4×C22⋊C4—73no—
266C4×C22⋊C4—73no—
267C4×C22⋊C4—73no—
268C4×C22⋊C4C2×D713yes—
269C43—73no—
270C43—73no—
271C43—71no—
272C43C2×D711yescharacteristic
273C23×C7—23no—
274C23×C7—21no—
275C23×C7—23no—
276C23×C7C2511yescharacteristic
277C22×D7—21no—
278C22×D7—23no—
279C22×D7—21no—
280C22×D7—23no—
281C22×D7—23no—
282C22×D7C2×#4116yes—
283C2×C4×C7—23no—
284C2×C4×C7—23no—
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—44no—
295C2×C4×C7C2×#4116yes—
296C2×C4×C7C2×#4116yes—
297C2×C4×C7C2×#4116yes—
298C22⋊D7—44no—
299C22⋊D7—44no—
300C2×Dic7—23no—
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×Dic7C2×#4116yes—
312C2×Dic7C2×#4116yes—
313C2×Dic7C2×#4116yes—
314D28—44no—
315C4×D7—224no—
316C4×D7—224no—
317C4×D7—44no—
318C4×D7#126116yescomplemented
319Dic14—44no—
320C2×#41—1412no—
321C22×Q8—71no—
322C22×D4—71no—
323C22×D4—71no—
324C22×D4—71no—
325C23×C4—71no—
326C23×C4—73no—
327C23×C4—73no—
328C23×C4—71no—
329C23×C4C22×D711yescharacteristic
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⋊C4—73no—
353C2×C22⋊C4C22×D713yes—
354C2×C22⋊C4C22×D713yes—
355C2×C42—73no—
356C2×C42—73no—
357C2×C42—73no—
358C2×C42—73no—
359C2×C42—73no—
360C2×C42—73no—
361C2×C42—73no—
362C2×C42—73no—
363C2×C42—1412no—
364C2×C42—1412no—
365C2×C42—144no—
366C2×C42C22×D713yes—
367C2×C42C22×D713yes—
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—41no—
387C22×C7—43no—
388C22×C7—43no—
389C22×C7C22×#4111yescharacteristic
390C22×C7C22×#4113yes—
391C22×C7C22×#4113yes—
392C2×D7—26no—
393C2×D7—26no—
394C2×D7—41no—
395C2×D7—43no—
396C2×D7—43no—
397C2×D7C2×#12614yes—
398C4×C7—26no—
399C4×C7—26no—
400C4×C7—41no—
401C4×C7—43no—
402C4×C7—43no—
403C4×C7C2×#12614yes—
404Dic7—26no—
405Dic7—26no—
406Dic7—41no—
407Dic7—43no—
408Dic7—43no—
409Dic7C2×#12614yes—
410C24—71no—
411C24—71no—
412C24C23×D711yescharacteristic
413#41—2816no—
414C2×Q8—146no—
415C2×D4—146no—
416C2×D4—146no—
417C2×D4—146no—
418C22×C4—26no—
419C22×C4—71no—
420C22×C4—712no—
421C22×C4—73no—
422C22×C4—73no—
423C22×C4—71no—
424C22×C4—73no—
425C22×C4—73no—
426C22×C4—146no—
427C22×C4—146no—
428C22×C4—146no—
429C22×C4—146no—
430C22×C4—146no—
431C22×C4—146no—
432C22×C4—146no—
433C22×C4C23×D711yescharacteristic
434C22×C4C23×D713yes—
435C22×C4C23×D713yes—
436C22×C4C23×D713yes—
437C22×C4C23×D713yes—
438C22×C4C23×D711yescharacteristic
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—146no—
452C22⋊C4—146no—
453C22⋊C4—146no—
454C22⋊C4—146no—
455C22⋊C4—146no—
456C22⋊C4—146no—
457C22⋊C4—146no—
458C22⋊C4—146no—
459C42—26no—
460C42—26no—
461C42—26no—
462C42—712no—
463C42—146no—
464C42—146no—
465C42—146no—
466C42—146no—
467C42—146no—
468C42—146no—
469C42—146no—
470C42#115714yescomplemented
471C2×C7—81no—
472C2×C7C22×#12611yescharacteristic
473C2×C7#344413yes—
474C2×C7#344413yes—
475D7—24no—
476D7—81no—
477C23—21no—
478C23—23no—
479C23—23no—
480C23—76no—
481C23—141no—
482C23—143no—
483C23—141no—
484C23—143no—
485C23—143no—
486C23C24×D711yescharacteristic
487Q8—284no—
488D4—284no—
489D4—284no—
490D4—284no—
491C2×C4—23no—
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—44no—
503C2×C4—76no—
504C2×C4—716no—
505C2×C4—76no—
506C2×C4—76no—
507C2×C4—1424no—
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×C4C2×#115716yes—
522C2×C4D7×#4116yes—
523C2×C4D7×#4116yes—
524C7#3664111yescharacteristic, complemented, Sylow
525C22—43no—
526C22—41no—
527C22—43no—
528C22—74no—
529C22—146no—
530C22—146no—
531C22—283no—
532C22—281no—
533C22—283no—
534C22C22×#115711yescharacteristic
535C22C2×D7×#4113yes—
536C22C2×D7×#4113yes—
537C4—26no—
538C4—26no—
539C4—43no—
540C4—41no—
541C4—43no—
542C4—74no—
543C4—146no—
544C4—146no—
545C4—283no—
546C4—281no—
547C4—283no—
548C4D7×#12614yes—
549C2—81no—
550C2—144no—
551C2—561no—
552C2#1174290413yes—
553C2C2×D7×#12611yescharacteristic
554C2#1174318713yes—
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC4×C7×#126C2
prime radicalC22×#1157C22
hypercenterC4×#126D7
hypocenterC7#36641
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
1. C4×C7×#126C2semidirect
2. #11740565C2semidirect
3. #11740549C2semidirect
4. #11733403C2semidirect
5. #11733265C2semidirect
6. #11732891C2semidirect
7. #11732736C2semidirect
8. #11731762C2semidirect
9. #11731738C2semidirect
10. #11731200C2semidirect
11. C4×#6461C2semidirect
13. C4×#6442C2semidirect
14. C43×D7C2semidirect
15. C4×#6439C2semidirect
151. C4×#126D7semidirect
191. C42×C7#41semidirect
215. C4×Dic7#41semidirect
318. C4×D7#126semidirect
470. C42#1157semidirect
524. C7#36641semidirect

Maximal subgroups

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

subgroupindex
C4×C7×#1262
#117405652
#117405492
#117334032
#117332652
#117328912
#117327362
#117317622
#117317382
#117312002
C4×#64612
#117310082
C4×#64422
C43×D72
C4×#64392
#366417