Finite Group Databasebeta

← D3×#6502 #13059927

Subgroups — D3×#6502 #13059927

Order 1344.

852 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C7×D4C211yesmaximal, characteristic, complemented
2C2×D3×C22⋊D7C211yesmaximal, characteristic, complemented
3C2×D3×C22⋊D7C211yesmaximal, characteristic, complemented
4C22×D3×Dic7C211yesmaximal, characteristic, complemented
5#10621422C211yesmaximal, characteristic, complemented
6C3×#6502C211yesmaximal, characteristic, complemented
7#10621133C211yesmaximal, characteristic, complemented
8#10621128C211yesmaximal, characteristic, complemented
9#10621127C211yesmaximal, characteristic, complemented
10#10621120C211yesmaximal, characteristic, complemented
11D3×C22⋊Dic7C211yesmaximal, characteristic, complemented
12D3×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
13#10621015C211yesmaximal, characteristic, complemented
14#10620978C211yesmaximal, characteristic, complemented
15D3×Dic7⋊C4C211yesmaximal, characteristic, complemented
16C2×#6502—31nomaximal, Hall
17C23×D3×C7C2211yescharacteristic
18C23×D3×C7C2211yescharacteristic
19C22×D3×D7C2211yescharacteristic
20C2×C3×C7×D4C2211yescharacteristic, complemented
21C2×#4268C2211yescharacteristic, complemented
22C2×#4268C2211yescharacteristic, complemented
23C22×Dic21C2211yescharacteristic, complemented
24C2×C7×#67C2211yescharacteristic, complemented
25C2×C7×#67C2211yescharacteristic, complemented
26D3×C7×D4—24no—
27C2×C7×D12C2211yescharacteristic, complemented
28C2×C4×D3×C7C2211yescharacteristic
29C2×C3×C22⋊D7C2211yescharacteristic, complemented
30C2×C3×C22⋊D7C2211yescharacteristic, complemented
31C22×C3×Dic7C2211yescharacteristic, complemented
32D3×C22⋊D7—24no—
33D3×C22⋊D7—24no—
34C2×#4247C2211yescharacteristic, complemented
35C2×#4247C2211yescharacteristic, complemented
36C2×#4245C2211yescharacteristic, complemented
37C2×#4245C2211yescharacteristic, complemented
38C2×D3×Dic7—24no—
39C2×D3×Dic7C2211yescharacteristic
40C2×D3×Dic7C2211yescharacteristic
41C2×D3×Dic7C2211yescharacteristic
42C2×D3×Dic7C2211yescharacteristic, complemented
43C2×D3×Dic7C2211yescharacteristic, complemented
44#66636C2211yescharacteristic, complemented
45#66631C2211yescharacteristic, complemented
46#66629C2211yescharacteristic, complemented
47C3×C22⋊Dic7C2211yescharacteristic, complemented
48C3×(C2×D7)⋊C4C2211yescharacteristic, complemented
49C3×Dic7⋊C4C2211yescharacteristic, complemented
50#66577C2211yescharacteristic, complemented
51Dic7⋊Dic3C2211yescharacteristic, complemented
52#66575C2211yescharacteristic, complemented
53(C2×D3)⋊Dic7C2211yescharacteristic, complemented
54(C2×D3)⋊Dic7C2211yescharacteristic, complemented
55(C2×D7)⋊Dic3C2211yescharacteristic, complemented
56C22×C7×D4—31no—
57C22×C22⋊D7—31no—
58C22×C22⋊D7—31no—
59C23×Dic7—31no—
60C2×C22⋊Dic7—31no—
61#6502—31no—
62#6502—31no—
63#6502—31no—
64#6502—31no—
65#6502—31no—
66#6502—31no—
67#6502—31no—
68#6502D311yescharacteristic, direct product factor
69C2×(C2×D7)⋊C4—31no—
70C2×Dic7⋊C4—31no—
71D3×#121—71nomaximal, Hall
72C23×C3×C7C2311yescharacteristic
73C23×C3×C7C2311yescharacteristic
74C22×D21C2311yescharacteristic
75C22×D3×C7—22no—
76C22×D3×C7—22no—
77C22×D3×C7—22no—
78C22×D3×C7—22no—
79C22×D3×C7—22no—
80C22×D3×C7D414yescomplemented
81C22×D3×C7C2311yescharacteristic
82C22×D3×C7C2311yescharacteristic
83C22×D3×C7C2311yescharacteristic
84C22×C3×D7C2311yescharacteristic
85C2×D3×D7—22no—
86C2×D3×D7—22no—
87C2×D3×D7—22no—
88C3×C7×D4—22no—
89C2×C3×C4×C7C2311yescharacteristic
90#4268—22no—
91#4268—22no—
92C2×Dic21—22no—
93C2×Dic21C2311yescharacteristic
94C2×Dic21C2311yescharacteristic
95C2×Dic21C2311yescharacteristic
96C7×#67—22no—
97C7×#67—22no—
98C2×C7×Dic3C2311yescharacteristic
99C7×D12—22no—
100C4×D3×C7—22no—
101C3×C22⋊D7—22no—
102C3×C22⋊D7—22no—
103C2×C3×Dic7—22no—
104C2×C3×Dic7C2311yescharacteristic
105C2×C3×Dic7C2311yescharacteristic
106C2×C3×Dic7C2311yescharacteristic
107#4247—22no—
108#4247—22no—
109#4245—22no—
110#4245—22no—
111D3×Dic7—22no—
112D3×Dic7—22no—
113D3×Dic7—22no—
114D3×Dic7—22no—
115D3×Dic7D414yescomplemented
116C24×C7—31no—
117C24×C7—31no—
118C23×D7—31no—
119C2×C7×D4—31no—
120C2×C7×D4—31no—
121C2×C7×D4—31no—
122C2×C7×D4—64no—
123C2×C7×D4C2×D311yescharacteristic, complemented
124C22×C4×C7—31no—
125C2×C22⋊D7—31no—
126C2×C22⋊D7—31no—
127C2×C22⋊D7—31no—
128C2×C22⋊D7—31no—
129C2×C22⋊D7—31no—
130C2×C22⋊D7—31no—
131C2×C22⋊D7—64no—
132C2×C22⋊D7—64no—
133C2×C22⋊D7C2×D311yescharacteristic, complemented
134C2×C22⋊D7C2×D311yescharacteristic, complemented
135C22×Dic7—31no—
136C22×Dic7—31no—
137C22×Dic7—31no—
138C22×Dic7—31no—
139C22×Dic7—31no—
140C22×Dic7—31no—
141C22×Dic7—64no—
142C22×Dic7C2×D311yescharacteristic, complemented
143C22⋊Dic7—31no—
144C22⋊Dic7—31no—
145C22⋊Dic7—31no—
146C22⋊Dic7C2×D311yescharacteristic, complemented
147(C2×D7)⋊C4—31no—
148(C2×D7)⋊C4—31no—
149(C2×D7)⋊C4—31no—
150(C2×D7)⋊C4C2×D311yescharacteristic, complemented
151Dic7⋊C4—31no—
152Dic7⋊C4—31no—
153Dic7⋊C4—31no—
154Dic7⋊C4C2×D311yescharacteristic, complemented
155C2×D3×D4—71no—
156C2×D3×D4—71no—
157C2×D3×D4D711yescharacteristic, complemented
158C22×C4×D3—71no—
159C3×#121—71no—
160#939—71no—
161#939—71no—
162#938—71no—
163#930—71no—
164#895—71no—
165D3×C4⋊C4—71no—
166#884—71no—
167#884—71no—
168D3×C22⋊C4—71no—
169D3×C22⋊C4—71no—
170C22×C3×C7—21no—
171C22×C3×C7—21no—
172C22×C3×C7—21no—
173C22×C3×C7—21no—
174C22×C3×C7—21no—
175C22×C3×C7C2×D412yescomplemented
176C22×C3×C7C2411yescharacteristic
177C2×D21—21no—
178C2×D21—21no—
179C2×D21—21no—
180C2×D3×C7—21no—
181C2×D3×C7—21no—
182C2×D3×C7—28no—
183C2×D3×C7—21no—
184C2×D3×C7—21no—
185C2×D3×C7—21no—
186C2×D3×C7—44no—
187C2×D3×C7C2×D412yes—
188C2×D3×C7C2×D412yes—
189C2×D3×C7C2×D412yescomplemented
190C2×D3×C7#4112yes—
191C2×C3×D7—21no—
192C2×C3×D7—21no—
193C2×C3×D7—21no—
194D3×D7—44no—
195C3×C4×C7—21no—
196Dic21—21no—
197Dic21—21no—
198Dic21C2×D412yescomplemented
199C3×Dic7—21no—
200C3×Dic7—21no—
201C3×Dic7C2×D412yescomplemented
202C7×Dic3—21no—
203C2×#121—211noSylow
204C23×C7—31no—
205C23×C7—34no—
206C23×C7—31no—
207C23×C7—31no—
208C23×C7—62no—
209C23×C7—62no—
210C23×C7—62no—
211C23×C7—62no—
212C23×C7—62no—
213C23×C7C22×D311yescharacteristic
214C23×C7C22×D311yescharacteristic
215C22×D7—31no—
216C22×D7—62no—
217C22×D7—62no—
218C22×D7—62no—
219C22×D7C22×D311yescharacteristic
220C7×D4—22no—
221C7×D4—62no—
222C7×D4—62no—
223C7×D4—62no—
224C2×C4×C7—31no—
225C2×C4×C7—62no—
226C2×C4×C7C22×D311yescharacteristic
227C22⋊D7—22no—
228C22⋊D7—22no—
229C22⋊D7—62no—
230C22⋊D7—62no—
231C22⋊D7—62no—
232C22⋊D7—62no—
233C22⋊D7—62no—
234C22⋊D7—62no—
235C2×Dic7—22no—
236C2×Dic7—31no—
237C2×Dic7—34no—
238C2×Dic7—31no—
239C2×Dic7—31no—
240C2×Dic7—62no—
241C2×Dic7—62no—
242C2×Dic7—62no—
243C2×Dic7—62no—
244C2×Dic7—62no—
245C2×Dic7C22×D311yescharacteristic
246C2×Dic7C22×D311yescharacteristic
247C2×Dic7C22×D311yescharacteristic
248C23×D3—71no—
249C23×D3C2×D711yescharacteristic
250C23×D3C2×D711yescharacteristic
251C2×C3×D4—71no—
252C2×C3×D4—71no—
253C2×C3×D4C2×D711yescharacteristic, complemented
254C22×C3×C4—71no—
255C2×#67—71no—
256C2×#67—71no—
257C2×#67—71no—
258C2×#67—71no—
259C2×#67C2×D711yescharacteristic, complemented
260C2×#67C2×D711yescharacteristic, complemented
261C22×Dic3—71no—
262D3×D4—24no—
263D3×D4—144no—
264D3×D4—144no—
265C2×D12—71no—
266C2×D12—71no—
267C2×D12C2×D711yescharacteristic, complemented
268C2×C4×D3—71no—
269C2×C4×D3—71no—
270C2×C4×D3—71no—
271C2×C4×D3—71no—
272C2×C4×D3—71no—
273C2×C4×D3—144no—
274C2×C4×D3C2×D711yescharacteristic
275C3×C4⋊C4—71no—
276C3×C22⋊C4—71no—
277C3×C22⋊C4—71no—
278#217—71no—
279#217—71no—
280(C2×D3)⋊C4—71no—
281(C2×D3)⋊C4—71no—
282(C2×D3)⋊C4—71no—
283(C2×D3)⋊C4—71no—
284C4⋊Dic3—71no—
285Dic3⋊C4—71no—
286Dic3⋊C4—71no—
287C2×C3×C7—22no—
288C2×C3×C7—41no—
289C2×C3×C7C22×D411yescharacteristic
290C2×C3×C7C22×D411yescharacteristic
291C2×C3×C7C2×#4111yescharacteristic
292D21—41no—
293C3×D7—41no—
294D3×C7—22no—
295D3×C7—41no—
296D3×C7#12114yescomplemented
297C22×D4—31no—
298C22×D4—211no—
299C22×D4—211no—
300C23×C4—211no—
301#121—71no—
302#121—211no—
303#121—211no—
304#121—211no—
305#121—211no—
306#121—211no—
307#121—211no—
308#121—211no—
309C2×C4⋊C4—211no—
310C2×C22⋊C4—211no—
311C2×C22⋊C4—211no—
312C22×C7—21no—
313C22×C7—21no—
314C22×C7—21no—
315C22×C7—21no—
316C22×C7—21no—
317C22×C7—32no—
318C22×C7—32no—
319C22×C7—32no—
320C22×C7—32no—
321C22×C7—68no—
322C22×C7—61no—
323C22×C7—61no—
324C22×C7—61no—
325C22×C7—61no—
326C22×C7—61no—
327C22×C7—124no—
328C22×C7D3×D412yescomplemented
329C22×C7C23×D311yescharacteristic
330C2×D7—21no—
331C2×D7—21no—
332C2×D7—21no—
333C2×D7—61no—
334C2×D7—61no—
335C2×D7—61no—
336C2×D7—124no—
337C4×C7—21no—
338C4×C7—61no—
339Dic7—21no—
340Dic7—21no—
341Dic7—32no—
342Dic7—61no—
343Dic7—61no—
344Dic7D3×D412yescomplemented
345C23×C3—71no—
346C23×C3C22×D711yescharacteristic
347C23×C3C22×D711yescharacteristic
348C22×D3—22no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—71no—
354C22×D3—142no—
355C22×D3—142no—
356C22×D3—142no—
357C22×D3C22⋊D714yescomplemented
358C22×D3C22×D711yescharacteristic
359C22×D3C22×D711yescharacteristic
360C22×D3C22×D711yescharacteristic
361C3×D4—22no—
362C3×D4—142no—
363C3×D4—142no—
364C2×C3×C4—71no—
365C2×C3×C4—71no—
366C2×C3×C4—71no—
367C2×C3×C4—142no—
368C2×C3×C4C22×D711yescharacteristic
369#67—22no—
370#67—22no—
371#67—142no—
372#67—142no—
373#67—142no—
374#67—142no—
375C2×Dic3—71no—
376C2×Dic3—71no—
377C2×Dic3—71no—
378C2×Dic3—142no—
379C2×Dic3C22×D711yescharacteristic
380D12—22no—
381D12—142no—
382D12—142no—
383C4×D3—22no—
384C4×D3—74no—
385C4×D3—142no—
386C4×D3—142no—
387C4×D3—142no—
388C4×D3—142no—
389C3×C7C2×#12111yescharacteristic, complemented, Hall
390C24—31no—
391C24—31no—
392C24—211no—
393C2×D4—31no—
394C2×D4—31no—
395C2×D4—31no—
396C2×D4—64no—
397C2×D4—71no—
398C2×D4—71no—
399C2×D4—211no—
400C2×D4—211no—
401C2×D4—211no—
402C2×D4—211no—
403C2×D4—211no—
404C2×D4—211no—
405C2×D4—424no—
406C2×D4—424no—
407C2×D4D3×D711yescharacteristic, complemented
408C22×C4—31no—
409C22×C4—71no—
410C22×C4—211no—
411C22×C4—211no—
412C22×C4—211no—
413C22×C4—211no—
414C22×C4—211no—
415C22×C4—211no—
416C22×C4—424no—
417C4⋊C4—71no—
418C4⋊C4—211no—
419C4⋊C4—211no—
420C4⋊C4—211no—
421C22⋊C4—71no—
422C22⋊C4—71no—
423C22⋊C4—211no—
424C22⋊C4—211no—
425C22⋊C4—211no—
426C22⋊C4—211no—
427C22⋊C4—211no—
428C22⋊C4—211no—
429C2×C7—22no—
430C2×C7—34no—
431C2×C7—41no—
432C2×C7—62no—
433C2×C7—121no—
434C2×C7C2×D3×D411yescharacteristic
435C2×C7C2×D3×D411yescharacteristic
436C2×C7D3×#4111yescharacteristic
437D7—41no—
438D7—121no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—141no—
445C22×C3—141no—
446C22×C3—141no—
447C22×C3C2×C22⋊D712yescomplemented
448C22×C3C23×D711yescharacteristic
449C2×D3—21no—
450C2×D3—21no—
451C2×D3—28no—
452C2×D3—21no—
453C2×D3—21no—
454C2×D3—21no—
455C2×D3—44no—
456C2×D3—141no—
457C2×D3—141no—
458C2×D3—141no—
459C2×D3—284no—
460C2×D3D4×D712yes—
461C2×D3#115912yes—
462C2×D3C2×C22⋊D712yes—
463C2×D3C2×C22⋊D712yescomplemented
464C3×C4—21no—
465C3×C4—72no—
466C3×C4—141no—
467C3×C4—141no—
468Dic3—21no—
469Dic3—72no—
470Dic3—141no—
471Dic3—141no—
472C23—31no—
473C23—34no—
474C23—31no—
475C23—31no—
476C23—62no—
477C23—62no—
478C23—62no—
479C23—62no—
480C23—62no—
481C23—71no—
482C23—211no—
483C23—422no—
484C23—422no—
485C23—422no—
486C23C2×D3×D711yescharacteristic
487C23C2×D3×D711yescharacteristic
488D4—22no—
489D4—62no—
490D4—62no—
491D4—62no—
492D4—142no—
493D4—142no—
494D4—422no—
495D4—422no—
496D4—422no—
497D4—422no—
498D4—422no—
499D4—422no—
500C2×C4—31no—
501C2×C4—62no—
502C2×C4—71no—
503C2×C4—71no—
504C2×C4—71no—
505C2×C4—142no—
506C2×C4—214no—
507C2×C4—211no—
508C2×C4—211no—
509C2×C4—211no—
510C2×C4—422no—
511C2×C4—422no—
512C2×C4—422no—
513C2×C4—422no—
514C2×C4—422no—
515C2×C4C2×D3×D711yescharacteristic
516C7D3×#12111yescharacteristic, complemented, Sylow
517C2×C3—22no—
518C2×C3—41no—
519C2×C3—281no—
520C2×C3C2×D4×D711yescharacteristic
521C2×C3C2×#115911yescharacteristic
522C2×C3C22×C22⋊D711yescharacteristic
523D3—22no—
524D3—41no—
525D3—281no—
526D3#650214yesdirect product factor
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—32no—
533C22—32no—
534C22—32no—
535C22—32no—
536C22—68no—
537C22—61no—
538C22—61no—
539C22—61no—
540C22—61no—
541C22—61no—
542C22—124no—
543C22—141no—
544C22—141no—
545C22—141no—
546C22—421no—
547C22—421no—
548C22—421no—
549C22—844no—
550C22D3×C22⋊D712yescomplemented
551C22C22×D3×D711yescharacteristic
552C4—21no—
553C4—61no—
554C4—72no—
555C4—141no—
556C4—141no—
557C4—212no—
558C4—421no—
559C4—421no—
560C3C2×#650211yescharacteristic, complemented, Sylow
561C2—22no—
562C2—34no—
563C2—41no—
564C2—62no—
565C2—121no—
566C2—281no—
567C2—841no—
568C2D3×D4×D711yescharacteristic
569C2D3×#115911yescharacteristic
570C2C2×D3×C22⋊D711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC2×C3×C7×D4C22
hypercenterC2×D4D3×D7
hypocenterC3×C7C2×#121
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D3×C7×D4C2semidirect
2. C2×D3×C22⋊D7C2semidirect
3. C2×D3×C22⋊D7C2semidirect
4. C22×D3×Dic7C2semidirect
5. #10621422C2semidirect
6. C3×#6502C2semidirect
7. #10621133C2semidirect
8. #10621128C2semidirect
9. #10621127C2semidirect
10. #10621120C2semidirect
11. D3×C22⋊Dic7C2semidirect
12. D3×(C2×D7)⋊C4C2semidirect
13. #10621015C2semidirect
14. #10620978C2semidirect
15. D3×Dic7⋊C4C2semidirect
20. C2×C3×C7×D4C22semidirect
21. C2×#4268C22semidirect
22. C2×#4268C22semidirect
23. C22×Dic21C22semidirect
24. C2×C7×#67C22semidirect
25. C2×C7×#67C22semidirect
27. C2×C7×D12C22semidirect
29. C2×C3×C22⋊D7C22semidirect
30. C2×C3×C22⋊D7C22semidirect
31. C22×C3×Dic7C22semidirect
34. C2×#4247C22semidirect
35. C2×#4247C22semidirect
36. C2×#4245C22semidirect
37. C2×#4245C22semidirect
42. C2×D3×Dic7C22semidirect
43. C2×D3×Dic7C22semidirect
44. #66636C22semidirect
45. #66631C22semidirect
46. #66629C22semidirect
47. C3×C22⋊Dic7C22semidirect
48. C3×(C2×D7)⋊C4C22semidirect
49. C3×Dic7⋊C4C22semidirect
50. #66577C22semidirect
51. Dic7⋊Dic3C22semidirect
52. #66575C22semidirect
53. (C2×D3)⋊Dic7C22semidirect
54. (C2×D3)⋊Dic7C22semidirect
55. (C2×D7)⋊Dic3C22semidirect
68. #6502D3direct (N × H)
80. C22×D3×C7D4semidirect
115. D3×Dic7D4semidirect
123. C2×C7×D4C2×D3semidirect
133. C2×C22⋊D7C2×D3semidirect
134. C2×C22⋊D7C2×D3semidirect
142. C22×Dic7C2×D3semidirect
146. C22⋊Dic7C2×D3semidirect
150. (C2×D7)⋊C4C2×D3semidirect
154. Dic7⋊C4C2×D3semidirect
157. C2×D3×D4D7semidirect
175. C22×C3×C7C2×D4semidirect
189. C2×D3×C7C2×D4semidirect
198. Dic21C2×D4semidirect
201. C3×Dic7C2×D4semidirect
253. C2×C3×D4C2×D7semidirect
259. C2×#67C2×D7semidirect
260. C2×#67C2×D7semidirect
267. C2×D12C2×D7semidirect
296. D3×C7#121semidirect
328. C22×C7D3×D4semidirect
344. Dic7D3×D4semidirect
357. C22×D3C22⋊D7semidirect
389. C3×C7C2×#121semidirect
407. C2×D4D3×D7semidirect
447. C22×C3C2×C22⋊D7semidirect
463. C2×D3C2×C22⋊D7semidirect
516. C7D3×#121semidirect
526. D3#6502direct (N × H)
550. C22D3×C22⋊D7semidirect
560. C3C2×#6502semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C7×D42
C2×D3×C22⋊D72
C22×D3×Dic72
#106214222
C3×#65022
#106211332
#106211282
#106211272
#106211202
D3×C22⋊Dic72
D3×(C2×D7)⋊C42
#106210152
#106209782
D3×Dic7⋊C42
C2×#65023
D3×#1217