Finite Group Databasebeta

← C3×D7×#833 #72246815

Subgroups — C3×D7×#833 #72246815

Order 4032.

980 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#10620672C211yesmaximal, characteristic, complemented
2C3×#10620493C212yesmaximal, complemented
3C3×C7×#833C211yesmaximal, characteristic, complemented
4C3×D7×#208C212yesmaximal, complemented
5C2×C32×D4×D7C211yesmaximal, characteristic
6C3×D7×#100—31nomaximal
7D7×#833C311yesmaximal, characteristic, direct product factor
8C23×C32×D7C412yes—
9C2×C32×C7×D4C2211yescharacteristic
10C2×C32×C22⋊D7C412yes—
11C32×D4×D7—22no—
12C32×D4×D7—22no—
13C2×C32×D28C2211yescharacteristic
14C2×C32×C4×D7C2211yescharacteristic
15C3×#66627C2212yescomplemented
16C3×C7×#208C2212yescomplemented
17C3×#66557—22no—
18C3×D7×C3⋊C8—22no—
19C2×C3×D4×D7—21no—
20C2×C3×D4×D7D311yescharacteristic
21C2×C3×D4×D7C2×C311yescharacteristic
22C3×D7×M16—32no—
23D7×#208C2×C312yescomplemented
24C3×C7×#100—31no—
25#10620672C2×C311yescharacteristic, complemented
26C7×#833C2×C311yescharacteristic, complemented
27C3×#6407—31no—
28C3×#6397—32no—
29#10620493C2×C312yescomplemented
30C2×C3×#833—71nomaximal, Hall
31C23×C32×C7C2×C412yes—
32C22×C32×D7—22no—
33C22×C32×D7—22no—
34C22×C32×D7—44no—
35C22×C32×D7C2×C411yescharacteristic
36C22×C32×D7C2×C412yes—
37C32×C7×D4—22no—
38C2×C32×C4×C7C2311yescharacteristic
39C32×C22⋊D7—24no—
40C2×C32×Dic7C2×C411yescharacteristic
41C32×D28—22no—
42C32×C4×D7D412yes—
43C32×C4×D7D412yes—
44C3×C3⋊(C7⋊C8)—22no—
45C3×C7×C3⋊C8—22no—
46D7×#100—31noHall
47C23×C3×D7—22no—
48C23×C3×D7Dic312yes—
49C23×C3×D7C3×C412yes—
50C2×C3×C7×D4—21no—
51C2×C3×C7×D4C2×D311yescharacteristic
52C2×C3×C7×D4C22×C311yescharacteristic
53C2×C3×C22⋊D7—22no—
54C2×C3×C22⋊D7Dic312yes—
55C2×C3×C22⋊D7C3×C412yes—
56C3×D4×D7—22no—
57C3×D4×D7—22no—
58C3×D4×D7—22no—
59C3×D4×D7—22no—
60C3×D4×D7—22no—
61C3×D4×D7—22no—
62C3×D4×D7—22no—
63C3×D4×D7—22no—
64C2×C3×D28—21no—
65C2×C3×D28C2×D311yescharacteristic
66C2×C3×D28C22×C311yescharacteristic
67C2×C3×C4×D7—21no—
68C2×C3×C4×D7C2×D311yescharacteristic
69C2×C3×C4×D7C22×C311yescharacteristic
70C3×C7×M16—32no—
71#66627C22×C312yescomplemented
72C7×#208C22×C312yescomplemented
73C3×#1136—32no—
74C3×#1131—62no—
75C3×C8×D7—62no—
76#66557—22no—
77D7×C3⋊C8—22no—
78C22×C32×D4—71no—
79C2×C3×#208—72no—
80C3×#833—71no—
81C3×#833—72no—
82C3×#833D711yescharacteristic, direct product factor
83C22×C32×C7—22no—
84C22×C32×C7—42no—
85C22×C32×C7C22×C411yescharacteristic
86C2×C32×D7—22no—
87C2×C32×D7—22no—
88C2×C32×D7—44no—
89C2×C32×D7—44no—
90C2×C32×D7—42no—
91C2×C32×D7C22⋊C411yescharacteristic
92C2×C32×D7C22⋊C411yescharacteristic
93C32×C4×C7C2×D412yes—
94C32×Dic7C22⋊C412yes—
95C2×D4×D7C3×D311yescharacteristic
96D7×M16—32no—
97C7×#100—31no—
98#6407—31no—
99#6397—32no—
100C2×C3×#100—211no—
101C2×#833—71no—
102C23×C3×C7—22no—
103C23×C3×C7C2×Dic312yes—
104C23×C3×C7C2×C3×C412yes—
105C22×C3×D7—22no—
106C22×C3×D7—22no—
107C22×C3×D7—22no—
108C22×C3×D7—22no—
109C22×C3×D7—22no—
110C22×C3×D7—22no—
111C22×C3×D7—22no—
112C22×C3×D7—22no—
113C22×C3×D7—21no—
114C22×C3×D7—22no—
115C22×C3×D7—44no—
116C22×C3×D7—44no—
117C22×C3×D7—44no—
118C22×C3×D7—44no—
119C22×C3×D7C2×Dic311yescharacteristic
120C22×C3×D7C2×Dic312yes—
121C22×C3×D7C2×C3×C411yescharacteristic
122C22×C3×D7C2×C3×C412yes—
123C3×C7×D4—22no—
124C3×C7×D4—22no—
125C3×C7×D4—22no—
126C3×C7×D4—22no—
127C2×C3×C4×C7—21no—
128C2×C3×C4×C7C22×D311yescharacteristic
129C2×C3×C4×C7C23×C311yescharacteristic
130C3×C22⋊D7—24no—
131C3×C22⋊D7—24no—
132C3×C22⋊D7—24no—
133C3×C22⋊D7—24no—
134C2×C3×Dic7—21no—
135C2×C3×Dic7C2×Dic311yescharacteristic
136C2×C3×Dic7C2×C3×C411yescharacteristic
137C3×D28—22no—
138C3×D28—22no—
139C3×D28—22no—
140C3×D28—22no—
141C3×C4×D7—22no—
142C3×C4×D7—22no—
143C3×C4×D7#6712yes—
144C3×C4×D7#6712yes—
145C3×C4×D7C3×D412yes—
146C3×C4×D7C3×D412yes—
147C3×C7×C8—62no—
148C3⋊(C7⋊C8)—22no—
149C3×C7⋊C8—62no—
150C7×C3⋊C8—22no—
151C24×C32—72no—
152C2×C32×D4—72no—
153C2×C32×D4—71no—
154C2×C32×D4—142no—
155C2×C32×D4—142no—
156C2×C32×D4C2×D711yescharacteristic
157C22×C32×C4—71no—
158C3×#208—72no—
159C3×#208—142no—
160C3×#208C2×D712yescomplemented
161C2×C3×C3⋊C8—142no—
162C2×C32×C7—21no—
163C2×C32×C7—42no—
164C2×C32×C7C2×C22⋊C411yescharacteristic
165C32×D7—21no—
166C32×D7—42no—
167C32×D7#10012yescomplemented
168C23×D7C3×Dic312yes—
169C2×C7×D4C2×C3×D311yescharacteristic
170C2×C22⋊D7C3×Dic312yes—
171D4×D7—22no—
172D4×D7—22no—
173C2×D28C2×C3×D311yescharacteristic
174C2×C4×D7C2×C3×D311yescharacteristic
175C7×M16—32no—
176#1136—32no—
177#1131—62no—
178C8×D7—62no—
179C22×C3×D4—71no—
180C22×C3×D4—71no—
181C22×C3×D4—141no—
182C2×C3×M16—212no—
183C2×#208—72no—
184C3×#100—31no—
185C3×#100—212no—
186C3×#100—211no—
187#833—71no—
188#833—72no—
189#833C3×D711yescharacteristic, direct product factor
190C22×C3×C7—22no—
191C22×C3×C7—22no—
192C22×C3×C7—22no—
193C22×C3×C7—22no—
194C22×C3×C7—21no—
195C22×C3×C7—42no—
196C22×C3×C7—42no—
197C22×C3×C7—42no—
198C22×C3×C7—42no—
199C22×C3×C7C22×Dic311yescharacteristic
200C22×C3×C7C22×C3×C411yescharacteristic
201C2×C3×D7—22no—
202C2×C3×D7—22no—
203C2×C3×D7—22no—
204C2×C3×D7—22no—
205C2×C3×D7—22no—
206C2×C3×D7—22no—
207C2×C3×D7—22no—
208C2×C3×D7—22no—
209C2×C3×D7—21no—
210C2×C3×D7—21no—
211C2×C3×D7—44no—
212C2×C3×D7—44no—
213C2×C3×D7—44no—
214C2×C3×D7—44no—
215C2×C3×D7—44no—
216C2×C3×D7—44no—
217C2×C3×D7—44no—
218C2×C3×D7—44no—
219C2×C3×D7—42no—
220C2×C3×D7—42no—
221C2×C3×D7—42no—
222C2×C3×D7—42no—
223C2×C3×D7#21711yescharacteristic
224C2×C3×D7#21711yescharacteristic
225C2×C3×D7C3×C22⋊C411yescharacteristic
226C2×C3×D7C3×C22⋊C411yescharacteristic
227C3×C4×C7—22no—
228C3×C4×C7C2×#6712yes—
229C3×C4×C7C2×C3×D412yes—
230C3×Dic7—22no—
231C3×Dic7#21712yes—
232C3×Dic7C3×C22⋊C412yes—
233C23×C32—71no—
234C23×C32—72no—
235C23×C32—142no—
236C23×C32—142no—
237C23×C32—284no—
238C23×C32C4×D712yes—
239C32×D4—22no—
240C32×D4—144no—
241C32×D4—142no—
242C2×C32×C4—71no—
243C2×C32×C4—72no—
244C2×C32×C4—72no—
245C2×C32×C4C22×D711yescharacteristic
246C3×C3⋊C8—22no—
247C3×C3⋊C8—142no—
248C2×#100—211noSylow
249C32×C7C2×#10011yescharacteristic, complemented, Hall
250C23×C7C2×C3×Dic312yes—
251C22×D7—22no—
252C22×D7—22no—
253C22×D7—44no—
254C22×D7C2×C3×Dic311yescharacteristic
255C22×D7C2×C3×Dic312yes—
256C7×D4—22no—
257C2×C4×C7C22×C3×D311yescharacteristic
258C22⋊D7—24no—
259C2×Dic7C2×C3×Dic311yescharacteristic
260D28—22no—
261C4×D7C3×#6712yes—
262C4×D7C3×#6712yes—
263C7×C8—62no—
264C7⋊C8—62no—
265C24×C3—72no—
266C24×C3—72no—
267C24×C3—142no—
268C2×C3×D4—21no—
269C2×C3×D4—72no—
270C2×C3×D4—72no—
271C2×C3×D4—71no—
272C2×C3×D4—71no—
273C2×C3×D4—141no—
274C2×C3×D4—142no—
275C2×C3×D4—142no—
276C2×C3×D4—142no—
277C2×C3×D4—142no—
278C2×C3×D4—142no—
279C2×C3×D4—142no—
280C2×C3×D4—142no—
281C2×C3×D4—142no—
282C2×C3×D4—142no—
283C2×C3×D4D3×D711yescharacteristic
284C2×C3×D4C2×C3×D711yescharacteristic
285C22×C3×C4—71no—
286C22×C3×C4—71no—
287C22×C3×C4—141no—
288C3×M16—32no—
289C3×M16—212no—
290C3×M16—422no—
291C2×C3×C8—422no—
292#208—72no—
293#208—142no—
294#208C2×C3×D712yescomplemented
295C2×C3⋊C8—142no—
296C2×C3×C7—21no—
297C2×C3×C7—21no—
298C2×C3×C7—21no—
299C2×C3×C7—21no—
300C2×C3×C7—21no—
301C2×C3×C7—42no—
302C2×C3×C7—42no—
303C2×C3×C7—42no—
304C2×C3×C7—42no—
305C2×C3×C7C2×#21711yescharacteristic
306C2×C3×C7C2×C3×C22⋊C411yescharacteristic
307C3×D7—21no—
308C3×D7—21no—
309C3×D7—21no—
310C3×D7—21no—
311C3×D7—22no—
312C3×D7—42no—
313C3×D7—42no—
314C3×D7—42no—
315C3×D7—42no—
316C3×D7#83312yesdirect product factor
317C3×D7C3×#10012yescomplemented
318C22×C32—22no—
319C22×C32—42no—
320C22×C32—71no—
321C22×C32—71no—
322C22×C32—142no—
323C22×C32—142no—
324C22×C32—282no—
325C22×C32—284no—
326C22×C32—284no—
327C22×C32C2×C4×D711yescharacteristic
328C32×C4—72no—
329C32×C4D4×D712yes—
330C22×D4—71no—
331C2×M16—212no—
332#100—31no—
333#100—212no—
334#100—211no—
335C22×C7—22no—
336C22×C7—42no—
337C22×C7C22×C3×Dic311yescharacteristic
338C2×D7—22no—
339C2×D7—22no—
340C2×D7—44no—
341C2×D7—44no—
342C2×D7—42no—
343C2×D7C3×#21711yescharacteristic
344C2×D7C3×#21711yescharacteristic
345C4×C7C2×C3×#6712yes—
346Dic7C3×#21712yes—
347C23×C3—22no—
348C23×C3—71no—
349C23×C3—71no—
350C23×C3—72no—
351C23×C3—72no—
352C23×C3—141no—
353C23×C3—142no—
354C23×C3—142no—
355C23×C3—142no—
356C23×C3—142no—
357C23×C3—142no—
358C23×C3—142no—
359C23×C3—142no—
360C23×C3—142no—
361C23×C3—142no—
362C23×C3—284no—
363C23×C3—284no—
364C23×C3—284no—
365C23×C3—284no—
366C23×C3Dic3×D712yes—
367C23×C3C3×C4×D712yes—
368C3×D4—22no—
369C3×D4—22no—
370C3×D4—22no—
371C3×D4—22no—
372C3×D4—142no—
373C3×D4—142no—
374C3×D4—144no—
375C3×D4—144no—
376C3×D4—144no—
377C3×D4—144no—
378C3×D4—142no—
379C3×D4—142no—
380C2×C3×C4—21no—
381C2×C3×C4—71no—
382C2×C3×C4—71no—
383C2×C3×C4—72no—
384C2×C3×C4—72no—
385C2×C3×C4—72no—
386C2×C3×C4—72no—
387C2×C3×C4—142no—
388C2×C3×C4—142no—
389C2×C3×C4—141no—
390C2×C3×C4C2×D3×D711yescharacteristic
391C2×C3×C4C22×C3×D711yescharacteristic
392C3×C8—62no—
393C3×C8—422no—
394C3⋊C8—22no—
395C3⋊C8—142no—
396C3×C7—21no—
397C3×C7C2×#83311yescharacteristic, complemented
398C3×C7C2×C3×#10011yescharacteristic, complemented
399C2×C32—21no—
400C2×C32—42no—
401C2×C32—72no—
402C2×C32—141no—
403C2×C32—282no—
404C2×C32D7×C22⋊C411yescharacteristic
405C24—72no—
406C2×D4—72no—
407C2×D4—71no—
408C2×D4—142no—
409C2×D4—142no—
410C2×D4C3×D3×D711yescharacteristic
411C22×C4—71no—
412M16—32no—
413M16—212no—
414M16—422no—
415C2×C8—422no—
416C2×C7—21no—
417C2×C7—42no—
418C2×C7C2×C3×#21711yescharacteristic
419D7—21no—
420D7—42no—
421D7C3×#83312yesdirect product factor
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—71no—
432C22×C3—71no—
433C22×C3—71no—
434C22×C3—71no—
435C22×C3—141no—
436C22×C3—141no—
437C22×C3—142no—
438C22×C3—142no—
439C22×C3—142no—
440C22×C3—142no—
441C22×C3—142no—
442C22×C3—142no—
443C22×C3—142no—
444C22×C3—142no—
445C22×C3—282no—
446C22×C3—282no—
447C22×C3—282no—
448C22×C3—282no—
449C22×C3—284no—
450C22×C3—284no—
451C22×C3—284no—
452C22×C3—284no—
453C22×C3—284no—
454C22×C3—284no—
455C22×C3—284no—
456C22×C3—284no—
457C22×C3C2×Dic3×D711yescharacteristic
458C22×C3C2×C3×C4×D711yescharacteristic
459C3×C4—22no—
460C3×C4—72no—
461C3×C4—72no—
462C3×C4—142no—
463C3×C4D7×#6712yes—
464C3×C4C3×D4×D712yes—
465C32D7×#10011yescharacteristic, complemented, Sylow
466C23—71no—
467C23—72no—
468C23—142no—
469C23—142no—
470C23—284no—
471C23C3×Dic3×D712yes—
472D4—22no—
473D4—144no—
474D4—142no—
475C2×C4—71no—
476C2×C4—72no—
477C2×C4—72no—
478C2×C4C2×C3×D3×D711yescharacteristic
479C8—62no—
480C8—422no—
481C7C2×C3×#83311yescharacteristic, complemented, Sylow
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—42no—
488C2×C3—42no—
489C2×C3—42no—
490C2×C3—42no—
491C2×C3—72no—
492C2×C3—72no—
493C2×C3—142no—
494C2×C3—141no—
495C2×C3—141no—
496C2×C3—141no—
497C2×C3—141no—
498C2×C3—282no—
499C2×C3—282no—
500C2×C3—282no—
501C2×C3—282no—
502C2×C3D7×#21711yescharacteristic
503C2×C3C3×D7×C22⋊C411yescharacteristic
504C22—22no—
505C22—42no—
506C22—71no—
507C22—71no—
508C22—142no—
509C22—142no—
510C22—282no—
511C22—284no—
512C22—284no—
513C22C2×C3×Dic3×D711yescharacteristic
514C4—72no—
515C4C3×D7×#6712yes—
516C3—21no—
517C3D7×#83311yescharacteristic, direct product factor
518C3C3×D7×#10011yescharacteristic, complemented
519C2—21no—
520C2—42no—
521C2—72no—
522C2—141no—
523C2—282no—
524C2C3×D7×#21711yescharacteristic
subgroupG/H
centerC2×C3D7×#217
commutatorC22×C3×C7C22×C3×C4
FrattiniC2×C4C2×C3×D3×D7
FittingC2×C32×C7×D4C22
socleC2×C32×C7C2×C22⋊C4
prime radicalC2×C32×D4×D7C2
cosocleC2×C3×C4×C7C23×C3
hypercenterC2×C3×D4D3×D7
hypocenterC3×C7C2×C3×#100
LCSG ▷ C22×C3×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×#10620672C2semidirect
2. C3×#10620493C2semidirect
3. C3×C7×#833C2semidirect
4. C3×D7×#208C2semidirect
7. D7×#833C3direct (N × H)
15. C3×#66627C22semidirect
16. C3×C7×#208C22semidirect
23. D7×#208C2×C3semidirect
25. #10620672C2×C3semidirect
26. C7×#833C2×C3semidirect
29. #10620493C2×C3semidirect
71. #66627C22×C3semidirect
72. C7×#208C22×C3semidirect
82. C3×#833D7direct (N × H)
160. C3×#208C2×D7semidirect
167. C32×D7#100semidirect
189. #833C3×D7direct (N × H)
249. C32×C7C2×#100semidirect
294. #208C2×C3×D7semidirect
316. C3×D7#833direct (N × H)
317. C3×D7C3×#100semidirect
397. C3×C7C2×#833semidirect
398. C3×C7C2×C3×#100semidirect
421. D7C3×#833direct (N × H)
465. C32D7×#100semidirect
481. C7C2×C3×#833semidirect
517. C3D7×#833direct (N × H)
518. C3C3×D7×#100semidirect

Maximal subgroups

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

subgroupindex
C3×#106206722
C3×#106204932
C3×C7×#8332
C3×D7×#2082
C2×C32×D4×D72
C3×D7×#1003
D7×#8333
C2×C3×#8337