Finite Group Databasebeta

← C3×#69398 #11775105

Subgroups — C3×#69398 #11775105

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5791C211yesmaximal, characteristic
2C2×C32×#95C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4C3×#4452C212yesmaximal, complemented
5C3×#4451C212yesmaximal, complemented
6C3×#1504—31nomaximal
7#69398C311yesmaximal, characteristic, direct product factor
8C23×C32×C4—21no—
9C23×C32×C4C2211yescharacteristic
10C2×C3×#235C411yescharacteristic, complemented
11C3×#953—21no—
12C3×#930C411yescharacteristic, complemented
13C3×#930C2211yescharacteristic
14C3×#929—21no—
15C3×C4×#67—21no—
16C3×C4×#67—21no—
17C3×#926C411yescharacteristic, complemented
18C3×#924C411yescharacteristic, complemented
19C3×#924C2211yescharacteristic
20C2×C3×#208—21no—
21C32×#95—21no—
22C32×#95C2212yes—
23C3×#830—21no—
24C3×#830C2212yes—
25C3×#525—31no—
26#5791C2×C311yescharacteristic
27C3×#407—31no—
28C2×C3×#95—21no—
29C2×C3×#95D311yescharacteristic, complemented
30C2×C3×#95C2×C311yescharacteristic, complemented
31#5207C2×C311yescharacteristic, complemented
32C3×#328—32no—
33C3×#327—32no—
34#4452C2×C312yescomplemented
35#4451C2×C312yescomplemented
36C24×C32D411yescharacteristic
37C22×C32×C4—24no—
38C22×C32×C4—22no—
39C22×C32×C4—42no—
40C22×C32×C4—42no—
41C22×C32×C4—42no—
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4C2×C411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C3×#235—42no—
52C2×C3×D12C2×C411yescharacteristic, complemented
53C2×C3×C4×D3—21no—
54C2×C3×Dic6C2×C411yescharacteristic, complemented
55C3×#217—21no—
56C3×#217—21no—
57C3×#217—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic, complemented
61C3×C4⋊Dic3C2×C411yescharacteristic, complemented
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C3×#208—42no—
66C2×C3×C3⋊C8—22no—
67#1504—31noSylow
68C2×C3×#41—31no—
69C23×C3×C4—22no—
70C23×C3×C4—21no—
71C23×C3×C4—21no—
72C23×C3×C4—21no—
73C23×C3×C4C2×D311yescharacteristic
74C23×C3×C4C22×C311yescharacteristic
75C2×#235C3×C411yescharacteristic, complemented
76C2×C3×M16—61no—
77C3×#123—61no—
78C3×C22⋊Q8—31no—
79C3×C22⋊Q8—31no—
80C3×#121—31no—
81C3×#121—31no—
82C3×#120—61no—
83C3×C4×D4—61no—
84C3×C4×D4—61no—
85C3×#117—31no—
86#953—21no—
87#930C3×C411yescharacteristic, complemented
88#930C22×C311yescharacteristic
89#929—21no—
90C4×#67—21no—
91C4×#67—21no—
92#926C3×C411yescharacteristic, complemented
93#924C3×C411yescharacteristic, complemented
94#924C22×C311yescharacteristic
95C2×#208—21no—
96C3×C22⋊C8—32no—
97C3×C22⋊C8—61no—
98C3×#95—22no—
99C3×#95—21no—
100C3×#95—21no—
101C3×#95—22no—
102C3×#95C2×D312yes—
103C3×#95C22×C312yes—
104#830—21no—
105#830C22×C312yes—
106C23×C32—22no—
107C23×C32—22no—
108C23×C32—21no—
109C23×C32—21no—
110C23×C32C22⋊C411yescharacteristic
111C23×C32C22⋊C411yescharacteristic
112C23×C32C2×D411yescharacteristic
113C22×C3×D3—21no—
114C2×C32×C4—24no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—48no—
122C2×C32×C4—42no—
123C2×C32×C4—42no—
124C2×C32×C4C22⋊C411yescharacteristic
125C2×C32×C4C22⋊C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C3×#67—42no—
129C3×#67—42no—
130C3×#67—41no—
131C3×#67—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C3×D12—41no—
136C3×C4×D3—42no—
137C3×Dic6—41no—
138C3×C3⋊C8—42no—
139#525—31no—
140#407—31no—
141C2×#95C3×D311yescharacteristic, complemented
142#328—32no—
143#327—32no—
144C24×C3—21no—
145C24×C3#6711yescharacteristic
146C24×C3C3×D411yescharacteristic
147C3×#41—122no—
148C2×C3×Q8—31no—
149C2×C3×D4—31no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C22×C3×C4—24no—
154C22×C3×C4—28no—
155C22×C3×C4—24no—
156C22×C3×C4—24no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—42no—
166C22×C3×C4—42no—
167C22×C3×C4—44no—
168C22×C3×C4—44no—
169C22×C3×C4—44no—
170C22×C3×C4—42no—
171C22×C3×C4—42no—
172C22×C3×C4—42no—
173C22×C3×C4—42no—
174C22×C3×C4—61no—
175C22×C3×C4C4×D311yescharacteristic
176C22×C3×C4C4×D311yescharacteristic
177C22×C3×C4D1211yescharacteristic
178C22×C3×C4D1211yescharacteristic
179C22×C3×C4#6711yescharacteristic
180C22×C3×C4C2×C3×C411yescharacteristic
181C22×C3×C4C2×C3×C411yescharacteristic
182C22×C3×C4C3×D411yescharacteristic
183C22×C3×C4C3×D411yescharacteristic
184C22×C3×C4C3×D411yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C23×C311yescharacteristic
187C2×#67—21no—
188C2×#67—21no—
189C2×#67—21no—
190#235—42no—
191C2×D12C2×C3×C411yescharacteristic, complemented
192C2×C4×D3—21no—
193C2×Dic6C2×C3×C411yescharacteristic, complemented
194C3×M16—122no—
195C2×C3×C8—62no—
196C3×C4⋊C4—31no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C42—61no—
206#217—21no—
207#217—21no—
208#217—21no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—21no—
211C4⋊Dic3C2×C3×C411yescharacteristic, complemented
212C4⋊Dic3C2×C3×C411yescharacteristic, complemented
213Dic3⋊C4—21no—
214Dic3⋊C4—21no—
215C4×Dic3—21no—
216#208—42no—
217C2×C3⋊C8—22no—
218C22×C32—24no—
219C22×C32—24no—
220C22×C32—21no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32#9912yes—
227C22×C32#10412yes—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32AGL(1,ℤ/8)11yescharacteristic
230C22×C32#13711yescharacteristic
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C32×C4—21no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—21no—
238C32×C4—44no—
239C3×Dic3—41no—
240C3×Dic3—41no—
241C3×Dic3—41no—
242C2×#41—31no—
243C23×C4—21no—
244C23×C4C2×C3×D311yescharacteristic
245C2×M16—61no—
246#123—61no—
247C22⋊Q8—31no—
248C22⋊Q8—31no—
249#121—31no—
250#121—31no—
251#120—61no—
252C4×D4—61no—
253C4×D4—61no—
254#117—31no—
255C22⋊C8—32no—
256C22⋊C8—61no—
257#95—21no—
258#95C2×C3×D312yes—
259C23×C3—24no—
260C23×C3—22no—
261C23×C3—24no—
262C23×C3—22no—
263C23×C3—22no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—22no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—61no—
275C23×C3(C2×D3)⋊C411yescharacteristic
276C23×C3(C2×D3)⋊C411yescharacteristic
277C23×C3C3×C22⋊C411yescharacteristic
278C23×C3C3×C22⋊C411yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C23×C3C2×C3×D411yescharacteristic
281C22×D3—21no—
282C3×Q8—121no—
283C3×D4—121no—
284C3×D4—122no—
285C3×D4—122no—
286C3×D4—121no—
287C3×D4—121no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—28no—
293C2×C3×C4—24no—
294C2×C3×C4—24no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—44no—
314C2×C3×C4—416no—
315C2×C3×C4—48no—
316C2×C3×C4—48no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—44no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—61no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—122no—
326C2×C3×C4(C2×D3)⋊C411yescharacteristic
327C2×C3×C4(C2×D3)⋊C411yescharacteristic
328C2×C3×C4C3×C22⋊C411yescharacteristic
329C2×C3×C4C3×C22⋊C411yescharacteristic
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4C22×C3×C411yescharacteristic
333C2×C3×C4C2×C3×D411yescharacteristic
334#67—42no—
335#67—42no—
336#67—41no—
337#67—41no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341D12—41no—
342C4×D3—42no—
343Dic6—41no—
344C3×C8—122no—
345C3⋊C8—42no—
346C2×C32—21no—
347C2×C32—22no—
348C2×C32—22no—
349C2×C32—21no—
350C2×C32C2×#9911yescharacteristic
351C2×C32#41711yescharacteristic
352C2×C32C2×#10411yescharacteristic
353C3×D3—81no—
354C24C3×#6711yescharacteristic
355#41—122no—
356C2×Q8—31no—
357C2×D4—31no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—61no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—61no—
367C22×C4C3×C4×D311yescharacteristic
368C22×C4C3×C4×D311yescharacteristic
369C22×C4C3×D1211yescharacteristic
370C22×C4C3×D1211yescharacteristic
371C22×C4C3×#6711yescharacteristic
372C22×C4C22×C3×D311yescharacteristic
373M16—122no—
374C2×C8—62no—
375C4⋊C4—31no—
376C4⋊C4—31no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C22⋊C4—61no—
380C22⋊C4—61no—
381C22⋊C4—61no—
382C22⋊C4—61no—
383C22⋊C4—61no—
384C42—61no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—28no—
388C22×C3—24no—
389C22×C3—24no—
390C22×C3—22no—
391C22×C3—28no—
392C22×C3—24no—
393C22×C3—24no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—121no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3#80512yes—
418C22×C3#80612yes—
419C22×C3C3×#9912yes—
420C22×C3C3×#10412yes—
421C22×C3C2×(C2×D3)⋊C411yescharacteristic
422C22×C3#93211yescharacteristic
423C22×C3#94211yescharacteristic
424C22×C3C2×C3×C22⋊C411yescharacteristic
425C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
426C22×C3C3×#13711yescharacteristic
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—48no—
443C3×C4—44no—
444C3×C4—44no—
445C3×C4—121no—
446C3×C4—121no—
447C3×C4—121no—
448Dic3—41no—
449Dic3—41no—
450Dic3—41no—
451C32#150411yescharacteristic, complemented, Sylow
452C23—21no—
453C23—21no—
454C23—22no—
455C23—22no—
456C23—61no—
457C23C3×(C2×D3)⋊C411yescharacteristic
458C23C3×(C2×D3)⋊C411yescharacteristic
459C23C2×C3×#6711yescharacteristic
460Q8—121no—
461D4—121no—
462D4—121no—
463D4—121no—
464D4—122no—
465D4—122no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—48no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—122no—
480C2×C4C3×(C2×D3)⋊C411yescharacteristic
481C2×C4C3×(C2×D3)⋊C411yescharacteristic
482C2×C4C2×C3×C4×D311yescharacteristic
483C2×C4C2×C3×D1211yescharacteristic
484C8—122no—
485C2×C3—22no—
486C2×C3—22no—
487C2×C3—24no—
488C2×C3—24no—
489C2×C3—21no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—241no—
501C2×C3C2×#80511yescharacteristic
502C2×C3C2×#80611yescharacteristic
503C2×C3#496611yescharacteristic
504C2×C3C2×C3×#9911yescharacteristic
505C2×C3C3×#41711yescharacteristic
506C2×C3C2×C3×#10411yescharacteristic
507D3—81no—
508C22—24no—
509C22—24no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22C3×#80512yes—
520C22C3×#80612yes—
521C22C2×C3×(C2×D3)⋊C411yescharacteristic
522C22C3×#93211yescharacteristic
523C22C3×#94211yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—44no—
529C4—121no—
530C4—121no—
531C4—121no—
532C3—21no—
533C3#6939811yescharacteristic, direct product factor
534C3C3×#150411yescharacteristic, complemented
535C2—21no—
536C2—21no—
537C2—22no—
538C2—22no—
539C2—241no—
540C2C2×C3×#80511yescharacteristic
541C2C2×C3×#80611yescharacteristic
542C2C3×#496611yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#95C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5791C2
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#1504
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
2. C2×C32×#95C2semidirect
3. C3×#5207C2semidirect
4. C3×#4452C2semidirect
5. C3×#4451C2semidirect
7. #69398C3direct (N × H)
10. C2×C3×#235C4semidirect
12. C3×#930C4semidirect
17. C3×#926C4semidirect
18. C3×#924C4semidirect
29. C2×C3×#95D3semidirect
30. C2×C3×#95C2×C3semidirect
31. #5207C2×C3semidirect
34. #4452C2×C3semidirect
35. #4451C2×C3semidirect
52. C2×C3×D12C2×C4semidirect
54. C2×C3×Dic6C2×C4semidirect
60. C3×C4⋊Dic3C2×C4semidirect
61. C3×C4⋊Dic3C2×C4semidirect
75. C2×#235C3×C4semidirect
87. #930C3×C4semidirect
92. #926C3×C4semidirect
93. #924C3×C4semidirect
141. C2×#95C3×D3semidirect
191. C2×D12C2×C3×C4semidirect
193. C2×Dic6C2×C3×C4semidirect
211. C4⋊Dic3C2×C3×C4semidirect
212. C4⋊Dic3C2×C3×C4semidirect
451. C32#1504semidirect
533. C3#69398direct (N × H)
534. C3C3×#1504semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
C2×C32×#952
C3×#52072
C3×#44522
C3×#44512
C3×#15043
#693983