Finite Group Databasebeta

← C3×#70165 #11794649

Subgroups — C3×#70165 #11794649

Order 1152.

649 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#102C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C3×#4975C211yesmaximal, characteristic, complemented
5C3×#4551C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2071—31nomaximal
9#70165C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C3×#217—21no—
14C2×C3×#217—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×Dic3⋊C4—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C32×#102—22no—
22C3×#832—22no—
23C2×C3×#102—21no—
24C2×C3×#102—31no—
25C2×C3×#102D311yescharacteristic
26C2×C3×#102C2×C311yescharacteristic
27C3×#390—31no—
28C3×#384—31no—
29#5221C2×C311yescharacteristic
30C2×#832C2×C311yescharacteristic
31#4975C2×C311yescharacteristic, complemented
32C3×#340—31no—
33C3×#340—31no—
34C3×#336—31no—
35#4551C2×C311yescharacteristic, complemented
36#4550C2×C311yescharacteristic, complemented
37#4529C2×C311yescharacteristic, complemented
38C24×C32—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4D412yes—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C3×#217—42no—
57C3×#217—42no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×Dic3⋊C4—42no—
63C3×Dic3⋊C4—42no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#2071—31noSylow
70C22×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C22×C3×D4C22×C311yescharacteristic
73C22×C3×C8—21no—
74C22×C3×C8—31no—
75C22×C3×C8C2×D311yescharacteristic
76C22×C3×C8C22×C311yescharacteristic
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—61no—
81C2×C3×C4⋊C4—61no—
82C2×C3×C4⋊C4C2×D311yescharacteristic
83C2×C3×C4⋊C4C22×C311yescharacteristic
84C2×C3×C22⋊C4—61no—
85C2×C3×C22⋊C4—61no—
86C2×C3×C42—31no—
87C2×#217—21no—
88C2×#217—21no—
89C2×C4⋊Dic3C22×C311yescharacteristic
90C2×C4⋊Dic3C22×C311yescharacteristic
91C2×Dic3⋊C4—21no—
92C2×Dic3⋊C4—21no—
93C2×C4×Dic3C22×C311yescharacteristic
94C22×C3⋊C8C22×C311yescharacteristic
95C3×#102—24no—
96C3×#102—22no—
97C3×#102—22no—
98C3×#102—62no—
99#832—22no—
100C23×C32—22no—
101C23×C32—41no—
102C23×C32—41no—
103C23×C32—41no—
104C23×C32—41no—
105C23×C32—41no—
106C23×C32—41no—
107C23×C32C2×D411yescharacteristic
108C32×D4—22no—
109C32×D4—22no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3D812yes—
132C2×C3×Dic3SD1612yes—
133C32×C8—41no—
134C3×C3⋊C8—41no—
135C2×#102—31no—
136C2×#102C3×D311yescharacteristic
137#390—31no—
138#384—31no—
139#340—31no—
140#340—31no—
141#336—31no—
142C24×C3—21no—
143C24×C3—21no—
144C24×C3—41no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—22no—
158C2×C3×D4—41no—
159C2×C3×D4—41no—
160C2×C3×D4—41no—
161C2×C3×D4#6712yes—
162C2×C3×D4C3×D412yes—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—41no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C23×C311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3C3×D411yescharacteristic
176C22×Dic3C3×D411yescharacteristic
177C2×C3×C8—22no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—41no—
185C2×C3×C8—41no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—122no—
200C3×C4⋊C4—122no—
201C3×C22⋊C4—122no—
202C3×C22⋊C4—122no—
203C3×C42—61no—
204C3×C42—61no—
205#217—42no—
206#217—42no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211Dic3⋊C4—42no—
212Dic3⋊C4—42no—
213C4×Dic3—21no—
214C4×Dic3—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C22×C32—42no—
219C22×C32—42no—
220C22×C32—42no—
221C22×C32—81no—
222C22×C32—81no—
223C22×C32—81no—
224C22×C32—81no—
225C22×C32#12111yescharacteristic
226C22×C32#12311yescharacteristic
227C22×C32#12411yescharacteristic
228C22×C32C2×D811yescharacteristic
229C22×C32C2×SD1611yescharacteristic
230C22×C32AGL(1,ℤ/8)11yescharacteristic
231C22×C32#13711yescharacteristic
232C32×C4—81no—
233C32×C4#12311yescharacteristic
234C32×C4#12311yescharacteristic
235C32×C4#12611yescharacteristic
236C32×C4#12611yescharacteristic
237C3×Dic3—22no—
238C3×Dic3—22no—
239C3×Dic3—81no—
240C3×Dic3—81no—
241C22×D4C2×C3×D311yescharacteristic
242C22×C8—31no—
243C22×C8C2×C3×D311yescharacteristic
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—61no—
247C2×C4⋊C4—61no—
248C2×C4⋊C4C2×C3×D311yescharacteristic
249C2×C22⋊C4—61no—
250C2×C22⋊C4—61no—
251C2×C42—31no—
252#102—22no—
253#102—62no—
254C23×C3—22no—
255C23×C3—22no—
256C23×C3—21no—
257C23×C3—42no—
258C23×C3—42no—
259C23×C3—42no—
260C23×C3—41no—
261C23×C3—41no—
262C23×C3—41no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3—41no—
268C23×C3—41no—
269C23×C3—41no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—81no—
273C23×C3—81no—
274C23×C3—81no—
275C23×C3—81no—
276C23×C3D3×D411yescharacteristic
277C23×C3C2×C3×D411yescharacteristic
278C3×D4—24no—
279C3×D4—22no—
280C3×D4—22no—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—42no—
284C3×D4—42no—
285C3×D4—42no—
286C3×D4—41no—
287C3×D4—41no—
288C3×D4—41no—
289C3×D4—41no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—32no—
297C2×C3×C4—32no—
298C2×C3×C4—42no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—81no—
310C2×C3×C4—81no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×C3×C4C2×C3×D411yescharacteristic
324C2×C3×C4C3×#4111yescharacteristic
325C2×C3×C4C3×#4111yescharacteristic
326C2×C3×C4C3×#4111yescharacteristic
327C2×C3×C4C3×#4111yescharacteristic
328C2×C3×C4C3×#4111yescharacteristic
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3C3×D812yes—
340C2×Dic3C3×SD1612yes—
341C3×C8—42no—
342C3×C8—41no—
343C3×C8—41no—
344C3×C8—121no—
345C3⋊C8—41no—
346C2×C32—82no—
347C2×C32#39711yescharacteristic
348C2×C32#45911yescharacteristic
349C2×C32#46111yescharacteristic
350C2×C32#48011yescharacteristic
351C2×C32#48111yescharacteristic
352C2×C32#48611yescharacteristic
353C2×C32#48911yescharacteristic
354C24—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4C3×#6712yes—
361C22×C4—21no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4C22×C3×D311yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—61no—
371C2×C8—61no—
372C2×C8—61no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—122no—
380C4⋊C4—122no—
381C22⋊C4—122no—
382C22⋊C4—122no—
383C42—61no—
384C42—61no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—44no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—82no—
400C22×C3—82no—
401C22×C3—82no—
402C22×C3—82no—
403C22×C3—82no—
404C22×C3—82no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3—81no—
408C22×C3—81no—
409C22×C3—81no—
410C22×C3—81no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3#88311yescharacteristic
414C22×C3#88511yescharacteristic
415C22×C3D3×D811yescharacteristic
416C22×C3#91111yescharacteristic
417C22×C3D3×SD1611yescharacteristic
418C22×C3#91511yescharacteristic
419C22×C3#93911yescharacteristic
420C22×C3C3×#12111yescharacteristic
421C22×C3C3×#12311yescharacteristic
422C22×C3C3×#12411yescharacteristic
423C22×C3C2×C3×D811yescharacteristic
424C22×C3C2×C3×SD1611yescharacteristic
425C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
426C22×C3C3×#13711yescharacteristic
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—62no—
432C3×C4—62no—
433C3×C4—82no—
434C3×C4—81no—
435C3×C4—81no—
436C3×C4—241no—
437C3×C4—241no—
438C3×C4#87911yescharacteristic
439C3×C4#87911yescharacteristic
440C3×C4#92911yescharacteristic
441C3×C4#93511yescharacteristic
442C3×C4C3×#12311yescharacteristic
443C3×C4C3×#12311yescharacteristic
444C3×C4C3×#12611yescharacteristic
445C3×C4C3×#12611yescharacteristic
446Dic3—22no—
447Dic3—22no—
448Dic3—81no—
449Dic3—81no—
450C32#207111yescharacteristic, complemented, Sylow
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23C3×D3×D411yescharacteristic
459D4—22no—
460D4—22no—
461D4—41no—
462D4—41no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4C3×#23511yescharacteristic
479C2×C4C3×#23511yescharacteristic
480C2×C4C3×#23711yescharacteristic
481C2×C4C3×#23711yescharacteristic
482C2×C4C3×#23711yescharacteristic
483C2×C4C2×C3×#6711yescharacteristic
484C8—41no—
485C8—121no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—84no—
494C2×C3—82no—
495C2×C3—82no—
496C2×C3#476011yescharacteristic
497C2×C3#476511yescharacteristic
498C2×C3#477411yescharacteristic
499C2×C3#477711yescharacteristic
500C2×C3#495211yescharacteristic
501C2×C3#515011yescharacteristic
502C2×C3#516211yescharacteristic
503C2×C3C3×#39711yescharacteristic
504C2×C3C3×#45911yescharacteristic
505C2×C3C3×#46111yescharacteristic
506C2×C3C3×#48011yescharacteristic
507C2×C3C3×#48111yescharacteristic
508C2×C3C3×#48611yescharacteristic
509C2×C3C3×#48911yescharacteristic
510C22—42no—
511C22—42no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22C3×#88311yescharacteristic
518C22C3×#88511yescharacteristic
519C22C3×D3×D811yescharacteristic
520C22C3×#91111yescharacteristic
521C22C3×D3×SD1611yescharacteristic
522C22C3×#91511yescharacteristic
523C22C3×#93911yescharacteristic
524C4—62no—
525C4—62no—
526C4—81no—
527C4—241no—
528C4—241no—
529C4C3×#87911yescharacteristic
530C4C3×#87911yescharacteristic
531C4C3×#92911yescharacteristic
532C4C3×#93511yescharacteristic
533C3—21no—
534C3#7016511yescharacteristic, direct product factor
535C3C3×#207111yescharacteristic, complemented
536C2—82no—
537C2C3×#476011yescharacteristic
538C2C3×#476511yescharacteristic
539C2C3×#477411yescharacteristic
540C2C3×#477711yescharacteristic
541C2C3×#495211yescharacteristic
542C2C3×#515011yescharacteristic
543C2C3×#516211yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC2×C3×#102D3
hypocenterC3C3×#2071
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
4. C3×#4975C2semidirect
5. C3×#4551C2semidirect
6. C3×#4550C2semidirect
7. C3×#4529C2semidirect
9. #70165C3direct (N × H)
31. #4975C2×C3semidirect
35. #4551C2×C3semidirect
36. #4550C2×C3semidirect
37. #4529C2×C3semidirect
450. C32#2071semidirect
534. C3#70165direct (N × H)
535. C3C3×#2071semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1022
C3×#52212
C2×C3×#8322
C3×#49752
C3×#45512
C3×#45502
C3×#45292
C3×#20713
#701653