Finite Group Databasebeta

← C3×#68902 #11794652

Subgroups — C3×#68902 #11794652

Order 1152.

605 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#821C211yesmaximal, characteristic
2C3×#4988C211yesmaximal, characteristic
3C3×#4975C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C32×#340C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2071—31nomaximal
9#68902C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×Dic3⋊C4—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#821—22no—
22C3×#809—22no—
23C2×C3×#102—31no—
24C2×C3×#102—31no—
25C3×#390—31no—
26C3×#384—31no—
27C2×#821C2×C311yescharacteristic
28#4988C2×C311yescharacteristic
29#4975C2×C311yescharacteristic, complemented
30C2×#809C2×C311yescharacteristic
31C3×#340—21no—
32C3×#340—31no—
33C3×#340D311yescharacteristic, complemented
34C3×#340C2×C311yescharacteristic, complemented
35C3×#336—31no—
36#4550C2×C311yescharacteristic, complemented
37#4529C2×C311yescharacteristic, complemented
38C23×C3×D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3—21no—
43C22×C3×Dic3D411yescharacteristic
44C22×C3×Dic3D411yescharacteristic
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12D412yes—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C3×(C2×D3)⋊C4—42no—
59C3×(C2×D3)⋊C4—42no—
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—31no—
71C22×D12C22×C311yescharacteristic
72C22×C3×C8—21no—
73C22×C3×C8—31no—
74C22×C3×C8C2×D311yescharacteristic
75C22×C3×C8C22×C311yescharacteristic
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—61no—
80C2×C3×C4⋊C4—61no—
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×C3×C4⋊C4C2×D311yescharacteristic
83C2×C3×C4⋊C4C22×C311yescharacteristic
84C2×C3×C4⋊C4C22×C311yescharacteristic
85C2×C3×C22⋊C4—61no—
86C2×C3×C22⋊C4—61no—
87C2×C3×C42—31no—
88C2×(C2×D3)⋊C4—21no—
89C2×(C2×D3)⋊C4—21no—
90C2×C4⋊Dic3C22×C311yescharacteristic
91C2×Dic3⋊C4—21no—
92C2×Dic3⋊C4—21no—
93C2×C4×Dic3C22×C311yescharacteristic
94C22×C3⋊C8C22×C311yescharacteristic
95C3×#102—62no—
96C3×#102—62no—
97#821—22no—
98#809—22no—
99C23×C32C2×D411yescharacteristic
100C22×C3×D3—22no—
101C22×C3×D3—41no—
102C22×C3×D3—41no—
103C22×C3×D3—41no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—41no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3D812yes—
127C2×C3×Dic3SD1612yes—
128C3×D12—22no—
129C3×D12—22no—
130C3×D12—41no—
131C3×D12—41no—
132C32×C8—41no—
133C3×C3⋊C8—41no—
134C2×#102—31no—
135C2×#102—31no—
136#390—31no—
137#384—31no—
138#340—31no—
139#340C3×D311yescharacteristic, complemented
140#336—31no—
141C24×C3—61no—
142C23×D3—21no—
143C2×C3×D4—32no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—41no—
157C22×C3×C4—41no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C23×C311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3C3×D411yescharacteristic
163C22×Dic3C3×D411yescharacteristic
164C2×D12—21no—
165C2×D12—21no—
166C2×D12—21no—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12C3×D412yes—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—41no—
178C2×C3×C8—41no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—41no—
193C3×C4⋊C4—41no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—122no—
197C3×C4⋊C4—122no—
198C3×C22⋊C4—122no—
199C3×C22⋊C4—122no—
200C3×C42—61no—
201C3×C42—61no—
202(C2×D3)⋊C4—42no—
203(C2×D3)⋊C4—42no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206Dic3⋊C4—42no—
207Dic3⋊C4—42no—
208C4×Dic3—21no—
209C4×Dic3—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C22×C32#12111yescharacteristic
214C22×C32#12311yescharacteristic
215C22×C32#12411yescharacteristic
216C22×C32C2×D811yescharacteristic
217C22×C32C2×SD1611yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32#13711yescharacteristic
220C2×C3×D3—42no—
221C2×C3×D3—42no—
222C2×C3×D3—42no—
223C2×C3×D3—81no—
224C2×C3×D3—81no—
225C2×C3×D3—81no—
226C2×C3×D3—81no—
227C32×C4—81no—
228C32×C4—81no—
229C32×C4#12311yescharacteristic
230C32×C4#12311yescharacteristic
231C32×C4#12611yescharacteristic
232C32×C4#12611yescharacteristic
233C3×Dic3—22no—
234C3×Dic3—22no—
235C3×Dic3—81no—
236C22×D4—31no—
237C22×C8—31no—
238C22×C8C2×C3×D311yescharacteristic
239C2×C4⋊C4—31no—
240C2×C4⋊C4—61no—
241C2×C4⋊C4—61no—
242C2×C4⋊C4C2×C3×D311yescharacteristic
243C2×C4⋊C4C2×C3×D311yescharacteristic
244C2×C22⋊C4—61no—
245C2×C22⋊C4—61no—
246C2×C42—31no—
247#102—62no—
248#102—62no—
249C23×C3—21no—
250C23×C3—62no—
251C23×C3—121no—
252C23×C3—121no—
253C23×C3—121no—
254C23×C3—121no—
255C23×C3—121no—
256C23×C3—121no—
257C23×C3D3×D411yescharacteristic
258C23×C3C2×C3×D411yescharacteristic
259C22×D3—22no—
260C22×D3—41no—
261C22×D3—41no—
262C22×D3—41no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3—41no—
266C3×D4—62no—
267C3×D4—62no—
268C3×D4—121no—
269C3×D4—121no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—32no—
277C2×C3×C4—32no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—81no—
297C2×C3×C4—81no—
298C2×C3×C4—81no—
299C2×C3×C4—81no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4#23711yescharacteristic
308C2×C3×C4#23911yescharacteristic
309C2×C3×C4C2×C3×D411yescharacteristic
310C2×C3×C4C3×#4111yescharacteristic
311C2×C3×C4C3×#4111yescharacteristic
312C2×C3×C4C3×#4111yescharacteristic
313C2×C3×C4C3×#4111yescharacteristic
314C2×C3×C4C3×#4111yescharacteristic
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—21no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3C3×D812yes—
323C2×Dic3C3×SD1612yes—
324D12—22no—
325D12—22no—
326D12—41no—
327D12—41no—
328C3×C8—42no—
329C3×C8—41no—
330C3×C8—41no—
331C3×C8—121no—
332C3⋊C8—41no—
333C2×C32#39711yescharacteristic
334C2×C32#45911yescharacteristic
335C2×C32#46111yescharacteristic
336C2×C32#48011yescharacteristic
337C2×C32#48111yescharacteristic
338C2×C32#48611yescharacteristic
339C2×C32#48911yescharacteristic
340C3×D3—82no—
341C24—61no—
342C2×D4—32no—
343C2×D4—61no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—31no—
351C22×C4—31no—
352C22×C4—61no—
353C22×C4C22×C3×D311yescharacteristic
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—61no—
358C2×C8—61no—
359C2×C8—61no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—122no—
367C4⋊C4—122no—
368C22⋊C4—122no—
369C22⋊C4—122no—
370C42—61no—
371C42—61no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—122no—
380C22×C3—122no—
381C22×C3—122no—
382C22×C3—241no—
383C22×C3—241no—
384C22×C3—241no—
385C22×C3—241no—
386C22×C3#88411yescharacteristic
387C22×C3#88511yescharacteristic
388C22×C3#89411yescharacteristic
389C22×C3D3×D811yescharacteristic
390C22×C3D3×SD1611yescharacteristic
391C22×C3#91411yescharacteristic
392C22×C3#91811yescharacteristic
393C22×C3C3×#12111yescharacteristic
394C22×C3C3×#12311yescharacteristic
395C22×C3C3×#12411yescharacteristic
396C22×C3C2×C3×D811yescharacteristic
397C22×C3C2×C3×SD1611yescharacteristic
398C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
399C22×C3C3×#13711yescharacteristic
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—42no—
403C2×D3—81no—
404C2×D3—81no—
405C2×D3—81no—
406C2×D3—81no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—62no—
412C3×C4—62no—
413C3×C4—82no—
414C3×C4—82no—
415C3×C4—81no—
416C3×C4—81no—
417C3×C4—81no—
418C3×C4—81no—
419C3×C4—241no—
420C3×C4#87611yescharacteristic
421C3×C4#88311yescharacteristic
422C3×C4#89411yescharacteristic
423C3×C4#89811yescharacteristic
424C3×C4C3×#12311yescharacteristic
425C3×C4C3×#12311yescharacteristic
426C3×C4C3×#12611yescharacteristic
427C3×C4C3×#12611yescharacteristic
428Dic3—22no—
429Dic3—22no—
430Dic3—81no—
431C32#207111yescharacteristic, complemented, Sylow
432C23—62no—
433C23—121no—
434C23—121no—
435C23—121no—
436C23—121no—
437C23—121no—
438C23—121no—
439C23C3×D3×D411yescharacteristic
440D4—62no—
441D4—62no—
442D4—121no—
443D4—121no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4C3×#23511yescharacteristic
460C2×C4C3×#23511yescharacteristic
461C2×C4C3×#23511yescharacteristic
462C2×C4C3×D3×D411yescharacteristic
463C2×C4C3×#23711yescharacteristic
464C2×C4C3×#23911yescharacteristic
465C8—41no—
466C8—121no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—242no—
475C2×C3#467511yescharacteristic
476C2×C3#476011yescharacteristic
477C2×C3#478611yescharacteristic
478C2×C3#479411yescharacteristic
479C2×C3#481811yescharacteristic
480C2×C3#486311yescharacteristic
481C2×C3#488211yescharacteristic
482C2×C3C3×#39711yescharacteristic
483C2×C3C3×#45911yescharacteristic
484C2×C3C3×#46111yescharacteristic
485C2×C3C3×#48011yescharacteristic
486C2×C3C3×#48111yescharacteristic
487C2×C3C3×#48611yescharacteristic
488C2×C3C3×#48911yescharacteristic
489D3—82no—
490C22—122no—
491C22—122no—
492C22—122no—
493C22—241no—
494C22—241no—
495C22—241no—
496C22—241no—
497C22C3×#88411yescharacteristic
498C22C3×#88511yescharacteristic
499C22C3×#89411yescharacteristic
500C22C3×D3×D811yescharacteristic
501C22C3×D3×SD1611yescharacteristic
502C22C3×#91411yescharacteristic
503C22C3×#91811yescharacteristic
504C4—62no—
505C4—62no—
506C4—81no—
507C4—81no—
508C4—241no—
509C4C3×#87611yescharacteristic
510C4C3×#88311yescharacteristic
511C4C3×#89411yescharacteristic
512C4C3×#89811yescharacteristic
513C3—21no—
514C3#6890211yescharacteristic, direct product factor
515C3C3×#207111yescharacteristic, complemented
516C2—242no—
517C2C3×#467511yescharacteristic
518C2C3×#476011yescharacteristic
519C2C3×#478611yescharacteristic
520C2C3×#479411yescharacteristic
521C2C3×#481811yescharacteristic
522C2C3×#486311yescharacteristic
523C2C3×#488211yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC3×#340D3
hypocenterC3C3×#2071
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
3. C3×#4975C2semidirect
5. C32×#340C2semidirect
6. C3×#4550C2semidirect
7. C3×#4529C2semidirect
9. #68902C3direct (N × H)
29. #4975C2×C3semidirect
33. C3×#340D3semidirect
34. C3×#340C2×C3semidirect
36. #4550C2×C3semidirect
37. #4529C2×C3semidirect
139. #340C3×D3semidirect
431. C32#2071semidirect
514. C3#68902direct (N × H)
515. C3C3×#2071semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8212
C3×#49882
C3×#49752
C2×C3×#8092
C32×#3402
C3×#45502
C3×#45292
C3×#20713
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