Finite Group Databasebeta

← C3×#68104 #11774016

Subgroups — C3×#68104 #11774016

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#885C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3C3×#4718C211yesmaximal, characteristic, complemented
4C32×#323C211yesmaximal, characteristic, complemented
5C3×#4525C211yesmaximal, characteristic, complemented
6C3×#4468C211yesmaximal, characteristic, complemented
7C3×#4468C211yesmaximal, characteristic, complemented
8C3×#1469—31nomaximal
9#68104C311yesmaximal, characteristic, direct product factor
10C22×C3×#67C411yescharacteristic
11C22×C3×Dic6C411yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×C3×#217C411yescharacteristic
14C2×C3×(C2×D3)⋊C4C411yescharacteristic
15C2×C3×(C2×D3)⋊C4C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C3×#885—21no—
18C3×#885—21no—
19C3×#885—21no—
20C3×#885—21no—
21C32×C22⋊C8C2211yescharacteristic
22C32×C22⋊C8C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#815—21no—
26C3×Dic3⋊C8—21no—
27C3×Dic3⋊C8—21no—
28C3×C8×Dic3—21no—
29C2×C3×#124—31no—
30C2×#885C2×C311yescharacteristic
31C3×#432—31no—
32C3×#431—31no—
33#4719C2×C311yescharacteristic, complemented
34#4718C2×C311yescharacteristic, complemented
35C3×#323—21no—
36C3×#323—31no—
37C3×#323—31no—
38C3×#323—31no—
39C3×#323D311yescharacteristic, complemented
40C3×#323C2×C311yescharacteristic, complemented
41#4525C2×C311yescharacteristic, complemented
42#4468C2×C311yescharacteristic, complemented
43#4468C2×C311yescharacteristic, complemented
44C24×C32C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4C2×C411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—42no—
51C22×C3×Dic3C2×C411yescharacteristic
52C22×C3×Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C411yescharacteristic
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—42no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C32×C22⋊C4—21no—
60C32×C22⋊C4—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#1469—31noSylow
74C22×C3×Q8—31no—
75C22×C3×D4—31no—
76C22×#67C3×C411yescharacteristic
77C22×Dic6C3×C411yescharacteristic
78C3×#124—61no—
79C3×#124—61no—
80C3×#124—61no—
81C3×#124—61no—
82C2×C3×C22⋊C4—21no—
83C2×C3×C22⋊C4—31no—
84C2×C3×C22⋊C4—31no—
85C2×C3×C22⋊C4—31no—
86C2×C3×C22⋊C4C2×D311yescharacteristic
87C2×C3×C22⋊C4C22×C311yescharacteristic
88C2×C3×C42—31no—
89C2×#217C3×C411yescharacteristic
90C2×(C2×D3)⋊C4C3×C411yescharacteristic
91C2×(C2×D3)⋊C4C22×C311yescharacteristic
92C2×C4×Dic3C22×C311yescharacteristic
93#885—21no—
94#885—21no—
95#885—21no—
96#885—21no—
97C3×C4⋊C8—61no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—21no—
100C3×C22⋊C8—21no—
101C3×C22⋊C8—31no—
102C3×C22⋊C8—31no—
103C3×C22⋊C8C2×D311yescharacteristic
104C3×C22⋊C8C2×D311yescharacteristic
105C3×C22⋊C8C22×C311yescharacteristic
106C3×C22⋊C8C22×C311yescharacteristic
107C3×#97—61no—
108C3×C4×C8—61no—
109#830C22×C311yescharacteristic
110#830C22×C311yescharacteristic
111#815—21no—
112Dic3⋊C8—21no—
113Dic3⋊C8—21no—
114C8×Dic3—21no—
115C23×C32—21no—
116C23×C32—21no—
117C23×C32—21no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32C22×C411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C2×C32×C4—21no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C3×#67—42no—
132C3×#67—42no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3C22⋊C411yescharacteristic
139C2×C3×Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C3×Dic6—42no—
143C3×Dic6—42no—
144C32×C8—41no—
145C32×C8—41no—
146C3×C3⋊C8—41no—
147C3×C3⋊C8—41no—
148C2×#124—31no—
149#432—31no—
150#431—31no—
151#323—31no—
152#323—31no—
153#323—31no—
154#323C3×D311yescharacteristic, complemented
155C24×C3—21no—
156C24×C3—31no—
157C24×C3C4×D311yescharacteristic
158C24×C3C2×C3×C411yescharacteristic
159C23×D3C2×C3×C411yescharacteristic
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×Q8—122no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—122no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4C4×D311yescharacteristic
172C22×C3×C4C2×C3×C411yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C23×C311yescharacteristic
175C2×#67—21no—
176C2×#67—21no—
177C2×#67—42no—
178C22×Dic3C2×C3×C411yescharacteristic
179C22×Dic3C2×C3×C411yescharacteristic
180C22×Dic3C2×C3×C411yescharacteristic
181C2×Dic6—21no—
182C2×Dic6—21no—
183C2×Dic6—42no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—41no—
189C2×C3×C8—41no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—41no—
197C3×C22⋊C4—41no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C42—31no—
205C3×C42—31no—
206C3×C42—31no—
207C3×C42—31no—
208#217—21no—
209#217—21no—
210(C2×D3)⋊C4—21no—
211(C2×D3)⋊C4—21no—
212(C2×D3)⋊C4—21no—
213(C2×D3)⋊C4—21no—
214C4×Dic3C3×D411yescharacteristic
215C4×Dic3C3×D411yescharacteristic
216C4×Dic3C3×D411yescharacteristic
217C4×Dic3C3×D411yescharacteristic
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C22×C32—21no—
221C22×C32—21no—
222C22×C32—41no—
223C22×C32—41no—
224C22×C32—41no—
225C22×C32—81no—
226C22×C32—81no—
227C22×C32C2×C22⋊C411yescharacteristic
228C22×C32#13111yescharacteristic
229C22×C32#13111yescharacteristic
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—81no—
234C2×C3×D3—81no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—41no—
238C3×Dic3—21no—
239C3×Dic3—21no—
240C3×Dic3—21no—
241C3×Dic3—41no—
242C3×Dic3#10012yes—
243C22×Q8—31no—
244C22×D4—31no—
245#124—61no—
246#124—61no—
247#124—61no—
248#124—61no—
249C2×C22⋊C4—31no—
250C2×C22⋊C4—31no—
251C2×C22⋊C4—31no—
252C2×C22⋊C4C2×C3×D311yescharacteristic
253C2×C42—31no—
254C4⋊C8—61no—
255C4⋊C8—61no—
256C22⋊C8—31no—
257C22⋊C8—31no—
258C22⋊C8C2×C3×D311yescharacteristic
259C22⋊C8C2×C3×D311yescharacteristic
260#97—61no—
261C4×C8—61no—
262C23×C3—22no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3—41no—
275C23×C3—41no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3—81no—
280C23×C3—81no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3C2×C4×D311yescharacteristic
284C23×C3C22×C3×C411yescharacteristic
285C22×D3—21no—
286C22×D3—21no—
287C22×D3—21no—
288C22×D3—41no—
289C22×D3—41no—
290C3×Q8—122no—
291C3×Q8—122no—
292C3×D4—122no—
293C3×D4—122no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—62no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—81no—
312C2×C3×C4—81no—
313C2×C3×C4—121no—
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4C2×C3×D411yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318#67—42no—
319#67—42no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—22no—
323C2×Dic3—21no—
324C2×Dic3—41no—
325C2×Dic3C3×C22⋊C411yescharacteristic
326C2×Dic3C3×C22⋊C411yescharacteristic
327C2×Dic3C3×C22⋊C411yescharacteristic
328C2×Dic3C3×C22⋊C411yescharacteristic
329Dic6—42no—
330Dic6—42no—
331C3×C8—41no—
332C3×C8—41no—
333C3×C8—41no—
334C3×C8—41no—
335C3×C8—81no—
336C3×C8—81no—
337C3×C8—121no—
338C3×C8—121no—
339C3⋊C8—41no—
340C3⋊C8—41no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—81no—
344C2×C32#40811yescharacteristic
345C2×C32#41011yescharacteristic
346C2×C32C2×#10011yescharacteristic
347C3×D3—81no—
348C24—31no—
349C24C3×C4×D311yescharacteristic
350C2×Q8—61no—
351C2×Q8—61no—
352C2×Q8—122no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—122no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4C3×C4×D311yescharacteristic
360C22×C4C22×C3×D311yescharacteristic
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—61no—
364C2×C8—61no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C42—31no—
374C42—31no—
375C42—31no—
376C42—31no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—42no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—81no—
394C22×C3—81no—
395C22×C3—81no—
396C22×C3—81no—
397C22×C3—81no—
398C22×C3—81no—
399C22×C3—82no—
400C22×C3—82no—
401C22×C3—121no—
402C22×C3—121no—
403C22×C3—121no—
404C22×C3—241no—
405C22×C3—241no—
406C22×C3D3×C22⋊C411yescharacteristic
407C22×C3#90111yescharacteristic
408C22×C3#90711yescharacteristic
409C22×C3C2×C3×C22⋊C411yescharacteristic
410C22×C3C3×#13111yescharacteristic
411C22×C3C3×#13111yescharacteristic
412C2×D3—41no—
413C2×D3—41no—
414C2×D3—41no—
415C2×D3—81no—
416C2×D3—81no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—32no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—61no—
427C3×C4—61no—
428C3×C4—61no—
429C3×C4—81no—
430C3×C4—121no—
431Dic3—21no—
432Dic3—21no—
433Dic3—21no—
434Dic3—41no—
435Dic3C3×#10012yes—
436C32#146911yescharacteristic, complemented, Sylow
437C23—21no—
438C23—21no—
439C23—21no—
440C23—41no—
441C23—41no—
442C23—61no—
443C23—61no—
444C23—61no—
445C23—121no—
446C23—121no—
447C23C2×C3×C4×D311yescharacteristic
448Q8—122no—
449Q8—122no—
450D4—122no—
451D4—122no—
452C2×C4—21no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—62no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—121no—
464C2×C4C3×D3×D411yescharacteristic
465C2×C4C3×D3×D411yescharacteristic
466C8—41no—
467C8—41no—
468C8—121no—
469C8—121no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—41no—
478C2×C3—41no—
479C2×C3—82no—
480C2×C3—81no—
481C2×C3—81no—
482C2×C3—241no—
483C2×C3#472711yescharacteristic
484C2×C3#474011yescharacteristic
485C2×C3D3×#10011yescharacteristic
486C2×C3C3×#40811yescharacteristic
487C2×C3C3×#41011yescharacteristic
488C2×C3C2×C3×#10011yescharacteristic
489D3—81no—
490C22—21no—
491C22—21no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—81no—
496C22—81no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22—241no—
501C22—241no—
502C22C3×D3×C22⋊C411yescharacteristic
503C22C3×#90111yescharacteristic
504C22C3×#90711yescharacteristic
505C4—21no—
506C4—21no—
507C4—32no—
508C4—41no—
509C4—61no—
510C4—61no—
511C4—61no—
512C4—121no—
513C3—21no—
514C3#6810411yescharacteristic, direct product factor
515C3C3×#146911yescharacteristic, complemented
516C2—21no—
517C2—21no—
518C2—81no—
519C2—241no—
520C2C3×#472711yescharacteristic
521C2C3×#474011yescharacteristic
522C2C3×D3×#10011yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#67C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#323D3
hypocenterC3C3×#1469
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#323

Complements

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

NH ≅ G/Ntype
2. C3×#4719C2semidirect
3. C3×#4718C2semidirect
4. C32×#323C2semidirect
5. C3×#4525C2semidirect
6. C3×#4468C2semidirect
7. C3×#4468C2semidirect
9. #68104C3direct (N × H)
33. #4719C2×C3semidirect
34. #4718C2×C3semidirect
39. C3×#323D3semidirect
40. C3×#323C2×C3semidirect
41. #4525C2×C3semidirect
42. #4468C2×C3semidirect
43. #4468C2×C3semidirect
154. #323C3×D3semidirect
436. C32#1469semidirect
514. C3#68104direct (N × H)
515. C3C3×#1469semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8852
C3×#47192
C3×#47182
C32×#3232
C3×#45252
C3×#44682
C3×#14693
#681043