Finite Group Databasebeta

← C3×#69035 #11787618

Subgroups — C3×#69035 #11787618

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5748C211yesmaximal, characteristic
2C3×#5745C211yesmaximal, characteristic, complemented
3C3×#5129C211yesmaximal, characteristic, complemented
4C3×#5005C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic, complemented
6C32×#344C211yesmaximal, characteristic, complemented
7C3×#4558C211yesmaximal, characteristic, complemented
8C3×#1881—31nomaximal
9#69035C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#909—21no—
18C3×#909C412yescomplemented
19C3×#908—21no—
20C3×#908C412yescomplemented
21C3×#907—22no—
22C3×D3×M16—22no—
23C3×#904—22no—
24C3×#901—22no—
25C3×(C2×D3)⋊C8—22no—
26C3×#810—21no—
27C3×#809—21no—
28C3×#805—22no—
29C3×#575—31no—
30C3×#568—31no—
31#5748C2×C311yescharacteristic
32#5745C2×C311yescharacteristic, complemented
33C3×#421—31no—
34C3×#416—31no—
35C3×#408—31no—
36#5129C2×C311yescharacteristic, complemented
37#5005C2×C311yescharacteristic, complemented
38#5002C2×C311yescharacteristic, complemented
39C3×#344—21no—
40C3×#344D311yescharacteristic, complemented
41C3×#344C2×C311yescharacteristic, complemented
42C3×#341—31no—
43#4558C2×C311yescharacteristic, complemented
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235C2×C412yes—
54C3×#235D412yes—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×Dic6C2×C411yescharacteristic
60C2×C3×Dic6D411yescharacteristic
61C32×M16—21no—
62C32×M16—21no—
63C32×M16—21no—
64C32×M16C2×C412yes—
65C2×C32×C8—21no—
66C2×C32×C8D412yes—
67C32×C4⋊C4—21no—
68C32×C22⋊C4—21no—
69C32×C42—21no—
70C3×#208—21no—
71C3×#208D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C3×Dic12—22no—
77C3×D24—22no—
78C3×#204—22no—
79C3×#204—22no—
80C3×ΓL(1,𝔽25)—24no—
81C3×D3×C8—24no—
82#1881—31noSylow
83C2×C3×#41—31no—
84C2×C3×#41—31no—
85C2×#235C22×C311yescharacteristic
86C2×#235C22×C311yescharacteristic
87C3×#137—32no—
88C3×#137—61no—
89C3×AGL(1,ℤ/8)—32no—
90C3×AGL(1,ℤ/8)—61no—
91C3×#135—62no—
92C3×#131—62no—
93C3×#131—62no—
94C2×C3×M16—21no—
95C2×C3×M16—21no—
96C2×C3×M16—31no—
97C2×C3×M16—62no—
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×M16C2×D311yescharacteristic
100C2×C3×M16C22×C311yescharacteristic
101C2×C3×M16C22×C311yescharacteristic
102C22×C3×C8—31no—
103C3×#117—21no—
104C3×#117C2×D311yescharacteristic
105C3×#117C22×C311yescharacteristic
106C2×#208C22×C311yescharacteristic
107C22×C3⋊C8C22×C311yescharacteristic
108#909—21no—
109#909C3×C412yescomplemented
110#908—21no—
111#908C3×C412yescomplemented
112#907—22no—
113D3×M16—22no—
114#904—22no—
115#901—22no—
116C3×#104—62no—
117C3×#103—61no—
118C3×#102—61no—
119C3×C22⋊C8—62no—
120(C2×D3)⋊C8—22no—
121#810—21no—
122#809—21no—
123#805—22no—
124C23×C32#4111yescharacteristic
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C2×C32×C4—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C3×#67—22no—
135C3×#67—22no—
136C3×#67—41no—
137C3×#67—41no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C3×D12—21no—
141C3×D12—21no—
142C3×D12—21no—
143C3×D12C22⋊C412yes—
144C3×C4×D3—22no—
145C3×C4×D3—22no—
146C3×C4×D3—41no—
147C3×C4×D3—41no—
148C3×Dic6—21no—
149C3×Dic6—21no—
150C3×Dic6—21no—
151C3×Dic6C22⋊C412yes—
152C32×C8—22no—
153C32×C8—22no—
154C3×C3⋊C8—22no—
155C3×C3⋊C8—41no—
156#575—31no—
157#568—31no—
158#421—31no—
159#416—31no—
160#408—31no—
161#344C3×D311yescharacteristic, complemented
162#341—31no—
163C3×#41—32no—
164C3×#41—32no—
165C3×#41—61no—
166C3×#41—61no—
167C3×#41—61no—
168C3×#41—61no—
169C3×#41—61no—
170C3×#41—61no—
171C2×C3×Q8—31no—
172C2×C3×Q8—31no—
173C2×C3×D4—31no—
174C2×C3×D4—31no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C23×C311yescharacteristic
182C2×#67—21no—
183C2×#67—21no—
184#235—21no—
185#235—21no—
186#235—21no—
187#235—21no—
188#235—21no—
189#235—21no—
190#235C2×C3×C412yes—
191#235C3×D412yes—
192C2×D12C2×C3×C411yescharacteristic
193C2×D12C3×D411yescharacteristic
194C2×C4×D3—21no—
195C2×C4×D3—21no—
196C2×Dic6C2×C3×C411yescharacteristic
197C2×Dic6C3×D411yescharacteristic
198C3×Q16—62no—
199C3×SD16—62no—
200C3×SD16—62no—
201C3×D8—62no—
202C3×M16—21no—
203C3×M16—21no—
204C3×M16—21no—
205C3×M16—21no—
206C3×M16—21no—
207C3×M16—21no—
208C3×M16—22no—
209C3×M16—32no—
210C3×M16—41no—
211C3×M16—41no—
212C3×M16—41no—
213C3×M16—64no—
214C3×M16—61no—
215C3×M16C4×D312yes—
216C3×M16C2×C3×C412yes—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—22no—
220C2×C3×C8—41no—
221C2×C3×C8—64no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C2×C3×C8D1212yes—
227C2×C3×C8C3×D412yes—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—41no—
231C3×C22⋊C4—22no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—41no—
237#208—21no—
238#208C3×D412yes—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243Dic12—22no—
244D24—22no—
245#204—22no—
246#204—22no—
247ΓL(1,𝔽25)—24no—
248D3×C8—24no—
249C22×C32—41no—
250C22×C32C4×D411yescharacteristic
251C22×C32#12111yescharacteristic
252C22×C32#12311yescharacteristic
253C2×C3×D3—22no—
254C2×C3×D3—42no—
255C2×C3×D3—41no—
256C2×C3×D3—81no—
257C32×C4—81no—
258C32×C4C2×C22⋊C411yescharacteristic
259C32×C4C4×D411yescharacteristic
260C32×C4#12011yescharacteristic
261C32×C4#12111yescharacteristic
262C3×Dic3—22no—
263C3×Dic3—41no—
264C2×#41—31no—
265C2×#41—31no—
266#137—32no—
267#137—61no—
268AGL(1,ℤ/8)—32no—
269AGL(1,ℤ/8)—61no—
270#135—62no—
271#131—62no—
272#131—62no—
273C2×M16—31no—
274C2×M16—62no—
275C2×M16C2×C3×D311yescharacteristic
276C2×M16C2×C3×D311yescharacteristic
277C22×C8—31no—
278#117C2×C3×D311yescharacteristic
279#104—62no—
280#103—61no—
281#102—61no—
282C22⋊C8—62no—
283C23×C3—21no—
284C23×C3—61no—
285C23×C3—61no—
286C23×C3#23511yescharacteristic
287C23×C3C3×#4111yescharacteristic
288C22×D3—21no—
289C22×D3—21no—
290C3×Q8—32no—
291C3×Q8—61no—
292C3×Q8—61no—
293C3×Q8—61no—
294C3×D4—32no—
295C3×D4—62no—
296C3×D4—62no—
297C3×D4—61no—
298C3×D4—61no—
299C3×D4—61no—
300C3×D4—121no—
301C3×D4—121no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—42no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—61no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—61no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23911yescharacteristic
323C2×C3×C4C22×C3×C411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325C2×C3×C4C2×C3×D411yescharacteristic
326C2×C3×C4C2×C3×D411yescharacteristic
327C2×C3×C4C2×C3×D411yescharacteristic
328C2×C3×C4C3×#4111yescharacteristic
329#67—22no—
330#67—22no—
331#67—41no—
332#67—41no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335D12—21no—
336D12—21no—
337D12—21no—
338D12C3×C22⋊C412yes—
339C4×D3—22no—
340C4×D3—22no—
341C4×D3—41no—
342C4×D3—41no—
343Dic6—21no—
344Dic6—21no—
345Dic6—21no—
346Dic6C3×C22⋊C412yes—
347C3×C8—22no—
348C3×C8—22no—
349C3×C8—22no—
350C3×C8—22no—
351C3×C8—42no—
352C3×C8—42no—
353C3×C8—62no—
354C3×C8—121no—
355C3⋊C8—22no—
356C3⋊C8—41no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32#38611yescharacteristic
361C3×D3—42no—
362C3×D3—81no—
363#41—32no—
364#41—32no—
365#41—61no—
366#41—61no—
367#41—61no—
368#41—61no—
369#41—61no—
370#41—61no—
371C2×Q8—31no—
372C2×Q8—31no—
373C2×D4—31no—
374C2×D4—31no—
375C2×D4—61no—
376C2×D4—61no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4C22×C3×D311yescharacteristic
380Q16—62no—
381SD16—62no—
382SD16—62no—
383D8—62no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—32no—
388M16—64no—
389M16—61no—
390M16C3×C4×D312yes—
391C2×C8—21no—
392C2×C8—64no—
393C2×C8—61no—
394C2×C8—61no—
395C2×C8—61no—
396C2×C8—61no—
397C2×C8C3×D1212yes—
398C4⋊C4—21no—
399C22⋊C4—21no—
400C42—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—62no—
407C22×C3—81no—
408C22×C3—122no—
409C22×C3—121no—
410C22×C3—241no—
411C22×C3C4×D1211yescharacteristic
412C22×C3#88411yescharacteristic
413C22×C3#89411yescharacteristic
414C22×C3C3×C4×D411yescharacteristic
415C22×C3C3×#12111yescharacteristic
416C22×C3C3×#12311yescharacteristic
417C2×D3—22no—
418C2×D3—42no—
419C2×D3—41no—
420C2×D3—81no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—62no—
426C3×C4—81no—
427C3×C4—81no—
428C3×C4—82no—
429C3×C4—121no—
430C3×C4D3×C22⋊C411yescharacteristic
431C3×C4#88211yescharacteristic
432C3×C4#89311yescharacteristic
433C3×C4#89511yescharacteristic
434C3×C4C2×C3×C22⋊C411yescharacteristic
435C3×C4C3×C4×D411yescharacteristic
436C3×C4C3×#12011yescharacteristic
437C3×C4C3×#12111yescharacteristic
438Dic3—22no—
439Dic3—41no—
440C32#188111yescharacteristic, complemented, Sylow
441C23—61no—
442C23—61no—
443C23C3×#23511yescharacteristic
444Q8—32no—
445Q8—61no—
446Q8—61no—
447Q8—61no—
448D4—32no—
449D4—62no—
450D4—62no—
451D4—61no—
452D4—61no—
453D4—61no—
454D4—121no—
455D4—121no—
456C2×C4—41no—
457C2×C4—61no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—61no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4C2×C3×C4×D311yescharacteristic
464C2×C4C2×C3×D1211yescharacteristic
465C2×C4C3×D3×D411yescharacteristic
466C2×C4C3×D3×D411yescharacteristic
467C2×C4C3×D3×D411yescharacteristic
468C2×C4C3×#23911yescharacteristic
469C8—22no—
470C8—22no—
471C8—62no—
472C8—121no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—41no—
481C2×C3—41no—
482C2×C3—41no—
483C2×C3—122no—
484C2×C3—241no—
485C2×C3#466511yescharacteristic
486C2×C3C3×#38611yescharacteristic
487D3—42no—
488D3—81no—
489C22—41no—
490C22—62no—
491C22—122no—
492C22—121no—
493C22—241no—
494C22C3×C4×D1211yescharacteristic
495C22C3×#88411yescharacteristic
496C22C3×#89411yescharacteristic
497C4—62no—
498C4—81no—
499C4—121no—
500C4C3×D3×C22⋊C411yescharacteristic
501C4C3×#88211yescharacteristic
502C4C3×#89311yescharacteristic
503C4C3×#89511yescharacteristic
504C3—21no—
505C3#6903511yescharacteristic, direct product factor
506C3C3×#188111yescharacteristic, complemented
507C2—21no—
508C2—21no—
509C2—21no—
510C2—122no—
511C2—241no—
512C2C3×#466511yescharacteristic
subgroupG/H
centerC3×C4#882
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#344C2
socleC2×C32#386
prime radicalC3×#5748C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#344D3
hypocenterC3C3×#1881
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#344

Complements

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

NH ≅ G/Ntype
2. C3×#5745C2semidirect
3. C3×#5129C2semidirect
4. C3×#5005C2semidirect
5. C3×#5002C2semidirect
6. C32×#344C2semidirect
7. C3×#4558C2semidirect
9. #69035C3direct (N × H)
18. C3×#909C4semidirect
20. C3×#908C4semidirect
32. #5745C2×C3semidirect
36. #5129C2×C3semidirect
37. #5005C2×C3semidirect
38. #5002C2×C3semidirect
40. C3×#344D3semidirect
41. C3×#344C2×C3semidirect
43. #4558C2×C3semidirect
109. #909C3×C4semidirect
111. #908C3×C4semidirect
161. #344C3×D3semidirect
440. C32#1881semidirect
505. C3#69035direct (N × H)
506. C3C3×#1881semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
C3×#57452
C3×#51292
C3×#50052
C3×#50022
C32×#3442
C3×#45582
C3×#18813
#690353