Finite Group Databasebeta

← C3×#70003 #11793883

Subgroups — C3×#70003 #11793883

Order 1152.

643 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#949C211yesmaximal, characteristic
2C32×#408C211yesmaximal, characteristic, complemented
3C3×#5232C211yesmaximal, characteristic, complemented
4C2×C3×#823C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×#819C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8C3×#2051—31nomaximal
9#70003C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C3×#949—22no—
15C3×#949—22no—
16C2×C3×#215—21no—
17C2×C3×#213—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C32×C22⋊C8—22no—
22C3×#835—21no—
23C3×#832—21no—
24C3×#823—22no—
25C3×#821—22no—
26C3×#819—22no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C2×#949C2×C311yescharacteristic
29C2×C3×#108—31no—
30C3×#417—31no—
31C2×C3×#102—31no—
32C2×C3×#100—31no—
33C3×#408—21no—
34C3×#408D311yescharacteristic, complemented
35C3×#408C2×C311yescharacteristic, complemented
36#5232C2×C311yescharacteristic, complemented
37C2×#823C2×C311yescharacteristic, complemented
38C2×#821C2×C311yescharacteristic, complemented
39C2×#819C2×C311yescharacteristic, complemented
40C3×#343—31no—
41#4554C2×C311yescharacteristic, complemented
42C23×C3×D3—21no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12D412yes—
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8D412yes—
65C3×#215—24no—
66C3×#213—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208D412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#2051—31noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C22×C311yescharacteristic
79C22×C3×D4—31no—
80C22×D12C22×C311yescharacteristic
81C3×AGL(1,ℤ/8)—62no—
82C3×AGL(1,ℤ/8)—62no—
83C2×C3×SD16—61no—
84C2×C3×D8—61no—
85C2×C3×M16—21no—
86C2×C3×M16—31no—
87C2×C3×M16—31no—
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×M16C22×C311yescharacteristic
90C22×C3×C8—21no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C22×C311yescharacteristic
93C2×C3×C4⋊C4—31no—
94#949—22no—
95#949—22no—
96C2×#215—21no—
97C2×#213—21no—
98C2×C4⋊Dic3C22×C311yescharacteristic
99C2×#208C22×C311yescharacteristic
100C2×#208C22×C311yescharacteristic
101C3×#108—62no—
102C3×#103—61no—
103C3×#102—61no—
104C3×#102—62no—
105C3×#100—62no—
106C3×C22⋊C8—24no—
107C3×C22⋊C8—22no—
108C3×C22⋊C8—22no—
109#835—21no—
110#832—21no—
111#823—22no—
112#821—22no—
113#819—22no—
114C23×C32—21no—
115C23×C32#4111yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—81no—
120C22×C3×D3—81no—
121C32×Q8—21no—
122C32×Q8—21no—
123C32×D4—21no—
124C32×D4—21no—
125C32×D4—41no—
126C32×D4—41no—
127C2×C32×C4—21no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3×Dic3—41no—
137C2×C3×Dic3—81no—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—41no—
141C3×D12—41no—
142C32×C8—22no—
143C32×C8—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C2×AGL(1,ℤ/8)—31no—
147C2×#108—31no—
148#417—31no—
149C2×#102—31no—
150C2×#100—31no—
151#408C3×D311yescharacteristic, complemented
152#343—31no—
153C24×C3—61no—
154C23×D3—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41—41no—
164C3×#41—41no—
165C3×#41—41no—
166C3×#41—41no—
167C2×C3×Q8—21no—
168C2×C3×Q8D1211yescharacteristic
169C2×C3×Q8C3×D411yescharacteristic
170C2×C3×D4—22no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—32no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4D1211yescharacteristic
181C2×C3×D4C3×D411yescharacteristic
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C23×C311yescharacteristic
189C22×Dic3—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12C3×D412yes—
196C3×SD16—64no—
197C3×D8—64no—
198C3×M16—21no—
199C3×M16—21no—
200C3×M16—21no—
201C3×M16—21no—
202C3×M16—32no—
203C3×M16—41no—
204C3×M16—41no—
205C3×M16—61no—
206C3×M16—61no—
207C3×M16—61no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—22no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—22no—
216C2×C3×C8—41no—
217C2×C3×C8—41no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C2×C3×C8#6712yes—
221C2×C3×C8C3×D412yes—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224#215—24no—
225#213—24no—
226C4⋊Dic3—21no—
227C4⋊Dic3—21no—
228#208—21no—
229#208—21no—
230#208—21no—
231#208C3×D412yes—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32—41no—
237C22×C32—41no—
238C22×C32—41no—
239C22×C32#12111yescharacteristic
240C22×C32#12311yescharacteristic
241C22×C32#12411yescharacteristic
242C2×C3×D3—42no—
243C2×C3×D3—82no—
244C2×C3×D3—81no—
245C2×C3×D3—81no—
246C2×C3×D3—82no—
247C32×C4—41no—
248C32×C4#12011yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12311yescharacteristic
252C3×Dic3—81no—
253C2×#41C2×C3×D311yescharacteristic
254C22×D4—31no—
255AGL(1,ℤ/8)—62no—
256AGL(1,ℤ/8)—62no—
257C2×SD16—61no—
258C2×D8—61no—
259C2×M16—31no—
260C2×M16—31no—
261C2×M16C2×C3×D311yescharacteristic
262C22×C8C2×C3×D311yescharacteristic
263C2×C4⋊C4—31no—
264#108—62no—
265#103—61no—
266#102—61no—
267#102—62no—
268#100—62no—
269C22⋊C8—22no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—121no—
276C23×C3—121no—
277C23×C3—241no—
278C23×C3—241no—
279C23×C3#23511yescharacteristic
280C23×C3C3×#4111yescharacteristic
281C22×D3—22no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—81no—
285C22×D3—81no—
286C3×Q8—21no—
287C3×Q8—21no—
288C3×Q8—21no—
289C3×Q8—21no—
290C3×Q8—41no—
291C3×Q8—41no—
292C3×D4—21no—
293C3×D4—21no—
294C3×D4—21no—
295C3×D4—21no—
296C3×D4—41no—
297C3×D4—41no—
298C3×D4—42no—
299C3×D4—42no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—121no—
307C3×D4—121no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—121no—
324C2×C3×C4—241no—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4#23711yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C2×C3×D411yescharacteristic
333C2×C3×C4C2×C3×D411yescharacteristic
334C2×C3×C4C2×C3×D411yescharacteristic
335C2×C3×C4C3×#4111yescharacteristic
336C2×C3×C4C3×#4111yescharacteristic
337C2×Dic3—41no—
338C2×Dic3—81no—
339D12—22no—
340D12—22no—
341D12—41no—
342D12—41no—
343C3×C8—22no—
344C3×C8—22no—
345C3×C8—42no—
346C3×C8—42no—
347C3×C8—41no—
348C3×C8—41no—
349C3×C8—62no—
350C3×C8—121no—
351C3⋊C8—22no—
352C3⋊C8—41no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32—81no—
356C2×C32#39411yescharacteristic
357C2×C32#47111yescharacteristic
358C2×C32#47211yescharacteristic
359C3×D3—82no—
360C24—61no—
361#41—21no—
362#41—21no—
363#41—21no—
364#41—21no—
365C2×Q8C3×D1211yescharacteristic
366C2×D4—21no—
367C2×D4—32no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4C3×D1211yescharacteristic
374C22×C4—21no—
375C22×C4—61no—
376C22×C4C22×C3×D311yescharacteristic
377SD16—64no—
378D8—64no—
379M16—21no—
380M16—21no—
381M16—32no—
382M16—61no—
383M16—61no—
384M16—61no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—61no—
389C2×C8—61no—
390C2×C8C3×#6712yes—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—122no—
412C22×C3—242no—
413C22×C3—242no—
414C22×C3—241no—
415C22×C3—241no—
416C22×C3#88311yescharacteristic
417C22×C3#88511yescharacteristic
418C22×C3#93011yescharacteristic
419C22×C3C3×#12111yescharacteristic
420C22×C3C3×#12311yescharacteristic
421C22×C3C3×#12411yescharacteristic
422C2×D3—42no—
423C2×D3—82no—
424C2×D3—81no—
425C2×D3—81no—
426C2×D3—82no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—241no—
435C3×C4#88211yescharacteristic
436C3×C4#88611yescharacteristic
437C3×C4#93811yescharacteristic
438C3×C4#93911yescharacteristic
439C3×C4C3×#12011yescharacteristic
440C3×C4C3×#12111yescharacteristic
441C3×C4C3×#12111yescharacteristic
442C3×C4C3×#12311yescharacteristic
443Dic3—81no—
444C32#205111yescharacteristic, complemented, Sylow
445C23—21no—
446C23—62no—
447C23—121no—
448C23—121no—
449C23—241no—
450C23—241no—
451C23C3×#23511yescharacteristic
452Q8—21no—
453Q8—21no—
454D4—21no—
455D4—21no—
456D4—41no—
457D4—41no—
458D4—62no—
459D4—62no—
460D4—121no—
461D4—121no—
462C2×C4—21no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—121no—
466C2×C4—241no—
467C2×C4C2×C3×D1211yescharacteristic
468C2×C4C3×D3×D411yescharacteristic
469C2×C4C3×D3×D411yescharacteristic
470C2×C4C3×#23711yescharacteristic
471C2×C4C3×#23711yescharacteristic
472C2×C4C2×C3×#6711yescharacteristic
473C8—22no—
474C8—41no—
475C8—62no—
476C8—121no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—82no—
487C2×C3—81no—
488C2×C3—81no—
489C2×C3—242no—
490C2×C3#496111yescharacteristic
491C2×C3#514111yescharacteristic
492C2×C3#514211yescharacteristic
493C2×C3C3×#39411yescharacteristic
494C2×C3C3×#47111yescharacteristic
495C2×C3C3×#47211yescharacteristic
496D3—82no—
497C22—21no—
498C22—21no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—122no—
503C22—242no—
504C22—242no—
505C22—241no—
506C22—241no—
507C22C3×#88311yescharacteristic
508C22C3×#88511yescharacteristic
509C22C3×#93011yescharacteristic
510C4—41no—
511C4—241no—
512C4C3×#88211yescharacteristic
513C4C3×#88611yescharacteristic
514C4C3×#93811yescharacteristic
515C4C3×#93911yescharacteristic
516C3—21no—
517C3#7000311yescharacteristic, direct product factor
518C3C3×#205111yescharacteristic, complemented
519C2—21no—
520C2—21no—
521C2—81no—
522C2—242no—
523C2C3×#496111yescharacteristic
524C2C3×#514111yescharacteristic
525C2C3×#514211yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#408C2
socleC22×C32#121
prime radicalC2×C3×#949C2
hypercenterC3×#408D3
hypocenterC3C3×#2051
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#408

Complements

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

NH ≅ G/Ntype
2. C32×#408C2semidirect
3. C3×#5232C2semidirect
4. C2×C3×#823C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×#819C2semidirect
7. C3×#4554C2semidirect
9. #70003C3direct (N × H)
34. C3×#408D3semidirect
35. C3×#408C2×C3semidirect
36. #5232C2×C3semidirect
37. C2×#823C2×C3semidirect
38. C2×#821C2×C3semidirect
39. C2×#819C2×C3semidirect
41. #4554C2×C3semidirect
151. #408C3×D3semidirect
444. C32#2051semidirect
517. C3#70003direct (N × H)
518. C3C3×#2051semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9492
C32×#4082
C3×#52322
C2×C3×#8232
C2×C3×#8212
C2×C3×#8192
C3×#45542
C3×#20513
#700033