Finite Group Databasebeta

← C3×#70307 #11793880

Subgroups — C3×#70307 #11793880

Order 1152.

645 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#949C211yesmaximal, characteristic
2C32×#417C211yesmaximal, characteristic, complemented
3C3×#5234C211yesmaximal, characteristic, complemented
4C2×C3×#823C211yesmaximal, characteristic, complemented
5C2×C3×#822C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C3×#4530C211yesmaximal, characteristic, complemented
8C3×#2051—31nomaximal
9#70307C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C3×#949—22no—
15C3×#949—22no—
16C2×C3×#215—21no—
17C2×C3×#213—21no—
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C32×#103—21no—
22C32×#102—21no—
23C3×#830—22no—
24C3×#823—22no—
25C3×#822—22no—
26C3×#809—22no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C2×#949C2×C311yescharacteristic
29C2×C3×#108—31no—
30C3×#417—21no—
31C3×#417D311yescharacteristic, complemented
32C3×#417C2×C311yescharacteristic, complemented
33C2×C3×#102—31no—
34C2×C3×#100—31no—
35C3×#408—31no—
36#5234C2×C311yescharacteristic, complemented
37C2×#823C2×C311yescharacteristic, complemented
38C2×#822C2×C311yescharacteristic, complemented
39C2×#809C2×C311yescharacteristic, complemented
40C3×#343—31no—
41#4530C2×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×C4—21no—
52C22×C32×C4C2311yescharacteristic
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—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C3×#215—24no—
65C3×#213—24no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208D412yes—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
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—31no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C22×C311yescharacteristic
94#949—22no—
95#949—22no—
96C2×#215—21no—
97C2×#213—21no—
98C2×#208C22×C311yescharacteristic
99C2×#208C22×C311yescharacteristic
100C22×C3⋊C8C22×C311yescharacteristic
101C3×#108—62no—
102C3×#103—22no—
103C3×#103—21no—
104C3×#103—21no—
105C3×#102—22no—
106C3×#102—21no—
107C3×#102—21no—
108C3×#102—62no—
109C3×#100—62no—
110C3×C22⋊C8—62no—
111#830—22no—
112#823—22no—
113#822—22no—
114#809—22no—
115C23×C32—21no—
116C23×C32#4111yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—81no—
121C22×C3×D3—81no—
122C32×Q8—21no—
123C32×Q8—21no—
124C32×D4—21no—
125C32×D4—21no—
126C32×D4—41no—
127C32×D4—41no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—81no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143C32×C8—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—41no—
147C2×AGL(1,ℤ/8)—31no—
148C2×#108—31no—
149#417C3×D311yescharacteristic, complemented
150C2×#102—31no—
151C2×#100—31no—
152#408—31no—
153#343—31no—
154C24×C3—61no—
155C23×D3—21no—
156C3×#41—22no—
157C3×#41—22no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41—21no—
164C3×#41—21no—
165C3×#41—21no—
166C3×#41—41no—
167C3×#41—41no—
168C2×C3×Q8—21no—
169C2×C3×Q8#6711yescharacteristic
170C2×C3×Q8C3×D411yescharacteristic
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—32no—
175C2×C3×D4—41no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4#6711yescharacteristic
182C2×C3×D4C3×D411yescharacteristic
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—41no—
189C22×C3×C4—41no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C23×C311yescharacteristic
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12C3×D412yes—
198C3×SD16—64no—
199C3×D8—64no—
200C3×M16—21no—
201C3×M16—21no—
202C3×M16—21no—
203C3×M16—21no—
204C3×M16—32no—
205C3×M16—41no—
206C3×M16—41no—
207C3×M16—61no—
208C3×M16—61no—
209C3×M16—61no—
210C2×C3×C8—22no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—32no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—41no—
224#215—24no—
225#213—24no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208C3×D412yes—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8C3×D412yes—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32—41no—
238C22×C32—41no—
239C22×C32—41no—
240C22×C32#12111yescharacteristic
241C22×C32#12311yescharacteristic
242C22×C32#12411yescharacteristic
243C2×C3×D3—42no—
244C2×C3×D3—82no—
245C2×C3×D3—81no—
246C2×C3×D3—81no—
247C2×C3×D3—82no—
248C32×C4—41no—
249C32×C4—81no—
250C32×C4#12011yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12111yescharacteristic
253C32×C4#12311yescharacteristic
254C2×#41C2×C3×D311yescharacteristic
255C22×D4—31no—
256AGL(1,ℤ/8)—62no—
257AGL(1,ℤ/8)—62no—
258C2×SD16—61no—
259C2×D8—61no—
260C2×M16—31no—
261C2×M16—31no—
262C2×M16C2×C3×D311yescharacteristic
263C22×C8—31no—
264C2×C4⋊C4C2×C3×D311yescharacteristic
265#108—62no—
266#103—21no—
267#102—21no—
268#102—62no—
269#100—62no—
270C22⋊C8—62no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—41no—
275C23×C3—62no—
276C23×C3—121no—
277C23×C3—121no—
278C23×C3—241no—
279C23×C3—241no—
280C23×C3#23711yescharacteristic
281C23×C3C3×#4111yescharacteristic
282C22×D3—22no—
283C22×D3—41no—
284C22×D3—41no—
285C22×D3—81no—
286C22×D3—81no—
287C3×Q8—22no—
288C3×Q8—21no—
289C3×Q8—21no—
290C3×Q8—21no—
291C3×Q8—21no—
292C3×Q8—41no—
293C3×D4—22no—
294C3×D4—21no—
295C3×D4—21no—
296C3×D4—21no—
297C3×D4—21no—
298C3×D4—41no—
299C3×D4—42no—
300C3×D4—42no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—41no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—121no—
308C3×D4—121no—
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—41no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—42no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—82no—
328C2×C3×C4—81no—
329C2×C3×C4—81no—
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×C3×D411yescharacteristic
337C2×C3×C4C2×C3×D411yescharacteristic
338C2×C3×C4C2×C3×D411yescharacteristic
339C2×C3×C4C2×C3×D411yescharacteristic
340C2×C3×C4C3×#4111yescharacteristic
341C2×C3×C4C3×#4111yescharacteristic
342D12—22no—
343D12—22no—
344D12—41no—
345D12—41no—
346C3×C8—42no—
347C3×C8—41no—
348C3×C8—41no—
349C3×C8—62no—
350C3×C8—62no—
351C3×C8—121no—
352C3⋊C8—22no—
353C3⋊C8—22no—
354C3⋊C8—41no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—81no—
358C2×C32#39411yescharacteristic
359C2×C32#47111yescharacteristic
360C2×C32#47211yescharacteristic
361C3×D3—82no—
362C24—61no—
363#41—21no—
364#41—21no—
365#41—21no—
366#41—21no—
367C2×Q8C3×#6711yescharacteristic
368C2×D4—21no—
369C2×D4—32no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4C3×#6711yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4C22×C3×D311yescharacteristic
379SD16—64no—
380D8—64no—
381M16—21no—
382M16—21no—
383M16—32no—
384M16—61no—
385M16—61no—
386M16—61no—
387C2×C8—21no—
388C2×C8—32no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—61no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—42no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—122no—
414C22×C3—242no—
415C22×C3—242no—
416C22×C3—241no—
417C22×C3—241no—
418C22×C3#88311yescharacteristic
419C22×C3#88511yescharacteristic
420C22×C3#93911yescharacteristic
421C22×C3C3×#12111yescharacteristic
422C22×C3C3×#12311yescharacteristic
423C22×C3C3×#12411yescharacteristic
424C2×D3—42no—
425C2×D3—82no—
426C2×D3—81no—
427C2×D3—81no—
428C2×D3—82no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—42no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—82no—
437C3×C4—81no—
438C3×C4—81no—
439C3×C4#88411yescharacteristic
440C3×C4#88411yescharacteristic
441C3×C4#92911yescharacteristic
442C3×C4#93711yescharacteristic
443C3×C4C3×#12011yescharacteristic
444C3×C4C3×#12111yescharacteristic
445C3×C4C3×#12111yescharacteristic
446C3×C4C3×#12311yescharacteristic
447C32#205111yescharacteristic, complemented, Sylow
448C23—21no—
449C23—62no—
450C23—121no—
451C23—121no—
452C23—241no—
453C23—241no—
454C23C3×#23711yescharacteristic
455Q8—21no—
456Q8—21no—
457D4—21no—
458D4—21no—
459D4—41no—
460D4—41no—
461D4—62no—
462D4—62no—
463D4—121no—
464D4—121no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—81no—
470C2×C4C3×#23511yescharacteristic
471C2×C4C3×#23511yescharacteristic
472C2×C4C3×D3×D411yescharacteristic
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C3×D3×D411yescharacteristic
475C2×C4C2×C3×#6711yescharacteristic
476C8—41no—
477C8—62no—
478C8—62no—
479C8—121no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—82no—
490C2×C3—81no—
491C2×C3—81no—
492C2×C3—242no—
493C2×C3#495911yescharacteristic
494C2×C3#519911yescharacteristic
495C2×C3#520311yescharacteristic
496C2×C3C3×#39411yescharacteristic
497C2×C3C3×#47111yescharacteristic
498C2×C3C3×#47211yescharacteristic
499D3—82no—
500C22—21no—
501C22—21no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—122no—
506C22—242no—
507C22—242no—
508C22—241no—
509C22—241no—
510C22C3×#88311yescharacteristic
511C22C3×#88511yescharacteristic
512C22C3×#93911yescharacteristic
513C4—41no—
514C4—81no—
515C4C3×#88411yescharacteristic
516C4C3×#88411yescharacteristic
517C4C3×#92911yescharacteristic
518C4C3×#93711yescharacteristic
519C3—21no—
520C3#7030711yescharacteristic, direct product factor
521C3C3×#205111yescharacteristic, complemented
522C2—21no—
523C2—21no—
524C2—81no—
525C2—242no—
526C2C3×#495911yescharacteristic
527C2C3×#519911yescharacteristic
528C2C3×#520311yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#417C2
socleC22×C32#121
prime radicalC2×C3×#949C2
hypercenterC3×#417D3
hypocenterC3C3×#2051
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
2. C32×#417C2semidirect
3. C3×#5234C2semidirect
4. C2×C3×#823C2semidirect
5. C2×C3×#822C2semidirect
6. C2×C3×#809C2semidirect
7. C3×#4530C2semidirect
9. #70307C3direct (N × H)
31. C3×#417D3semidirect
32. C3×#417C2×C3semidirect
36. #5234C2×C3semidirect
37. C2×#823C2×C3semidirect
38. C2×#822C2×C3semidirect
39. C2×#809C2×C3semidirect
41. #4530C2×C3semidirect
149. #417C3×D3semidirect
447. C32#2051semidirect
520. C3#70307direct (N × H)
521. 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×#4172
C3×#52342
C2×C3×#8232
C2×C3×#8222
C2×C3×#8092
C3×#45302
C3×#20513
#703073