Finite Group Databasebeta

← C3×#70196 #11793889

Subgroups — C3×#70196 #11793889

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#932C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic, complemented
3C2×C3×#833C211yesmaximal, characteristic, complemented
4C3×#5110C211yesmaximal, characteristic, complemented
5C2×C3×#819C211yesmaximal, characteristic, complemented
6C3×#4966C211yesmaximal, characteristic, complemented
7C3×#4530C211yesmaximal, characteristic, complemented
8C3×#2051—31nomaximal
9#70196C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#214—21no—
15C3×#932—22no—
16C3×#932—22no—
17C2×C3×#213—21no—
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C32×#102—22no—
22C3×#833—22no—
23C3×(C2×D3)⋊C8—22no—
24C3×#819—22no—
25C3×#810—21no—
26C3×#809—21no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C2×#932C2×C311yescharacteristic
29C2×C3×#108—31no—
30C3×#417—31no—
31C2×C3×#102—21no—
32C2×C3×#102D311yescharacteristic, complemented
33C2×C3×#102C2×C311yescharacteristic, complemented
34C2×C3×#100—31no—
35C3×#408—31no—
36C2×#833C2×C311yescharacteristic, complemented
37#5110C2×C311yescharacteristic, complemented
38C2×#819C2×C311yescharacteristic, complemented
39#4966C2×C311yescharacteristic, complemented
40C3×#343—31no—
41#4530C2×C311yescharacteristic, complemented
42C24×C32—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4D412yes—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×C3×#67—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8D412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C3×#214—24no—
65C3×#213—24no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#2051—31noSylow
76C2×C3×#41—31no—
77C22×C3×D4—21no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C22×C311yescharacteristic
80C2×#235C22×C311yescharacteristic
81C3×AGL(1,ℤ/8)—62no—
82C3×AGL(1,ℤ/8)—62no—
83C2×C3×SD16—61no—
84C2×C3×D8—61no—
85C2×C3×M16—31no—
86C2×C3×M16—31no—
87C2×C3×M16—31no—
88C22×C3×C8—21no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C22×C311yescharacteristic
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C22×C311yescharacteristic
94C2×#214—21no—
95#932—22no—
96#932—22no—
97C2×#213—21no—
98C2×#208C22×C311yescharacteristic
99C2×#208C22×C311yescharacteristic
100C2×#208C22×C311yescharacteristic
101C3×#108—62no—
102C3×#103—61no—
103C3×#102—24no—
104C3×#102—22no—
105C3×#102—22no—
106C3×#102—61no—
107C3×#100—62no—
108C3×C22⋊C8—62no—
109#833—22no—
110(C2×D3)⋊C8—22no—
111#819—22no—
112#810—21no—
113#809—21no—
114C23×C32—22no—
115C23×C32—41no—
116C23×C32—41no—
117C23×C32—81no—
118C23×C32—81no—
119C23×C32#4111yescharacteristic
120C22×C3×D3—21no—
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—41no—
124C32×D4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—81no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C3×#67—41no—
134C3×#67—41no—
135C2×C3×Dic3—21no—
136C3×D12—21no—
137C3×D12—21no—
138C3×C4×D3—41no—
139C3×C4×D3—41no—
140C3×Dic6—21no—
141C3×Dic6—21no—
142C32×C8—22no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C3×C3⋊C8—41no—
146C2×AGL(1,ℤ/8)—31no—
147C2×#108—31no—
148#417—31no—
149C2×#102C3×D311yescharacteristic, complemented
150C2×#100—31no—
151#408—31no—
152#343—31no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—41no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C3×#41—61no—
160C2×C3×Q8—31no—
161C2×C3×D4—22no—
162C2×C3×D4—22no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—22no—
174C2×C3×D4—31no—
175C2×C3×D4—41no—
176C2×C3×D4—41no—
177C2×C3×D4—41no—
178C2×C3×D4—61no—
179C2×C3×D4D1212yes—
180C2×C3×D4C3×D412yes—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—41no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C23×C311yescharacteristic
188C2×#67—21no—
189#235—21no—
190#235—21no—
191#235—21no—
192#235—21no—
193C2×D12C3×D411yescharacteristic
194C2×C4×D3—21no—
195C2×Dic6C3×D411yescharacteristic
196C3×SD16—64no—
197C3×D8—64no—
198C3×M16—32no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C3×M16—61no—
203C3×M16—61no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—22no—
209C2×C3×C8—41no—
210C2×C3×C8—41no—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C2×C3×C8#6712yes—
215C2×C3×C8C3×D412yes—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—41no—
222#214—24no—
223#213—24no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208C3×D412yes—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—42no—
236C22×C32—82no—
237C22×C32—82no—
238C22×C32—81no—
239C22×C32—81no—
240C22×C32#12111yescharacteristic
241C22×C32#12311yescharacteristic
242C22×C32#12411yescharacteristic
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—41no—
246C32×C4—81no—
247C32×C4#12011yescharacteristic
248C32×C4#12111yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12311yescharacteristic
251C3×Dic3—41no—
252C2×#41—31no—
253C22×D4C2×C3×D311yescharacteristic
254AGL(1,ℤ/8)—62no—
255AGL(1,ℤ/8)—62no—
256C2×SD16—61no—
257C2×D8—61no—
258C2×M16—31no—
259C2×M16—31no—
260C2×M16—31no—
261C22×C8C2×C3×D311yescharacteristic
262C2×C4⋊C4C2×C3×D311yescharacteristic
263#108—62no—
264#103—61no—
265#102—22no—
266#102—61no—
267#100—62no—
268C22⋊C8—62no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—42no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—41no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—61no—
280C23×C3—81no—
281C23×C3—81no—
282C23×C3—81no—
283C23×C3—81no—
284C23×C3—82no—
285C23×C3—82no—
286C23×C3#23711yescharacteristic
287C23×C3C3×#4111yescharacteristic
288C22×D3—21no—
289C3×Q8—61no—
290C3×Q8—61no—
291C3×D4—24no—
292C3×D4—22no—
293C3×D4—22no—
294C3×D4—22no—
295C3×D4—22no—
296C3×D4—42no—
297C3×D4—42no—
298C3×D4—42no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—61no—
304C3×D4—61no—
305C3×D4—121no—
306C3×D4—121no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—42no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—61no—
317C2×C3×C4—82no—
318C2×C3×C4—81no—
319C2×C3×C4—81no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4C2×D1211yescharacteristic
323C2×C3×C4#23511yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4#23711yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C2×C3×D411yescharacteristic
329C2×C3×C4C2×C3×D411yescharacteristic
330C2×C3×C4C2×C3×D411yescharacteristic
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C3×#4111yescharacteristic
333C2×C3×C4C3×#4111yescharacteristic
334#67—41no—
335#67—41no—
336C2×Dic3—21no—
337D12—21no—
338D12—21no—
339C4×D3—41no—
340C4×D3—41no—
341Dic6—21no—
342Dic6—21no—
343C3×C8—22no—
344C3×C8—22no—
345C3×C8—42no—
346C3×C8—62no—
347C3×C8—121no—
348C3×C8—121no—
349C3⋊C8—22no—
350C3⋊C8—41no—
351C3⋊C8—41no—
352C2×C32—21no—
353C2×C32—21no—
354C2×C32—82no—
355C2×C32#39411yescharacteristic
356C2×C32#47111yescharacteristic
357C2×C32#47211yescharacteristic
358C3×D3—81no—
359C24—21no—
360#41—61no—
361#41—61no—
362#41—61no—
363#41—61no—
364C2×Q8—31no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—31no—
371C2×D4—61no—
372C2×D4C3×D1212yes—
373C22×C4—21no—
374C22×C4—61no—
375C22×C4C22×C3×D311yescharacteristic
376SD16—64no—
377D8—64no—
378M16—32no—
379M16—61no—
380M16—61no—
381M16—61no—
382M16—61no—
383M16—61no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—61no—
387C2×C8—61no—
388C2×C8—61no—
389C2×C8C3×#6712yes—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—44no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—82no—
405C22×C3—82no—
406C22×C3—84no—
407C22×C3—84no—
408C22×C3—82no—
409C22×C3—82no—
410C22×C3—82no—
411C22×C3—82no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3#88511yescharacteristic
420C22×C3#88611yescharacteristic
421C22×C3#93811yescharacteristic
422C22×C3C3×#12111yescharacteristic
423C22×C3C3×#12311yescharacteristic
424C22×C3C3×#12411yescharacteristic
425C2×D3—41no—
426C2×D3—41no—
427C2×D3—41no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—82no—
433C3×C4—81no—
434C3×C4—81no—
435C3×C4—121no—
436C3×C4#88211yescharacteristic
437C3×C4#88311yescharacteristic
438C3×C4#93011yescharacteristic
439C3×C4#93911yescharacteristic
440C3×C4C3×#12011yescharacteristic
441C3×C4C3×#12111yescharacteristic
442C3×C4C3×#12111yescharacteristic
443C3×C4C3×#12311yescharacteristic
444Dic3—41no—
445C32#205111yescharacteristic, complemented, Sylow
446C23—22no—
447C23—41no—
448C23—41no—
449C23—61no—
450C23—81no—
451C23—81no—
452C23C3×#23711yescharacteristic
453Q8—61no—
454Q8—61no—
455D4—22no—
456D4—22no—
457D4—41no—
458D4—41no—
459D4—61no—
460D4—61no—
461D4—121no—
462D4—121no—
463C2×C4—41no—
464C2×C4—61no—
465C2×C4—81no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4C2×C3×D1211yescharacteristic
469C2×C4C3×#23511yescharacteristic
470C2×C4C3×D3×D411yescharacteristic
471C2×C4C3×D3×D411yescharacteristic
472C2×C4C3×#23711yescharacteristic
473C2×C4C2×C3×#6711yescharacteristic
474C8—22no—
475C8—62no—
476C8—121no—
477C8—121no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—84no—
488C2×C3—82no—
489C2×C3—82no—
490C2×C3—241no—
491C2×C3#496111yescharacteristic
492C2×C3#516011yescharacteristic
493C2×C3#517711yescharacteristic
494C2×C3C3×#39411yescharacteristic
495C2×C3C3×#47111yescharacteristic
496C2×C3C3×#47211yescharacteristic
497D3—81no—
498C22—21no—
499C22—21no—
500C22—42no—
501C22—82no—
502C22—82no—
503C22—81no—
504C22—81no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22C3×#88511yescharacteristic
509C22C3×#88611yescharacteristic
510C22C3×#93811yescharacteristic
511C4—81no—
512C4—121no—
513C4C3×#88211yescharacteristic
514C4C3×#88311yescharacteristic
515C4C3×#93011yescharacteristic
516C4C3×#93911yescharacteristic
517C3—21no—
518C3#7019611yescharacteristic, direct product factor
519C3C3×#205111yescharacteristic, complemented
520C2—21no—
521C2—21no—
522C2—82no—
523C2—241no—
524C2C3×#496111yescharacteristic
525C2C3×#516011yescharacteristic
526C2C3×#517711yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC22×C32#121
prime radicalC2×C3×#932C2
hypercenterC2×C3×#102D3
hypocenterC3C3×#2051
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C32×#102C2semidirect
3. C2×C3×#833C2semidirect
4. C3×#5110C2semidirect
5. C2×C3×#819C2semidirect
6. C3×#4966C2semidirect
7. C3×#4530C2semidirect
9. #70196C3direct (N × H)
32. C2×C3×#102D3semidirect
33. C2×C3×#102C2×C3semidirect
36. C2×#833C2×C3semidirect
37. #5110C2×C3semidirect
38. C2×#819C2×C3semidirect
39. #4966C2×C3semidirect
41. #4530C2×C3semidirect
149. C2×#102C3×D3semidirect
445. C32#2051semidirect
518. C3#70196direct (N × H)
519. C3C3×#2051semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9322
C2×C32×#1022
C2×C3×#8332
C3×#51102
C2×C3×#8192
C3×#49662
C3×#45302
C3×#20513
#701963