Finite Group Databasebeta

← C3×#70086 #11784863

Subgroups — C3×#70086 #11784863

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 497 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C2×C32×#100C211yesmaximal, characteristic, complemented
3C3×#5221C211yesmaximal, characteristic, complemented
4C2×C3×#825C212yesmaximal, complemented
5C3×#5133C212yesmaximal, complemented
6C3×#1792—31nomaximal
7#70086C311yesmaximal, characteristic, direct product factor
8C22×C32×D4C2211yescharacteristic
9C22×C3×#67—22no—
10C3×#1004—22no—
11C3×#1004—24no—
12C3×#1004C414yescomplemented
13C2×C3×#237—22no—
14C2×C3×D3×D4—22no—
15C2×C3×#235C2212yes—
16C2×C32×M16C2212yescomplemented
17C2×C3×#217—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
19C2×C3×C4×Dic3C2211yescharacteristic, complemented
20C32×#100—22no—
21C3×#825—24no—
22C3×#821—22no—
23C3×#816—22no—
24C2×C3×H(5,𝔽2)—31no—
25C2×#1004C2×C311yescharacteristic
26C2×C3×#104—32no—
27C3×#417—32no—
28C2×C3×#100—21no—
29C2×C3×#100D311yescharacteristic, complemented
30C2×C3×#100C2×C311yescharacteristic, complemented
31C3×#390—31no—
32#5221C2×C311yescharacteristic, complemented
33C2×#825C2×C312yescomplemented
34#5133C2×C312yescomplemented
35C24×C32D412yes—
36C23×C3×D3—22no—
37C2×C32×D4—22no—
38C2×C32×D4—22no—
39C2×C32×D4C2×C412yes—
40C2×C32×D4D412yes—
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—24no—
43C2×C3×#67—28no—
44C2×C3×#67—28no—
45C2×C3×#67—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C3×#237—28no—
50C3×#237—28no—
51C3×D3×D4—28no—
52C3×D3×D4—28no—
53C3×#235—22no—
54C3×#235—22no—
55C3×#235C2×C414yes—
56C3×#235D414yes—
57C2×C3×D12D412yes—
58C2×C3×C4×D3—22no—
59C2×C3×Dic6D412yes—
60C32×M16—22no—
61C32×M16—22no—
62C2×C32×C8—22no—
63C3×#217—44no—
64C3×C4⋊Dic3—22no—
65C3×C4×Dic3—22no—
66#1792—31noSylow
67C3×H(5,𝔽2)—34no—
68C3×H(5,𝔽2)—64no—
69C3×H(5,𝔽2)—62no—
70C2×C3×#41—32no—
71C2×C3×#41—62no—
72C22×C3×D4—21no—
73C22×C3×D4—62no—
74C22×C3×D4—62no—
75C22×C3×D4C2×D311yescharacteristic
76C22×C3×D4C22×C311yescharacteristic
77C22×#67—22no—
78#1004—22no—
79#1004—24no—
80#1004C3×C414yescomplemented
81C2×#237—22no—
82C2×D3×D4—22no—
83C2×#235C22×C312yes—
84C2×C3×M16—22no—
85C2×C3×M16C2×D312yescomplemented
86C2×C3×M16C22×C312yescomplemented
87C2×C3×C4⋊C4—31no—
88C2×C3×C22⋊C4—62no—
89C2×C3×C42—31no—
90C2×#217—22no—
91C2×C4⋊Dic3C22×C311yescharacteristic, complemented
92C2×C4×Dic3C22×C311yescharacteristic, complemented
93C3×#104—64no—
94C3×#103—62no—
95C3×#102—62no—
96C3×#100—24no—
97C3×#100—22no—
98C3×#100—22no—
99#825—24no—
100#821—22no—
101#816—22no—
102C23×C32—22no—
103C23×C32—22no—
104C23×C32—42no—
105C23×C32—42no—
106C23×C32C22⋊C414yes—
107C23×C32C2×D411yescharacteristic
108C22×C3×D3—22no—
109C22×C3×D3—28no—
110C22×C3×D3—82no—
111C22×C3×D3—82no—
112C32×D4—24no—
113C32×D4—24no—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D412yes—
116C2×C32×C4C2×D412yes—
117C2×C32×C4C2×D411yescharacteristic
118C3×#67—216no—
119C3×#67—24no—
120C3×#67—24no—
121C2×C3×Dic3—28no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—41no—
128C3×D12—22no—
129C3×D12C22⋊C414yescomplemented
130C3×C4×D3—24no—
131C3×C4×D3—24no—
132C3×Dic6—22no—
133C3×Dic6C22⋊C414yescomplemented
134C32×C8—42no—
135C2×H(5,𝔽2)—31no—
136C2×#104—32no—
137#417—32no—
138C2×#100C3×D311yescharacteristic, complemented
139#390—31no—
140C24×C3—22no—
141C24×C3—62no—
142C24×C3D1212yes—
143C24×C3C3×D412yes—
144C23×D3—22no—
145C3×#41—34no—
146C3×#41—34no—
147C3×#41—68no—
148C3×#41—68no—
149C3×#41—62no—
150C3×#41—62no—
151C2×C3×Q8—32no—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—22no—
158C2×C3×D4—32no—
159C2×C3×D4—42no—
160C2×C3×D4—42no—
161C2×C3×D4—68no—
162C2×C3×D4—68no—
163C2×C3×D4—64no—
164C2×C3×D4—68no—
165C2×C3×D4—68no—
166C2×C3×D4—62no—
167C2×C3×D4C4×D312yes—
168C2×C3×D4#6712yes—
169C2×C3×D4C2×C3×C412yes—
170C2×C3×D4C3×D412yes—
171C22×C3×C4—21no—
172C22×C3×C4—62no—
173C22×C3×C4—62no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C23×C311yescharacteristic
178C2×#67—24no—
179C2×#67—28no—
180C2×#67—28no—
181C2×#67—22no—
182C22×Dic3—22no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185#237—28no—
186#237—28no—
187D3×D4—28no—
188D3×D4—28no—
189#235—22no—
190#235—22no—
191#235C2×C3×C414yes—
192#235C3×D414yes—
193C2×D12C3×D412yes—
194C2×C4×D3—22no—
195C2×Dic6C3×D412yes—
196C3×M16—24no—
197C3×M16—22no—
198C3×M16—22no—
199C3×M16—22no—
200C3×M16—22no—
201C3×M16—42no—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8—42no—
205C3×C4⋊C4—62no—
206C3×C22⋊C4—124no—
207C3×C42—62no—
208#217—44no—
209C4⋊Dic3—22no—
210C4×Dic3—22no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32—24no—
214C22×C32—44no—
215C22×C32—42no—
216C22×C32—42no—
217C22×C32—82no—
218C22×C32C2×C22⋊C411yescharacteristic
219C22×C32#12011yescharacteristic
220C22×C32#12011yescharacteristic
221C2×C3×D3—24no—
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—88no—
225C32×C4C2×C22⋊C412yes—
226C32×C4#12012yes—
227C3×Dic3—24no—
228C3×Dic3—42no—
229C3×Dic3—81no—
230H(5,𝔽2)—34no—
231H(5,𝔽2)—64no—
232H(5,𝔽2)—62no—
233C2×#41—32no—
234C2×#41—62no—
235C22×D4—62no—
236C22×D4—62no—
237C22×D4C2×C3×D311yescharacteristic
238C2×M16C2×C3×D312yescomplemented
239C2×C4⋊C4—31no—
240C2×C22⋊C4—62no—
241C2×C42—31no—
242#104—64no—
243#103—62no—
244#102—62no—
245#100—22no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—24no—
251C23×C3—21no—
252C23×C3—42no—
253C23×C3—42no—
254C23×C3—42no—
255C23×C3—42no—
256C23×C3—42no—
257C23×C3—42no—
258C23×C3—68no—
259C23×C3—62no—
260C23×C3—82no—
261C23×C3—82no—
262C23×C3—242no—
263C23×C3—242no—
264C23×C3(C2×D3)⋊C414yes—
265C23×C3C3×C22⋊C414yes—
266C23×C3C2×D1211yescharacteristic
267C23×C3C2×C3×D411yescharacteristic
268C22×D3—22no—
269C22×D3—28no—
270C22×D3—82no—
271C22×D3—82no—
272C3×Q8—34no—
273C3×Q8—62no—
274C3×D4—24no—
275C3×D4—24no—
276C3×D4—24no—
277C3×D4—24no—
278C3×D4—34no—
279C3×D4—44no—
280C3×D4—44no—
281C3×D4—616no—
282C3×D4—64no—
283C3×D4—64no—
284C3×D4—62no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—68no—
290C2×C3×C4—62no—
291C2×C3×C4—64no—
292C2×C3×C4—64no—
293C2×C3×C4—62no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—122no—
297C2×C3×C4—121no—
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4D3×D412yes—
300C2×C3×C4D3×D412yes—
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C22×C3×C411yescharacteristic
303C2×C3×C4C2×C3×D412yes—
304C2×C3×C4C2×C3×D412yes—
305C2×C3×C4C2×C3×D411yescharacteristic
306#67—216no—
307#67—24no—
308#67—24no—
309C2×Dic3—28no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—42no—
315C2×Dic3—41no—
316D12—22no—
317D12C3×C22⋊C414yescomplemented
318C4×D3—24no—
319C4×D3—24no—
320Dic6—22no—
321Dic6C3×C22⋊C414yescomplemented
322C3×C8—44no—
323C3×C8—42no—
324C3×C8—42no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32—44no—
328C2×C32#37911yescharacteristic
329C2×C32#45311yescharacteristic
330C2×C32#45511yescharacteristic
331C3×D3—44no—
332C24—62no—
333C24C3×D1212yes—
334#41—34no—
335#41—34no—
336#41—68no—
337#41—68no—
338#41—62no—
339#41—62no—
340C2×Q8—32no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—32no—
344C2×D4—68no—
345C2×D4—68no—
346C2×D4—64no—
347C2×D4—68no—
348C2×D4—68no—
349C2×D4—62no—
350C2×D4C3×C4×D312yes—
351C2×D4C3×#6712yes—
352C22×C4—62no—
353C22×C4—62no—
354C22×C4—61no—
355C22×C4—61no—
356C22×C4C22×C3×D311yescharacteristic
357M16—22no—
358M16—22no—
359C2×C8—22no—
360C4⋊C4—62no—
361C22⋊C4—124no—
362C42—62no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—24no—
368C22×C3—24no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—44no—
375C22×C3—44no—
376C22×C3—44no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—64no—
382C22×C3—82no—
383C22×C3—82no—
384C22×C3—84no—
385C22×C3—82no—
386C22×C3—82no—
387C22×C3—84no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3—248no—
391C22×C3#88211yescharacteristic
392C22×C3#88211yescharacteristic
393C22×C3C2×(C2×D3)⋊C411yescharacteristic
394C22×C3C2×C3×C22⋊C411yescharacteristic
395C22×C3C3×#12011yescharacteristic
396C22×C3C3×#12011yescharacteristic
397C2×D3—24no—
398C2×D3—42no—
399C2×D3—42no—
400C2×D3—88no—
401C3×C4—22no—
402C3×C4—22no—
403C3×C4—64no—
404C3×C4—122no—
405C3×C4—241no—
406C3×C4D3×C22⋊C412yes—
407C3×C4#93712yes—
408C3×C4C2×C3×C22⋊C412yes—
409C3×C4C3×#12012yes—
410Dic3—24no—
411Dic3—42no—
412Dic3—81no—
413C32#179211yescharacteristic, complemented, Sylow
414C23—22no—
415C23—22no—
416C23—42no—
417C23—42no—
418C23—68no—
419C23—62no—
420C23—242no—
421C23—242no—
422C23C3×(C2×D3)⋊C414yes—
423C23C2×C3×D1211yescharacteristic
424Q8—34no—
425Q8—62no—
426D4—24no—
427D4—24no—
428D4—34no—
429D4—616no—
430D4—64no—
431D4—64no—
432D4—62no—
433C2×C4—68no—
434C2×C4—62no—
435C2×C4—64no—
436C2×C4—64no—
437C2×C4—62no—
438C2×C4—121no—
439C2×C4—121no—
440C2×C4—122no—
441C2×C4—121no—
442C2×C4C2×C3×C4×D311yescharacteristic
443C2×C4C3×D3×D412yes—
444C2×C4C3×D3×D412yes—
445C2×C4C2×C3×#6711yescharacteristic
446C8—42no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—41no—
455C2×C3—41no—
456C2×C3—44no—
457C2×C3—44no—
458C2×C3—84no—
459C2×C3—124no—
460C2×C3#474611yescharacteristic
461C2×C3#474711yescharacteristic
462C2×C3#495511yescharacteristic
463C2×C3C3×#37911yescharacteristic
464C2×C3C3×#45311yescharacteristic
465C2×C3C3×#45511yescharacteristic
466D3—44no—
467C22—21no—
468C22—21no—
469C22—24no—
470C22—44no—
471C22—42no—
472C22—42no—
473C22—64no—
474C22—82no—
475C22—122no—
476C22—122no—
477C22—248no—
478C22C3×#88211yescharacteristic
479C22C3×#88211yescharacteristic
480C22C2×C3×(C2×D3)⋊C411yescharacteristic
481C4—64no—
482C4—122no—
483C4—241no—
484C4C3×D3×C22⋊C412yes—
485C4C3×#93712yes—
486C3—21no—
487C3#7008611yescharacteristic, direct product factor
488C3C3×#179211yescharacteristic, complemented
489C2—21no—
490C2—21no—
491C2—44no—
492C2—124no—
493C2C3×#474611yescharacteristic
494C2C3×#474711yescharacteristic
495C2C3×#495511yescharacteristic
subgroupG/H
centerC22×C3#882
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#100C2
socleC22×C32#120
prime radicalC2×C3×#1004C2
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#100D3
hypocenterC3C3×#1792
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

Complements

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

NH ≅ G/Ntype
2. C2×C32×#100C2semidirect
3. C3×#5221C2semidirect
4. C2×C3×#825C2semidirect
5. C3×#5133C2semidirect
7. #70086C3direct (N × H)
12. C3×#1004C4semidirect
16. C2×C32×M16C22semidirect
18. C2×C3×C4⋊Dic3C22semidirect
19. C2×C3×C4×Dic3C22semidirect
29. C2×C3×#100D3semidirect
30. C2×C3×#100C2×C3semidirect
32. #5221C2×C3semidirect
33. C2×#825C2×C3semidirect
34. #5133C2×C3semidirect
80. #1004C3×C4semidirect
85. C2×C3×M16C2×D3semidirect
86. C2×C3×M16C22×C3semidirect
91. C2×C4⋊Dic3C22×C3semidirect
92. C2×C4×Dic3C22×C3semidirect
129. C3×D12C22⋊C4semidirect
133. C3×Dic6C22⋊C4semidirect
138. C2×#100C3×D3semidirect
238. C2×M16C2×C3×D3semidirect
317. D12C3×C22⋊C4semidirect
321. Dic6C3×C22⋊C4semidirect
413. C32#1792semidirect
487. C3#70086direct (N × H)
488. C3C3×#1792semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×C32×#1002
C3×#52212
C2×C3×#8252
C3×#51332
C3×#17923
#700863