Finite Group Databasebeta

← C2×C3×#5095 #11864900

Subgroups — C2×C3×#5095 #11864900

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2C2×C32×C4⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×#942C212yesmaximal, complemented
4C2×C3×#836C211yesmaximal, characteristic, complemented
5C3×#5095C218yesmaximal, direct product factor
6C2×C3×#805C212yesmaximal, complemented
7C2×C3×#456—31nomaximal
8C2×#5095C311yesmaximal, characteristic, direct product factor
9C22×C32×Q8C2211yescharacteristic
10C22×C32×Q8C2211yescharacteristic
11C3×#1007—22no—
12C3×#1007—24no—
13C3×#1007C2214yes—
14C2×C3×#239—22no—
15C2×C3×D3×Q8—22no—
16C2×C3×#235—22no—
17C2×C3×#235C2212yes—
18C32×C4⋊Q8—22no—
19C32×C4⋊Q8C2214yescomplemented
20C2×C32×C4⋊C4—22no—
21C2×C32×C42C2211yescharacteristic
22C2×C3×#216—22no—
23C3×#942—24no—
24C3×#942C2218yescomplemented
25C2×C3×#215—22no—
26C2×C3×#208C2212yes—
27C3×#836C2214yescomplemented
28C3×#805C2218yescomplemented
29C2×C3×2−1+4—31no—
30C2×#1007C2×C311yescharacteristic
31C2×C3×#137—32no—
32C2×C3×C4⋊Q8—21no—
33C2×C3×C4⋊Q8D311yescharacteristic, complemented
34C2×C3×C4⋊Q8C2×C311yescharacteristic, complemented
35C2×#942C2×C312yescomplemented
36C3×#456—38no—
37C2×C3×#104—32no—
38C2×C3×#101—31no—
39C2×#836C2×C311yescharacteristic, complemented
40#5095C2×C318yesdirect product factor
41C2×#805C2×C312yescomplemented
42C2×C32×Q8—22no—
43C2×C32×Q8—22no—
44C2×C32×Q8—21no—
45C2×C32×Q8—22no—
46C2×C32×Q8—22no—
47C2×C32×Q8D412yes—
48C2×C32×Q8C2312yes—
49C2×C32×Q8C2312yes—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4D412yes—
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—22no—
55C3×#239—28no—
56C3×#239—28no—
57C3×D3×Q8—28no—
58C3×D3×Q8—28no—
59C3×#235—28no—
60C3×#235—28no—
61C3×#235—22no—
62C3×#235—22no—
63C3×#235D414yes—
64C3×#235C2314yes—
65C2×C3×D12—22no—
66C2×C3×D12D412yes—
67C2×C3×C4×D3—24no—
68C2×C3×C4×D3—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6D412yes—
71C32×C4⋊C4—28no—
72C32×C42—21no—
73C32×C42C2312yes—
74C3×#216—28no—
75C3×#215—28no—
76C3×#208—22no—
77C3×#208C2314yes—
78C2×C3×C3⋊C8—22no—
79C2×#456—31noSylow
80C3×2−1+4—34no—
81C3×2−1+4—64no—
82C3×2−1+4—62no—
83C2×C3×#41—32no—
84C2×C3×#41—62no—
85C2×C3×#41—62no—
86C22×C3×Q8—21no—
87C22×C3×Q8—21no—
88C22×C3×Q8—62no—
89C22×C3×Q8C2×D311yescharacteristic
90C22×C3×Q8C2×D311yescharacteristic
91C22×C3×Q8C22×C311yescharacteristic
92C22×C3×Q8C22×C311yescharacteristic
93#1007—22no—
94#1007—24no—
95#1007C22×C314yes—
96C2×#239—22no—
97C2×D3×Q8—22no—
98C2×#235—22no—
99C2×#235C22×C312yes—
100C3×#137—38no—
101C3×#137—64no—
102C2×C3×Q16—62no—
103C2×C3×SD16—62no—
104C2×C3×M16—32no—
105C3×C4⋊Q8—24no—
106C3×C4⋊Q8—22no—
107C3×C4⋊Q8—22no—
108C3×C4⋊Q8—24no—
109C3×C4⋊Q8C2×D314yescomplemented
110C3×C4⋊Q8C22×C314yescomplemented
111C2×C3×C4⋊C4—24no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C42—21no—
115C2×C3×C42C2×D311yescharacteristic
116C2×C3×C42C22×C311yescharacteristic
117C2×#216—22no—
118#942—24no—
119#942C22×C318yescomplemented
120C2×#215—22no—
121C2×#208C22×C312yes—
122C3×#104—38no—
123C3×#101—34no—
124#836C22×C314yescomplemented
125#805C22×C318yescomplemented
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—22no—
128C32×Q8—24no—
129C32×Q8—24no—
130C32×Q8—24no—
131C32×Q8—42no—
132C2×C32×C4—24no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2×D414yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2411yescharacteristic
144C3×#67—24no—
145C3×#67—24no—
146C2×C3×Dic3—22no—
147C3×D12—28no—
148C3×D12—22no—
149C3×D12C2×D414yes—
150C3×C4×D3—216no—
151C3×C4×D3—24no—
152C3×C4×D3—24no—
153C3×Dic6—28no—
154C3×Dic6—22no—
155C3×Dic6C2×D414yes—
156C3×C3⋊C8—24no—
157C2×2−1+4—31no—
158C2×#137—32no—
159C2×C4⋊Q8C3×D311yescharacteristic, complemented
160#456—38no—
161C2×#104—32no—
162C2×#101—31no—
163C3×#41—34no—
164C3×#41—34no—
165C3×#41—68no—
166C3×#41—68no—
167C3×#41—68no—
168C3×#41—62no—
169C3×#41—62no—
170C3×#41—68no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—21no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—21no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—32no—
186C2×C3×Q8—42no—
187C2×C3×Q8—42no—
188C2×C3×Q8—42no—
189C2×C3×Q8—42no—
190C2×C3×Q8—62no—
191C2×C3×Q8—68no—
192C2×C3×Q8—68no—
193C2×C3×Q8#6712yes—
194C2×C3×Q8C3×D412yes—
195C2×C3×Q8C22×D312yes—
196C2×C3×Q8C22×D312yes—
197C2×C3×Q8C23×C312yes—
198C2×C3×Q8C23×C312yes—
199C2×C3×D4—32no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—64no—
211C22×C3×C4—62no—
212C22×C3×C4#6712yes—
213C22×C3×C4C3×D412yes—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C23×C311yescharacteristic
216C2×#67—22no—
217#239—28no—
218#239—28no—
219D3×Q8—28no—
220D3×Q8—28no—
221#235—28no—
222#235—28no—
223#235—22no—
224#235—22no—
225#235C3×D414yes—
226#235C23×C314yes—
227C2×D12—22no—
228C2×D12C3×D412yes—
229C2×C4×D3—24no—
230C2×C4×D3—22no—
231C2×Dic6—22no—
232C2×Dic6C3×D412yes—
233C3×Q16—68no—
234C3×SD16—68no—
235C3×M16—34no—
236C3×M16—62no—
237C2×C3×C8—62no—
238C3×C4⋊C4—216no—
239C3×C4⋊C4—28no—
240C3×C4⋊C4—28no—
241C3×C42—22no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—22no—
245C3×C42C22×D312yes—
246C3×C42C23×C312yes—
247#216—28no—
248#215—28no—
249#208—22no—
250#208C23×C314yes—
251C2×C3⋊C8—22no—
252C22×C32—22no—
253C22×C32#12011yescharacteristic
254C22×C32#12011yescharacteristic
255C22×C32C22×D411yescharacteristic
256C2×C3×D3—24no—
257C2×C3×D3—44no—
258C32×C4—24no—
259C32×C4—24no—
260C32×C4—42no—
261C32×C4#12012yes—
262C32×C4C22×D412yes—
263C3×Dic3—24no—
2642−1+4—34no—
2652−1+4—64no—
2662−1+4—62no—
267C2×#41—32no—
268C2×#41—62no—
269C2×#41—62no—
270C22×Q8—62no—
271C22×Q8C2×C3×D311yescharacteristic
272C22×Q8C2×C3×D311yescharacteristic
273#137—38no—
274#137—64no—
275C2×Q16—62no—
276C2×SD16—62no—
277C2×M16—32no—
278C4⋊Q8—22no—
279C4⋊Q8C2×C3×D314yescomplemented
280C2×C4⋊C4—22no—
281C2×C42C2×C3×D311yescharacteristic
282#104—38no—
283#101—34no—
284C23×C3—21no—
285C23×C3—62no—
286C23×C3C2×#6711yescharacteristic
287C23×C3C2×C3×D411yescharacteristic
288C22×D3—22no—
289C3×Q8—24no—
290C3×Q8—24no—
291C3×Q8—24no—
292C3×Q8—24no—
293C3×Q8—24no—
294C3×Q8—24no—
295C3×Q8—34no—
296C3×Q8—44no—
297C3×Q8—44no—
298C3×Q8—44no—
299C3×Q8—44no—
300C3×Q8—42no—
301C3×Q8—42no—
302C3×Q8—68no—
303C3×Q8—62no—
304C3×D4—34no—
305C3×D4—68no—
306C3×D4—64no—
307C3×D4—64no—
308C3×D4—62no—
309C2×C3×C4—24no—
310C2×C3×C4—28no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—24no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—24no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—616no—
336C2×C3×C4—62no—
337C2×C3×C4—64no—
338C2×C3×C4—64no—
339C2×C3×C4D3×D412yes—
340C2×C3×C4D3×D412yes—
341C2×C3×C4C2×#6714yes—
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×C3×D412yes—
344C2×C3×C4C2×C3×D412yes—
345C2×C3×C4C2×C3×D414yes—
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C24×C311yescharacteristic
349#67—24no—
350#67—24no—
351C2×Dic3—22no—
352D12—28no—
353D12—22no—
354D12C2×C3×D414yes—
355C4×D3—216no—
356C4×D3—24no—
357C4×D3—24no—
358Dic6—28no—
359Dic6—22no—
360Dic6C2×C3×D414yes—
361C3×C8—64no—
362C3⋊C8—24no—
363C2×C32—21no—
364C2×C32—21no—
365C2×C32#45612yescomplemented
366C2×C32C2×#12011yescharacteristic
367C3×D3—44no—
368#41—34no—
369#41—34no—
370#41—68no—
371#41—68no—
372#41—68no—
373#41—62no—
374#41—62no—
375#41—68no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—32no—
382C2×Q8—62no—
383C2×Q8—68no—
384C2×Q8—68no—
385C2×Q8C3×#6712yes—
386C2×Q8C22×C3×D312yes—
387C2×Q8C22×C3×D312yes—
388C2×D4—32no—
389C2×D4—62no—
390C2×D4—62no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—64no—
394C22×C4—62no—
395C22×C4C3×#6712yes—
396C22×C4C22×C3×D311yescharacteristic
397Q16—68no—
398SD16—68no—
399M16—34no—
400M16—62no—
401C2×C8—62no—
402C4⋊C4—28no—
403C42—21no—
404C42C22×C3×D312yes—
405C22×C3—24no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—64no—
412C22×C3—124no—
413C22×C3#93711yescharacteristic
414C22×C3#93711yescharacteristic
415C22×C3C3×#12011yescharacteristic
416C22×C3C3×#12011yescharacteristic
417C22×C3C22×#6711yescharacteristic
418C22×C3C22×C3×D411yescharacteristic
419C2×D3—24no—
420C2×D3—44no—
421C3×C4—28no—
422C3×C4—24no—
423C3×C4—24no—
424C3×C4—24no—
425C3×C4—24no—
426C3×C4—22no—
427C3×C4—22no—
428C3×C4—44no—
429C3×C4—44no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—64no—
433C3×C4#93712yes—
434C3×C4C3×#12012yes—
435C3×C4C2×D3×D412yes—
436C3×C4C22×C3×D412yes—
437Dic3—24no—
438C32C2×#45611yescharacteristic, complemented, Sylow
439C23—62no—
440C23C2×C3×#6711yescharacteristic
441Q8—24no—
442Q8—24no—
443Q8—24no—
444Q8—34no—
445Q8—42no—
446Q8—68no—
447Q8—62no—
448D4—34no—
449D4—68no—
450D4—64no—
451D4—64no—
452D4—62no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—616no—
461C2×C4—62no—
462C2×C4—64no—
463C2×C4—64no—
464C2×C4C3×D3×D412yes—
465C2×C4C3×D3×D412yes—
466C2×C4C2×C3×#6714yes—
467C2×C4C2×C3×#6711yescharacteristic
468C2×C4C23×C3×D311yescharacteristic
469C8—64no—
470C2×C3—22no—
471C2×C3—22no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—22no—
478C2×C3—124no—
479C2×C3#509512yesdirect product factor
480C2×C3C3×#45612yescomplemented
481C2×C3C2×#93711yescharacteristic
482C2×C3C2×C3×#12011yescharacteristic
483D3—44no—
484C22—22no—
485C22—64no—
486C22—124no—
487C22C3×#93711yescharacteristic
488C22C3×#93711yescharacteristic
489C22C22×C3×#6711yescharacteristic
490C4—24no—
491C4—24no—
492C4—42no—
493C4—64no—
494C4C3×#93712yes—
495C4C2×C3×D3×D412yes—
496C3—21no—
497C3C2×#509511yescharacteristic, direct product factor
498C3C2×C3×#45611yescharacteristic, complemented
499C2—21no—
500C2—21no—
501C2—124no—
502C2C3×#509512yesdirect product factor
503C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4⋊Q8C2
socleC22×C32#120
prime radicalC2×C3×#1007C2
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C2×C3×#456
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4⋊Q8C2semidirect
3. C2×C3×#942C2semidirect
4. C2×C3×#836C2semidirect
5. C3×#5095C2direct (N × H)
6. C2×C3×#805C2semidirect
8. C2×#5095C3direct (N × H)
19. C32×C4⋊Q8C22semidirect
24. C3×#942C22semidirect
27. C3×#836C22semidirect
28. C3×#805C22semidirect
33. C2×C3×C4⋊Q8D3semidirect
34. C2×C3×C4⋊Q8C2×C3semidirect
35. C2×#942C2×C3semidirect
39. C2×#836C2×C3semidirect
40. #5095C2×C3direct (N × H)
41. C2×#805C2×C3semidirect
109. C3×C4⋊Q8C2×D3semidirect
110. C3×C4⋊Q8C22×C3semidirect
119. #942C22×C3semidirect
124. #836C22×C3semidirect
125. #805C22×C3semidirect
159. C2×C4⋊Q8C3×D3semidirect
279. C4⋊Q8C2×C3×D3semidirect
365. C2×C32#456semidirect
438. C32C2×#456semidirect
479. C2×C3#5095direct (N × H)
480. C2×C3C3×#456semidirect
497. C3C2×#5095direct (N × H)
498. C3C2×C3×#456semidirect
502. C2C3×#5095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×C32×C4⋊Q82
C2×C3×#9422
C2×C3×#8362
C3×#50952
C2×C3×#8052
C2×C3×#4563
C2×#50953