Finite Group Databasebeta

← C2×#10591648 #11864927

Subgroups — C2×#10591648 #11864927

Order 1152.

1489 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2C2×C3×#944C211yesmaximal, characteristic, complemented
3C2×#63827C212yesmaximal, complemented
4C2×#63663C211yesmaximal, characteristic, complemented
5#10591648C218yesmaximal, direct product factor
6C2×#63569C212yesmaximal, complemented
7C2×#5246—31nomaximal
8C2×#5095—31nomaximal
9C22×C32×Q8C2211yescharacteristic
10C3×#1007—22no—
11C3×#1007—24no—
12C3×#1007C2214yes—
13C2×C3×#239—22no—
14C2×C3×D3×Q8—22no—
15C2×C3×#235—22no—
16C2×C3×#235C2212yes—
17C22×C3×Dic6C2211yescharacteristic
18C2×#3748C2212yes—
19C3×#944—22no—
20C3×#944C2214yescomplemented
21C2×C3×Dic3⋊C4—22no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×#3718—22no—
24#63827—24no—
25#63827C2218yescomplemented
26C2×#3715—22no—
27#63663C2214yescomplemented
28#63569C2218yescomplemented
29C2×C3×2−1+4—31no—
30C2×#1007D311yescharacteristic
31C2×C3×C4⋊Q8—31no—
32C2×#951—32no—
33C2×#944D311yescharacteristic, complemented
34C2×#942—32no—
35#5246—38no—
36C2×#837—32no—
37C2×#836—31no—
38C2×#836—31no—
39C2×#836—61no—
40#5095—38no—
41C2×#805—32no—
42C2×C32×Q8—22no—
43C2×C32×Q8—22no—
44C2×C32×Q8D412yes—
45C2×C32×Q8C2312yes—
46C22×C32×C4D412yes—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—22no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C3×#239—28no—
52C3×#239—28no—
53C3×D3×Q8—28no—
54C3×D3×Q8—28no—
55C3×#235—28no—
56C3×#235—28no—
57C3×#235—22no—
58C3×#235—22no—
59C3×#235D414yes—
60C3×#235C2314yes—
61C2×C3×D12—22no—
62C2×C3×D12D412yes—
63C2×C3×C4×D3—24no—
64C2×C3×C4×D3—22no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6D412yes—
70C2×C3×Dic6C2312yes—
71#3748—22no—
72#3748C2314yes—
73C2×C3⋊(C3⋊C8)—22no—
74C3×Dic3⋊C4—28no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3C2312yes—
77#3718—28no—
78#3715—28no—
79C2×#456—91noSylow
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—31no—
88C22×C3×Q8—62no—
89C22×C3×Q8C2×D311yescharacteristic
90C22×C3×Q8C2×D311yescharacteristic
91#1007—22no—
92#1007—24no—
93#1007C2×D314yes—
94C2×#239—22no—
95C2×D3×Q8—22no—
96C2×#235—22no—
97C2×#235C2×D312yes—
98C22×Dic6C2×D311yescharacteristic
99C3×C4⋊Q8—34no—
100C3×C4⋊Q8—62no—
101C2×C3×C4⋊C4—62no—
102C2×C3×C42—31no—
103#951—38no—
104#951—64no—
105#944—22no—
106#944C2×D314yescomplemented
107C2×#216—62no—
108C2×#216—62no—
109#942—38no—
110#942—64no—
111C2×#215—62no—
112C2×#214—62no—
113C2×Dic3⋊C4—22no—
114C2×C4×Dic3C2×D311yescharacteristic
115C2×#208—32no—
116C2×#208—32no—
117C2×#208—62no—
118#837—38no—
119#836—34no—
120#836—34no—
121#836—64no—
122#805—38no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C32×Q8—24no—
126C32×Q8—24no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D412yes—
131C2×C32×C4C2×D414yes—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2411yescharacteristic
134C3×#67—24no—
135C3×#67—24no—
136C2×C3×Dic3—24no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×D12—28no—
143C3×D12—22no—
144C3×D12C2×D414yes—
145C3×C4×D3—216no—
146C3×C4×D3—24no—
147C3×C4×D3—24no—
148C3×Dic6—28no—
149C3×Dic6—22no—
150C3×Dic6—24no—
151C3×Dic6—42no—
152C3×Dic6C2×D414yes—
153C3⋊(C3⋊C8)—24no—
154C2×2−1+4—31no—
155C2×#137—92no—
156C2×C4⋊Q8—31no—
157#456—98no—
158C2×#104—92no—
159C2×#101—91no—
160C3×#41—34no—
161C3×#41—34no—
162C3×#41—68no—
163C3×#41—68no—
164C3×#41—68no—
165C3×#41—62no—
166C3×#41—62no—
167C3×#41—68no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—22no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—32no—
175C2×C3×Q8—32no—
176C2×C3×Q8—42no—
177C2×C3×Q8—42no—
178C2×C3×Q8—62no—
179C2×C3×Q8—68no—
180C2×C3×Q8—68no—
181C2×C3×Q8—61no—
182C2×C3×Q8—62no—
183C2×C3×Q8—62no—
184C2×C3×Q8#6712yes—
185C2×C3×Q8#6712yes—
186C2×C3×Q8C22×D312yes—
187C2×C3×Q8C22×D312yes—
188C2×C3×D4—32no—
189C2×C3×D4—62no—
190C2×C3×D4—62no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—64no—
194C22×C3×C4—61no—
195C22×C3×C4—62no—
196C22×C3×C4—61no—
197C22×C3×C4#6712yes—
198C22×C3×C4#6712yes—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—22no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204#239—28no—
205#239—28no—
206D3×Q8—28no—
207D3×Q8—28no—
208#235—28no—
209#235—28no—
210#235—22no—
211#235—22no—
212#235#6714yes—
213#235C22×D314yes—
214C2×D12—22no—
215C2×D12#6712yes—
216C2×C4×D3—24no—
217C2×C4×D3—22no—
218C2×Dic6—22no—
219C2×Dic6—22no—
220C2×Dic6—22no—
221C2×Dic6—21no—
222C2×Dic6#6712yes—
223C2×Dic6C22×D312yes—
224C3×C4⋊C4—68no—
225C3×C42—32no—
226C3×C42—61no—
227#216—68no—
228#216—68no—
229#215—68no—
230#214—68no—
231Dic3⋊C4—28no—
232C4×Dic3—21no—
233C4×Dic3C22×D312yes—
234#208—34no—
235#208—34no—
236#208—64no—
237#208—62no—
238#208—62no—
239#208—122no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—122no—
243C22×C32—22no—
244C22×C32#12011yescharacteristic
245C22×C32#12011yescharacteristic
246C22×C32C22×D411yescharacteristic
247C2×C3×D3—24no—
248C2×C3×D3—44no—
249C32×C4—24no—
250C32×C4#12012yes—
251C32×C4C22×D412yes—
252C3×Dic3—24no—
253C3×Dic3—24no—
254C3×Dic3—42no—
2552−1+4—34no—
2562−1+4—64no—
2572−1+4—62no—
258C2×#41—32no—
259C2×#41—62no—
260C2×#41—62no—
261C22×Q8—31no—
262C22×Q8—62no—
263C22×Q8D3211yescharacteristic
264#137—98no—
265#137—184no—
266C2×Q16—182no—
267C2×SD16—182no—
268C2×M16—92no—
269C4⋊Q8—34no—
270C4⋊Q8—62no—
271C2×C4⋊C4—62no—
272C2×C42—31no—
273#104—98no—
274#101—94no—
275C23×C3—21no—
276C23×C3—62no—
277C23×C3C2×#6711yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—22no—
280C3×Q8—24no—
281C3×Q8—24no—
282C3×Q8—24no—
283C3×Q8—24no—
284C3×Q8—34no—
285C3×Q8—44no—
286C3×Q8—44no—
287C3×Q8—68no—
288C3×Q8—62no—
289C3×Q8—64no—
290C3×Q8—122no—
291C3×D4—34no—
292C3×D4—68no—
293C3×D4—64no—
294C3×D4—64no—
295C3×D4—62no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—616no—
308C2×C3×C4—64no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—64no—
312C2×C3×C4—64no—
313C2×C3×C4—62no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4D3×D412yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4C2×#6714yes—
319C2×C3×C4C2×#6714yes—
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6712yes—
323C2×C3×C4C2×#6712yes—
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326#67—24no—
327#67—24no—
328C2×Dic3—24no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334D12—28no—
335D12—22no—
336D12C2×#6714yes—
337C4×D3—216no—
338C4×D3—24no—
339C4×D3—24no—
340Dic6—28no—
341Dic6—22no—
342Dic6—24no—
343Dic6—42no—
344Dic6C2×#6714yes—
345C3⋊C8—64no—
346C3⋊C8—64no—
347C3⋊C8—124no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32#45612yescomplemented
351C2×C32C2×#12011yescharacteristic
352C3×D3—44no—
353#41—34no—
354#41—34no—
355#41—68no—
356#41—68no—
357#41—68no—
358#41—62no—
359#41—68no—
360#41—62no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—32no—
364C2×Q8—32no—
365C2×Q8—62no—
366C2×Q8—68no—
367C2×Q8—68no—
368C2×Q8—61no—
369C2×Q8—62no—
370C2×Q8—62no—
371C2×Q8#62512yes—
372C2×Q8C2×D3212yes—
373C2×D4—32no—
374C2×D4—62no—
375C2×D4—62no—
376C22×C4—64no—
377C22×C4—61no—
378C22×C4—62no—
379C22×C4—61no—
380C22×C4#62512yes—
381C22×C4C2×D3211yescharacteristic
382Q16—188no—
383SD16—188no—
384M16—94no—
385M16—182no—
386C2×C8—182no—
387C4⋊C4—68no—
388C42—32no—
389C42—61no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—42no—
396C22×C3—64no—
397C22×C3—124no—
398C22×C3#93711yescharacteristic
399C22×C3#93711yescharacteristic
400C22×C3#95311yescharacteristic
401C22×C3#95311yescharacteristic
402C22×C3C22×#6711yescharacteristic
403C22×C3C22×#6711yescharacteristic
404C2×D3—24no—
405C2×D3—44no—
406C3×C4—24no—
407C3×C4—24no—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—44no—
411C3×C4—64no—
412C3×C4—64no—
413C3×C4—122no—
414C3×C4#93712yes—
415C3×C4#95312yes—
416C3×C4C2×D3×D412yes—
417C3×C4C22×#6712yes—
418Dic3—24no—
419Dic3—24no—
420Dic3—42no—
421C32C2×#45611yescharacteristic, complemented, Sylow
422C23—62no—
423C23C2×#62511yescharacteristic
424Q8—24no—
425Q8—24no—
426Q8—34no—
427Q8—68no—
428Q8—62no—
429Q8—64no—
430Q8—122no—
431D4—34no—
432D4—68no—
433D4—64no—
434D4—64no—
435D4—62no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—616no—
439C2×C4—64no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—64no—
443C2×C4—64no—
444C2×C4—62no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4C2×#62514yes—
448C2×C4C2×#62511yescharacteristic
449C2×C4D3×#6712yes—
450C2×C4D3×#6712yes—
451C2×C4C22×D3211yescharacteristic
452C8—184no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—22no—
458C2×C3—21no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—124no—
462C2×C3#509512yescomplemented
463C2×C3#524612yescomplemented
464C2×C3C2×#93711yescharacteristic
465C2×C3C2×#95311yescharacteristic
466D3—44no—
467C22—22no—
468C22—64no—
469C22—124no—
470C22#6397611yescharacteristic
471C22#6397611yescharacteristic
472C22C22×#62511yescharacteristic
473C4—24no—
474C4—64no—
475C4—64no—
476C4—122no—
477C4#6397612yes—
478C4C2×D3×#6712yes—
479C3—21no—
480C3C2×#509511yescharacteristic, complemented
481C3C2×#524611yescharacteristic, complemented
482C2—21no—
483C2—21no—
484C2—124no—
485C2#1059164812yesdirect product factor
486C2C2×#6397611yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC2×C3×#1007C2
hypercenterC22×Q8D32
hypocenterC32C2×#456
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#944C2semidirect
3. C2×#63827C2semidirect
4. C2×#63663C2semidirect
5. #10591648C2direct (N × H)
6. C2×#63569C2semidirect
20. C3×#944C22semidirect
25. #63827C22semidirect
27. #63663C22semidirect
28. #63569C22semidirect
33. C2×#944D3semidirect
106. #944C2×D3semidirect
350. C2×C32#456semidirect
421. C32C2×#456semidirect
462. C2×C3#5095semidirect
463. C2×C3#5246semidirect
480. C3C2×#5095semidirect
481. C3C2×#5246semidirect
485. C2#10591648direct (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×C3×#9442
C2×#638272
C2×#636632
#105916482
C2×#635692
C2×#52463
C2×#50953