Finite Group Databasebeta

← C2×#10591649 #11864925

Subgroups — C2×#10591649 #11864925

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×#64153C211yesmaximal, characteristic, complemented
3C2×#63831C212yesmaximal, complemented
4C2×C3×#836C211yesmaximal, characteristic, complemented
5#10591649C218yesmaximal, direct product factor
6C2×#63568C212yesmaximal, complemented
7C2×#5246—31nomaximal
8C2×#4752—31nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C3×#1007—22no—
12C3×#1007—24no—
13C3×#1007C2214yes—
14C2×C3×#239—22no—
15C2×C3×D3×Q8—22no—
16C2×C3×#235—22no—
17C2×C3×#235C2212yes—
18#64153—22no—
19#64153C2214yescomplemented
20C2×#3750—22no—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#208C2212yes—
23C2×#3719—22no—
24#63831—24no—
25#63831C2218yescomplemented
26C2×#3716—22no—
27C3×#836C2214yescomplemented
28#63568C2218yescomplemented
29C2×C3×2−1+4—31no—
30C2×#1007D311yescharacteristic
31C2×#951—32no—
32C2×#944—31no—
33C2×#944—31no—
34C2×#944—61no—
35C2×#909—32no—
36C2×C3×#101—31no—
37#5246—38no—
38C2×#837—32no—
39C2×#836D311yescharacteristic, complemented
40C2×#825—32no—
41#4752—38no—
42C2×C32×Q8—22no—
43C2×C32×Q8—22no—
44C2×C32×Q8D412yes—
45C2×C32×Q8C2312yes—
46C22×C32×C4D412yes—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3—21no—
50C2×#634—22no—
51C2×#634—22no—
52C2×#634—21no—
53C2×#634C2312yes—
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—
71#3750—28no—
72C4×C3⋊Dic3—21no—
73C4×C3⋊Dic3C2312yes—
74C3×#208—22no—
75C3×#208C2314yes—
76C2×C3×C3⋊C8—22no—
77#3719—28no—
78#3716—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—62no—
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×Q8C2×D311yescharacteristic
90#1007—22no—
91#1007—24no—
92#1007C2×D314yes—
93C2×#239—22no—
94C2×D3×Q8—22no—
95C2×#235—22no—
96C2×#235C2×D312yes—
97C22×Dic6—31no—
98C22×Dic6—31no—
99C22×Dic6—61no—
100C2×C3×M16—32no—
101#951—38no—
102#951—64no—
103#944—34no—
104#944—34no—
105#944—64no—
106#944—64no—
107#944—62no—
108#944—62no—
109C2×#216—62no—
110C2×#214—62no—
111C2×Dic3⋊C4—64no—
112C2×Dic3⋊C4—62no—
113C2×Dic3⋊C4—62no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—61no—
117C2×#208C2×D312yes—
118#909—38no—
119#909—64no—
120C2×Dic12—62no—
121C2×#204—62no—
122C3×#101—34no—
123#837—38no—
124#836C2×D314yescomplemented
125#825—38no—
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—22no—
128C32×Q8—24no—
129C32×Q8—24no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4C2×D414yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3—24no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142#634—24no—
143#634—42no—
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—92no—
159C2×C4⋊Q8—91no—
160#456—98no—
161C2×#104—92no—
162C2×#101—31no—
163C3×#41—34no—
164C3×#41—34no—
165C3×#41—68no—
166C3×#41—68no—
167C3×#41—68no—
168C3×#41—62no—
169C3×#41—68no—
170C3×#41—62no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—22no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—32no—
178C2×C3×Q8—42no—
179C2×C3×Q8—42no—
180C2×C3×Q8—62no—
181C2×C3×Q8—68no—
182C2×C3×Q8—68no—
183C2×C3×Q8D1212yes—
184C2×C3×Q8#6712yes—
185C2×C3×Q8C22×D312yes—
186C2×C3×Q8C22×D312yes—
187C2×C3×D4—32no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—64no—
193C22×C3×C4—62no—
194C22×C3×C4D1212yes—
195C22×C3×C4#6712yes—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—22no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—62no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205#239—28no—
206#239—28no—
207D3×Q8—28no—
208D3×Q8—28no—
209#235—28no—
210#235—28no—
211#235—22no—
212#235—22no—
213#235#6714yes—
214#235C22×D314yes—
215C2×D12—22no—
216C2×D12#6712yes—
217C2×C4×D3—24no—
218C2×C4×D3—22no—
219C2×Dic6—22no—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C2×Dic6—122no—
231C2×Dic6—122no—
232C2×Dic6#6712yes—
233C3×M16—34no—
234C3×M16—62no—
235C2×C3×C8—62no—
236#216—68no—
237#214—68no—
238Dic3⋊C4—616no—
239Dic3⋊C4—68no—
240Dic3⋊C4—68no—
241C4×Dic3—32no—
242C4×Dic3—32no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247#208—22no—
248#208C22×D314yes—
249C2×C3⋊C8—22no—
250Dic12—68no—
251#204—68no—
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#12012yes—
260C32×C4C22×D412yes—
261C3⋊Dic3—24no—
262C3⋊Dic3—42no—
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×Q8—91no—
272C22×Q8D3211yescharacteristic
273#137—98no—
274#137—184no—
275C2×Q16—182no—
276C2×SD16—182no—
277C2×M16—32no—
278C4⋊Q8—94no—
279C4⋊Q8—182no—
280C2×C4⋊C4—182no—
281C2×C42—91no—
282#104—98no—
283#101—34no—
284C23×C3—21no—
285C23×C3—62no—
286C23×C3C2×D1211yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C22×D3—22no—
289C3×Q8—24no—
290C3×Q8—24no—
291C3×Q8—24no—
292C3×Q8—24no—
293C3×Q8—34no—
294C3×Q8—44no—
295C3×Q8—44no—
296C3×Q8—68no—
297C3×Q8—62no—
298C3×D4—34no—
299C3×D4—68no—
300C3×D4—64no—
301C3×D4—64no—
302C3×D4—62no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—24no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—616no—
315C2×C3×C4—62no—
316C2×C3×C4—64no—
317C2×C3×C4—64no—
318C2×C3×C4C2×D1214yes—
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4D3×D412yes—
321C2×C3×C4D3×D412yes—
322C2×C3×C4C2×#6714yes—
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6712yes—
325C2×C3×C4C2×#6712yes—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—24no—
329#67—24no—
330C2×Dic3—22no—
331C2×Dic3—64no—
332C2×Dic3—68no—
333C2×Dic3—64no—
334C2×Dic3—64no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—64no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346D12—28no—
347D12—22no—
348D12C2×#6714yes—
349C4×D3—216no—
350C4×D3—24no—
351C4×D3—24no—
352Dic6—28no—
353Dic6—22no—
354Dic6—64no—
355Dic6—64no—
356Dic6—124no—
357Dic6—124no—
358Dic6—122no—
359Dic6—122no—
360Dic6C2×#6714yes—
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—68no—
375#41—62no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—32no—
379C2×Q8—62no—
380C2×Q8—68no—
381C2×Q8—68no—
382C2×Q8—92no—
383C2×Q8—181no—
384C2×Q8—182no—
385C2×Q8—182no—
386C2×Q8#62612yes—
387C2×Q8C2×D3212yes—
388C2×D4—32no—
389C2×D4—62no—
390C2×D4—62no—
391C22×C4—64no—
392C22×C4—62no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4#62612yes—
396C22×C4C2×D3211yescharacteristic
397Q16—188no—
398SD16—188no—
399M16—34no—
400M16—62no—
401C2×C8—62no—
402C4⋊C4—188no—
403C42—92no—
404C42—181no—
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#88211yescharacteristic
414C22×C3#88211yescharacteristic
415C22×C3#95311yescharacteristic
416C22×C3#95311yescharacteristic
417C22×C3C22×D1211yescharacteristic
418C22×C3C22×#6711yescharacteristic
419C2×D3—24no—
420C2×D3—44no—
421C3×C4—24no—
422C3×C4—24no—
423C3×C4—22no—
424C3×C4—22no—
425C3×C4—44no—
426C3×C4—64no—
427C3×C4#88212yes—
428C3×C4#95312yes—
429C3×C4C2×D3×D412yes—
430C3×C4C22×#6712yes—
431Dic3—24no—
432Dic3—68no—
433Dic3—64no—
434Dic3—64no—
435Dic3—124no—
436Dic3—122no—
437Dic3—122no—
438C32C2×#45611yescharacteristic, complemented, Sylow
439C23—62no—
440C23C2×#62611yescharacteristic
441Q8—24no—
442Q8—24no—
443Q8—34no—
444Q8—68no—
445Q8—62no—
446Q8—184no—
447Q8—362no—
448D4—34no—
449D4—68no—
450D4—64no—
451D4—64no—
452D4—62no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—616no—
456C2×C4—62no—
457C2×C4—64no—
458C2×C4—64no—
459C2×C4—184no—
460C2×C4—182no—
461C2×C4—182no—
462C2×C4—361no—
463C2×C4—361no—
464C2×C4C2×#62614yes—
465C2×C4C2×#62611yescharacteristic
466C2×C4D3×#6712yes—
467C2×C4D3×#6712yes—
468C2×C4C22×D3211yescharacteristic
469C8—64no—
470C2×C3—22no—
471C2×C3—22no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—124no—
479C2×C3#475212yescomplemented
480C2×C3#524612yescomplemented
481C2×C3C2×#88211yescharacteristic
482C2×C3C2×#95311yescharacteristic
483D3—44no—
484C22—22no—
485C22—64no—
486C22—124no—
487C22#6397711yescharacteristic
488C22#6397711yescharacteristic
489C22C22×#62611yescharacteristic
490C4—24no—
491C4—64no—
492C4—184no—
493C4—362no—
494C4#6397712yes—
495C4C2×D3×#6712yes—
496C3—21no—
497C3C2×#475211yescharacteristic, complemented
498C3C2×#524611yescharacteristic, complemented
499C2—21no—
500C2—21no—
501C2—124no—
502C2#1059164912yesdirect product factor
503C2C2×#6397711yescharacteristic
subgroupG/H
centerC22#63977
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×#64153C2semidirect
3. C2×#63831C2semidirect
4. C2×C3×#836C2semidirect
5. #10591649C2direct (N × H)
6. C2×#63568C2semidirect
19. #64153C22semidirect
25. #63831C22semidirect
27. C3×#836C22semidirect
28. #63568C22semidirect
39. C2×#836D3semidirect
124. #836C2×D3semidirect
365. C2×C32#456semidirect
438. C32C2×#456semidirect
479. C2×C3#4752semidirect
480. C2×C3#5246semidirect
497. C3C2×#4752semidirect
498. C3C2×#5246semidirect
502. C2#10591649direct (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×#641532
C2×#638312
C2×C3×#8362
#105916492
C2×#635682
C2×#52463
C2×#47523