Finite Group Databasebeta

← C2×#10590532 #11865713

Subgroups — C2×#10590532 #11865713

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2C2×#63860C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic
5C2×#63637C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590532C218yesmaximal, direct product factor
9C2×#5028—31nomaximal
10C2×#4767—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×C4×Dic3—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#887—22no—
21C3×#887C2214yescomplemented
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63860—22no—
25#63860C2214yes—
26C2×#3719—24no—
27C2×#3719C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yes—
30#63637C2214yescomplemented
31C3×#809C2214yes—
32Dic3⋊(C3⋊C8)C2214yescomplemented
33C2×C3×C4×Q8—31no—
34C22×#216—31no—
35C22×#215—31no—
36C2×#936—31no—
37C22×#214—31no—
38C22×Dic12—31no—
39C2×#887D311yescharacteristic, complemented
40C2×#875—31no—
41C2×C3×#102—31no—
42C2×Dic3⋊C8—31no—
43#5028—38no—
44C2×#810—31no—
45C2×#810—31no—
46C2×#810—61no—
47C2×#809D311yescharacteristic
48C2×C4⋊(C3⋊C8)—31no—
49#4767—38no—
50C23×C3×D3—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C2×#634—22no—
55C2×#634—22no—
56C2×#634—21no—
57C2×#634C2312yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6D414yes—
68C2×C3×Dic6C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×Dic3⋊C4—24no—
74C3×C4×Dic3—24no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79(C2×D3)⋊Dic3—24no—
80(C2×D3)⋊Dic3—24no—
81#3719—28no—
82#3715—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C22×Dic6C2×D311yescharacteristic
91C22×C3×C8—31no—
92C3×C4×Q8—34no—
93C3×C4×Q8—62no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—61no—
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C42—31no—
99C2×C3×C42—61no—
100C2×#217—61no—
101C2×#217—61no—
102C2×#216—34no—
103C2×#216—64no—
104C2×#215—34no—
105C2×#215—64no—
106#936—34no—
107#936—62no—
108C2×#214—34no—
109C2×#214—64no—
110C2×(C2×D3)⋊C4—61no—
111C2×(C2×D3)⋊C4—61no—
112C2×Dic3⋊C4—21no—
113C2×C4×Dic3—21no—
114C2×C4×Dic3C2×D311yescharacteristic
115C22×C3⋊C8—31no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—61no—
118C22×C3⋊C8C2×D311yescharacteristic
119C2×Dic12—34no—
120C2×Dic12—64no—
121#887—22no—
122#887C2×D314yescomplemented
123#875—34no—
124#875—62no—
125C3×#102—34no—
126Dic3⋊C8—34no—
127#810—34no—
128#810—34no—
129#810—64no—
130#809C2×D314yes—
131C4⋊(C3⋊C8)—34no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—42no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4—22no—
138C2×C32×C4—42no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145#634—22no—
146#634—22no—
147#634—42no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3C2×D412yes—
153C2×C3×Dic3C2×D412yes—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—42no—
157C3×Dic6—24no—
158C3×Dic6—22no—
159C3×Dic6C2×D414yes—
160C3⋊(C3⋊C8)—22no—
161C3×C3⋊C8—22no—
162C22×Q16—91no—
163C22×SD16—91no—
164C2×#124—91no—
165C2×C4×Q8—31no—
166#464—98no—
167C2×C4⋊C8—91no—
168C2×#103—91no—
169C2×#102—31no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×Q8—34no—
173C2×C3×Q8—32no—
174C2×C3×Q8—62no—
175C2×C3×Q8—61no—
176C2×C3×D4—32no—
177C2×C3×D4—62no—
178C2×C3×D4—62no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—31no—
185C22×C3×C4—41no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3#6711yescharacteristic
194C22×Dic3#6711yescharacteristic
195C2×D12—22no—
196C2×D12—22no—
197C2×D12—21no—
198C2×D12C22×D312yes—
199C2×Dic6—22no—
200C2×Dic6—21no—
201C2×Dic6—32no—
202C2×Dic6—32no—
203C2×Dic6—62no—
204C2×Dic6—64no—
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—121no—
212C2×Dic6—122no—
213C2×Dic6D1214yes—
214C2×Dic6C22×D312yes—
215C2×C3×C8—32no—
216C2×C3×C8—62no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—41no—
221C3×C4⋊C4—64no—
222C3×C4⋊C4C22×D312yes—
223C3×C4⋊C4C22×D312yes—
224C3×C42—32no—
225C3×C42—32no—
226C3×C42—64no—
227#217—64no—
228#217—64no—
229#216—68no—
230#215—68no—
231#214—68no—
232(C2×D3)⋊C4—64no—
233(C2×D3)⋊C4—64no—
234Dic3⋊C4—24no—
235C4×Dic3—24no—
236C4×Dic3#6712yes—
237C4×Dic3C22×D312yes—
238C2×C3⋊C8—22no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—122no—
245C2×C3⋊C8C22×D312yes—
246Dic12—68no—
247C22×C32#12112yes—
248C22×C32#13512yes—
249C22×C32#13712yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—84no—
255C32×C4—42no—
256C32×C4#12112yes—
257C32×C4C22×D411yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3⋊Dic3—42no—
260C3×Dic3—24no—
261C3×Dic3—22no—
262C3×Dic3—22no—
263C22×Q8—31no—
264C22×Q8—91no—
265C22×D4—31no—
266C2×Q16—94no—
267C2×Q16—184no—
268C2×SD16—94no—
269C2×SD16—184no—
270C22×C8—31no—
271C22×C8—91no—
272#124—94no—
273#124—182no—
274C4×Q8—34no—
275C4×Q8—62no—
276C2×C4⋊C4—61no—
277C2×C4⋊C4D3211yescharacteristic
278C2×C22⋊C4—181no—
279C2×C22⋊C4—181no—
280C2×C42—31no—
281C2×C42—61no—
282C4⋊C8—94no—
283#103—94no—
284#102—34no—
285C23×C3—21no—
286C23×C3—62no—
287C23×C3—122no—
288C23×C3—122no—
289C23×C3—122no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—22no—
293C22×D3—42no—
294C22×D3—42no—
295C22×D3—42no—
296C3×Q8—34no—
297C3×Q8—64no—
298C3×Q8—62no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—122no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—32no—
309C2×C3×C4—32no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—64no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—82no—
318C2×C3×C4C2×D1212yes—
319C2×C3×C4#23512yes—
320C2×C3×C4#23512yes—
321C2×C3×C4D3×D412yes—
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×Dic3—24no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—122no—
333C2×Dic3—124no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3C2×#6712yes—
337C2×Dic3C2×#6712yes—
338D12—22no—
339D12—22no—
340D12—42no—
341Dic6—24no—
342Dic6—22no—
343Dic6—64no—
344Dic6—62no—
345Dic6—62no—
346Dic6—62no—
347Dic6—62no—
348Dic6—122no—
349Dic6—124no—
350Dic6—122no—
351Dic6—122no—
352Dic6C2×D1214yes—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—122no—
358C2×C32#46414yescomplemented
359C2×C32C2×#12111yescharacteristic
360C2×C32C2×#13511yescharacteristic
361C2×C32C2×#13711yescharacteristic
362C3×D3—82no—
363C24—61no—
364C2×Q8—32no—
365C2×Q8—34no—
366C2×Q8—62no—
367C2×Q8—61no—
368C2×Q8—92no—
369C2×Q8—181no—
370C2×Q8—182no—
371C2×Q8—182no—
372C2×D4—32no—
373C2×D4—62no—
374C2×D4—62no—
375C2×D4—61no—
376C22×C4—21no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—61no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382Q16—188no—
383SD16—188no—
384C2×C8—32no—
385C2×C8—62no—
386C2×C8—92no—
387C2×C8—182no—
388C4⋊C4—21no—
389C4⋊C4—64no—
390C4⋊C4C2×D3212yes—
391C22⋊C4—184no—
392C22⋊C4—184no—
393C42—32no—
394C42—32no—
395C42—64no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—244no—
404C22×C3#88412yes—
405C22×C3#91212yes—
406C22×C3#91512yes—
407C22×C3#93012yes—
408C22×C3#94212yes—
409C22×C3#95012yes—
410C22×C3C2×D3×D411yescharacteristic
411C22×C3C22×#6711yescharacteristic
412C2×D3—42no—
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—84no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—64no—
422C3×C4—62no—
423C3×C4—62no—
424C3×C4—82no—
425C3×C4#88412yes—
426C3×C4#93012yes—
427C3×C4C22×D1211yescharacteristic
428C3×C4C2×#23511yescharacteristic
429C3×C4C2×#23511yescharacteristic
430C3×C4C2×D3×D411yescharacteristic
431Dic3—24no—
432Dic3—22no—
433Dic3—22no—
434Dic3—124no—
435Dic3—122no—
436Dic3—122no—
437C32C2×#46411yescharacteristic, complemented, Sylow
438C23—62no—
439C23—122no—
440C23—122no—
441C23—122no—
442C23D3×#6711yescharacteristic
443Q8—34no—
444Q8—62no—
445Q8—64no—
446Q8—182no—
447Q8—182no—
448Q8—362no—
449D4—62no—
450D4—62no—
451D4—122no—
452C2×C4—22no—
453C2×C4—32no—
454C2×C4—32no—
455C2×C4—42no—
456C2×C4—62no—
457C2×C4—64no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—182no—
461C2×C4—362no—
462C2×C4#379812yes—
463C2×C4D3×D1212yes—
464C2×C4D3×#6711yescharacteristic
465C2×C4C22×D3211yescharacteristic
466C8—62no—
467C8—182no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—24no—
471C2×C3—21no—
472C2×C3—242no—
473C2×C3#476714yescomplemented
474C2×C3#502814yescomplemented
475C2×C3C2×#88411yescharacteristic
476C2×C3C2×#91211yescharacteristic
477C2×C3C2×#91511yescharacteristic
478C2×C3C2×#93011yescharacteristic
479C2×C3C2×#94211yescharacteristic
480C2×C3C2×#95011yescharacteristic
481D3—82no—
482C22—122no—
483C22—122no—
484C22—122no—
485C22—244no—
486C22#6390612yes—
487C22#6393312yes—
488C22#6394612yes—
489C22C2×D3×#6711yescharacteristic
490C4—42no—
491C4—62no—
492C4—62no—
493C4—64no—
494C4—362no—
495C4#6390612yes—
496C4C2×#379811yescharacteristic
497C4C2×D3×D1211yescharacteristic
498C3—21no—
499C3C2×#476711yescharacteristic, complemented
500C3C2×#502811yescharacteristic, complemented
501C2—242no—
502C2#1059053214yesdirect product factor
503C2C2×#6390611yescharacteristic
504C2C2×#6393311yescharacteristic
505C2C2×#6394611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#887C2semidirect
3. C22×#3719C2semidirect
5. C2×#63637C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590532C2direct (N × H)
21. C3×#887C22semidirect
27. C2×#3719C22semidirect
30. #63637C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
39. C2×#887D3semidirect
122. #887C2×D3semidirect
358. C2×C32#464semidirect
437. C32C2×#464semidirect
473. C2×C3#4767semidirect
474. C2×C3#5028semidirect
499. C3C2×#4767semidirect
500. C3C2×#5028semidirect
502. C2#10590532direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×#638602
C22×#37192
C22×#37152
C2×#636372
C2×C3×#8092
C2×Dic3⋊(C3⋊C8)2
#105905322
C2×#50283
C2×#47673