Finite Group Databasebeta

← C2×#10590536 #11865711

Subgroups — C2×#10590536 #11865711

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2C2×#63864C211yesmaximal, characteristic
3C22×#3718C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic
5C2×#63636C211yesmaximal, characteristic
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590536C218yesmaximal, direct product factor
9C2×#5028—31nomaximal
10C2×#4798—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
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×#3722—21no—
23C2×#3722—21no—
24#63864—22no—
25#63864C2214yes—
26C2×#3718—24no—
27C2×#3718C2214yescomplemented
28C2×#3717—24no—
29C2×#3717C2214yes—
30#63636C2214yes—
31C3×#810C2214yescomplemented
32Dic3⋊(C3⋊C8)C2214yescomplemented
33C2×C3×C4×Q8—31no—
34C2×#947—31no—
35C22×#216—31no—
36C22×#216—31no—
37C22×#215—31no—
38C22×#204—31no—
39C2×#887D311yescharacteristic, complemented
40C2×#875—31no—
41C2×C3×#103—31no—
42C2×Dic3⋊C8—31no—
43#5028—38no—
44C2×#810D311yescharacteristic, complemented
45C2×#809—31no—
46C2×#809—31no—
47C2×#809—61no—
48C2×C4⋊(C3⋊C8)—31no—
49#4798—38no—
50C23×C3⋊D3—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D414yes—
67C2×C3×Dic6C2312yes—
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#3722—24no—
80#3722—24no—
81#3718—28no—
82#3717—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×Dic6C2×D311yescharacteristic
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—
100#947—34no—
101#947—62no—
102C2×#216—34no—
103C2×#216—34no—
104C2×#216—64no—
105C2×#216—64no—
106C2×#215—34no—
107C2×#215—64no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
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×#204—34no—
120C2×#204—64no—
121#887—22no—
122#887C2×D314yescomplemented
123#875—34no—
124#875—62no—
125C3×#103—34no—
126Dic3⋊C8—34no—
127#810C2×D314yescomplemented
128#809—34no—
129#809—34no—
130#809—64no—
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
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—42no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3C2×D412yes—
153C2×C3×Dic3C2×D412yes—
154C3×Dic6—24no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
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—31no—
169C2×#102—91no—
170C23×D3—61no—
171C23×D3—61no—
172C23×D3—121no—
173C2×C3×Q8—34no—
174C2×C3×Q8—32no—
175C2×C3×Q8—32no—
176C2×C3×Q8—62no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—62no—
180C2×C3×Q8—62no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—31no—
185C22×C3×C4—31no—
186C22×C3×C4—41no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3#6711yescharacteristic
194C22×Dic3#6711yescharacteristic
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—62no—
198C2×D12—64no—
199C2×D12—62no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—122no—
206C2×D12—121no—
207C2×Dic6—22no—
208C2×Dic6—21no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6D1214yes—
213C2×Dic6C22×D312yes—
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#216—68no—
228#216—68no—
229#215—68no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
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—
246#204—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—24no—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×Q8—31no—
265C22×D4—91no—
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—34no—
284#102—94no—
285C23×C3—21no—
286C23×C3D3×D411yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—122no—
291C22×D3—124no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—242no—
299C22×D3—242no—
300C3×Q8—34no—
301C3×Q8—64no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—122no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—32no—
313C2×C3×C4—32no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—64no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—82no—
323C2×C3×C4—122no—
324C2×C3×C4C2×D1212yes—
325C2×C3×C4#23512yes—
326C2×C3×C4#23512yes—
327C2×C3×C4D3×D412yes—
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×Dic3—24no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—42no—
338C2×Dic3C2×#6712yes—
339C2×Dic3C2×#6712yes—
340D12—64no—
341D12—62no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—122no—
346D12—124no—
347D12—122no—
348D12—122no—
349Dic6—24no—
350Dic6—22no—
351Dic6—22no—
352Dic6—22no—
353Dic6—42no—
354Dic6C2×D1214yes—
355C3×C8—62no—
356C3⋊C8—22no—
357C3⋊C8—62no—
358C3⋊C8—62no—
359C3⋊C8—122no—
360C2×C32#46414yescomplemented
361C2×C32C2×#12111yescharacteristic
362C2×C32C2×#13511yescharacteristic
363C2×C32C2×#13711yescharacteristic
364C3⋊D3—82no—
365C24—181no—
366C2×Q8—32no—
367C2×Q8—32no—
368C2×Q8—34no—
369C2×Q8—62no—
370C2×Q8—61no—
371C2×Q8—61no—
372C2×Q8—62no—
373C2×Q8—62no—
374C2×D4—92no—
375C2×D4—182no—
376C2×D4—182no—
377C2×D4—181no—
378C22×C4—21no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4C2×D3211yescharacteristic
384Q16—188no—
385SD16—188no—
386C2×C8—32no—
387C2×C8—62no—
388C2×C8—92no—
389C2×C8—182no—
390C4⋊C4—21no—
391C4⋊C4—64no—
392C4⋊C4C2×D3212yes—
393C22⋊C4—184no—
394C22⋊C4—184no—
395C42—32no—
396C42—32no—
397C42—64no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3#88412yes—
403C22×C3#91612yes—
404C22×C3#91812yes—
405C22×C3#93012yes—
406C22×C3#94212yes—
407C22×C3#95012yes—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C22×#6711yescharacteristic
410C2×D3—124no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—242no—
418C2×D3—242no—
419C2×D3—248no—
420C2×D3—244no—
421C2×D3—244no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—64no—
428C3×C4—62no—
429C3×C4—62no—
430C3×C4—82no—
431C3×C4—122no—
432C3×C4#88412yes—
433C3×C4#93012yes—
434C3×C4C22×D1211yescharacteristic
435C3×C4C2×#23511yescharacteristic
436C3×C4C2×#23511yescharacteristic
437C3×C4C2×D3×D411yescharacteristic
438Dic3—24no—
439Dic3—22no—
440Dic3—22no—
441Dic3—42no—
442C32C2×#46411yescharacteristic, complemented, Sylow
443C23—182no—
444C23—362no—
445C23—362no—
446C23—362no—
447C23D3×#6711yescharacteristic
448Q8—34no—
449Q8—62no—
450Q8—64no—
451Q8—62no—
452Q8—62no—
453Q8—122no—
454D4—182no—
455D4—182no—
456D4—362no—
457C2×C4—22no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—42no—
461C2×C4—62no—
462C2×C4—64no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—122no—
467C2×C4#379812yes—
468C2×C4D3×D1212yes—
469C2×C4D3×#6711yescharacteristic
470C2×C4C22×D3211yescharacteristic
471C8—62no—
472C8—182no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—24no—
476C2×C3—21no—
477C2×C3#479814yescomplemented
478C2×C3#502814yescomplemented
479C2×C3C2×#88411yescharacteristic
480C2×C3C2×#91611yescharacteristic
481C2×C3C2×#91811yescharacteristic
482C2×C3C2×#93011yescharacteristic
483C2×C3C2×#94211yescharacteristic
484C2×C3C2×#95011yescharacteristic
485D3—244no—
486D3—242no—
487D3—242no—
488C22—362no—
489C22—362no—
490C22—362no—
491C22—724no—
492C22#6390612yes—
493C22#6393512yes—
494C22#6394812yes—
495C22C2×D3×#6711yescharacteristic
496C4—42no—
497C4—62no—
498C4—62no—
499C4—64no—
500C4—122no—
501C4#6390612yes—
502C4C2×#379811yescharacteristic
503C4C2×D3×D1211yescharacteristic
504C3—21no—
505C3C2×#479811yescharacteristic, complemented
506C3C2×#502811yescharacteristic, complemented
507C2—722no—
508C2#1059053614yesdirect product factor
509C2C2×#6390611yescharacteristic
510C2C2×#6393511yescharacteristic
511C2C2×#6394811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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×#3718C2semidirect
6. C2×C3×#810C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590536C2direct (N × H)
21. C3×#887C22semidirect
27. C2×#3718C22semidirect
31. C3×#810C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
39. C2×#887D3semidirect
44. C2×#810D3semidirect
122. #887C2×D3semidirect
127. #810C2×D3semidirect
360. C2×C32#464semidirect
442. C32C2×#464semidirect
477. C2×C3#4798semidirect
478. C2×C3#5028semidirect
505. C3C2×#4798semidirect
506. C3C2×#5028semidirect
508. C2#10590536direct (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×#638642
C22×#37182
C22×#37172
C2×#636362
C2×C3×#8102
C2×Dic3⋊(C3⋊C8)2
#105905362
C2×#50283
C2×#47983