Finite Group Databasebeta

← C2×#10591564 #11865490

Subgroups — C2×#10591564 #11865490

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×Dic3×D12C211yesmaximal, characteristic
4C22×#3715C211yesmaximal, characteristic
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591564C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63566C211yesmaximal, characteristic, complemented
9C2×#5162—31nomaximal
10C2×#5083—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×D3×Dic3—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#944—22no—
18C3×#944C2214yescomplemented
19C2×C3×#215—24no—
20C2×C3×#215C2214yes—
21C2×C3×Dic3⋊C4—21no—
22C2×C3×Dic3⋊C4—21no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26Dic3×D12—22no—
27Dic3×D12C2214yes—
28C2×#3715—24no—
29C2×#3715C2214yes—
30#63662C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63566C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×C4⋊Q8—31no—
35C2×#944D311yescharacteristic, complemented
36C22×#215—31no—
37C22×#215D311yescharacteristic
38C2×D4×Dic3—31no—
39C22×#214—31no—
40C2×C4×D12—31no—
41C2×#835—31no—
42C2×#835—31no—
43C2×#835—31no—
44C2×#835—61no—
45#5162—38no—
46C2×#816—31no—
47C2×Dic3⋊C8—31no—
48#5083—38no—
49C2×C4⋊(C3⋊C8)—31no—
50C23×C3×D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12D414yes—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×D3×Dic3—24no—
70C2×D3×Dic3—44no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#215—28no—
76C3×Dic3⋊C4—24no—
77C3×Dic3⋊C4—24no—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83#3715—28no—
84C2×#461—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8—31no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×D4—31no—
90C23×Dic3—61no—
91C22×D12C2×D311yescharacteristic
92C22×C4×D3—61no—
93C22×Dic6C2×D311yescharacteristic
94C2×C3×SD16—34no—
95C2×C3×SD16—64no—
96C22×C3×C8—31no—
97C3×C4⋊Q8—34no—
98C3×C4⋊Q8—62no—
99C2×C3×C4⋊C4—61no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C42—31no—
102C2×#217—61no—
103#944—22no—
104#944C2×D314yescomplemented
105C2×#215—24no—
106C2×#215—34no—
107C2×#215—64no—
108C2×#215C2×D314yes—
109D4×Dic3—34no—
110D4×Dic3—62no—
111C2×#214—34no—
112C2×#214—64no—
113C2×(C2×D3)⋊C4—61no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×Dic3⋊C4—21no—
118C2×Dic3⋊C4—21no—
119C2×C4×Dic3C2×D311yescharacteristic
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123C22×C3⋊C8C2×D311yescharacteristic
124C4×D12—34no—
125C4×D12—62no—
126#835—34no—
127#835—34no—
128#835—34no—
129#835—64no—
130#816—34no—
131Dic3⋊C8—34no—
132C4⋊(C3⋊C8)—34no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—24no—
135C22×C3×D3—22no—
136C22×C3×D3—42no—
137C22×C3×D3—42no—
138C32×Q8—22no—
139C32×Q8—22no—
140C32×Q8—42no—
141C2×C32×C4—22no—
142C2×C32×C4—42no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—42no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3SD1614yescomplemented
153C2×C3×Dic3C2×D412yes—
154C2×C3×Dic3C2×D412yes—
155C3×D12—24no—
156C3×D12—22no—
157C3×D12C2×D414yes—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—42no—
161D3×Dic3—48no—
162C3⋊(C3⋊C8)—22no—
163C3×C3⋊C8—22no—
164C22×SD16—31no—
165C22×SD16—91no—
166C2×C4⋊Q8—31no—
167C2×C4×D4—91no—
168#461—98no—
169C2×C4⋊C8—91no—
170C2×#103—91no—
171C2×#103—91no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—24no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—32no—
183C2×C3×Q8—41no—
184C2×C3×Q8—42no—
185C2×C3×Q8—61no—
186C2×C3×Q8—62no—
187C2×C3×Q8—62no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C2×C3×D4—34no—
191C2×C3×D4—32no—
192C2×C3×D4—62no—
193C2×C3×D4—61no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—41no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—64no—
207C22×Dic3—121no—
208C22×Dic3—124no—
209C22×Dic3#6711yescharacteristic
210C22×Dic3#6711yescharacteristic
211C2×D12—21no—
212C2×D12—22no—
213C2×D12#6714yes—
214C2×D12C22×D312yes—
215C2×C4×D3—64no—
216C2×C4×D3—124no—
217C2×Dic6—22no—
218C2×Dic6—22no—
219C2×Dic6—21no—
220C2×Dic6C22×D312yes—
221C3×SD16—68no—
222C2×C3×C8—32no—
223C2×C3×C8—62no—
224C3×C4⋊C4—64no—
225C3×C4⋊C4—64no—
226C3×C42—32no—
227C3×C42—32no—
228#217—64no—
229#215—28no—
230#215—68no—
231#214—68no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—121no—
239Dic3⋊C4—24no—
240Dic3⋊C4—24no—
241C4×Dic3#6712yes—
242C4×Dic3C22×D312yes—
243C2×C3⋊C8—22no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—122no—
250C2×C3⋊C8C22×D312yes—
251C22×C32#12112yes—
252C22×C32C2×SD1612yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—24no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—48no—
259C32×C4—42no—
260C32×C4#12112yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—42no—
264C3×Dic3—22no—
265C3×Dic3—42no—
266C3×Dic3C2×SD1614yescomplemented
267C22×Q8—31no—
268C22×Q8D3211yescharacteristic
269C22×D4—31no—
270C23×C4—181no—
271C2×SD16—34no—
272C2×SD16—64no—
273C2×SD16—94no—
274C2×SD16—184no—
275C22×C8—31no—
276C22×C8—91no—
277C4⋊Q8—34no—
278C4⋊Q8—62no—
279C4×D4—94no—
280C4×D4—182no—
281C2×C4⋊C4—61no—
282C2×C4⋊C4—61no—
283C2×C4⋊C4—91no—
284C2×C22⋊C4—181no—
285C2×C42—31no—
286C4⋊C8—94no—
287#103—94no—
288#103—94no—
289C23×C3—21no—
290C23×C3—64no—
291C23×C3—62no—
292C23×C3—122no—
293C23×C3—122no—
294C23×C3D3×D411yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3—24no—
297C22×D3—22no—
298C22×D3—42no—
299C22×D3—42no—
300C3×Q8—24no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—42no—
306C3×Q8—44no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—62no—
310C3×Q8—62no—
311C3×Q8—122no—
312C3×D4—34no—
313C3×D4—64no—
314C3×D4—62no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—34no—
322C2×C3×C4—32no—
323C2×C3×C4—32no—
324C2×C3×C4—42no—
325C2×C3×C4—44no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—122no—
331C2×C3×C4D3×D412yes—
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4#23712yes—
334C2×C3×C4#23712yes—
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6712yes—
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—42no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—128no—
348C2×Dic3—242no—
349C2×Dic3#21514yescomplemented
350C2×Dic3C2×#6712yes—
351C2×Dic3C2×#6712yes—
352D12—24no—
353D12—22no—
354D12C2×#6714yes—
355C4×D3—128no—
356Dic6—22no—
357Dic6—22no—
358Dic6—42no—
359C3×C8—62no—
360C3⋊C8—22no—
361C3⋊C8—62no—
362C3⋊C8—62no—
363C3⋊C8—122no—
364C2×C32#46114yescomplemented
365C2×C32C2×#12111yescharacteristic
366C2×C32C22×SD1611yescharacteristic
367C2×C32C2×#13711yescharacteristic
368C3×D3—44no—
369C24—61no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—32no—
374C2×Q8—61no—
375C2×Q8—62no—
376C2×Q8—62no—
377C2×Q8C2×D3212yes—
378C2×D4—32no—
379C2×D4—34no—
380C2×D4—62no—
381C2×D4—61no—
382C22×C4—21no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—61no—
386C22×C4—184no—
387C22×C4—181no—
388C22×C4—364no—
389C22×C4C2×D3211yescharacteristic
390SD16—68no—
391SD16—188no—
392C2×C8—32no—
393C2×C8—62no—
394C2×C8—92no—
395C2×C8—182no—
396C4⋊C4—64no—
397C4⋊C4—64no—
398C4⋊C4—92no—
399C4⋊C4—181no—
400C22⋊C4—184no—
401C42—32no—
402C42—32no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—64no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—128no—
411C22×C3D3×SD1612yes—
412C22×C3#91512yes—
413C22×C3#93812yes—
414C22×C3#93912yes—
415C22×C3C2×#21512yes—
416C22×C3#94212yes—
417C22×C3C2×D3×D411yescharacteristic
418C22×C3C22×#6711yescharacteristic
419C2×D3—24no—
420C2×D3—48no—
421C2×D3—42no—
422C2×D3—42no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—34no—
427C3×C4—44no—
428C3×C4—42no—
429C3×C4—42no—
430C3×C4—62no—
431C3×C4—122no—
432C3×C4#93812yes—
433C3×C4#93912yes—
434C3×C4C2×D3×D411yescharacteristic
435C3×C4C2×#23711yescharacteristic
436C3×C4C2×#23711yescharacteristic
437C3×C4C22×#6711yescharacteristic
438Dic3—22no—
439Dic3—42no—
440Dic3—122no—
441Dic3—122no—
442Dic3—242no—
443Dic3C2×#21514yescomplemented
444C32C2×#46111yescharacteristic, complemented, Sylow
445C23—62no—
446C23—64no—
447C23—122no—
448C23—122no—
449C23D3×#6711yescharacteristic
450Q8—22no—
451Q8—22no—
452Q8—42no—
453Q8—62no—
454Q8—62no—
455Q8—122no—
456D4—34no—
457D4—62no—
458D4—64no—
459C2×C4—22no—
460C2×C4—32no—
461C2×C4—34no—
462C2×C4—32no—
463C2×C4—42no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—122no—
467C2×C4—182no—
468C2×C4—368no—
469C2×C4—362no—
470C2×C4#380512yes—
471C2×C4D3×#6712yes—
472C2×C4D3×#6711yescharacteristic
473C2×C4C22×D3211yescharacteristic
474C8—62no—
475C8—182no—
476C2×C3—21no—
477C2×C3—24no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—124no—
481C2×C3#508314yescomplemented
482C2×C3#516214yescomplemented
483C2×C3C2×D3×SD1611yescharacteristic
484C2×C3C2×#91511yescharacteristic
485C2×C3C2×#93811yescharacteristic
486C2×C3C2×#93911yescharacteristic
487C2×C3C22×#21511yescharacteristic
488C2×C3C2×#94211yescharacteristic
489D3—44no—
490C22—64no—
491C22—122no—
492C22—128no—
493C22—122no—
494C22D3×#21512yes—
495C22#6394612yes—
496C22#6397012yes—
497C22C2×D3×#6711yescharacteristic
498C4—34no—
499C4—42no—
500C4—62no—
501C4—122no—
502C4—362no—
503C4#6397012yes—
504C4C2×#380511yescharacteristic
505C4C2×D3×#6711yescharacteristic
506C3—21no—
507C3C2×#508311yescharacteristic, complemented
508C3C2×#516211yescharacteristic, complemented
509C2—124no—
510C2#1059156414yesdirect product factor
511C2C2×D3×#21511yescharacteristic
512C2C2×#6394611yescharacteristic
513C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32C2×#461
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#944C2semidirect
5. C2×#63662C2semidirect
6. #10591564C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63566C2semidirect
18. C3×#944C22semidirect
30. #63662C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63566C22semidirect
35. C2×#944D3semidirect
104. #944C2×D3semidirect
152. C2×C3×Dic3SD16semidirect
266. C3×Dic3C2×SD16semidirect
349. C2×Dic3#215semidirect
364. C2×C32#461semidirect
443. Dic3C2×#215semidirect
444. C32C2×#461semidirect
481. C2×C3#5083semidirect
482. C2×C3#5162semidirect
507. C3C2×#5083semidirect
508. C3C2×#5162semidirect
510. C2#10591564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9442
C22×C3×#2152
C2×Dic3×D122
C22×#37152
C2×#636622
#105915642
C2×Dic3⋊(C3⋊C8)2
C2×#635662
C2×#51623
C2×#50833