Finite Group Databasebeta

← C2×#10590504 #11866978

Subgroups — C2×#10590504 #11866978

Order 1152.

1257 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic, complemented
2C2×#63908C211yesmaximal, characteristic, complemented
3C22×#3713C211yesmaximal, characteristic, complemented
4C22×#3711C211yesmaximal, characteristic, complemented
5C2×#63635C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590504C218yesmaximal, direct product factor
9C2×#5039—31nomaximal
10C2×#4782—31nomaximal
11C22×C3×D12—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×#625—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#895—22no—
22C3×#895C2214yescomplemented
23C2×(C2×D3)⋊Dic3—21no—
24#63908—22no—
25#63908C2214yescomplemented
26C2×#3713—24no—
27C2×#3713C2214yescomplemented
28C2×#3711—24no—
29C2×#3711C2214yescomplemented
30#63635C2214yescomplemented
31C3×#809C2214yescomplemented
32#63563C2214yescomplemented
33C2×C3×#121—31no—
34C2×#938—31no—
35C22×#213—31no—
36C22×#213—31no—
37C2×#930—31no—
38C22×#208—31no—
39C22×ΓL(1,𝔽25)—31no—
40C2×#895D311yescharacteristic, complemented
41C2×C3×#102—31no—
42C2×#832—31no—
43C2×#821—31no—
44#5039—38no—
45C2×#809D311yescharacteristic, complemented
46C2×#808—31no—
47C2×#808—31no—
48C2×#808—61no—
49#4782—38no—
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C23×C3×D3D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—24no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—44no—
65C2×C3×D12C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×#625—24no—
72C2×#625—44no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2312yes—
77C2×C3⋊(C3⋊C8)D414yescomplemented
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×(C2×D3)⋊C4—24no—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83#3713—28no—
84#3711—28no—
85C2×#469—91noSylow
86C22×C3×D4—31no—
87C22×C3×D4—31no—
88C22×C3×D4—61no—
89C23×C3×C4—31no—
90C22×#67—61no—
91C22×#67—61no—
92C22×D12—21no—
93C22×D12C2×D311yescharacteristic
94C22×D12C2×D311yescharacteristic
95C22×C4×D3C2×D311yescharacteristic
96C22×C3×C8—31no—
97C3×#121—34no—
98C3×#121—62no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C22⋊C4—61no—
103C2×#217—61no—
104#938—34no—
105#938—62no—
106C2×#213—34no—
107C2×#213—34no—
108C2×#213—64no—
109C2×#213—64no—
110#930—34no—
111#930—62no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—61no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×#208—34no—
118C2×#208—64no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123C2×ΓL(1,𝔽25)—34no—
124C2×ΓL(1,𝔽25)—64no—
125#895—22no—
126#895C2×D314yescomplemented
127C3×#102—34no—
128#832—34no—
129#821—34no—
130#809C2×D314yescomplemented
131#808—34no—
132#808—34no—
133#808—64no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—22no—
138C22×C3×D3—22no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C22×C3×D3—42no—
146C22×C3×D3C2×D412yes—
147C2×C32×C4—22no—
148C2×C32×C4—42no—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—42no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3C2×D412yes—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—48no—
162C3×D12—42no—
163C3×D12—42no—
164C3×C4×D3—24no—
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167#625—48no—
168C3⋊(C3⋊C8)C2×D414yescomplemented
169C3×C3⋊C8—22no—
170C22×D8—91no—
171C22×M16—91no—
172C2×#121—31no—
173C2×#121—91no—
174#469—98no—
175C2×#106—91no—
176C2×#102—31no—
177C2×#102—91no—
178C24×C3—31no—
179C24×C3—61no—
180C24×C3—61no—
181C23×D3—21no—
182C23×D3—21no—
183C23×D3#6711yescharacteristic
184C2×C3×D4—32no—
185C2×C3×D4—32no—
186C2×C3×D4—64no—
187C2×C3×D4—62no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C2×C3×D4—61no—
191C2×C3×D4—62no—
192C2×C3×D4—61no—
193C2×C3×D4—124no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—41no—
201C22×C3×C4—62no—
202C22×C3×C4—62no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—64no—
206C2×#67—64no—
207C2×#67—124no—
208C2×#67—124no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—121no—
212C22×Dic3#6711yescharacteristic
213C2×D12—22no—
214C2×D12—22no—
215C2×D12—22no—
216C2×D12—22no—
217C2×D12—24no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—44no—
221C2×D12C22×D312yes—
222C2×D12C22×D312yes—
223C2×C4×D3—22no—
224C2×C4×D3—22no—
225C2×C4×D3#6712yes—
226C2×C4×D3C22×D312yes—
227C2×C3×C8—32no—
228C2×C3×C8—62no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4C22×D312yes—
234C3×C4⋊C4C22×D312yes—
235C3×C22⋊C4—64no—
236#217—64no—
237#213—68no—
238#213—68no—
239(C2×D3)⋊C4—24no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—121no—
247#208—68no—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—34no—
250C2×C3⋊C8—34no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—64no—
255C2×C3⋊C8C22×D312yes—
256ΓL(1,𝔽25)—68no—
257C22×C32#12112yes—
258C22×C32AGL(1,ℤ/8)12yes—
259C22×C32AGL(1,ℤ/8)12yes—
260C22×C32C22×D411yescharacteristic
261C2×C3×D3—22no—
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3—44no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—84no—
272C2×C3×D3—84no—
273C32×C4—42no—
274C32×C4#12112yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—42no—
278C3×Dic3—22no—
279C22×D4—31no—
280C22×D4—31no—
281C22×D4—61no—
282C22×D4—181no—
283C23×C4—31no—
284C2×D8—94no—
285C2×D8—184no—
286C2×M16—94no—
287C2×M16—184no—
288C22×C8—31no—
289C22×C8—91no—
290#121—34no—
291#121—62no—
292#121—94no—
293#121—182no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4D3211yescharacteristic
296C2×C22⋊C4—61no—
297C2×C22⋊C4—181no—
298#106—94no—
299#102—34no—
300#102—94no—
301C23×C3—21no—
302C23×C3—32no—
303C23×C3—62no—
304C23×C3—62no—
305C23×C3—62no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3—122no—
309C23×C3—122no—
310C23×C3—122no—
311C23×C3—122no—
312C23×C3—122no—
313C23×C3—122no—
314C23×C3D3×D411yescharacteristic
315C23×C3C2×#6711yescharacteristic
316C22×D3—22no—
317C22×D3—22no—
318C22×D3—22no—
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—42no—
322C22×D3—42no—
323C22×D3—42no—
324C22×D3—42no—
325C22×D3—42no—
326C22×D3—42no—
327C22×D3C2×#6712yes—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—62no—
332C3×D4—128no—
333C3×D4—122no—
334C3×D4—122no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—62no—
346C2×C3×C4—64no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—82no—
350C2×C3×C4#23512yes—
351C2×C3×C4D3×D412yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23712yes—
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—128no—
359#67—128no—
360C2×Dic3—22no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3—242no—
367C2×Dic3C2×#6712yes—
368D12—22no—
369D12—22no—
370D12—22no—
371D12—22no—
372D12—48no—
373D12—42no—
374D12—42no—
375C4×D3—24no—
376C4×D3—22no—
377C4×D3—22no—
378C3×C8—62no—
379C3⋊C8—22no—
380C3⋊C8—34no—
381C3⋊C8—34no—
382C3⋊C8—64no—
383C2×C32#46914yescomplemented
384C2×C32C2×#12111yescharacteristic
385C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
386C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
387C3×D3—42no—
388C3×D3—82no—
389C3×D3—82no—
390C24—31no—
391C24—61no—
392C24—61no—
393C2×D4—32no—
394C2×D4—32no—
395C2×D4—64no—
396C2×D4—62no—
397C2×D4—62no—
398C2×D4—62no—
399C2×D4—62no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—124no—
403C2×D4—184no—
404C2×D4—364no—
405C22×C4—21no—
406C22×C4—31no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—62no—
410C22×C4—62no—
411C22×C4—181no—
412C22×C4C2×D3211yescharacteristic
413D8—188no—
414M16—188no—
415C2×C8—32no—
416C2×C8—62no—
417C2×C8—92no—
418C2×C8—94no—
419C4⋊C4—21no—
420C4⋊C4—92no—
421C4⋊C4—181no—
422C4⋊C4C2×D3212yes—
423C22⋊C4—64no—
424C22⋊C4—184no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—62no—
430C22×C3—62no—
431C22×C3—62no—
432C22×C3—124no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3—244no—
440C22×C3—244no—
441C22×C3#88412yes—
442C22×C3#91112yes—
443C22×C3#91412yes—
444C22×C3#93212yes—
445C22×C3#93912yes—
446C22×C3#94912yes—
447C22×C3C2×D3×D411yescharacteristic
448C22×C3C22×#6711yescharacteristic
449C2×D3—22no—
450C2×D3—22no—
451C2×D3—22no—
452C2×D3—44no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—84no—
460C2×D3—84no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—62no—
467C3×C4—82no—
468C3×C4#88412yes—
469C3×C4#93912yes—
470C3×C4C2×#23511yescharacteristic
471C3×C4C2×D3×D411yescharacteristic
472C3×C4C2×D3×D411yescharacteristic
473C3×C4C2×#23711yescharacteristic
474Dic3—22no—
475Dic3—122no—
476Dic3—122no—
477Dic3—242no—
478C32C2×#46911yescharacteristic, complemented, Sylow
479C23—32no—
480C23—62no—
481C23—62no—
482C23—62no—
483C23—62no—
484C23—62no—
485C23—122no—
486C23—122no—
487C23—122no—
488C23—122no—
489C23—122no—
490C23—122no—
491C23D3×#6711yescharacteristic
492D4—62no—
493D4—62no—
494D4—62no—
495D4—62no—
496D4—128no—
497D4—122no—
498D4—122no—
499D4—368no—
500C2×C4—22no—
501C2×C4—32no—
502C2×C4—42no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—64no—
507C2×C4—182no—
508C2×C4—362no—
509C2×C4#379512yes—
510C2×C4#380212yes—
511C2×C4D3×#6711yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—62no—
514C8—94no—
515C2×C3—21no—
516C2×C3—24no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—122no—
520C2×C3—242no—
521C2×C3—242no—
522C2×C3#478214yescomplemented
523C2×C3#503914yescomplemented
524C2×C3C2×#88411yescharacteristic
525C2×C3C2×#91111yescharacteristic
526C2×C3C2×#91411yescharacteristic
527C2×C3C2×#93211yescharacteristic
528C2×C3C2×#93911yescharacteristic
529C2×C3C2×#94911yescharacteristic
530D3—42no—
531D3—82no—
532D3—82no—
533C22—62no—
534C22—62no—
535C22—62no—
536C22—124no—
537C22—122no—
538C22—122no—
539C22—122no—
540C22—122no—
541C22—122no—
542C22—122no—
543C22—244no—
544C22—244no—
545C22#6388512yes—
546C22#6393212yes—
547C22#6393912yes—
548C22C2×D3×#6711yescharacteristic
549C4—42no—
550C4—62no—
551C4—362no—
552C4#6388512yes—
553C4C2×#379511yescharacteristic
554C4C2×#380211yescharacteristic
555C3—21no—
556C3C2×#478211yescharacteristic, complemented
557C3C2×#503911yescharacteristic, complemented
558C2—122no—
559C2—242no—
560C2—242no—
561C2#1059050414yesdirect product factor
562C2C2×#6388511yescharacteristic
563C2C2×#6393211yescharacteristic
564C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#469
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×#895C2semidirect
2. C2×#63908C2semidirect
3. C22×#3713C2semidirect
4. C22×#3711C2semidirect
5. C2×#63635C2semidirect
6. C2×C3×#809C2semidirect
7. C2×#63563C2semidirect
8. #10590504C2direct (N × H)
22. C3×#895C22semidirect
25. #63908C22semidirect
27. C2×#3713C22semidirect
29. C2×#3711C22semidirect
30. #63635C22semidirect
31. C3×#809C22semidirect
32. #63563C22semidirect
40. C2×#895D3semidirect
45. C2×#809D3semidirect
77. C2×C3⋊(C3⋊C8)D4semidirect
126. #895C2×D3semidirect
130. #809C2×D3semidirect
168. C3⋊(C3⋊C8)C2×D4semidirect
383. C2×C32#469semidirect
478. C32C2×#469semidirect
522. C2×C3#4782semidirect
523. C2×C3#5039semidirect
556. C3C2×#4782semidirect
557. C3C2×#5039semidirect
561. C2#10590504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×#639082
C22×#37132
C22×#37112
C2×#636352
C2×C3×#8092
C2×#635632
#105905042
C2×#50393
C2×#47823