Finite Group Databasebeta

← C2×#10590982 #11867938

Subgroups — C2×#10590982 #11867938

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2C2×#63823C211yesmaximal, characteristic, complemented
3C22×#3713C211yesmaximal, characteristic, complemented
4C2×#63815C211yesmaximal, characteristic, complemented
5C2×#63649C211yesmaximal, characteristic, complemented
6C2×C3×#823C211yesmaximal, characteristic, complemented
7C2×#63558C211yesmaximal, characteristic, complemented
8#10590982C218yesmaximal, direct product factor
9C2×#5199—31nomaximal
10C2×#4749—31nomaximal
11C2×C3×#235C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#908—22no—
19C3×#908C2214yescomplemented
20C2×C3×D24—21no—
21C2×C3×#204—21no—
22C2×#3715—21no—
23#63823—22no—
24#63823C2214yescomplemented
25C2×#3713—21no—
26C2×#3713—21no—
27C2×#3713—22no—
28C2×#3713—21no—
29C2×#3713C2214yescomplemented
30C2×#3711—21no—
31#63815—22no—
32#63815C2214yescomplemented
33C2×D3×C3⋊C8—21no—
34#63649C2214yescomplemented
35C3×#823C2214yescomplemented
36#63558C2214yescomplemented
37C2×C3×AGL(1,ℤ/8)—31no—
38C2×#949—31no—
39C2×#948—31no—
40C2×#932—31no—
41C22×#213—31no—
42C22×#213—31no—
43C2×#908D311yescharacteristic, complemented
44C2×#907—31no—
45C2×C3×#100—31no—
46C2×#833—31no—
47#5199—38no—
48C2×#823—31no—
49C2×#823D311yescharacteristic, complemented
50C2×#822—31no—
51C2×#822—31no—
52C2×#822—61no—
53#4749—38no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235D412yes—
61C3×#235C2312yes—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77C32×M16—21no—
78C32×M16C2312yes—
79C2×C32×C8—21no—
80#3748—21no—
81#3748C2312yes—
82C2×C3⋊(C3⋊C8)—21no—
83C2×C3⋊(C3⋊C8)D411yescharacteristic
84C2×C3⋊(C3⋊C8)D412yes—
85C2×C3⋊(C3⋊C8)D411yescharacteristic
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#208—21no—
88C3×#208C2312yes—
89C2×C3×C3⋊C8—21no—
90C3×D24—24no—
91C3×#204—24no—
92#3715—24no—
93#3713—24no—
94#3713—24no—
95#3713—24no—
96#3711—24no—
97D3×C3⋊C8—24no—
98C2×#472—91noSylow
99C2×C3×#41—31no—
100C22×C3×D4—31no—
101C22×C3×D4—31no—
102C2×#235C2×D311yescharacteristic
103C22×D12C2×D311yescharacteristic
104C22×D12C2×D311yescharacteristic
105C3×AGL(1,ℤ/8)—34no—
106C3×AGL(1,ℤ/8)—62no—
107C2×C3×SD16—61no—
108C2×C3×D8—61no—
109C2×C3×M16—21no—
110C2×C3×M16—31no—
111C2×C3×M16C2×D311yescharacteristic
112C2×C3×M16C2×D311yescharacteristic
113#949—34no—
114#949—62no—
115#948—34no—
116#948—62no—
117C2×#215—61no—
118C2×#214—61no—
119#932—34no—
120#932—62no—
121C2×#213—34no—
122C2×#213—34no—
123C2×#213—61no—
124C2×#213—61no—
125C2×#213—62no—
126C2×#213—61no—
127C2×#213—61no—
128C2×#213—62no—
129C2×#213—61no—
130C2×#213—61no—
131C2×#208—31no—
132C2×#208—31no—
133C2×#208—61no—
134C2×#208—61no—
135C2×#208C2×D311yescharacteristic
136C22×C3⋊C8—31no—
137C22×C3⋊C8—31no—
138C22×C3⋊C8—61no—
139C22×C3⋊C8—61no—
140#908—22no—
141#908C2×D314yescomplemented
142#907—34no—
143#907—62no—
144C2×D24—21no—
145C2×#204—21no—
146C2×ΓL(1,𝔽25)—61no—
147C2×D3×C8—61no—
148C3×#100—34no—
149#833—34no—
150#823—34no—
151#823C2×D314yescomplemented
152#822—34no—
153#822—34no—
154#822—64no—
155C23×C32#4111yescharacteristic
156C22×C3×D3—21no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—41no—
160C22×C3×D3—41no—
161C22×C3×D3—41no—
162C22×C3×D3—41no—
163C22×C3×D3—82no—
164C22×C3×D3—82no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4#4111yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C3×#67—22no—
172C3×#67—22no—
173C2×C3×Dic3—21no—
174C3×D12—21no—
175C3×D12—22no—
176C3×D12—22no—
177C3×D12—22no—
178C3×D12—22no—
179C3×D12—41no—
180C3×D12—41no—
181C3×D12—41no—
182C3×D12—41no—
183C3×D12C2×D412yes—
184C3×C4×D3—22no—
185C3×C4×D3—22no—
186C3×Dic6—21no—
187C3×Dic6C2×D412yes—
188C32×C8—22no—
189C3⋊(C3⋊C8)—22no—
190C3⋊(C3⋊C8)C2×D412yes—
191C3⋊(C3⋊C8)C2×D412yes—
192C3×C3⋊C8—22no—
193C2×AGL(1,ℤ/8)—31no—
194C2×AGL(1,ℤ/8)—91no—
195C22×D8—91no—
196C2×#131—91no—
197#472—98no—
198C2×#108—91no—
199C2×#100—31no—
200C2×#100—91no—
201C24×C3—61no—
202C24×C3—61no—
203C23×D3—21no—
204C23×D3—21no—
205C3×#41—32no—
206C3×#41—32no—
207C3×#41—61no—
208C3×#41—61no—
209C2×C3×Q8—31no—
210C2×C3×D4—31no—
211C2×C3×D4—32no—
212C2×C3×D4—32no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C22×C3×C4—21no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229#235—21no—
230#235—21no—
231#235#6712yes—
232#235C22×D312yes—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12#6711yescharacteristic
244C2×D12C22×D312yes—
245C2×D12C22×D312yes—
246C2×C4×D3—21no—
247C2×Dic6#6711yescharacteristic
248C3×SD16—64no—
249C3×D8—64no—
250C3×M16—21no—
251C3×M16—21no—
252C3×M16—22no—
253C3×M16—32no—
254C3×M16—41no—
255C3×M16—61no—
256C3×M16C22×D312yes—
257C3×M16C22×D312yes—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—41no—
261C2×C3×C8—61no—
262#215—64no—
263#214—64no—
264#213—64no—
265#213—64no—
266#213—64no—
267#213—64no—
268#213—64no—
269#213—64no—
270#208—21no—
271#208—32no—
272#208—32no—
273#208—62no—
274#208—64no—
275#208—61no—
276#208—61no—
277#208—121no—
278#208C22×D312yes—
279C2×C3⋊C8—21no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—31no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—32no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—62no—
292C2×C3⋊C8—64no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8—61no—
295C2×C3⋊C8—121no—
296D24—24no—
297#204—24no—
298ΓL(1,𝔽25)—64no—
299D3×C8—64no—
300C22×C32—22no—
301C22×C32#12111yescharacteristic
302C22×C32#12111yescharacteristic
303C22×C32C2×#4111yescharacteristic
304C2×C3×D3—22no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—42no—
308C2×C3×D3—82no—
309C2×C3×D3—82no—
310C2×C3×D3—82no—
311C2×C3×D3—82no—
312C2×C3×D3—82no—
313C2×C3×D3—82no—
314C32×C4#12111yescharacteristic
315C32×C4#12111yescharacteristic
316C32×C4C22×D411yescharacteristic
317C32×C4C22×D411yescharacteristic
318C3×Dic3—22no—
319C2×#41—31no—
320C22×D4—31no—
321C22×D4—31no—
322AGL(1,ℤ/8)—34no—
323AGL(1,ℤ/8)—62no—
324AGL(1,ℤ/8)—94no—
325AGL(1,ℤ/8)—182no—
326C2×SD16—61no—
327C2×SD16—181no—
328C2×D8—61no—
329C2×D8—94no—
330C2×D8—181no—
331C2×D8—181no—
332C2×D8—182no—
333C2×D8—181no—
334#131—94no—
335#131—182no—
336C2×M16—31no—
337C2×M16—91no—
338C2×M16—181no—
339C2×M16D3211yescharacteristic
340C22×C8—91no—
341C22×C8—181no—
342#108—94no—
343#100—34no—
344#100—94no—
345C23×C3—21no—
346C23×C3—61no—
347C23×C3—62no—
348C23×C3—62no—
349C23×C3—121no—
350C23×C3—121no—
351C23×C3—121no—
352C23×C3—121no—
353C23×C3—242no—
354C23×C3—242no—
355C23×C3#23511yescharacteristic
356C23×C3#23711yescharacteristic
357C22×D3—21no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—41no—
361C22×D3—41no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3—82no—
365C22×D3—82no—
366C3×Q8—32no—
367C3×Q8—61no—
368C3×D4—32no—
369C3×D4—62no—
370C3×D4—62no—
371C3×D4—61no—
372C3×D4—62no—
373C3×D4—62no—
374C3×D4—62no—
375C3×D4—62no—
376C3×D4—121no—
377C3×D4—121no—
378C3×D4—121no—
379C3×D4—121no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—61no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4#23511yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4#23711yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—22no—
402#67—22no—
403C2×Dic3—21no—
404D12—21no—
405D12—22no—
406D12—22no—
407D12—22no—
408D12—22no—
409D12—41no—
410D12—41no—
411D12—41no—
412D12—41no—
413D12C2×#6712yes—
414C4×D3—22no—
415C4×D3—22no—
416Dic6—21no—
417Dic6C2×#6712yes—
418C3×C8—22no—
419C3×C8—22no—
420C3×C8—42no—
421C3×C8—62no—
422C3⋊C8—22no—
423C3⋊C8—32no—
424C3⋊C8—32no—
425C3⋊C8—32no—
426C3⋊C8—32no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—62no—
430C3⋊C8—62no—
431C3⋊C8—122no—
432C2×C32—21no—
433C2×C32—21no—
434C2×C32#47212yescomplemented
435C2×C32C2×#12111yescharacteristic
436C3×D3—42no—
437C3×D3—82no—
438C3×D3—82no—
439C24—61no—
440C24—61no—
441#41—32no—
442#41—32no—
443#41—61no—
444#41—61no—
445C2×Q8—31no—
446C2×D4—32no—
447C2×D4—32no—
448C2×D4—31no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—61no—
455C2×D4—61no—
456C2×D4—61no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4—61no—
460C22×C4—61no—
461C22×C4C2×D3211yescharacteristic
462SD16—64no—
463SD16—184no—
464D8—64no—
465D8—184no—
466D8—184no—
467D8—184no—
468M16—21no—
469M16—32no—
470M16—61no—
471M16—92no—
472M16—184no—
473M16—181no—
474M16C2×D3212yes—
475C2×C8—21no—
476C2×C8—61no—
477C2×C8—92no—
478C2×C8—91no—
479C2×C8—91no—
480C2×C8—92no—
481C2×C8—184no—
482C2×C8—181no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—42no—
489C22×C3—62no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—242no—
494C22×C3—242no—
495C22×C3—242no—
496C22×C3—242no—
497C22×C3—242no—
498C22×C3—242no—
499C22×C3#88411yescharacteristic
500C22×C3#88411yescharacteristic
501C22×C3#93911yescharacteristic
502C22×C3#93911yescharacteristic
503C22×C3C2×#23511yescharacteristic
504C22×C3C2×#23711yescharacteristic
505C2×D3—22no—
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—82no—
510C2×D3—82no—
511C2×D3—82no—
512C2×D3—82no—
513C2×D3—82no—
514C2×D3—82no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—62no—
520C3×C4#88411yescharacteristic
521C3×C4#88411yescharacteristic
522C3×C4#93911yescharacteristic
523C3×C4#93911yescharacteristic
524C3×C4C2×D3×D411yescharacteristic
525C3×C4C2×D3×D411yescharacteristic
526C3×C4C2×D3×D411yescharacteristic
527C3×C4C22×#6711yescharacteristic
528Dic3—22no—
529C32C2×#47211yescharacteristic, complemented, Sylow
530C23—61no—
531C23—62no—
532C23—62no—
533C23—121no—
534C23—121no—
535C23—121no—
536C23—121no—
537C23—242no—
538C23—242no—
539C23#379511yescharacteristic
540Q8—32no—
541Q8—61no—
542D4—32no—
543D4—62no—
544D4—62no—
545D4—62no—
546D4—62no—
547D4—62no—
548D4—62no—
549D4—61no—
550D4—121no—
551D4—121no—
552D4—121no—
553D4—121no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4#379511yescharacteristic
558C2×C4#380211yescharacteristic
559C2×C4#380211yescharacteristic
560C2×C4D3×#6711yescharacteristic
561C2×C4D3×#6711yescharacteristic
562C2×C4C22×D3211yescharacteristic
563C8—22no—
564C8—62no—
565C8—92no—
566C8—92no—
567C8—182no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—22no—
573C2×C3—21no—
574C2×C3—41no—
575C2×C3—41no—
576C2×C3—122no—
577C2×C3—242no—
578C2×C3—242no—
579C2×C3#474912yescomplemented
580C2×C3#519912yescomplemented
581C2×C3C2×#88411yescharacteristic
582C2×C3C2×#93911yescharacteristic
583D3—42no—
584D3—82no—
585D3—82no—
586C22—22no—
587C22—62no—
588C22—122no—
589C22—122no—
590C22—122no—
591C22—242no—
592C22—242no—
593C22—242no—
594C22—242no—
595C22—242no—
596C22—242no—
597C22#6388511yescharacteristic
598C22#6388511yescharacteristic
599C22C2×#379511yescharacteristic
600C4—62no—
601C4#6388511yescharacteristic
602C4#6388511yescharacteristic
603C4C2×#380211yescharacteristic
604C4C2×D3×#6711yescharacteristic
605C3—21no—
606C3C2×#474911yescharacteristic, complemented
607C3C2×#519911yescharacteristic, complemented
608C2—21no—
609C2—21no—
610C2—122no—
611C2—242no—
612C2—242no—
613C2#1059098212yesdirect product factor
614C2C2×#6388511yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32#121
hypercenterC2×M16D32
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. C2×#63823C2semidirect
3. C22×#3713C2semidirect
4. C2×#63815C2semidirect
5. C2×#63649C2semidirect
6. C2×C3×#823C2semidirect
7. C2×#63558C2semidirect
8. #10590982C2direct (N × H)
19. C3×#908C22semidirect
24. #63823C22semidirect
29. C2×#3713C22semidirect
32. #63815C22semidirect
34. #63649C22semidirect
35. C3×#823C22semidirect
36. #63558C22semidirect
43. C2×#908D3semidirect
49. C2×#823D3semidirect
141. #908C2×D3semidirect
151. #823C2×D3semidirect
434. C2×C32#472semidirect
529. C32C2×#472semidirect
579. C2×C3#4749semidirect
580. C2×C3#5199semidirect
606. C3C2×#4749semidirect
607. C3C2×#5199semidirect
613. C2#10590982direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×#638232
C22×#37132
C2×#638152
C2×#636492
C2×C3×#8232
C2×#635582
#105909822
C2×#51993
C2×#47493