Finite Group Databasebeta

← C2×#10591680 #11867879

Subgroups — C2×#10591680 #11867879

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64158C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5#10591680C218yesmaximal, direct product factor
6C2×#63577C211yesmaximal, characteristic, complemented
7C2×#63560C211yesmaximal, characteristic, complemented
8C2×#63559C211yesmaximal, characteristic, complemented
9C2×#5203—31nomaximal
10C2×#5141—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14#64158—22no—
15#64158C2214yes—
16C2×#3755—21no—
17C2×#3753—21no—
18C2×#3748C2211yescharacteristic
19C3×#951—22no—
20C3×#951C2214yescomplemented
21C3×#948—22no—
22C3×#948C2214yescomplemented
23C2×C3×#216—21no—
24C2×C3×#214—21no—
25C2×C3×#208—21no—
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8—21no—
29C22×C3×C3⋊C8C2211yescharacteristic
30C2×#3717—21no—
31C2×#3717—21no—
32C2×#3717—22no—
33C2×#3717C2214yescomplemented
34#63577C2214yescomplemented
35#63560C2214yescomplemented
36#63559C2214yescomplemented
37C2×C3×#137—31no—
38C2×C3×#131—31no—
39C2×#951D311yescharacteristic, complemented
40C2×#949—31no—
41C2×#949—31no—
42C2×#949—61no—
43C2×#948D311yescharacteristic, complemented
44C22×#215—31no—
45C22×#204—31no—
46C2×#836—31no—
47#5203—38no—
48#5141—38no—
49C2×#824—31no—
50C2×#823—31no—
51C2×#823—31no—
52C2×#822—31no—
53C2×#819—31no—
54C23×C3⋊D3—21no—
55C32×#41—21no—
56C32×#41—21no—
57C32×#41D412yes—
58C32×#41C2312yes—
59C2×C32×Q8D411yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4D411yescharacteristic
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C22×C3×Dic3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2312yes—
77#3755—24no—
78#3753—24no—
79#3748—21no—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C3×#216—24no—
83C3×#214—24no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208—24no—
87C3×#208C2312yes—
88C3×#208C2312yes—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8—21no—
91C2×C3×C3⋊C8—24no—
92C2×C3×C3⋊C8D411yescharacteristic
93C2×C3×C3⋊C8D411yescharacteristic
94C2×C3×C3⋊C8D412yes—
95C2×C3×C3⋊C8C2312yes—
96#3717—24no—
97#3717—24no—
98C2×#471—91noSylow
99C2×C3×#41—21no—
100C2×C3×#41C2×D311yescharacteristic
101C2×C3×#41C2×D311yescharacteristic
102C22×C3×Q8—31no—
103C22×D12—31no—
104C22×D12—31no—
105C22×D12—61no—
106C22×Dic6C2×D311yescharacteristic
107C3×#137—34no—
108C3×#137—62no—
109C2×C3×Q16—61no—
110C2×C3×SD16—61no—
111C3×#131—34no—
112C3×#131—62no—
113C2×C3×M16—31no—
114C2×C3×M16—31no—
115C2×C3×M16—61no—
116C22×C3×C8—31no—
117C22×C3×C8—61no—
118#951—22no—
119#951C2×D314yescomplemented
120#949—34no—
121#949—34no—
122#949—64no—
123#949—64no—
124#949—62no—
125#949—62no—
126#948—22no—
127#948C2×D314yescomplemented
128C2×#216—21no—
129C2×#215—34no—
130C2×#215—62no—
131C2×#215—61no—
132C2×#215—61no—
133C2×#215—61no—
134C2×#215—61no—
135C2×#215—62no—
136C2×#214—21no—
137C2×#213—62no—
138C2×#213—61no—
139C2×#213—61no—
140C2×#208—21no—
141C2×#208—31no—
142C2×#208—31no—
143C2×#208—61no—
144C2×#208C2×D311yescharacteristic
145C2×#208C2×D311yescharacteristic
146C22×C3⋊C8—21no—
147C22×C3⋊C8C2×D311yescharacteristic
148C2×#204—34no—
149C2×#204—61no—
150C2×#204—61no—
151C2×#204—62no—
152#836—34no—
153#824—34no—
154#823—34no—
155#823—34no—
156#822—34no—
157#819—34no—
158C23×C32—21no—
159C23×C32#4111yescharacteristic
160C22×C3⋊D3—22no—
161C22×C3⋊D3—41no—
162C22×C3⋊D3—41no—
163C22×C3⋊D3—82no—
164C32×Q8—21no—
165C32×Q8C2×D412yes—
166C32×D4—22no—
167C32×D4—22no—
168C32×D4—21no—
169C32×D4C2×D412yes—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4111yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—41no—
182C4⋊(C3⋊D3)—41no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—41no—
185C2×C3×Dic3—41no—
186C3×Dic6—22no—
187C3×Dic6—22no—
188C3×Dic6—41no—
189C3×Dic6—41no—
190C3⋊(C3⋊C8)—22no—
191C3×C3⋊C8—22no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8C2×D412yes—
194C3×C3⋊C8C2×D412yes—
195C2×#137—31no—
196C2×AGL(1,ℤ/8)—91no—
197C22×SD16—91no—
198C2×#131—31no—
199#471—98no—
200C2×#108—91no—
201C2×#101—91no—
202C2×#100—91no—
203C23×D3—61no—
204C23×D3—61no—
205C23×D3—121no—
206C3×#41—21no—
207C3×#41—21no—
208C3×#41—21no—
209C3×#41—21no—
210C3×#41—22no—
211C3×#41—22no—
212C3×#41—41no—
213C3×#41—41no—
214C3×#41D1212yes—
215C3×#41#6712yes—
216C3×#41C22×D312yes—
217C3×#41C22×D312yes—
218C2×C3×Q8—21no—
219C2×C3×Q8—32no—
220C2×C3×Q8—61no—
221C2×C3×Q8—61no—
222C2×C3×Q8—61no—
223C2×C3×Q8—61no—
224C2×C3×Q8—61no—
225C2×C3×Q8D1211yescharacteristic
226C2×C3×Q8#6711yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—41no—
231C2×C3×D4D1211yescharacteristic
232C2×C3×D4#6711yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—41no—
237C22×C3×C4—61no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C22×Dic3—21no—
241C2×D12—32no—
242C2×D12—32no—
243C2×D12—62no—
244C2×D12—62no—
245C2×D12—62no—
246C2×D12—61no—
247C2×D12—61no—
248C2×D12—61no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12—61no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—121no—
257C2×D12—121no—
258C2×D12—121no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6C22×D312yes—
265C3×Q16—64no—
266C3×SD16—64no—
267C3×M16—32no—
268C3×M16—32no—
269C3×M16—64no—
270C3×M16—61no—
271C3×M16—61no—
272C2×C3×C8—31no—
273C2×C3×C8—31no—
274C2×C3×C8—32no—
275C2×C3×C8—32no—
276C2×C3×C8—64no—
277C2×C3×C8—61no—
278C2×C3×C8—61no—
279#216—24no—
280#215—68no—
281#215—64no—
282#215—64no—
283#215—64no—
284#215—64no—
285#214—24no—
286#213—68no—
287#213—64no—
288#213—64no—
289#208—21no—
290#208—21no—
291#208—24no—
292#208—32no—
293#208—32no—
294#208—62no—
295#208—62no—
296#208—61no—
297#208—61no—
298#208C22×D312yes—
299#208C22×D312yes—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—24no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8#6711yescharacteristic
307C2×C3⋊C8#6711yescharacteristic
308C2×C3⋊C8#6712yes—
309C2×C3⋊C8C22×D312yes—
310#204—64no—
311#204—64no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—42no—
315C22×C32#12111yescharacteristic
316C22×C32#12111yescharacteristic
317C22×C32C2×#4111yescharacteristic
318C2×C3⋊D3—42no—
319C2×C3⋊D3—82no—
320C2×C3⋊D3—82no—
321C2×C3⋊D3—82no—
322C32×C4—22no—
323C32×C4#12111yescharacteristic
324C32×C4#12111yescharacteristic
325C32×C4C22×D411yescharacteristic
326C32×C4C22×D411yescharacteristic
327C3×Dic3—42no—
328C2×#41D3211yescharacteristic
329C22×Q8—31no—
330C22×D4—91no—
331#137—34no—
332#137—62no—
333AGL(1,ℤ/8)—94no—
334AGL(1,ℤ/8)—182no—
335C2×Q16—61no—
336C2×SD16—61no—
337C2×SD16—94no—
338C2×SD16—181no—
339C2×SD16—181no—
340C2×SD16—182no—
341C2×SD16—181no—
342C2×D8—181no—
343#131—34no—
344#131—62no—
345C2×M16—31no—
346C2×M16—31no—
347C2×M16—61no—
348C2×M16—91no—
349C22×C8—31no—
350C22×C8—61no—
351#108—94no—
352#101—94no—
353#100—94no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—41no—
358C23×C3#23511yescharacteristic
359C23×C3#23711yescharacteristic
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—122no—
363C22×D3—122no—
364C22×D3—122no—
365C22×D3—121no—
366C22×D3—121no—
367C22×D3—121no—
368C22×D3—121no—
369C22×D3—244no—
370C22×D3—242no—
371C22×D3—242no—
372C3×Q8—21no—
373C3×Q8—21no—
374C3×Q8—22no—
375C3×Q8—41no—
376C3×Q8—62no—
377C3×Q8—62no—
378C3×Q8—121no—
379C3×Q8—121no—
380C3×Q8C2×D1212yes—
381C3×Q8C2×#6712yes—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—21no—
387C3×D4—21no—
388C3×D4—22no—
389C3×D4—41no—
390C3×D4—42no—
391C3×D4—42no—
392C3×D4C2×D1212yes—
393C3×D4C2×#6712yes—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—62no—
410C2×C3×C4—121no—
411C2×C3×C4—121no—
412C2×C3×C4C2×D1211yescharacteristic
413C2×C3×C4C2×D1211yescharacteristic
414C2×C3×C4#23511yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4#23711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C2×#6711yescharacteristic
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C23×D311yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424C2×Dic3—22no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427D12—64no—
428D12—62no—
429D12—62no—
430D12—62no—
431D12—62no—
432D12—122no—
433D12—122no—
434D12—122no—
435D12—121no—
436D12—121no—
437D12—121no—
438D12—121no—
439Dic6—22no—
440Dic6—22no—
441Dic6—41no—
442Dic6—41no—
443C3×C8—32no—
444C3×C8—32no—
445C3×C8—62no—
446C3×C8—62no—
447C3⋊C8—22no—
448C3⋊C8—22no—
449C3⋊C8—64no—
450C3⋊C8—62no—
451C3⋊C8—62no—
452C3⋊C8C2×#6712yes—
453C3⋊C8C2×#6712yes—
454C2×C32—21no—
455C2×C32—21no—
456C2×C32—42no—
457C2×C32#47112yescomplemented
458C2×C32C2×#12111yescharacteristic
459C3⋊D3—82no—
460C24—181no—
461#41—21no—
462#41—21no—
463#41#62612yes—
464#41C2×D3212yes—
465C2×Q8—32no—
466C2×Q8—61no—
467C2×Q8—61no—
468C2×Q8—61no—
469C2×Q8—61no—
470C2×Q8—61no—
471C2×Q8#62611yescharacteristic
472C2×D4—21no—
473C2×D4—92no—
474C2×D4—181no—
475C2×D4—181no—
476C2×D4—181no—
477C2×D4—181no—
478C2×D4—181no—
479C2×D4#62611yescharacteristic
480C22×C4—21no—
481C22×C4—61no—
482C22×C4C2×D3211yescharacteristic
483Q16—64no—
484SD16—64no—
485SD16—184no—
486SD16—184no—
487SD16—184no—
488D8—184no—
489M16—32no—
490M16—32no—
491M16—64no—
492M16—61no—
493M16—61no—
494M16—92no—
495M16—181no—
496C2×C8—32no—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—32no—
500C2×C8—64no—
501C2×C8—61no—
502C2×C8—61no—
503C2×C8—181no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—82no—
516C22×C3#93011yescharacteristic
517C22×C3#93011yescharacteristic
518C22×C3#93911yescharacteristic
519C22×C3#93911yescharacteristic
520C22×C3C2×#23511yescharacteristic
521C22×C3C2×#23711yescharacteristic
522C2×D3—124no—
523C2×D3—122no—
524C2×D3—122no—
525C2×D3—242no—
526C2×D3—242no—
527C2×D3—244no—
528C2×D3—244no—
529C2×D3—244no—
530C2×D3—242no—
531C2×D3—242no—
532C2×D3—242no—
533C2×D3—242no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—42no—
541C3×C4—122no—
542C3×C4#93011yescharacteristic
543C3×C4#93011yescharacteristic
544C3×C4#93911yescharacteristic
545C3×C4#93911yescharacteristic
546C3×C4C22×D1211yescharacteristic
547C3×C4C2×D3×D411yescharacteristic
548C3×C4C22×#6711yescharacteristic
549C3×C4C22×#6711yescharacteristic
550Dic3—42no—
551C32C2×#47111yescharacteristic, complemented, Sylow
552C23—21no—
553C23—182no—
554C23—361no—
555C23—361no—
556C23—722no—
557C23#380411yescharacteristic
558Q8—21no—
559Q8—62no—
560Q8—62no—
561Q8—121no—
562Q8—121no—
563Q8C2×#62612yes—
564D4—22no—
565D4—22no—
566D4—21no—
567D4—182no—
568D4—182no—
569D4—361no—
570D4—361no—
571D4C2×#62612yes—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—62no—
576C2×C4—121no—
577C2×C4—121no—
578C2×C4#380411yescharacteristic
579C2×C4C2×#62611yescharacteristic
580C2×C4C2×#62611yescharacteristic
581C2×C4D3×#6711yescharacteristic
582C2×C4D3×#6711yescharacteristic
583C2×C4C22×D3211yescharacteristic
584C8—32no—
585C8—32no—
586C8—62no—
587C8—62no—
588C8—182no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—22no—
595C2×C3—41no—
596C2×C3—41no—
597C2×C3—42no—
598C2×C3—42no—
599C2×C3—82no—
600C2×C3#514112yescomplemented
601C2×C3#520312yescomplemented
602C2×C3C2×#93011yescharacteristic
603C2×C3C2×#93911yescharacteristic
604D3—244no—
605D3—242no—
606D3—242no—
607C22—22no—
608C22—22no—
609C22—42no—
610C22—362no—
611C22—722no—
612C22—722no—
613C22—722no—
614C22#6397811yescharacteristic
615C22#6397811yescharacteristic
616C22C2×#380411yescharacteristic
617C4—22no—
618C4—122no—
619C4#6397811yescharacteristic
620C4#6397811yescharacteristic
621C4C22×#62611yescharacteristic
622C4C2×D3×#6711yescharacteristic
623C3—21no—
624C3C2×#514111yescharacteristic, complemented
625C3C2×#520311yescharacteristic, complemented
626C2—21no—
627C2—21no—
628C2—42no—
629C2—722no—
630C2#1059168012yesdirect product factor
631C2C2×#6397811yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32#121
prime radicalC2×#64158C2
hypercenterC2×#41D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×C3×#948C2semidirect
4. C22×#3717C2semidirect
5. #10591680C2direct (N × H)
6. C2×#63577C2semidirect
7. C2×#63560C2semidirect
8. C2×#63559C2semidirect
20. C3×#951C22semidirect
22. C3×#948C22semidirect
33. C2×#3717C22semidirect
34. #63577C22semidirect
35. #63560C22semidirect
36. #63559C22semidirect
39. C2×#951D3semidirect
43. C2×#948D3semidirect
119. #951C2×D3semidirect
127. #948C2×D3semidirect
457. C2×C32#471semidirect
551. C32C2×#471semidirect
600. C2×C3#5141semidirect
601. C2×C3#5203semidirect
624. C3C2×#5141semidirect
625. C3C2×#5203semidirect
630. C2#10591680direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641582
C2×C3×#9512
C2×C3×#9482
C22×#37172
#105916802
C2×#635772
C2×#635602
C2×#635592
C2×#52033
C2×#51413