Finite Group Databasebeta

← C2×#10590987 #11867939

Subgroups — C2×#10590987 #11867939

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic, complemented
2C2×#63830C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C2×#63817C211yesmaximal, characteristic, complemented
5C2×C3×#823C211yesmaximal, characteristic, complemented
6C2×C3×#822C211yesmaximal, characteristic, complemented
7C2×#63559C211yesmaximal, characteristic, complemented
8#10590987C218yesmaximal, direct product factor
9C2×#4897—31nomaximal
10C2×#4749—31nomaximal
11C2×#3828C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15#64117—22no—
16#64117C2214yescomplemented
17C2×#3745—21no—
18C2×#3744—21no—
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63830—22no—
23#63830C2214yescomplemented
24C2×#3716—21no—
25C2×#3714—21no—
26C2×#3714—21no—
27C2×#3714—22no—
28C2×#3714—21no—
29C2×#3714C2214yescomplemented
30C2×#3712—21no—
31#63817—22no—
32#63817C2214yescomplemented
33C2×#3710—21no—
34C3×#823C2214yescomplemented
35C3×#822C2214yescomplemented
36#63559C2214yescomplemented
37C2×#932—31no—
38C22×#213—31no—
39C2×#908—31no—
40C2×#908—31no—
41C2×#908—31no—
42C2×#908—61no—
43C2×#907—31no—
44C22×D24—31no—
45C2×#901—31no—
46C2×C3×#108—31no—
47C2×C3×#100—31no—
48C2×#823—31no—
49C2×#823—31no—
50C2×#823D311yescharacteristic, complemented
51C2×#822D311yescharacteristic, complemented
52#4897—38no—
53#4749—38no—
54C23×C3⋊D3—21no—
55C23×C3×D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—21no—
58#3828—21no—
59#3828—21no—
60#3828D412yes—
61#3828C2312yes—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)D411yescharacteristic
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C4×C3⋊D3—21no—
70C2×#634D411yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C32×M16—21no—
78C32×M16C2312yes—
79C2×C32×C8—21no—
80#3745—24no—
81#3744—24no—
82C3×#208—21no—
83C3×#208—21no—
84C3×#208C2312yes—
85C3×#208C2312yes—
86C2×C3×C3⋊C8—21no—
87C2×C3×C3⋊C8—21no—
88C2×C3×C3⋊C8D411yescharacteristic
89C2×C3×C3⋊C8D412yes—
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92#3716—24no—
93#3714—24no—
94#3714—24no—
95#3714—24no—
96#3712—24no—
97#3710—24no—
98C2×#472—91noSylow
99C22×C3×D4—31no—
100C2×#235—31no—
101C2×#235—31no—
102C2×#235—61no—
103C22×D12—31no—
104C22×D12—31no—
105C22×D12—61no—
106C22×D12C2×D311yescharacteristic
107C2×C3×M16—21no—
108C2×C3×M16—31no—
109C2×C3×M16—31no—
110C2×C3×M16C2×D311yescharacteristic
111C2×C3×M16C2×D311yescharacteristic
112C22×C3×C8—31no—
113C2×#214—61no—
114#932—34no—
115#932—62no—
116C2×#213—34no—
117C2×#213—61no—
118C2×#213—61no—
119C2×#213—61no—
120C2×#213—62no—
121C2×#208C2×D311yescharacteristic
122C2×#208C2×D311yescharacteristic
123C22×C3⋊C8C2×D311yescharacteristic
124#908—34no—
125#908—34no—
126#908—34no—
127#908—64no—
128#908—62no—
129#908—62no—
130#908—64no—
131#908—62no—
132#907—34no—
133#907—62no—
134C2×D24—34no—
135C2×D24—61no—
136C2×D24—61no—
137C2×D24—62no—
138C2×D24—61no—
139C2×D24—61no—
140C2×D24—62no—
141C2×D24—61no—
142C2×#204—61no—
143C2×#204—61no—
144C2×#204—62no—
145C2×#204—61no—
146#901—34no—
147#901—62no—
148C2×ΓL(1,𝔽25)—61no—
149C2×ΓL(1,𝔽25)—61no—
150C2×D3×C8—61no—
151C2×D3×C8—61no—
152C3×#108—34no—
153C3×#100—34no—
154#823—34no—
155#823—34no—
156#823C2×D314yescomplemented
157#822C2×D314yescomplemented
158C23×C32#4111yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3⋊D3—22no—
161C22×C3⋊D3—41no—
162C22×C3⋊D3—41no—
163C22×C3⋊D3—82no—
164C22×C3×D3—22no—
165C22×C3×D3—41no—
166C22×C3×D3—41no—
167C22×C3×D3—82no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4111yescharacteristic
173C2×C32×C4C2411yescharacteristic
174#638—22no—
175#638—22no—
176C2×C3⋊Dic3—21no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)—21no—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—41no—
181C4⋊(C3⋊D3)—41no—
182C4⋊(C3⋊D3)C2×D412yes—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—22no—
185#634—21no—
186#634C2×D412yes—
187C3×D12—22no—
188C3×D12—22no—
189C3×D12—41no—
190C3×D12—41no—
191C32×C8—22no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8C2×D412yes—
195C3×C3⋊C8C2×D412yes—
196C2×AGL(1,ℤ/8)—91no—
197C2×AGL(1,ℤ/8)—91no—
198C22×D8—91no—
199C2×#131—91no—
200#472—98no—
201C2×#108—31no—
202C2×#100—31no—
203C2×#100—91no—
204C24×C3—61no—
205C23×D3—21no—
206C23×D3—61no—
207C23×D3—61no—
208C23×D3—121no—
209C2×C3×D4—32no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C22×C3×C4—21no—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C2×#67—61no—
219C2×#67—61no—
220C2×#67—121no—
221#235—32no—
222#235—32no—
223#235—32no—
224#235—32no—
225#235—62no—
226#235—62no—
227#235—61no—
228#235—61no—
229#235—61no—
230#235—61no—
231#235—121no—
232#235—121no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—31no—
239C2×D12—31no—
240C2×D12—32no—
241C2×D12—32no—
242C2×D12—61no—
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×D12C22×D312yes—
260C2×C4×D3—61no—
261C2×C4×D3—61no—
262C2×C4×D3—121no—
263C2×Dic6—31no—
264C2×Dic6—31no—
265C2×Dic6—61no—
266C3×M16—22no—
267C3×M16—21no—
268C3×M16—21no—
269C3×M16—22no—
270C3×M16—32no—
271C3×M16—32no—
272C3×M16—61no—
273C3×M16—61no—
274C3×M16C22×D312yes—
275C3×M16C22×D312yes—
276C2×C3×C8—22no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—31no—
280C2×C3×C8—31no—
281C2×C3×C8—32no—
282C2×C3×C8—32no—
283C2×C3×C8—61no—
284C2×C3×C8—61no—
285#214—64no—
286#213—64no—
287#213—64no—
288#213—64no—
289#208—21no—
290#208—21no—
291#208C22×D312yes—
292#208C22×D312yes—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8D1211yescharacteristic
296C2×C3⋊C8D1211yescharacteristic
297C2×C3⋊C8D1212yes—
298C2×C3⋊C8C22×D312yes—
299D24—64no—
300D24—64no—
301D24—68no—
302D24—64no—
303D24—64no—
304D24—64no—
305#204—64no—
306#204—64no—
307#204—68no—
308#204—64no—
309ΓL(1,𝔽25)—64no—
310ΓL(1,𝔽25)—64no—
311D3×C8—64no—
312D3×C8—64no—
313C22×C32—22no—
314C22×C32#12111yescharacteristic
315C22×C32#12111yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C2×C3⋊D3—22no—
318C2×C3⋊D3—42no—
319C2×C3⋊D3—42no—
320C2×C3⋊D3—82no—
321C2×C3⋊D3—82no—
322C2×C3⋊D3—82no—
323C2×C3×D3—42no—
324C2×C3×D3—82no—
325C2×C3×D3—82no—
326C2×C3×D3—82no—
327C32×C4#12111yescharacteristic
328C32×C4#12111yescharacteristic
329C32×C4C22×D411yescharacteristic
330C32×C4C22×D411yescharacteristic
331C3⋊Dic3—22no—
332C2×#41—91no—
333C22×D4—31no—
334C22×D4—91no—
335AGL(1,ℤ/8)—94no—
336AGL(1,ℤ/8)—94no—
337AGL(1,ℤ/8)—182no—
338AGL(1,ℤ/8)—182no—
339C2×SD16—181no—
340C2×SD16—181no—
341C2×D8—94no—
342C2×D8—181no—
343C2×D8—181no—
344C2×D8—181no—
345C2×D8—182no—
346C2×D8—181no—
347#131—94no—
348#131—182no—
349C2×M16—31no—
350C2×M16—31no—
351C2×M16—181no—
352C2×M16D3211yescharacteristic
353C22×C8—31no—
354C22×C8—181no—
355#108—34no—
356#100—34no—
357#100—94no—
358C23×C3—21no—
359C23×C3—62no—
360C23×C3—121no—
361C23×C3—121no—
362C23×C3—242no—
363C23×C3#23511yescharacteristic
364C23×C3#23911yescharacteristic
365C22×D3—22no—
366C22×D3—41no—
367C22×D3—41no—
368C22×D3—61no—
369C22×D3—61no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—82no—
373C22×D3—121no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—121no—
378C22×D3—121no—
379C22×D3—121no—
380C22×D3—121no—
381C22×D3—244no—
382C22×D3—242no—
383C22×D3—242no—
384C3×D4—62no—
385C3×D4—62no—
386C3×D4—121no—
387C3×D4—121no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4C2×D1211yescharacteristic
395C2×C3×C4C2×D1211yescharacteristic
396C2×C3×C4#23511yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4#23911yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—62no—
407#67—62no—
408#67—62no—
409#67—62no—
410#67—122no—
411#67—122no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—121no—
415D12—22no—
416D12—22no—
417D12—32no—
418D12—32no—
419D12—41no—
420D12—41no—
421D12—62no—
422D12—64no—
423D12—61no—
424D12—61no—
425D12—62no—
426D12—62no—
427D12—62no—
428D12—62no—
429D12—122no—
430D12—121no—
431D12—122no—
432D12—122no—
433D12—121no—
434D12—121no—
435D12—121no—
436D12—121no—
437C4×D3—62no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—122no—
442C4×D3—122no—
443Dic6—32no—
444Dic6—32no—
445Dic6—62no—
446Dic6—61no—
447Dic6—61no—
448Dic6—121no—
449C3×C8—24no—
450C3×C8—22no—
451C3×C8—22no—
452C3×C8—32no—
453C3×C8—32no—
454C3×C8—62no—
455C3×C8—62no—
456C3⋊C8—22no—
457C3⋊C8—22no—
458C3⋊C8C2×D1212yes—
459C3⋊C8C2×D1212yes—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32#47212yescomplemented
463C2×C32C2×#12111yescharacteristic
464C3⋊D3—42no—
465C3⋊D3—82no—
466C3×D3—82no—
467C24—61no—
468C24—181no—
469#41—92no—
470#41—92no—
471#41—181no—
472#41—181no—
473C2×Q8—91no—
474C2×D4—32no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—61no—
480C2×D4—92no—
481C2×D4—91no—
482C2×D4—181no—
483C2×D4—181no—
484C2×D4—181no—
485C2×D4—181no—
486C2×D4—181no—
487C2×D4—181no—
488C22×C4—181no—
489C22×C4C2×D3211yescharacteristic
490SD16—184no—
491SD16—184no—
492D8—184no—
493D8—184no—
494D8—184no—
495D8—184no—
496M16—21no—
497M16—32no—
498M16—32no—
499M16—61no—
500M16—61no—
501M16—184no—
502M16C2×D3212yes—
503C2×C8—21no—
504C2×C8—32no—
505C2×C8—31no—
506C2×C8—31no—
507C2×C8—32no—
508C2×C8—61no—
509C2×C8—61no—
510C2×C8—184no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—42no—
517C22×C3—122no—
518C22×C3—242no—
519C22×C3—242no—
520C22×C3—242no—
521C22×C3#88411yescharacteristic
522C22×C3#88411yescharacteristic
523C22×C3#89511yescharacteristic
524C22×C3#89511yescharacteristic
525C22×C3C2×#23511yescharacteristic
526C22×C3C2×#23911yescharacteristic
527C2×D3—42no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—82no—
531C2×D3—82no—
532C2×D3—82no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—124no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—242no—
540C2×D3—242no—
541C2×D3—242no—
542C2×D3—244no—
543C2×D3—244no—
544C2×D3—244no—
545C2×D3—242no—
546C2×D3—242no—
547C2×D3—242no—
548C2×D3—242no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4#88411yescharacteristic
554C3×C4#88411yescharacteristic
555C3×C4#89511yescharacteristic
556C3×C4#89511yescharacteristic
557C3×C4C22×D1211yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560C3×C4C2×D3×D411yescharacteristic
561Dic3—62no—
562Dic3—62no—
563Dic3—122no—
564C32C2×#47211yescharacteristic, complemented, Sylow
565C23—62no—
566C23—121no—
567C23—121no—
568C23—181no—
569C23—182no—
570C23—242no—
571C23—361no—
572C23—361no—
573C23—722no—
574C23#379911yescharacteristic
575Q8—92no—
576Q8—181no—
577D4—62no—
578D4—62no—
579D4—92no—
580D4—121no—
581D4—121no—
582D4—182no—
583D4—182no—
584D4—182no—
585D4—182no—
586D4—181no—
587D4—361no—
588D4—361no—
589C2×C4—181no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4#379911yescharacteristic
593C2×C4D3×D1211yescharacteristic
594C2×C4D3×D1211yescharacteristic
595C2×C4#381111yescharacteristic
596C2×C4#381111yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—22no—
599C8—32no—
600C8—32no—
601C8—62no—
602C8—62no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—22no—
608C2×C3—21no—
609C2×C3—41no—
610C2×C3—41no—
611C2×C3—242no—
612C2×C3#474912yescomplemented
613C2×C3#489712yescomplemented
614C2×C3C2×#88411yescharacteristic
615C2×C3C2×#89511yescharacteristic
616D3—82no—
617D3—122no—
618D3—122no—
619D3—242no—
620D3—244no—
621D3—242no—
622D3—242no—
623C22—22no—
624C22—122no—
625C22—182no—
626C22—242no—
627C22—242no—
628C22—242no—
629C22—362no—
630C22—362no—
631C22—722no—
632C22—722no—
633C22—722no—
634C22#6391011yescharacteristic
635C22#6391011yescharacteristic
636C22C2×#379911yescharacteristic
637C4—182no—
638C4#6391011yescharacteristic
639C4#6391011yescharacteristic
640C4C2×D3×D1211yescharacteristic
641C4C2×#381111yescharacteristic
642C3—21no—
643C3C2×#474911yescharacteristic, complemented
644C3C2×#489711yescharacteristic, complemented
645C2—21no—
646C2—21no—
647C2—242no—
648C2—362no—
649C2—722no—
650C2#1059098712yesdirect product factor
651C2C2×#6391011yescharacteristic
subgroupG/H
centerC22#63910
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×#64117C2semidirect
2. C2×#63830C2semidirect
3. C22×#3714C2semidirect
4. C2×#63817C2semidirect
5. C2×C3×#823C2semidirect
6. C2×C3×#822C2semidirect
7. C2×#63559C2semidirect
8. #10590987C2direct (N × H)
16. #64117C22semidirect
23. #63830C22semidirect
29. C2×#3714C22semidirect
32. #63817C22semidirect
34. C3×#823C22semidirect
35. C3×#822C22semidirect
36. #63559C22semidirect
50. C2×#823D3semidirect
51. C2×#822D3semidirect
156. #823C2×D3semidirect
157. #822C2×D3semidirect
462. C2×C32#472semidirect
564. C32C2×#472semidirect
612. C2×C3#4749semidirect
613. C2×C3#4897semidirect
643. C3C2×#4749semidirect
644. C3C2×#4897semidirect
650. C2#10590987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641172
C2×#638302
C22×#37142
C2×#638172
C2×C3×#8232
C2×C3×#8222
C2×#635592
#105909872
C2×#48973
C2×#47493