Finite Group Databasebeta

← C2×#10590979 #11867891

Subgroups — C2×#10590979 #11867891

Order 1152.

989 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic, complemented
2C22×#3715C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic
4C2×#63815C211yesmaximal, characteristic, complemented
5C2×#63649C211yesmaximal, characteristic, complemented
6C2×C3×#823C211yesmaximal, characteristic, complemented
7C2×#63560C211yesmaximal, characteristic, complemented
8#10590979C218yesmaximal, direct product factor
9C2×#5203—31nomaximal
10C2×#4748—31nomaximal
11C2×C3×#235C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#909—22no—
19C3×#909C2214yescomplemented
20C2×C3×Dic12—21no—
21C2×C3×#204—21no—
22C2×#3715—21no—
23C2×#3715—21no—
24C2×#3715—22no—
25C2×#3715—21no—
26C2×#3715C2214yescomplemented
27#63823—22no—
28#63823C2214yes—
29C2×#3713—21no—
30C2×#3711—21no—
31#63815—22no—
32#63815C2214yescomplemented
33C2×D3×C3⋊C8—21no—
34#63649C2214yescomplemented
35C3×#823C2214yescomplemented
36#63560C2214yescomplemented
37C2×C3×#137—31no—
38C2×#949—31no—
39C2×#948—31no—
40C22×#215—31no—
41C22×#214—31no—
42C2×#932—31no—
43C2×#909D311yescharacteristic, complemented
44C2×#907—31no—
45C2×C3×#100—31no—
46C2×#836—31no—
47#5203—38no—
48C2×#824—31no—
49C2×#823D311yescharacteristic, complemented
50C2×#822—31no—
51C2×#822—31no—
52C2×#822—61no—
53#4748—38no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—21no—
57C22×C3×Dic3—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×D12D411yescharacteristic
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6D411yescharacteristic
76C2×C3×Dic6C2312yes—
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×Dic12—24no—
91C3×#204—24no—
92#3715—24no—
93#3715—24no—
94#3715—24no—
95#3713—24no—
96#3711—24no—
97D3×C3⋊C8—24no—
98C2×#471—91noSylow
99C2×C3×#41—31no—
100C22×C3×Q8—31no—
101C22×C3×D4—31no—
102C2×#235C2×D311yescharacteristic
103C22×D12C2×D311yescharacteristic
104C22×Dic6C2×D311yescharacteristic
105C3×#137—34no—
106C3×#137—62no—
107C2×C3×Q16—61no—
108C2×C3×SD16—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—34no—
118C2×#215—61no—
119C2×#215—61no—
120C2×#215—62no—
121C2×#215—61no—
122C2×#214—34no—
123C2×#214—61no—
124C2×#214—61no—
125C2×#214—62no—
126C2×#214—61no—
127#932—34no—
128#932—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#909—22no—
141#909C2×D314yescomplemented
142#907—34no—
143#907—62no—
144C2×Dic12—21no—
145C2×#204—21no—
146C2×ΓL(1,𝔽25)—61no—
147C2×D3×C8—61no—
148C3×#100—34no—
149#836—34no—
150#824—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—41no—
159C22×C3×D3—41no—
160C22×C3×D3—82no—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4#4111yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C3×#67—22no—
168C3×#67—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C3×D12—21no—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—41no—
177C3×D12—41no—
178C3×D12C2×D412yes—
179C3×C4×D3—22no—
180C3×C4×D3—22no—
181C3×Dic6—21no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—41no—
185C3×Dic6—41no—
186C3×Dic6C2×D412yes—
187C32×C8—22no—
188C3⋊(C3⋊C8)—22no—
189C3⋊(C3⋊C8)C2×D412yes—
190C3⋊(C3⋊C8)C2×D412yes—
191C3×C3⋊C8—22no—
192C2×#137—31no—
193C2×AGL(1,ℤ/8)—91no—
194C22×SD16—91no—
195C2×#131—91no—
196#471—98no—
197C2×#108—91no—
198C2×#101—91no—
199C2×#100—31no—
200C24×C3—61no—
201C23×D3—21no—
202C3×#41—32no—
203C3×#41—32no—
204C3×#41—61no—
205C3×#41—61no—
206C2×C3×Q8—31no—
207C2×C3×Q8—32no—
208C2×C3×Q8—61no—
209C2×C3×Q8—61no—
210C2×C3×Q8—61no—
211C2×C3×Q8—61no—
212C2×C3×Q8—61no—
213C2×C3×D4—31no—
214C2×C3×D4—32no—
215C2×C3×D4—61no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C2×C3×D4—61no—
221C22×C3×C4—21no—
222C22×C3×C4—61no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—21no—
227C22×Dic3—21no—
228#235—21no—
229#235—21no—
230#235#6712yes—
231#235C22×D312yes—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12#6711yescharacteristic
238C2×D12C22×D312yes—
239C2×C4×D3—21no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—21no—
243C2×Dic6—21no—
244C2×Dic6—21no—
245C2×Dic6#6711yescharacteristic
246C2×Dic6C22×D312yes—
247C3×Q16—64no—
248C3×SD16—64no—
249C3×M16—21no—
250C3×M16—21no—
251C3×M16—22no—
252C3×M16—32no—
253C3×M16—41no—
254C3×M16—61no—
255C3×M16C22×D312yes—
256C3×M16C22×D312yes—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—41no—
260C2×C3×C8—61no—
261#215—64no—
262#215—64no—
263#215—64no—
264#214—64no—
265#214—64no—
266#214—64no—
267#213—64no—
268#213—64no—
269#208—21no—
270#208—32no—
271#208—32no—
272#208—62no—
273#208—64no—
274#208—61no—
275#208—61no—
276#208—121no—
277#208C22×D312yes—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8—61no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8—64no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8—121no—
295Dic12—24no—
296#204—24no—
297ΓL(1,𝔽25)—64no—
298D3×C8—64no—
299C22×C32—22no—
300C22×C32#12111yescharacteristic
301C22×C32#12111yescharacteristic
302C22×C32C2×#4111yescharacteristic
303C2×C3×D3—22no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—82no—
307C2×C3×D3—82no—
308C2×C3×D3—82no—
309C32×C4#12111yescharacteristic
310C32×C4#12111yescharacteristic
311C32×C4C22×D411yescharacteristic
312C32×C4C22×D411yescharacteristic
313C3×Dic3—22no—
314C3×Dic3—42no—
315C2×#41—31no—
316C22×Q8—31no—
317C22×D4—31no—
318#137—34no—
319#137—62no—
320AGL(1,ℤ/8)—94no—
321AGL(1,ℤ/8)—182no—
322C2×Q16—61no—
323C2×SD16—61no—
324C2×SD16—94no—
325C2×SD16—181no—
326C2×SD16—181no—
327C2×SD16—182no—
328C2×SD16—181no—
329C2×D8—181no—
330#131—94no—
331#131—182no—
332C2×M16—31no—
333C2×M16—91no—
334C2×M16—181no—
335C2×M16D3211yescharacteristic
336C22×C8—91no—
337C22×C8—181no—
338#108—94no—
339#101—94no—
340#100—34no—
341C23×C3—21no—
342C23×C3—61no—
343C23×C3—62no—
344C23×C3—121no—
345C23×C3—121no—
346C23×C3—242no—
347C23×C3#23511yescharacteristic
348C23×C3#23711yescharacteristic
349C22×D3—21no—
350C22×D3—22no—
351C22×D3—41no—
352C22×D3—41no—
353C22×D3—82no—
354C3×Q8—32no—
355C3×Q8—61no—
356C3×Q8—62no—
357C3×Q8—62no—
358C3×Q8—121no—
359C3×Q8—121no—
360C3×D4—32no—
361C3×D4—62no—
362C3×D4—62no—
363C3×D4—61no—
364C3×D4—62no—
365C3×D4—62no—
366C3×D4—121no—
367C3×D4—121no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23711yescharacteristic
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392#67—22no—
393#67—22no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398D12—21no—
399D12—22no—
400D12—22no—
401D12—41no—
402D12—41no—
403D12C2×#6712yes—
404C4×D3—22no—
405C4×D3—22no—
406Dic6—21no—
407Dic6—22no—
408Dic6—22no—
409Dic6—41no—
410Dic6—41no—
411Dic6C2×#6712yes—
412C3×C8—22no—
413C3×C8—22no—
414C3×C8—42no—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—32no—
418C3⋊C8—32no—
419C3⋊C8—32no—
420C3⋊C8—32no—
421C3⋊C8—62no—
422C3⋊C8—62no—
423C3⋊C8—62no—
424C3⋊C8—62no—
425C3⋊C8—122no—
426C2×C32—21no—
427C2×C32—21no—
428C2×C32#47112yescomplemented
429C2×C32C2×#12111yescharacteristic
430C3×D3—42no—
431C3×D3—82no—
432C24—61no—
433#41—32no—
434#41—32no—
435#41—61no—
436#41—61no—
437C2×Q8—32no—
438C2×Q8—31no—
439C2×Q8—61no—
440C2×Q8—61no—
441C2×Q8—61no—
442C2×Q8—61no—
443C2×Q8—61no—
444C2×D4—32no—
445C2×D4—31no—
446C2×D4—61no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4C2×D3211yescharacteristic
455Q16—64no—
456SD16—64no—
457SD16—184no—
458SD16—184no—
459SD16—184no—
460D8—184no—
461M16—21no—
462M16—32no—
463M16—61no—
464M16—92no—
465M16—184no—
466M16—181no—
467M16C2×D3212yes—
468C2×C8—21no—
469C2×C8—61no—
470C2×C8—92no—
471C2×C8—91no—
472C2×C8—91no—
473C2×C8—92no—
474C2×C8—184no—
475C2×C8—181no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—42no—
482C22×C3—62no—
483C22×C3—122no—
484C22×C3—122no—
485C22×C3—242no—
486C22×C3—242no—
487C22×C3—242no—
488C22×C3#88411yescharacteristic
489C22×C3#88411yescharacteristic
490C22×C3#93911yescharacteristic
491C22×C3#93911yescharacteristic
492C22×C3C2×#23511yescharacteristic
493C22×C3C2×#23711yescharacteristic
494C2×D3—22no—
495C2×D3—42no—
496C2×D3—42no—
497C2×D3—82no—
498C2×D3—82no—
499C2×D3—82no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—62no—
505C3×C4—122no—
506C3×C4#88411yescharacteristic
507C3×C4#88411yescharacteristic
508C3×C4#93911yescharacteristic
509C3×C4#93911yescharacteristic
510C3×C4C2×D3×D411yescharacteristic
511C3×C4C2×D3×D411yescharacteristic
512C3×C4C2×D3×D411yescharacteristic
513C3×C4C22×#6711yescharacteristic
514Dic3—22no—
515Dic3—42no—
516C32C2×#47111yescharacteristic, complemented, Sylow
517C23—61no—
518C23—62no—
519C23—121no—
520C23—121no—
521C23—242no—
522C23#379511yescharacteristic
523Q8—32no—
524Q8—61no—
525Q8—62no—
526Q8—62no—
527Q8—121no—
528Q8—121no—
529D4—32no—
530D4—62no—
531D4—62no—
532D4—62no—
533D4—62no—
534D4—61no—
535D4—121no—
536D4—121no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4#379511yescharacteristic
544C2×C4#380211yescharacteristic
545C2×C4#380211yescharacteristic
546C2×C4D3×#6711yescharacteristic
547C2×C4D3×#6711yescharacteristic
548C2×C4C22×D3211yescharacteristic
549C8—22no—
550C8—62no—
551C8—92no—
552C8—92no—
553C8—182no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—22no—
559C2×C3—21no—
560C2×C3—41no—
561C2×C3—41no—
562C2×C3—122no—
563C2×C3—242no—
564C2×C3#474812yescomplemented
565C2×C3#520312yescomplemented
566C2×C3C2×#88411yescharacteristic
567C2×C3C2×#93911yescharacteristic
568D3—42no—
569D3—82no—
570C22—22no—
571C22—62no—
572C22—122no—
573C22—122no—
574C22—242no—
575C22—242no—
576C22—242no—
577C22#6388511yescharacteristic
578C22#6388511yescharacteristic
579C22C2×#379511yescharacteristic
580C4—62no—
581C4—122no—
582C4#6388511yescharacteristic
583C4#6388511yescharacteristic
584C4C2×#380211yescharacteristic
585C4C2×D3×#6711yescharacteristic
586C3—21no—
587C3C2×#474811yescharacteristic, complemented
588C3C2×#520311yescharacteristic, complemented
589C2—21no—
590C2—21no—
591C2—122no—
592C2—242no—
593C2#1059097912yesdirect product factor
594C2C2×#6388511yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63823C2
hypercenterC2×M16D32
hypocenterC32C2×#471
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×#909C2semidirect
2. C22×#3715C2semidirect
4. C2×#63815C2semidirect
5. C2×#63649C2semidirect
6. C2×C3×#823C2semidirect
7. C2×#63560C2semidirect
8. #10590979C2direct (N × H)
19. C3×#909C22semidirect
26. C2×#3715C22semidirect
32. #63815C22semidirect
34. #63649C22semidirect
35. C3×#823C22semidirect
36. #63560C22semidirect
43. C2×#909D3semidirect
49. C2×#823D3semidirect
141. #909C2×D3semidirect
151. #823C2×D3semidirect
428. C2×C32#471semidirect
516. C32C2×#471semidirect
564. C2×C3#4748semidirect
565. C2×C3#5203semidirect
587. C3C2×#4748semidirect
588. C3C2×#5203semidirect
593. C2#10590979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9092
C22×#37152
C2×#638232
C2×#638152
C2×#636492
C2×C3×#8232
C2×#635602
#105909792
C2×#52033
C2×#47483