Finite Group Databasebeta

← C2×#10591674 #11861061

Subgroups — C2×#10591674 #11861061

Order 1152.

1013 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#950C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C2×#63814C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5#10591674C218yesmaximal, direct product factor
6C2×#63577C211yesmaximal, characteristic, complemented
7C2×#63568C211yesmaximal, characteristic, complemented
8C2×#63555C211yesmaximal, characteristic, complemented
9C2×#5197—31nomaximal
10C2×#5145—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#950C414yescomplemented
16C3×#950C2214yes—
17C3×#948—22no—
18C3×#948C2214yescomplemented
19C2×C3×#216C411yescharacteristic, complemented
20C2×C3×#215C411yescharacteristic, complemented
21C2×C3×#214C411yescharacteristic, complemented
22C2×C3×#213C411yescharacteristic, complemented
23C2×C3×#208—21no—
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8—21no—
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3711—21no—
29#63814—22no—
30#63814C2214yescomplemented
31C2×D3×C3⋊C8—21no—
32#63664C2214yescomplemented
33#63577C2214yescomplemented
34#63568C2214yescomplemented
35#63555C2214yescomplemented
36C2×C3×#135—31no—
37C2×C3×#131—31no—
38C2×#950D311yescharacteristic
39C2×#948—31no—
40C2×#948D311yescharacteristic, complemented
41C2×#901—31no—
42C2×#837—31no—
43C2×#837—31no—
44C2×#837—31no—
45C2×#837—61no—
46#5197—38no—
47#5145—38no—
48C2×#825—31no—
49C2×#822—31no—
50C2×#819—31no—
51C2×#815—31no—
52C2×#815—31no—
53C32×#41—21no—
54C32×#41—21no—
55C32×#41C2×C412yes—
56C32×#41C2312yes—
57C2×C32×Q8C2×C411yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2×C411yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3—21no—
63C2×C3×#67—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235C2×C412yes—
67C3×#235C2312yes—
68C2×C3×D12C2×C411yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2×C411yescharacteristic
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3C2312yes—
73#3748—21no—
74#3748C2312yes—
75C2×C3⋊(C3⋊C8)—21no—
76C3×#216C2×C414yescomplemented
77C3×#215C2×C414yescomplemented
78C3×#214C2×C414yescomplemented
79C3×#213C2×C414yescomplemented
80C3×#208—21no—
81C3×#208—24no—
82C3×#208C2312yes—
83C2×C3×C3⋊C8—21no—
84C2×C3×C3⋊C8—24no—
85C2×C3×C3⋊C8C2×C411yescharacteristic
86C2×C3×C3⋊C8C2×C411yescharacteristic
87C2×C3×C3⋊C8C2×C412yes—
88C2×C3×C3⋊C8D411yescharacteristic
89C2×C3×C3⋊C8D411yescharacteristic
90C2×C3×C3⋊C8D412yes—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3711—24no—
94D3×C3⋊C8—24no—
95C2×#444—91noSylow
96C2×C3×#41—21no—
97C2×C3×#41—31no—
98C2×C3×#41C2×D311yescharacteristic
99C2×C3×#41C2×D311yescharacteristic
100C2×#235C2×D311yescharacteristic
101C3×#135—34no—
102C3×#135—34no—
103C2×C3×Q16—31no—
104C2×C3×SD16—31no—
105C2×C3×SD16—31no—
106C2×C3×D8—31no—
107C3×#131—34no—
108C3×#131—62no—
109C2×C3×M16—31no—
110C2×C3×M16—61no—
111C22×C3×C8—31no—
112C22×C3×C8—31no—
113C22×C3×C8—61no—
114#950Dic314yescomplemented
115#950C2×D314yes—
116#948—22no—
117#948—34no—
118#948—62no—
119#948C2×D314yescomplemented
120C2×#216Dic311yescharacteristic, complemented
121C2×#215Dic311yescharacteristic, complemented
122C2×#214Dic311yescharacteristic, complemented
123C2×#213Dic311yescharacteristic, complemented
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—61no—
127C2×#208—21no—
128C2×#208—31no—
129C2×#208—31no—
130C2×#208—61no—
131C2×#208—61no—
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8—21no—
134C22×C3⋊C8—61no—
135C22×C3⋊C8C2×D311yescharacteristic
136C22×C3⋊C8C2×D311yescharacteristic
137#901—34no—
138#901—62no—
139C2×ΓL(1,𝔽25)—61no—
140C2×D3×C8—61no—
141#837—34no—
142#837—34no—
143#837—34no—
144#837—64no—
145#825—34no—
146#822—34no—
147#819—34no—
148#815—34no—
149#815—34no—
150C23×C32—21no—
151C23×C32#4111yescharacteristic
152C22×C3×D3—21no—
153C32×Q8—21no—
154C32×Q8C22×C412yes—
155C32×D4—22no—
156C32×D4—22no—
157C32×D4—21no—
158C32×D4C22×C412yes—
159C2×C32×C4—21no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4C22×C411yescharacteristic
163C2×C32×C4C22×C411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4#4111yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—42no—
170C3×#67—22no—
171C3×#67—22no—
172C2×C3×Dic3—21no—
173C3×D12—21no—
174C3×D12C22×C412yes—
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×Dic6—21no—
178C3×Dic6C22×C412yes—
179C3⋊(C3⋊C8)—22no—
180C3×C3⋊C8—22no—
181C3×C3⋊C8C22×C412yes—
182C3×C3⋊C8C22×C412yes—
183C3×C3⋊C8C2×D412yes—
184C3×C3⋊C8C2×D412yes—
185C2×#135—31no—
186C2×#131—31no—
187C2×#131—91no—
188#444—98no—
189C2×#108—91no—
190C2×#104—91no—
191C2×#104—91no—
192C2×#97—91no—
193C3×#41—21no—
194C3×#41—21no—
195C3×#41—21no—
196C3×#41—21no—
197C3×#41—22no—
198C3×#41—22no—
199C3×#41—32no—
200C3×#41—32no—
201C3×#41—41no—
202C3×#41—41no—
203C3×#41—61no—
204C3×#41—61no—
205C3×#41C4×D312yes—
206C3×#41C2×Dic312yes—
207C3×#41C22×D312yes—
208C3×#41C22×D312yes—
209C2×C3×Q8—21no—
210C2×C3×Q8—31no—
211C2×C3×Q8C4×D311yescharacteristic
212C2×C3×Q8C2×Dic311yescharacteristic
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—31no—
217C2×C3×D4—41no—
218C2×C3×D4—61no—
219C2×C3×D4C4×D311yescharacteristic
220C2×C3×D4C2×Dic311yescharacteristic
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—41no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231C22×Dic3—121no—
232#235—21no—
233#235—21no—
234#235C2×Dic312yes—
235#235C22×D312yes—
236C2×D12C2×Dic311yescharacteristic
237C2×C4×D3—21no—
238C2×Dic6C2×Dic311yescharacteristic
239C3×Q16—34no—
240C3×SD16—34no—
241C3×SD16—34no—
242C3×D8—34no—
243C3×M16—32no—
244C3×M16—64no—
245C3×M16—61no—
246C2×C3×C8—31no—
247C2×C3×C8—31no—
248C2×C3×C8—32no—
249C2×C3×C8—31no—
250C2×C3×C8—31no—
251C2×C3×C8—32no—
252C2×C3×C8—32no—
253C2×C3×C8—32no—
254C2×C3×C8—64no—
255C2×C3×C8—61no—
256#216C2×Dic314yescomplemented
257#215C2×Dic314yescomplemented
258#214C2×Dic314yescomplemented
259#213C2×Dic314yescomplemented
260C4×Dic3—32no—
261C4×Dic3—32no—
262C4×Dic3—62no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C4×Dic3—121no—
266#208—21no—
267#208—24no—
268#208—32no—
269#208—32no—
270#208—62no—
271#208—61no—
272#208—61no—
273#208—64no—
274#208—121no—
275#208C22×D312yes—
276C2×C3⋊C8—21no—
277C2×C3⋊C8—24no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—61no—
280C2×C3⋊C8—64no—
281C2×C3⋊C8—121no—
282C2×C3⋊C8C2×Dic311yescharacteristic
283C2×C3⋊C8C2×Dic311yescharacteristic
284C2×C3⋊C8C2×Dic312yes—
285C2×C3⋊C8#6711yescharacteristic
286C2×C3⋊C8#6711yescharacteristic
287C2×C3⋊C8#6712yes—
288C2×C3⋊C8C22×D312yes—
289C2×C3⋊C8C22×D312yes—
290ΓL(1,𝔽25)—64no—
291D3×C8—64no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—42no—
295C22×C32C4×D411yescharacteristic
296C22×C32C4×D411yescharacteristic
297C22×C32C2×#4111yescharacteristic
298C2×C3×D3—22no—
299C2×C3×D3—42no—
300C32×C4—22no—
301C32×C4C4×D411yescharacteristic
302C32×C4C4×D411yescharacteristic
303C32×C4C23×C411yescharacteristic
304C32×C4C22×D411yescharacteristic
305C3⋊Dic3—42no—
306C3×Dic3—22no—
307C2×#41—31no—
308C2×#41D3211yescharacteristic
309#135—34no—
310#135—34no—
311C2×Q16—31no—
312C2×SD16—31no—
313C2×SD16—31no—
314C2×D8—31no—
315#131—34no—
316#131—62no—
317#131—94no—
318#131—182no—
319C2×M16—31no—
320C2×M16—61no—
321C2×M16—91no—
322C2×M16—181no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8—61no—
326C22×C8—181no—
327C2×C42—91no—
328#108—94no—
329#104—94no—
330#104—94no—
331#97—94no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—41no—
336C23×C3—61no—
337C23×C3#23511yescharacteristic
338C23×C3#23711yescharacteristic
339C22×D3—21no—
340C3×Q8—21no—
341C3×Q8—21no—
342C3×Q8—22no—
343C3×Q8—32no—
344C3×Q8—41no—
345C3×Q8—61no—
346C3×Q8C2×C4×D312yes—
347C3×Q8C22×Dic312yes—
348C3×D4—22no—
349C3×D4—22no—
350C3×D4—22no—
351C3×D4—22no—
352C3×D4—21no—
353C3×D4—21no—
354C3×D4—22no—
355C3×D4—32no—
356C3×D4—41no—
357C3×D4—42no—
358C3×D4—42no—
359C3×D4—62no—
360C3×D4—62no—
361C3×D4—61no—
362C3×D4C2×C4×D312yes—
363C3×D4C22×Dic312yes—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4C2×C4×D311yescharacteristic
383C2×C3×C4C2×C4×D311yescharacteristic
384C2×C3×C4#23511yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23711yescharacteristic
388C2×C3×C4C22×Dic311yescharacteristic
389C2×C3×C4C22×Dic311yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394#67—22no—
395#67—22no—
396C2×Dic3—21no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—122no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3—124no—
403D12—21no—
404D12C22×Dic312yes—
405C4×D3—22no—
406C4×D3—22no—
407Dic6—21no—
408Dic6C22×Dic312yes—
409C3×C8—32no—
410C3×C8—32no—
411C3×C8—32no—
412C3×C8—32no—
413C3×C8—62no—
414C3⋊C8—22no—
415C3⋊C8—62no—
416C3⋊C8—62no—
417C3⋊C8—122no—
418C3⋊C8C22×Dic312yes—
419C3⋊C8C22×Dic312yes—
420C3⋊C8C2×#6712yes—
421C3⋊C8C2×#6712yes—
422C2×C32—21no—
423C2×C32—21no—
424C2×C32—42no—
425C2×C32#44412yescomplemented
426C2×C32C2×C4×D411yescharacteristic
427C3×D3—42no—
428#41—21no—
429#41—21no—
430#41—32no—
431#41—32no—
432#41—61no—
433#41—61no—
434#41D3×Dic312yes—
435#41C2×D3212yes—
436C2×Q8—31no—
437C2×Q8D3×Dic311yescharacteristic
438C2×D4—21no—
439C2×D4—31no—
440C2×D4—61no—
441C2×D4D3×Dic311yescharacteristic
442C22×C4—21no—
443C22×C4—61no—
444C22×C4—181no—
445C22×C4C2×D3211yescharacteristic
446Q16—34no—
447SD16—34no—
448SD16—34no—
449D8—34no—
450M16—32no—
451M16—64no—
452M16—61no—
453M16—92no—
454M16—184no—
455M16—181no—
456C2×C8—32no—
457C2×C8—32no—
458C2×C8—31no—
459C2×C8—31no—
460C2×C8—32no—
461C2×C8—32no—
462C2×C8—31no—
463C2×C8—31no—
464C2×C8—64no—
465C2×C8—61no—
466C2×C8—184no—
467C2×C8—181no—
468C42—92no—
469C42—181no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—62no—
482C22×C3—82no—
483C22×C3—122no—
484C22×C3C4×#6711yescharacteristic
485C22×C3C4×#6711yescharacteristic
486C22×C3D4×Dic311yescharacteristic
487C22×C3D4×Dic311yescharacteristic
488C22×C3C2×#23511yescharacteristic
489C22×C3C2×#23711yescharacteristic
490C2×D3—22no—
491C2×D3—42no—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—42no—
499C3×C4—62no—
500C3×C4C4×#6711yescharacteristic
501C3×C4C4×#6711yescharacteristic
502C3×C4D4×Dic311yescharacteristic
503C3×C4D4×Dic311yescharacteristic
504C3×C4C22×C4×D311yescharacteristic
505C3×C4C2×D3×D411yescharacteristic
506C3×C4C23×Dic311yescharacteristic
507C3×C4C22×#6711yescharacteristic
508Dic3—22no—
509Dic3—122no—
510Dic3—122no—
511Dic3—124no—
512C32C2×#44411yescharacteristic, complemented, Sylow
513C23—21no—
514C23—61no—
515C23#380411yescharacteristic
516Q8—21no—
517Q8—32no—
518Q8—61no—
519Q8C2×D3×Dic312yes—
520D4—22no—
521D4—22no—
522D4—21no—
523D4—32no—
524D4—62no—
525D4—62no—
526D4—61no—
527D4C2×D3×Dic312yes—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—61no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—182no—
535C2×C4—362no—
536C2×C4C2×D3×Dic311yescharacteristic
537C2×C4C2×D3×Dic311yescharacteristic
538C2×C4#380411yescharacteristic
539C2×C4D3×#6711yescharacteristic
540C2×C4D3×#6711yescharacteristic
541C2×C4C22×D3211yescharacteristic
542C8—32no—
543C8—32no—
544C8—32no—
545C8—32no—
546C8—62no—
547C8—182no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—22no—
554C2×C3—41no—
555C2×C3—41no—
556C2×C3—42no—
557C2×C3—42no—
558C2×C3—82no—
559C2×C3—122no—
560C2×C3#514512yescomplemented
561C2×C3#519712yescomplemented
562C2×C3C2×C4×#6711yescharacteristic
563C2×C3C2×D4×Dic311yescharacteristic
564D3—42no—
565C22—22no—
566C22—22no—
567C22—42no—
568C22—62no—
569C22—122no—
570C22Dic3×#6711yescharacteristic
571C22Dic3×#6711yescharacteristic
572C22C2×#380411yescharacteristic
573C4—22no—
574C4—62no—
575C4—362no—
576C4Dic3×#6711yescharacteristic
577C4Dic3×#6711yescharacteristic
578C4C22×D3×Dic311yescharacteristic
579C4C2×D3×#6711yescharacteristic
580C3—21no—
581C3C2×#514511yescharacteristic, complemented
582C3C2×#519711yescharacteristic, complemented
583C2—21no—
584C2—21no—
585C2—42no—
586C2—122no—
587C2#1059167412yesdirect product factor
588C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×C3×#950C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#948C2semidirect
3. C2×#63814C2semidirect
4. C2×#63664C2semidirect
5. #10591674C2direct (N × H)
6. C2×#63577C2semidirect
7. C2×#63568C2semidirect
8. C2×#63555C2semidirect
15. C3×#950C4semidirect
18. C3×#948C22semidirect
19. C2×C3×#216C4semidirect
20. C2×C3×#215C4semidirect
21. C2×C3×#214C4semidirect
22. C2×C3×#213C4semidirect
30. #63814C22semidirect
32. #63664C22semidirect
33. #63577C22semidirect
34. #63568C22semidirect
35. #63555C22semidirect
40. C2×#948D3semidirect
76. C3×#216C2×C4semidirect
77. C3×#215C2×C4semidirect
78. C3×#214C2×C4semidirect
79. C3×#213C2×C4semidirect
114. #950Dic3semidirect
119. #948C2×D3semidirect
120. C2×#216Dic3semidirect
121. C2×#215Dic3semidirect
122. C2×#214Dic3semidirect
123. C2×#213Dic3semidirect
256. #216C2×Dic3semidirect
257. #215C2×Dic3semidirect
258. #214C2×Dic3semidirect
259. #213C2×Dic3semidirect
425. C2×C32#444semidirect
512. C32C2×#444semidirect
560. C2×C3#5145semidirect
561. C2×C3#5197semidirect
581. C3C2×#5145semidirect
582. C3C2×#5197semidirect
587. C2#10591674direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9502
C2×C3×#9482
C2×#638142
C2×#636642
#105916742
C2×#635772
C2×#635682
C2×#635552
C2×#51973
C2×#51453