Finite Group Databasebeta

← C2×#10591175 #11866700

Subgroups — C2×#10591175 #11866700

Order 1152.

1289 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5#10591175C218yesmaximal, direct product factor
6C2×#63573C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5114—31nomaximal
10C2×#5041—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×D12C2211yescharacteristic
15C2×#3757—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17#64133—22no—
18#64133C2214yescomplemented
19C2×#3750—21no—
20C3×#930—22no—
21C3×#930C2214yes—
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8—24no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yescomplemented
30#63573C2214yescomplemented
31#63567C2214yescomplemented
32#63563C2214yescomplemented
33C23×C3×C8—31no—
34C2×C3×#121—31no—
35C22×#214—31no—
36C2×#930D311yescharacteristic
37C2×#924—31no—
38C2×#924—31no—
39C2×#924—61no—
40C23×C3⋊C8D311yescharacteristic, complemented
41C22×#204—31no—
42C2×#832—31no—
43#5114—38no—
44C2×#821—31no—
45C2×#817—31no—
46C2×#816—31no—
47#5041—38no—
48C2×#810—31no—
49C2×#808—31no—
50C24×C32D411yescharacteristic
51C23×C3×D3—21no—
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D412yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3—21no—
60C2×#634—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634C2312yes—
64C2×C3×#67—24no—
65C2×C3×#67—44no—
66C22×C3×Dic3—21no—
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71#3757—24no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74#3750—24no—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8—28no—
80C2×C3×C3⋊C8D414yescomplemented
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2312yes—
83#3716—28no—
84C2×#465—91noSylow
85C22×C3×D4—31no—
86C22×C3×D4—61no—
87C23×C3×C4—21no—
88C23×C3×C4C2×D311yescharacteristic
89C23×C3×C4C2×D311yescharacteristic
90C22×#67—21no—
91C22×D12C2×D311yescharacteristic
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C22×C3×C8—34no—
98C22×C3×C8—64no—
99C3×#121—34no—
100C3×#121—62no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—61no—
103C2×#217—62no—
104C2×#217—61no—
105C2×#217—61no—
106C2×#214—34no—
107C2×#214—64no—
108#930—22no—
109#930C2×D314yes—
110C2×(C2×D3)⋊C4—21no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—61no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115#924—34no—
116#924—34no—
117#924—64no—
118#924—64no—
119#924—62no—
120#924—62no—
121C2×Dic3⋊C4—62no—
122C2×Dic3⋊C4—61no—
123C2×Dic3⋊C4—61no—
124C22×C3⋊C8—24no—
125C22×C3⋊C8C2×D311yescharacteristic
126C22×C3⋊C8C2×D311yescharacteristic
127C22×C3⋊C8C2×D314yescomplemented
128C2×#204—34no—
129C2×#204—64no—
130#832—34no—
131#821—34no—
132#817—34no—
133#816—34no—
134#810—34no—
135#808—34no—
136C23×C32—22no—
137C23×C32—22no—
138C23×C32SD1614yescomplemented
139C23×C32C2×D412yes—
140C23×C32C2×D411yescharacteristic
141C22×C3×D3—22no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C2×C32×C4—22no—
146C2×C32×C4—24no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—42no—
157C2×C3⋊Dic3—42no—
158#634—22no—
159#634—22no—
160#634—42no—
161C3×#67—48no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—42no—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—42no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8C2×D414yescomplemented
169C22×SD16—91no—
170C23×C8—31no—
171C2×C22⋊Q8—91no—
172C2×#121—31no—
173#465—98no—
174C2×#106—91no—
175C2×#103—91no—
176C2×#102—91no—
177C24×C3—21no—
178C24×C3—61no—
179C24×C3D1211yescharacteristic
180C24×C3#6711yescharacteristic
181C23×D3—21no—
182C2×C3×D4—32no—
183C2×C3×D4—64no—
184C2×C3×D4—61no—
185C2×C3×D4—62no—
186C2×C3×D4—62no—
187C2×C3×D4—124no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—42no—
197C22×C3×C4—42no—
198C22×C3×C4—61no—
199C22×C3×C4D1211yescharacteristic
200C22×C3×C4D1212yes—
201C22×C3×C4#6711yescharacteristic
202C22×C3×C4#6712yes—
203C22×C3×C4C22×D312yes—
204C22×C3×C4C22×D312yes—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—24no—
208C2×#67—44no—
209C22×Dic3—21no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C2×D12—22no—
217C2×D12—22no—
218C2×D12—21no—
219C2×D12C22×D312yes—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C2×Dic6—122no—
231C2×Dic6—122no—
232C2×C3×C8—34no—
233C2×C3×C8—32no—
234C2×C3×C8—32no—
235C2×C3×C8—68no—
236C2×C3×C8—62no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—61no—
239C3×C22⋊C4—64no—
240#217—68no—
241#217—64no—
242#217—64no—
243#214—68no—
244(C2×D3)⋊C4—24no—
245C4⋊Dic3—21no—
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3C22×D312yes—
253Dic3⋊C4—68no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—28no—
258C2×C3⋊C8#6714yescomplemented
259C2×C3⋊C8C22×D312yes—
260C2×C3⋊C8C22×D312yes—
261#204—68no—
262C22×C32—22no—
263C22×C32—22no—
264C22×C32—28no—
265C22×C32#12112yes—
266C22×C32C2×SD1612yes—
267C22×C32C2×SD1614yescomplemented
268C22×C32#13512yes—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—84no—
274C32×C4—22no—
275C32×C4#12112yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C2×#4111yescharacteristic
278C3⋊Dic3—42no—
279C3⋊Dic3—42no—
280C3×Dic3—42no—
281C22×Q8—91no—
282C22×D4—31no—
283C22×D4—61no—
284C23×C4D3211yescharacteristic
285C2×SD16—94no—
286C2×SD16—184no—
287C22×C8—31no—
288C22×C8—31no—
289C22×C8—34no—
290C22×C8—64no—
291C22⋊Q8—94no—
292C22⋊Q8—182no—
293#121—34no—
294#121—62no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—181no—
298C2×C22⋊C4—61no—
299C2×C22⋊C4—181no—
300#106—94no—
301#103—94no—
302#102—94no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—24no—
308C23×C3—22no—
309C23×C3—21no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—62no—
313C23×C3—122no—
314C23×C3—122no—
315C23×C3—122no—
316C23×C3#20414yescomplemented
317C23×C3#21414yescomplemented
318C23×C3C2×D1212yes—
319C23×C3C2×D1211yescharacteristic
320C23×C3C2×#6712yes—
321C23×C3C2×#6711yescharacteristic
322C22×D3—22no—
323C22×D3—42no—
324C22×D3—42no—
325C22×D3—42no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—128no—
329C3×D4—122no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—44no—
346C2×C3×C4—42no—
347C2×C3×C4—62no—
348C2×C3×C4—122no—
349C2×C3×C4C2×D1212yes—
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4#23512yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4#23712yes—
354C2×C3×C4C2×#6712yes—
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—48no—
360C2×Dic3—22no—
361C2×Dic3—42no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—124no—
369C2×Dic3—124no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374D12—22no—
375D12—22no—
376D12—42no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—122no—
382Dic6—122no—
383Dic6—124no—
384Dic6—122no—
385Dic6—122no—
386C3×C8—34no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8C2×#6714yescomplemented
390C2×C32—24no—
391C2×C32#46514yescomplemented
392C2×C32C2×#12111yescharacteristic
393C2×C32C22×SD1611yescharacteristic
394C2×C32C2×#13511yescharacteristic
395C3×D3—82no—
396C24—61no—
397C24#62611yescharacteristic
398C2×Q8—92no—
399C2×Q8—181no—
400C2×Q8—182no—
401C2×Q8—182no—
402C2×D4—32no—
403C2×D4—64no—
404C2×D4—62no—
405C2×D4—61no—
406C2×D4—62no—
407C2×D4—124no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—61no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4#62612yes—
414C22×C4#62611yescharacteristic
415C22×C4C2×D3212yes—
416C22×C4C2×D3211yescharacteristic
417SD16—188no—
418C2×C8—32no—
419C2×C8—34no—
420C2×C8—32no—
421C2×C8—68no—
422C2×C8—62no—
423C4⋊C4—32no—
424C4⋊C4—61no—
425C4⋊C4—92no—
426C4⋊C4—181no—
427C4⋊C4—184no—
428C22⋊C4—64no—
429C22⋊C4—184no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—28no—
434C22×C3—22no—
435C22×C3—28no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—24no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—42no—
442C22×C3—48no—
443C22×C3—42no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—244no—
448C22×C3C2×#20412yes—
449C22×C3C2×#20414yescomplemented
450C22×C3#90412yes—
451C22×C3#93012yes—
452C22×C3C2×#21412yes—
453C22×C3C2×#21414yescomplemented
454C22×C3#93912yes—
455C22×C3#95012yes—
456C22×C3C22×D1211yescharacteristic
457C22×C3C22×#6711yescharacteristic
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C2×D3—84no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—42no—
468C3×C4—122no—
469C3×C4#93012yes—
470C3×C4#93912yes—
471C3×C4C2×#23511yescharacteristic
472C3×C4C2×D3×D411yescharacteristic
473C3×C4C2×#23711yescharacteristic
474C3×C4C22×#6711yescharacteristic
475Dic3—42no—
476Dic3—124no—
477Dic3—124no—
478Dic3—122no—
479Dic3—122no—
480Dic3—122no—
481Dic3—122no—
482C32C2×#46511yescharacteristic, complemented, Sylow
483C23—22no—
484C23—22no—
485C23—62no—
486C23—122no—
487C23—122no—
488C23—122no—
489C23#371614yescomplemented
490C23C2×#62612yes—
491C23C2×#62611yescharacteristic
492Q8—182no—
493Q8—182no—
494Q8—362no—
495D4—62no—
496D4—62no—
497D4—128no—
498D4—122no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—62no—
504C2×C4—122no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—362no—
508C2×C4—362no—
509C2×C4#380412yes—
510C2×C4C2×#62612yes—
511C2×C4C2×#62611yescharacteristic
512C2×C4D3×#6712yes—
513C2×C4C22×D3211yescharacteristic
514C8—34no—
515C8—62no—
516C2×C3—24no—
517C2×C3—24no—
518C2×C3—21no—
519C2×C3—24no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—44no—
523C2×C3—242no—
524C2×C3#504114yescomplemented
525C2×C3#511414yescomplemented
526C2×C3C22×#20411yescharacteristic
527C2×C3C2×#90411yescharacteristic
528C2×C3C2×#93011yescharacteristic
529C2×C3C22×#21411yescharacteristic
530C2×C3C2×#93911yescharacteristic
531C2×C3C2×#95011yescharacteristic
532D3—82no—
533C22—22no—
534C22—28no—
535C22—22no—
536C22—122no—
537C22—122no—
538C22—122no—
539C22—244no—
540C22C2×#371612yes—
541C22C2×#371614yescomplemented
542C22#6382912yes—
543C22#6397812yes—
544C22C22×#62611yescharacteristic
545C4—22no—
546C4—122no—
547C4—362no—
548C4—362no—
549C4#6397812yes—
550C4C2×#380411yescharacteristic
551C4C2×D3×#6711yescharacteristic
552C3—21no—
553C3C2×#504111yescharacteristic, complemented
554C3C2×#511411yescharacteristic, complemented
555C2—24no—
556C2—242no—
557C2#1059117514yesdirect product factor
558C2C22×#371611yescharacteristic
559C2C2×#6382911yescharacteristic
560C2C2×#6397811yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32C2×#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64133C2semidirect
3. C23×C3×C3⋊C8C2semidirect
4. C22×#3716C2semidirect
5. #10591175C2direct (N × H)
6. C2×#63573C2semidirect
7. C2×#63567C2semidirect
8. C2×#63563C2semidirect
18. #64133C22semidirect
27. C22×C3×C3⋊C8C22semidirect
29. C2×#3716C22semidirect
30. #63573C22semidirect
31. #63567C22semidirect
32. #63563C22semidirect
40. C23×C3⋊C8D3semidirect
80. C2×C3×C3⋊C8D4semidirect
127. C22×C3⋊C8C2×D3semidirect
138. C23×C32SD16semidirect
168. C3×C3⋊C8C2×D4semidirect
258. C2×C3⋊C8#67semidirect
267. C22×C32C2×SD16semidirect
316. C23×C3#204semidirect
317. C23×C3#214semidirect
389. C3⋊C8C2×#67semidirect
391. C2×C32#465semidirect
449. C22×C3C2×#204semidirect
453. C22×C3C2×#214semidirect
482. C32C2×#465semidirect
489. C23#3716semidirect
524. C2×C3#5041semidirect
525. C2×C3#5114semidirect
541. C22C2×#3716semidirect
553. C3C2×#5041semidirect
554. C3C2×#5114semidirect
557. C2#10591175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9302
C23×C3×C3⋊C82
C22×#37162
#105911752
C2×#635732
C2×#635672
C2×#635632
C2×#51143
C2×#50413