Finite Group Databasebeta

← C2×#10591179 #11866699

Subgroups — C2×#10591179 #11866699

Order 1152.

1297 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10591179C218yesmaximal, direct product factor
6C2×#63574C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5048—31nomaximal
10C2×#5041—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×C3⋊(C3⋊C8)—24no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2214yescomplemented
19C2×C3×#217—21no—
20C3×#930—22no—
21C3×#930C2214yes—
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924—22no—
26C3×#924C2214yescomplemented
27C2×C3×Dic3⋊C4—21no—
28C2×#3715—24no—
29C2×#3715C2214yescomplemented
30#63574C2214yescomplemented
31#63565C2214yescomplemented
32#63562C2214yescomplemented
33C2×C3×C22⋊Q8—31no—
34C2×C3×#121—31no—
35C22×#215—31no—
36C22×#214—31no—
37C2×#930D311yescharacteristic
38C2×#924D311yescharacteristic, complemented
39C23×C3⋊C8—31no—
40C23×C3⋊C8—31no—
41C23×C3⋊C8—61no—
42C2×#835—31no—
43C2×#832—31no—
44#5048—38no—
45#5041—38no—
46C2×#810—31no—
47C2×#809—31no—
48C2×#808—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
58C2×C3×#67—24no—
59C2×C3×#67—44no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)—28no—
73C2×C3⋊(C3⋊C8)D414yescomplemented
74C2×C3⋊(C3⋊C8)C2312yes—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#217—24no—
77C3×(C2×D3)⋊C4—24no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—24no—
83#3715—28no—
84C2×#465—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×C3×D4—61no—
88C23×C3×C4—21no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C2×D311yescharacteristic
91C22×#67—21no—
92C22×D12C2×D311yescharacteristic
93C22×Dic6C2×D311yescharacteristic
94C3×C22⋊Q8—34no—
95C3×C22⋊Q8—62no—
96C3×#121—34no—
97C3×#121—62no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C22⋊C4—61no—
102C2×C3×C22⋊C4—61no—
103C2×#217—21no—
104C2×#215—34no—
105C2×#215—64no—
106C2×#214—34no—
107C2×#214—64no—
108#930—22no—
109#930C2×D314yes—
110C2×(C2×D3)⋊C4—21no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4⋊Dic3C2×D311yescharacteristic
113#924—22no—
114#924C2×D314yescomplemented
115C2×Dic3⋊C4—21no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—34no—
121C22×C3⋊C8—34no—
122C22×C3⋊C8—61no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8—64no—
125C22×C3⋊C8—64no—
126C22×C3⋊C8—64no—
127C22×C3⋊C8—68no—
128#835—34no—
129#832—34no—
130#810—34no—
131#809—34no—
132#808—34no—
133#808—34no—
134C23×C32—22no—
135C23×C32—22no—
136C23×C32SD1614yescomplemented
137C23×C32C2×D412yes—
138C23×C32C2×D411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C2×C32×C4—22no—
144C2×C32×C4—24no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C3×#67—48no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—42no—
157C2×C3×Dic3—42no—
158C2×C3×Dic3—42no—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—42no—
162C3×Dic6—22no—
163C3×Dic6—22no—
164C3×Dic6—42no—
165C3⋊(C3⋊C8)—22no—
166C3⋊(C3⋊C8)C2×D414yescomplemented
167C22×SD16—91no—
168C23×C8—91no—
169C2×C22⋊Q8—31no—
170C2×#121—31no—
171#465—98no—
172C2×#106—91no—
173C2×#103—91no—
174C2×#102—91no—
175C24×C3—21no—
176C24×C3—61no—
177C24×C3#6711yescharacteristic
178C24×C3#6711yescharacteristic
179C23×D3—21no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8—62no—
183C2×C3×Q8—62no—
184C2×C3×D4—32no—
185C2×C3×D4—64no—
186C2×C3×D4—62no—
187C2×C3×D4—62no—
188C2×C3×D4—61no—
189C2×C3×D4—124no—
190C22×C3×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4—61no—
203C22×C3×C4#6711yescharacteristic
204C22×C3×C4#6712yes—
205C22×C3×C4#6711yescharacteristic
206C22×C3×C4#6712yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—24no—
212C2×#67—44no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C2×D12—22no—
217C2×D12—22no—
218C2×D12—21no—
219C2×D12C22×D312yes—
220C2×Dic6—22no—
221C2×Dic6—22no—
222C2×Dic6—21no—
223C2×Dic6C22×D312yes—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—64no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—64no—
230C3×C22⋊C4—64no—
231#217—24no—
232#215—68no—
233#214—68no—
234(C2×D3)⋊C4—24no—
235C4⋊Dic3—21no—
236C4⋊Dic3—21no—
237C4⋊Dic3C22×D312yes—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—24no—
240C2×C3⋊C8—34no—
241C2×C3⋊C8—34no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—64no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—68no—
250C2×C3⋊C8—68no—
251C2×C3⋊C8—616no—
252C2×C3⋊C8—64no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C22×C32—22no—
256C22×C32—22no—
257C22×C32—28no—
258C22×C32#12112yes—
259C22×C32C2×SD1612yes—
260C22×C32C2×SD1614yescomplemented
261C22×C32#13512yes—
262C22×C32C22×D411yescharacteristic
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—84no—
267C32×C4—22no—
268C32×C4#12112yes—
269C32×C4C22×D411yescharacteristic
270C32×C4C2×#4111yescharacteristic
271C3×Dic3—42no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×D4—31no—
276C22×D4—61no—
277C23×C4D3211yescharacteristic
278C2×SD16—94no—
279C2×SD16—184no—
280C22×C8—91no—
281C22×C8—91no—
282C22×C8—94no—
283C22×C8—184no—
284C22⋊Q8—34no—
285C22⋊Q8—62no—
286#121—34no—
287#121—62no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—61no—
291C2×C22⋊C4—61no—
292C2×C22⋊C4—61no—
293#106—94no—
294#103—94no—
295#102—94no—
296C23×C3—24no—
297C23×C3—24no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—24no—
303C23×C3—22no—
304C23×C3—21no—
305C23×C3—62no—
306C23×C3—122no—
307C23×C3—122no—
308C23×C3—122no—
309C23×C3#21414yescomplemented
310C23×C3#21514yescomplemented
311C23×C3C2×#6712yes—
312C23×C3C2×#6712yes—
313C23×C3C2×#6711yescharacteristic
314C23×C3C2×#6711yescharacteristic
315C22×D3—22no—
316C22×D3—42no—
317C22×D3—42no—
318C22×D3—42no—
319C3×Q8—62no—
320C3×Q8—62no—
321C3×Q8—122no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—128no—
325C3×D4—122no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—28no—
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—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—122no—
347C2×C3×C4—122no—
348C2×C3×C4—122no—
349C2×C3×C4D3×D412yes—
350C2×C3×C4D3×D412yes—
351C2×C3×C4#23712yes—
352C2×C3×C4#23712yes—
353C2×C3×C4C2×#6712yes—
354C2×C3×C4C2×#6712yes—
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—48no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—42no—
364C2×Dic3—42no—
365C2×Dic3—42no—
366D12—22no—
367D12—22no—
368D12—42no—
369Dic6—22no—
370Dic6—22no—
371Dic6—42no—
372C3⋊C8—34no—
373C3⋊C8—34no—
374C3⋊C8—64no—
375C3⋊C8—64no—
376C3⋊C8—62no—
377C3⋊C8—62no—
378C2×C32—24no—
379C2×C32#46514yescomplemented
380C2×C32C2×#12111yescharacteristic
381C2×C32C22×SD1611yescharacteristic
382C2×C32C2×#13511yescharacteristic
383C3×D3—82no—
384C24—61no—
385C24#62511yescharacteristic
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—62no—
389C2×Q8—62no—
390C2×D4—32no—
391C2×D4—64no—
392C2×D4—62no—
393C2×D4—61no—
394C2×D4—62no—
395C2×D4—124no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4#62512yes—
402C22×C4#62511yescharacteristic
403C22×C4C2×D3212yes—
404C22×C4C2×D3211yescharacteristic
405SD16—188no—
406C2×C8—92no—
407C2×C8—94no—
408C2×C8—92no—
409C2×C8—188no—
410C2×C8—182no—
411C4⋊C4—32no—
412C4⋊C4—32no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—64no—
416C22⋊C4—64no—
417C22⋊C4—64no—
418C22×C3—24no—
419C22×C3—216no—
420C22×C3—24no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—28no—
424C22×C3—28no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—24no—
431C22×C3—22no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3—244no—
436C22×C3C2×#21412yes—
437C22×C3C2×#21414yescomplemented
438C22×C3#93912yes—
439C22×C3#93912yes—
440C22×C3C2×#21512yes—
441C22×C3C2×#21514yescomplemented
442C22×C3#95012yes—
443C22×C3#95012yes—
444C22×C3C22×#6711yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—42no—
449C2×D3—84no—
450C3×C4—24no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—122no—
457C3×C4—122no—
458C3×C4—122no—
459C3×C4#93912yes—
460C3×C4#93912yes—
461C3×C4C2×D3×D411yescharacteristic
462C3×C4C2×D3×D411yescharacteristic
463C3×C4C2×#23711yescharacteristic
464C3×C4C2×#23711yescharacteristic
465Dic3—42no—
466Dic3—42no—
467Dic3—42no—
468C32C2×#46511yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—62no—
472C23—122no—
473C23—122no—
474C23—122no—
475C23#371514yescomplemented
476C23C2×#62512yes—
477C23C2×#62511yescharacteristic
478Q8—62no—
479Q8—62no—
480Q8—122no—
481D4—62no—
482D4—62no—
483D4—128no—
484D4—122no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—122no—
493C2×C4—122no—
494C2×C4—122no—
495C2×C4#380512yes—
496C2×C4C2×#62512yes—
497C2×C4C2×#62511yescharacteristic
498C2×C4#381112yes—
499C2×C4C22×D3211yescharacteristic
500C8—94no—
501C8—182no—
502C2×C3—28no—
503C2×C3—24no—
504C2×C3—24no—
505C2×C3—21no—
506C2×C3—24no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—242no—
510C2×C3#504114yescomplemented
511C2×C3#504814yescomplemented
512C2×C3C22×#21411yescharacteristic
513C2×C3C2×#93911yescharacteristic
514C2×C3C2×#93911yescharacteristic
515C2×C3C22×#21511yescharacteristic
516C2×C3C2×#95011yescharacteristic
517C2×C3C2×#95011yescharacteristic
518D3—82no—
519C22—22no—
520C22—28no—
521C22—22no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22—244no—
526C22#6382212yes—
527C22C2×#371512yes—
528C22C2×#371514yescomplemented
529C22#6398012yes—
530C22C22×#62511yescharacteristic
531C4—22no—
532C4—122no—
533C4—122no—
534C4—122no—
535C4#6398012yes—
536C4C2×#380511yescharacteristic
537C4C2×#381111yescharacteristic
538C3—21no—
539C3C2×#504111yescharacteristic, complemented
540C3C2×#504811yescharacteristic, complemented
541C2—24no—
542C2—242no—
543C2#1059117914yesdirect product factor
544C2C2×#6382211yescharacteristic
545C2C22×#371511yescharacteristic
546C2C2×#6398011yescharacteristic
subgroupG/H
centerC23C2×#625
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. C23×C3⋊(C3⋊C8)C2semidirect
3. C2×C3×#924C2semidirect
4. C22×#3715C2semidirect
5. #10591179C2direct (N × H)
6. C2×#63574C2semidirect
7. C2×#63565C2semidirect
8. C2×#63562C2semidirect
18. C22×C3⋊(C3⋊C8)C22semidirect
26. C3×#924C22semidirect
29. C2×#3715C22semidirect
30. #63574C22semidirect
31. #63565C22semidirect
32. #63562C22semidirect
38. C2×#924D3semidirect
73. C2×C3⋊(C3⋊C8)D4semidirect
114. #924C2×D3semidirect
136. C23×C32SD16semidirect
166. C3⋊(C3⋊C8)C2×D4semidirect
260. C22×C32C2×SD16semidirect
309. C23×C3#214semidirect
310. C23×C3#215semidirect
379. C2×C32#465semidirect
437. C22×C3C2×#214semidirect
441. C22×C3C2×#215semidirect
468. C32C2×#465semidirect
475. C23#3715semidirect
510. C2×C3#5041semidirect
511. C2×C3#5048semidirect
528. C22C2×#3715semidirect
539. C3C2×#5041semidirect
540. C3C2×#5048semidirect
543. C2#10591179direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊(C3⋊C8)2
C2×C3×#9302
C2×C3×#9242
C22×#37152
#105911792
C2×#635742
C2×#635652
C2×#635622
C2×#50483
C2×#50413