Finite Group Databasebeta

← C2×#10590970 #11863789

Subgroups — C2×#10590970 #11863789

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C22×#3744C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590970C218yesmaximal, direct product factor
9C2×#4808—31nomaximal
10C2×#4733—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×#624—21no—
17C2×#3799—24no—
18C2×#3799—22no—
19C2×#3799—24no—
20C2×#3799C2214yes—
21C22×C32×C8C2211yescharacteristic
22C2×#3744—24no—
23C2×#3744C2214yescomplemented
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×Dic3⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63857—22no—
29#63857C2214yescomplemented
30C2×#3719—24no—
31C2×#3719C2214yescomplemented
32C3×(C2×D3)⋊C8C2214yescomplemented
33C3×#816C2214yescomplemented
34#63564C2214yescomplemented
35C22×#239—31no—
36C22×#235—31no—
37C22×#216—31no—
38C2×#924—31no—
39C22×Dic12—31no—
40C22×#204—31no—
41C22×#204—31no—
42C22×#204—61no—
43C2×#897—31no—
44C2×C3×#103—31no—
45C2×C3×C22⋊C8—31no—
46C2×#821—31no—
47C2×(C2×D3)⋊C8D311yescharacteristic, complemented
48C2×#816D311yescharacteristic, complemented
49C2×#809—31no—
50#4808—38no—
51#4733—38no—
52C23×C3⋊D3—21no—
53C23×C3×D3D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)D414yes—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×#634—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634C2312yes—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yes—
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×#624—28no—
78C2×#624—24no—
79#3799—216no—
80#3799—28no—
81#3799—28no—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84#3744—28no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89Dic3⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91#3719—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C23×C3×C4—31no—
95C22×#67—61no—
96C2×#239—34no—
97C2×#239—64no—
98C2×#239—64no—
99C2×#239—62no—
100C2×#235—34no—
101C2×#235—64no—
102C2×#235—62no—
103C2×#235—64no—
104C22×D12—31no—
105C22×D12—31no—
106C22×D12—61no—
107C22×D12—61no—
108C22×C4×D3—61no—
109C22×C4×D3—61no—
110C22×C4×D3C2×D311yescharacteristic
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C22×Dic6C2×D311yescharacteristic
115C22×C3×C8—21no—
116C22×C3×C8—31no—
117C22×C3×C8C2×D311yescharacteristic
118C22×C3×C8C2×D311yescharacteristic
119C2×C3×C4⋊C4—31no—
120C2×#217—61no—
121C2×#216—34no—
122C2×#216—64no—
123C2×(C2×D3)⋊C4—61no—
124C2×C4⋊Dic3—61no—
125C2×C4⋊Dic3C2×D311yescharacteristic
126#924—34no—
127#924—62no—
128C2×Dic3⋊C4—61no—
129C22×C3⋊C8C2×D311yescharacteristic
130C2×Dic12—34no—
131C2×Dic12—64no—
132C2×#204—34no—
133C2×#204—34no—
134C2×#204—64no—
135C2×#204—64no—
136C2×#204—64no—
137C2×#204—68no—
138#897—34no—
139#897—62no—
140C3×#103—34no—
141C3×C22⋊C8—34no—
142#821—34no—
143(C2×D3)⋊C8C2×D314yescomplemented
144#816C2×D314yescomplemented
145#809—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3—24no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3C2×D412yes—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—42no—
161C4⋊(C3⋊D3)—24no—
162C4⋊(C3⋊D3)—22no—
163C4⋊(C3⋊D3)C2×D414yes—
164#634—22no—
165#634—22no—
166#634—42no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—24no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—42no—
172C2×C3×Dic3C2×D412yes—
173C3×C4×D3—24no—
174C3×C4×D3—22no—
175C3×C4×D3—22no—
176C3×Dic6—24no—
177C3×Dic6—22no—
178C3×Dic6C2×D414yes—
179#626—216no—
180#624—216no—
181C32×C8—22no—
182C3×C3⋊C8—22no—
183C22×#41—91no—
184C22×Q16—91no—
185C22×SD16—91no—
186C2×C22⋊Q8—91no—
187#452—98no—
188C2×#103—31no—
189C2×#102—91no—
190C2×C22⋊C8—31no—
191C24×C3—31no—
192C23×D3—61no—
193C23×D3—61no—
194C23×D3—121no—
195C23×D3D1211yescharacteristic
196C2×C3×Q8—34no—
197C2×C3×Q8—32no—
198C2×C3×Q8—61no—
199C2×C3×Q8—62no—
200C22×C3×C4—21no—
201C22×C3×C4—31no—
202C22×C3×C4—32no—
203C22×C3×C4—32no—
204C22×C3×C4—61no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—64no—
211C2×#67—68no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—121no—
217C22×Dic3D1211yescharacteristic
218#239—68no—
219#239—68no—
220#239—616no—
221#235—68no—
222#235—616no—
223#235—68no—
224C2×D12—34no—
225C2×D12—34no—
226C2×D12—32no—
227C2×D12—32no—
228C2×D12—64no—
229C2×D12—62no—
230C2×D12—68no—
231C2×D12—64no—
232C2×D12—62no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—62no—
236C2×D12—122no—
237C2×D12—121no—
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3—64no—
241C2×C4×D3—68no—
242C2×C4×D3—68no—
243C2×C4×D3—64no—
244C2×C4×D3D1212yes—
245C2×C4×D3C22×D312yes—
246C2×Dic6—21no—
247C2×Dic6—22no—
248C2×Dic6—32no—
249C2×Dic6—32no—
250C2×Dic6—62no—
251C2×Dic6—64no—
252C2×Dic6—62no—
253C2×Dic6—62no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—61no—
257C2×Dic6—61no—
258C2×Dic6—121no—
259C2×Dic6—122no—
260C2×Dic6D1214yes—
261C2×Dic6C22×D312yes—
262C2×C3×C8—24no—
263C2×C3×C8—22no—
264C2×C3×C8—22no—
265C2×C3×C8—22no—
266C2×C3×C8—32no—
267C2×C3×C8—62no—
268C2×C3×C8C22×D312yes—
269C2×C3×C8C22×D312yes—
270C3×C4⋊C4—32no—
271C3×C4⋊C4—61no—
272#217—64no—
273#216—68no—
274(C2×D3)⋊C4—64no—
275C4⋊Dic3—21no—
276C4⋊Dic3—64no—
277C4⋊Dic3C22×D312yes—
278Dic3⋊C4—64no—
279C2×C3⋊C8—22no—
280C2×C3⋊C8C22×D312yes—
281Dic12—68no—
282#204—68no—
283#204—68no—
284#204—616no—
285C22×C32#12012yes—
286C22×C32#13512yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—24no—
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—48no—
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C2×C3×D3—44no—
297C32×C4#12012yes—
298C32×C4C22×D411yescharacteristic
299C32×C4C22×D411yescharacteristic
300C3⋊Dic3—42no—
301C3×Dic3—22no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C2×#41—94no—
305C2×#41—182no—
306C2×#41—184no—
307C2×#41—184no—
308C22×Q8—31no—
309C22×Q8—91no—
310C22×D4—91no—
311C22×D4—181no—
312C23×C4—31no—
313C23×C4—181no—
314C2×Q16—94no—
315C2×Q16—184no—
316C2×SD16—94no—
317C2×SD16—184no—
318C22×C8—31no—
319C22×C8D3211yescharacteristic
320C22⋊Q8—94no—
321C22⋊Q8—182no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—181no—
324C2×C22⋊C4—181no—
325#103—34no—
326#102—94no—
327C22⋊C8—34no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3C2×D1211yescharacteristic
334C23×C3D3×D411yescharacteristic
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—64no—
339C22×D3—64no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—122no—
343C22×D3—124no—
344C22×D3—122no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—242no—
349C22×D3—242no—
350C22×D3C2×D1212yes—
351C3×Q8—34no—
352C3×Q8—64no—
353C3×Q8—62no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—32no—
359C2×C3×C4—62no—
360C2×C3×C4—64no—
361C2×C3×C4—62no—
362C2×C3×C4—64no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—122no—
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4C2×D1212yes—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D412yes—
371C2×C3×C4D3×D412yes—
372C2×C3×C4D3×D412yes—
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375#67—616no—
376C2×Dic3—24no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—42no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—124no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3C2×D1212yes—
388D12—34no—
389D12—34no—
390D12—64no—
391D12—616no—
392D12—64no—
393D12—64no—
394D12—62no—
395D12—62no—
396D12—122no—
397D12—124no—
398C4×D3—24no—
399C4×D3—22no—
400C4×D3—22no—
401C4×D3—616no—
402C4×D3—616no—
403Dic6—24no—
404Dic6—22no—
405Dic6—64no—
406Dic6—62no—
407Dic6—62no—
408Dic6—62no—
409Dic6—62no—
410Dic6—122no—
411Dic6—124no—
412Dic6—122no—
413Dic6—122no—
414Dic6C2×D1214yes—
415C3×C8—24no—
416C3×C8—22no—
417C3×C8—22no—
418C3×C8—62no—
419C3⋊C8—22no—
420C2×C32#45214yescomplemented
421C2×C32C2×#12011yescharacteristic
422C2×C32C2×#13511yescharacteristic
423C2×C32C2×#13711yescharacteristic
424C3⋊D3—44no—
425C3×D3—42no—
426C24—31no—
427C24—181no—
428#41—188no—
429#41—188no—
430#41—1816no—
431C2×Q8—32no—
432C2×Q8—34no—
433C2×Q8—61no—
434C2×Q8—62no—
435C2×Q8—92no—
436C2×Q8—181no—
437C2×Q8—182no—
438C2×Q8—182no—
439C2×D4—92no—
440C2×D4—94no—
441C2×D4—184no—
442C2×D4—188no—
443C2×D4—182no—
444C2×D4—181no—
445C22×C4—31no—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—61no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—61no—
452C22×C4—184no—
453C22×C4—188no—
454C22×C4—181no—
455C22×C4C2×D3211yescharacteristic
456Q16—188no—
457SD16—188no—
458C2×C8—22no—
459C2×C8—32no—
460C2×C8—62no—
461C2×C8C2×D3212yes—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—184no—
465C22⋊C4—184no—
466C22×C3—21no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—124no—
474C22×C3#88212yes—
475C22×C3#88212yes—
476C22×C3#90412yes—
477C22×C3#90912yes—
478C22×C3#91612yes—
479C22×C3#91812yes—
480C22×C3C22×D1211yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—44no—
486C2×D3—64no—
487C2×D3—64no—
488C2×D3—124no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—128no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—128no—
495C2×D3—242no—
496C2×D3—242no—
497C2×D3—248no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—22no—
501C3×C4—62no—
502C3×C4—64no—
503C3×C4—122no—
504C3×C4#88212yes—
505C3×C4#88212yes—
506C3×C4C22×D1211yescharacteristic
507C3×C4C2×D3×D411yescharacteristic
508C3×C4C2×D3×D411yescharacteristic
509C3×C4C2×D3×D411yescharacteristic
510Dic3—24no—
511Dic3—22no—
512Dic3—42no—
513Dic3—124no—
514Dic3—122no—
515Dic3—122no—
516C32C2×#45211yescharacteristic, complemented, Sylow
517C23—32no—
518C23—62no—
519C23—62no—
520C23—62no—
521C23—182no—
522C23—184no—
523C23—362no—
524C23—362no—
525C23D3×D1211yescharacteristic
526Q8—34no—
527Q8—62no—
528Q8—64no—
529Q8—182no—
530Q8—182no—
531Q8—362no—
532D4—94no—
533D4—1816no—
534D4—182no—
535D4—184no—
536C2×C4—32no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—64no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—64no—
543C2×C4—62no—
544C2×C4—122no—
545C2×C4—1816no—
546C2×C4—182no—
547C2×C4—362no—
548C2×C4D3×D1212yes—
549C2×C4D3×D1211yescharacteristic
550C2×C4#381112yes—
551C2×C4C22×D3211yescharacteristic
552C8—22no—
553C8—62no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—24no—
557C2×C3—21no—
558C2×C3—122no—
559C2×C3#473314yescomplemented
560C2×C3#480814yescomplemented
561C2×C3C2×#88211yescharacteristic
562C2×C3C2×#88211yescharacteristic
563C2×C3C2×#90411yescharacteristic
564C2×C3C2×#90911yescharacteristic
565C2×C3C2×#91611yescharacteristic
566C2×C3C2×#91811yescharacteristic
567D3—42no—
568D3—124no—
569D3—124no—
570D3—244no—
571C22—62no—
572C22—62no—
573C22—62no—
574C22—124no—
575C22—184no—
576C22—362no—
577C22—362no—
578C22—368no—
579C22#6380112yes—
580C22#6380612yes—
581C22#6392312yes—
582C22C2×D3×D1211yescharacteristic
583C4—62no—
584C4—64no—
585C4—122no—
586C4—362no—
587C4#6392312yes—
588C4C2×D3×D1211yescharacteristic
589C4C2×#381111yescharacteristic
590C3—21no—
591C3C2×#473311yescharacteristic, complemented
592C3C2×#480811yescharacteristic, complemented
593C2—122no—
594C2—364no—
595C2#1059097014yesdirect product factor
596C2C2×#6380111yescharacteristic
597C2C2×#6380611yescharacteristic
598C2C2×#6392311yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3799C2
hypercenterC22×C8D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×#3744C2semidirect
3. C2×#63857C2semidirect
4. C22×#3719C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63564C2semidirect
8. #10590970C2direct (N × H)
23. C2×#3744C22semidirect
29. #63857C22semidirect
31. C2×#3719C22semidirect
32. C3×(C2×D3)⋊C8C22semidirect
33. C3×#816C22semidirect
34. #63564C22semidirect
47. C2×(C2×D3)⋊C8D3semidirect
48. C2×#816D3semidirect
143. (C2×D3)⋊C8C2×D3semidirect
144. #816C2×D3semidirect
420. C2×C32#452semidirect
516. C32C2×#452semidirect
559. C2×C3#4733semidirect
560. C2×C3#4808semidirect
591. C3C2×#4733semidirect
592. C3C2×#4808semidirect
595. C2#10590970direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×#37442
C2×#638572
C22×#37192
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C2×#635642
#105909702
C2×#48083
C2×#47333