Finite Group Databasebeta

← C2×#10591399 #11800966

Subgroups — C2×#10591399 #11800966

Order 1152.

7265 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
1C24×D32C211yesmaximal, characteristic
2C22×#3752C211yesmaximal, characteristic, complemented
3C22×C3×(C2×D3)⋊C4C212yesmaximal, complemented
4C22×#3722C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊Dic3C212yesmaximal, complemented
6#10591399C218yesmaximal, direct product factor
7C2×#4955—32nomaximal
8C24×C3⋊D3C2211yescharacteristic
9C24×C3×D3C2212yes—
10C23×D32—24no—
11C23×D32—24no—
12C23×D32—28no—
13C23×D32—28no—
14C23×D32C418yescomplemented
15C23×D32C2214yes—
16C23×C32×C4C2211yescharacteristic, complemented
17C23×C3⋊Dic3C2211yescharacteristic, complemented
18C23×C3×Dic3C2212yescomplemented
19C2×#3752—24no—
20C2×#3752C2214yescomplemented
21C2×C3×(C2×D3)⋊C4—28no—
22C2×C3×(C2×D3)⋊C4C2218yescomplemented
23C2×#3722—24no—
24C2×#3722C2214yescomplemented
25C2×(C2×D3)⋊Dic3—28no—
26C2×(C2×D3)⋊Dic3C2218yescomplemented
27C25×D3—32no—
28C22×C3×C22⋊C4—32no—
29C22×#217—32no—
30C22×(C2×D3)⋊C4—32no—
31C22×(C2×D3)⋊C4—32no—
32C22×(C2×D3)⋊C4—32no—
33C22×(C2×D3)⋊C4—61no—
34C22×(C2×D3)⋊C4D312yescomplemented
35#4955—316no—
36C24×C32C2311yescharacteristic
37C23×C3⋊D3—24no—
38C23×C3⋊D3—24no—
39C23×C3⋊D3C2×C414yes—
40C23×C3⋊D3D414yes—
41C23×C3⋊D3D414yes—
42C23×C3⋊D3C2312yes—
43C23×C3×D3—24no—
44C23×C3×D3—24no—
45C23×C3×D3—24no—
46C23×C3×D3—24no—
47C23×C3×D3C2×C418yes—
48C23×C3×D3D418yes—
49C23×C3×D3D418yes—
50C23×C3×D3C2314yes—
51C22×D32—232no—
52C22×D32—264no—
53C22×D32—232no—
54C22×D32—232no—
55C22×D32—28no—
56C22×D32—28no—
57C22×D32—264no—
58C22×D32—216no—
59C22×D32—216no—
60C22×D32C2×C4116yescomplemented
61C22×C32×C4—22no—
62C22×C32×C4—24no—
63C22×C32×C4C2312yescomplemented
64C22×C3⋊Dic3—22no—
65C22×C3⋊Dic3—24no—
66C22×C3⋊Dic3C2312yescomplemented
67C22×C3×Dic3—24no—
68C22×C3×Dic3—24no—
69C22×C3×Dic3—24no—
70C22×C3×Dic3C2314yescomplemented
71#3752—28no—
72C3×(C2×D3)⋊C4—216no—
73#3722—28no—
74(C2×D3)⋊Dic3—216no—
75C2×#379—91noSylow
76C25×C3—32no—
77C24×D3—32no—
78C24×D3—316no—
79C24×D3—38no—
80C24×D3—61no—
81C24×D3—68no—
82C24×D3—68no—
83C24×D3—68no—
84C24×D3—68no—
85C24×D3—68no—
86C24×D3—68no—
87C24×D3C2×D312yes—
88C23×C3×C4—21no—
89C23×C3×C4—32no—
90C23×C3×C4C2×D312yescomplemented
91C23×Dic3—32no—
92C23×Dic3—61no—
93C23×Dic3C2×D312yescomplemented
94C2×C3×C22⋊C4—38no—
95C2×C3×C22⋊C4—68no—
96C2×#217—38no—
97C2×#217—68no—
98C2×(C2×D3)⋊C4—28no—
99C2×(C2×D3)⋊C4—38no—
100C2×(C2×D3)⋊C4—38no—
101C2×(C2×D3)⋊C4—38no—
102C2×(C2×D3)⋊C4—64no—
103C2×(C2×D3)⋊C4—68no—
104C2×(C2×D3)⋊C4—68no—
105C2×(C2×D3)⋊C4—68no—
106C2×(C2×D3)⋊C4—68no—
107C2×(C2×D3)⋊C4C2×D318yescomplemented
108C23×C32C22×C412yes—
109C23×C32C2×D414yes—
110C23×C32C2×D412yes—
111C23×C32C2×D412yes—
112C23×C32C2×D414yes—
113C23×C32C2411yescharacteristic
114C22×C3⋊D3—216no—
115C22×C3⋊D3—28no—
116C22×C3⋊D3—216no—
117C22×C3⋊D3—28no—
118C22×C3⋊D3—24no—
119C22×C3⋊D3—24no—
120C22×C3⋊D3C22⋊C4116yescomplemented
121C22×C3⋊D3C22×C414yes—
122C22×C3⋊D3C2×D414yes—
123C22×C3⋊D3C2×D414yes—
124C22×C3×D3—216no—
125C22×C3×D3—216no—
126C22×C3×D3—216no—
127C22×C3×D3—216no—
128C22×C3×D3—216no—
129C22×C3×D3—216no—
130C22×C3×D3—24no—
131C22×C3×D3—24no—
132C22×C3×D3—24no—
133C22×C3×D3—24no—
134C22×C3×D3C22⋊C4132yescomplemented
135C22×C3×D3C22×C418yes—
136C22×C3×D3C2×D418yes—
137C22×C3×D3C2×D418yes—
138C2×D32—232no—
139C2×D32—264no—
140C2×D32—232no—
141C2×D32—2256no—
142C2×D32—232no—
143C2×D32—264no—
144C2×C32×C4—22no—
145C2×C32×C4—24no—
146C2×C32×C4—44no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—24no—
149C2×C3⋊Dic3—44no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—24no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3—48no—
154C26—91no—
155C22×C22⋊C4—32no—
156C22×C22⋊C4—91no—
157C22×C22⋊C4—92no—
158C22×C22⋊C4—91no—
159#379—98no—
160C24×C3—21no—
161C24×C3—38no—
162C24×C3—38no—
163C24×C3—38no—
164C24×C3—34no—
165C24×C3—64no—
166C24×C3—64no—
167C24×C3—64no—
168C24×C3—64no—
169C24×C3C22×D312yes—
170C23×D3—24no—
171C23×D3—24no—
172C23×D3—24no—
173C23×D3—24no—
174C23×D3—38no—
175C23×D3—38no—
176C23×D3—38no—
177C23×D3—34no—
178C23×D3—332no—
179C23×D3—64no—
180C23×D3—64no—
181C23×D3—64no—
182C23×D3—62no—
183C23×D3—664no—
184C23×D3—616no—
185C23×D3—616no—
186C23×D3—664no—
187C23×D3—616no—
188C23×D3—616no—
189C23×D3—664no—
190C23×D3—664no—
191C23×D3—664no—
192C23×D3—664no—
193C23×D3—64no—
194C23×D3—64no—
195C23×D3—64no—
196C23×D3—64no—
197C23×D3—664no—
198C23×D3—616no—
199C23×D3—616no—
200C23×D3—124no—
201C23×D3—124no—
202C23×D3C4×D318yes—
203C23×D3D1218yes—
204C23×D3#6718yes—
205C23×D3C22×D314yes—
206C22×C3×C4—24no—
207C22×C3×C4—24no—
208C22×C3×C4—24no—
209C22×C3×C4—24no—
210C22×C3×C4—22no—
211C22×C3×C4—34no—
212C22×C3×C4—44no—
213C22×C3×C4—64no—
214C22×C3×C4—64no—
215C22×C3×C4—64no—
216C22×C3×C4C22×D314yescomplemented
217C22×Dic3—24no—
218C22×Dic3—24no—
219C22×Dic3—24no—
220C22×Dic3—34no—
221C22×Dic3—62no—
222C22×Dic3—64no—
223C22×Dic3—64no—
224C22×Dic3—64no—
225C22×Dic3—64no—
226C22×Dic3—124no—
227C22×Dic3C22×D314yescomplemented
228C3×C22⋊C4—616no—
229#217—616no—
230(C2×D3)⋊C4—216no—
231(C2×D3)⋊C4—616no—
232(C2×D3)⋊C4—616no—
233(C2×D3)⋊C4—616no—
234(C2×D3)⋊C4—616no—
235C22×C32C2×C22⋊C414yes—
236C22×C32C2×C22⋊C418yes—
237C22×C32#12014yes—
238C22×C32#12018yes—
239C22×C32#12014yes—
240C22×C32C23×C411yescharacteristic
241C22×C32C22×D412yes—
242C22×C32C22×D411yescharacteristic
243C22×C32C22×D411yescharacteristic
244C22×C32C22×D412yes—
245C2×C3⋊D3—28no—
246C2×C3⋊D3—24no—
247C2×C3⋊D3—28no—
248C2×C3⋊D3—24no—
249C2×C3⋊D3—232no—
250C2×C3⋊D3C2×C22⋊C418yescomplemented
251C2×C3×D3—28no—
252C2×C3×D3—28no—
253C2×C3×D3—28no—
254C2×C3×D3—28no—
255C2×C3×D3—28no—
256C2×C3×D3—28no—
257C2×C3×D3—264no—
258C2×C3×D3C2×C22⋊C4116yescomplemented
259D32—2128no—
260C32×C4—42no—
261C3⋊Dic3—42no—
262C3×Dic3—44no—
263C25—32no—
264C25—94no—
265C25—98no—
266C25—91no—
267C25—188no—
268C25—188no—
269C25—184no—
270C25—184no—
271C23×C4—32no—
272C23×C4—91no—
273C23×C4D3211yescharacteristic, complemented
274C2×C22⋊C4—38no—
275C2×C22⋊C4—68no—
276C2×C22⋊C4—94no—
277C2×C22⋊C4—98no—
278C2×C22⋊C4—94no—
279C2×C22⋊C4—184no—
280C2×C22⋊C4—184no—
281C2×C22⋊C4—188no—
282C23×C3—21no—
283C23×C3—22no—
284C23×C3—24no—
285C23×C3—22no—
286C23×C3—24no—
287C23×C3—22no—
288C23×C3—332no—
289C23×C3—38no—
290C23×C3—38no—
291C23×C3—38no—
292C23×C3—616no—
293C23×C3—616no—
294C23×C3—616no—
295C23×C3—616no—
296C23×C3—616no—
297C23×C3—616no—
298C23×C3—64no—
299C23×C3—64no—
300C23×C3—64no—
301C23×C3—64no—
302C23×C3C2×C4×D314yes—
303C23×C3C2×D1214yes—
304C23×C3D3×D414yes—
305C23×C3D3×D414yes—
306C23×C3D3×D414yes—
307C23×C3D3×D414yes—
308C23×C3C2×#6714yes—
309C23×C3C23×D312yes—
310C22×D3—216no—
311C22×D3—216no—
312C22×D3—216no—
313C22×D3—216no—
314C22×D3—216no—
315C22×D3—216no—
316C22×D3—24no—
317C22×D3—24no—
318C22×D3—24no—
319C22×D3—24no—
320C22×D3—332no—
321C22×D3—38no—
322C22×D3—38no—
323C22×D3—38no—
324C22×D3—616no—
325C22×D3—64no—
326C22×D3—64no—
327C22×D3—64no—
328C22×D3—664no—
329C22×D3—664no—
330C22×D3—6512no—
331C22×D3—664no—
332C22×D3—664no—
333C22×D3—664no—
334C22×D3—664no—
335C22×D3—616no—
336C22×D3—616no—
337C22×D3—616no—
338C22×D3—616no—
339C22×D3—616no—
340C22×D3—616no—
341C22×D3—64no—
342C22×D3—64no—
343C22×D3—64no—
344C22×D3—64no—
345C22×D3—664no—
346C22×D3—124no—
347C22×D3—124no—
348C22×D3—1216no—
349C22×D3—1216no—
350C22×D3—128no—
351C22×D3—128no—
352C22×D3(C2×D3)⋊C4132yescomplemented
353C22×D3C2×C4×D318yes—
354C22×D3C2×D1218yes—
355C22×D3C2×#6718yes—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—44no—
361C2×C3×C4—48no—
362C2×C3×C4—48no—
363C2×C3×C4—64no—
364C2×C3×C4—64no—
365C2×C3×C4—64no—
366C2×C3×C4—128no—
367C2×Dic3—24no—
368C2×Dic3—24no—
369C2×Dic3—24no—
370C2×Dic3—48no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—124no—
376C2×Dic3—128no—
377C2×Dic3—128no—
378C2×C32#37918yescomplemented
379C2×C32C22×C22⋊C411yescharacteristic
380C2×C32C22×C22⋊C412yes—
381C2×C32C2×#12011yescharacteristic
382C2×C32C2×#12012yes—
383C2×C32C2×#12011yescharacteristic
384C3⋊D3—28no—
385C3×D3—216no—
386C24—34no—
387C24—38no—
388C24—38no—
389C24—38no—
390C24—64no—
391C24—64no—
392C24—64no—
393C24—64no—
394C24—916no—
395C24—92no—
396C24—94no—
397C24—94no—
398C24—94no—
399C24—1816no—
400C24—1816no—
401C24—1864no—
402C24—188no—
403C24—188no—
404C24—1832no—
405C24—1864no—
406C24—1832no—
407C24—1832no—
408C24—184no—
409C24—184no—
410C24C2×D3211yescharacteristic
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—34no—
414C22×C4—64no—
415C22×C4—64no—
416C22×C4—64no—
417C22×C4—92no—
418C22×C4—184no—
419C22×C4—182no—
420C22×C4C2×D3212yescomplemented
421C22⋊C4—616no—
422C22⋊C4—188no—
423C22⋊C4—188no—
424C22⋊C4—1816no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—28no—
431C22×C3—24no—
432C22×C3—28no—
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—316no—
436C22×C3—664no—
437C22×C3—68no—
438C22×C3—68no—
439C22×C3—68no—
440C22×C3—68no—
441C22×C3—68no—
442C22×C3—68no—
443C22×C3D3×C22⋊C418yes—
444C22×C3D3×C22⋊C418yes—
445C22×C3#88218yes—
446C22×C3#88218yes—
447C22×C3C2×(C2×D3)⋊C418yes—
448C22×C3#93718yes—
449C22×C3#93718yes—
450C22×C3C22×C4×D312yes—
451C22×C3C22×D1212yes—
452C22×C3C2×D3×D412yes—
453C22×C3C2×D3×D412yes—
454C22×C3C2×D3×D412yes—
455C22×C3C2×D3×D412yes—
456C22×C3C22×#6712yes—
457C2×D3—264no—
458C2×D3—28no—
459C2×D3—28no—
460C2×D3—28no—
461C2×D3—28no—
462C2×D3—28no—
463C2×D3—28no—
464C2×D3—316no—
465C2×D3—68no—
466C2×D3—6256no—
467C2×D3—664no—
468C2×D3—68no—
469C2×D3—68no—
470C2×D3—68no—
471C2×D3—68no—
472C2×D3—68no—
473C2×D3—68no—
474C2×D3—1232no—
475C2×D3—124no—
476C2×D3—128no—
477C2×D3—128no—
478C2×D3—124no—
479C2×D3C2×(C2×D3)⋊C4116yescomplemented
480C3×C4—44no—
481C3×C4—44no—
482C3×C4—124no—
483Dic3—44no—
484Dic3—124no—
485Dic3—124no—
486C32C2×#37911yescharacteristic, complemented, Sylow
487C23—38no—
488C23—38no—
489C23—38no—
490C23—332no—
491C23—64no—
492C23—64no—
493C23—64no—
494C23—64no—
495C23—616no—
496C23—616no—
497C23—616no—
498C23—616no—
499C23—616no—
500C23—616no—
501C23—94no—
502C23—94no—
503C23—94no—
504C23—916no—
505C23—1864no—
506C23—1832no—
507C23—18256no—
508C23—1832no—
509C23—1864no—
510C23—1832no—
511C23—184no—
512C23—184no—
513C23—1816no—
514C23—1816no—
515C23—188no—
516C23—188no—
517C23C4×D3212yes—
518C23D3×D1214yes—
519C23#380212yes—
520C23D3×#6714yes—
521C23#381112yes—
522C23C22×D3211yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—44no—
526C2×C4—64no—
527C2×C4—64no—
528C2×C4—64no—
529C2×C4—128no—
530C2×C4—184no—
531C2×C4—182no—
532C2×C4—364no—
533C2×C3—28no—
534C2×C3—21no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—21no—
539C2×C3—616no—
540C2×C3#4955116yescomplemented
541C2×C3C2×D3×C22⋊C412yes—
542C2×C3C2×D3×C22⋊C412yes—
543C2×C3C2×#88212yes—
544C2×C3C2×#88212yes—
545C2×C3C22×(C2×D3)⋊C412yes—
546C2×C3C2×#93712yes—
547C2×C3C2×#93712yes—
548D3—216no—
549D3—616no—
550D3—128no—
551C22—316no—
552C22—664no—
553C22—68no—
554C22—68no—
555C22—68no—
556C22—68no—
557C22—68no—
558C22—68no—
559C22—98no—
560C22—18128no—
561C22—1832no—
562C22—184no—
563C22—188no—
564C22—188no—
565C22—184no—
566C22D3×(C2×D3)⋊C418yes—
567C22#6392114yes—
568C22#6392218yes—
569C22#6392314yes—
570C22#6398314yes—
571C22C2×C4×D3211yescharacteristic
572C22C2×D3×D1212yes—
573C22C2×#380211yescharacteristic
574C22C2×D3×#6712yes—
575C22C2×#381111yescharacteristic
576C4—42no—
577C4—124no—
578C4—362no—
579C3—21no—
580C3C2×#495512yescomplemented
581C2—616no—
582C2—188no—
583C2#1059139918yesdirect product factor
584C2C2×D3×(C2×D3)⋊C412yes—
585C2C2×#6392111yescharacteristic
586C2C2×#6392212yes—
587C2C2×#6392311yescharacteristic
588C2C2×#6398311yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×D32C2
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#379
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3752C2semidirect
3. C22×C3×(C2×D3)⋊C4C2semidirect
4. C22×#3722C2semidirect
5. C22×(C2×D3)⋊Dic3C2semidirect
6. #10591399C2direct (N × H)
14. C23×D32C4semidirect
16. C23×C32×C4C22semidirect
17. C23×C3⋊Dic3C22semidirect
18. C23×C3×Dic3C22semidirect
20. C2×#3752C22semidirect
22. C2×C3×(C2×D3)⋊C4C22semidirect
24. C2×#3722C22semidirect
26. C2×(C2×D3)⋊Dic3C22semidirect
34. C22×(C2×D3)⋊C4D3semidirect
60. C22×D32C2×C4semidirect
63. C22×C32×C4C23semidirect
66. C22×C3⋊Dic3C23semidirect
70. C22×C3×Dic3C23semidirect
90. C23×C3×C4C2×D3semidirect
93. C23×Dic3C2×D3semidirect
107. C2×(C2×D3)⋊C4C2×D3semidirect
120. C22×C3⋊D3C22⋊C4semidirect
134. C22×C3×D3C22⋊C4semidirect
216. C22×C3×C4C22×D3semidirect
227. C22×Dic3C22×D3semidirect
250. C2×C3⋊D3C2×C22⋊C4semidirect
258. C2×C3×D3C2×C22⋊C4semidirect
273. C23×C4D32semidirect
352. C22×D3(C2×D3)⋊C4semidirect
378. C2×C32#379semidirect
420. C22×C4C2×D32semidirect
479. C2×D3C2×(C2×D3)⋊C4semidirect
486. C32C2×#379semidirect
540. C2×C3#4955semidirect
580. C3C2×#4955semidirect
583. C2#10591399direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D322
C22×#37522
C22×C3×(C2×D3)⋊C42
C22×#37222
C22×(C2×D3)⋊Dic32
#105913992
C2×#49553