Finite Group Databasebeta

← C2×#10594475 #11903206

Subgroups — C2×#10594475 #11903206

Order 1152.

2717 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic, complemented
2C2×C3×#898C212yesmaximal, complemented
3C2×#63912C211yesmaximal, characteristic, complemented
4C2×#63912C211yesmaximal, characteristic, complemented
5C2×#63910C212yesmaximal, complemented
6C2×#63902C211yesmaximal, characteristic, complemented
7C2×#63900C211yesmaximal, characteristic, complemented
8C2×#63890C212yesmaximal, complemented
9C2×#63880C212yesmaximal, complemented
10C2×#63874C211yesmaximal, characteristic, complemented
11C2×#63870C211yesmaximal, characteristic, complemented
12#10594475C2116yesmaximal, direct product factor
13C2×#5709—32nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#626C2212yes—
18C22×#626C2212yes—
19C22×#625C2211yescharacteristic
20C22×#624C2212yes—
21C22×D3×Dic3C2212yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64102C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4⋊Dic3C2212yes—
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×C4×Dic3C2212yes—
33C3×#898C22116yescomplemented
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2212yes—
38C2×#3722C2212yes—
39#63912C2218yescomplemented
40#63912C2218yescomplemented
41#63910C22116yescomplemented
42#63902C2218yescomplemented
43#63900C2218yescomplemented
44#63890C22116yescomplemented
45#63880C22116yescomplemented
46#63874C2218yescomplemented
47#63870C2218yescomplemented
48C2×C3×#126—32no—
49#5709—332no—
50C2×#898D312yescomplemented
51C2×#895—32no—
52C2×#894—32no—
53C2×#893—32no—
54C2×#893—61no—
55C2×D3×C4⋊C4—32no—
56C2×#889—32no—
57C2×#886—32no—
58C2×#884—32no—
59C2×#884—32no—
60C2×#884—32no—
61C2×#67⋊C4—32no—
62C2×#67⋊C4—32no—
63C2×C4×D12—32no—
64C2×#872—32no—
65C23×C3⋊D3C2311yescharacteristic
66C23×C3⋊D3C2311yescharacteristic
67C23×C3×D3C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4⋊(C3⋊D3)—24no—
74C2×C4⋊(C3⋊D3)C2314yes—
75C2×C4×C3⋊D3—24no—
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3C2314yes—
78C2×C4×C3⋊D3C2314yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×#626—28no—
83C2×#626—44no—
84C2×#626C2318yes—
85C2×#626C2318yes—
86C2×#625—24no—
87C2×#625C2314yes—
88C2×#624—44no—
89C2×#624C2318yes—
90C2×D3×Dic3—44no—
91C2×D3×Dic3C2318yes—
92C32×C4⋊C4C2314yes—
93#3752C2314yes—
94#3752C2314yes—
95C4×C3⋊Dic3C2314yes—
96C3×(C2×D3)⋊C4C2318yes—
97C3×(C2×D3)⋊C4C2318yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×C4⋊Dic3C2318yes—
100C3×Dic3⋊C4C2318yes—
101C3×C4×Dic3C2318yes—
102#3724C2314yes—
103#3724C2314yes—
104#3724C2314yes—
105Dic3⋊Dic3C2318yes—
106#3722C2318yes—
107C2×#553—91noSylow
108C22×#67—32no—
109C22×#67—32no—
110C22×#67—32no—
111C23×Dic3—32no—
112C22×D12—32no—
113C22×D12—32no—
114C22×D12—32no—
115C22×D12—61no—
116C22×C4×D3—32no—
117C22×C4×D3—32no—
118C22×C4×D3—32no—
119C22×C4×D3—32no—
120C22×C4×D3—32no—
121C22×C4×D3—61no—
122C22×C4×D3—61no—
123C3×#126—316no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—32no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4C2×D312yes—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C42—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—61no—
137C2×(C2×D3)⋊C4—61no—
138C2×(C2×D3)⋊C4C2×D312yes—
139C2×(C2×D3)⋊C4C2×D312yes—
140C2×(C2×D3)⋊C4C2×D312yes—
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3C2×D312yes—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4C2×D312yes—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—61no—
150C2×C4×Dic3C2×D312yes—
151#898C2×D3116yescomplemented
152#895—316no—
153#894—316no—
154#893—316no—
155#893—68no—
156D3×C4⋊C4—316no—
157#889—316no—
158#886—316no—
159#884—316no—
160#884—316no—
161#884—316no—
162#67⋊C4—316no—
163#67⋊C4—316no—
164C4×D12—316no—
165#872—316no—
166C23×C32C2411yescharacteristic
167C22×C3⋊D3—22no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3#4114yes—
173C22×C3⋊D3C2412yes—
174C22×C3⋊D3C2412yes—
175C22×C3×D3—24no—
176C22×C3×D3—24no—
177C22×C3×D3—24no—
178C22×C3×D3C2414yes—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4C2412yes—
183C2×C32×C4C2412yes—
184C2×C32×C4C2412yes—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3#4114yes—
187C2×C3⋊Dic3C2412yes—
188C2×C3⋊Dic3C2412yes—
189C4⋊(C3⋊D3)—28no—
190C4×C3⋊D3—28no—
191C4×C3⋊D3—28no—
192C2×C3×Dic3—24no—
193C2×C3×Dic3—24no—
194C2×C3×Dic3—24no—
195C2×C3×Dic3C2414yes—
196C2×C3×Dic3C2414yes—
197C2×C3×Dic3C2414yes—
198#626—216no—
199#626—48no—
200#625—28no—
201#624—48no—
202D3×Dic3—48no—
203#553—916no—
204C2×#126—32no—
205C2×#125—91no—
206C2×#123—92no—
207C2×#121—91no—
208C2×#121—91no—
209C2×#121—92no—
210C2×C4×D4—92no—
211C2×C4×D4—91no—
212C2×C4×D4—91no—
213C2×#117—91no—
214C22×C4⋊C4—91no—
215C24×C3—32no—
216C23×D3—32no—
217C23×D3—32no—
218C23×D3—61no—
219C23×D3—61no—
220C23×D3C22×D312yes—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D312yes—
230C2×#67—38no—
231C2×#67—38no—
232C2×#67—38no—
233C2×#67—68no—
234C2×#67—68no—
235C2×#67—124no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—38no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3—124no—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C2×D12—38no—
246C2×D12—38no—
247C2×D12—38no—
248C2×D12—64no—
249C2×D12—68no—
250C2×D12—68no—
251C2×D12—68no—
252C2×D12—124no—
253C2×C4×D3—38no—
254C2×C4×D3—38no—
255C2×C4×D3—38no—
256C2×C4×D3—38no—
257C2×C4×D3—38no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—68no—
261C2×C4×D3—68no—
262C2×C4×D3—124no—
263C2×C4×D3—124no—
264C2×C4×D3—124no—
265C2×C4×D3—124no—
266C2×C4×D3—124no—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—38no—
269C3×C4⋊C4—38no—
270C3×C4⋊C4C22×D318yes—
271C3×C22⋊C4—38no—
272C3×C22⋊C4—38no—
273C3×C22⋊C4—38no—
274C3×C42—38no—
275(C2×D3)⋊C4—38no—
276(C2×D3)⋊C4—38no—
277(C2×D3)⋊C4—38no—
278(C2×D3)⋊C4—38no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4C22×D318yes—
282(C2×D3)⋊C4C22×D318yes—
283(C2×D3)⋊C4C22×D318yes—
284C4⋊Dic3—38no—
285C4⋊Dic3C22×D318yes—
286Dic3⋊C4—38no—
287Dic3⋊C4—38no—
288Dic3⋊C4—38no—
289Dic3⋊C4—38no—
290Dic3⋊C4C22×D318yes—
291C4×Dic3—38no—
292C4×Dic3—64no—
293C4×Dic3C22×D318yes—
294C22×C32C2×#4112yes—
295C22×C32C2×#4112yes—
296C22×C32H(5,𝔽2)12yes—
297C22×C32C2511yescharacteristic
298C2×C3⋊D3—22no—
299C2×C3⋊D3—28no—
300C2×C3⋊D3—22no—
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3⋊D3—22no—
304C2×C3⋊D3—44no—
305C2×C3⋊D3C2×#4114yes—
306C2×C3×D3—24no—
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—48no—
310C32×C4—22no—
311C32×C4—22no—
312C32×C4—22no—
313C3⋊Dic3—22no—
314C3⋊Dic3C2×#4114yes—
315C3×Dic3—24no—
316C3×Dic3—24no—
317C3×Dic3—24no—
318C22×D4—92no—
319C22×D4—92no—
320C22×D4—91no—
321C22×D4—91no—
322C23×C4—92no—
323C23×C4—92no—
324C23×C4—91no—
325C23×C4—91no—
326#126—316no—
327#125—98no—
328#123—916no—
329#121—98no—
330#121—98no—
331#121—916no—
332C4×D4—916no—
333C4×D4—98no—
334C4×D4—98no—
335#117—98no—
336C2×C4⋊C4—32no—
337C2×C4⋊C4—32no—
338C2×C4⋊C4—98no—
339C2×C4⋊C4—91no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—92no—
343C2×C4⋊C4D3211yescharacteristic
344C2×C22⋊C4—32no—
345C2×C22⋊C4—32no—
346C2×C22⋊C4—32no—
347C2×C22⋊C4—92no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C42—32no—
351C2×C42—91no—
352C23×C3—21no—
353C23×C3—34no—
354C23×C3—64no—
355C23×C3—64no—
356C23×C3—64no—
357C23×C3C23×D312yes—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3—38no—
362C22×D3—34no—
363C22×D3—34no—
364C22×D3—64no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—64no—
371C22×D3—64no—
372C22×D3—64no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3C23×D314yes—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—34no—
386C2×C3×C4—34no—
387C2×C3×C4—34no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—64no—
391C2×C3×C4—64no—
392C2×C3×C4—64no—
393C2×C3×C4C23×D314yes—
394C2×C3×C4C23×D314yes—
395C2×C3×C4C23×D314yes—
396#67—616no—
397#67—616no—
398#67—128no—
399C2×Dic3—24no—
400C2×Dic3—24no—
401C2×Dic3—24no—
402C2×Dic3—38no—
403C2×Dic3—34no—
404C2×Dic3—34no—
405C2×Dic3—64no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—64no—
409C2×Dic3—122no—
410C2×Dic3—128no—
411C2×Dic3C23×D314yes—
412C2×Dic3C23×D314yes—
413C2×Dic3C23×D314yes—
414D12—616no—
415D12—616no—
416D12—616no—
417D12—128no—
418C4×D3—616no—
419C4×D3—616no—
420C4×D3—128no—
421C4×D3—128no—
422C4×D3—128no—
423C4×D3—128no—
424C4×D3—128no—
425C2×C32#55314yescomplemented
426C2×C32C22×#4111yescharacteristic
427C2×C32C22×#4111yescharacteristic
428C2×C32C2×H(5,𝔽2)11yescharacteristic
429C3⋊D3—24no—
430C3⋊D3—42no—
431C3×D3—44no—
432C24—32no—
433C24—91no—
434C24—91no—
435C2×D4—98no—
436C2×D4—98no—
437C2×D4—94no—
438C2×D4—94no—
439C2×D4—184no—
440C2×D4—188no—
441C2×D4—184no—
442C2×D4—364no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—98no—
447C22×C4—98no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—94no—
451C22×C4—94no—
452C22×C4—184no—
453C22×C4—184no—
454C22×C4—364no—
455C22×C4—364no—
456C22×C4C2×D3211yescharacteristic
457C22×C4C2×D3211yescharacteristic
458C22×C4C2×D3211yescharacteristic
459C4⋊C4—38no—
460C4⋊C4—38no—
461C4⋊C4—94no—
462C4⋊C4—94no—
463C4⋊C4—94no—
464C4⋊C4—98no—
465C4⋊C4C2×D3214yes—
466C22⋊C4—38no—
467C22⋊C4—38no—
468C22⋊C4—38no—
469C22⋊C4—98no—
470C22⋊C4—94no—
471C22⋊C4—94no—
472C42—38no—
473C42—94no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—21no—
478C22×C3—64no—
479C22×C3—64no—
480C22×C3—64no—
481C22×C3—128no—
482C22×C3D3×#4114yes—
483C22×C3D3×#4114yes—
484C22×C3#100914yes—
485C22×C3C24×D312yes—
486C2×D3—24no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—38no—
490C2×D3—48no—
491C2×D3—64no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—616no—
495C2×D3—64no—
496C2×D3—64no—
497C2×D3—64no—
498C2×D3—64no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—128no—
503C2×D3—122no—
504C2×D3—128no—
505C2×D3—128no—
506C3×C4—24no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—42no—
511C3×C4—42no—
512C3×C4—64no—
513C3×C4—64no—
514C3×C4—64no—
515Dic3—24no—
516Dic3—24no—
517Dic3—24no—
518Dic3—38no—
519Dic3—64no—
520Dic3—64no—
521Dic3—122no—
522C32C2×#55311yescharacteristic, complemented, Sylow
523C23—34no—
524C23—64no—
525C23—64no—
526C23—64no—
527C23—94no—
528C23—92no—
529C23—92no—
530C23—182no—
531C23—182no—
532C23—182no—
533C23—182no—
534C23—182no—
535C23C22×D3211yescharacteristic
536D4—188no—
537D4—1816no—
538D4—188no—
539D4—368no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—34no—
544C2×C4—34no—
545C2×C4—34no—
546C2×C4—64no—
547C2×C4—64no—
548C2×C4—64no—
549C2×C4—94no—
550C2×C4—92no—
551C2×C4—92no—
552C2×C4—188no—
553C2×C4—188no—
554C2×C4—182no—
555C2×C4—368no—
556C2×C4—368no—
557C2×C4C22×D3212yes—
558C2×C4C22×D3212yes—
559C2×C4C22×D3212yes—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—24no—
564C2×C3—124no—
565C2×C3#570918yescomplemented
566C2×C3C2×D3×#4112yes—
567C2×C3C2×D3×#4112yes—
568C2×C3C2×#100912yes—
569D3—44no—
570D3—68no—
571D3—124no—
572D3—124no—
573D3—124no—
574C22—64no—
575C22—64no—
576C22—64no—
577C22—94no—
578C22—128no—
579C22—182no—
580C22—182no—
581C22—188no—
582C22—182no—
583C22—182no—
584C22—182no—
585C22—364no—
586C22#6430612yes—
587C22#6431212yes—
588C22#6432012yes—
589C22C23×D3211yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—64no—
594C4—64no—
595C4—64no—
596C4—94no—
597C4—182no—
598C3—21no—
599C3C2×#570912yescomplemented
600C2—124no—
601C2—184no—
602C2—362no—
603C2#1059447514yesdirect product factor
604C2C2×#6430611yescharacteristic
605C2C2×#6431211yescharacteristic
606C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
2. C2×C3×#898C2semidirect
3. C2×#63912C2semidirect
4. C2×#63912C2semidirect
5. C2×#63910C2semidirect
6. C2×#63902C2semidirect
7. C2×#63900C2semidirect
8. C2×#63890C2semidirect
9. C2×#63880C2semidirect
10. C2×#63874C2semidirect
11. C2×#63870C2semidirect
12. #10594475C2direct (N × H)
26. #64102C22semidirect
33. C3×#898C22semidirect
39. #63912C22semidirect
40. #63912C22semidirect
41. #63910C22semidirect
42. #63902C22semidirect
43. #63900C22semidirect
44. #63890C22semidirect
45. #63880C22semidirect
46. #63874C22semidirect
47. #63870C22semidirect
50. C2×#898D3semidirect
151. #898C2×D3semidirect
425. C2×C32#553semidirect
522. C32C2×#553semidirect
565. C2×C3#5709semidirect
599. C3C2×#5709semidirect
603. C2#10594475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641022
C2×C3×#8982
C2×#639122
C2×#639102
C2×#639022
C2×#639002
C2×#638902
C2×#638802
C2×#638742
C2×#638702
#105944752
C2×#57093