Finite Group Databasebeta

← C2×#10593942 #11903397

Subgroups — C2×#10593942 #11903397

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×#63898C211yesmaximal, characteristic
5C2×#63896C212yesmaximal, complemented
6C2×#63877C212yesmaximal, complemented
7C2×#63873C211yesmaximal, characteristic, complemented
8C2×#63863C211yesmaximal, characteristic
9C2×#63861C212yesmaximal, complemented
10C2×#63859C212yesmaximal, complemented
11C2×#63843C211yesmaximal, characteristic, complemented
12#10593942C2116yesmaximal, direct product factor
13C2×#5671—31nomaximal
14C2×#5568—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C4×#634C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×C4×Dic3C2212yes—
32C3×#875C2218yes—
33C3×C4×Dic6C2218yescomplemented
34C2×#3724C2212yes—
35C2×#3724C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×Dic32C2212yes—
41#63898C2218yes—
42#63896C22116yescomplemented
43#63877C22116yescomplemented
44#63873C2218yescomplemented
45#63863C2218yes—
46#63861C22116yescomplemented
47#63859C22116yescomplemented
48#63843C2218yescomplemented
49C2×C3×#124—31no—
50C2×C3×C4×Q8—31no—
51C2×#947—31no—
52C2×Q8×Dic3—31no—
53C2×#944—31no—
54C2×#944—31no—
55C2×#936—31no—
56C2×D4×Dic3—31no—
57#5671—316no—
58#5568—316no—
59C2×#898—32no—
60C2×#896—32no—
61C2×#893—31no—
62C2×#887—31no—
63C2×#879—32no—
64C2×#879—32no—
65C2×#878—32no—
66C2×#877—32no—
67C2×#876—32no—
68C2×#875D311yescharacteristic
69C2×#872—32no—
70C2×C4×Dic6—31no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6—61no—
73C2×C4×Dic6D311yescharacteristic, complemented
74C23×C3×D3C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C2×#634—24no—
83C2×#634C2314yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C2×C3×D12—24no—
88C2×C3×D12C2314yes—
89C2×C3×Dic6—24no—
90C2×C3×Dic6—24no—
91C2×C3×Dic6C2314yes—
92C2×C3×Dic6C2314yes—
93C2×D3×Dic3—28no—
94C2×D3×Dic3C2318yes—
95C32×C42C2314yes—
96C4⋊(C3⋊Dic3)C2314yes—
97#3750C2314yes—
98#3750C2314yes—
99C4×C3⋊Dic3C2314yes—
100C4×C3⋊Dic3C2314yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×C4⋊Dic3C2314yes—
104C3×Dic3⋊C4C2318yes—
105C3×C4×Dic3C2318yes—
106#3724C2318yes—
107#3724C2318yes—
108Dic3⋊Dic3C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—31no—
115C22×C3×Q8—31no—
116C22×C3×D4—31no—
117C23×Dic3—32no—
118C22×D12C2×D311yescharacteristic
119C22×C4×D3—32no—
120C22×Dic6—31no—
121C22×Dic6—31no—
122C22×Dic6—61no—
123C22×Dic6C2×D311yescharacteristic
124C22×Dic6C2×D311yescharacteristic
125C3×#124—38no—
126C3×C4×Q8—38no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C42—21no—
132C2×C3×C42—32no—
133C2×C3×C42C2×D311yescharacteristic
134C2×C3×C42C2×D311yescharacteristic
135C2×#217—32no—
136C2×#217—32no—
137C2×#217—32no—
138#947—38no—
139Q8×Dic3—38no—
140#944—38no—
141#944—38no—
142#936—38no—
143D4×Dic3—38no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4C2×D312yes—
148C2×(C2×D3)⋊C4C2×D312yes—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—61no—
153C2×C4⋊Dic3C2×D311yescharacteristic
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—61no—
164C2×Dic3⋊C4—61no—
165C2×Dic3⋊C4C2×D312yes—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3—61no—
174C2×C4×Dic3C2×D312yes—
175#898—316no—
176#896—316no—
177#893—38no—
178#887—38no—
179#879—316no—
180#879—316no—
181#878—316no—
182#877—316no—
183#876—316no—
184#875C2×D318yes—
185#872—316no—
186C4×Dic6—38no—
187C4×Dic6—38no—
188C4×Dic6—68no—
189C4×Dic6C2×D318yescomplemented
190C23×C32C2411yescharacteristic
191C22×C3×D3—24no—
192C22×C3×D3—24no—
193C22×C3×D3—24no—
194C22×C3×D3C2414yes—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4#4114yes—
198C2×C32×C4C2412yes—
199C2×C32×C4C2412yes—
200C2×C32×C4C2412yes—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3#4114yes—
205C2×C3⋊Dic3C2412yes—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208C2×C3⋊Dic3C2412yes—
209#634—28no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2414yes—
216C3×D12—28no—
217C3×Dic6—28no—
218C3×Dic6—28no—
219D3×Dic3—216no—
220#556—916no—
221C2×C4⋊Q8—91no—
222C2×#126—92no—
223C2×#126—92no—
224C2×#124—31no—
225C2×#124—91no—
226C2×C22⋊Q8—92no—
227C2×C4×Q8—31no—
228C2×C4×Q8—91no—
229C2×C4×Q8—91no—
230C2×C4×D4—91no—
231C2×#117—92no—
232C24×C3—32no—
233C23×D3C22×D312yes—
234C2×C3×Q8—34no—
235C2×C3×Q8—34no—
236C2×C3×Q8—64no—
237C2×C3×Q8—64no—
238C2×C3×D4—34no—
239C2×C3×D4—64no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—38no—
261C22×Dic3—61no—
262C22×Dic3—61no—
263C22×Dic3—61no—
264C22×Dic3—61no—
265C22×Dic3—68no—
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D312yes—
269C2×D12—24no—
270C2×D12C22×D314yes—
271C2×C4×D3—38no—
272C2×C4×D3—68no—
273C2×Dic6—24no—
274C2×Dic6—24no—
275C2×Dic6—34no—
276C2×Dic6—34no—
277C2×Dic6—64no—
278C2×Dic6—64no—
279C2×Dic6—64no—
280C2×Dic6—68no—
281C2×Dic6C22×D314yes—
282C2×Dic6C22×D314yes—
283C3×C4⋊C4—34no—
284C3×C4⋊C4—38no—
285C3×C22⋊C4—38no—
286C3×C22⋊C4—38no—
287C3×C42—24no—
288C3×C42—38no—
289C3×C42C22×D314yes—
290C3×C42C22×D314yes—
291#217—38no—
292#217—38no—
293#217—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4C22×D318yes—
298(C2×D3)⋊C4C22×D318yes—
299C4⋊Dic3—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—38no—
302C4⋊Dic3—64no—
303C4⋊Dic3C22×D314yes—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307Dic3⋊C4—34no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4—64no—
314Dic3⋊C4—64no—
315Dic3⋊C4C22×D318yes—
316C4×Dic3—34no—
317C4×Dic3—34no—
318C4×Dic3—34no—
319C4×Dic3—34no—
320C4×Dic3—38no—
321C4×Dic3—38no—
322C4×Dic3—64no—
323C4×Dic3—64no—
324C4×Dic3C22×D318yes—
325C22×C32C2×#4112yes—
326C22×C32C2×#4112yes—
327C22×C322−1+412yes—
328C22×C32C2511yescharacteristic
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—48no—
333C32×C4—22no—
334C32×C4—22no—
335C32×C4C2×#4114yes—
336C3⋊Dic3—22no—
337C3⋊Dic3—22no—
338C3⋊Dic3—22no—
339C3⋊Dic3C2×#4114yes—
340C3×Dic3—24no—
341C3×Dic3—24no—
342C3×Dic3—24no—
343C22×Q8—31no—
344C22×Q8—31no—
345C22×Q8—91no—
346C22×D4—31no—
347C23×C4—92no—
348C4⋊Q8—98no—
349#126—916no—
350#126—916no—
351#124—38no—
352#124—98no—
353C22⋊Q8—916no—
354C4×Q8—38no—
355C4×Q8—98no—
356C4×Q8—98no—
357C4×D4—98no—
358#117—916no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—32no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C42—32no—
373C2×C42—92no—
374C2×C42—91no—
375C2×C42—91no—
376C2×C42D3211yescharacteristic
377C23×C3—21no—
378C23×C3—34no—
379C23×C3—64no—
380C23×C3—64no—
381C23×C3—64no—
382C23×C3C23×D311yescharacteristic
383C23×C3C23×D311yescharacteristic
384C22×D3—24no—
385C22×D3—24no—
386C22×D3—24no—
387C22×D3C23×D314yes—
388C3×Q8—68no—
389C3×Q8—68no—
390C3×D4—68no—
391C2×C3×C4—24no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—34no—
401C2×C3×C4—34no—
402C2×C3×C4—34no—
403C2×C3×C4—42no—
404C2×C3×C4—64no—
405C2×C3×C4—64no—
406C2×C3×C4—64no—
407C2×C3×C4#23514yes—
408C2×C3×C4#23714yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D312yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—34no—
419C2×Dic3—34no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—64no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—616no—
434C2×Dic3—64no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—122no—
442C2×Dic3—122no—
443C2×Dic3C23×D314yes—
444C2×Dic3C23×D314yes—
445C2×Dic3C23×D314yes—
446D12—28no—
447C4×D3—616no—
448Dic6—28no—
449Dic6—28no—
450Dic6—68no—
451Dic6—68no—
452Dic6—616no—
453C2×C32#55614yescomplemented
454C2×C32C22×#4111yescharacteristic
455C2×C32C22×#4111yescharacteristic
456C2×C32C2×2−1+411yescharacteristic
457C3×D3—44no—
458C24—32no—
459C2×Q8—34no—
460C2×Q8—34no—
461C2×Q8—64no—
462C2×Q8—64no—
463C2×Q8—94no—
464C2×Q8—184no—
465C2×D4—34no—
466C2×D4—64no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—32no—
470C22×C4—98no—
471C22×C4—91no—
472C22×C4—91no—
473C22×C4—91no—
474C22×C4—91no—
475C22×C4—188no—
476C22×C4C2×D3211yescharacteristic
477C22×C4C2×D3211yescharacteristic
478C22×C4C2×D3211yescharacteristic
479C4⋊C4—34no—
480C4⋊C4—38no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—98no—
484C4⋊C4—94no—
485C4⋊C4—94no—
486C4⋊C4—94no—
487C22⋊C4—38no—
488C22⋊C4—38no—
489C22⋊C4—98no—
490C22⋊C4—98no—
491C22⋊C4—98no—
492C42—38no—
493C42—98no—
494C42—94no—
495C42—94no—
496C42C2×D3214yes—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—64no—
502C22×C3—64no—
503C22×C3—64no—
504C22×C3—128no—
505C22×C3C2×#23512yes—
506C22×C3C2×#23712yes—
507C22×C3#100712yes—
508C22×C3D3×#4112yes—
509C22×C3D3×#4112yes—
510C22×C3#101012yes—
511C22×C3C24×D311yescharacteristic
512C22×C3C24×D311yescharacteristic
513C2×D3—24no—
514C2×D3—24no—
515C2×D3—24no—
516C2×D3—48no—
517C3×C4—24no—
518C3×C4—22no—
519C3×C4—22no—
520C3×C4—22no—
521C3×C4—22no—
522C3×C4—24no—
523C3×C4—42no—
524C3×C4—64no—
525C3×C4—64no—
526C3×C4—64no—
527C3×C4C2×#23514yes—
528C3×C4C2×#23714yes—
529Dic3—24no—
530Dic3—24no—
531Dic3—24no—
532Dic3—34no—
533Dic3—34no—
534Dic3—64no—
535Dic3—64no—
536Dic3—62no—
537Dic3—62no—
538Dic3—62no—
539Dic3—62no—
540Dic3—62no—
541Dic3—62no—
542Dic3—122no—
543Dic3—122no—
544C32C2×#55611yescharacteristic, complemented, Sylow
545C23—34no—
546C23—64no—
547C23—64no—
548C23—64no—
549C23C22×D3211yescharacteristic
550Q8—68no—
551Q8—68no—
552Q8—188no—
553D4—68no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—34no—
557C2×C4—34no—
558C2×C4—34no—
559C2×C4—64no—
560C2×C4—64no—
561C2×C4—64no—
562C2×C4—94no—
563C2×C4—92no—
564C2×C4—92no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—1816no—
568C2×C4—182no—
569C2×C4—182no—
570C2×C4—182no—
571C2×C4#379514yes—
572C2×C4C22×D3212yes—
573C2×C4C22×D3212yes—
574C2×C4C22×D3212yes—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—24no—
579C2×C3—124no—
580C2×C3#556814yescomplemented
581C2×C3#567114yescomplemented
582C2×C3C22×#23511yescharacteristic
583C2×C3C22×#23711yescharacteristic
584C2×C3C2×#100711yescharacteristic
585C2×C3C2×D3×#4111yescharacteristic
586C2×C3C2×D3×#4111yescharacteristic
587C2×C3C2×#101011yescharacteristic
588D3—44no—
589C22—64no—
590C22—64no—
591C22—64no—
592C22—128no—
593C22C2×#379512yes—
594C22#6429712yes—
595C22#6430612yes—
596C22C23×D3211yescharacteristic
597C4—22no—
598C4—22no—
599C4—64no—
600C4—64no—
601C4—64no—
602C4—94no—
603C4—182no—
604C4—182no—
605C4—182no—
606C4C2×#379514yes—
607C3—21no—
608C3C2×#556811yescharacteristic, complemented
609C3C2×#567111yescharacteristic, complemented
610C2—124no—
611C2#1059394214yesdirect product factor
612C2C22×#379511yescharacteristic
613C2C2×#6429711yescharacteristic
614C2C2×#6430611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C2×C3×C4×Dic6C2semidirect
5. C2×#63896C2semidirect
6. C2×#63877C2semidirect
7. C2×#63873C2semidirect
9. C2×#63861C2semidirect
10. C2×#63859C2semidirect
11. C2×#63843C2semidirect
12. #10593942C2direct (N × H)
26. C4×#634C22semidirect
33. C3×C4×Dic6C22semidirect
42. #63896C22semidirect
43. #63877C22semidirect
44. #63873C22semidirect
46. #63861C22semidirect
47. #63859C22semidirect
48. #63843C22semidirect
73. C2×C4×Dic6D3semidirect
189. C4×Dic6C2×D3semidirect
453. C2×C32#556semidirect
544. C32C2×#556semidirect
580. C2×C3#5568semidirect
581. C2×C3#5671semidirect
608. C3C2×#5568semidirect
609. C3C2×#5671semidirect
611. C2#10593942direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×#8752
C2×C3×C4×Dic62
C2×#638982
C2×#638962
C2×#638772
C2×#638732
C2×#638632
C2×#638612
C2×#638592
C2×#638432
#105939422
C2×#56713
C2×#55683