Finite Group Databasebeta

← C2×#10593850 #11903398

Subgroups — C2×#10593850 #11903398

Order 1152.

2389 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×#63894C211yesmaximal, characteristic
5C2×#63888C212yesmaximal, complemented
6C2×#63868C212yesmaximal, complemented
7C2×#63866C211yesmaximal, characteristic, complemented
8C2×#63864C211yesmaximal, characteristic
9C2×#63848C212yesmaximal, complemented
10C2×#63844C211yesmaximal, characteristic, complemented
11C2×#63836C212yesmaximal, complemented
12#10593850C2116yesmaximal, direct product factor
13C2×#5568—31nomaximal
14C2×#5584—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#624C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23#64084C2218yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C3×C4×Dic6C2218yescomplemented
33C3×C4×Dic6C2218yescomplemented
34C2×#3724C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×#3722C2212yes—
38C2×#3722C2212yes—
39C2×#3722C2212yes—
40C2×Dic32C2212yes—
41#63894C2218yes—
42#63888C22116yescomplemented
43#63868C22116yescomplemented
44#63866C2218yescomplemented
45#63864C2218yes—
46#63848C22116yescomplemented
47#63844C2218yescomplemented
48#63836C22116yescomplemented
49C2×C3×C4×Q8—31no—
50C2×C3×C4×Q8—31no—
51C2×#947—31no—
52C2×#946—32no—
53C2×#944—31no—
54#5584—316no—
55#5568—316no—
56C2×#898—32no—
57C2×#898—32no—
58C2×#898—32no—
59C2×#896—32no—
60C2×#893—31no—
61C2×#892—32no—
62C2×#887—31no—
63C2×#876—32no—
64C2×#875—31no—
65C2×#875—31no—
66C2×#875—31no—
67C2×#875—61no—
68C2×C4×D12—31no—
69C2×#872—32no—
70C2×#869—31no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6D311yescharacteristic, complemented
73C2×C4×Dic6D311yescharacteristic, complemented
74C23×C3⋊D3C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C2×C4⋊(C3⋊D3)—24no—
80C2×C4⋊(C3⋊D3)C2314yes—
81C2×#634—24no—
82C2×#634C2314yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×Dic6—24no—
90C2×C3×Dic6—24no—
91C2×C3×Dic6C2314yes—
92C2×C3×Dic6C2314yes—
93C2×#624—28no—
94C2×#624C2318yes—
95C32×C42C2314yes—
96#3752C2318yes—
97#3752C2318yes—
98C3×C4⋊Dic3C2314yes—
99C3×C4⋊Dic3C2314yes—
100C3×Dic3⋊C4C2314yes—
101C3×Dic3⋊C4C2318yes—
102C3×Dic3⋊C4C2314yes—
103C3×C4×Dic3C2318yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106#3724C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109#3722C2318yes—
110#3722C2318yes—
111#3722C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—31no—
115C22×C3×Q8—31no—
116C22×D12—31no—
117C22×D12—31no—
118C22×D12—61no—
119C22×C4×D3—32no—
120C22×C4×D3—32no—
121C22×Dic6—31no—
122C22×Dic6—31no—
123C22×Dic6—61no—
124C22×Dic6C2×D311yescharacteristic
125C22×Dic6C2×D311yescharacteristic
126C3×C4×Q8—38no—
127C3×C4×Q8—38no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C42—21no—
134C2×C3×C42—31no—
135C2×C3×C42—31no—
136C2×C3×C42—32no—
137C2×C3×C42C2×D311yescharacteristic
138C2×C3×C42C2×D311yescharacteristic
139#947—38no—
140#946—316no—
141#944—38no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—62no—
153C2×(C2×D3)⋊C4—62no—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—32no—
156C2×C4⋊Dic3C2×D311yescharacteristic
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4C2×D311yescharacteristic
163C2×Dic3⋊C4C2×D311yescharacteristic
164C2×Dic3⋊C4C2×D312yes—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3C2×D311yescharacteristic
168C2×C4×Dic3C2×D312yes—
169C2×C4×Dic3C2×D311yescharacteristic
170#898—316no—
171#898—316no—
172#898—316no—
173#896—316no—
174#893—38no—
175#892—316no—
176#887—38no—
177#876—316no—
178#875—38no—
179#875—38no—
180#875—38no—
181#875—68no—
182C4×D12—38no—
183#872—316no—
184#869—38no—
185C4×Dic6—38no—
186C4×Dic6C2×D318yescomplemented
187C4×Dic6C2×D318yescomplemented
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—24no—
190C22×C3⋊D3—24no—
191C22×C3⋊D3—24no—
192C22×C3⋊D3C2414yes—
193C2×C32×C4—22no—
194C2×C32×C4—22no—
195C2×C32×C4#4114yes—
196C2×C32×C4C2412yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3C2414yes—
201C4⋊(C3⋊D3)—28no—
202#634—28no—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3#4114yes—
209C2×C3×Dic3C2412yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C3×Dic6—28no—
216C3×Dic6—28no—
217#624—216no—
218#556—916no—
219C2×C4⋊Q8—91no—
220C2×#126—92no—
221C2×#126—92no—
222C2×#124—91no—
223C2×#124—91no—
224C2×C22⋊Q8—92no—
225C2×C4×Q8—31no—
226C2×C4×Q8—31no—
227C2×C4×Q8—91no—
228C2×C4×D4—91no—
229C2×#117—92no—
230C23×D3—32no—
231C23×D3—32no—
232C23×D3—62no—
233C2×C3×Q8—34no—
234C2×C3×Q8—34no—
235C2×C3×Q8—64no—
236C2×C3×Q8—64no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—32no—
243C22×C3×C4—32no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
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—32no—
253C22×Dic3—32no—
254C22×Dic3—62no—
255C22×Dic3C22×D311yescharacteristic
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D311yescharacteristic
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D311yescharacteristic
261C2×D12—34no—
262C2×D12—34no—
263C2×D12—64no—
264C2×D12—64no—
265C2×D12—64no—
266C2×D12—124no—
267C2×C4×D3—38no—
268C2×C4×D3—38no—
269C2×C4×D3—68no—
270C2×C4×D3—68no—
271C2×Dic6—24no—
272C2×Dic6—24no—
273C2×Dic6—34no—
274C2×Dic6—34no—
275C2×Dic6—64no—
276C2×Dic6—64no—
277C2×Dic6—64no—
278C2×Dic6—124no—
279C2×Dic6C22×D314yes—
280C2×Dic6C22×D314yes—
281C3×C4⋊C4—34no—
282C3×C4⋊C4—34no—
283C3×C4⋊C4—38no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—34no—
286C3×C42—24no—
287C3×C42—34no—
288C3×C42—34no—
289C3×C42—38no—
290C3×C42C22×D314yes—
291C3×C42C22×D314yes—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—68no—
303(C2×D3)⋊C4—68no—
304C4⋊Dic3—38no—
305C4⋊Dic3—38no—
306C4⋊Dic3C22×D314yes—
307C4⋊Dic3C22×D314yes—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4C22×D314yes—
313Dic3⋊C4C22×D314yes—
314Dic3⋊C4C22×D318yes—
315C4×Dic3—38no—
316C4×Dic3—38no—
317C4×Dic3C22×D314yes—
318C4×Dic3C22×D318yes—
319C4×Dic3C22×D314yes—
320C22×C32C2×#4112yes—
321C22×C32C2×#4112yes—
322C22×C322−1+412yes—
323C22×C32C2511yescharacteristic
324C2×C3⋊D3—24no—
325C2×C3⋊D3—24no—
326C2×C3⋊D3—24no—
327C2×C3⋊D3—48no—
328C32×C4—22no—
329C32×C4—22no—
330C32×C4C2×#4114yes—
331C3⋊Dic3—24no—
332C3×Dic3—24no—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3C2×#4114yes—
338C22×Q8—31no—
339C22×Q8—31no—
340C22×Q8—91no—
341C22×D4—91no—
342C23×C4—92no—
343C4⋊Q8—98no—
344#126—916no—
345#126—916no—
346#124—98no—
347#124—98no—
348C22⋊Q8—916no—
349C4×Q8—38no—
350C4×Q8—38no—
351C4×Q8—98no—
352C4×D4—98no—
353#117—916no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—92no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C22⋊C4—92no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C42—32no—
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—92no—
371C2×C42D3211yescharacteristic
372C23×C3—21no—
373C23×C3C23×D311yescharacteristic
374C23×C3C23×D311yescharacteristic
375C22×D3—34no—
376C22×D3—34no—
377C22×D3—64no—
378C22×D3—64no—
379C22×D3—64no—
380C22×D3—64no—
381C22×D3—64no—
382C22×D3—64no—
383C22×D3—64no—
384C22×D3—124no—
385C22×D3—124no—
386C22×D3—124no—
387C3×Q8—68no—
388C3×Q8—68no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—34no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—34no—
401C2×C3×C4—34no—
402C2×C3×C4—32no—
403C2×C3×C4—32no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—64no—
407C2×C3×C4—64no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4#23514yes—
412C2×C3×C4#23914yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×C3×C4C23×D312yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D312yes—
418C2×C3×C4C23×D312yes—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—24no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—34no—
425C2×Dic3—34no—
426C2×Dic3—64no—
427C2×Dic3—64no—
428C2×Dic3—64no—
429C2×Dic3—124no—
430C2×Dic3#23514yes—
431C2×Dic3C23×D312yes—
432C2×Dic3C23×D314yes—
433C2×Dic3C23×D312yes—
434C2×Dic3C23×D312yes—
435C2×Dic3C23×D314yes—
436C2×Dic3C23×D312yes—
437D12—68no—
438D12—68no—
439D12—128no—
440C4×D3—616no—
441C4×D3—616no—
442Dic6—28no—
443Dic6—28no—
444Dic6—68no—
445Dic6—68no—
446Dic6—128no—
447C2×C32#55614yescomplemented
448C2×C32C22×#4111yescharacteristic
449C2×C32C22×#4111yescharacteristic
450C2×C32C2×2−1+411yescharacteristic
451C3⋊D3—44no—
452C24—92no—
453C2×Q8—34no—
454C2×Q8—34no—
455C2×Q8—64no—
456C2×Q8—64no—
457C2×Q8—94no—
458C2×Q8—184no—
459C2×D4—94no—
460C2×D4—184no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—32no—
464C22×C4—31no—
465C22×C4—32no—
466C22×C4—31no—
467C22×C4—98no—
468C22×C4—92no—
469C22×C4—188no—
470C22×C4C2×D3211yescharacteristic
471C22×C4C2×D3211yescharacteristic
472C22×C4C2×D3211yescharacteristic
473C4⋊C4—34no—
474C4⋊C4—34no—
475C4⋊C4—38no—
476C4⋊C4—34no—
477C4⋊C4—34no—
478C4⋊C4—98no—
479C4⋊C4—98no—
480C4⋊C4—98no—
481C22⋊C4—98no—
482C22⋊C4—98no—
483C22⋊C4—98no—
484C22⋊C4—98no—
485C22⋊C4—98no—
486C42—38no—
487C42—34no—
488C42—34no—
489C42—98no—
490C42C2×D3214yes—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3C2×#23512yes—
496C22×C3C2×#23512yes—
497C22×C3C2×#23912yes—
498C22×C3#100712yes—
499C22×C3D3×#4112yes—
500C22×C3#101012yes—
501C22×C3C24×D311yescharacteristic
502C22×C3C24×D311yescharacteristic
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3—124no—
510C2×D3—124no—
511C2×D3—124no—
512C2×D3—128no—
513C2×D3—128no—
514C2×D3—248no—
515C3×C4—22no—
516C3×C4—22no—
517C3×C4—22no—
518C3×C4—22no—
519C3×C4—24no—
520C3×C4—34no—
521C3×C4—42no—
522C3×C4—42no—
523C3×C4—64no—
524C3×C4—64no—
525C3×C4—62no—
526C3×C4—62no—
527C3×C4—62no—
528C3×C4C2×#23514yes—
529C3×C4C2×#23914yes—
530Dic3—24no—
531Dic3—22no—
532Dic3—24no—
533Dic3—22no—
534Dic3—22no—
535Dic3—64no—
536Dic3—64no—
537Dic3—124no—
538Dic3C2×#23514yes—
539C32C2×#55611yescharacteristic, complemented, Sylow
540C23—94no—
541C23—184no—
542C23—184no—
543C23—184no—
544C23C22×D3211yescharacteristic
545Q8—68no—
546Q8—68no—
547Q8—188no—
548D4—188no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—34no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—34no—
555C2×C4—32no—
556C2×C4—34no—
557C2×C4—32no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—64no—
561C2×C4—64no—
562C2×C4—62no—
563C2×C4—94no—
564C2×C4—1816no—
565C2×C4—184no—
566C2×C4#379914yes—
567C2×C4C22×D3212yes—
568C2×C4C22×D3212yes—
569C2×C4C22×D3212yes—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—24no—
574C2×C3#556814yescomplemented
575C2×C3#558414yescomplemented
576C2×C3C22×#23511yescharacteristic
577C2×C3C22×#23511yescharacteristic
578C2×C3C22×#23911yescharacteristic
579C2×C3C2×#100711yescharacteristic
580C2×C3C2×D3×#4111yescharacteristic
581C2×C3C2×#101011yescharacteristic
582D3—124no—
583D3—124no—
584D3—244no—
585C22—184no—
586C22—184no—
587C22—184no—
588C22—368no—
589C22#6429712yes—
590C22C2×#379912yes—
591C22D3×#23512yes—
592C22C23×D3211yescharacteristic
593C4—22no—
594C4—22no—
595C4—34no—
596C4—62no—
597C4—62no—
598C4—64no—
599C4—64no—
600C4—62no—
601C4—184no—
602C4C2×#379914yes—
603C3—21no—
604C3C2×#558411yescharacteristic, complemented
605C3C2×#556811yescharacteristic, complemented
606C2—364no—
607C2#1059385014yesdirect product factor
608C2C2×#6429711yescharacteristic
609C2C22×#379911yescharacteristic
610C2C2×D3×#23511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
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
2. C2×C3×C4×Dic6C2semidirect
3. C2×C3×C4×Dic6C2semidirect
5. C2×#63888C2semidirect
6. C2×#63868C2semidirect
7. C2×#63866C2semidirect
9. C2×#63848C2semidirect
10. C2×#63844C2semidirect
11. C2×#63836C2semidirect
12. #10593850C2direct (N × H)
32. C3×C4×Dic6C22semidirect
33. C3×C4×Dic6C22semidirect
42. #63888C22semidirect
43. #63868C22semidirect
44. #63866C22semidirect
46. #63848C22semidirect
47. #63844C22semidirect
48. #63836C22semidirect
72. C2×C4×Dic6D3semidirect
73. C2×C4×Dic6D3semidirect
186. C4×Dic6C2×D3semidirect
187. C4×Dic6C2×D3semidirect
447. C2×C32#556semidirect
539. C32C2×#556semidirect
574. C2×C3#5568semidirect
575. C2×C3#5584semidirect
604. C3C2×#5584semidirect
605. C3C2×#5568semidirect
607. C2#10593850direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640842
C2×C3×C4×Dic62
C2×#638942
C2×#638882
C2×#638682
C2×#638662
C2×#638642
C2×#638482
C2×#638442
C2×#638362
#105938502
C2×#55683
C2×#55843