Finite Group Databasebeta

← C2×#10594352 #11901688

Subgroups — C2×#10594352 #11901688

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic
2C2×C3×#888C211yesmaximal, characteristic, complemented
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×#63897C212yesmaximal, complemented
5C2×#63894C211yesmaximal, characteristic, complemented
6C2×#63888C212yesmaximal, complemented
7C2×#63874C211yesmaximal, characteristic, complemented
8C2×#63871C211yesmaximal, characteristic, complemented
9C2×#63868C212yesmaximal, complemented
10C2×#63864C212yesmaximal, complemented
11C2×#63864C211yesmaximal, characteristic, complemented
12#10594352C2116yesmaximal, direct product factor
13C2×#5733—31nomaximal
14C2×#5582—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2212yes—
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2212yes—
20C22×#624C2212yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3752C2212yes—
23#64104C2218yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#888C2218yescomplemented
31C3×#887C2218yescomplemented
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×#3722C2211yescharacteristic
36C2×#3722C2212yes—
37C2×#3722C2212yes—
38C2×#3722C2212yes—
39C2×#3722C2212yes—
40C2×#3722C2211yescharacteristic
41#63897C22116yescomplemented
42#63894C2218yescomplemented
43#63888C22116yescomplemented
44#63874C2218yescomplemented
45#63871C2218yescomplemented
46#63868C22116yescomplemented
47#63864C2218yescomplemented
48#63864C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×C4×Q8—31no—
51C2×#947—31no—
52C2×#947—32no—
53C2×#946—31no—
54C2×#946—32no—
55#5733—316no—
56#5582—316no—
57C2×#898—32no—
58C2×#897—31no—
59C2×#896—32no—
60C2×#895—31no—
61C2×#895—31no—
62C2×#895—61no—
63C2×#894—32no—
64C2×#894—32no—
65C2×#893—31no—
66C2×#888D311yescharacteristic, complemented
67C2×#887D311yescharacteristic, complemented
68C2×#876—32no—
69C2×#875—32no—
70C2×#875—31no—
71C2×C4×D12—31no—
72C2×#872—31no—
73C2×#872—31no—
74C23×C3⋊D3C2312yes—
75C23×C3⋊D3C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C4⋊(C3⋊D3)—24no—
80C2×C4⋊(C3⋊D3)—44no—
81C2×C4⋊(C3⋊D3)C2314yes—
82C2×C4⋊(C3⋊D3)C2318yes—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3C2314yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6—44no—
93C2×C3×Dic6C2314yes—
94C2×C3×Dic6C2318yes—
95C2×#624—44no—
96C2×#624C2318yes—
97C32×C4⋊C4C2314yes—
98#3752C2318yes—
99C3×C4⋊Dic3C2314yes—
100C3×Dic3⋊C4C2318yes—
101C3×Dic3⋊C4C2318yes—
102C3×C4×Dic3C2318yes—
103C3×C4×Dic3C2314yes—
104C3×C4×Dic3C2314yes—
105#3724C2314yes—
106#3724C2314yes—
107Dic3⋊Dic3C2318yes—
108#3722C2314yes—
109#3722C2318yes—
110#3722C2318yes—
111#3722C2318yes—
112#3722C2318yes—
113#3722C2314yes—
114C2×#542—91noSylow
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C22×D12—31no—
118C22×D12—31no—
119C22×D12—32no—
120C22×D12—32no—
121C22×D12—61no—
122C22×D12—62no—
123C22×C4×D3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—32no—
126C22×C4×D3—32no—
127C22×C4×D3—61no—
128C22×Dic6C2×D311yescharacteristic
129C22×Dic6C2×D312yes—
130C3×C4⋊Q8—38no—
131C3×C4×Q8—38no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—32no—
134C2×C3×C4⋊C4—32no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4C2×D311yescharacteristic
137C2×C3×C4⋊C4C2×D311yescharacteristic
138C2×C3×C42—31no—
139C2×C3×C42—31no—
140C2×C3×C42—32no—
141#947—316no—
142#947—38no—
143#946—38no—
144#946—316no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—62no—
160C2×C4⋊Dic3—32no—
161C2×C4⋊Dic3C2×D311yescharacteristic
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4C2×D312yes—
168C2×Dic3⋊C4C2×D312yes—
169C2×C4×Dic3C2×D311yescharacteristic
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D312yes—
172#898—316no—
173#897—38no—
174#896—316no—
175#895—38no—
176#895—38no—
177#895—68no—
178#894—316no—
179#894—316no—
180#893—38no—
181#888C2×D318yescomplemented
182#887C2×D318yescomplemented
183#876—316no—
184#875—38no—
185#875—316no—
186C4×D12—38no—
187#872—38no—
188#872—38no—
189C23×C32C2411yescharacteristic
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3—24no—
193C22×C3⋊D3—24no—
194C22×C3⋊D3—22no—
195C22×C3⋊D3—24no—
196C22×C3⋊D3C2412yes—
197C22×C3⋊D3C2414yes—
198C2×C32×C4—24no—
199C2×C32×C4#4114yes—
200C2×C32×C4C2414yes—
201C2×C32×C4C2412yes—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3C2412yes—
204C4⋊(C3⋊D3)—28no—
205C4⋊(C3⋊D3)—48no—
206C4×C3⋊D3—28no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2412yes—
219C3×Dic6—28no—
220C3×Dic6—48no—
221#624—48no—
222#542—916no—
223C2×C4⋊Q8—31no—
224C2×#126—92no—
225C2×#124—91no—
226C2×#124—92no—
227C2×#123—92no—
228C2×C22⋊Q8—92no—
229C2×C22⋊Q8—91no—
230C2×#121—91no—
231C2×C4×Q8—31no—
232C2×C4×D4—91no—
233C2×#117—91no—
234C23×D3—31no—
235C23×D3—32no—
236C23×D3—32no—
237C23×D3—31no—
238C23×D3—61no—
239C23×D3—62no—
240C2×C3×Q8—34no—
241C2×C3×Q8—38no—
242C2×C3×Q8—64no—
243C2×C3×Q8—124no—
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—32no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—32no—
252C22×C3×C4C22×D312yes—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—61no—
259C22×Dic3C22×D311yescharacteristic
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D312yes—
265C2×D12—34no—
266C2×D12—34no—
267C2×D12—38no—
268C2×D12—38no—
269C2×D12—64no—
270C2×D12—68no—
271C2×D12—64no—
272C2×D12—64no—
273C2×D12—124no—
274C2×D12—124no—
275C2×D12—124no—
276C2×D12—128no—
277C2×C4×D3—34no—
278C2×C4×D3—34no—
279C2×C4×D3—38no—
280C2×C4×D3—38no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—64no—
284C2×C4×D3—124no—
285C2×C4×D3—124no—
286C2×C4×D3—124no—
287C2×Dic6—24no—
288C2×Dic6—44no—
289C2×Dic6C22×D314yes—
290C2×Dic6C22×D318yes—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4—38no—
294C3×C4⋊C4—38no—
295C3×C4⋊C4C22×D314yes—
296C3×C4⋊C4C22×D314yes—
297C3×C42—34no—
298C3×C42—34no—
299C3×C42—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—34no—
303(C2×D3)⋊C4—34no—
304(C2×D3)⋊C4—34no—
305(C2×D3)⋊C4—34no—
306(C2×D3)⋊C4—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—38no—
309(C2×D3)⋊C4—38no—
310(C2×D3)⋊C4—38no—
311(C2×D3)⋊C4—38no—
312(C2×D3)⋊C4—38no—
313(C2×D3)⋊C4—38no—
314(C2×D3)⋊C4—68no—
315C4⋊Dic3—38no—
316C4⋊Dic3C22×D314yes—
317Dic3⋊C4—34no—
318Dic3⋊C4—34no—
319Dic3⋊C4—34no—
320Dic3⋊C4—34no—
321Dic3⋊C4—38no—
322Dic3⋊C4C22×D318yes—
323Dic3⋊C4C22×D318yes—
324C4×Dic3C22×D314yes—
325C4×Dic3C22×D314yes—
326C4×Dic3C22×D318yes—
327C22×C32C2×#4112yes—
328C22×C32H(5,𝔽2)12yes—
329C22×C322−1+412yes—
330C22×C32C2511yescharacteristic
331C2×C3⋊D3—22no—
332C2×C3⋊D3—22no—
333C2×C3⋊D3—24no—
334C2×C3⋊D3—24no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—24no—
337C2×C3⋊D3—44no—
338C2×C3⋊D3—48no—
339C32×C4—24no—
340C32×C4C2×#4114yes—
341C3⋊Dic3—22no—
342C3×Dic3—24no—
343C3×Dic3—22no—
344C3×Dic3—24no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C22×Q8—31no—
349C22×Q8—32no—
350C22×D4—91no—
351C22×D4—92no—
352C23×C4—92no—
353C23×C4—91no—
354C4⋊Q8—38no—
355#126—916no—
356#124—98no—
357#124—916no—
358#123—916no—
359C22⋊Q8—916no—
360C22⋊Q8—98no—
361#121—98no—
362C4×Q8—38no—
363C4×D4—98no—
364#117—98no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4D3211yescharacteristic
372C2×C22⋊C4—91no—
373C2×C22⋊C4—91no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C22⋊C4—92no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—32no—
382C23×C3—21no—
383C23×C3C23×D311yescharacteristic
384C23×C3C23×D311yescharacteristic
385C22×D3—32no—
386C22×D3—34no—
387C22×D3—34no—
388C22×D3—32no—
389C22×D3—62no—
390C22×D3—64no—
391C22×D3—64no—
392C22×D3—62no—
393C22×D3—64no—
394C22×D3—64no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—64no—
398C22×D3—62no—
399C22×D3—64no—
400C22×D3—62no—
401C22×D3—64no—
402C22×D3—64no—
403C22×D3—62no—
404C22×D3—122no—
405C22×D3—122no—
406C22×D3—124no—
407C22×D3—124no—
408C22×D3—124no—
409C3×Q8—68no—
410C3×Q8—128no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—34no—
419C2×C3×C4—32no—
420C2×C3×C4—32no—
421C2×C3×C4—34no—
422C2×C3×C4—44no—
423C2×C3×C4—62no—
424C2×C3×C4—64no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—64no—
428C2×C3×C4—62no—
429C2×C3×C4#23514yes—
430C2×C3×C4#23914yes—
431C2×C3×C4C23×D314yes—
432C2×C3×C4C23×D314yes—
433C2×C3×C4C23×D312yes—
434C2×C3×C4C23×D312yes—
435C2×Dic3—24no—
436C2×Dic3—22no—
437C2×Dic3—24no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—32no—
442C2×Dic3—32no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—122no—
447C2×Dic3C23×D312yes—
448C2×Dic3C23×D312yes—
449C2×Dic3C23×D312yes—
450C2×Dic3C23×D312yes—
451C2×Dic3C23×D314yes—
452C2×Dic3C23×D314yes—
453D12—68no—
454D12—68no—
455D12—128no—
456D12—128no—
457D12—128no—
458D12—1216no—
459C4×D3—68no—
460C4×D3—68no—
461C4×D3—128no—
462C4×D3—128no—
463C4×D3—128no—
464Dic6—28no—
465Dic6—48no—
466C2×C32#54214yescomplemented
467C2×C32C22×#4111yescharacteristic
468C2×C32C2×H(5,𝔽2)11yescharacteristic
469C2×C32C2×2−1+411yescharacteristic
470C3⋊D3—42no—
471C3⋊D3—44no—
472C24—91no—
473C24—92no—
474C2×Q8—34no—
475C2×Q8—38no—
476C2×Q8—64no—
477C2×Q8—124no—
478C2×D4—94no—
479C2×D4—98no—
480C2×D4—184no—
481C2×D4—364no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—32no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—32no—
488C22×C4—98no—
489C22×C4—91no—
490C22×C4—94no—
491C22×C4—184no—
492C22×C4—364no—
493C22×C4C2×D3212yes—
494C22×C4C2×D3211yescharacteristic
495C4⋊C4—34no—
496C4⋊C4—38no—
497C4⋊C4—38no—
498C4⋊C4—94no—
499C4⋊C4—94no—
500C4⋊C4—98no—
501C4⋊C4C2×D3214yes—
502C22⋊C4—94no—
503C22⋊C4—94no—
504C22⋊C4—98no—
505C22⋊C4—98no—
506C22⋊C4—98no—
507C22⋊C4—98no—
508C22⋊C4—98no—
509C42—34no—
510C42—34no—
511C42—38no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—21no—
516C22×C3C2×#23512yes—
517C22×C3#100412yes—
518C22×C3C2×#23912yes—
519C22×C3#100712yes—
520C22×C3#100712yes—
521C22×C3#100912yes—
522C22×C3C24×D311yescharacteristic
523C22×C3C24×D311yescharacteristic
524C2×D3—64no—
525C2×D3—62no—
526C2×D3—64no—
527C2×D3—64no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—64no—
531C2×D3—62no—
532C2×D3—64no—
533C2×D3—62no—
534C2×D3—64no—
535C2×D3—64no—
536C2×D3—62no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—124no—
540C2×D3—124no—
541C2×D3—124no—
542C2×D3—128no—
543C2×D3—124no—
544C2×D3—128no—
545C2×D3—124no—
546C2×D3—128no—
547C2×D3—248no—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—24no—
551C3×C4—44no—
552C3×C4—62no—
553C3×C4—64no—
554C3×C4—62no—
555C3×C4—62no—
556C3×C4—64no—
557C3×C4—62no—
558C3×C4C2×#23514yes—
559C3×C4C2×#23914yes—
560Dic3—24no—
561Dic3—22no—
562Dic3—24no—
563Dic3—22no—
564Dic3—22no—
565Dic3—22no—
566Dic3—62no—
567Dic3—62no—
568Dic3—122no—
569C32C2×#54211yescharacteristic, complemented, Sylow
570C23—92no—
571C23—94no—
572C23—182no—
573C23—184no—
574C23—184no—
575C23—182no—
576C23—182no—
577C23—184no—
578C23C22×D3211yescharacteristic
579Q8—68no—
580Q8—128no—
581D4—188no—
582D4—368no—
583C2×C4—24no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—34no—
587C2×C4—32no—
588C2×C4—32no—
589C2×C4—34no—
590C2×C4—64no—
591C2×C4—62no—
592C2×C4—64no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—92no—
597C2×C4—182no—
598C2×C4—188no—
599C2×C4—368no—
600C2×C4#379914yes—
601C2×C4C22×D3214yes—
602C2×C4C22×D3212yes—
603C2×C3—24no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3#558214yescomplemented
608C2×C3#573314yescomplemented
609C2×C3C22×#23511yescharacteristic
610C2×C3C2×#100411yescharacteristic
611C2×C3C22×#23911yescharacteristic
612C2×C3C2×#100711yescharacteristic
613C2×C3C2×#100711yescharacteristic
614C2×C3C2×#100911yescharacteristic
615D3—124no—
616D3—122no—
617D3—124no—
618D3—122no—
619D3—124no—
620D3—244no—
621C22—182no—
622C22—184no—
623C22—184no—
624C22—182no—
625C22—182no—
626C22—184no—
627C22—364no—
628C22—368no—
629C22C2×#379912yes—
630C22#6431412yes—
631C22#6431612yes—
632C22C23×D3211yescharacteristic
633C4—24no—
634C4—64no—
635C4—62no—
636C4—64no—
637C4—62no—
638C4—62no—
639C4—62no—
640C4—182no—
641C4C2×#379914yes—
642C3—21no—
643C3C2×#558211yescharacteristic, complemented
644C3C2×#573311yescharacteristic, complemented
645C2—362no—
646C2—364no—
647C2#1059435214yesdirect product factor
648C2C22×#379911yescharacteristic
649C2C2×#6431411yescharacteristic
650C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#64104C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#888C2semidirect
3. C2×C3×#887C2semidirect
4. C2×#63897C2semidirect
5. C2×#63894C2semidirect
6. C2×#63888C2semidirect
7. C2×#63874C2semidirect
8. C2×#63871C2semidirect
9. C2×#63868C2semidirect
10. C2×#63864C2semidirect
11. C2×#63864C2semidirect
12. #10594352C2direct (N × H)
30. C3×#888C22semidirect
31. C3×#887C22semidirect
41. #63897C22semidirect
42. #63894C22semidirect
43. #63888C22semidirect
44. #63874C22semidirect
45. #63871C22semidirect
46. #63868C22semidirect
47. #63864C22semidirect
48. #63864C22semidirect
66. C2×#888D3semidirect
67. C2×#887D3semidirect
181. #888C2×D3semidirect
182. #887C2×D3semidirect
466. C2×C32#542semidirect
569. C32C2×#542semidirect
607. C2×C3#5582semidirect
608. C2×C3#5733semidirect
643. C3C2×#5582semidirect
644. C3C2×#5733semidirect
647. C2#10594352direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C3×#8882
C2×C3×#8872
C2×#638972
C2×#638942
C2×#638882
C2×#638742
C2×#638712
C2×#638682
C2×#638642
#105943522
C2×#57333
C2×#55823