Finite Group Databasebeta

← C2×#10594556 #11903412

Subgroups — C2×#10594556 #11903412

Order 1152.

2385 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic, complemented
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63907C212yesmaximal
5C2×C4×#626C211yesmaximal, characteristic
6C2×#63868C212yesmaximal, complemented
7C2×#63861C212yesmaximal, complemented
8C2×#63857C211yesmaximal, characteristic, complemented
9C2×#63849C211yesmaximal, characteristic, complemented
10C2×#63844C211yesmaximal, characteristic, complemented
11C2×Dic3×Dic6C212yesmaximal, complemented
12#10594556C2116yesmaximal, direct product factor
13C2×#5732—31nomaximal
14C2×#5533—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2212yes—
19C22×#626C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2212yes—
22C2×C4⋊(C3⋊Dic3)C2212yes—
23#64106C2218yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#892C2218yescomplemented
31C3×#888C2218yescomplemented
32C2×#3724C2212yes—
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×#3722C2212yes—
36C2×#3722C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×Dic32C2212yes—
40C2×Dic32C2212yes—
41#63907C22116yes—
42C4×#626C2218yes—
43#63868C22116yescomplemented
44#63861C22116yescomplemented
45#63857C2218yescomplemented
46#63849C2218yescomplemented
47#63844C2218yescomplemented
48Dic3×Dic6C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×#117—31no—
51C2×#947—32no—
52C2×Q8×Dic3—32no—
53C2×C4×#67—31no—
54C2×#924—31no—
55#5732—316no—
56#5533—316no—
57C2×#898—32no—
58C2×#898—32no—
59C2×#897—31no—
60C2×#897—31no—
61C2×#897—31no—
62C2×#897—61no—
63C2×#892—31no—
64C2×#892—31no—
65C2×#892D311yescharacteristic, complemented
66C2×#888D311yescharacteristic, complemented
67C2×#887—31no—
68C2×#885—32no—
69C2×#879—32no—
70C2×#876—32no—
71C2×C4×D12—31no—
72C2×C4×Dic6—32no—
73C2×C4×Dic6—31no—
74C23×C3⋊D3C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C2×C4×C3⋊D3—24no—
81C2×C4×C3⋊D3C2314yes—
82C2×#634—24no—
83C2×#634C2314yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3C2314yes—
91C2×C3×Dic6—28no—
92C2×C3×Dic6C2318yes—
93C2×#626—24no—
94C2×#626C2314yes—
95C32×C4⋊C4C2314yes—
96#3752C2318yes—
97C4⋊(C3⋊Dic3)C2318yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×C4⋊Dic3C2314yes—
100C3×C4⋊Dic3C2314yes—
101C3×Dic3⋊C4C2318yes—
102C3×C4×Dic3C2314yes—
103C3×C4×Dic3C2318yes—
104#3724C2318yes—
105Dic3⋊Dic3C2314yes—
106Dic3⋊Dic3C2318yes—
107#3722C2318yes—
108#3722C2314yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2314yes—
111Dic32C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—32no—
115C23×C3×C4—31no—
116C22×#67—31no—
117C22×D12—31no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C4×D3—61no—
121C22×C4×D3C2×D311yescharacteristic
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—61no—
125C22×Dic6C2×D312yes—
126C3×C4⋊Q8—38no—
127C3×#117—38no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C22⋊C4—32no—
135C2×C3×C42—31no—
136C2×C3×C42—32no—
137C2×#217—31no—
138C2×#217—32no—
139#947—316no—
140Q8×Dic3—316no—
141C4×#67—38no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—62no—
151C2×(C2×D3)⋊C4C2×D312yes—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—32no—
156C2×C4⋊Dic3—62no—
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×C4⋊Dic3C2×D311yescharacteristic
159#924—38no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4C2×D312yes—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3C2×D311yescharacteristic
170C2×C4×Dic3C2×D312yes—
171#898—316no—
172#898—316no—
173#897—38no—
174#897—38no—
175#897—38no—
176#897—68no—
177#892—38no—
178#892—38no—
179#892C2×D318yescomplemented
180#888C2×D318yescomplemented
181#887—38no—
182#885—316no—
183#879—316no—
184#876—316no—
185C4×D12—38no—
186C4×Dic6—316no—
187C4×Dic6—38no—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3C2412yes—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3C2412yes—
197C2×C32×C4—24no—
198C2×C32×C4#4114yes—
199C2×C32×C4C2414yes—
200C2×C32×C4C2412yes—
201C2×C3⋊Dic3—24no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3C2412yes—
204C2×C3⋊Dic3C2414yes—
205C4×C3⋊D3—28no—
206#634—28no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3#4114yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C3×C4×D3—28no—
218C3×Dic6—216no—
219#626—28no—
220#556—916no—
221C2×C4⋊Q8—31no—
222C2×#126—92no—
223C2×#126—92no—
224C2×#124—92no—
225C2×C22⋊Q8—91no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×Q8—92no—
229C2×C4×D4—91no—
230C2×#117—31no—
231C2×#117—91no—
232C24×C3—31no—
233C23×D3—31no—
234C23×D3—31no—
235C23×D3—61no—
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—38no—
238C2×C3×Q8—68no—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—31no—
242C22×C3×C4—32no—
243C22×C3×C4—32no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—34no—
247C22×C3×C4—64no—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D312yes—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—34no—
253C2×#67—64no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—32no—
257C22×Dic3—32no—
258C22×Dic3—61no—
259C22×Dic3—62no—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C2×D12—34no—
266C2×D12—64no—
267C2×C4×D3—24no—
268C2×C4×D3—34no—
269C2×C4×D3—34no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—124no—
274C2×C4×D3C22×D314yes—
275C2×Dic6—28no—
276C2×Dic6—34no—
277C2×Dic6—34no—
278C2×Dic6—64no—
279C2×Dic6—64no—
280C2×Dic6—64no—
281C2×Dic6—124no—
282C2×Dic6C22×D318yes—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—34no—
286C3×C4⋊C4—38no—
287C3×C4⋊C4C22×D314yes—
288C3×C4⋊C4C22×D314yes—
289C3×C22⋊C4—38no—
290C3×C42—34no—
291C3×C42—38no—
292#217—34no—
293#217—38no—
294(C2×D3)⋊C4—34no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—68no—
303(C2×D3)⋊C4C22×D318yes—
304C4⋊Dic3—38no—
305C4⋊Dic3—38no—
306C4⋊Dic3—34no—
307C4⋊Dic3—38no—
308C4⋊Dic3—68no—
309C4⋊Dic3C22×D314yes—
310C4⋊Dic3C22×D314yes—
311Dic3⋊C4—34no—
312Dic3⋊C4—38no—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4C22×D318yes—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—38no—
319C4×Dic3—38no—
320C4×Dic3C22×D314yes—
321C4×Dic3C22×D318yes—
322C22×C32C2×#4112yes—
323C22×C32C2×#4112yes—
324C22×C322−1+412yes—
325C22×C32C2511yescharacteristic
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3—44no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C2×C3×D3—44no—
334C32×C4—24no—
335C32×C4C2×#4114yes—
336C3⋊Dic3—24no—
337C3⋊Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—22no—
341C3×Dic3—24no—
342C3×Dic3C2×#4114yes—
343C22×Q8—32no—
344C22×Q8—91no—
345C22×D4—91no—
346C23×C4—31no—
347C23×C4—91no—
348C4⋊Q8—38no—
349#126—916no—
350#126—916no—
351#124—916no—
352C22⋊Q8—98no—
353C22⋊Q8—98no—
354C4×Q8—98no—
355C4×Q8—916no—
356C4×D4—98no—
357#117—38no—
358#117—98no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4D3211yescharacteristic
367C2×C22⋊C4—32no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4—91no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C42—32no—
374C2×C42—31no—
375C2×C42—92no—
376C2×C42—92no—
377C23×C3—21no—
378C23×C3—32no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3C23×D311yescharacteristic
383C23×C3C23×D311yescharacteristic
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—32no—
388C22×D3—32no—
389C22×D3—62no—
390C22×D3—64no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—122no—
398C22×D3—122no—
399C22×D3C23×D312yes—
400C3×Q8—616no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—34no—
407C2×C3×C4—32no—
408C2×C3×C4—34no—
409C2×C3×C4—34no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—44no—
413C2×C3×C4—62no—
414C2×C3×C4—64no—
415C2×C3×C4—64no—
416C2×C3×C4—62no—
417C2×C3×C4—68no—
418C2×C3×C4#23514yes—
419C2×C3×C4#23914yes—
420C2×C3×C4C23×D314yes—
421C2×C3×C4C23×D314yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D312yes—
424#67—68no—
425C2×Dic3—22no—
426C2×Dic3—24no—
427C2×Dic3—22no—
428C2×Dic3—24no—
429C2×Dic3—32no—
430C2×Dic3—32no—
431C2×Dic3—34no—
432C2×Dic3—34no—
433C2×Dic3—62no—
434C2×Dic3—64no—
435C2×Dic3—64no—
436C2×Dic3—62no—
437C2×Dic3—64no—
438C2×Dic3—62no—
439C2×Dic3—124no—
440C2×Dic3—122no—
441C2×Dic3#23714yes—
442C2×Dic3C23×D314yes—
443C2×Dic3C23×D314yes—
444C2×Dic3C23×D312yes—
445C2×Dic3C23×D312yes—
446C2×Dic3C23×D312yes—
447D12—68no—
448C4×D3—28no—
449C4×D3—68no—
450C4×D3—68no—
451C4×D3—128no—
452Dic6—216no—
453Dic6—68no—
454Dic6—68no—
455Dic6—128no—
456C2×C32#55614yescomplemented
457C2×C32C22×#4111yescharacteristic
458C2×C32C22×#4111yescharacteristic
459C2×C32C2×2−1+411yescharacteristic
460C3⋊D3—42no—
461C3×D3—42no—
462C24—31no—
463C24—91no—
464C2×Q8—38no—
465C2×Q8—68no—
466C2×Q8—94no—
467C2×Q8—184no—
468C2×D4—94no—
469C2×D4—184no—
470C22×C4—31no—
471C22×C4—31no—
472C22×C4—32no—
473C22×C4—31no—
474C22×C4—32no—
475C22×C4—34no—
476C22×C4—64no—
477C22×C4—91no—
478C22×C4—92no—
479C22×C4—94no—
480C22×C4—184no—
481C22×C4C2×D3212yes—
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—34no—
484C4⋊C4—34no—
485C4⋊C4—38no—
486C4⋊C4—94no—
487C4⋊C4—98no—
488C4⋊C4—98no—
489C4⋊C4—98no—
490C4⋊C4C2×D3214yes—
491C22⋊C4—38no—
492C22⋊C4—98no—
493C22⋊C4—94no—
494C22⋊C4—94no—
495C22⋊C4—98no—
496C22⋊C4—98no—
497C42—38no—
498C42—34no—
499C42—98no—
500C42—98no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—62no—
508C22×C3—124no—
509C22×C3C2×#23512yes—
510C22×C3C2×#23712yes—
511C22×C3C2×#23912yes—
512C22×C3#100712yes—
513C22×C3D3×#4112yes—
514C22×C3#101012yes—
515C22×C3C24×D311yescharacteristic
516C22×C3C24×D311yescharacteristic
517C2×D3—22no—
518C2×D3—22no—
519C2×D3—22no—
520C2×D3—44no—
521C2×D3—64no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—128no—
531C2×D3—124no—
532C2×D3—124no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—34no—
537C3×C4—44no—
538C3×C4—62no—
539C3×C4—64no—
540C3×C4—64no—
541C3×C4—62no—
542C3×C4C2×#23514yes—
543C3×C4C2×#23914yes—
544Dic3—22no—
545Dic3—24no—
546Dic3—22no—
547Dic3—24no—
548Dic3—64no—
549Dic3—62no—
550Dic3—64no—
551Dic3—62no—
552Dic3—124no—
553Dic3—122no—
554Dic3C2×#23714yes—
555C32C2×#55611yescharacteristic, complemented, Sylow
556C23—32no—
557C23—62no—
558C23—62no—
559C23—62no—
560C23—92no—
561C23—182no—
562C23—182no—
563C23—182no—
564C23C22×D3211yescharacteristic
565Q8—616no—
566Q8—188no—
567D4—188no—
568C2×C4—24no—
569C2×C4—34no—
570C2×C4—32no—
571C2×C4—32no—
572C2×C4—34no—
573C2×C4—32no—
574C2×C4—34no—
575C2×C4—62no—
576C2×C4—64no—
577C2×C4—64no—
578C2×C4—62no—
579C2×C4—68no—
580C2×C4—92no—
581C2×C4—94no—
582C2×C4—182no—
583C2×C4—184no—
584C2×C4—188no—
585C2×C4#379914yes—
586C2×C4C22×D3214yes—
587C2×C4C22×D3212yes—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—24no—
592C2×C3—122no—
593C2×C3#553314yescomplemented
594C2×C3#573214yescomplemented
595C2×C3C22×#23511yescharacteristic
596C2×C3C22×#23711yescharacteristic
597C2×C3C22×#23911yescharacteristic
598C2×C3C2×#100711yescharacteristic
599C2×C3C2×D3×#4111yescharacteristic
600C2×C3C2×#101011yescharacteristic
601D3—42no—
602D3—124no—
603D3—122no—
604D3—122no—
605C22—62no—
606C22—62no—
607C22—62no—
608C22—124no—
609C22—182no—
610C22—182no—
611C22—182no—
612C22—364no—
613C22C2×#379912yes—
614C22D3×#23712yes—
615C22#6431512yes—
616C22C23×D3211yescharacteristic
617C4—24no—
618C4—34no—
619C4—62no—
620C4—64no—
621C4—64no—
622C4—62no—
623C4—182no—
624C4—184no—
625C4C2×#379914yes—
626C3—21no—
627C3C2×#553311yescharacteristic, complemented
628C3C2×#573211yescharacteristic, complemented
629C2—122no—
630C2—362no—
631C2#1059455614yesdirect product factor
632C2C22×#379911yescharacteristic
633C2C2×D3×#23711yescharacteristic
634C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#556
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×#64106C2semidirect
2. C2×C3×#892C2semidirect
3. C2×C3×#888C2semidirect
6. C2×#63868C2semidirect
7. C2×#63861C2semidirect
8. C2×#63857C2semidirect
9. C2×#63849C2semidirect
10. C2×#63844C2semidirect
11. C2×Dic3×Dic6C2semidirect
12. #10594556C2direct (N × H)
23. #64106C22semidirect
30. C3×#892C22semidirect
31. C3×#888C22semidirect
43. #63868C22semidirect
44. #63861C22semidirect
45. #63857C22semidirect
46. #63849C22semidirect
47. #63844C22semidirect
48. Dic3×Dic6C22semidirect
65. C2×#892D3semidirect
66. C2×#888D3semidirect
179. #892C2×D3semidirect
180. #888C2×D3semidirect
456. C2×C32#556semidirect
555. C32C2×#556semidirect
593. C2×C3#5533semidirect
594. C2×C3#5732semidirect
627. C3C2×#5533semidirect
628. C3C2×#5732semidirect
631. C2#10594556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×C3×#8922
C2×C3×#8882
C2×#639072
C2×C4×#6262
C2×#638682
C2×#638612
C2×#638572
C2×#638492
C2×#638442
C2×Dic3×Dic62
#105945562
C2×#57323
C2×#55333