Finite Group Databasebeta

← C2×#10594448 #11900857

Subgroups — C2×#10594448 #11900857

Order 1152.

2501 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×C3×#890C211yesmaximal, characteristic, complemented
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×#63895C212yesmaximal
6C2×#63888C212yesmaximal
7C2×C4×#624C211yesmaximal, characteristic
8C2×#63869C211yesmaximal, characteristic, complemented
9C2×#63849C211yesmaximal, characteristic
10C2×#63843C212yesmaximal, complemented
11C2×#63838C212yesmaximal, complemented
12#10594448C2116yesmaximal, direct product factor
13C2×#5728—31nomaximal
14C2×#5688—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C22×#627C2212yes—
18C22×#624C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2212yes—
24#64101C2218yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#890C2218yescomplemented
33C3×#888C2218yescomplemented
34C2×#3724C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×#3722C2212yes—
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2212yes—
40C2×Dic32C2211yescharacteristic
41#63918C2218yescomplemented
42#63895C22116yes—
43#63888C22116yes—
44C4×#624C2218yes—
45#63869C2218yescomplemented
46#63849C2218yes—
47#63843C22116yescomplemented
48#63838C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×#125—31no—
51C2×#946—32no—
52C2×Q8×Dic3—32no—
53#5728—316no—
54#5688—316no—
55C2×#897—32no—
56C2×#896—32no—
57C2×#896—32no—
58C2×#892—31no—
59C2×#892—31no—
60C2×#892—31no—
61C2×#892—31no—
62C2×#892—61no—
63C2×#890—31no—
64C2×#890D311yescharacteristic, complemented
65C2×#888—31no—
66C2×#888D311yescharacteristic, complemented
67C2×#887—32no—
68C2×#887—32no—
69C2×#887—32no—
70C2×C42×D3—31no—
71C2×C42×D3—31no—
72C2×#870—31no—
73C2×#869—31no—
74C23×C3⋊D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C4×C3⋊D3Q818yescomplemented
80C2×C4×C3⋊D3C2314yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×Dic6—28no—
88C2×C3×Dic6C2318yes—
89C2×#627—28no—
90C2×#627C2318yes—
91C2×#624—24no—
92C2×#624—24no—
93C2×#624C2314yes—
94C2×#624C2314yes—
95C32×C4⋊C4C2314yes—
96#3752C2318yes—
97C4⋊(C3⋊Dic3)C2314yes—
98C4×C3⋊Dic3C2318yes—
99C3×C4⋊Dic3C2314yes—
100C3×C4⋊Dic3C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×Dic3⋊C4C2318yes—
103C3×Dic3⋊C4C2318yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106#3724C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109#3722C2318yes—
110Dic32C2314yes—
111Dic32C2318yes—
112Dic32C2314yes—
113C2×#533—91noSylow
114C22×C3×Q8—32no—
115C22×C4×D3—31no—
116C22×C4×D3—31no—
117C22×C4×D3—31no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—61no—
122C22×Dic6—32no—
123C22×Dic6—32no—
124C22×Dic6C2×D312yes—
125C3×C4⋊Q8—38no—
126C3×#125—38no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137#946—316no—
138Q8×Dic3—316no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—62no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—61no—
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×C4⋊Dic3C2×D312yes—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4C2×D312yes—
157C2×Dic3⋊C4C2×D312yes—
158C2×C4×Dic3—32no—
159C2×C4×Dic3—32no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—32no—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—62no—
167C2×C4×Dic3C2×D311yescharacteristic
168C2×C4×Dic3C2×D311yescharacteristic
169#897—316no—
170#896—316no—
171#896—316no—
172#892—38no—
173#892—38no—
174#892—38no—
175#892—38no—
176#892—68no—
177#890—38no—
178#890C2×D318yescomplemented
179#888—38no—
180#888C2×D318yescomplemented
181#887—316no—
182#887—316no—
183#887—316no—
184C42×D3—38no—
185C42×D3—38no—
186#870—38no—
187#869—38no—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3C2×Q814yes—
192C22×C3⋊D3C2412yes—
193C2×C32×C4—24no—
194C2×C32×C4C2×Q814yes—
195C2×C32×C4C2414yes—
196C2×C32×C4C2412yes—
197C2×C3⋊Dic3—24no—
198C2×C3⋊Dic3C2×Q814yes—
199C2×C3⋊Dic3C2414yes—
200C2×C3⋊Dic3C2412yes—
201C4×C3⋊D3C2×Q8116yescomplemented
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3#4114yes—
207C2×C3×Dic3#4114yes—
208C2×C3×Dic3C2414yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C3×Dic6—216no—
215#627—216no—
216#624—28no—
217#624—28no—
218#533—916no—
219C2×C4⋊Q8—31no—
220C2×C4⋊Q8—91no—
221C2×#125—31no—
222C2×#125—91no—
223C2×C22⋊Q8—92no—
224C2×C22⋊Q8—92no—
225C2×C4×Q8—92no—
226C2×C4×Q8—92no—
227C2×#117—91no—
228C2×#117—91no—
229C22×C42—91no—
230C23×D3—31no—
231C23×D3—31no—
232C23×D3—61no—
233C2×C3×Q8—38no—
234C2×C3×Q8—68no—
235C22×C3×C4—21no—
236C22×C3×C4—22no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—32no—
243C22×C3×C4C22×D312yes—
244C22×C3×C4C22×D312yes—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×Dic3—31no—
248C22×Dic3—31no—
249C22×Dic3—32no—
250C22×Dic3—32no—
251C22×Dic3—61no—
252C22×Dic3—62no—
253C22×Dic3C22×D311yescharacteristic
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D311yescharacteristic
259C2×C4×D3—38no—
260C2×C4×D3—38no—
261C2×C4×D3—34no—
262C2×C4×D3—34no—
263C2×C4×D3—34no—
264C2×C4×D3—34no—
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—64no—
268C2×C4×D3—68no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×Dic6—28no—
274C2×Dic6—38no—
275C2×Dic6—38no—
276C2×Dic6—68no—
277C2×Dic6—68no—
278C2×Dic6C22×D318yes—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—38no—
281C3×C4⋊C4—38no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—34no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4C22×D314yes—
286C3×C4⋊C4C22×D314yes—
287C3×C42—34no—
288C3×C42—34no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—68no—
294C4⋊Dic3—34no—
295C4⋊Dic3—34no—
296C4⋊Dic3—38no—
297C4⋊Dic3—38no—
298C4⋊Dic3—64no—
299C4⋊Dic3C22×D314yes—
300C4⋊Dic3C22×D314yes—
301C4⋊Dic3C22×D318yes—
302Dic3⋊C4—38no—
303Dic3⋊C4—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4—38no—
306Dic3⋊C4C22×D318yes—
307Dic3⋊C4C22×D318yes—
308C4×Dic3—38no—
309C4×Dic3—38no—
310C4×Dic3—34no—
311C4×Dic3—34no—
312C4×Dic3—34no—
313C4×Dic3—34no—
314C4×Dic3—38no—
315C4×Dic3—38no—
316C4×Dic3—68no—
317C4×Dic3C22×D314yes—
318C4×Dic3C22×D314yes—
319C22×C32C22×Q812yes—
320C22×C32C2×#4112yes—
321C22×C32C2×#4112yes—
322C22×C32C2511yescharacteristic
323C2×C3⋊D3—28no—
324C2×C3⋊D3—22no—
325C2×C3⋊D3—22no—
326C2×C3⋊D3C22×Q814yes—
327C32×C4—24no—
328C32×C4C22×Q814yes—
329C3⋊Dic3—24no—
330C3⋊Dic3C22×Q814yes—
331C3×Dic3—22no—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—24no—
335C3×Dic3C2×#4114yes—
336C3×Dic3C2×#4114yes—
337C22×Q8—32no—
338C22×Q8—92no—
339C23×C4—91no—
340C23×C4—91no—
341C23×C4—91no—
342C4⋊Q8—38no—
343C4⋊Q8—98no—
344#125—38no—
345#125—98no—
346C22⋊Q8—916no—
347C22⋊Q8—916no—
348C4×Q8—916no—
349C4×Q8—916no—
350#117—98no—
351#117—98no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4—32no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—92no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—92no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4D3211yescharacteristic
362C2×C22⋊C4—92no—
363C2×C22⋊C4—92no—
364C2×C42—31no—
365C2×C42—31no—
366C2×C42—98no—
367C2×C42—92no—
368C2×C42—91no—
369C2×C42—91no—
370C2×C42—92no—
371C23×C3—21no—
372C23×C3C23×D311yescharacteristic
373C23×C3C23×D311yescharacteristic
374C22×D3—34no—
375C22×D3—34no—
376C22×D3—32no—
377C22×D3—32no—
378C22×D3—64no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—122no—
385C22×D3—122no—
386C3×Q8—616no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—34no—
393C2×C3×C4—34no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—34no—
399C2×C3×C4—34no—
400C2×C3×C4—44no—
401C2×C3×C4—62no—
402C2×C3×C4—64no—
403C2×C3×C4—62no—
404C2×C3×C4—64no—
405C2×C3×C4D3×Q814yes—
406C2×C3×C4D3×Q814yes—
407C2×C3×C4C23×D314yes—
408C2×C3×C4C23×D314yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—34no—
416C2×Dic3—34no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—34no—
420C2×Dic3—34no—
421C2×Dic3—64no—
422C2×Dic3—62no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—124no—
427C2×Dic3#23714yes—
428C2×Dic3#23914yes—
429C2×Dic3C23×D312yes—
430C2×Dic3C23×D312yes—
431C2×Dic3C23×D314yes—
432C2×Dic3C23×D314yes—
433C2×Dic3C23×D312yes—
434C2×Dic3C23×D312yes—
435C4×D3—316no—
436C4×D3—316no—
437C4×D3—616no—
438C4×D3—68no—
439C4×D3—68no—
440C4×D3—68no—
441C4×D3—68no—
442Dic6—216no—
443Dic6—616no—
444Dic6—616no—
445C2×C32#53314yescomplemented
446C2×C32C23×Q811yescharacteristic
447C2×C32C22×#4111yescharacteristic
448C2×C32C22×#4111yescharacteristic
449C3⋊D3—24no—
450C24—91no—
451C2×Q8—38no—
452C2×Q8—68no—
453C2×Q8—98no—
454C2×Q8—188no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—31no—
458C22×C4—31no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—94no—
462C22×C4—94no—
463C22×C4—91no—
464C22×C4—94no—
465C22×C4—98no—
466C22×C4—92no—
467C22×C4—184no—
468C22×C4—184no—
469C22×C4C2×D3212yes—
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—34no—
472C4⋊C4—34no—
473C4⋊C4—38no—
474C4⋊C4—38no—
475C4⋊C4—38no—
476C4⋊C4—98no—
477C4⋊C4—98no—
478C4⋊C4—98no—
479C4⋊C4—94no—
480C4⋊C4C2×D3214yes—
481C22⋊C4—98no—
482C22⋊C4—98no—
483C42—34no—
484C42—34no—
485C42—94no—
486C42—94no—
487C42—98no—
488C42—98no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—21no—
493C22×C3C2×#23712yes—
494C22×C3C2×D3×Q812yes—
495C22×C3C2×D3×Q812yes—
496C22×C3C2×#23912yes—
497C22×C3D3×#4112yes—
498C22×C3D3×#4112yes—
499C22×C3C24×D311yescharacteristic
500C22×C3C24×D311yescharacteristic
501C2×D3—34no—
502C2×D3—34no—
503C2×D3—64no—
504C2×D3—68no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—68no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—128no—
513C3×C4—24no—
514C3×C4—24no—
515C3×C4—24no—
516C3×C4—34no—
517C3×C4—34no—
518C3×C4—44no—
519C3×C4—62no—
520C3×C4—64no—
521C3×C4—62no—
522C3×C4—64no—
523C3×C4C2×D3×Q814yes—
524C3×C4C2×D3×Q814yes—
525Dic3—24no—
526Dic3—24no—
527Dic3—22no—
528Dic3—22no—
529Dic3—34no—
530Dic3—34no—
531Dic3—64no—
532Dic3—64no—
533Dic3—64no—
534Dic3—124no—
535Dic3C2×#23714yes—
536Dic3C2×#23914yes—
537C32C2×#53311yescharacteristic, complemented, Sylow
538C23—94no—
539C23—92no—
540C23—182no—
541C23—182no—
542C23C22×D3211yescharacteristic
543Q8—616no—
544Q8—1816no—
545C2×C4—24no—
546C2×C4—34no—
547C2×C4—34no—
548C2×C4—32no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—34no—
553C2×C4—34no—
554C2×C4—62no—
555C2×C4—64no—
556C2×C4—62no—
557C2×C4—64no—
558C2×C4—94no—
559C2×C4—92no—
560C2×C4—916no—
561C2×C4—94no—
562C2×C4—188no—
563C2×C4—188no—
564C2×C4—184no—
565C2×C4#379714yes—
566C2×C4C22×D3214yes—
567C2×C4C22×D3212yes—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—24no—
572C2×C3#568814yescomplemented
573C2×C3#572814yescomplemented
574C2×C3C22×#23711yescharacteristic
575C2×C3C22×D3×Q811yescharacteristic
576C2×C3C22×D3×Q811yescharacteristic
577C2×C3C22×#23911yescharacteristic
578C2×C3C2×D3×#4111yescharacteristic
579C2×C3C2×D3×#4111yescharacteristic
580D3—64no—
581D3—64no—
582D3—124no—
583C22—94no—
584C22—182no—
585C22—182no—
586C22—188no—
587C22C2×#379712yes—
588C22D3×#23712yes—
589C22D3×#23912yes—
590C22C23×D3211yescharacteristic
591C4—24no—
592C4—34no—
593C4—34no—
594C4—62no—
595C4—64no—
596C4—62no—
597C4—64no—
598C4—94no—
599C4—184no—
600C4C2×#379714yes—
601C3—21no—
602C3C2×#568811yescharacteristic, complemented
603C3C2×#572811yescharacteristic, complemented
604C2—184no—
605C2#1059444814yesdirect product factor
606C2C22×#379711yescharacteristic
607C2C2×D3×#23711yescharacteristic
608C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#533
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×#890C2semidirect
3. C2×C3×#888C2semidirect
4. C2×#63918C2semidirect
8. C2×#63869C2semidirect
10. C2×#63843C2semidirect
11. C2×#63838C2semidirect
12. #10594448C2direct (N × H)
32. C3×#890C22semidirect
33. C3×#888C22semidirect
41. #63918C22semidirect
45. #63869C22semidirect
47. #63843C22semidirect
48. #63838C22semidirect
64. C2×#890D3semidirect
66. C2×#888D3semidirect
79. C2×C4×C3⋊D3Q8semidirect
178. #890C2×D3semidirect
180. #888C2×D3semidirect
201. C4×C3⋊D3C2×Q8semidirect
445. C2×C32#533semidirect
537. C32C2×#533semidirect
572. C2×C3#5688semidirect
573. C2×C3#5728semidirect
602. C3C2×#5688semidirect
603. C3C2×#5728semidirect
605. C2#10594448direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641012
C2×C3×#8902
C2×C3×#8882
C2×#639182
C2×#638952
C2×#638882
C2×C4×#6242
C2×#638692
C2×#638492
C2×#638432
C2×#638382
#105944482
C2×#57283
C2×#56883