Finite Group Databasebeta

← C2×#10591528 #11857527

Subgroups — C2×#10591528 #11857527

Order 1152.

1681 conjugacy classes of subgroups.

The subgroup lattice has 667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C2×#63955C212yesmaximal, complemented
3C2×#63661C211yesmaximal, characteristic, complemented
4C2×C3×#834C211yesmaximal, characteristic, complemented
5C2×#63580C212yesmaximal, complemented
6#10591528C218yesmaximal, direct product factor
7C2×#5240—31nomaximal
8C2×#4740—31nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C3×#67C411yescharacteristic, complemented
11C22×C3×#67C2211yescharacteristic
12C23×C3×Dic3C411yescharacteristic, complemented
13C23×C3×Dic3C2211yescharacteristic
14C2×C3×#237—22no—
15C2×C3×#237—24no—
16C2×C3×#237—22no—
17C2×C3×#237C414yescomplemented
18C2×C3×#237C2214yes—
19C22×C3×C4×D3C411yescharacteristic, complemented
20C22×C3×Dic6C411yescharacteristic, complemented
21C2×#3757C2212yes—
22C2×C3×#217C2212yes—
23C2×Dic3⋊Dic3—22no—
24#63955—24no—
25#63955C2218yescomplemented
26C2×Dic32—22no—
27#63661C2214yescomplemented
28C3×#834C2214yescomplemented
29#63580C2218yescomplemented
30C22×C3×#41—31no—
31C22×#237D311yescharacteristic
32C2×#926—32no—
33C2×#877—32no—
34C2×C3×#99—31no—
35#5240—38no—
36C2×#834—31no—
37C2×#834—31no—
38C2×#834—32no—
39C2×#834—61no—
40C2×#834D311yescharacteristic, complemented
41C2×#806—32no—
42#4740—38no—
43C24×C32C2×C411yescharacteristic
44C24×C32C2311yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C2×C32×D4—22no—
47C2×C32×D4—22no—
48C2×C32×D4C2×C412yes—
49C2×C32×D4C2312yes—
50C22×C32×C4C2×C411yescharacteristic
51C22×C3⋊Dic3—22no—
52C2×C3×#67—22no—
53C2×C3×#67—22no—
54C2×C3×#67—22no—
55C2×C3×#67—22no—
56C2×C3×#67C2×C412yes—
57C2×C3×#67C2×C414yescomplemented
58C2×C3×#67C2312yes—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3C2×C411yescharacteristic
64C22×C3×Dic3C2×C411yescharacteristic
65C22×C3×Dic3C2×C411yescharacteristic
66C22×C3×Dic3C2×C412yes—
67C22×C3×Dic3C2×C414yescomplemented
68C22×C3×Dic3D412yes—
69C22×C3×Dic3D414yes—
70C22×C3×Dic3D412yes—
71C22×C3×Dic3C2312yes—
72C3×#237—28no—
73C3×#237—28no—
74C3×#237—28no—
75C3×#237—28no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3C2×C414yescomplemented
80C2×C3×Dic6—22no—
81C2×C3×Dic6—22no—
82C2×C3×Dic6C2×C414yescomplemented
83#3757—22no—
84#3757C2314yes—
85C3×#217—22no—
86C3×#217C2314yes—
87Dic3⋊Dic3—28no—
88Dic32—28no—
89C2×#410—91noSylow
90C2×C3×#41—34no—
91C2×C3×#41—34no—
92C2×C3×#41—62no—
93C2×C3×#41—62no—
94C2×C3×#41—64no—
95C22×C3×Q8—31no—
96C22×C3×D4—21no—
97C22×C3×D4—31no—
98C22×C3×D4—31no—
99C22×C3×D4C2×D311yescharacteristic
100C22×C3×D4C2×D311yescharacteristic
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×C3×C4—31no—
104C22×#67Dic311yescharacteristic, complemented
105C22×#67C2×D311yescharacteristic
106C23×Dic3Dic311yescharacteristic, complemented
107C23×Dic3C2×D311yescharacteristic
108C2×#237—24no—
109C2×#237—22no—
110C2×#237—22no—
111C2×#237Dic314yescomplemented
112C2×#237C2×D314yes—
113C22×C4×D3Dic311yescharacteristic, complemented
114C22×Dic6Dic311yescharacteristic, complemented
115C2×C3×C22⋊C4—32no—
116C2×#217—32no—
117C2×#217—32no—
118C2×#217—62no—
119C2×#217C2×D312yes—
120#926—38no—
121#926—64no—
122C2×C4⋊Dic3—62no—
123C2×Dic3⋊C4—62no—
124C2×C4×Dic3—62no—
125C2×C4×Dic3—62no—
126#877—38no—
127#877—64no—
128C3×#99—34no—
129#834—34no—
130#834—34no—
131#834—38no—
132#834—64no—
133#834C2×D314yescomplemented
134#806—38no—
135C23×C32—21no—
136C23×C32—21no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32C22×C411yescharacteristic
140C23×C32C22×C412yes—
141C23×C32C22×C411yescharacteristic
142C23×C32C2×D412yes—
143C23×C32C2×D412yes—
144C23×C32C2411yescharacteristic
145C22×C3×D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3—42no—
148C22×C3×D3C22×C412yes—
149C32×D4—24no—
150C32×D4—24no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4C22×C412yes—
154C2×C3⋊Dic3—24no—
155C2×C3⋊Dic3—44no—
156C3×#67—24no—
157C3×#67—24no—
158C3×#67—28no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—24no—
162C2×C3×Dic3—24no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3—44no—
165C2×C3×Dic3C22⋊C412yes—
166C2×C3×Dic3C22⋊C412yes—
167C2×C3×Dic3C22⋊C412yes—
168C2×C3×Dic3C22⋊C411yescharacteristic
169C2×C3×Dic3C22⋊C411yescharacteristic
170C2×C3×Dic3C22⋊C414yes—
171C2×C3×Dic3C22⋊C414yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C2×D414yes—
176C2×C3×Dic3C2×D414yes—
177C3×C4×D3—24no—
178C3×C4×D3—24no—
179C3×Dic6—28no—
180C22×#41—31no—
181C2×#117—92no—
182#410—98no—
183C2×#99—31no—
184C2×#99—92no—
185C2×#99—91no—
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—31no—
189C24×C3C4×D311yescharacteristic
190C24×C3C2×Dic311yescharacteristic
191C24×C3C22×D311yescharacteristic
192C24×C3C22×D311yescharacteristic
193C23×D3C2×Dic311yescharacteristic
194C3×#41—68no—
195C3×#41—68no—
196C3×#41—68no—
197C3×#41—68no—
198C2×C3×Q8—34no—
199C2×C3×Q8—62no—
200C2×C3×Q8—62no—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—22no—
206C2×C3×D4—22no—
207C2×C3×D4—32no—
208C2×C3×D4—34no—
209C2×C3×D4—32no—
210C2×C3×D4—42no—
211C2×C3×D4—42no—
212C2×C3×D4—62no—
213C2×C3×D4—62no—
214C2×C3×D4—62no—
215C2×C3×D4—62no—
216C2×C3×D4C4×D312yes—
217C2×C3×D4C2×Dic312yes—
218C2×C3×D4C22×D312yes—
219C2×C3×D4C22×D312yes—
220C22×C3×C4—21no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—34no—
227C22×C3×C4—32no—
228C22×C3×C4—31no—
229C22×C3×C4—34no—
230C22×C3×C4—34no—
231C22×C3×C4—62no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4—62no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C22×C3×C4—62no—
238C22×C3×C4C4×D311yescharacteristic
239C22×C3×C4C2×Dic311yescharacteristic
240C2×#67—22no—
241C2×#67—22no—
242C2×#67—22no—
243C2×#67—22no—
244C2×#67C2×Dic312yes—
245C2×#67C2×Dic314yescomplemented
246C2×#67C22×D312yes—
247C22×Dic3—22no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—22no—
251C22×Dic3—62no—
252C22×Dic3—62no—
253C22×Dic3—122no—
254C22×Dic3C2×Dic311yescharacteristic
255C22×Dic3C2×Dic311yescharacteristic
256C22×Dic3C2×Dic311yescharacteristic
257C22×Dic3C2×Dic312yes—
258C22×Dic3C2×Dic314yescomplemented
259C22×Dic3#6714yes—
260C22×Dic3#6712yes—
261C22×Dic3#6712yes—
262C22×Dic3C22×D312yes—
263#237—28no—
264#237—28no—
265#237—28no—
266#237—28no—
267C2×C4×D3—22no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3C2×Dic314yescomplemented
271C2×Dic6—22no—
272C2×Dic6—22no—
273C2×Dic6C2×Dic314yescomplemented
274C3×C22⋊C4—34no—
275C3×C22⋊C4—62no—
276#217—22no—
277#217—34no—
278#217—34no—
279#217—64no—
280#217—62no—
281#217—62no—
282#217—122no—
283#217C22×D314yes—
284C4⋊Dic3—68no—
285Dic3⋊C4—68no—
286C4×Dic3—68no—
287C4×Dic3—68no—
288C22×C32—24no—
289C22×C32—22no—
290C22×C32—22no—
291C22×C32—41no—
292C22×C32—42no—
293C22×C32—41no—
294C22×C32—42no—
295C22×C32—42no—
296C22×C32—42no—
297C22×C32C2×C22⋊C411yescharacteristic
298C22×C32C2×C22⋊C412yes—
299C22×C32C2×C22⋊C411yescharacteristic
300C22×C32C23×C411yescharacteristic
301C22×C32C22×D412yes—
302C2×C3×D3—22no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C32×C4—22no—
307C3⋊Dic3—44no—
308C3×Dic3—22no—
309C3×Dic3—44no—
310C3×Dic3C2×C22⋊C414yes—
311C3×Dic3C2×C22⋊C412yes—
312C3×Dic3C2×C22⋊C412yes—
313C2×#41—34no—
314C2×#41—34no—
315C2×#41—62no—
316C2×#41—62no—
317C2×#41—64no—
318C22×Q8—31no—
319C22×D4—31no—
320C22×D4—31no—
321C22×D4D3211yescharacteristic
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325#117—98no—
326#117—184no—
327C2×C4⋊C4—182no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—92no—
330C2×C42—182no—
331#99—34no—
332#99—98no—
333#99—94no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—32no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—61no—
352C23×C3—61no—
353C23×C3—82no—
354C23×C3—82no—
355C23×C3—122no—
356C23×C3C2×C4×D311yescharacteristic
357C23×C3C2×C4×D312yes—
358C23×C3C2×C4×D311yescharacteristic
359C23×C3D3×D412yes—
360C23×C3D3×D412yes—
361C23×C3C22×Dic311yescharacteristic
362C23×C3C22×Dic312yes—
363C23×C3C22×Dic311yescharacteristic
364C23×C3C2×#6712yes—
365C23×C3C2×#6712yes—
366C23×C3C23×D311yescharacteristic
367C23×C3C23×D311yescharacteristic
368C22×D3—21no—
369C22×D3—21no—
370C22×D3—42no—
371C22×D3C22×Dic312yes—
372C3×Q8—68no—
373C3×D4—24no—
374C3×D4—24no—
375C3×D4—24no—
376C3×D4—24no—
377C3×D4—44no—
378C3×D4—44no—
379C3×D4—68no—
380C3×D4—64no—
381C3×D4—64no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—32no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—32no—
391C2×C3×C4—32no—
392C2×C3×C4—34no—
393C2×C3×C4—34no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—34no—
397C2×C3×C4—34no—
398C2×C3×C4—32no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—64no—
402C2×C3×C4—64no—
403C2×C3×C4—64no—
404C2×C3×C4—64no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—64no—
408C2×C3×C4—124no—
409C2×C3×C4C2×C4×D312yes—
410C2×C3×C4C22×Dic312yes—
411#67—24no—
412#67—24no—
413#67—28no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—24no—
419C2×Dic3—44no—
420C2×Dic3—64no—
421C2×Dic3—64no—
422C2×Dic3—124no—
423C2×Dic3—124no—
424C2×Dic3—124no—
425C2×Dic3—244no—
426C2×Dic3#21712yes—
427C2×Dic3#21712yes—
428C2×Dic3#21712yes—
429C2×Dic3#21711yescharacteristic
430C2×Dic3#21711yescharacteristic
431C2×Dic3#21714yes—
432C2×Dic3#21714yes—
433C2×Dic3C22×Dic312yes—
434C2×Dic3C22×Dic312yes—
435C2×Dic3C22×Dic312yes—
436C2×Dic3C2×#6714yes—
437C2×Dic3C2×#6714yes—
438C4×D3—24no—
439C4×D3—24no—
440Dic6—28no—
441C2×C32—22no—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32—22no—
445C2×C32—42no—
446C2×C32#41012yescomplemented
447C2×C32C22×C22⋊C411yescharacteristic
448C3×D3—42no—
449C24—31no—
450C24D3×Dic311yescharacteristic
451C24C2×D3211yescharacteristic
452#41—68no—
453#41—68no—
454#41—68no—
455#41—68no—
456C2×Q8—34no—
457C2×Q8—62no—
458C2×Q8—62no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—32no—
462C2×D4—32no—
463C2×D4—34no—
464C2×D4—62no—
465C2×D4—62no—
466C2×D4—62no—
467C2×D4—62no—
468C2×D4D3×Dic312yes—
469C2×D4C2×D3212yes—
470C22×C4—32no—
471C22×C4—31no—
472C22×C4—31no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—32no—
476C22×C4—34no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—34no—
480C22×C4—62no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—62no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—62no—
487C22×C4—182no—
488C22×C4D3×Dic311yescharacteristic
489C4⋊C4—188no—
490C22⋊C4—34no—
491C22⋊C4—62no—
492C22⋊C4—94no—
493C22⋊C4—182no—
494C42—188no—
495C22×C3—24no—
496C22×C3—22no—
497C22×C3—24no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—44no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—41no—
510C22×C3—42no—
511C22×C3—41no—
512C22×C3—42no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—62no—
522C22×C3—82no—
523C22×C3—81no—
524C22×C3—81no—
525C22×C3—82no—
526C22×C3—82no—
527C22×C3—82no—
528C22×C3—122no—
529C22×C3—122no—
530C22×C3—122no—
531C22×C3D3×C22⋊C411yescharacteristic
532C22×C3D3×C22⋊C412yes—
533C22×C3D3×C22⋊C411yescharacteristic
534C22×C3C2×#21711yescharacteristic
535C22×C3C2×#21712yes—
536C22×C3C2×#21711yescharacteristic
537C22×C3C22×C4×D311yescharacteristic
538C22×C3C2×D3×D412yes—
539C22×C3C23×Dic311yescharacteristic
540C22×C3C22×#6712yes—
541C2×D3—22no—
542C2×D3—42no—
543C2×D3—42no—
544C2×D3—42no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—32no—
548C3×C4—32no—
549C3×C4—34no—
550C3×C4—42no—
551C3×C4—62no—
552C3×C4—124no—
553Dic3—22no—
554Dic3—44no—
555Dic3—124no—
556Dic3—124no—
557Dic3—244no—
558Dic3C2×#21714yes—
559Dic3C2×#21712yes—
560Dic3C2×#21712yes—
561C32C2×#41011yescharacteristic, complemented, Sylow
562C23—21no—
563C23—21no—
564C23—32no—
565C23—42no—
566C23—42no—
567C23—61no—
568C23—61no—
569C23—122no—
570C23C2×D3×Dic311yescharacteristic
571C23C2×D3×Dic312yes—
572C23C2×D3×Dic311yescharacteristic
573C23D3×#6712yes—
574C23D3×#6712yes—
575C23C22×D3211yescharacteristic
576Q8—68no—
577D4—24no—
578D4—24no—
579D4—68no—
580D4—64no—
581D4—64no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—34no—
587C2×C4—34no—
588C2×C4—32no—
589C2×C4—32no—
590C2×C4—34no—
591C2×C4—34no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—32no—
595C2×C4—32no—
596C2×C4—64no—
597C2×C4—64no—
598C2×C4—64no—
599C2×C4—64no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—64no—
603C2×C4—124no—
604C2×C4—184no—
605C2×C4—364no—
606C2×C4C2×D3×Dic312yes—
607C2×C3—22no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—22no—
611C2×C3—22no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—22no—
615C2×C3—22no—
616C2×C3—21no—
617C2×C3—42no—
618C2×C3—41no—
619C2×C3—41no—
620C2×C3—42no—
621C2×C3—42no—
622C2×C3—42no—
623C2×C3—82no—
624C2×C3—122no—
625C2×C3#474012yescomplemented
626C2×C3#524012yescomplemented
627C2×C3C2×D3×C22⋊C411yescharacteristic
628C2×C3C22×#21711yescharacteristic
629D3—42no—
630C22—24no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—62no—
640C22—122no—
641C22—122no—
642C22—122no—
643C22D3×#21711yescharacteristic
644C22D3×#21712yes—
645C22D3×#21711yescharacteristic
646C22C22×D3×Dic311yescharacteristic
647C22C2×D3×#6712yes—
648C4—22no—
649C4—32no—
650C4—32no—
651C4—34no—
652C4—62no—
653C4—124no—
654C4—364no—
655C3—21no—
656C3C2×#474011yescharacteristic, complemented
657C3C2×#524011yescharacteristic, complemented
658C2—22no—
659C2—21no—
660C2—21no—
661C2—22no—
662C2—42no—
663C2—122no—
664C2#1059152812yesdirect product factor
665C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC22×C32×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#237C2
cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#410
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63955C2semidirect
3. C2×#63661C2semidirect
4. C2×C3×#834C2semidirect
5. C2×#63580C2semidirect
6. #10591528C2direct (N × H)
10. C22×C3×#67C4semidirect
12. C23×C3×Dic3C4semidirect
17. C2×C3×#237C4semidirect
19. C22×C3×C4×D3C4semidirect
20. C22×C3×Dic6C4semidirect
25. #63955C22semidirect
27. #63661C22semidirect
28. C3×#834C22semidirect
29. #63580C22semidirect
40. C2×#834D3semidirect
57. C2×C3×#67C2×C4semidirect
67. C22×C3×Dic3C2×C4semidirect
79. C2×C3×C4×D3C2×C4semidirect
82. C2×C3×Dic6C2×C4semidirect
104. C22×#67Dic3semidirect
106. C23×Dic3Dic3semidirect
111. C2×#237Dic3semidirect
113. C22×C4×D3Dic3semidirect
114. C22×Dic6Dic3semidirect
133. #834C2×D3semidirect
245. C2×#67C2×Dic3semidirect
258. C22×Dic3C2×Dic3semidirect
270. C2×C4×D3C2×Dic3semidirect
273. C2×Dic6C2×Dic3semidirect
446. C2×C32#410semidirect
561. C32C2×#410semidirect
625. C2×C3#4740semidirect
626. C2×C3#5240semidirect
656. C3C2×#4740semidirect
657. C3C2×#5240semidirect
664. C2#10591528direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×#639552
C2×#636612
C2×C3×#8342
C2×#635802
#105915282
C2×#52403
C2×#47403