Finite Group Databasebeta

← C2×#10595142 #11902619

Subgroups — C2×#10595142 #11902619

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#627C211yesmaximal, characteristic, complemented
2C22×#3805C211yesmaximal, characteristic, complemented
3C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#939C212yesmaximal, complemented
5C2×#63982C211yesmaximal, characteristic, complemented
6C2×#63980C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C212yesmaximal, complemented
8C2×#63959C212yesmaximal, complemented
9#10595142C2116yesmaximal, direct product factor
10C2×#63915C211yesmaximal, characteristic, complemented
11C2×#63893C212yesmaximal, complemented
12C2×#63838C211yesmaximal, characteristic, complemented
13C2×#5598—32nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yes—
20C22×#627—28no—
21C22×#627C2212yes—
22C22×#627C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#627C2218yescomplemented
25C22×#625C2211yescharacteristic
26C2×#3805—28no—
27C2×#3805C2218yescomplemented
28C22×D3×Dic3C2212yes—
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31D4×C3⋊Dic3C2218yescomplemented
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C3×#217C2212yes—
35C3×#939C22116yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2212yes—
38#63982C2218yescomplemented
39#63980C2218yescomplemented
40Dic3×#67C22116yescomplemented
41C2×#3724C2211yescharacteristic
42C2×Dic3⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45#63959C22116yescomplemented
46C2×Dic32C2212yes—
47#63915C2218yescomplemented
48#63893C22116yescomplemented
49#63838C2218yescomplemented
50C22×#237—32no—
51C23×Dic6—32no—
52C2×C3×#121—32no—
53C2×#939—32no—
54C2×#939D312yescomplemented
55C2×#936—32no—
56C2×D4×Dic3—32no—
57C2×D4×Dic3—32no—
58C2×D4×Dic3—61no—
59C2×C4×#67—32no—
60#5598—332no—
61C2×#897—32no—
62C2×#887—32no—
63C2×#885—32no—
64C2×#885—32no—
65C2×#878—32no—
66C2×#878—32no—
67C24×C32C2311yescharacteristic
68C24×C32C2311yescharacteristic
69C23×C3×D3C2312yes—
70C2×C32×D4—24no—
71C2×C32×D4C2314yes—
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3—24no—
74C22×C3⋊Dic3—24no—
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2314yes—
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2314yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C2×C3×#67—28no—
82C2×C3×#67—28no—
83C2×C3×#67C2318yes—
84C2×C3×#67C2318yes—
85C22×C3×Dic3—28no—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2318yes—
89C22×C3×Dic3C2312yes—
90C2×#627—24no—
91C2×#627—28no—
92C2×#627—232no—
93C2×#627D418yescomplemented
94C2×#627C2318yes—
95C2×#627C2314yes—
96C2×#627C2314yes—
97C2×#625—24no—
98C2×#625C2314yes—
99#3805—232no—
100C2×D3×Dic3—28no—
101C2×D3×Dic3C2318yes—
102#3757C2314yes—
103#3757C2314yes—
104C4⋊(C3⋊Dic3)C2314yes—
105C4×C3⋊Dic3C2314yes—
106C3×#217C2318yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×Dic3⋊C4C2318yes—
109#3724C2314yes—
110Dic3⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113Dic32C2318yes—
114C2×#548—91noSylow
115C22×C3×D4—21no—
116C22×C3×D4—32no—
117C22×C3×D4—32no—
118C22×C3×D4C2×D312yes—
119C23×C3×C4—32no—
120C22×#67—32no—
121C22×#67C2×D312yes—
122C22×#67C2×D312yes—
123C23×Dic3—32no—
124C23×Dic3—32no—
125C23×Dic3—32no—
126C23×Dic3—61no—
127C23×Dic3—61no—
128C23×Dic3C2×D312yes—
129C2×#237—316no—
130C2×#237—616no—
131C22×C4×D3—32no—
132C22×Dic6—32no—
133C22×Dic6—32no—
134C22×Dic6—32no—
135C22×Dic6—32no—
136C22×Dic6—316no—
137C22×Dic6—616no—
138C3×#121—316no—
139C2×C3×C4⋊C4—32no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C22⋊C4—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—32no—
145C2×#217—32no—
146C2×#217—61no—
147C2×#217—61no—
148C2×#217C2×D312yes—
149#939—316no—
150#939C2×D3116yescomplemented
151#936—316no—
152D4×Dic3—316no—
153D4×Dic3—316no—
154D4×Dic3—68no—
155C4×#67—316no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4C2×D312yes—
159C2×C4⋊Dic3—32no—
160C2×C4⋊Dic3—32no—
161C2×C4⋊Dic3—61no—
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—61no—
169#897—316no—
170#887—316no—
171#885—316no—
172#885—316no—
173#878—316no—
174#878—316no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32—22no—
180C23×C32#4114yescomplemented
181C23×C32C2412yes—
182C23×C32C2412yes—
183C23×C32C2411yescharacteristic
184C22×C3×D3—24no—
185C22×C3×D3—24no—
186C22×C3×D3—24no—
187C22×C3×D3C2414yes—
188C32×D4—28no—
189C2×C32×C4—22no—
190C2×C32×C4C2412yes—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—28no—
195C2×C3⋊Dic3—28no—
196C2×C3⋊Dic3C2×D414yes—
197C2×C3⋊Dic3C2412yes—
198C2×C3⋊Dic3C2412yes—
199C2×C3⋊Dic3C2412yes—
200C2×C3⋊Dic3C2412yes—
201C3×#67—216no—
202C3×#67—216no—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—216no—
206C2×C3×Dic3C2×D418yes—
207C2×C3×Dic3C2414yes—
208C2×C3×Dic3C2414yes—
209C2×C3×Dic3C2414yes—
210#627—28no—
211#627—216no—
212#627C2×D4116yescomplemented
213#625—28no—
214D3×Dic3—216no—
215C22×#41—91no—
216C23×Q8—91no—
217#548—916no—
218C2×#124—91no—
219C2×#124—92no—
220C2×C22⋊Q8—91no—
221C2×C22⋊Q8—92no—
222C2×#121—32no—
223C2×#121—91no—
224C2×C4×Q8—91no—
225C2×C4×D4—92no—
226C2×C4×D4—91no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—32no—
230C24×C3C22×D312yes—
231C24×C3C22×D312yes—
232C23×D3C22×D312yes—
233C2×C3×D4—28no—
234C2×C3×D4—28no—
235C2×C3×D4—24no—
236C2×C3×D4—38no—
237C2×C3×D4—38no—
238C2×C3×D4—68no—
239C2×C3×D4—68no—
240C2×C3×D4C22×D318yes—
241C22×C3×C4—21no—
242C22×C3×C4—32no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—38no—
246C22×C3×C4—68no—
247C22×C3×C4C22×D312yes—
248C2×#67—28no—
249C2×#67—28no—
250C2×#67—38no—
251C2×#67—68no—
252C2×#67C22×D318yes—
253C2×#67C22×D318yes—
254C22×Dic3—28no—
255C22×Dic3—32no—
256C22×Dic3—38no—
257C22×Dic3—32no—
258C22×Dic3—32no—
259C22×Dic3—32no—
260C22×Dic3—38no—
261C22×Dic3—38no—
262C22×Dic3—61no—
263C22×Dic3—61no—
264C22×Dic3—61no—
265C22×Dic3—61no—
266C22×Dic3—64no—
267C22×Dic3—64no—
268C22×Dic3—68no—
269C22×Dic3—68no—
270C22×Dic3—68no—
271C22×Dic3—124no—
272C22×Dic3—124no—
273C22×Dic3C22×D312yes—
274C22×Dic3C22×D312yes—
275C22×Dic3C22×D318yes—
276C22×Dic3C22×D312yes—
277#237—664no—
278C2×C4×D3—38no—
279C2×C4×D3—68no—
280C2×Dic6—316no—
281C2×Dic6—38no—
282C2×Dic6—38no—
283C2×Dic6—38no—
284C2×Dic6—38no—
285C2×Dic6—664no—
286C2×Dic6—68no—
287C2×Dic6—68no—
288C2×Dic6—68no—
289C3×C4⋊C4—38no—
290C3×C22⋊C4—38no—
291C3×C22⋊C4—38no—
292#217—38no—
293#217—38no—
294#217—38no—
295#217—38no—
296#217—64no—
297#217—64no—
298#217C22×D318yes—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4C22×D318yes—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304C4⋊Dic3—64no—
305Dic3⋊C4—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4C22×D318yes—
308C4×Dic3—38no—
309C4×Dic3—38no—
310C4×Dic3—38no—
311C4×Dic3—64no—
312C22×C32—22no—
313C22×C32—28no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—44no—
319C22×C32C22×D412yes—
320C22×C32C2×#4112yes—
321C22×C32C2×#4114yescomplemented
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—
329C3⋊Dic3—22no—
330C3⋊Dic3—22no—
331C3⋊Dic3—22no—
332C3⋊Dic3C22×D414yes—
333C3×Dic3—24no—
334C3×Dic3—24no—
335C3×Dic3C22×D418yes—
336C2×#41—98no—
337C2×#41—188no—
338C22×Q8—91no—
339C22×Q8—92no—
340C22×Q8—91no—
341C22×Q8—98no—
342C22×Q8—188no—
343C22×D4—32no—
344C22×D4—32no—
345C22×D4—91no—
346C22×D4D3211yescharacteristic
347C23×C4—32no—
348C23×C4—92no—
349C23×C4—91no—
350C23×C4—91no—
351#124—98no—
352#124—916no—
353C22⋊Q8—98no—
354C22⋊Q8—916no—
355#121—316no—
356#121—98no—
357C4×Q8—98no—
358C4×D4—916no—
359C4×D4—98no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4—91no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—32no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4—91no—
370C2×C42—92no—
371C2×C42—91no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—24no—
382C23×C3—34no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—64no—
388C23×C3—64no—
389C23×C3—64no—
390C23×C3#23718yescomplemented
391C23×C3C23×D314yes—
392C23×C3C23×D314yes—
393C23×C3C23×D312yes—
394C22×D3—24no—
395C22×D3—24no—
396C22×D3—24no—
397C22×D3C23×D314yes—
398C3×D4—216no—
399C3×D4—216no—
400C3×D4—616no—
401C3×D4—616no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—22no—
405C2×C3×C4—38no—
406C2×C3×C4—34no—
407C2×C3×C4—34no—
408C2×C3×C4—34no—
409C2×C3×C4—616no—
410C2×C3×C4—64no—
411C2×C3×C4—64no—
412C2×C3×C4C23×D314yes—
413#67—216no—
414#67—216no—
415#67—616no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—216no—
419C2×Dic3—38no—
420C2×Dic3—34no—
421C2×Dic3—34no—
422C2×Dic3—34no—
423C2×Dic3—34no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—616no—
430C2×Dic3—616no—
431C2×Dic3—64no—
432C2×Dic3—64no—
433C2×Dic3—64no—
434C2×Dic3—616no—
435C2×Dic3—128no—
436C2×Dic3—128no—
437C2×Dic3—122no—
438C2×Dic3—122no—
439C2×Dic3—122no—
440C2×Dic3D3×D418yes—
441C2×Dic3C23×D314yes—
442C2×Dic3C23×D314yes—
443C2×Dic3C23×D314yes—
444C4×D3—616no—
445Dic6—332no—
446Dic6—616no—
447Dic6—616no—
448Dic6—616no—
449C2×C32—24no—
450C2×C32—42no—
451C2×C32#54814yescomplemented
452C2×C32C23×D411yescharacteristic
453C2×C32C22×#4111yescharacteristic
454C2×C32C2×2−1+411yescharacteristic
455C3×D3—44no—
456C24—32no—
457C24C2×D3211yescharacteristic
458C24C2×D3211yescharacteristic
459#41—1832no—
460C2×Q8—94no—
461C2×Q8—98no—
462C2×Q8—98no—
463C2×Q8—94no—
464C2×Q8—188no—
465C2×Q8—184no—
466C2×Q8—1832no—
467C2×D4—24no—
468C2×D4—38no—
469C2×D4—38no—
470C2×D4—68no—
471C2×D4—68no—
472C2×D4—94no—
473C2×D4—184no—
474C2×D4C2×D3214yes—
475C22×C4—32no—
476C22×C4—38no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—68no—
480C22×C4—98no—
481C22×C4—91no—
482C22×C4—94no—
483C22×C4—94no—
484C22×C4—91no—
485C22×C4—91no—
486C22×C4—91no—
487C22×C4—188no—
488C22×C4—184no—
489C22×C4—184no—
490C22×C4C2×D3211yescharacteristic
491C4⋊C4—38no—
492C4⋊C4—98no—
493C4⋊C4—94no—
494C4⋊C4—94no—
495C22⋊C4—38no—
496C22⋊C4—38no—
497C22⋊C4—98no—
498C22⋊C4—98no—
499C22⋊C4—94no—
500C22⋊C4—94no—
501C42—98no—
502C42—94no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—216no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—24no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—24no—
514C22×C3—21no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—48no—
519C22×C3—42no—
520C22×C3—48no—
521C22×C3—48no—
522C22×C3—64no—
523C22×C3—64no—
524C22×C3—64no—
525C22×C3—128no—
526C22×C3C2×D3×D414yes—
527C22×C3C2×#23714yes—
528C22×C3C2×#23718yescomplemented
529C22×C3#101014yes—
530C22×C3C24×D312yes—
531C2×D3—24no—
532C2×D3—24no—
533C2×D3—24no—
534C2×D3—48no—
535C3×C4—24no—
536C3×C4—24no—
537C3×C4—38no—
538C3×C4—64no—
539C3×C4—64no—
540Dic3—24no—
541Dic3—24no—
542Dic3—38no—
543Dic3—64no—
544Dic3—64no—
545Dic3—64no—
546Dic3—64no—
547Dic3—122no—
548Dic3—122no—
549Dic3—122no—
550Dic3C2×D3×D418yes—
551C32C2×#54811yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—34no—
558C23—64no—
559C23—64no—
560C23—64no—
561C23#380514yescomplemented
562C23C22×D3212yes—
563C23C22×D3212yes—
564C23C22×D3211yescharacteristic
565Q8—916no—
566Q8—1816no—
567Q8—188no—
568D4—28no—
569D4—616no—
570D4—616no—
571D4—188no—
572C2×C4—22no—
573C2×C4—38no—
574C2×C4—34no—
575C2×C4—34no—
576C2×C4—34no—
577C2×C4—616no—
578C2×C4—64no—
579C2×C4—64no—
580C2×C4—94no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—92no—
584C2×C4—92no—
585C2×C4—1816no—
586C2×C4—188no—
587C2×C4—188no—
588C2×C4—182no—
589C2×C4—182no—
590C2×C4—182no—
591C2×C4C22×D3212yes—
592C2×C3—28no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—24no—
596C2×C3—21no—
597C2×C3—44no—
598C2×C3—44no—
599C2×C3—44no—
600C2×C3—124no—
601C2×C3#559818yescomplemented
602C2×C3C22×D3×D412yes—
603C2×C3C22×#23712yes—
604C2×C3C2×#101012yes—
605D3—44no—
606C22—22no—
607C22—22no—
608C22—28no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—44no—
613C22—64no—
614C22—64no—
615C22—64no—
616C22—128no—
617C22#6430912yes—
618C22D32×D412yes—
619C22C2×#380512yes—
620C22C2×#380514yescomplemented
621C22C23×D3211yescharacteristic
622C4—22no—
623C4—38no—
624C4—64no—
625C4—64no—
626C4—94no—
627C4—182no—
628C4—182no—
629C4—182no—
630C3—21no—
631C3C2×#559812yescomplemented
632C2—24no—
633C2—42no—
634C2—124no—
635C2#1059514214yesdirect product factor
636C2C2×#6430911yescharacteristic
637C2C2×D32×D411yescharacteristic
638C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×#627C2semidirect
2. C22×#3805C2semidirect
3. C2×D4×C3⋊Dic3C2semidirect
4. C2×C3×#939C2semidirect
5. C2×#63982C2semidirect
6. C2×#63980C2semidirect
7. C2×Dic3×#67C2semidirect
8. C2×#63959C2semidirect
9. #10595142C2direct (N × H)
10. C2×#63915C2semidirect
11. C2×#63893C2semidirect
12. C2×#63838C2semidirect
24. C22×#627C22semidirect
27. C2×#3805C22semidirect
31. D4×C3⋊Dic3C22semidirect
35. C3×#939C22semidirect
38. #63982C22semidirect
39. #63980C22semidirect
40. Dic3×#67C22semidirect
45. #63959C22semidirect
47. #63915C22semidirect
48. #63893C22semidirect
49. #63838C22semidirect
54. C2×#939D3semidirect
93. C2×#627D4semidirect
150. #939C2×D3semidirect
180. C23×C32#41semidirect
212. #627C2×D4semidirect
321. C22×C32C2×#41semidirect
390. C23×C3#237semidirect
451. C2×C32#548semidirect
528. C22×C3C2×#237semidirect
551. C32C2×#548semidirect
561. C23#3805semidirect
601. C2×C3#5598semidirect
620. C22C2×#3805semidirect
631. C3C2×#5598semidirect
635. C2#10595142direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×#38052
C2×D4×C3⋊Dic32
C2×C3×#9392
C2×#639822
C2×#639802
C2×Dic3×#672
C2×#639592
#105951422
C2×#639152
C2×#638932
C2×#638382
C2×#55983