Finite Group Databasebeta

← C2×#10595206 #11903155

Subgroups — C2×#10595206 #11903155

Order 1152.

2717 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#939C212yesmaximal, complemented
3C2×#63980C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C2×Dic3×#67C212yesmaximal, complemented
6C2×#63969C212yesmaximal, complemented
7C22×#3724C211yesmaximal, characteristic, complemented
8C2×#63957C211yesmaximal, characteristic, complemented
9#10595206C2116yesmaximal, direct product factor
10C2×#63902C211yesmaximal, characteristic, complemented
11C2×#63870C211yesmaximal, characteristic, complemented
12C2×#63861C212yesmaximal, complemented
13C2×#5601—32nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yes—
20C22×#625C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×#3757C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24D4×C3⋊Dic3C2218yescomplemented
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×#217C2212yes—
28C3×#939C22116yescomplemented
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31#63980C2218yescomplemented
32#63980C2218yescomplemented
33Dic3×#67C22116yescomplemented
34#63969C22116yescomplemented
35C2×#3724C2212yes—
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×#3724C2218yescomplemented
40C2×Dic3⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42C2×(C2×D3)⋊Dic3C2212yes—
43#63957C2218yescomplemented
44C2×Dic32C2212yes—
45#63902C2218yescomplemented
46#63870C2218yescomplemented
47#63861C22116yescomplemented
48C2×C3×#121—32no—
49C2×#939—32no—
50C2×#939—32no—
51C2×#939D312yescomplemented
52C2×#935—32no—
53C2×D4×Dic3—32no—
54C2×D4×Dic3—32no—
55C2×D4×Dic3—61no—
56C2×C4×#67—32no—
57C22×Dic3⋊C4—32no—
58#5601—332no—
59C2×#898—32no—
60C2×#889—32no—
61C2×#883—32no—
62C2×#67⋊C4—32no—
63C2×#879—32no—
64C2×#877—32no—
65C24×C32C2311yescharacteristic
66C24×C32C2311yescharacteristic
67C23×C3×D3C2312yes—
68C2×C32×D4—24no—
69C2×C32×D4C2314yes—
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3—24no—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2314yes—
77C22×C3⋊Dic3C2314yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C3×#67—28no—
80C2×C3×#67—44no—
81C2×C3×#67C2318yes—
82C2×C3×#67C2318yes—
83C22×C3×Dic3—44no—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2318yes—
88C2×#625—24no—
89C2×#625C2314yes—
90C2×D3×Dic3—44no—
91C2×D3×Dic3C2318yes—
92#3757C2314yes—
93#3757C2314yes—
94C4⋊(C3⋊Dic3)C2314yes—
95C4×C3⋊Dic3C2314yes—
96C3×#217C2318yes—
97C3×(C2×D3)⋊C4C2318yes—
98C3×Dic3⋊C4C2318yes—
99#3724C2318yes—
100#3724C2314yes—
101#3724C2314yes—
102#3724C2314yes—
103Dic3⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yes—
105(C2×D3)⋊Dic3C2318yes—
106Dic32C2318yes—
107C2×#553—91noSylow
108C22×C3×D4—21no—
109C22×C3×D4—32no—
110C22×C3×D4—32no—
111C22×C3×D4C2×D312yes—
112C23×C3×C4—32no—
113C22×#67—32no—
114C22×#67C2×D312yes—
115C22×#67C2×D312yes—
116C23×Dic3—32no—
117C23×Dic3—32no—
118C23×Dic3—32no—
119C23×Dic3—61no—
120C23×Dic3—61no—
121C23×Dic3C2×D312yes—
122C22×C4×D3—32no—
123C3×#121—316no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4—32no—
127C2×#217—32no—
128C2×#217—32no—
129C2×#217—32no—
130C2×#217—32no—
131C2×#217—61no—
132C2×#217—61no—
133C2×#217C2×D312yes—
134#939—316no—
135#939—316no—
136#939C2×D3116yescomplemented
137#935—316no—
138D4×Dic3—316no—
139D4×Dic3—316no—
140D4×Dic3—68no—
141C4×#67—316no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4C2×D312yes—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—61no—
148C2×Dic3⋊C4—32no—
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—316no—
155C2×Dic3⋊C4C2×D312yes—
156C2×C4×Dic3—32no—
157C2×C4×Dic3—32no—
158C2×C4×Dic3—32no—
159C2×C4×Dic3—61no—
160#898—316no—
161#889—316no—
162#883—316no—
163#67⋊C4—316no—
164#879—316no—
165#877—316no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32#4114yes—
172C23×C32C2412yes—
173C23×C32C2412yes—
174C23×C32C2411yescharacteristic
175C22×C3×D3—24no—
176C22×C3×D3—24no—
177C22×C3×D3—24no—
178C22×C3×D3C2414yes—
179C32×D4—28no—
180C2×C32×C4—22no—
181C2×C32×C4C2412yes—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—28no—
186C2×C3⋊Dic3—28no—
187C2×C3⋊Dic3#4114yes—
188C2×C3⋊Dic3C2412yes—
189C2×C3⋊Dic3C2412yes—
190C2×C3⋊Dic3C2412yes—
191C2×C3⋊Dic3C2412yes—
192C3×#67—216no—
193C3×#67—48no—
194C2×C3×Dic3—24no—
195C2×C3×Dic3—24no—
196C2×C3×Dic3—24no—
197C2×C3×Dic3—48no—
198C2×C3×Dic3C2414yes—
199C2×C3×Dic3C2414yes—
200C2×C3×Dic3C2414yes—
201#625—28no—
202D3×Dic3—48no—
203#553—916no—
204C2×#126—92no—
205C2×#125—91no—
206C2×#123—92no—
207C2×#121—32no—
208C2×#121—91no—
209C2×#121—91no—
210C2×C4×D4—91no—
211C2×C4×D4—92no—
212C2×C4×D4—91no—
213C2×#117—91no—
214C22×C4⋊C4—91no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—32no—
218C24×C3C22×D312yes—
219C24×C3C22×D312yes—
220C23×D3C22×D312yes—
221C2×C3×D4—28no—
222C2×C3×D4—28no—
223C2×C3×D4—24no—
224C2×C3×D4—38no—
225C2×C3×D4—38no—
226C2×C3×D4—68no—
227C2×C3×D4—124no—
228C2×C3×D4C22×D318yes—
229C22×C3×C4—21no—
230C22×C3×C4—32no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—38no—
234C22×C3×C4—124no—
235C22×C3×C4C22×D312yes—
236C2×#67—28no—
237C2×#67—38no—
238C2×#67—44no—
239C2×#67—68no—
240C2×#67C22×D318yes—
241C2×#67C22×D318yes—
242C22×Dic3—32no—
243C22×Dic3—38no—
244C22×Dic3—32no—
245C22×Dic3—32no—
246C22×Dic3—32no—
247C22×Dic3—38no—
248C22×Dic3—38no—
249C22×Dic3—44no—
250C22×Dic3—61no—
251C22×Dic3—61no—
252C22×Dic3—61no—
253C22×Dic3—61no—
254C22×Dic3—64no—
255C22×Dic3—64no—
256C22×Dic3—68no—
257C22×Dic3—68no—
258C22×Dic3—124no—
259C22×Dic3—124no—
260C22×Dic3—124no—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D318yes—
265C2×C4×D3—38no—
266C2×C4×D3—124no—
267C3×C4⋊C4—38no—
268C3×C22⋊C4—38no—
269C3×C22⋊C4—38no—
270#217—38no—
271#217—38no—
272#217—38no—
273#217—38no—
274#217—64no—
275#217—64no—
276#217C22×D318yes—
277(C2×D3)⋊C4—38no—
278(C2×D3)⋊C4—38no—
279(C2×D3)⋊C4C22×D318yes—
280C4⋊Dic3—38no—
281C4⋊Dic3—38no—
282C4⋊Dic3—64no—
283Dic3⋊C4—38no—
284Dic3⋊C4—38no—
285Dic3⋊C4—38no—
286Dic3⋊C4—38no—
287Dic3⋊C4—38no—
288Dic3⋊C4—38no—
289Dic3⋊C4C22×D318yes—
290C4×Dic3—38no—
291C4×Dic3—38no—
292C4×Dic3—38no—
293C4×Dic3—64no—
294C22×C32—22no—
295C22×C32—28no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—44no—
301C22×C32C2×#4114yes—
302C22×C32C2×#4112yes—
303C22×C32C2×#4112yes—
304C22×C32H(5,𝔽2)12yes—
305C22×C32C2511yescharacteristic
306C2×C3×D3—24no—
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—48no—
310C32×C4—22no—
311C3⋊Dic3—22no—
312C3⋊Dic3—22no—
313C3⋊Dic3—22no—
314C3⋊Dic3C2×#4114yes—
315C3×Dic3—24no—
316C3×Dic3—24no—
317C3×Dic3—24no—
318C22×D4—32no—
319C22×D4—32no—
320C22×D4—91no—
321C22×D4D3211yescharacteristic
322C23×C4—32no—
323C23×C4—92no—
324C23×C4—91no—
325C23×C4—91no—
326#126—916no—
327#125—98no—
328#123—916no—
329#121—316no—
330#121—98no—
331#121—98no—
332C4×D4—98no—
333C4×D4—916no—
334C4×D4—98no—
335#117—98no—
336C2×C4⋊C4—32no—
337C2×C4⋊C4—91no—
338C2×C4⋊C4—91no—
339C2×C4⋊C4—92no—
340C2×C4⋊C4—98no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—92no—
343C2×C4⋊C4—91no—
344C2×C22⋊C4—32no—
345C2×C22⋊C4—32no—
346C2×C22⋊C4—92no—
347C2×C22⋊C4—92no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C42—92no—
351C2×C42—91no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—24no—
362C23×C3—34no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—64no—
368C23×C3—64no—
369C23×C3—64no—
370C23×C3#23718yes—
371C23×C3C23×D314yes—
372C23×C3C23×D314yes—
373C23×C3C23×D312yes—
374C22×D3—24no—
375C22×D3—24no—
376C22×D3—24no—
377C22×D3C23×D314yes—
378C3×D4—216no—
379C3×D4—216no—
380C3×D4—616no—
381C3×D4—128no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—34no—
386C2×C3×C4—34no—
387C2×C3×C4—34no—
388C2×C3×C4—64no—
389C2×C3×C4—64no—
390C2×C3×C4—64no—
391C2×C3×C4—128no—
392C2×C3×C4C23×D314yes—
393#67—216no—
394#67—48no—
395#67—616no—
396C2×Dic3—24no—
397C2×Dic3—24no—
398C2×Dic3—24no—
399C2×Dic3—38no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—34no—
404C2×Dic3—48no—
405C2×Dic3—64no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—616no—
411C2×Dic3—616no—
412C2×Dic3—64no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3—128no—
416C2×Dic3—128no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3—128no—
421C2×Dic3C23×D314yes—
422C2×Dic3C23×D314yes—
423C2×Dic3C23×D314yes—
424C4×D3—128no—
425C2×C32—24no—
426C2×C32—42no—
427C2×C32#55314yescomplemented
428C2×C32C22×#4111yescharacteristic
429C2×C32C22×#4111yescharacteristic
430C2×C32C2×H(5,𝔽2)11yescharacteristic
431C3×D3—44no—
432C24—32no—
433C24C2×D3211yescharacteristic
434C24C2×D3211yescharacteristic
435C2×D4—24no—
436C2×D4—38no—
437C2×D4—38no—
438C2×D4—68no—
439C2×D4—94no—
440C2×D4—124no—
441C2×D4—184no—
442C2×D4C2×D3214yes—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—38no—
447C22×C4—98no—
448C22×C4—91no—
449C22×C4—94no—
450C22×C4—94no—
451C22×C4—91no—
452C22×C4—91no—
453C22×C4—91no—
454C22×C4—124no—
455C22×C4—184no—
456C22×C4—184no—
457C22×C4—364no—
458C22×C4C2×D3211yescharacteristic
459C4⋊C4—38no—
460C4⋊C4—94no—
461C4⋊C4—94no—
462C4⋊C4—98no—
463C4⋊C4—94no—
464C4⋊C4—98no—
465C4⋊C4—94no—
466C22⋊C4—38no—
467C22⋊C4—38no—
468C22⋊C4—98no—
469C22⋊C4—98no—
470C22⋊C4—94no—
471C22⋊C4—94no—
472C42—98no—
473C42—94no—
474C22×C3—24no—
475C22×C3—24no—
476C22×C3—216no—
477C22×C3—24no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—24no—
485C22×C3—21no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—48no—
490C22×C3—42no—
491C22×C3—48no—
492C22×C3—48no—
493C22×C3—64no—
494C22×C3—64no—
495C22×C3—64no—
496C22×C3—128no—
497C22×C3C2×#23718yes—
498C22×C3C2×#23714yes—
499C22×C3#100414yes—
500C22×C3D3×#4114yes—
501C22×C3C24×D312yes—
502C2×D3—24no—
503C2×D3—24no—
504C2×D3—24no—
505C2×D3—48no—
506C3×C4—24no—
507C3×C4—24no—
508C3×C4—64no—
509C3×C4—64no—
510C3×C4—64no—
511Dic3—24no—
512Dic3—24no—
513Dic3—24no—
514Dic3—38no—
515Dic3—64no—
516Dic3—64no—
517Dic3—64no—
518Dic3—64no—
519Dic3—122no—
520Dic3—122no—
521Dic3—122no—
522C32C2×#55311yescharacteristic, complemented, Sylow
523C23—22no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—22no—
528C23—34no—
529C23—64no—
530C23—64no—
531C23—64no—
532C23#380514yes—
533C23C22×D3212yes—
534C23C22×D3212yes—
535C23C22×D3211yescharacteristic
536D4—28no—
537D4—616no—
538D4—128no—
539D4—188no—
540C2×C4—22no—
541C2×C4—34no—
542C2×C4—34no—
543C2×C4—34no—
544C2×C4—64no—
545C2×C4—64no—
546C2×C4—64no—
547C2×C4—94no—
548C2×C4—92no—
549C2×C4—92no—
550C2×C4—92no—
551C2×C4—92no—
552C2×C4—128no—
553C2×C4—188no—
554C2×C4—188no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—182no—
558C2×C4—368no—
559C2×C4C22×D3212yes—
560C2×C3—28no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—24no—
565C2×C3—44no—
566C2×C3—44no—
567C2×C3—44no—
568C2×C3—124no—
569C2×C3#560118yescomplemented
570C2×C3C22×#23712yes—
571C2×C3C2×#100412yes—
572C2×C3C2×D3×#4112yes—
573D3—44no—
574C22—22no—
575C22—22no—
576C22—28no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—44no—
581C22—64no—
582C22—64no—
583C22—64no—
584C22—128no—
585C22#6431212yes—
586C22#6431312yes—
587C22C2×#380514yes—
588C22C2×#380512yes—
589C22C23×D3211yescharacteristic
590C4—22no—
591C4—64no—
592C4—64no—
593C4—64no—
594C4—94no—
595C4—182no—
596C4—182no—
597C4—182no—
598C3—21no—
599C3C2×#560112yescomplemented
600C2—24no—
601C2—42no—
602C2—124no—
603C2#1059520614yesdirect product factor
604C2C2×#6431211yescharacteristic
605C2C2×#6431311yescharacteristic
606C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. C2×C3×#939C2semidirect
3. C2×#63980C2semidirect
4. C2×#63980C2semidirect
5. C2×Dic3×#67C2semidirect
6. C2×#63969C2semidirect
7. C22×#3724C2semidirect
8. C2×#63957C2semidirect
9. #10595206C2direct (N × H)
10. C2×#63902C2semidirect
11. C2×#63870C2semidirect
12. C2×#63861C2semidirect
24. D4×C3⋊Dic3C22semidirect
28. C3×#939C22semidirect
31. #63980C22semidirect
32. #63980C22semidirect
33. Dic3×#67C22semidirect
34. #63969C22semidirect
39. C2×#3724C22semidirect
43. #63957C22semidirect
45. #63902C22semidirect
46. #63870C22semidirect
47. #63861C22semidirect
51. C2×#939D3semidirect
136. #939C2×D3semidirect
427. C2×C32#553semidirect
522. C32C2×#553semidirect
569. C2×C3#5601semidirect
599. C3C2×#5601semidirect
603. C2#10595206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9392
C2×#639802
C2×Dic3×#672
C2×#639692
C22×#37242
C2×#639572
#105952062
C2×#639022
C2×#638702
C2×#638612
C2×#56013