Finite Group Databasebeta

← D3×#64308 #13181264

Subgroups — D3×#64308 #13181264

Order 1728.

4214 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724619C211yesmaximal, characteristic, complemented
2#11724581C212yesmaximal, complemented
3C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×#64308C211yesmaximal, characteristic, complemented
5C3×D3×#235C212yesmaximal, complemented
6D3×#3811C214yesmaximal, complemented
7#11724420C214yesmaximal, complemented
8D32×D12C214yesmaximal, complemented
9#11724390C214yesmaximal, complemented
10#11724384C214yesmaximal, complemented
11D3×#3799C214yesmaximal, complemented
12D3×#1009—32nomaximal
13C2×#64308—31nomaximal
14C22×D3×C3⋊D3C2212yescomplemented
15C2×D33C2214yescomplemented
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
17C3×#3828C2212yescomplemented
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C32×#235C2212yescomplemented
20C2×C32×C4×D3C2211yescharacteristic, complemented
21#89049C2214yescomplemented
22C4⋊#1113C2214yescomplemented
23#89041C2214yescomplemented
24#89039C2218yescomplemented
25C2×#6292C2212yescomplemented
26C3⋊D3×D12C2214yescomplemented
27D3×C4⋊(C3⋊D3)C2214yescomplemented
28D3×C4⋊(C3⋊D3)C2214yescomplemented
29D3×C4⋊(C3⋊D3)C2214yescomplemented
30#89022C2214yescomplemented
31#89018C2214yescomplemented
32C3×#3811C2214yescomplemented
33C3×D3×#67C2214yescomplemented
34C3×#3804C2214yescomplemented
35C3×D3×D12C2212yescomplemented
36C3×D3×D12C2214yescomplemented
37C3×C4×D32C2214yescomplemented
38C3×#3799C2214yescomplemented
39C3×#3799C2212yescomplemented
40C3×#3798C2214yescomplemented
41C3×#3795C2212yescomplemented
42C3×D3×Dic6C2212yescomplemented
43#88965C2218yescomplemented
44#88962C2218yescomplemented
45#88955C2214yescomplemented
46#88955C2218yescomplemented
47#88954C2218yescomplemented
48#88952C2214yescomplemented
49D3×#626C2218yescomplemented
50D3×#626C2218yescomplemented
51D3×#624C2214yescomplemented
52#64366—32no—
53C22×C4⋊(C3⋊D3)—31no—
54C3×#1009—32no—
55C3×D3×#41—32no—
56C2×C3×#235—32no—
57C2×#3811—34no—
58#64320—34no—
59D3×#239—34no—
60#64314—38no—
61#64314—34no—
62D32×D4—38no—
63D32×D4—34no—
64#64308—31no—
65#64308—32no—
66#64308—32no—
67#64308—34no—
68#64308—34no—
69#64308—34no—
70#64308—34no—
71#64308—62no—
72#64308D311yescharacteristic, direct product factor
73#64307—32no—
74#64307—34no—
75D3×#235—34no—
76D3×#235D312yescomplemented
77C2×D3×D12—32no—
78C2×D3×D12—34no—
79C2×D3×D12—34no—
80C2×D3×D12—61no—
81C2×#3799—34no—
82C22×C3⋊(C3⋊D3)C2312yescomplemented
83C22×C3×C3⋊D3C2312yescomplemented
84C22×C32×D3C2311yescharacteristic
85C2×#1113C2314yescomplemented
86C2×D3×C3⋊D3—44no—
87C2×D3×C3⋊D3C2314yes—
88C2×D3×C3⋊D3C2318yescomplemented
89C2×D3×C3⋊D3C2314yescomplemented
90C2×C3×D32C2314yes—
91C2×C3×D32C2314yescomplemented
92D33—48no—
93C2×C33×C4C2311yescharacteristic, complemented
94C4⋊(C3⋊(C3⋊D3))C2314yescomplemented
95C3×#638C2314yescomplemented
96C3×C4⋊(C3⋊D3)C2314yescomplemented
97C3×C4⋊(C3⋊D3)C2312yescomplemented
98C3×C4×C3⋊D3C2314yescomplemented
99C3×#634C2312yescomplemented
100C32×#67C2314yescomplemented
101C2×C32×Dic3C2311yescharacteristic, complemented
102C32×D12C2312yescomplemented
103C32×C4×D3C2312yes—
104C32×C4×D3C2312yescomplemented
105C32×C4×D3C2314yescomplemented
106C32×Dic6C2312yescomplemented
107#6295C2318yescomplemented
108#6294C2314yescomplemented
109#6292C2318yescomplemented
110#6292C2318yescomplemented
111#6291C2318yescomplemented
112#6289C2318yescomplemented
113C3×#627C2314yescomplemented
114C3×#626C2314yescomplemented
115C3×#626C2318yescomplemented
116C3×#626C2314yescomplemented
117C3×#625C2314yescomplemented
118C3×#624C2314yescomplemented
119C3×#624C2314yescomplemented
120C3×D3×Dic3C2314yes—
121C3×D3×Dic3C2314yescomplemented
122D3×H(5,𝔽2)—91no—
123C2×#1009—92no—
124C23×C3⋊D3—32no—
125C22×D32—34no—
126C22×D32—38no—
127C22×D32—34no—
128C22×D32—62no—
129C32×#41—32no—
130C22×C32×C4—31no—
131#3832—34no—
132D4×C3⋊D3—38no—
133D4×C3⋊D3—34no—
134#3828—34no—
135#3828C2×D312yescomplemented
136C2×C4⋊(C3⋊D3)—32no—
137C2×C4⋊(C3⋊D3)—32no—
138C2×C4⋊(C3⋊D3)—31no—
139C2×C4⋊(C3⋊D3)—34no—
140C2×C4⋊(C3⋊D3)—34no—
141C2×C4⋊(C3⋊D3)—34no—
142C2×C4⋊(C3⋊D3)—61no—
143C2×C4⋊(C3⋊D3)—62no—
144C2×C4⋊(C3⋊D3)—121no—
145C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
146C2×C3×#67—34no—
147C3×#239—34no—
148C3×#239—32no—
149C3×D3×Q8—32no—
150C3×#237—34no—
151C3×#237—32no—
152C3×D3×D4—34no—
153C3×D3×D4—38no—
154C3×D3×D4—32no—
155C3×D3×D4—34no—
156C3×#235—22no—
157C3×#235—32no—
158C3×#235—32no—
159C3×#235—34no—
160C3×#235—32no—
161C3×#235—34no—
162C3×#235—34no—
163C3×#235—34no—
164C3×#235—32no—
165C3×#235—62no—
166C3×#235C2×D312yescomplemented
167C3×#235C2×D312yescomplemented
168C2×C3×D12—32no—
169C2×C3×D12—32no—
170C2×C3×D12—34no—
171C2×C3×D12—61no—
172C2×C3×C4×D3—21no—
173C2×C3×C4×D3—34no—
174C2×C3×C4×D3—34no—
175C2×C3×C4×D3C2×D312yescomplemented
176C2×C3×Dic6—32no—
177#3811—34no—
178#3811—34no—
179#3811—38no—
180#3811—38no—
181#3811—38no—
182#3811—38no—
183#3811—34no—
184#3811—38no—
185#3811—68no—
186#3811C2×D314yescomplemented
187D3×#67—38no—
188D3×#67—38no—
189D3×#67—38no—
190D3×#67—38no—
191D3×#67C2×D314yescomplemented
192C2×#626—34no—
193C2×#626—38no—
194C2×#626—38no—
195C2×#626—62no—
196C2×#624—34no—
197#3804—38no—
198#3804C2×D314yescomplemented
199#3802—34no—
200#3802—38no—
201D3×D12—38no—
202D3×D12—38no—
203D3×D12—34no—
204D3×D12—34no—
205D3×D12—34no—
206D3×D12—34no—
207D3×D12—34no—
208D3×D12—34no—
209D3×D12—34no—
210D3×D12—34no—
211D3×D12—34no—
212D3×D12—34no—
213D3×D12—38no—
214D3×D12—38no—
215D3×D12—38no—
216D3×D12—64no—
217D3×D12—64no—
218D3×D12—64no—
219D3×D12—64no—
220D3×D12C2×D312yescomplemented
221D3×D12C2×D314yescomplemented
222C4×D32—38no—
223C4×D32C2×D314yescomplemented
224#3799—34no—
225#3799—34no—
226#3799—34no—
227#3799—34no—
228#3799—34no—
229#3799—38no—
230#3799—38no—
231#3799—38no—
232#3799—64no—
233#3799—64no—
234#3799C2×D314yescomplemented
235#3799C2×D312yescomplemented
236#3798—38no—
237#3798C2×D314yescomplemented
238#3796—34no—
239#3796—38no—
240#3795—34no—
241#3795C2×D312yescomplemented
242D3×Dic6C2×D312yescomplemented
243C22×C33C2411yescharacteristic
244C2×C3⋊(C3⋊D3)—42no—
245C2×C3⋊(C3⋊D3)C2414yes—
246C2×C3×C3⋊D3—42no—
247C2×C3×C3⋊D3C2414yes—
248C2×C3×C3⋊D3C2414yes—
249C2×C32×D3—22no—
250C2×C32×D3C2414yes—
251C2×C32×D3C2411yescharacteristic
252C2×C32×D3C2411yescharacteristic
253#1113—44no—
254D3×C3⋊D3—28no—
255D3×C3⋊D3—44no—
256D3×C3⋊D3—48no—
257C3×D32—28no—
258C3×D32—44no—
259C33×C4C2412yes—
260C3×C3⋊Dic3C2414yes—
261C32×Dic3C2414yes—
262C32×Dic3C2412yes—
263C3×H(5,𝔽2)—91no—
264C2×C3×#41—92no—
265#1009—32no—
266#1009—92no—
267#1009—94no—
268#1009—94no—
269#1009—98no—
270#1009—94no—
271#1009—94no—
272#1009—94no—
273#1009—92no—
274#1009—92no—
275#1009—92no—
276#1009—182no—
277D3×#41—32no—
278D3×#41—94no—
279C2×#239—94no—
280#1004—91no—
281#1004—94no—
282#1004—94no—
283C2×D3×D4—94no—
284C2×D3×D4—94no—
285C2×D3×D4—94no—
286C2×D3×D4—98no—
287C2×D3×D4—91no—
288C2×#235—32no—
289C2×#235—94no—
290C22×D12—94no—
291C22×D12—92no—
292C22×D12—181no—
293C23×C32—31no—
294C22×C3⋊D3—34no—
295C22×C3⋊D3—32no—
296C22×C3⋊D3—34no—
297C22×C3⋊D3—38no—
298C22×C3⋊D3—34no—
299C22×C3⋊D3—62no—
300C22×C3⋊D3—64no—
301C22×C3⋊D3—122no—
302C22×C3⋊D3—124no—
303C22×C3⋊D3C22×D312yescomplemented
304C22×C3×D3—21no—
305C22×C3×D3—34no—
306C22×C3×D3—34no—
307C22×C3×D3—34no—
308C22×C3×D3—38no—
309C22×C3×D3—62no—
310C22×C3×D3C22×D312yes—
311C2×D32—38no—
312C2×D32—34no—
313C2×D32—38no—
314C2×D32—38no—
315C2×D32—38no—
316C2×D32—38no—
317C2×D32—64no—
318C2×D32—64no—
319C2×D32—68no—
320C2×D32—1216no—
321C2×D32—128no—
322C2×D32—128no—
323C2×D32—128no—
324C2×D32C22×D314yes—
325C2×D32C22×D314yescomplemented
326C32×Q8—32no—
327C32×D4—34no—
328C32×D4—32no—
329C2×C32×C4—21no—
330C2×C32×C4—22no—
331C2×C32×C4—31no—
332C2×C32×C4—32no—
333C2×C32×C4—34no—
334C2×C32×C4—32no—
335C2×C32×C4—41no—
336C2×C32×C4C22×D312yescomplemented
337C2×C32×C4C22×D311yescharacteristic, complemented
338#638—38no—
339#638C22×D314yescomplemented
340C4⋊(C3⋊D3)—38no—
341C4⋊(C3⋊D3)—38no—
342C4⋊(C3⋊D3)—34no—
343C4⋊(C3⋊D3)—34no—
344C4⋊(C3⋊D3)—34no—
345C4⋊(C3⋊D3)—64no—
346C4⋊(C3⋊D3)—64no—
347C4⋊(C3⋊D3)—64no—
348C4⋊(C3⋊D3)—124no—
349C4⋊(C3⋊D3)C22×D314yescomplemented
350C4⋊(C3⋊D3)C22×D312yescomplemented
351C4×C3⋊D3—38no—
352C4×C3⋊D3C22×D314yescomplemented
353#634C22×D312yescomplemented
354C3×#67—24no—
355C3×#67—34no—
356C3×#67—34no—
357C3×#67—34no—
358C3×#67—34no—
359C3×#67—38no—
360C3×#67—34no—
361C3×#67—34no—
362C3×#67—64no—
363C3×#67C22×D314yescomplemented
364C3×#67C22×D314yescomplemented
365C2×C3×Dic3—21no—
366C2×C3×Dic3—34no—
367C2×C3×Dic3—34no—
368C2×C3×Dic3C22×D312yescomplemented
369C3×D12—22no—
370C3×D12—38no—
371C3×D12—34no—
372C3×D12—34no—
373C3×D12—34no—
374C3×D12—34no—
375C3×D12—32no—
376C3×D12—32no—
377C3×D12—64no—
378C3×D12—62no—
379C3×D12C22×D312yescomplemented
380C3×D12C22×D312yescomplemented
381C3×C4×D3—22no—
382C3×C4×D3—24no—
383C3×C4×D3—22no—
384C3×C4×D3—34no—
385C3×C4×D3—34no—
386C3×C4×D3—34no—
387C3×C4×D3—34no—
388C3×C4×D3—34no—
389C3×C4×D3—38no—
390C3×C4×D3—34no—
391C3×C4×D3—64no—
392C3×C4×D3C22×D312yes—
393C3×C4×D3C22×D312yes—
394C3×C4×D3C22×D312yescomplemented
395C3×C4×D3C22×D312yescomplemented
396C3×C4×D3C22×D314yescomplemented
397C3×C4×D3C22×D314yescomplemented
398C3×Dic6—22no—
399C3×Dic6—32no—
400C3×Dic6—32no—
401C3×Dic6—34no—
402C3×Dic6—34no—
403C3×Dic6—62no—
404C3×Dic6C22×D312yescomplemented
405C3×Dic6C22×D312yescomplemented
406#627C22×D314yescomplemented
407#626—38no—
408#626—38no—
409#626—38no—
410#626—38no—
411#626—38no—
412#626—38no—
413#626—38no—
414#626—38no—
415#626—68no—
416#626—68no—
417#626—68no—
418#626C22×D314yescomplemented
419#626C22×D314yescomplemented
420#626C22×D318yescomplemented
421#625—38no—
422#625C22×D314yescomplemented
423#624—34no—
424#624—38no—
425#624—38no—
426#624—68no—
427#624C22×D314yescomplemented
428#624C22×D314yescomplemented
429D3×Dic3—38no—
430D3×Dic3C22×D314yes—
431D3×Dic3C22×D314yescomplemented
432C2×H(5,𝔽2)—271noSylow
433C2×C33—21no—
434C2×C33C2511yescharacteristic
435C3⋊(C3⋊D3)—24no—
436C3×C3⋊D3—24no—
437C3×C3⋊D3—24no—
438C32×D3—21no—
439C32×D3—24no—
440C32×D3H(5,𝔽2)12yescomplemented
441C23×D3—98no—
442C23×D3—94no—
443C23×D3—94no—
444C23×D3—92no—
445C23×D3—182no—
446C3×#41—32no—
447C3×#41—32no—
448C3×#41—62no—
449C3×#41—94no—
450C3×#41—94no—
451C3×#41—92no—
452C3×#41—94no—
453C3×#41—92no—
454C3×#41—92no—
455C2×C3×Q8—92no—
456C2×C3×D4—92no—
457C2×C3×D4—94no—
458C2×C3×D4—94no—
459C2×C3×D4—94no—
460C2×C3×D4—91no—
461C22×C3×C4—32no—
462C22×C3×C4—61no—
463C22×C3×C4—94no—
464C2×#67—34no—
465C2×#67—98no—
466C2×#67—98no—
467C2×#67—94no—
468C2×#67—94no—
469C2×#67—92no—
470#239—34no—
471#239—32no—
472#239—98no—
473#239—98no—
474#239—94no—
475#239—94no—
476#239—94no—
477#239—94no—
478#239—184no—
479D3×Q8—32no—
480#237—34no—
481#237—32no—
482#237—94no—
483#237—98no—
484D3×D4—34no—
485D3×D4—38no—
486D3×D4—32no—
487D3×D4—34no—
488D3×D4—94no—
489D3×D4—94no—
490D3×D4—98no—
491D3×D4—98no—
492D3×D4—98no—
493D3×D4—94no—
494D3×D4—94no—
495D3×D4—98no—
496D3×D4—98no—
497D3×D4—98no—
498D3×D4—98no—
499D3×D4—98no—
500D3×D4—98no—
501D3×D4—98no—
502D3×D4—98no—
503D3×D4—98no—
504D3×D4—98no—
505D3×D4—94no—
506D3×D4—94no—
507D3×D4—94no—
508D3×D4—184no—
509D3×D4—188no—
510#235—32no—
511#235—32no—
512#235—34no—
513#235—32no—
514#235—34no—
515#235—34no—
516#235—32no—
517#235—34no—
518#235—62no—
519#235—98no—
520#235—98no—
521#235—94no—
522#235—98no—
523#235—94no—
524#235—94no—
525#235—94no—
526#235—184no—
527#235D3212yescomplemented
528C2×D12—32no—
529C2×D12—32no—
530C2×D12—34no—
531C2×D12—61no—
532C2×D12—98no—
533C2×D12—94no—
534C2×D12—94no—
535C2×D12—94no—
536C2×D12—94no—
537C2×D12—94no—
538C2×D12—94no—
539C2×D12—94no—
540C2×D12—94no—
541C2×D12—98no—
542C2×D12—98no—
543C2×D12—94no—
544C2×D12—92no—
545C2×D12—91no—
546C2×D12—94no—
547C2×D12—184no—
548C2×D12—184no—
549C2×D12—184no—
550C2×D12—181no—
551C2×D12—182no—
552C2×D12—182no—
553C2×D12—361no—
554C2×C4×D3—34no—
555C2×C4×D3—34no—
556C2×C4×D3—94no—
557C2×C4×D3—98no—
558C2×C4×D3D3211yescharacteristic, complemented
559C2×Dic6—32no—
560C22×C32—21no—
561C22×C32—22no—
562C22×C32—31no—
563C22×C32—34no—
564C22×C32—31no—
565C22×C32—41no—
566C22×C32—62no—
567C22×C32C23×D312yes—
568C22×C32C23×D311yescharacteristic
569C2×C3⋊D3—34no—
570C2×C3⋊D3—38no—
571C2×C3⋊D3—42no—
572C2×C3⋊D3—68no—
573C2×C3⋊D3—64no—
574C2×C3⋊D3—68no—
575C2×C3⋊D3—124no—
576C2×C3⋊D3—124no—
577C2×C3⋊D3—122no—
578C2×C3⋊D3—128no—
579C2×C3⋊D3—124no—
580C2×C3⋊D3—124no—
581C2×C3⋊D3—244no—
582C2×C3⋊D3—244no—
583C2×C3⋊D3C23×D314yes—
584C2×C3⋊D3C23×D314yes—
585C2×C3×D3—24no—
586C2×C3×D3—24no—
587C2×C3×D3—21no—
588C2×C3×D3—21no—
589C2×C3×D3—24no—
590C2×C3×D3—38no—
591C2×C3×D3—34no—
592C2×C3×D3—34no—
593C2×C3×D3—64no—
594C2×C3×D3—64no—
595C2×C3×D3—68no—
596C2×C3×D3—68no—
597C2×C3×D3—128no—
598C2×C3×D3—124no—
599C2×C3×D3—124no—
600C2×C3×D3C23×D314yes—
601C2×C3×D3C23×D312yes—
602C2×C3×D3C23×D314yes—
603C2×C3×D3C23×D312yes—
604D32—28no—
605D32—44no—
606D32—616no—
607D32—128no—
608D32—128no—
609D32—128no—
610D32—128no—
611D32—128no—
612D32—128no—
613D32—124no—
614D32—248no—
615C32×C4—22no—
616C32×C4—22no—
617C32×C4—22no—
618C32×C4—32no—
619C32×C4—34no—
620C32×C4—42no—
621C32×C4C23×D312yes—
622C32×C4C23×D312yes—
623C32×C4C23×D312yes—
624C3⋊Dic3C23×D314yes—
625C3×Dic3—24no—
626C3×Dic3—22no—
627C3×Dic3—34no—
628C3×Dic3—34no—
629C3×Dic3—64no—
630C3×Dic3C23×D314yes—
631C3×Dic3C23×D312yes—
632C3×Dic3C23×D314yes—
633C3×Dic3C23×D312yes—
634H(5,𝔽2)—91no—
635H(5,𝔽2)—274no—
636H(5,𝔽2)—274no—
637H(5,𝔽2)—271no—
638H(5,𝔽2)—272no—
639H(5,𝔽2)—274no—
640C2×#41—92no—
641C2×#41—274no—
642C22×D4—271no—
643C22×D4—274no—
644C22×D4—274no—
645C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
646C23×C3—32no—
647C23×C3—61no—
648C23×C3—94no—
649C23×C3—94no—
650C23×C3—92no—
651C22×D3—34no—
652C22×D3—34no—
653C22×D3—34no—
654C22×D3—38no—
655C22×D3—62no—
656C22×D3—98no—
657C22×D3—94no—
658C22×D3—98no—
659C22×D3—98no—
660C22×D3—98no—
661C22×D3—98no—
662C22×D3—94no—
663C22×D3—92no—
664C22×D3—94no—
665C22×D3—98no—
666C22×D3—94no—
667C22×D3—184no—
668C22×D3—184no—
669C22×D3—188no—
670C22×D3—182no—
671C22×D3—184no—
672C22×D3—362no—
673C22×D3—364no—
674C22×D3—368no—
675C22×D3—3616no—
676C22×D3—368no—
677C22×D3—368no—
678C22×D3C2×D3211yescharacteristic
679C3×Q8—32no—
680C3×Q8—32no—
681C3×Q8—62no—
682C3×Q8—94no—
683C3×Q8—92no—
684C3×D4—34no—
685C3×D4—34no—
686C3×D4—32no—
687C3×D4—32no—
688C3×D4—62no—
689C3×D4—64no—
690C3×D4—94no—
691C3×D4—94no—
692C3×D4—98no—
693C3×D4—94no—
694C3×D4—94no—
695C3×D4—92no—
696C3×D4—94no—
697C2×C3×C4—21no—
698C2×C3×C4—22no—
699C2×C3×C4—32no—
700C2×C3×C4—32no—
701C2×C3×C4—32no—
702C2×C3×C4—34no—
703C2×C3×C4—34no—
704C2×C3×C4—32no—
705C2×C3×C4—32no—
706C2×C3×C4—41no—
707C2×C3×C4—62no—
708C2×C3×C4—62no—
709C2×C3×C4—64no—
710C2×C3×C4—61no—
711C2×C3×C4—94no—
712C2×C3×C4—94no—
713C2×C3×C4—94no—
714C2×C3×C4—94no—
715C2×C3×C4—94no—
716C2×C3×C4C2×D3211yescharacteristic, complemented
717C2×C3×C4C2×D3212yescomplemented
718#67—34no—
719#67—34no—
720#67—34no—
721#67—34no—
722#67—34no—
723#67—38no—
724#67—34no—
725#67—64no—
726#67—98no—
727#67—98no—
728#67—98no—
729#67—98no—
730#67—98no—
731#67—98no—
732#67—188no—
733#67C2×D3214yescomplemented
734C2×Dic3—34no—
735C2×Dic3—34no—
736C2×Dic3—94no—
737C2×Dic3C2×D3211yescharacteristic, complemented
738D12—34no—
739D12—38no—
740D12—34no—
741D12—34no—
742D12—32no—
743D12—34no—
744D12—32no—
745D12—64no—
746D12—62no—
747D12—98no—
748D12—98no—
749D12—98no—
750D12—98no—
751D12—98no—
752D12—98no—
753D12—94no—
754D12—94no—
755D12—94no—
756D12—184no—
757D12—184no—
758D12—184no—
759D12—188no—
760D12—188no—
761D12—364no—
762D12C2×D3212yescomplemented
763C4×D3—34no—
764C4×D3—34no—
765C4×D3—34no—
766C4×D3—34no—
767C4×D3—34no—
768C4×D3—34no—
769C4×D3—38no—
770C4×D3—64no—
771C4×D3—98no—
772C4×D3—98no—
773C4×D3—98no—
774C4×D3—98no—
775C4×D3—188no—
776C4×D3C2×D3212yes—
777C4×D3C2×D3214yescomplemented
778C4×D3C2×D3212yescomplemented
779Dic6—32no—
780Dic6—32no—
781Dic6—34no—
782Dic6—34no—
783Dic6—62no—
784Dic6C2×D3212yescomplemented
785C2×C32—21no—
786C2×C32—22no—
787C2×C32—22no—
788C2×C32—22no—
789C2×C32—21no—
790C2×C32—32no—
791C2×C32—41no—
792C2×C32—42no—
793C2×C32—42no—
794C2×C32—61no—
795C2×C32—64no—
796C2×C32C24×D312yes—
797C2×C32C24×D311yescharacteristic
798C3⋊D3—24no—
799C3⋊D3—24no—
800C3⋊D3—68no—
801C3⋊D3—64no—
802C3⋊D3—124no—
803C3⋊D3—128no—
804C3⋊D3—244no—
805C3×D3—22no—
806C3×D3—24no—
807C3×D3—22no—
808C3×D3—24no—
809C3×D3—22no—
810C3×D3—44no—
811C3×D3—68no—
812C3×D3—64no—
813C3×D3—64no—
814C3×D3—124no—
815C3×D3—124no—
816C3×D3#100914yescomplemented
817C24—272no—
818C24—274no—
819#41—32no—
820#41—94no—
821#41—94no—
822#41—92no—
823#41—92no—
824#41—94no—
825#41—92no—
826#41—274no—
827#41—278no—
828#41—278no—
829#41—274no—
830#41—274no—
831C2×Q8—92no—
832C2×D4—92no—
833C2×D4—94no—
834C2×D4—94no—
835C2×D4—94no—
836C2×D4—91no—
837C2×D4—274no—
838C2×D4—274no—
839C2×D4—274no—
840C2×D4—272no—
841C2×D4—274no—
842C2×D4—278no—
843C2×D4—274no—
844C2×D4—274no—
845C2×D4—278no—
846C2×D4—278no—
847C2×D4—278no—
848C2×D4—278no—
849C2×D4—274no—
850C2×D4—274no—
851C2×D4—271no—
852C22×C4—31no—
853C22×C4—94no—
854C22×C4—274no—
855C22×C3—21no—
856C22×C3—22no—
857C22×C3—32no—
858C22×C3—34no—
859C22×C3—32no—
860C22×C3—34no—
861C22×C3—41no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—64no—
865C22×C3—64no—
866C22×C3—64no—
867C22×C3—94no—
868C22×C3—94no—
869C22×C3—188no—
870C22×C3—362no—
871C22×C3—364no—
872C22×C3C22×D3211yescharacteristic
873C22×C3C22×D3212yes—
874C2×D3—22no—
875C2×D3—34no—
876C2×D3—34no—
877C2×D3—38no—
878C2×D3—64no—
879C2×D3—64no—
880C2×D3—68no—
881C2×D3—68no—
882C2×D3—98no—
883C2×D3—94no—
884C2×D3—128no—
885C2×D3—124no—
886C2×D3—124no—
887C2×D3—188no—
888C2×D3—184no—
889C2×D3—1816no—
890C2×D3—188no—
891C2×D3—364no—
892C2×D3—368no—
893C2×D3—364no—
894C2×D3—368no—
895C2×D3—364no—
896C2×D3—368no—
897C2×D3—368no—
898C2×D3—368no—
899C2×D3—368no—
900C2×D3—368no—
901C2×D3—362no—
902C2×D3—364no—
903C2×D3—364no—
904C2×D3—728no—
905C2×D3—724no—
906C2×D3—724no—
907C2×D3C22×D3214yes—
908C2×D3C22×D3211yescharacteristic
909C2×D3C22×D3211yescharacteristic
910C3×C4—22no—
911C3×C4—22no—
912C3×C4—22no—
913C3×C4—32no—
914C3×C4—34no—
915C3×C4—32no—
916C3×C4—34no—
917C3×C4—42no—
918C3×C4—64no—
919C3×C4—62no—
920C3×C4—94no—
921C3×C4C22×D3212yes—
922C3×C4C22×D3212yes—
923C3×C4C22×D3212yes—
924Dic3—34no—
925Dic3—34no—
926Dic3—64no—
927Dic3C22×D3212yes—
928Dic3C22×D3214yes—
929C32—21no—
930C32—22no—
931C32—41no—
932C32C2×#100912yescomplemented
933C32D3×H(5,𝔽2)11yescharacteristic, complemented
934C23—31no—
935C23—94no—
936C23—94no—
937C23—92no—
938C23—274no—
939C23—274no—
940C23—278no—
941C23—274no—
942C23—272no—
943C23—1084no—
944C23—1088no—
945Q8—32no—
946Q8—94no—
947Q8—92no—
948D4—34no—
949D4—32no—
950D4—98no—
951D4—94no—
952D4—94no—
953D4—94no—
954D4—94no—
955D4—94no—
956D4—92no—
957D4—278no—
958D4—278no—
959D4—278no—
960D4—278no—
961D4—274no—
962C2×C4—31no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—34no—
966C2×C4—94no—
967C2×C4—94no—
968C2×C4—94no—
969C2×C4—94no—
970C2×C4—94no—
971C2×C4—278no—
972C2×C4—274no—
973C2×C4D3311yescharacteristic, complemented
974C2×C3—22no—
975C2×C3—21no—
976C2×C3—22no—
977C2×C3—22no—
978C2×C3—21no—
979C2×C3—34no—
980C2×C3—42no—
981C2×C3—42no—
982C2×C3—41no—
983C2×C3—62no—
984C2×C3—62no—
985C2×C3—64no—
986C2×C3—64no—
987C2×C3—62no—
988C2×C3—124no—
989C2×C3—184no—
990C2×C3—184no—
991C2×C3C23×D3211yescharacteristic
992C2×C3C23×D3212yes—
993D3—21no—
994D3—24no—
995D3—64no—
996D3—64no—
997D3—68no—
998D3—124no—
999D3—124no—
1000D3—184no—
1001D3—188no—
1002D3—364no—
1003D3—368no—
1004D3—724no—
1005D3#6430812yesdirect product factor
1006C22—31no—
1007C22—31no—
1008C22—34no—
1009C22—62no—
1010C22—94no—
1011C22—94no—
1012C22—188no—
1013C22—274no—
1014C22—362no—
1015C22—364no—
1016C22—548no—
1017C22—1082no—
1018C22—1084no—
1019C22—1088no—
1020C22—1084no—
1021C22C2×D3311yescharacteristic
1022C4—32no—
1023C4—34no—
1024C4—94no—
1025C4C2×D3312yes—
1026C3—21no—
1027C3—22no—
1028C3—41no—
1029C3C2×#6430811yescharacteristic, complemented
1030C3D3×#100912yescomplemented
1031C2—21no—
1032C2—32no—
1033C2—61no—
1034C2—64no—
1035C2—184no—
1036C2—184no—
1037C2—544no—
1038C2C22×D3311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D33
commutator, socle, cosocleC2×C33C25
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33C2×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11724619C2semidirect
2. #11724581C2semidirect
3. C2×D3×C4⋊(C3⋊D3)C2semidirect
4. C3×#64308C2semidirect
5. C3×D3×#235C2semidirect
6. D3×#3811C2semidirect
7. #11724420C2semidirect
8. D32×D12C2semidirect
9. #11724390C2semidirect
10. #11724384C2semidirect
11. D3×#3799C2semidirect
14. C22×D3×C3⋊D3C22semidirect
15. C2×D33C22semidirect
16. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
17. C3×#3828C22semidirect
18. C2×C3×C4⋊(C3⋊D3)C22semidirect
19. C32×#235C22semidirect
20. C2×C32×C4×D3C22semidirect
21. #89049C22semidirect
22. C4⋊#1113C22semidirect
23. #89041C22semidirect
24. #89039C22semidirect
25. C2×#6292C22semidirect
26. C3⋊D3×D12C22semidirect
27. D3×C4⋊(C3⋊D3)C22semidirect
28. D3×C4⋊(C3⋊D3)C22semidirect
29. D3×C4⋊(C3⋊D3)C22semidirect
30. #89022C22semidirect
31. #89018C22semidirect
32. C3×#3811C22semidirect
33. C3×D3×#67C22semidirect
34. C3×#3804C22semidirect
35. C3×D3×D12C22semidirect
36. C3×D3×D12C22semidirect
37. C3×C4×D32C22semidirect
38. C3×#3799C22semidirect
39. C3×#3799C22semidirect
40. C3×#3798C22semidirect
41. C3×#3795C22semidirect
42. C3×D3×Dic6C22semidirect
43. #88965C22semidirect
44. #88962C22semidirect
45. #88955C22semidirect
46. #88955C22semidirect
47. #88954C22semidirect
48. #88952C22semidirect
49. D3×#626C22semidirect
50. D3×#626C22semidirect
51. D3×#624C22semidirect
72. #64308D3direct (N × H)
76. D3×#235D3semidirect
82. C22×C3⋊(C3⋊D3)C23semidirect
83. C22×C3×C3⋊D3C23semidirect
85. C2×#1113C23semidirect
88. C2×D3×C3⋊D3C23semidirect
89. C2×D3×C3⋊D3C23semidirect
91. C2×C3×D32C23semidirect
93. C2×C33×C4C23semidirect
94. C4⋊(C3⋊(C3⋊D3))C23semidirect
95. C3×#638C23semidirect
96. C3×C4⋊(C3⋊D3)C23semidirect
97. C3×C4⋊(C3⋊D3)C23semidirect
98. C3×C4×C3⋊D3C23semidirect
99. C3×#634C23semidirect
100. C32×#67C23semidirect
101. C2×C32×Dic3C23semidirect
102. C32×D12C23semidirect
104. C32×C4×D3C23semidirect
105. C32×C4×D3C23semidirect
106. C32×Dic6C23semidirect
107. #6295C23semidirect
108. #6294C23semidirect
109. #6292C23semidirect
110. #6292C23semidirect
111. #6291C23semidirect
112. #6289C23semidirect
113. C3×#627C23semidirect
114. C3×#626C23semidirect
115. C3×#626C23semidirect
116. C3×#626C23semidirect
117. C3×#625C23semidirect
118. C3×#624C23semidirect
119. C3×#624C23semidirect
121. C3×D3×Dic3C23semidirect
135. #3828C2×D3semidirect
145. C2×C4⋊(C3⋊D3)C2×D3semidirect
166. C3×#235C2×D3semidirect
167. C3×#235C2×D3semidirect
175. C2×C3×C4×D3C2×D3semidirect
186. #3811C2×D3semidirect
191. D3×#67C2×D3semidirect
198. #3804C2×D3semidirect
220. D3×D12C2×D3semidirect
221. D3×D12C2×D3semidirect
223. C4×D32C2×D3semidirect
234. #3799C2×D3semidirect
235. #3799C2×D3semidirect
237. #3798C2×D3semidirect
241. #3795C2×D3semidirect
242. D3×Dic6C2×D3semidirect
303. C22×C3⋊D3C22×D3semidirect
325. C2×D32C22×D3semidirect
336. C2×C32×C4C22×D3semidirect
337. C2×C32×C4C22×D3semidirect
339. #638C22×D3semidirect
349. C4⋊(C3⋊D3)C22×D3semidirect
350. C4⋊(C3⋊D3)C22×D3semidirect
352. C4×C3⋊D3C22×D3semidirect
353. #634C22×D3semidirect
363. C3×#67C22×D3semidirect
364. C3×#67C22×D3semidirect
368. C2×C3×Dic3C22×D3semidirect
379. C3×D12C22×D3semidirect
380. C3×D12C22×D3semidirect
394. C3×C4×D3C22×D3semidirect
395. C3×C4×D3C22×D3semidirect
396. C3×C4×D3C22×D3semidirect
397. C3×C4×D3C22×D3semidirect
404. C3×Dic6C22×D3semidirect
405. C3×Dic6C22×D3semidirect
406. #627C22×D3semidirect
418. #626C22×D3semidirect
419. #626C22×D3semidirect
420. #626C22×D3semidirect
422. #625C22×D3semidirect
427. #624C22×D3semidirect
428. #624C22×D3semidirect
431. D3×Dic3C22×D3semidirect
440. C32×D3H(5,𝔽2)semidirect
527. #235D32semidirect
558. C2×C4×D3D32semidirect
645. C33C2×H(5,𝔽2)semidirect
716. C2×C3×C4C2×D32semidirect
717. C2×C3×C4C2×D32semidirect
733. #67C2×D32semidirect
737. C2×Dic3C2×D32semidirect
762. D12C2×D32semidirect
777. C4×D3C2×D32semidirect
778. C4×D3C2×D32semidirect
784. Dic6C2×D32semidirect
816. C3×D3#1009semidirect
932. C32C2×#1009semidirect
933. C32D3×H(5,𝔽2)semidirect
973. C2×C4D33semidirect
1005. D3#64308direct (N × H)
1029. C3C2×#64308semidirect
1030. C3D3×#1009semidirect

Maximal subgroups

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

subgroupindex
#117246192
#117245812
C2×D3×C4⋊(C3⋊D3)2
C3×#643082
C3×D3×#2352
D3×#38112
#117244202
D32×D122
#117243902
#117243842
D3×#37992
D3×#10093
C2×#643083