Finite Group Databasebeta

← #13181266

Subgroups — #13181266

Order 1728.

4128 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊#1113C211yesmaximal, characteristic, complemented
2#11724580C212yesmaximal, complemented
3C3⋊D3×#235C211yesmaximal, characteristic, complemented
4C3×#64308C212yesmaximal, complemented
5C3×#64306C211yesmaximal, characteristic, complemented
6#11724440C214yesmaximal, complemented
7#11724416C214yesmaximal, complemented
8D3×#3802C212yesmaximal, complemented
9D32×D12C212yesmaximal, complemented
10#11724391C212yesmaximal, complemented
11#11724390C212yesmaximal, complemented
12#11724389C212yesmaximal, complemented
13#11724385C214yesmaximal, complemented
14#11724380C212yesmaximal, complemented
15#10596692—31nomaximal
16D3×#1009—32nomaximal
17C22×#1113C2212yescomplemented
18C2×D33C2214yescomplemented
19#89076C2211yescharacteristic, complemented
20C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C32×#235C2211yescharacteristic, complemented
23C32×#235C2212yescomplemented
24C2×#6295C2212yescomplemented
25C4⋊#1113C2212yescomplemented
26C4⋊#1113C2212yescomplemented
27C4⋊#1113C2212yescomplemented
28C4⋊#1113C2212yescomplemented
29C3⋊D3×#67C2212yescomplemented
30C3⋊D3×#67C2218yescomplemented
31#89028C2212yescomplemented
32#89026C2214yescomplemented
33C3⋊D3×D12C2211yescharacteristic, complemented
34D3×C4⋊(C3⋊D3)C2214yescomplemented
35C4×D3×C3⋊D3C2212yescomplemented
36#89021C2214yescomplemented
37#89020C2212yescomplemented
38#89018C2211yescharacteristic, complemented
39#89017C2214yescomplemented
40C3⋊D3×Dic6C2211yescharacteristic, complemented
41#89014C2211yescharacteristic, complemented
42C3×#3811C2212yescomplemented
43C3×#3811C2218yescomplemented
44C3×#3805C2212yescomplemented
45C3×#3802C2211yescharacteristic, complemented
46C3×D3×D12C2214yescomplemented
47C3×D3×D12C2214yescomplemented
48C3×C4×D32C2212yescomplemented
49C3×#3799C2214yescomplemented
50C3×#3799C2214yescomplemented
51C3×#3798C2212yescomplemented
52C3×#3797C2211yescharacteristic, complemented
53C3×#3796C2212yescomplemented
54#88965C2214yescomplemented
55#88964C2214yescomplemented
56#88960C2218yescomplemented
57#88955C2214yescomplemented
58#88955C2218yescomplemented
59#88954C2214yescomplemented
60#88953C2214yescomplemented
61#88953C2218yescomplemented
62D3×#626C2218yescomplemented
63D3×#625C2214yescomplemented
64#88949C2214yescomplemented
65#64366—32no—
66#41×C3⋊D3—31no—
67C3×#1009—32no—
68C3×#1009—32no—
69C3×D3×#41—32no—
70#64320—34no—
71#64320—32no—
72#64319—32no—
73D3×#239—34no—
74#64314—38no—
75#64314—34no—
76#64313—34no—
77#64313—32no—
78D32×D4—38no—
79D32×D4—34no—
80D32×D4—34no—
81D32×D4—32no—
82#64308—34no—
83#64308D312yescomplemented
84#64307—32no—
85#64307—32no—
86#64307—34no—
87#64307—34no—
88#64307—62no—
89#64306—32no—
90#64306D311yescharacteristic, complemented
91D3×#235—32no—
92D3×#235—34no—
93D3×#235—61no—
94C2×#3802—31no—
95C2×#3802—32no—
96C2×D3×D12—32no—
97C2×D3×D12—34no—
98C22×C3×C3⋊D3C2311yescharacteristic
99C22×C3×C3⋊D3C2314yescomplemented
100C2×#1113—44no—
101C2×#1113C2314yes—
102C2×#1113C2314yescomplemented
103C2×D3×C3⋊D3C2312yes—
104C2×D3×C3⋊D3C2318yescomplemented
105C2×C3×D32C2312yes—
106C2×C3×D32C2318yescomplemented
107D33—48no—
108C2×C33×C4C2311yescharacteristic, complemented
109#6312C2312yescomplemented
110C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic, complemented
111C4×C3⋊(C3⋊D3)C2312yescomplemented
112#6308C2311yescharacteristic, complemented
113C2×C3×C3⋊Dic3C2311yescharacteristic, complemented
114C3×C4⋊(C3⋊D3)C2314yescomplemented
115C3×C4⋊(C3⋊D3)C2314yescomplemented
116C3×C4×C3⋊D3C2311yescharacteristic
117C3×C4×C3⋊D3C2311yescharacteristic
118C3×C4×C3⋊D3C2311yescharacteristic, complemented
119C3×C4×C3⋊D3C2311yescharacteristic, complemented
120C32×#67C2314yescomplemented
121C32×#67C2312yescomplemented
122C32×D12C2312yescomplemented
123C32×D12C2311yescharacteristic, complemented
124C32×C4×D3C2314yescomplemented
125C32×C4×D3C2312yescomplemented
126C32×Dic6C2312yescomplemented
127C32×Dic6C2311yescharacteristic, complemented
128#6295C2314yescomplemented
129#6295C2314yescomplemented
130#6293C2312yescomplemented
131#6292C2318yescomplemented
132#6292C2312yescomplemented
133#6291C2312yescomplemented
134#6290C2318yescomplemented
135#6290C2312yescomplemented
136#6289C2312yescomplemented
137Dic3×C3⋊D3C2312yes—
138Dic3×C3⋊D3C2318yescomplemented
139D3×C3⋊Dic3C2312yescomplemented
140C3×#627C2312yescomplemented
141C3×#626C2318yescomplemented
142C3×#626C2314yescomplemented
143C3×#626C2318yescomplemented
144C3×#625C2312yescomplemented
145C3×#624C2312yes—
146C3×#624C2318yescomplemented
147C3×D3×Dic3C2314yescomplemented
148D3×H(5,𝔽2)—92no—
149C2×#1009—91no—
150C22×D32—32no—
151C22×D32—34no—
152C22×D32—34no—
153C22×D32—38no—
154C32×#41—32no—
155C32×#41—31no—
156#3832—34no—
157#3832—31no—
158Q8×C3⋊D3—31no—
159#3830—32no—
160#3830—31no—
161D4×C3⋊D3—32no—
162D4×C3⋊D3—38no—
163D4×C3⋊D3—34no—
164D4×C3⋊D3—31no—
165#3828—32no—
166#3828—31no—
167#3828—34no—
168#3828—32no—
169#3828—61no—
170#3828—62no—
171#3828—121no—
172C2×C4⋊(C3⋊D3)—34no—
173C2×C4⋊(C3⋊D3)C2×D312yescomplemented
174C2×C4×C3⋊D3—32no—
175C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
176C3×#239—32no—
177C3×#239—34no—
178C3×#239—34no—
179C3×D3×Q8—32no—
180C3×#237—34no—
181C3×#237—32no—
182C3×D3×D4—34no—
183C3×D3×D4—38no—
184C3×D3×D4—38no—
185C3×D3×D4—32no—
186C3×D3×D4—34no—
187C3×D3×D4—34no—
188C3×#235—21no—
189C3×#235—22no—
190C3×#235—34no—
191C3×#235—34no—
192C3×#235—34no—
193C3×#235C2×D312yescomplemented
194C3×#235C2×D312yescomplemented
195C3×#235C2×D312yescomplemented
196C2×C3×D12—32no—
197C2×C3×D12—32no—
198C2×C3×D12—34no—
199C2×C3×D12—34no—
200C2×C3×D12—62no—
201C2×C3×C4×D3—32no—
202C2×C3×C4×D3—34no—
203C2×C3×C4×D3—61no—
204#3811—38no—
205#3811—34no—
206#3811—38no—
207#3811C2×D312yescomplemented
208#3811C2×D318yescomplemented
209D3×#67—38no—
210D3×#67—34no—
211D3×#67—38no—
212D3×#67—38no—
213D3×#67—38no—
214D3×#67—38no—
215D3×#67—38no—
216D3×#67—38no—
217D3×#67—62no—
218D3×#67—68no—
219C2×#626—34no—
220C2×#626—38no—
221C2×#625—32no—
222C2×#625—34no—
223#3805—34no—
224#3805C2×D312yescomplemented
225#3804—34no—
226#3804—38no—
227#3804—62no—
228#3802—34no—
229#3802—38no—
230#3802—32no—
231#3802—32no—
232#3802—32no—
233#3802—32no—
234#3802—34no—
235#3802—34no—
236#3802—34no—
237#3802—64no—
238#3802C2×D311yescharacteristic, complemented
239D3×D12—38no—
240D3×D12—34no—
241D3×D12—34no—
242D3×D12—34no—
243D3×D12—34no—
244D3×D12—32no—
245D3×D12—34no—
246D3×D12—34no—
247D3×D12—38no—
248D3×D12—38no—
249D3×D12—38no—
250D3×D12—64no—
251D3×D12—61no—
252D3×D12C2×D314yescomplemented
253D3×D12C2×D314yescomplemented
254C4×D32—34no—
255C4×D32—34no—
256C4×D32—38no—
257C4×D32—62no—
258C4×D32C2×D312yescomplemented
259#3799—32no—
260#3799—38no—
261#3799—61no—
262#3799C2×D314yescomplemented
263#3799C2×D314yescomplemented
264#3798—34no—
265#3798—34no—
266#3798—38no—
267#3798—62no—
268#3798C2×D312yescomplemented
269#3797C2×D311yescharacteristic, complemented
270#3796—34no—
271#3796—34no—
272#3796—38no—
273#3796—64no—
274#3796C2×D312yescomplemented
275#3795—32no—
276#3795—34no—
277#3795—34no—
278#3795—38no—
279#3795—64no—
280#3795—61no—
281D3×Dic6—32no—
282D3×Dic6—61no—
283C22×C33C2411yescharacteristic
284C2×C3⋊(C3⋊D3)C2412yes—
285C2×C3×C3⋊D3—22no—
286C2×C3×C3⋊D3—44no—
287C2×C3×C3⋊D3C2418yes—
288C2×C3×C3⋊D3C2411yescharacteristic
289C2×C3×C3⋊D3C2411yescharacteristic
290C2×C32×D3C2414yes—
291C2×C32×D3C2412yes—
292#1113—28no—
293#1113—44no—
294D3×C3⋊D3—24no—
295D3×C3⋊D3—48no—
296C3×D32—24no—
297C3×D32—48no—
298C33×C4C2411yescharacteristic
299C33×C4C2411yescharacteristic
300C3⋊(C3⋊Dic3)C2412yes—
301C3×C3⋊Dic3C2411yescharacteristic
302C3×C3⋊Dic3C2411yescharacteristic
303C32×Dic3C2414yes—
304C32×Dic3C2412yes—
305C3×H(5,𝔽2)—92no—
306C2×C3×#41—91no—
307#1009—32no—
308#1009—32no—
309#1009—92no—
310#1009—94no—
311#1009—92no—
312#1009—92no—
313#1009—92no—
314#1009—94no—
315#1009—94no—
316#1009—94no—
317#1009—182no—
318D3×#41—32no—
319D3×#41—94no—
320D3×#41—92no—
321D3×#41—94no—
322D3×#41—181no—
323C2×#239—92no—
324#1004—94no—
325#1004—94no—
326#1004—98no—
327#1004—92no—
328C2×D3×D4—92no—
329C2×D3×D4—94no—
330C2×D3×D4—94no—
331C2×D3×D4—94no—
332C2×D3×D4—92no—
333C2×D3×D4—98no—
334C2×#235—92no—
335C2×#235—91no—
336C22×D12—91no—
337C22×D12—92no—
338C22×C3⋊D3—32no—
339C22×C3⋊D3—38no—
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3⋊D3C22×D314yescomplemented
342C22×C3×D3—32no—
343C22×C3×D3—34no—
344C22×C3×D3—34no—
345C22×C3×D3—34no—
346C22×C3×D3—38no—
347C22×C3×D3—38no—
348C22×C3×D3—61no—
349C22×C3×D3—64no—
350C2×D32—38no—
351C2×D32—34no—
352C2×D32—34no—
353C2×D32—38no—
354C2×D32—34no—
355C2×D32—38no—
356C2×D32—38no—
357C2×D32—62no—
358C2×D32—68no—
359C2×D32—128no—
360C2×D32—1216no—
361C2×D32—128no—
362C2×D32—124no—
363C2×D32C22×D312yes—
364C2×D32C22×D318yescomplemented
365C32×Q8—32no—
366C32×Q8—31no—
367C32×D4—32no—
368C32×D4—34no—
369C32×D4—31no—
370C32×D4—32no—
371C2×C32×C4—21no—
372C2×C32×C4—22no—
373C2×C32×C4—34no—
374C2×C32×C4—32no—
375C2×C32×C4—41no—
376C2×C32×C4C22×D312yescomplemented
377C2×C32×C4C22×D311yescharacteristic, complemented
378#638—34no—
379#638—32no—
380#638—38no—
381#638—32no—
382#638—32no—
383#638—62no—
384#638—64no—
385#638—122no—
386C2×C3⋊Dic3—32no—
387C2×C3⋊Dic3C22×D311yescharacteristic, complemented
388C4⋊(C3⋊D3)—38no—
389C4⋊(C3⋊D3)—32no—
390C4⋊(C3⋊D3)—32no—
391C4⋊(C3⋊D3)—31no—
392C4⋊(C3⋊D3)—61no—
393C4⋊(C3⋊D3)—62no—
394C4⋊(C3⋊D3)—121no—
395C4⋊(C3⋊D3)C22×D314yescomplemented
396C4⋊(C3⋊D3)C22×D314yescomplemented
397C4×C3⋊D3—32no—
398C4×C3⋊D3—38no—
399C4×C3⋊D3—32no—
400C4×C3⋊D3—34no—
401C4×C3⋊D3—32no—
402C4×C3⋊D3—64no—
403C4×C3⋊D3—62no—
404C4×C3⋊D3—122no—
405C4×C3⋊D3C22×D311yescharacteristic
406C4×C3⋊D3C22×D311yescharacteristic
407C4×C3⋊D3C22×D311yescharacteristic, complemented
408C4×C3⋊D3C22×D311yescharacteristic, complemented
409#634—32no—
410#634—31no—
411#634—32no—
412#634—61no—
413#634—62no—
414#634—121no—
415C3×#67—22no—
416C3×#67—24no—
417C3×#67—34no—
418C3×#67—38no—
419C3×#67—38no—
420C3×#67—34no—
421C3×#67C22×D314yescomplemented
422C3×#67C22×D314yescomplemented
423C3×#67C22×D314yescomplemented
424C2×C3×Dic3—32no—
425C2×C3×Dic3—34no—
426C2×C3×Dic3—61no—
427C3×D12—21no—
428C3×D12—22no—
429C3×D12—38no—
430C3×D12—38no—
431C3×D12—34no—
432C3×D12—34no—
433C3×D12—34no—
434C3×D12—34no—
435C3×D12—34no—
436C3×D12—64no—
437C3×D12—64no—
438C3×D12C22×D312yescomplemented
439C3×D12C22×D312yescomplemented
440C3×D12C22×D312yescomplemented
441C3×C4×D3—24no—
442C3×C4×D3—22no—
443C3×C4×D3—34no—
444C3×C4×D3—32no—
445C3×C4×D3—32no—
446C3×C4×D3—32no—
447C3×C4×D3—32no—
448C3×C4×D3—34no—
449C3×C4×D3—38no—
450C3×C4×D3—38no—
451C3×C4×D3—61no—
452C3×C4×D3—61no—
453C3×C4×D3—61no—
454C3×C4×D3—61no—
455C3×C4×D3C22×D314yescomplemented
456C3×C4×D3C22×D314yescomplemented
457C3×C4×D3C22×D314yescomplemented
458C3×Dic6—21no—
459C3×Dic6—22no—
460C3×Dic6—34no—
461C3×Dic6C22×D312yescomplemented
462C3×Dic6C22×D312yescomplemented
463C3×Dic6C22×D312yescomplemented
464#627—34no—
465#627—62no—
466#627C22×D312yescomplemented
467#626—38no—
468#626—38no—
469#626—34no—
470#626—38no—
471#626—38no—
472#626—34no—
473#626—62no—
474#626—68no—
475#626—62no—
476#626C22×D318yescomplemented
477#626C22×D314yescomplemented
478#626C22×D318yescomplemented
479#625—38no—
480#625—38no—
481#625—34no—
482#625—34no—
483#625—34no—
484#625—62no—
485#625—68no—
486#625C22×D312yescomplemented
487#624—34no—
488#624—62no—
489#624C22×D312yes—
490#624C22×D318yescomplemented
491D3×Dic3—34no—
492D3×Dic3—34no—
493D3×Dic3—38no—
494D3×Dic3—38no—
495D3×Dic3—62no—
496D3×Dic3—62no—
497D3×Dic3—68no—
498D3×Dic3C22×D314yescomplemented
499C2×H(5,𝔽2)—271noSylow
500C2×C33—21no—
501C2×C33C2511yescharacteristic
502C3⋊(C3⋊D3)—22no—
503C3×C3⋊D3—28no—
504C3×C3⋊D3—21no—
505C3×C3⋊D3H(5,𝔽2)12yescomplemented
506C32×D3—24no—
507C32×D3—22no—
508C23×D3—92no—
509C23×D3—94no—
510C23×D3—94no—
511C23×D3—98no—
512C3×#41—32no—
513C3×#41—32no—
514C3×#41—32no—
515C3×#41—61no—
516C3×#41—62no—
517C3×#41—92no—
518C3×#41—94no—
519C3×#41—94no—
520C3×#41—92no—
521C3×#41—92no—
522C2×C3×Q8—91no—
523C2×C3×D4—94no—
524C2×C3×D4—94no—
525C2×C3×D4—92no—
526C2×C3×D4—91no—
527C2×C3×D4—98no—
528C2×C3×D4—92no—
529C22×C3×C4—92no—
530C22×C3×C4—91no—
531C2×#67—98no—
532C2×#67—94no—
533C2×#67—94no—
534C2×#67—98no—
535C2×#67—98no—
536C2×#67—92no—
537C2×#67—98no—
538#239—32no—
539#239—34no—
540#239—34no—
541#239—94no—
542#239—92no—
543#239—94no—
544#239—94no—
545#239—94no—
546#239—181no—
547#239—184no—
548D3×Q8—32no—
549D3×Q8—92no—
550D3×Q8—181no—
551#237—34no—
552#237—32no—
553#237—98no—
554#237—98no—
555#237—92no—
556#237—94no—
557#237—94no—
558#237—94no—
559#237—181no—
560#237—182no—
561D3×D4—34no—
562D3×D4—38no—
563D3×D4—38no—
564D3×D4—32no—
565D3×D4—34no—
566D3×D4—34no—
567D3×D4—94no—
568D3×D4—94no—
569D3×D4—94no—
570D3×D4—94no—
571D3×D4—98no—
572D3×D4—98no—
573D3×D4—98no—
574D3×D4—92no—
575D3×D4—98no—
576D3×D4—98no—
577D3×D4—94no—
578D3×D4—94no—
579D3×D4—98no—
580D3×D4—98no—
581D3×D4—98no—
582D3×D4—94no—
583D3×D4—94no—
584D3×D4—98no—
585D3×D4—98no—
586D3×D4—94no—
587D3×D4—94no—
588D3×D4—94no—
589D3×D4—181no—
590D3×D4—184no—
591D3×D4—182no—
592D3×D4—188no—
593#235—34no—
594#235—34no—
595#235—34no—
596#235—98no—
597#235—98no—
598#235—98no—
599#235—94no—
600#235—94no—
601#235—94no—
602#235—91no—
603#235—92no—
604#235—92no—
605#235—91no—
606#235—92no—
607#235—91no—
608#235—182no—
609#235—184no—
610#235—181no—
611#235—182no—
612#235—361no—
613#235D3211yescharacteristic, complemented
614#235D3212yescomplemented
615C2×D12—32no—
616C2×D12—32no—
617C2×D12—34no—
618C2×D12—34no—
619C2×D12—62no—
620C2×D12—92no—
621C2×D12—94no—
622C2×D12—92no—
623C2×D12—92no—
624C2×D12—92no—
625C2×D12—98no—
626C2×D12—94no—
627C2×D12—94no—
628C2×D12—98no—
629C2×D12—92no—
630C2×D12—91no—
631C2×D12—184no—
632C2×C4×D3—32no—
633C2×C4×D3—34no—
634C2×C4×D3—61no—
635C2×C4×D3—94no—
636C2×C4×D3—98no—
637C2×C4×D3—94no—
638C2×C4×D3—92no—
639C2×C4×D3—182no—
640C2×Dic6—91no—
641C22×C32—21no—
642C22×C32—22no—
643C22×C32—34no—
644C22×C32—32no—
645C22×C32—41no—
646C22×C32C23×D312yes—
647C22×C32C23×D311yescharacteristic
648C2×C3⋊D3—22no—
649C2×C3⋊D3—34no—
650C2×C3⋊D3—32no—
651C2×C3⋊D3—44no—
652C2×C3⋊D3—62no—
653C2×C3⋊D3—64no—
654C2×C3⋊D3—64no—
655C2×C3⋊D3—122no—
656C2×C3⋊D3—128no—
657C2×C3⋊D3C23×D318yes—
658C2×C3⋊D3C23×D311yescharacteristic
659C2×C3⋊D3C23×D311yescharacteristic
660C2×C3×D3—22no—
661C2×C3×D3—24no—
662C2×C3×D3—32no—
663C2×C3×D3—38no—
664C2×C3×D3—38no—
665C2×C3×D3—32no—
666C2×C3×D3—61no—
667C2×C3×D3—68no—
668C2×C3×D3—61no—
669C2×C3×D3—68no—
670C2×C3×D3—64no—
671C2×C3×D3—122no—
672C2×C3×D3—128no—
673C2×C3×D3—128no—
674C2×C3×D3—124no—
675C2×C3×D3—124no—
676C2×C3×D3—244no—
677C2×C3×D3C23×D314yes—
678C2×C3×D3C23×D314yes—
679C2×C3×D3C23×D314yes—
680D32—24no—
681D32—48no—
682D32—68no—
683D32—616no—
684D32—68no—
685D32—124no—
686D32—128no—
687D32—128no—
688D32—124no—
689D32—128no—
690D32—248no—
691C32×C4—21no—
692C32×C4—22no—
693C32×C4—21no—
694C32×C4—22no—
695C32×C4—34no—
696C32×C4—32no—
697C32×C4—41no—
698C32×C4—41no—
699C32×C4C23×D311yescharacteristic
700C32×C4C23×D312yes—
701C32×C4C23×D312yes—
702C32×C4C23×D311yescharacteristic
703C3⋊Dic3—32no—
704C3⋊Dic3—34no—
705C3⋊Dic3—64no—
706C3⋊Dic3—62no—
707C3⋊Dic3—122no—
708C3⋊Dic3C23×D311yescharacteristic
709C3⋊Dic3C23×D311yescharacteristic
710C3×Dic3—24no—
711C3×Dic3—22no—
712C3×Dic3—32no—
713C3×Dic3—32no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3C23×D314yes—
717C3×Dic3C23×D314yes—
718C3×Dic3C23×D314yes—
719H(5,𝔽2)—92no—
720H(5,𝔽2)—272no—
721H(5,𝔽2)—274no—
722H(5,𝔽2)—272no—
723H(5,𝔽2)—274no—
724H(5,𝔽2)—272no—
725C2×#41—91no—
726C2×#41—271no—
727C2×#41—272no—
728C2×#41—272no—
729C22×D4—272no—
730C22×D4—271no—
731C22×D4—272no—
732C22×D4—274no—
733C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
734C23×C3—92no—
735C23×C3—98no—
736C23×C3—91no—
737C23×C3—94no—
738C22×D3—32no—
739C22×D3—34no—
740C22×D3—34no—
741C22×D3—34no—
742C22×D3—38no—
743C22×D3—38no—
744C22×D3—61no—
745C22×D3—64no—
746C22×D3—94no—
747C22×D3—98no—
748C22×D3—94no—
749C22×D3—98no—
750C22×D3—94no—
751C22×D3—98no—
752C22×D3—98no—
753C22×D3—92no—
754C22×D3—98no—
755C22×D3—182no—
756C22×D3—188no—
757C22×D3—3616no—
758C22×D3—368no—
759C22×D3—368no—
760C22×D3—364no—
761C3×Q8—32no—
762C3×Q8—32no—
763C3×Q8—32no—
764C3×Q8—61no—
765C3×Q8—62no—
766C3×Q8—92no—
767C3×D4—34no—
768C3×D4—34no—
769C3×D4—34no—
770C3×D4—32no—
771C3×D4—32no—
772C3×D4—32no—
773C3×D4—62no—
774C3×D4—61no—
775C3×D4—64no—
776C3×D4—62no—
777C3×D4—94no—
778C3×D4—98no—
779C3×D4—98no—
780C3×D4—92no—
781C3×D4—94no—
782C3×D4—94no—
783C2×C3×C4—21no—
784C2×C3×C4—22no—
785C2×C3×C4—34no—
786C2×C3×C4—34no—
787C2×C3×C4—34no—
788C2×C3×C4—41no—
789C2×C3×C4—62no—
790C2×C3×C4—64no—
791C2×C3×C4—92no—
792C2×C3×C4—98no—
793C2×C3×C4—94no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—91no—
797C2×C3×C4—91no—
798C2×C3×C4—91no—
799C2×C3×C4C2×D3212yescomplemented
800C2×C3×C4C2×D3211yescharacteristic, complemented
801#67—34no—
802#67—38no—
803#67—38no—
804#67—34no—
805#67—98no—
806#67—98no—
807#67—94no—
808#67—98no—
809#67—94no—
810#67—98no—
811#67—92no—
812#67—94no—
813#67—92no—
814#67—98no—
815#67—92no—
816#67—98no—
817#67—182no—
818#67—188no—
819#67—182no—
820#67—184no—
821#67—182no—
822#67—362no—
823#67C2×D3212yescomplemented
824#67C2×D3214yescomplemented
825C2×Dic3—32no—
826C2×Dic3—34no—
827C2×Dic3—61no—
828C2×Dic3—94no—
829C2×Dic3—92no—
830C2×Dic3—98no—
831C2×Dic3—182no—
832D12—38no—
833D12—38no—
834D12—34no—
835D12—34no—
836D12—34no—
837D12—34no—
838D12—34no—
839D12—64no—
840D12—64no—
841D12—98no—
842D12—98no—
843D12—94no—
844D12—94no—
845D12—94no—
846D12—92no—
847D12—91no—
848D12—92no—
849D12—182no—
850D12—181no—
851D12—188no—
852D12—182no—
853D12—361no—
854D12C2×D3211yescharacteristic, complemented
855D12C2×D3212yescomplemented
856C4×D3—34no—
857C4×D3—32no—
858C4×D3—32no—
859C4×D3—32no—
860C4×D3—32no—
861C4×D3—34no—
862C4×D3—38no—
863C4×D3—38no—
864C4×D3—61no—
865C4×D3—61no—
866C4×D3—61no—
867C4×D3—61no—
868C4×D3—94no—
869C4×D3—94no—
870C4×D3—98no—
871C4×D3—98no—
872C4×D3—92no—
873C4×D3—94no—
874C4×D3—92no—
875C4×D3—92no—
876C4×D3—182no—
877C4×D3—182no—
878C4×D3—184no—
879C4×D3—182no—
880C4×D3—188no—
881C4×D3—362no—
882C4×D3C2×D3214yescomplemented
883C4×D3C2×D3212yescomplemented
884Dic6—34no—
885Dic6—94no—
886Dic6—91no—
887Dic6—92no—
888Dic6—92no—
889Dic6—182no—
890Dic6—182no—
891Dic6—181no—
892Dic6—361no—
893Dic6C2×D3211yescharacteristic, complemented
894Dic6C2×D3212yescomplemented
895C2×C32—21no—
896C2×C32—22no—
897C2×C32—21no—
898C2×C32—22no—
899C2×C32—41no—
900C2×C32—41no—
901C2×C32—42no—
902C2×C32—62no—
903C2×C32—64no—
904C2×C32—81no—
905C2×C32C24×D311yescharacteristic
906C2×C32C24×D312yes—
907C3⋊D3—21no—
908C3⋊D3—28no—
909C3⋊D3—62no—
910C3⋊D3—64no—
911C3⋊D3—122no—
912C3⋊D3—124no—
913C3⋊D3—242no—
914C3⋊D3#100912yescomplemented
915C3×D3—24no—
916C3×D3—24no—
917C3×D3—24no—
918C3×D3—34no—
919C3×D3—42no—
920C3×D3—44no—
921C3×D3—62no—
922C3×D3—68no—
923C3×D3—68no—
924C3×D3—62no—
925C3×D3—128no—
926C3×D3—121no—
927C24—274no—
928C24—272no—
929#41—32no—
930#41—31no—
931#41—92no—
932#41—94no—
933#41—94no—
934#41—92no—
935#41—92no—
936#41—272no—
937#41—274no—
938#41—278no—
939#41—274no—
940#41—272no—
941#41—271no—
942#41—271no—
943#41—274no—
944#41—274no—
945#41—271no—
946C2×Q8—91no—
947C2×Q8—271no—
948C2×D4—94no—
949C2×D4—94no—
950C2×D4—92no—
951C2×D4—91no—
952C2×D4—98no—
953C2×D4—92no—
954C2×D4—274no—
955C2×D4—271no—
956C2×D4—274no—
957C2×D4—272no—
958C2×D4—272no—
959C2×D4—278no—
960C2×D4—272no—
961C2×D4—272no—
962C2×D4—278no—
963C2×D4—272no—
964C2×D4—274no—
965C2×D4—272no—
966C2×D4—278no—
967C2×D4—274no—
968C2×D4—274no—
969C2×D4—278no—
970C2×D4—274no—
971C22×C4—92no—
972C22×C4—91no—
973C22×C4—272no—
974C22×C4—274no—
975C22×C3—21no—
976C22×C3—22no—
977C22×C3—34no—
978C22×C3—34no—
979C22×C3—34no—
980C22×C3—41no—
981C22×C3—62no—
982C22×C3—64no—
983C22×C3—91no—
984C22×C3—98no—
985C22×C3—91no—
986C22×C3—182no—
987C22×C3—184no—
988C22×C3—364no—
989C22×C3—368no—
990C22×C3C22×D3212yes—
991C22×C3C22×D3211yescharacteristic
992C2×D3—32no—
993C2×D3—32no—
994C2×D3—38no—
995C2×D3—38no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—68no—
999C2×D3—68no—
1000C2×D3—64no—
1001C2×D3—92no—
1002C2×D3—94no—
1003C2×D3—122no—
1004C2×D3—128no—
1005C2×D3—128no—
1006C2×D3—124no—
1007C2×D3—124no—
1008C2×D3—182no—
1009C2×D3—184no—
1010C2×D3—184no—
1011C2×D3—1816no—
1012C2×D3—188no—
1013C2×D3—188no—
1014C2×D3—244no—
1015C2×D3—362no—
1016C2×D3—364no—
1017C2×D3—368no—
1018C2×D3—368no—
1019C2×D3—364no—
1020C2×D3—368no—
1021C2×D3—368no—
1022C2×D3—728no—
1023C2×D3C22×D3214yes—
1024C2×D3C22×D3212yes—
1025C3×C4—21no—
1026C3×C4—22no—
1027C3×C4—21no—
1028C3×C4—22no—
1029C3×C4—34no—
1030C3×C4—34no—
1031C3×C4—34no—
1032C3×C4—41no—
1033C3×C4—41no—
1034C3×C4—62no—
1035C3×C4—64no—
1036C3×C4—91no—
1037C3×C4—91no—
1038C3×C4C22×D3211yescharacteristic
1039C3×C4C22×D3212yes—
1040C3×C4C22×D3212yes—
1041C3×C4C22×D3211yescharacteristic
1042Dic3—32no—
1043Dic3—32no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—92no—
1047Dic3—94no—
1048Dic3—182no—
1049Dic3—184no—
1050Dic3—362no—
1051Dic3C22×D3214yes—
1052Dic3C22×D3212yes—
1053C32—22no—
1054C32—21no—
1055C32—41no—
1056C32C2×#100911yescharacteristic, complemented
1057C32D3×H(5,𝔽2)12yescomplemented
1058C23—92no—
1059C23—98no—
1060C23—91no—
1061C23—94no—
1062C23—272no—
1063C23—278no—
1064C23—274no—
1065C23—274no—
1066C23—1084no—
1067C23—1088no—
1068Q8—32no—
1069Q8—31no—
1070Q8—92no—
1071Q8—272no—
1072Q8—271no—
1073D4—32no—
1074D4—34no—
1075D4—31no—
1076D4—32no—
1077D4—98no—
1078D4—98no—
1079D4—94no—
1080D4—92no—
1081D4—94no—
1082D4—94no—
1083D4—272no—
1084D4—278no—
1085D4—272no—
1086D4—274no—
1087D4—274no—
1088D4—278no—
1089D4—272no—
1090D4—272no—
1091D4—271no—
1092C2×C4—34no—
1093C2×C4—32no—
1094C2×C4—92no—
1095C2×C4—98no—
1096C2×C4—94no—
1097C2×C4—91no—
1098C2×C4—91no—
1099C2×C4—91no—
1100C2×C4—91no—
1101C2×C4—91no—
1102C2×C4—272no—
1103C2×C4—272no—
1104C2×C4—278no—
1105C2×C4—272no—
1106C2×C4—272no—
1107C2×C4D3311yescharacteristic, complemented
1108C2×C3—22no—
1109C2×C3—21no—
1110C2×C3—21no—
1111C2×C3—22no—
1112C2×C3—41no—
1113C2×C3—42no—
1114C2×C3—41no—
1115C2×C3—64no—
1116C2×C3—64no—
1117C2×C3—64no—
1118C2×C3—81no—
1119C2×C3—92no—
1120C2×C3—122no—
1121C2×C3—124no—
1122C2×C3—188no—
1123C2×C3—181no—
1124C2×C3C23×D3212yes—
1125C2×C3C23×D3211yescharacteristic
1126D3—24no—
1127D3—22no—
1128D3—34no—
1129D3—62no—
1130D3—62no—
1131D3—68no—
1132D3—68no—
1133D3—121no—
1134D3—128no—
1135D3—184no—
1136D3—182no—
1137D3—362no—
1138D3—364no—
1139D3—722no—
1140C22—34no—
1141C22—32no—
1142C22—91no—
1143C22—91no—
1144C22—98no—
1145C22—182no—
1146C22—184no—
1147C22—272no—
1148C22—364no—
1149C22—368no—
1150C22—544no—
1151C22—548no—
1152C22—1088no—
1153C22—1084no—
1154C22C2×D3311yescharacteristic
1155C4—32no—
1156C4—34no—
1157C4—91no—
1158C4—91no—
1159C4—272no—
1160C4C2×D3311yescharacteristic
1161C4C2×D3311yescharacteristic
1162C3—21no—
1163C3—22no—
1164C3—41no—
1165C3D3×#100912yescomplemented
1166C3#1059669211yescharacteristic, complemented
1167C2—21no—
1168C2—64no—
1169C2—62no—
1170C2—92no—
1171C2—181no—
1172C2—188no—
1173C2—542no—
1174C2C22×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. C2×C4⋊#1113C2semidirect
2. #11724580C2semidirect
3. C3⋊D3×#235C2semidirect
4. C3×#64308C2semidirect
5. C3×#64306C2semidirect
6. #11724440C2semidirect
7. #11724416C2semidirect
8. D3×#3802C2semidirect
9. D32×D12C2semidirect
10. #11724391C2semidirect
11. #11724390C2semidirect
12. #11724389C2semidirect
13. #11724385C2semidirect
14. #11724380C2semidirect
17. C22×#1113C22semidirect
18. C2×D33C22semidirect
19. #89076C22semidirect
20. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C32×#235C22semidirect
23. C32×#235C22semidirect
24. C2×#6295C22semidirect
25. C4⋊#1113C22semidirect
26. C4⋊#1113C22semidirect
27. C4⋊#1113C22semidirect
28. C4⋊#1113C22semidirect
29. C3⋊D3×#67C22semidirect
30. C3⋊D3×#67C22semidirect
31. #89028C22semidirect
32. #89026C22semidirect
33. C3⋊D3×D12C22semidirect
34. D3×C4⋊(C3⋊D3)C22semidirect
35. C4×D3×C3⋊D3C22semidirect
36. #89021C22semidirect
37. #89020C22semidirect
38. #89018C22semidirect
39. #89017C22semidirect
40. C3⋊D3×Dic6C22semidirect
41. #89014C22semidirect
42. C3×#3811C22semidirect
43. C3×#3811C22semidirect
44. C3×#3805C22semidirect
45. C3×#3802C22semidirect
46. C3×D3×D12C22semidirect
47. C3×D3×D12C22semidirect
48. C3×C4×D32C22semidirect
49. C3×#3799C22semidirect
50. C3×#3799C22semidirect
51. C3×#3798C22semidirect
52. C3×#3797C22semidirect
53. C3×#3796C22semidirect
54. #88965C22semidirect
55. #88964C22semidirect
56. #88960C22semidirect
57. #88955C22semidirect
58. #88955C22semidirect
59. #88954C22semidirect
60. #88953C22semidirect
61. #88953C22semidirect
62. D3×#626C22semidirect
63. D3×#625C22semidirect
64. #88949C22semidirect
83. #64308D3semidirect
90. #64306D3semidirect
99. C22×C3×C3⋊D3C23semidirect
102. C2×#1113C23semidirect
104. C2×D3×C3⋊D3C23semidirect
106. C2×C3×D32C23semidirect
108. C2×C33×C4C23semidirect
109. #6312C23semidirect
110. C4⋊(C3⋊(C3⋊D3))C23semidirect
111. C4×C3⋊(C3⋊D3)C23semidirect
112. #6308C23semidirect
113. C2×C3×C3⋊Dic3C23semidirect
114. C3×C4⋊(C3⋊D3)C23semidirect
115. C3×C4⋊(C3⋊D3)C23semidirect
118. C3×C4×C3⋊D3C23semidirect
119. C3×C4×C3⋊D3C23semidirect
120. C32×#67C23semidirect
121. C32×#67C23semidirect
122. C32×D12C23semidirect
123. C32×D12C23semidirect
124. C32×C4×D3C23semidirect
125. C32×C4×D3C23semidirect
126. C32×Dic6C23semidirect
127. C32×Dic6C23semidirect
128. #6295C23semidirect
129. #6295C23semidirect
130. #6293C23semidirect
131. #6292C23semidirect
132. #6292C23semidirect
133. #6291C23semidirect
134. #6290C23semidirect
135. #6290C23semidirect
136. #6289C23semidirect
138. Dic3×C3⋊D3C23semidirect
139. D3×C3⋊Dic3C23semidirect
140. C3×#627C23semidirect
141. C3×#626C23semidirect
142. C3×#626C23semidirect
143. C3×#626C23semidirect
144. C3×#625C23semidirect
146. C3×#624C23semidirect
147. C3×D3×Dic3C23semidirect
173. C2×C4⋊(C3⋊D3)C2×D3semidirect
175. C2×C4×C3⋊D3C2×D3semidirect
193. C3×#235C2×D3semidirect
194. C3×#235C2×D3semidirect
195. C3×#235C2×D3semidirect
207. #3811C2×D3semidirect
208. #3811C2×D3semidirect
224. #3805C2×D3semidirect
238. #3802C2×D3semidirect
252. D3×D12C2×D3semidirect
253. D3×D12C2×D3semidirect
258. C4×D32C2×D3semidirect
262. #3799C2×D3semidirect
263. #3799C2×D3semidirect
268. #3798C2×D3semidirect
269. #3797C2×D3semidirect
274. #3796C2×D3semidirect
341. C22×C3⋊D3C22×D3semidirect
364. C2×D32C22×D3semidirect
376. C2×C32×C4C22×D3semidirect
377. C2×C32×C4C22×D3semidirect
387. C2×C3⋊Dic3C22×D3semidirect
395. C4⋊(C3⋊D3)C22×D3semidirect
396. C4⋊(C3⋊D3)C22×D3semidirect
407. C4×C3⋊D3C22×D3semidirect
408. C4×C3⋊D3C22×D3semidirect
421. C3×#67C22×D3semidirect
422. C3×#67C22×D3semidirect
423. C3×#67C22×D3semidirect
438. C3×D12C22×D3semidirect
439. C3×D12C22×D3semidirect
440. C3×D12C22×D3semidirect
455. C3×C4×D3C22×D3semidirect
456. C3×C4×D3C22×D3semidirect
457. C3×C4×D3C22×D3semidirect
461. C3×Dic6C22×D3semidirect
462. C3×Dic6C22×D3semidirect
463. C3×Dic6C22×D3semidirect
466. #627C22×D3semidirect
476. #626C22×D3semidirect
477. #626C22×D3semidirect
478. #626C22×D3semidirect
486. #625C22×D3semidirect
490. #624C22×D3semidirect
498. D3×Dic3C22×D3semidirect
505. C3×C3⋊D3H(5,𝔽2)semidirect
613. #235D32semidirect
614. #235D32semidirect
733. C33C2×H(5,𝔽2)semidirect
799. C2×C3×C4C2×D32semidirect
800. C2×C3×C4C2×D32semidirect
823. #67C2×D32semidirect
824. #67C2×D32semidirect
854. D12C2×D32semidirect
855. D12C2×D32semidirect
882. C4×D3C2×D32semidirect
883. C4×D3C2×D32semidirect
893. Dic6C2×D32semidirect
894. Dic6C2×D32semidirect
914. C3⋊D3#1009semidirect
1056. C32C2×#1009semidirect
1057. C32D3×H(5,𝔽2)semidirect
1107. C2×C4D33semidirect
1165. C3D3×#1009semidirect
1166. C3#10596692semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#11132
#117245802
C3⋊D3×#2352
C3×#643082
C3×#643062
#117244402
#117244162
D3×#38022
D32×D122
#117243912
#117243902
#117243892
#117243852
#117243802
#105966923
D3×#10093