Finite Group Databasebeta

← C3×#10594795 #13174430

Subgroups — C3×#10594795 #13174430

Order 1728.

1498 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C2×C32×#208C211yesmaximal, characteristic, complemented
4C3×#63833C212yesmaximal, complemented
5C3×#63831C212yesmaximal, complemented
6C3×#63830C212yesmaximal, complemented
7C3×#63829C214yesmaximal, complemented
8C3×#63825C212yesmaximal, complemented
9C3×#5822—31nomaximal
10C3×#5748—31nomaximal
11#10594795C311yesmaximal, characteristic, direct product factor
12C22×C33×C4C2211yescharacteristic
13C2×C3×#638—21no—
14C3×#3828—21no—
15C3×#3828—21no—
16C3×#3828C2212yes—
17C3×#3828C2212yescomplemented
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C2×C3×C4×C3⋊D3—21no—
20C2×C3×#634C2211yescharacteristic, complemented
21C2×C32×#67—21no—
22C32×#235—21no—
23C32×#235—21no—
24C32×#235C2212yes—
25C32×#235C2212yescomplemented
26C2×C32×D12C2211yescharacteristic, complemented
27C2×C32×C4×D3—21no—
28C2×C32×Dic6C2211yescharacteristic, complemented
29C32×#208C2212yescomplemented
30C32×#208C2212yescomplemented
31C2×C32×C3⋊C8C2212yescomplemented
32C3×#3719C2214yescomplemented
33C3×#3717C2214yescomplemented
34C3×#3716C2214yescomplemented
35C3×#3714C2214yescomplemented
36C2×C32×#41—31no—
37C2×#3828C2×C311yescharacteristic, complemented
38C2×C3×#235—21no—
39C2×C3×#235—31no—
40C2×C3×#235—31no—
41C2×C3×#235—61no—
42C2×C3×#235D311yescharacteristic, complemented
43C2×C3×#235C2×C311yescharacteristic, complemented
44C2×C32×M16—31no—
45C3×#951—32no—
46C3×#950—34no—
47C3×#949—32no—
48C3×#942—32no—
49C3×#932—32no—
50C2×C3×#208—21no—
51C2×C3×#208D311yescharacteristic, complemented
52C2×C3×#208C2×C311yescharacteristic, complemented
53C3×#909—32no—
54C3×#909—32no—
55C3×#908—32no—
56C3×#908—32no—
57C3×#904—34no—
58#63833C2×C312yescomplemented
59#63831C2×C312yescomplemented
60#63830C2×C312yescomplemented
61#63829C2×C314yescomplemented
62#63825C2×C312yescomplemented
63C23×C33D411yescharacteristic
64C22×C3×C3⋊D3—21no—
65C22×C32×D3—21no—
66C2×C33×C4D411yescharacteristic
67C2×C33×C4D411yescharacteristic
68C2×C33×C4D411yescharacteristic
69C2×C33×C4C2311yescharacteristic
70C2×C33×C4C2311yescharacteristic
71C2×C33×C4C2311yescharacteristic
72C3×#638—22no—
73C3×#638—22no—
74C2×C3×C3⋊Dic3—21no—
75C3×C4⋊(C3⋊D3)—21no—
76C3×C4⋊(C3⋊D3)C2312yes—
77C3×C4×C3⋊D3—22no—
78C3×C4×C3⋊D3—22no—
79C3×#634—21no—
80C3×#634C2312yes—
81C32×#67—22no—
82C32×#67—22no—
83C2×C32×Dic3—21no—
84C32×D12—21no—
85C32×D12C2312yes—
86C32×C4×D3—22no—
87C32×C4×D3—22no—
88C32×Dic6—21no—
89C32×Dic6C2312yes—
90C32×C3⋊C8C2314yes—
91C3×#575—91no—
92#5822—31no—
93#5748—31no—
94C32×#41—32no—
95C32×#41—32no—
96C32×#41—61no—
97C32×#41—61no—
98C2×C32×Q8—31no—
99C2×C32×D4—31no—
100C2×C32×D4—61no—
101C22×C32×C4—21no—
102C22×C32×C4—21no—
103C22×C32×C4—21no—
104C22×C32×C4—41no—
105C22×C32×C4—61no—
106C22×C32×C4C2×D311yescharacteristic
107C22×C32×C4C2×D311yescharacteristic
108C22×C32×C4C22×C311yescharacteristic
109C2×#638—21no—
110#3828—21no—
111#3828—21no—
112#3828C22×C312yes—
113#3828C22×C312yescomplemented
114C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
115C2×C4×C3⋊D3—21no—
116C2×#634C22×C311yescharacteristic, complemented
117C2×C3×#67—22no—
118C2×C3×#67—21no—
119C2×C3×#67—21no—
120C2×C3×#67—62no—
121C2×C3×#67—61no—
122C2×C3×#67—61no—
123C3×#235—22no—
124C3×#235—22no—
125C3×#235—22no—
126C3×#235—22no—
127C3×#235—21no—
128C3×#235—21no—
129C3×#235—21no—
130C3×#235—21no—
131C3×#235—32no—
132C3×#235—32no—
133C3×#235—32no—
134C3×#235—32no—
135C3×#235—62no—
136C3×#235—62no—
137C3×#235—62no—
138C3×#235—62no—
139C3×#235—61no—
140C3×#235—61no—
141C3×#235—61no—
142C3×#235—61no—
143C3×#235C2×D312yes—
144C3×#235C2×D312yescomplemented
145C3×#235C22×C312yes—
146C3×#235C22×C312yescomplemented
147C2×C3×D12—21no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—61no—
151C2×C3×D12C2×D311yescharacteristic, complemented
152C2×C3×D12C22×C311yescharacteristic, complemented
153C2×C3×C4×D3—22no—
154C2×C3×C4×D3—21no—
155C2×C3×C4×D3—21no—
156C2×C3×C4×D3—62no—
157C2×C3×C4×D3—61no—
158C2×C3×C4×D3—61no—
159C2×C3×Dic6—21no—
160C2×C3×Dic6—31no—
161C2×C3×Dic6—31no—
162C2×C3×Dic6—61no—
163C2×C3×Dic6C2×D311yescharacteristic, complemented
164C2×C3×Dic6C22×C311yescharacteristic, complemented
165C32×M16—32no—
166C32×M16—32no—
167C2×C32×C8—32no—
168C3×#216—34no—
169C3×#215—34no—
170C3×#214—34no—
171C3×#213—34no—
172C3×#208—22no—
173C3×#208—22no—
174C3×#208C2×D312yescomplemented
175C3×#208C2×D312yescomplemented
176C3×#208C22×C312yescomplemented
177C3×#208C22×C312yescomplemented
178C2×C3×C3⋊C8—22no—
179C2×C3×C3⋊C8C2×D312yescomplemented
180C2×C3×C3⋊C8C22×C312yescomplemented
181C3×Dic12—34no—
182C3×D24—34no—
183C3×#204—34no—
184C3×#204—34no—
185#3719C22×C314yescomplemented
186#3717C22×C314yescomplemented
187#3716C22×C314yescomplemented
188#3714C22×C314yescomplemented
189C22×C33—41no—
190C22×C33C2×D411yescharacteristic
191C22×C33C2×D411yescharacteristic
192C22×C33C2×D411yescharacteristic
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—42no—
195C2×C32×D3—22no—
196C2×C32×D3—42no—
197C33×C4C2×D411yescharacteristic
198C33×C4C2×D411yescharacteristic
199C33×C4C2×D411yescharacteristic
200C33×C4C2411yescharacteristic
201C3×C3⋊Dic3—22no—
202C32×Dic3—22no—
203C2×C3×#41—31no—
204C2×C3×#41—31no—
205C2×C3×#41—61no—
206C2×C3×#41—91no—
207C2×#235—31no—
208C2×#235—31no—
209C2×#235—61no—
210C2×#235C3×D311yescharacteristic, complemented
211C3×#137—92no—
212C3×#137—92no—
213C3×AGL(1,ℤ/8)—92no—
214C3×AGL(1,ℤ/8)—92no—
215C3×#135—94no—
216C2×C3×M16—31no—
217C2×C3×M16—31no—
218C2×C3×M16—61no—
219#951—32no—
220#950—34no—
221#949—32no—
222#942—32no—
223#932—32no—
224C2×#208C3×D311yescharacteristic, complemented
225#909—32no—
226#909—32no—
227#908—32no—
228#908—32no—
229#904—34no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—41no—
234C23×C32—61no—
235C23×C32D1211yescharacteristic
236C23×C32#6711yescharacteristic
237C23×C32C3×D411yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3×D3—22no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—62no—
243C22×C3×D3—61no—
244C22×C3×D3—61no—
245C32×Q8—32no—
246C32×Q8—61no—
247C32×D4—32no—
248C32×D4—62no—
249C32×D4—62no—
250C32×D4—61no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—41no—
270C2×C32×C4—41no—
271C2×C32×C4—41no—
272C2×C32×C4—41no—
273C2×C32×C4—41no—
274C2×C32×C4—41no—
275C2×C32×C4—61no—
276C2×C32×C4—62no—
277C2×C32×C4—62no—
278C2×C32×C4D1211yescharacteristic
279C2×C32×C4D1211yescharacteristic
280C2×C32×C4D1211yescharacteristic
281C2×C32×C4#6711yescharacteristic
282C2×C32×C4#6711yescharacteristic
283C2×C32×C4#6711yescharacteristic
284C2×C32×C4C3×D411yescharacteristic
285C2×C32×C4C3×D411yescharacteristic
286C2×C32×C4C3×D411yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C23×C311yescharacteristic
294C2×C32×C4C23×C311yescharacteristic
295C2×C32×C4C23×C311yescharacteristic
296#638—22no—
297#638—22no—
298C2×C3⋊Dic3—21no—
299C4⋊(C3⋊D3)—21no—
300C4⋊(C3⋊D3)C23×C312yes—
301C4×C3⋊D3—22no—
302C4×C3⋊D3—22no—
303#634—21no—
304#634C23×C312yes—
305C3×#67—24no—
306C3×#67—24no—
307C3×#67—22no—
308C3×#67—22no—
309C3×#67—22no—
310C3×#67—22no—
311C3×#67—64no—
312C3×#67—64no—
313C3×#67—62no—
314C3×#67—62no—
315C3×#67—62no—
316C3×#67—62no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3—21no—
320C2×C3×Dic3—62no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C3×D12—22no—
324C3×D12—21no—
325C3×D12—21no—
326C3×D12—22no—
327C3×D12—32no—
328C3×D12—32no—
329C3×D12—62no—
330C3×D12—62no—
331C3×D12—61no—
332C3×D12—61no—
333C3×D12C22×D312yes—
334C3×D12C23×C312yes—
335C3×C4×D3—24no—
336C3×C4×D3—24no—
337C3×C4×D3—22no—
338C3×C4×D3—22no—
339C3×C4×D3—22no—
340C3×C4×D3—22no—
341C3×C4×D3—64no—
342C3×C4×D3—64no—
343C3×C4×D3—62no—
344C3×C4×D3—62no—
345C3×C4×D3—62no—
346C3×C4×D3—62no—
347C3×Dic6—22no—
348C3×Dic6—21no—
349C3×Dic6—21no—
350C3×Dic6—22no—
351C3×Dic6—32no—
352C3×Dic6—32no—
353C3×Dic6—62no—
354C3×Dic6—62no—
355C3×Dic6—61no—
356C3×Dic6—61no—
357C3×Dic6C22×D312yes—
358C3×Dic6C23×C312yes—
359C32×C8—34no—
360C3×C3⋊C8—24no—
361C3×C3⋊C8C22×D314yes—
362C3×C3⋊C8C23×C314yes—
363#575—91noSylow
364C2×C33—21no—
365C2×C33—21no—
366C2×C33—21no—
367C2×C33C22×D411yescharacteristic
368C3×C3⋊D3—42no—
369C32×D3—42no—
370C3×#41—32no—
371C3×#41—32no—
372C3×#41—32no—
373C3×#41—32no—
374C3×#41—62no—
375C3×#41—62no—
376C3×#41—62no—
377C3×#41—62no—
378C3×#41—61no—
379C3×#41—61no—
380C3×#41—61no—
381C3×#41—61no—
382C3×#41—92no—
383C3×#41—92no—
384C3×#41—181no—
385C3×#41—181no—
386C2×C3×Q8—31no—
387C2×C3×Q8—31no—
388C2×C3×Q8—61no—
389C2×C3×Q8—91no—
390C2×C3×D4—31no—
391C2×C3×D4—31no—
392C2×C3×D4—61no—
393C2×C3×D4—62no—
394C2×C3×D4—61no—
395C2×C3×D4—61no—
396C2×C3×D4—91no—
397C2×C3×D4—181no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—21no—
401C22×C3×C4—41no—
402C22×C3×C4—62no—
403C22×C3×C4—61no—
404C22×C3×C4—61no—
405C22×C3×C4—181no—
406C22×C3×C4D3211yescharacteristic
407C22×C3×C4C2×C3×D311yescharacteristic
408C22×C3×C4C2×C3×D311yescharacteristic
409C2×#67—21no—
410C2×#67—62no—
411C2×#67—61no—
412C2×#67—61no—
413#235—21no—
414#235—21no—
415#235—32no—
416#235—32no—
417#235—32no—
418#235—32no—
419#235—62no—
420#235—62no—
421#235—62no—
422#235—62no—
423#235—61no—
424#235—61no—
425#235—61no—
426#235—61no—
427#235C2×C3×D312yes—
428#235C2×C3×D312yescomplemented
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—61no—
432C2×D12C2×C3×D311yescharacteristic, complemented
433C2×C4×D3—21no—
434C2×C4×D3—62no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×Dic6—31no—
438C2×Dic6—31no—
439C2×Dic6—61no—
440C2×Dic6C2×C3×D311yescharacteristic, complemented
441C3×Q16—94no—
442C3×SD16—94no—
443C3×SD16—94no—
444C3×D8—94no—
445C3×M16—32no—
446C3×M16—32no—
447C3×M16—32no—
448C3×M16—32no—
449C3×M16—62no—
450C3×M16—62no—
451C2×C3×C8—32no—
452C2×C3×C8—32no—
453C2×C3×C8—62no—
454#216—34no—
455#215—34no—
456#214—34no—
457#213—34no—
458#208C2×C3×D312yescomplemented
459#208C2×C3×D312yescomplemented
460C2×C3⋊C8C2×C3×D312yescomplemented
461Dic12—34no—
462D24—34no—
463#204—34no—
464#204—34no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—42no—
481C22×C32—42no—
482C22×C32—42no—
483C22×C32—44no—
484C22×C32—62no—
485C22×C32—122no—
486C22×C32C2×D1211yescharacteristic
487C22×C32C2×D1211yescharacteristic
488C22×C32C2×D1211yescharacteristic
489C22×C32C2×#6711yescharacteristic
490C22×C32C2×#6711yescharacteristic
491C22×C32C2×#6711yescharacteristic
492C22×C32C2×C3×D411yescharacteristic
493C22×C32C2×C3×D411yescharacteristic
494C22×C32C2×C3×D411yescharacteristic
495C2×C3⋊D3—22no—
496C2×C3⋊D3—42no—
497C2×C3×D3—24no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—44no—
501C2×C3×D3—42no—
502C2×C3×D3—42no—
503C2×C3×D3—64no—
504C2×C3×D3—62no—
505C2×C3×D3—62no—
506C2×C3×D3—124no—
507C2×C3×D3—122no—
508C2×C3×D3—122no—
509C32×C4—21no—
510C32×C4—21no—
511C32×C4—21no—
512C32×C4—21no—
513C32×C4—21no—
514C32×C4—21no—
515C32×C4—21no—
516C32×C4—21no—
517C32×C4—21no—
518C32×C4—21no—
519C32×C4—21no—
520C32×C4—21no—
521C32×C4—41no—
522C32×C4—41no—
523C32×C4—41no—
524C32×C4—41no—
525C32×C4—62no—
526C32×C4C2×D1211yescharacteristic
527C32×C4C2×D1211yescharacteristic
528C32×C4C2×D1211yescharacteristic
529C32×C4C2×#6711yescharacteristic
530C32×C4C2×#6711yescharacteristic
531C32×C4C2×#6711yescharacteristic
532C32×C4C2×C3×D411yescharacteristic
533C32×C4C2×C3×D411yescharacteristic
534C32×C4C2×C3×D411yescharacteristic
535C32×C4C23×D311yescharacteristic
536C32×C4C23×D311yescharacteristic
537C32×C4C24×C311yescharacteristic
538C3⋊Dic3—22no—
539C3×Dic3—24no—
540C3×Dic3—22no—
541C3×Dic3—22no—
542C3×Dic3—64no—
543C3×Dic3—62no—
544C3×Dic3—62no—
545C2×#41—31no—
546C2×#41—91no—
547#137—92no—
548#137—92no—
549AGL(1,ℤ/8)—92no—
550AGL(1,ℤ/8)—92no—
551#135—94no—
552C2×M16—31no—
553C33#57511yescharacteristic, complemented, Sylow
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—41no—
558C23×C3—62no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—181no—
562C23×C3#62611yescharacteristic
563C23×C3C3×D1211yescharacteristic
564C23×C3C3×#6711yescharacteristic
565C22×D3—21no—
566C22×D3—62no—
567C22×D3—61no—
568C22×D3—61no—
569C3×Q8—32no—
570C3×Q8—32no—
571C3×Q8—62no—
572C3×Q8—62no—
573C3×Q8—61no—
574C3×Q8—61no—
575C3×Q8—92no—
576C3×Q8—181no—
577C3×D4—32no—
578C3×D4—32no—
579C3×D4—62no—
580C3×D4—62no—
581C3×D4—64no—
582C3×D4—64no—
583C3×D4—62no—
584C3×D4—62no—
585C3×D4—62no—
586C3×D4—62no—
587C3×D4—61no—
588C3×D4—61no—
589C3×D4—92no—
590C3×D4—182no—
591C3×D4—182no—
592C3×D4—181no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—64no—
618C2×C3×C4—64no—
619C2×C3×C4—62no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—181no—
627C2×C3×C4—182no—
628C2×C3×C4—182no—
629C2×C3×C4#62611yescharacteristic
630C2×C3×C4#62611yescharacteristic
631C2×C3×C4#62611yescharacteristic
632C2×C3×C4C3×D1211yescharacteristic
633C2×C3×C4C3×D1211yescharacteristic
634C2×C3×C4C3×D1211yescharacteristic
635C2×C3×C4C3×#6711yescharacteristic
636C2×C3×C4C3×#6711yescharacteristic
637C2×C3×C4C3×#6711yescharacteristic
638C2×C3×C4C2×D3211yescharacteristic
639C2×C3×C4C2×D3211yescharacteristic
640C2×C3×C4C2×D3211yescharacteristic
641C2×C3×C4C22×C3×D311yescharacteristic
642C2×C3×C4C22×C3×D311yescharacteristic
643C2×C3×C4C22×C3×D311yescharacteristic
644C2×C3×C4C22×C3×D311yescharacteristic
645C2×C3×C4C22×C3×D311yescharacteristic
646C2×C3×C4C22×C3×D311yescharacteristic
647#67—22no—
648#67—22no—
649#67—64no—
650#67—64no—
651#67—62no—
652#67—62no—
653#67—62no—
654#67—62no—
655C2×Dic3—21no—
656C2×Dic3—62no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659D12—21no—
660D12—32no—
661D12—32no—
662D12—62no—
663D12—62no—
664D12—61no—
665D12—61no—
666D12C22×C3×D312yes—
667C4×D3—22no—
668C4×D3—22no—
669C4×D3—64no—
670C4×D3—64no—
671C4×D3—62no—
672C4×D3—62no—
673C4×D3—62no—
674C4×D3—62no—
675Dic6—21no—
676Dic6—32no—
677Dic6—32no—
678Dic6—62no—
679Dic6—62no—
680Dic6—61no—
681Dic6—61no—
682Dic6C22×C3×D312yes—
683C3×C8—34no—
684C3×C8—34no—
685C3×C8—64no—
686C3⋊C8C22×C3×D314yes—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—22no—
691C2×C32—22no—
692C2×C32—22no—
693C2×C32—21no—
694C2×C32—21no—
695C2×C32—21no—
696C2×C32—21no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—21no—
700C2×C32—21no—
701C2×C32—21no—
702C2×C32—41no—
703C2×C32—41no—
704C2×C32—41no—
705C2×C32—41no—
706C2×C32—41no—
707C2×C32—41no—
708C2×C32—41no—
709C2×C32—42no—
710C2×C32—42no—
711C2×C32—42no—
712C2×C32—122no—
713C2×C32C22×D1211yescharacteristic
714C2×C32C22×#6711yescharacteristic
715C2×C32C22×C3×D411yescharacteristic
716C3⋊D3—42no—
717C3×D3—44no—
718C3×D3—42no—
719C3×D3—42no—
720C3×D3—124no—
721C3×D3—122no—
722C3×D3—122no—
723#41—32no—
724#41—32no—
725#41—61no—
726#41—61no—
727#41—92no—
728#41—92no—
729#41—181no—
730#41—181no—
731C2×Q8—31no—
732C2×Q8—91no—
733C2×D4—31no—
734C2×D4—61no—
735C2×D4—91no—
736C2×D4—181no—
737C22×C4—61no—
738C22×C4—181no—
739C22×C4C3×D3211yescharacteristic
740Q16—94no—
741SD16—94no—
742SD16—94no—
743D8—94no—
744M16—32no—
745M16—32no—
746C2×C8—32no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—44no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—64no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—124no—
770C22×C3—122no—
771C22×C3—122no—
772C22×C3—182no—
773C22×C3—362no—
774C22×C3C2×#62611yescharacteristic
775C22×C3C2×#62611yescharacteristic
776C22×C3C2×#62611yescharacteristic
777C22×C3C2×C3×D1211yescharacteristic
778C22×C3C2×C3×D1211yescharacteristic
779C22×C3C2×C3×D1211yescharacteristic
780C22×C3C2×C3×#6711yescharacteristic
781C22×C3C2×C3×#6711yescharacteristic
782C22×C3C2×C3×#6711yescharacteristic
783C2×D3—22no—
784C2×D3—42no—
785C2×D3—64no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—124no—
789C2×D3—122no—
790C2×D3—122no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—64no—
808C3×C4—62no—
809C3×C4—62no—
810C3×C4—182no—
811C3×C4C2×#62611yescharacteristic
812C3×C4C2×#62611yescharacteristic
813C3×C4C2×#62611yescharacteristic
814C3×C4C2×C3×D1211yescharacteristic
815C3×C4C2×C3×D1211yescharacteristic
816C3×C4C2×C3×D1211yescharacteristic
817C3×C4C2×C3×#6711yescharacteristic
818C3×C4C2×C3×#6711yescharacteristic
819C3×C4C2×C3×#6711yescharacteristic
820C3×C4C22×D3211yescharacteristic
821C3×C4C23×C3×D311yescharacteristic
822C3×C4C23×C3×D311yescharacteristic
823Dic3—22no—
824Dic3—64no—
825Dic3—62no—
826Dic3—62no—
827C32—21no—
828C32—21no—
829C32—21no—
830C32—41no—
831C32#574811yescharacteristic, complemented
832C32#582211yescharacteristic, complemented
833C32C3×#57511yescharacteristic, complemented
834C23—61no—
835C23—181no—
836C23C3×#62611yescharacteristic
837Q8—32no—
838Q8—61no—
839Q8—92no—
840Q8—181no—
841D4—32no—
842D4—62no—
843D4—62no—
844D4—61no—
845D4—92no—
846D4—182no—
847D4—182no—
848D4—181no—
849C2×C4—61no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—181no—
853C2×C4—182no—
854C2×C4—182no—
855C2×C4C3×#62611yescharacteristic
856C2×C4C3×#62611yescharacteristic
857C2×C4C3×#62611yescharacteristic
858C2×C4C2×C3×D3211yescharacteristic
859C2×C4C2×C3×D3211yescharacteristic
860C2×C4C2×C3×D3211yescharacteristic
861C8—34no—
862C2×C3—22no—
863C2×C3—22no—
864C2×C3—22no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—41no—
878C2×C3—41no—
879C2×C3—41no—
880C2×C3—41no—
881C2×C3—41no—
882C2×C3—41no—
883C2×C3—42no—
884C2×C3—42no—
885C2×C3—42no—
886C2×C3—41no—
887C2×C3—124no—
888C2×C3—122no—
889C2×C3—122no—
890C2×C3—362no—
891C2×C3C22×#62611yescharacteristic
892C2×C3C22×C3×D1211yescharacteristic
893C2×C3C22×C3×#6711yescharacteristic
894D3—42no—
895D3—124no—
896D3—122no—
897D3—122no—
898C22—41no—
899C22—62no—
900C22—122no—
901C22—182no—
902C22—362no—
903C22C2×C3×#62611yescharacteristic
904C22C2×C3×#62611yescharacteristic
905C22C2×C3×#62611yescharacteristic
906C4—62no—
907C4—182no—
908C4C2×C3×#62611yescharacteristic
909C4C2×C3×#62611yescharacteristic
910C4C2×C3×#62611yescharacteristic
911C4C22×C3×D3211yescharacteristic
912C3—21no—
913C3—21no—
914C3—21no—
915C3—41no—
916C3#1059479511yescharacteristic, direct product factor
917C3C3×#574811yescharacteristic, complemented
918C3C3×#582211yescharacteristic, complemented
919C2—21no—
920C2—21no—
921C2—21no—
922C2—122no—
923C2—362no—
924C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC3×C4C2×#626
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC22×C33×C4C22
socleC2×C33C22×D4
hypercenterC22×C3×C4D32
hypocenterC32C3×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×C32×#235C2semidirect
3. C2×C32×#208C2semidirect
4. C3×#63833C2semidirect
5. C3×#63831C2semidirect
6. C3×#63830C2semidirect
7. C3×#63829C2semidirect
8. C3×#63825C2semidirect
11. #10594795C3direct (N × H)
17. C3×#3828C22semidirect
18. C2×C3×C4⋊(C3⋊D3)C22semidirect
20. C2×C3×#634C22semidirect
25. C32×#235C22semidirect
26. C2×C32×D12C22semidirect
28. C2×C32×Dic6C22semidirect
29. C32×#208C22semidirect
30. C32×#208C22semidirect
31. C2×C32×C3⋊C8C22semidirect
32. C3×#3719C22semidirect
33. C3×#3717C22semidirect
34. C3×#3716C22semidirect
35. C3×#3714C22semidirect
37. C2×#3828C2×C3semidirect
42. C2×C3×#235D3semidirect
43. C2×C3×#235C2×C3semidirect
51. C2×C3×#208D3semidirect
52. C2×C3×#208C2×C3semidirect
58. #63833C2×C3semidirect
59. #63831C2×C3semidirect
60. #63830C2×C3semidirect
61. #63829C2×C3semidirect
62. #63825C2×C3semidirect
113. #3828C22×C3semidirect
114. C2×C4⋊(C3⋊D3)C22×C3semidirect
116. C2×#634C22×C3semidirect
144. C3×#235C2×D3semidirect
146. C3×#235C22×C3semidirect
151. C2×C3×D12C2×D3semidirect
152. C2×C3×D12C22×C3semidirect
163. C2×C3×Dic6C2×D3semidirect
164. C2×C3×Dic6C22×C3semidirect
174. C3×#208C2×D3semidirect
175. C3×#208C2×D3semidirect
176. C3×#208C22×C3semidirect
177. C3×#208C22×C3semidirect
179. C2×C3×C3⋊C8C2×D3semidirect
180. C2×C3×C3⋊C8C22×C3semidirect
185. #3719C22×C3semidirect
186. #3717C22×C3semidirect
187. #3716C22×C3semidirect
188. #3714C22×C3semidirect
210. C2×#235C3×D3semidirect
224. C2×#208C3×D3semidirect
428. #235C2×C3×D3semidirect
432. C2×D12C2×C3×D3semidirect
440. C2×Dic6C2×C3×D3semidirect
458. #208C2×C3×D3semidirect
459. #208C2×C3×D3semidirect
460. C2×C3⋊C8C2×C3×D3semidirect
553. C33#575semidirect
831. C32#5748semidirect
832. C32#5822semidirect
833. C32C3×#575semidirect
916. C3#10594795direct (N × H)
917. C3C3×#5748semidirect
918. C3C3×#5822semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C32×#2352
C2×C32×#2082
C3×#638332
C3×#638312
C3×#638302
C3×#638292
C3×#638252
C3×#58223
C3×#57483
#105947953