Finite Group Databasebeta

← C3×D3×#951 #13175060

Subgroups — C3×D3×#951 #13175060

Order 1728.

1356 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
1C32×D3×#41C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C3×#64160C211yesmaximal, characteristic, complemented
4C32×#951C211yesmaximal, characteristic, complemented
5C3×#63943C212yesmaximal, complemented
6C3×D3×#216C212yesmaximal, complemented
7C3×#63929C212yesmaximal, complemented
8C3×D3×#214C212yesmaximal, complemented
9C3×#63831C211yesmaximal, characteristic, complemented
10C3×#63827C211yesmaximal, characteristic, complemented
11C3×D3×#208C211yesmaximal, characteristic, complemented
12C2×C3×#951—31nomaximal
13C3×D3×#137—31nomaximal
14D3×#951C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic, complemented
17C32×#239C2211yescharacteristic
18C32×D3×Q8C2211yescharacteristic
19C32×#237—21no—
20C32×#237C2211yescharacteristic
21C32×D3×D4—21no—
22C32×D3×D4C2211yescharacteristic
23C32×#235—21no—
24C32×#235C2211yescharacteristic
25C2×C32×C4×D3—21no—
26C2×C32×C4×D3C2211yescharacteristic
27C2×C32×Dic6C2211yescharacteristic, complemented
28C2×C3×#627—21no—
29C2×C3×D3×Dic3—21no—
30C3×D3×Dic6—21no—
31C3×D3×Dic6—21no—
32C3×D3×Dic6C2212yes—
33C3×D3×Dic6C2212yescomplemented
34C3×#3756C2212yescomplemented
35C3×#3754C2212yescomplemented
36C3×#3748C2211yescharacteristic, complemented
37C32×#216C2212yescomplemented
38C32×#214C2212yescomplemented
39C32×#208C2211yescharacteristic, complemented
40C3×#3719C2212yescomplemented
41C3×#3718C2212yescomplemented
42C3×#3716C2212yescomplemented
43C3×#3715C2212yescomplemented
44C3×#3711C2212yescomplemented
45C3×D3×C3⋊C8C2212yes—
46C2×C32×#41—31no—
47C3×D3×#41—21no—
48C3×D3×#41D311yescharacteristic
49C3×D3×#41C2×C311yescharacteristic
50C2×C3×D3×Q8—31no—
51C22×C3×Dic6—31no—
52C2×D3×Dic6C2×C311yescharacteristic, complemented
53C32×#137—31no—
54#64160C2×C311yescharacteristic, complemented
55C3×#951—21no—
56C3×#951—31no—
57C3×#951—31no—
58C3×#951—31no—
59C3×#951—32no—
60C3×#951—32no—
61C3×#951—31no—
62C3×#951—61no—
63C3×#951D311yescharacteristic, direct product factor
64C3×#951C2×C311yescharacteristic, complemented
65C2×C3×#216—32no—
66C3×#942—31no—
67C2×C3×#214—32no—
68C2×C3×#208—31no—
69C3×#918—32no—
70C3×D3×Q16—32no—
71C3×#915—32no—
72C3×D3×SD16—32no—
73C3×#909—31no—
74C3×D3×M16—31no—
75#63943C2×C312yescomplemented
76D3×#216C2×C312yescomplemented
77#63929C2×C312yescomplemented
78D3×#214C2×C312yescomplemented
79#63831C2×C311yescharacteristic, complemented
80#63827C2×C311yescharacteristic, complemented
81D3×#208C2×C311yescharacteristic, complemented
82C22×C32×D3—21no—
83C22×C32×D3D411yescharacteristic
84C33×Q8C2311yescharacteristic
85C33×D4—21no—
86C33×D4C2311yescharacteristic
87C2×C33×C4—21no—
88C2×C33×C4C2311yescharacteristic
89C2×C3×C3⋊Dic3—21no—
90C3×#634—21no—
91C3×#634C2312yes—
92C32×#67—21no—
93C32×#67—21no—
94C32×#67—21no—
95C2×C32×Dic3—21no—
96C2×C32×Dic3—21no—
97C2×C32×Dic3D411yescharacteristic
98C32×D12—21no—
99C32×D12C2311yescharacteristic
100C32×C4×D3—21no—
101C32×C4×D3—21no—
102C32×C4×D3—21no—
103C32×C4×D3D411yescharacteristic
104C32×C4×D3D411yescharacteristic
105C32×C4×D3C2311yescharacteristic
106C32×C4×D3C2311yescharacteristic
107C32×Dic6—21no—
108C32×Dic6—21no—
109C32×Dic6C2312yes—
110C32×Dic6C2311yescharacteristic
111C3×#627—22no—
112C3×#627—22no—
113C3×D3×Dic3—22no—
114C3×D3×Dic3—22no—
115C3×C3⋊(C3⋊C8)C2312yes—
116C32×C3⋊C8C2312yes—
117C2×C3×#137—91no—
118C2×#951—31no—
119D3×#137—31no—
120C32×#41—21no—
121C32×#41—21no—
122C32×#41—21no—
123C32×#41—31no—
124C32×#41—31no—
125C32×#41—31no—
126C32×#41—41no—
127C32×#41—61no—
128C32×#41—61no—
129C32×#41C2×D311yescharacteristic
130C32×#41C2×D311yescharacteristic
131C32×#41C22×C311yescharacteristic
132C2×C32×Q8—31no—
133C2×C32×Q8—31no—
134C2×C32×D4—31no—
135C2×C32×D4—61no—
136C22×C32×C4—31no—
137C22×C32×C4—61no—
138C2×#634C22×C311yescharacteristic, complemented
139C22×C3×Dic3—61no—
140C3×#239—21no—
141C3×#239C2×D311yescharacteristic
142C3×#239C22×C311yescharacteristic
143C3×D3×Q8—21no—
144C3×D3×Q8—32no—
145C3×D3×Q8—32no—
146C3×D3×Q8—61no—
147C3×D3×Q8—61no—
148C3×D3×Q8C2×D311yescharacteristic
149C3×D3×Q8C22×C311yescharacteristic
150C3×#237—22no—
151C3×#237—21no—
152C3×#237—21no—
153C3×#237—21no—
154C3×#237C2×D311yescharacteristic
155C3×#237C22×C311yescharacteristic
156C3×D3×D4—22no—
157C3×D3×D4—21no—
158C3×D3×D4—21no—
159C3×D3×D4—21no—
160C3×D3×D4C2×D311yescharacteristic
161C3×D3×D4C22×C311yescharacteristic
162C3×#235—22no—
163C3×#235—21no—
164C3×#235—21no—
165C3×#235—21no—
166C3×#235C2×D311yescharacteristic
167C3×#235C22×C311yescharacteristic
168C2×C3×C4×D3—22no—
169C2×C3×C4×D3—21no—
170C2×C3×C4×D3—21no—
171C2×C3×C4×D3—21no—
172C2×C3×C4×D3—61no—
173C2×C3×C4×D3C2×D311yescharacteristic
174C2×C3×C4×D3C22×C311yescharacteristic
175C2×C3×Dic6—21no—
176C2×C3×Dic6—31no—
177C2×C3×Dic6—31no—
178C2×C3×Dic6—32no—
179C2×C3×Dic6—32no—
180C2×C3×Dic6—61no—
181C2×C3×Dic6—61no—
182C2×C3×Dic6—61no—
183C2×C3×Dic6—61no—
184C2×C3×Dic6—61no—
185C2×C3×Dic6C2×D311yescharacteristic, complemented
186C2×C3×Dic6C22×C311yescharacteristic, complemented
187C2×#627—21no—
188C2×D3×Dic3—21no—
189D3×Dic6—21no—
190D3×Dic6—21no—
191D3×Dic6C22×C312yes—
192D3×Dic6C22×C312yescomplemented
193C32×Q16—32no—
194C32×SD16—32no—
195C32×M16—31no—
196#3756C22×C312yescomplemented
197#3754C22×C312yescomplemented
198#3748C22×C311yescharacteristic, complemented
199C3×#216—22no—
200C3×#216—32no—
201C3×#216—32no—
202C3×#216—32no—
203C3×#216—32no—
204C3×#216—32no—
205C3×#216—62no—
206C3×#216C2×D312yescomplemented
207C3×#216C22×C312yescomplemented
208C3×#215—32no—
209C3×#214—22no—
210C3×#214—32no—
211C3×#214—32no—
212C3×#214—32no—
213C3×#214—32no—
214C3×#214—62no—
215C3×#214C2×D312yescomplemented
216C3×#214C22×C312yescomplemented
217C3×#208—21no—
218C3×#208—31no—
219C3×#208—31no—
220C3×#208—32no—
221C3×#208—61no—
222C3×#208C2×D311yescharacteristic, complemented
223C3×#208C22×C311yescharacteristic, complemented
224C2×C3×C3⋊C8—32no—
225C3×Dic12—32no—
226C3×#204—32no—
227C3×ΓL(1,𝔽25)—32no—
228C3×D3×C8—32no—
229#3719C22×C312yescomplemented
230#3718C22×C312yescomplemented
231#3716C22×C312yescomplemented
232#3715C22×C312yescomplemented
233#3711C22×C312yescomplemented
234D3×C3⋊C8C22×C312yes—
235C22×C33—21no—
236C22×C33C2×D411yescharacteristic
237C2×C32×D3—22no—
238C2×C32×D3—21no—
239C2×C32×D3—42no—
240C2×C32×D3C2×D411yescharacteristic
241C2×C32×D3C2×D411yescharacteristic
242C33×C4—21no—
243C33×C4C2×D411yescharacteristic
244C33×C4C2411yescharacteristic
245C3×C3⋊Dic3—22no—
246C32×Dic3—21no—
247C32×Dic3—22no—
248C32×Dic3C2×D411yescharacteristic
249C32×Dic3C2×D411yescharacteristic
250C2×C3×#41—31no—
251C2×C3×#41—31no—
252C2×C3×#41—61no—
253C22×C3×Q8—91no—
254D3×#41C3×D311yescharacteristic
255C2×D3×Q8—31no—
256C22×Dic6—31no—
257C3×#137—31no—
258C3×#137—31no—
259C3×#137—61no—
260C3×#137—91no—
261C3×#137—92no—
262C3×#137—92no—
263C3×#137—91no—
264C3×#137—91no—
265C2×C3×Q16—92no—
266C2×C3×SD16—92no—
267C2×C3×M16—91no—
268#951—31no—
269#951—31no—
270#951—31no—
271#951—32no—
272#951—32no—
273#951—31no—
274#951—61no—
275#951C3×D311yescharacteristic, direct product factor
276C2×#216—32no—
277#942—31no—
278C2×#214—32no—
279C2×#208—31no—
280#918—32no—
281D3×Q16—32no—
282#915—32no—
283D3×SD16—32no—
284#909—31no—
285D3×M16—31no—
286C23×C32—31no—
287C23×C32—61no—
288C22×C3×D3—22no—
289C22×C3×D3—21no—
290C22×C3×D3—21no—
291C22×C3×D3—21no—
292C22×C3×D3#6711yescharacteristic
293C22×C3×D3C3×D411yescharacteristic
294C32×Q8—21no—
295C32×Q8—21no—
296C32×Q8—21no—
297C32×Q8—32no—
298C32×Q8—31no—
299C32×Q8—41no—
300C32×Q8—61no—
301C32×Q8—61no—
302C32×Q8C22×D311yescharacteristic
303C32×Q8C22×D311yescharacteristic
304C32×Q8C23×C311yescharacteristic
305C32×D4—21no—
306C32×D4—22no—
307C32×D4—21no—
308C32×D4—21no—
309C32×D4—21no—
310C32×D4—21no—
311C32×D4—21no—
312C32×D4—31no—
313C32×D4—41no—
314C32×D4—41no—
315C32×D4—41no—
316C32×D4—42no—
317C32×D4—61no—
318C32×D4—61no—
319C32×D4—61no—
320C32×D4—61no—
321C32×D4C22×D311yescharacteristic
322C32×D4C22×D311yescharacteristic
323C32×D4C23×C311yescharacteristic
324C2×C32×C4—21no—
325C2×C32×C4—22no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—31no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—41no—
337C2×C32×C4—41no—
338C2×C32×C4—41no—
339C2×C32×C4—42no—
340C2×C32×C4—61no—
341C2×C32×C4—61no—
342C2×C32×C4—61no—
343C2×C32×C4—61no—
344C2×C32×C4—61no—
345C2×C32×C4C22×D311yescharacteristic
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C23×C311yescharacteristic
348C2×C3⋊Dic3—21no—
349#634—21no—
350#634C23×C312yes—
351C3×#67—22no—
352C3×#67—22no—
353C3×#67—22no—
354C3×#67—21no—
355C3×#67—21no—
356C3×#67—21no—
357C3×#67—21no—
358C3×#67—21no—
359C3×#67—21no—
360C2×C3×Dic3—22no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—41no—
367C2×C3×Dic3—62no—
368C2×C3×Dic3—62no—
369C2×C3×Dic3—61no—
370C2×C3×Dic3—61no—
371C2×C3×Dic3—121no—
372C2×C3×Dic3#6711yescharacteristic
373C2×C3×Dic3C3×D411yescharacteristic
374C3×D12—22no—
375C3×D12—21no—
376C3×D12—21no—
377C3×D12—21no—
378C3×D12C22×D311yescharacteristic
379C3×D12C23×C311yescharacteristic
380C3×C4×D3—22no—
381C3×C4×D3—22no—
382C3×C4×D3—22no—
383C3×C4×D3—21no—
384C3×C4×D3—21no—
385C3×C4×D3—21no—
386C3×C4×D3—21no—
387C3×C4×D3—21no—
388C3×C4×D3—21no—
389C3×C4×D3—21no—
390C3×C4×D3—21no—
391C3×C4×D3—21no—
392C3×C4×D3—21no—
393C3×C4×D3—62no—
394C3×C4×D3—62no—
395C3×C4×D3#6711yescharacteristic
396C3×C4×D3#6711yescharacteristic
397C3×C4×D3C3×D411yescharacteristic
398C3×C4×D3C3×D411yescharacteristic
399C3×C4×D3C22×D311yescharacteristic
400C3×C4×D3C22×D311yescharacteristic
401C3×C4×D3C23×C311yescharacteristic
402C3×C4×D3C23×C311yescharacteristic
403C3×Dic6—22no—
404C3×Dic6—21no—
405C3×Dic6—21no—
406C3×Dic6—21no—
407C3×Dic6—21no—
408C3×Dic6—21no—
409C3×Dic6—22no—
410C3×Dic6—32no—
411C3×Dic6—32no—
412C3×Dic6—41no—
413C3×Dic6—62no—
414C3×Dic6—62no—
415C3×Dic6—62no—
416C3×Dic6—61no—
417C3×Dic6—61no—
418C3×Dic6—62no—
419C3×Dic6—62no—
420C3×Dic6—121no—
421C3×Dic6C22×D311yescharacteristic
422C3×Dic6C22×D312yes—
423C3×Dic6C23×C312yes—
424C3×Dic6C23×C311yescharacteristic
425#627—22no—
426#627—22no—
427D3×Dic3—22no—
428D3×Dic3—22no—
429C32×C8—32no—
430C3⋊(C3⋊C8)C23×C312yes—
431C3×C3⋊C8—22no—
432C3×C3⋊C8—32no—
433C3×C3⋊C8—32no—
434C3×C3⋊C8—62no—
435C3×C3⋊C8C22×D312yes—
436C3×C3⋊C8C23×C312yes—
437C2×#137—91noSylow
438C2×C33—21no—
439C2×C33—41no—
440C2×C33C22×D411yescharacteristic
441C32×D3—21no—
442C32×D3—41no—
443C32×D3#13712yescomplemented
444C3×#41—21no—
445C3×#41—21no—
446C3×#41—21no—
447C3×#41—31no—
448C3×#41—31no—
449C3×#41—31no—
450C3×#41—31no—
451C3×#41—31no—
452C3×#41—31no—
453C3×#41—41no—
454C3×#41—61no—
455C3×#41—61no—
456C3×#41—61no—
457C3×#41—61no—
458C3×#41—61no—
459C3×#41—62no—
460C3×#41—61no—
461C3×#41—61no—
462C3×#41—62no—
463C3×#41D3211yescharacteristic
464C3×#41C2×C3×D311yescharacteristic
465C3×#41C2×C3×D311yescharacteristic
466C2×C3×Q8—31no—
467C2×C3×Q8—31no—
468C2×C3×Q8—31no—
469C2×C3×Q8—31no—
470C2×C3×Q8—61no—
471C2×C3×Q8—61no—
472C2×C3×Q8—92no—
473C2×C3×Q8—92no—
474C2×C3×Q8—91no—
475C2×C3×Q8—181no—
476C2×C3×Q8—181no—
477C2×C3×Q8—181no—
478C2×C3×D4—31no—
479C2×C3×D4—31no—
480C2×C3×D4—61no—
481C2×C3×D4—61no—
482C2×C3×D4—61no—
483C2×C3×D4—62no—
484C22×C3×C4—31no—
485C22×C3×C4—31no—
486C22×C3×C4—61no—
487C22×C3×C4—61no—
488C22×C3×C4—61no—
489C22×C3×C4—62no—
490C22×C3×C4—181no—
491C22×Dic3—61no—
492#239C2×C3×D311yescharacteristic
493D3×Q8—32no—
494D3×Q8—32no—
495D3×Q8—61no—
496D3×Q8—61no—
497D3×Q8C2×C3×D311yescharacteristic
498#237—21no—
499#237C2×C3×D311yescharacteristic
500D3×D4—21no—
501D3×D4C2×C3×D311yescharacteristic
502#235—21no—
503#235C2×C3×D311yescharacteristic
504C2×C4×D3—21no—
505C2×C4×D3—61no—
506C2×C4×D3C2×C3×D311yescharacteristic
507C2×Dic6—31no—
508C2×Dic6—31no—
509C2×Dic6—32no—
510C2×Dic6—32no—
511C2×Dic6—61no—
512C2×Dic6—61no—
513C2×Dic6—61no—
514C2×Dic6—61no—
515C2×Dic6—61no—
516C2×Dic6C2×C3×D311yescharacteristic, complemented
517C3×Q16—32no—
518C3×Q16—32no—
519C3×Q16—62no—
520C3×Q16—92no—
521C3×Q16—92no—
522C3×Q16—92no—
523C3×SD16—32no—
524C3×SD16—32no—
525C3×SD16—62no—
526C3×SD16—92no—
527C3×SD16—92no—
528C3×SD16—92no—
529C3×M16—31no—
530C3×M16—31no—
531C3×M16—61no—
532C3×M16—92no—
533C3×M16—91no—
534C2×C3×C8—92no—
535#216—32no—
536#216—32no—
537#216—32no—
538#216—32no—
539#216—32no—
540#216—62no—
541#216C2×C3×D312yescomplemented
542#215—32no—
543#214—32no—
544#214—32no—
545#214—32no—
546#214—32no—
547#214—62no—
548#214C2×C3×D312yescomplemented
549#208—31no—
550#208—31no—
551#208—32no—
552#208—61no—
553#208C2×C3×D311yescharacteristic, complemented
554C2×C3⋊C8—32no—
555Dic12—32no—
556#204—32no—
557ΓL(1,𝔽25)—32no—
558D3×C8—32no—
559C22×C32—21no—
560C22×C32—22no—
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—31no—
567C22×C32—31no—
568C22×C32—41no—
569C22×C32—41no—
570C22×C32—41no—
571C22×C32—42no—
572C22×C32—61no—
573C22×C32—62no—
574C22×C32—122no—
575C22×C32D3×D411yescharacteristic
576C22×C32C2×#6711yescharacteristic
577C22×C32C2×C3×D411yescharacteristic
578C2×C3×D3—22no—
579C2×C3×D3—22no—
580C2×C3×D3—22no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—21no—
584C2×C3×D3—21no—
585C2×C3×D3—42no—
586C2×C3×D3—44no—
587C2×C3×D3—42no—
588C2×C3×D3—42no—
589C2×C3×D3C2×#6711yescharacteristic
590C2×C3×D3C2×#6711yescharacteristic
591C2×C3×D3C2×C3×D411yescharacteristic
592C2×C3×D3C2×C3×D411yescharacteristic
593C32×C4—21no—
594C32×C4—22no—
595C32×C4—21no—
596C32×C4—21no—
597C32×C4—21no—
598C32×C4—21no—
599C32×C4—21no—
600C32×C4—21no—
601C32×C4—21no—
602C32×C4—21no—
603C32×C4—31no—
604C32×C4—31no—
605C32×C4—41no—
606C32×C4—41no—
607C32×C4—41no—
608C32×C4—41no—
609C32×C4—42no—
610C32×C4—61no—
611C32×C4—62no—
612C32×C4D3×D411yescharacteristic
613C32×C4C2×#6711yescharacteristic
614C32×C4C2×C3×D411yescharacteristic
615C32×C4C23×D311yescharacteristic
616C32×C4C23×D311yescharacteristic
617C32×C4C24×C311yescharacteristic
618C3⋊Dic3—22no—
619C3×Dic3—22no—
620C3×Dic3—22no—
621C3×Dic3—21no—
622C3×Dic3—22no—
623C3×Dic3—21no—
624C3×Dic3—21no—
625C3×Dic3—21no—
626C3×Dic3—42no—
627C3×Dic3—62no—
628C3×Dic3—62no—
629C3×Dic3—122no—
630C3×Dic3C2×#6711yescharacteristic
631C3×Dic3C2×#6711yescharacteristic
632C3×Dic3C2×C3×D411yescharacteristic
633C3×Dic3C2×C3×D411yescharacteristic
634C2×#41—31no—
635C22×Q8—91no—
636#137—31no—
637#137—91no—
638#137—92no—
639#137—92no—
640#137—91no—
641#137—91no—
642C2×Q16—92no—
643C2×SD16—92no—
644C2×M16—91no—
645C33C2×#13711yescharacteristic, complemented, Sylow
646C23×C3—31no—
647C23×C3—31no—
648C23×C3—61no—
649C23×C3—61no—
650C23×C3—61no—
651C23×C3—62no—
652C22×D3—21no—
653C22×D3C3×#6711yescharacteristic
654C3×Q8—21no—
655C3×Q8—21no—
656C3×Q8—21no—
657C3×Q8—32no—
658C3×Q8—31no—
659C3×Q8—32no—
660C3×Q8—31no—
661C3×Q8—41no—
662C3×Q8—61no—
663C3×Q8—62no—
664C3×Q8—61no—
665C3×Q8—61no—
666C3×Q8—62no—
667C3×Q8—61no—
668C3×Q8—61no—
669C3×Q8—92no—
670C3×Q8—121no—
671C3×Q8—182no—
672C3×Q8—182no—
673C3×Q8—181no—
674C3×Q8C2×D3211yescharacteristic
675C3×Q8C22×C3×D311yescharacteristic
676C3×Q8C22×C3×D311yescharacteristic
677C3×D4—22no—
678C3×D4—21no—
679C3×D4—21no—
680C3×D4—21no—
681C3×D4—21no—
682C3×D4—21no—
683C3×D4—21no—
684C3×D4—31no—
685C3×D4—31no—
686C3×D4—41no—
687C3×D4—41no—
688C3×D4—42no—
689C3×D4—41no—
690C3×D4—61no—
691C3×D4—61no—
692C3×D4—61no—
693C3×D4—62no—
694C3×D4—61no—
695C3×D4—61no—
696C3×D4—61no—
697C3×D4—61no—
698C3×D4—62no—
699C3×D4—62no—
700C3×D4—62no—
701C3×D4—61no—
702C3×D4—61no—
703C3×D4C2×D3211yescharacteristic
704C3×D4C22×C3×D311yescharacteristic
705C3×D4C22×C3×D311yescharacteristic
706C2×C3×C4—22no—
707C2×C3×C4—21no—
708C2×C3×C4—21no—
709C2×C3×C4—21no—
710C2×C3×C4—21no—
711C2×C3×C4—21no—
712C2×C3×C4—21no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—31no—
718C2×C3×C4—31no—
719C2×C3×C4—31no—
720C2×C3×C4—31no—
721C2×C3×C4—31no—
722C2×C3×C4—31no—
723C2×C3×C4—41no—
724C2×C3×C4—41no—
725C2×C3×C4—42no—
726C2×C3×C4—41no—
727C2×C3×C4—61no—
728C2×C3×C4—61no—
729C2×C3×C4—61no—
730C2×C3×C4—61no—
731C2×C3×C4—61no—
732C2×C3×C4—61no—
733C2×C3×C4—61no—
734C2×C3×C4—61no—
735C2×C3×C4—61no—
736C2×C3×C4—62no—
737C2×C3×C4—62no—
738C2×C3×C4—62no—
739C2×C3×C4—61no—
740C2×C3×C4—61no—
741C2×C3×C4—62no—
742C2×C3×C4—61no—
743C2×C3×C4—61no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—121no—
747C2×C3×C4—182no—
748C2×C3×C4—182no—
749C2×C3×C4—181no—
750C2×C3×C4C2×D3211yescharacteristic
751C2×C3×C4C22×C3×D311yescharacteristic
752C2×C3×C4C22×C3×D311yescharacteristic
753#67—21no—
754#67—21no—
755#67—21no—
756C2×Dic3—21no—
757C2×Dic3—21no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—61no—
761C2×Dic3—61no—
762C2×Dic3—121no—
763C2×Dic3C3×#6711yescharacteristic
764D12—21no—
765D12C22×C3×D311yescharacteristic
766C4×D3—21no—
767C4×D3—21no—
768C4×D3—21no—
769C4×D3—62no—
770C4×D3—62no—
771C4×D3C3×#6711yescharacteristic
772C4×D3C3×#6711yescharacteristic
773C4×D3C22×C3×D311yescharacteristic
774C4×D3C22×C3×D311yescharacteristic
775Dic6—21no—
776Dic6—21no—
777Dic6—32no—
778Dic6—32no—
779Dic6—62no—
780Dic6—62no—
781Dic6—62no—
782Dic6—61no—
783Dic6—61no—
784Dic6—62no—
785Dic6—62no—
786Dic6—121no—
787Dic6C22×C3×D311yescharacteristic
788Dic6C22×C3×D312yes—
789C3×C8—32no—
790C3×C8—32no—
791C3×C8—62no—
792C3×C8—92no—
793C3⋊C8—32no—
794C3⋊C8—32no—
795C3⋊C8—62no—
796C3⋊C8C22×C3×D312yes—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—21no—
801C2×C32—21no—
802C2×C32—21no—
803C2×C32—32no—
804C2×C32—41no—
805C2×C32—41no—
806C2×C32—41no—
807C2×C32—41no—
808C2×C32—41no—
809C2×C32—42no—
810C2×C32—41no—
811C2×C32—41no—
812C2×C32—61no—
813C2×C32—81no—
814C2×C32—81no—
815C2×C32—81no—
816C2×C32—82no—
817C2×C32—121no—
818C2×C32C2×D3×D411yescharacteristic
819C2×C32C22×#6711yescharacteristic
820C2×C32C22×C3×D411yescharacteristic
821C3×D3—21no—
822C3×D3—21no—
823C3×D3—22no—
824C3×D3—41no—
825C3×D3—42no—
826C3×D3—41no—
827C3×D3—41no—
828C3×D3#95112yesdirect product factor
829C3×D3C3×#13712yescomplemented
830#41—31no—
831#41—31no—
832#41—31no—
833#41—61no—
834#41—61no—
835#41C3×D3211yescharacteristic
836C2×Q8—31no—
837C2×Q8—31no—
838C2×Q8—92no—
839C2×Q8—92no—
840C2×Q8—91no—
841C2×Q8—181no—
842C2×Q8—181no—
843C2×Q8—181no—
844C2×D4—31no—
845C2×D4—61no—
846C22×C4—31no—
847C22×C4—61no—
848C22×C4—181no—
849Q16—32no—
850Q16—92no—
851Q16—92no—
852Q16—92no—
853SD16—32no—
854SD16—92no—
855SD16—92no—
856SD16—92no—
857M16—31no—
858M16—92no—
859M16—91no—
860C2×C8—92no—
861C22×C3—22no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—31no—
869C22×C3—31no—
870C22×C3—31no—
871C22×C3—31no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—42no—
875C22×C3—41no—
876C22×C3—61no—
877C22×C3—61no—
878C22×C3—62no—
879C22×C3—62no—
880C22×C3—62no—
881C22×C3—61no—
882C22×C3—61no—
883C22×C3—122no—
884C22×C3—122no—
885C22×C3—122no—
886C22×C3—124no—
887C22×C3D3×#6711yescharacteristic
888C22×C3C3×D3×D411yescharacteristic
889C22×C3C2×C3×#6711yescharacteristic
890C2×D3—22no—
891C2×D3—21no—
892C2×D3—42no—
893C2×D3C2×C3×#6711yescharacteristic
894C2×D3C2×C3×#6711yescharacteristic
895C3×C4—22no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—21no—
900C3×C4—21no—
901C3×C4—21no—
902C3×C4—21no—
903C3×C4—21no—
904C3×C4—21no—
905C3×C4—31no—
906C3×C4—31no—
907C3×C4—31no—
908C3×C4—31no—
909C3×C4—41no—
910C3×C4—41no—
911C3×C4—42no—
912C3×C4—41no—
913C3×C4—41no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—62no—
917C3×C4—61no—
918C3×C4—62no—
919C3×C4—61no—
920C3×C4—62no—
921C3×C4—122no—
922C3×C4—182no—
923C3×C4D3×#6711yescharacteristic
924C3×C4C3×D3×D411yescharacteristic
925C3×C4C2×C3×#6711yescharacteristic
926C3×C4C22×D3211yescharacteristic
927C3×C4C23×C3×D311yescharacteristic
928C3×C4C23×C3×D311yescharacteristic
929Dic3—22no—
930Dic3—21no—
931Dic3—62no—
932Dic3—62no—
933Dic3—122no—
934Dic3C2×C3×#6711yescharacteristic
935Dic3C2×C3×#6711yescharacteristic
936C32—21no—
937C32—21no—
938C32—21no—
939C32—41no—
940C32D3×#13711yescharacteristic, complemented
941C32C2×#95111yescharacteristic, complemented
942C32C2×C3×#13711yescharacteristic, complemented
943C23—31no—
944C23—61no—
945Q8—32no—
946Q8—31no—
947Q8—61no—
948Q8—61no—
949Q8—92no—
950Q8—182no—
951Q8—182no—
952Q8—181no—
953Q8C2×C3×D3211yescharacteristic
954D4—21no—
955D4—31no—
956D4—61no—
957D4—61no—
958D4—61no—
959D4—61no—
960D4C2×C3×D3211yescharacteristic
961C2×C4—21no—
962C2×C4—31no—
963C2×C4—31no—
964C2×C4—31no—
965C2×C4—31no—
966C2×C4—31no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—182no—
973C2×C4—182no—
974C2×C4—181no—
975C2×C4C2×C3×D3211yescharacteristic
976C8—32no—
977C8—92no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—32no—
985C2×C3—32no—
986C2×C3—41no—
987C2×C3—41no—
988C2×C3—41no—
989C2×C3—42no—
990C2×C3—41no—
991C2×C3—41no—
992C2×C3—41no—
993C2×C3—41no—
994C2×C3—62no—
995C2×C3—61no—
996C2×C3—61no—
997C2×C3—81no—
998C2×C3—81no—
999C2×C3—81no—
1000C2×C3—82no—
1001C2×C3—121no—
1002C2×C3—122no—
1003C2×C3—121no—
1004C2×C3—121no—
1005C2×C3C2×D3×#6711yescharacteristic
1006C2×C3C2×C3×D3×D411yescharacteristic
1007C2×C3C22×C3×#6711yescharacteristic
1008D3—21no—
1009D3—41no—
1010D3C3×#95112yesdirect product factor
1011C22—21no—
1012C22—31no—
1013C22—31no—
1014C22—62no—
1015C22—61no—
1016C22—122no—
1017C22C3×D3×#6711yescharacteristic
1018C4—21no—
1019C4—31no—
1020C4—31no—
1021C4—61no—
1022C4—62no—
1023C4—182no—
1024C4C3×D3×#6711yescharacteristic
1025C4C22×C3×D3211yescharacteristic
1026C3—21no—
1027C3—21no—
1028C3—21no—
1029C3—41no—
1030C3D3×#95111yescharacteristic, direct product factor
1031C3C3×D3×#13711yescharacteristic, complemented
1032C3C2×C3×#95111yescharacteristic, complemented
1033C2—21no—
1034C2—32no—
1035C2—41no—
1036C2—61no—
1037C2—121no—
1038C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC2×C3C2×D3×#67
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
prime radicalC32×D3×#41C2
hypercenterC3×#41D32
hypocenterC32C2×C3×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. C3×#64160C2semidirect
4. C32×#951C2semidirect
5. C3×#63943C2semidirect
6. C3×D3×#216C2semidirect
7. C3×#63929C2semidirect
8. C3×D3×#214C2semidirect
9. C3×#63831C2semidirect
10. C3×#63827C2semidirect
11. C3×D3×#208C2semidirect
14. D3×#951C3direct (N × H)
16. C2×C3×#634C22semidirect
27. C2×C32×Dic6C22semidirect
33. C3×D3×Dic6C22semidirect
34. C3×#3756C22semidirect
35. C3×#3754C22semidirect
36. C3×#3748C22semidirect
37. C32×#216C22semidirect
38. C32×#214C22semidirect
39. C32×#208C22semidirect
40. C3×#3719C22semidirect
41. C3×#3718C22semidirect
42. C3×#3716C22semidirect
43. C3×#3715C22semidirect
44. C3×#3711C22semidirect
52. C2×D3×Dic6C2×C3semidirect
54. #64160C2×C3semidirect
63. C3×#951D3direct (N × H)
64. C3×#951C2×C3semidirect
75. #63943C2×C3semidirect
76. D3×#216C2×C3semidirect
77. #63929C2×C3semidirect
78. D3×#214C2×C3semidirect
79. #63831C2×C3semidirect
80. #63827C2×C3semidirect
81. D3×#208C2×C3semidirect
138. C2×#634C22×C3semidirect
185. C2×C3×Dic6C2×D3semidirect
186. C2×C3×Dic6C22×C3semidirect
192. D3×Dic6C22×C3semidirect
196. #3756C22×C3semidirect
197. #3754C22×C3semidirect
198. #3748C22×C3semidirect
206. C3×#216C2×D3semidirect
207. C3×#216C22×C3semidirect
215. C3×#214C2×D3semidirect
216. C3×#214C22×C3semidirect
222. C3×#208C2×D3semidirect
223. C3×#208C22×C3semidirect
229. #3719C22×C3semidirect
230. #3718C22×C3semidirect
231. #3716C22×C3semidirect
232. #3715C22×C3semidirect
233. #3711C22×C3semidirect
275. #951C3×D3direct (N × H)
443. C32×D3#137semidirect
516. C2×Dic6C2×C3×D3semidirect
541. #216C2×C3×D3semidirect
548. #214C2×C3×D3semidirect
553. #208C2×C3×D3semidirect
645. C33C2×#137semidirect
828. C3×D3#951direct (N × H)
829. C3×D3C3×#137semidirect
940. C32D3×#137semidirect
941. C32C2×#951semidirect
942. C32C2×C3×#137semidirect
1010. D3C3×#951direct (N × H)
1030. C3D3×#951direct (N × H)
1031. C3C3×D3×#137semidirect
1032. C3C2×C3×#951semidirect

Maximal subgroups

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

subgroupindex
C32×D3×#412
C2×C3×D3×Dic62
C3×#641602
C32×#9512
C3×#639432
C3×D3×#2162
C3×#639292
C3×D3×#2142
C3×#638312
C3×#638272
C3×D3×#2082
C2×C3×#9513
C3×D3×#1373
D3×#9513