Finite Group Databasebeta

← C3×#10595456 #13175053

Subgroups — C3×#10595456 #13175053

Order 1728.

1408 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#1009C211yesmaximal, characteristic, complemented
2C3×#64308C211yesmaximal, characteristic, complemented
3C3×#64158C211yesmaximal, characteristic, complemented
4C32×#950C211yesmaximal, characteristic, complemented
5C3×#63949C212yesmaximal, complemented
6C3×#63939C212yesmaximal, complemented
7C3×#63934C212yesmaximal, complemented
8C3×D3×#213C212yesmaximal, complemented
9C2×C3×#3714C211yesmaximal, characteristic, complemented
10C3×#63823C211yesmaximal, characteristic, complemented
11C3×#63814C211yesmaximal, characteristic, complemented
12C3×#5835—31nomaximal
13C3×#5769—31nomaximal
14#10595456C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic, complemented
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C32×#239C2212yescomplemented
18C32×D3×D4—22no—
19C32×D3×D4C2212yescomplemented
20C32×#235—21no—
21C32×#235C2211yescharacteristic
22C32×#235C2211yescharacteristic, complemented
23C2×C32×D12—21no—
24C2×C32×D12C2211yescharacteristic, complemented
25C3×#3811—22no—
26C3×D3×D12—21no—
27C3×D3×D12C2212yescomplemented
28C3×#3799—21no—
29C3×#3799C2212yescomplemented
30C3×#3755C2212yescomplemented
31C3×#3753C2212yescomplemented
32C3×#3748C2211yescharacteristic, complemented
33C32×#216C2211yescharacteristic, complemented
34C32×#215C2211yescharacteristic, complemented
35C32×#214C2211yescharacteristic, complemented
36C32×#213C2211yescharacteristic, complemented
37C2×C32×C3⋊C8C2211yescharacteristic, complemented
38C3×#3715C2212yescomplemented
39C3×#3714C2212yescomplemented
40C3×#3714C2212yescomplemented
41C3×#3713C2212yescomplemented
42C3×#3711C2212yescomplemented
43C3×D3×C3⋊C8C2212yescomplemented
44C32×H(5,𝔽2)—31no—
45C3×#1009—21no—
46C3×#1009—31no—
47C3×#1009—31no—
48C3×#1009D311yescharacteristic, complemented
49C3×#1009C2×C311yescharacteristic, complemented
50#64308C2×C311yescharacteristic, complemented
51C32×#135—31no—
52#64158C2×C311yescharacteristic, complemented
53C3×#950—21no—
54C3×#950—32no—
55C3×#950D311yescharacteristic, complemented
56C3×#950C2×C311yescharacteristic, complemented
57C3×#949—31no—
58C3×#949—31no—
59C3×#949—31no—
60C3×#949—32no—
61C3×#949—61no—
62C3×#948—31no—
63C3×#932—31no—
64C3×#932—32no—
65C2×C3×#213—32no—
66C2×C3×#213—31no—
67C3×#919—32no—
68C3×#914—32no—
69C3×#914—32no—
70C3×D3×D8—32no—
71C2×C3×D24—31no—
72C3×#901—31no—
73#63949C2×C312yescomplemented
74#63939C2×C312yescomplemented
75#63934C2×C312yescomplemented
76D3×#213C2×C312yescomplemented
77C2×#3714C2×C311yescharacteristic, complemented
78#63823C2×C311yescharacteristic, complemented
79#63814C2×C311yescharacteristic, complemented
80C22×C3×C3⋊D3—21no—
81C22×C32×D3—21no—
82C22×C32×D3—22no—
83C2×C3×D32—22no—
84C33×Q8C2311yescharacteristic
85C33×D4—21no—
86C33×D4C2311yescharacteristic
87C2×C33×C4—21no—
88C2×C33×C4C2311yescharacteristic
89C3×C4⋊(C3⋊D3)—21no—
90C3×C4⋊(C3⋊D3)C2312yes—
91C32×#67—21no—
92C32×#67—22no—
93C32×#67D412yes—
94C32×D12—22no—
95C32×D12—21no—
96C32×D12D411yescharacteristic
97C32×D12C2311yescharacteristic
98C32×D12C2312yes—
99C32×C4×D3—21no—
100C32×C4×D3—22no—
101C32×C4×D3C2312yes—
102C32×Dic6D411yescharacteristic
103C32×Dic6C2311yescharacteristic
104C3×#626—22no—
105C3×#626—22no—
106C3×#624—22no—
107C3×C3⋊(C3⋊C8)C2312yes—
108C32×C3⋊C8C2311yescharacteristic
109C32×C3⋊C8C2311yescharacteristic
110C3×#576—91no—
111#5835—31no—
112#5769—31no—
113C32×#41—21no—
114C32×#41—21no—
115C32×#41—21no—
116C32×#41—31no—
117C32×#41—32no—
118C32×#41—31no—
119C32×#41—41no—
120C32×#41—61no—
121C32×#41C2×D311yescharacteristic, complemented
122C32×#41C2×D311yescharacteristic, complemented
123C32×#41C22×C311yescharacteristic, complemented
124C2×C32×D4—32no—
125C2×C32×D4—31no—
126C2×C32×D4—61no—
127C2×C32×D4—62no—
128C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
129C3×#239—22no—
130C3×#239—32no—
131C3×#239—61no—
132C3×#239C2×D312yescomplemented
133C3×#239C22×C312yescomplemented
134C3×D3×D4—24no—
135C3×D3×D4—22no—
136C3×D3×D4—22no—
137C3×D3×D4—22no—
138C3×D3×D4—32no—
139C3×D3×D4—61no—
140C3×D3×D4—62no—
141C3×D3×D4—62no—
142C3×D3×D4C2×D312yescomplemented
143C3×D3×D4C22×C312yescomplemented
144C3×#235—22no—
145C3×#235—21no—
146C3×#235—21no—
147C3×#235—21no—
148C3×#235—21no—
149C3×#235—32no—
150C3×#235—61no—
151C3×#235C2×D311yescharacteristic
152C3×#235C2×D311yescharacteristic, complemented
153C3×#235C22×C311yescharacteristic
154C3×#235C22×C311yescharacteristic, complemented
155C2×C3×D12—22no—
156C2×C3×D12—21no—
157C2×C3×D12—21no—
158C2×C3×D12—21no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—32no—
162C2×C3×D12—61no—
163C2×C3×D12—61no—
164C2×C3×D12C2×D311yescharacteristic, complemented
165C2×C3×D12C22×C311yescharacteristic, complemented
166#3811—22no—
167D3×D12—21no—
168D3×D12C22×C312yescomplemented
169#3799—21no—
170#3799C22×C312yescomplemented
171C32×Q16—31no—
172C32×SD16—31no—
173C32×SD16—31no—
174C32×D8—31no—
175C2×C32×C8—31no—
176#3755C22×C312yescomplemented
177#3753C22×C312yescomplemented
178#3748C22×C311yescharacteristic, complemented
179C3×#216—21no—
180C3×#216C2×D311yescharacteristic, complemented
181C3×#216C22×C311yescharacteristic, complemented
182C3×#215—21no—
183C3×#215—32no—
184C3×#215—32no—
185C3×#215—32no—
186C3×#215—62no—
187C3×#215C2×D311yescharacteristic, complemented
188C3×#215C22×C311yescharacteristic, complemented
189C3×#214—21no—
190C3×#214—32no—
191C3×#214C2×D311yescharacteristic, complemented
192C3×#214C22×C311yescharacteristic, complemented
193C3×#213—21no—
194C3×#213—32no—
195C3×#213—32no—
196C3×#213—32no—
197C3×#213—32no—
198C3×#213—32no—
199C3×#213—32no—
200C3×#213—62no—
201C3×#213C2×D311yescharacteristic, complemented
202C3×#213C22×C311yescharacteristic, complemented
203C3×#208—31no—
204C3×#208—31no—
205C3×#208—32no—
206C3×#208—61no—
207C2×C3×C3⋊C8—21no—
208C2×C3×C3⋊C8—32no—
209C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
210C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
211C3×D24—32no—
212C3×D24—32no—
213C3×ΓL(1,𝔽25)—32no—
214C3×D3×C8—32no—
215#3715C22×C312yescomplemented
216#3714C22×C312yescomplemented
217#3714C22×C312yescomplemented
218#3713C22×C312yescomplemented
219#3711C22×C312yescomplemented
220D3×C3⋊C8C22×C312yescomplemented
221C22×C33—21no—
222C22×C33C2×D411yescharacteristic
223C2×C3×C3⋊D3—22no—
224C2×C3×C3⋊D3—81no—
225C2×C32×D3—22no—
226C2×C32×D3—21no—
227C2×C32×D3—82no—
228C2×C32×D3—81no—
229C2×C32×D3C2×D412yes—
230C3×D32—82no—
231C33×C4—21no—
232C33×C4C2×D411yescharacteristic
233C33×C4C2411yescharacteristic
234C32×Dic3—21no—
235C32×Dic3C2×D412yes—
236C3×H(5,𝔽2)—31no—
237C3×H(5,𝔽2)—31no—
238C3×H(5,𝔽2)—61no—
239C3×H(5,𝔽2)—91no—
240#1009—31no—
241#1009—31no—
242#1009C3×D311yescharacteristic, complemented
243C3×AGL(1,ℤ/8)—92no—
244C3×AGL(1,ℤ/8)—92no—
245C3×AGL(1,ℤ/8)—91no—
246C3×AGL(1,ℤ/8)—91no—
247C3×#135—31no—
248C3×#135—31no—
249C3×#135—61no—
250C3×#135—92no—
251C2×C3×D8—91no—
252C2×C3×D8—92no—
253C3×#131—91no—
254#950—32no—
255#950C3×D311yescharacteristic, complemented
256#949—31no—
257#949—31no—
258#949—31no—
259#949—32no—
260#949—61no—
261#948—31no—
262#932—31no—
263#932—32no—
264C2×#213—32no—
265C2×#213—31no—
266#919—32no—
267#914—32no—
268#914—32no—
269D3×D8—32no—
270C2×D24—31no—
271#901—31no—
272C23×C32—62no—
273C23×C32—61no—
274C22×C3⋊D3—21no—
275C22×C3×D3—22no—
276C22×C3×D3—24no—
277C22×C3×D3—21no—
278C22×C3×D3—21no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—62no—
282C22×C3×D3—61no—
283C22×C3×D3—61no—
284C22×C3×D3—62no—
285C22×C3×D3—121no—
286C2×D32—22no—
287C32×Q8—21no—
288C32×Q8—21no—
289C32×Q8—21no—
290C32×Q8—31no—
291C32×Q8—31no—
292C32×Q8—41no—
293C32×Q8C22×D311yescharacteristic
294C32×Q8C22×D311yescharacteristic
295C32×Q8C23×C311yescharacteristic
296C32×D4—21no—
297C32×D4—22no—
298C32×D4—21no—
299C32×D4—21no—
300C32×D4—21no—
301C32×D4—21no—
302C32×D4—21no—
303C32×D4—32no—
304C32×D4—31no—
305C32×D4—32no—
306C32×D4—31no—
307C32×D4—41no—
308C32×D4—41no—
309C32×D4—41no—
310C32×D4—42no—
311C32×D4—62no—
312C32×D4—62no—
313C32×D4—61no—
314C32×D4—61no—
315C32×D4C22×D311yescharacteristic
316C32×D4C22×D311yescharacteristic
317C32×D4C23×C311yescharacteristic
318C2×C32×C4—21no—
319C2×C32×C4—22no—
320C2×C32×C4—21no—
321C2×C32×C4—21no—
322C2×C32×C4—21no—
323C2×C32×C4—21no—
324C2×C32×C4—21no—
325C2×C32×C4—32no—
326C2×C32×C4—41no—
327C2×C32×C4—41no—
328C2×C32×C4—41no—
329C2×C32×C4—42no—
330C2×C32×C4—62no—
331C2×C32×C4—61no—
332C2×C32×C4C22×D311yescharacteristic
333C2×C32×C4C22×D311yescharacteristic
334C2×C32×C4C23×C311yescharacteristic
335C4⋊(C3⋊D3)—21no—
336C4⋊(C3⋊D3)C23×C312yes—
337C3×#67—24no—
338C3×#67—21no—
339C3×#67—21no—
340C3×#67—22no—
341C3×#67—22no—
342C3×#67—22no—
343C3×#67—41no—
344C3×#67—62no—
345C3×#67—62no—
346C3×#67#6712yes—
347C3×#67C3×D412yes—
348C3×D12—22no—
349C3×D12—24no—
350C3×D12—22no—
351C3×D12—22no—
352C3×D12—21no—
353C3×D12—21no—
354C3×D12—21no—
355C3×D12—22no—
356C3×D12—21no—
357C3×D12—32no—
358C3×D12—32no—
359C3×D12—62no—
360C3×D12—62no—
361C3×D12—62no—
362C3×D12—61no—
363C3×D12—61no—
364C3×D12—121no—
365C3×D12#6711yescharacteristic
366C3×D12C3×D411yescharacteristic
367C3×D12C22×D312yes—
368C3×D12C22×D311yescharacteristic
369C3×D12C23×C311yescharacteristic
370C3×D12C23×C312yes—
371C3×C4×D3—24no—
372C3×C4×D3—21no—
373C3×C4×D3—21no—
374C3×C4×D3—22no—
375C3×C4×D3—22no—
376C3×C4×D3—22no—
377C3×C4×D3—41no—
378C3×C4×D3—62no—
379C3×C4×D3—62no—
380C3×C4×D3C22×D312yes—
381C3×C4×D3C23×C312yes—
382C3×Dic6—21no—
383C3×Dic6—21no—
384C3×Dic6#6711yescharacteristic
385C3×Dic6C3×D411yescharacteristic
386C3×Dic6C22×D311yescharacteristic
387C3×Dic6C23×C311yescharacteristic
388#626—22no—
389#626—22no—
390#624—22no—
391C32×C8—31no—
392C32×C8—31no—
393C3⋊(C3⋊C8)C23×C312yes—
394C3×C3⋊C8—21no—
395C3×C3⋊C8—21no—
396C3×C3⋊C8—32no—
397C3×C3⋊C8—32no—
398C3×C3⋊C8—62no—
399C3×C3⋊C8C22×D311yescharacteristic
400C3×C3⋊C8C22×D311yescharacteristic
401C3×C3⋊C8C23×C311yescharacteristic
402C3×C3⋊C8C23×C311yescharacteristic
403#576—91noSylow
404C2×C33—21no—
405C2×C33—41no—
406C2×C33C22×D411yescharacteristic
407C3×C3⋊D3—42no—
408C32×D3—22no—
409C32×D3—42no—
410C32×D3—41no—
411C3×#41—21no—
412C3×#41—21no—
413C3×#41—21no—
414C3×#41—31no—
415C3×#41—31no—
416C3×#41—32no—
417C3×#41—32no—
418C3×#41—31no—
419C3×#41—31no—
420C3×#41—41no—
421C3×#41—61no—
422C3×#41—61no—
423C3×#41—62no—
424C3×#41—61no—
425C3×#41—61no—
426C3×#41—62no—
427C3×#41—92no—
428C3×#41—181no—
429C3×#41D3211yescharacteristic, complemented
430C3×#41C2×C3×D311yescharacteristic, complemented
431C3×#41C2×C3×D311yescharacteristic, complemented
432C2×C3×D4—32no—
433C2×C3×D4—32no—
434C2×C3×D4—31no—
435C2×C3×D4—31no—
436C2×C3×D4—61no—
437C2×C3×D4—62no—
438C2×C3×D4—61no—
439C2×C3×D4—61no—
440C2×C3×D4—62no—
441C2×C3×D4—62no—
442C2×C3×D4—62no—
443C2×C3×D4—64no—
444C2×C3×D4—92no—
445C2×C3×D4—91no—
446C2×C3×D4—181no—
447C2×C3×D4—182no—
448#239—32no—
449#239—61no—
450#239C2×C3×D312yescomplemented
451D3×D4—22no—
452D3×D4—32no—
453D3×D4—61no—
454D3×D4—62no—
455D3×D4—62no—
456D3×D4C2×C3×D312yescomplemented
457#235—21no—
458#235—32no—
459#235—61no—
460#235C2×C3×D311yescharacteristic
461#235C2×C3×D311yescharacteristic, complemented
462C2×D12—21no—
463C2×D12—31no—
464C2×D12—31no—
465C2×D12—32no—
466C2×D12—61no—
467C2×D12—61no—
468C2×D12C2×C3×D311yescharacteristic, complemented
469C3×Q16—31no—
470C3×Q16—31no—
471C3×Q16—61no—
472C3×SD16—31no—
473C3×SD16—31no—
474C3×SD16—31no—
475C3×SD16—31no—
476C3×SD16—61no—
477C3×SD16—61no—
478C3×SD16—92no—
479C3×SD16—92no—
480C3×D8—31no—
481C3×D8—31no—
482C3×D8—61no—
483C3×D8—92no—
484C3×D8—92no—
485C3×D8—92no—
486C3×D8—92no—
487C3×M16—92no—
488C3×M16—91no—
489C2×C3×C8—31no—
490C2×C3×C8—31no—
491C2×C3×C8—61no—
492C2×C3×C8—92no—
493#216C2×C3×D311yescharacteristic, complemented
494#215—32no—
495#215—32no—
496#215—32no—
497#215—62no—
498#215C2×C3×D311yescharacteristic, complemented
499#214—32no—
500#214C2×C3×D311yescharacteristic, complemented
501#213—32no—
502#213—32no—
503#213—32no—
504#213—32no—
505#213—32no—
506#213—32no—
507#213—62no—
508#213C2×C3×D311yescharacteristic, complemented
509#208—31no—
510#208—31no—
511#208—32no—
512#208—61no—
513C2×C3⋊C8—32no—
514C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
515D24—32no—
516D24—32no—
517ΓL(1,𝔽25)—32no—
518D3×C8—32no—
519C22×C32—21no—
520C22×C32—22no—
521C22×C32—21no—
522C22×C32—21no—
523C22×C32—21no—
524C22×C32—21no—
525C22×C32—21no—
526C22×C32—32no—
527C22×C32—41no—
528C22×C32—41no—
529C22×C32—41no—
530C22×C32—42no—
531C22×C32—62no—
532C22×C32—61no—
533C22×C32—241no—
534C22×C32—242no—
535C22×C32D3×D411yescharacteristic
536C22×C32C2×#6711yescharacteristic
537C22×C32C2×C3×D411yescharacteristic
538C2×C3⋊D3—22no—
539C2×C3⋊D3—81no—
540C2×C3×D3—24no—
541C2×C3×D3—21no—
542C2×C3×D3—22no—
543C2×C3×D3—21no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—41no—
547C2×C3×D3—62no—
548C2×C3×D3—62no—
549C2×C3×D3—82no—
550C2×C3×D3—82no—
551C2×C3×D3—81no—
552C2×C3×D3—81no—
553C2×C3×D3—84no—
554C2×C3×D3—82no—
555C2×C3×D3—122no—
556C2×C3×D3—242no—
557C2×C3×D3—242no—
558C2×C3×D3—241no—
559C2×C3×D3—241no—
560C2×C3×D3—242no—
561C2×C3×D3C2×#6712yes—
562C2×C3×D3C2×C3×D412yes—
563D32—82no—
564C32×C4—21no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—32no—
575C32×C4—41no—
576C32×C4—41no—
577C32×C4—41no—
578C32×C4—41no—
579C32×C4—42no—
580C32×C4—61no—
581C32×C4D3×D411yescharacteristic
582C32×C4C2×#6711yescharacteristic
583C32×C4C2×C3×D411yescharacteristic
584C32×C4C23×D311yescharacteristic
585C32×C4C23×D311yescharacteristic
586C32×C4C24×C311yescharacteristic
587C3×Dic3—21no—
588C3×Dic3—21no—
589C3×Dic3—22no—
590C3×Dic3—41no—
591C3×Dic3C2×#6712yes—
592C3×Dic3C2×C3×D412yes—
593H(5,𝔽2)—31no—
594H(5,𝔽2)—91no—
595AGL(1,ℤ/8)—92no—
596AGL(1,ℤ/8)—92no—
597AGL(1,ℤ/8)—91no—
598AGL(1,ℤ/8)—91no—
599#135—31no—
600#135—92no—
601C2×D8—91no—
602C2×D8—92no—
603#131—91no—
604C33#57611yescharacteristic, complemented, Sylow
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—64no—
608C23×C3—62no—
609C23×C3—61no—
610C23×C3—61no—
611C23×C3—182no—
612C23×C3—181no—
613C22×D3—21no—
614C22×D3—22no—
615C22×D3—62no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—62no—
619C22×D3—121no—
620C3×Q8—21no—
621C3×Q8—21no—
622C3×Q8—21no—
623C3×Q8—31no—
624C3×Q8—31no—
625C3×Q8—31no—
626C3×Q8—31no—
627C3×Q8—41no—
628C3×Q8—61no—
629C3×Q8—61no—
630C3×Q8C2×D3211yescharacteristic
631C3×Q8C22×C3×D311yescharacteristic
632C3×Q8C22×C3×D311yescharacteristic
633C3×D4—22no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—32no—
641C3×D4—32no—
642C3×D4—31no—
643C3×D4—32no—
644C3×D4—32no—
645C3×D4—31no—
646C3×D4—31no—
647C3×D4—31no—
648C3×D4—41no—
649C3×D4—41no—
650C3×D4—42no—
651C3×D4—41no—
652C3×D4—62no—
653C3×D4—61no—
654C3×D4—61no—
655C3×D4—62no—
656C3×D4—62no—
657C3×D4—62no—
658C3×D4—64no—
659C3×D4—62no—
660C3×D4—62no—
661C3×D4—62no—
662C3×D4—64no—
663C3×D4—61no—
664C3×D4—61no—
665C3×D4—61no—
666C3×D4—61no—
667C3×D4—92no—
668C3×D4—121no—
669C3×D4—182no—
670C3×D4—182no—
671C3×D4—181no—
672C3×D4C2×D3211yescharacteristic
673C3×D4C22×C3×D311yescharacteristic
674C3×D4C22×C3×D311yescharacteristic
675C2×C3×C4—22no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—42no—
687C2×C3×C4—41no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—64no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—121no—
695C2×C3×C4—182no—
696C2×C3×C4C2×D3211yescharacteristic
697C2×C3×C4C22×C3×D311yescharacteristic
698C2×C3×C4C22×C3×D311yescharacteristic
699#67—21no—
700#67—22no—
701#67—62no—
702#67—62no—
703#67C3×#6712yes—
704D12—22no—
705D12—21no—
706D12—32no—
707D12—32no—
708D12—62no—
709D12—62no—
710D12—62no—
711D12—61no—
712D12—61no—
713D12—121no—
714D12C3×#6711yescharacteristic
715D12C22×C3×D312yes—
716D12C22×C3×D311yescharacteristic
717C4×D3—21no—
718C4×D3—22no—
719C4×D3—62no—
720C4×D3—62no—
721C4×D3C22×C3×D312yes—
722Dic6C3×#6711yescharacteristic
723Dic6C22×C3×D311yescharacteristic
724C3×C8—31no—
725C3×C8—31no—
726C3×C8—31no—
727C3×C8—31no—
728C3×C8—61no—
729C3×C8—61no—
730C3×C8—92no—
731C3⋊C8—32no—
732C3⋊C8—32no—
733C3⋊C8—62no—
734C3⋊C8C22×C3×D311yescharacteristic
735C3⋊C8C22×C3×D311yescharacteristic
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—41no—
743C2×C32—41no—
744C2×C32—41no—
745C2×C32—41no—
746C2×C32—41no—
747C2×C32—42no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—62no—
751C2×C32—81no—
752C2×C32—81no—
753C2×C32—81no—
754C2×C32—82no—
755C2×C32—122no—
756C2×C32—121no—
757C2×C32C2×D3×D411yescharacteristic
758C2×C32C22×#6711yescharacteristic
759C2×C32C22×C3×D411yescharacteristic
760C3⋊D3—42no—
761C3×D3—22no—
762C3×D3—22no—
763C3×D3—42no—
764C3×D3—44no—
765C3×D3—41no—
766C3×D3—42no—
767C3×D3—41no—
768C3×D3—42no—
769C3×D3—81no—
770C3×D3—122no—
771C3×D3—122no—
772C3×D3—242no—
773#41—31no—
774#41—32no—
775#41—31no—
776#41—61no—
777#41—92no—
778#41—181no—
779#41C3×D3211yescharacteristic, complemented
780C2×D4—32no—
781C2×D4—31no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—92no—
785C2×D4—91no—
786C2×D4—181no—
787C2×D4—182no—
788Q16—31no—
789SD16—31no—
790SD16—31no—
791SD16—92no—
792SD16—92no—
793D8—31no—
794D8—92no—
795D8—92no—
796D8—92no—
797D8—92no—
798M16—92no—
799M16—91no—
800C2×C8—31no—
801C2×C8—92no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—32no—
810C22×C3—32no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—42no—
814C22×C3—41no—
815C22×C3—62no—
816C22×C3—64no—
817C22×C3—62no—
818C22×C3—61no—
819C22×C3—62no—
820C22×C3—61no—
821C22×C3—121no—
822C22×C3—182no—
823C22×C3—241no—
824C22×C3—241no—
825C22×C3—242no—
826C22×C3—242no—
827C22×C3—242no—
828C22×C3—244no—
829C22×C3—721no—
830C22×C3—722no—
831C22×C3D3×#6711yescharacteristic
832C22×C3C3×D3×D411yescharacteristic
833C22×C3C2×C3×#6711yescharacteristic
834C2×D3—21no—
835C2×D3—22no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—82no—
839C2×D3—81no—
840C2×D3—122no—
841C2×D3—242no—
842C2×D3—242no—
843C2×D3—241no—
844C2×D3—241no—
845C2×D3—242no—
846C2×D3C2×C3×#6712yes—
847C3×C4—22no—
848C3×C4—21no—
849C3×C4—21no—
850C3×C4—21no—
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—32no—
858C3×C4—32no—
859C3×C4—41no—
860C3×C4—41no—
861C3×C4—42no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—62no—
865C3×C4—61no—
866C3×C4—61no—
867C3×C4—121no—
868C3×C4D3×#6711yescharacteristic
869C3×C4C3×D3×D411yescharacteristic
870C3×C4C2×C3×#6711yescharacteristic
871C3×C4C22×D3211yescharacteristic
872C3×C4C23×C3×D311yescharacteristic
873C3×C4C23×C3×D311yescharacteristic
874Dic3—21no—
875Dic3C2×C3×#6712yes—
876C32—21no—
877C32—21no—
878C32—21no—
879C32—41no—
880C32#576911yescharacteristic, complemented
881C32#583511yescharacteristic, complemented
882C32C3×#57611yescharacteristic, complemented
883C23—62no—
884C23—61no—
885C23—182no—
886C23—181no—
887Q8—31no—
888Q8—31no—
889Q8C2×C3×D3211yescharacteristic
890D4—21no—
891D4—32no—
892D4—31no—
893D4—32no—
894D4—31no—
895D4—62no—
896D4—62no—
897D4—61no—
898D4—61no—
899D4—92no—
900D4—182no—
901D4—182no—
902D4—181no—
903D4C2×C3×D3211yescharacteristic
904C2×C4—21no—
905C2×C4—32no—
906C2×C4—62no—
907C2×C4—61no—
908C2×C4—182no—
909C2×C4C2×C3×D3211yescharacteristic
910C8—31no—
911C8—31no—
912C8—92no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—42no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—62no—
928C2×C3—62no—
929C2×C3—81no—
930C2×C3—81no—
931C2×C3—81no—
932C2×C3—82no—
933C2×C3—122no—
934C2×C3—124no—
935C2×C3—122no—
936C2×C3—121no—
937C2×C3—122no—
938C2×C3—121no—
939C2×C3—241no—
940C2×C3—362no—
941C2×C3C2×D3×#6711yescharacteristic
942C2×C3C2×C3×D3×D411yescharacteristic
943C2×C3C22×C3×#6711yescharacteristic
944D3—22no—
945D3—41no—
946D3—42no—
947D3—122no—
948D3—122no—
949D3—242no—
950C22—21no—
951C22—32no—
952C22—62no—
953C22—61no—
954C22—182no—
955C22—241no—
956C22—242no—
957C22—721no—
958C22—722no—
959C22C3×D3×#6711yescharacteristic
960C4—21no—
961C4—32no—
962C4—61no—
963C4C3×D3×#6711yescharacteristic
964C4C22×C3×D3211yescharacteristic
965C3—21no—
966C3—21no—
967C3—21no—
968C3—41no—
969C3#1059545611yescharacteristic, direct product factor
970C3C3×#576911yescharacteristic, complemented
971C3C3×#583511yescharacteristic, complemented
972C2—21no—
973C2—41no—
974C2—62no—
975C2—122no—
976C2—121no—
977C2—362no—
978C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC2×C3C2×D3×#67
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C3×#576
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
1. C32×#1009C2semidirect
2. C3×#64308C2semidirect
3. C3×#64158C2semidirect
4. C32×#950C2semidirect
5. C3×#63949C2semidirect
6. C3×#63939C2semidirect
7. C3×#63934C2semidirect
8. C3×D3×#213C2semidirect
9. C2×C3×#3714C2semidirect
10. C3×#63823C2semidirect
11. C3×#63814C2semidirect
14. #10595456C3direct (N × H)
15. C33×#41C22semidirect
16. C2×C3×C4⋊(C3⋊D3)C22semidirect
17. C32×#239C22semidirect
19. C32×D3×D4C22semidirect
22. C32×#235C22semidirect
24. C2×C32×D12C22semidirect
27. C3×D3×D12C22semidirect
29. C3×#3799C22semidirect
30. C3×#3755C22semidirect
31. C3×#3753C22semidirect
32. C3×#3748C22semidirect
33. C32×#216C22semidirect
34. C32×#215C22semidirect
35. C32×#214C22semidirect
36. C32×#213C22semidirect
37. C2×C32×C3⋊C8C22semidirect
38. C3×#3715C22semidirect
39. C3×#3714C22semidirect
40. C3×#3714C22semidirect
41. C3×#3713C22semidirect
42. C3×#3711C22semidirect
43. C3×D3×C3⋊C8C22semidirect
48. C3×#1009D3semidirect
49. C3×#1009C2×C3semidirect
50. #64308C2×C3semidirect
52. #64158C2×C3semidirect
55. C3×#950D3semidirect
56. C3×#950C2×C3semidirect
73. #63949C2×C3semidirect
74. #63939C2×C3semidirect
75. #63934C2×C3semidirect
76. D3×#213C2×C3semidirect
77. C2×#3714C2×C3semidirect
78. #63823C2×C3semidirect
79. #63814C2×C3semidirect
121. C32×#41C2×D3semidirect
122. C32×#41C2×D3semidirect
123. C32×#41C22×C3semidirect
128. C2×C4⋊(C3⋊D3)C22×C3semidirect
132. C3×#239C2×D3semidirect
133. C3×#239C22×C3semidirect
142. C3×D3×D4C2×D3semidirect
143. C3×D3×D4C22×C3semidirect
152. C3×#235C2×D3semidirect
154. C3×#235C22×C3semidirect
164. C2×C3×D12C2×D3semidirect
165. C2×C3×D12C22×C3semidirect
168. D3×D12C22×C3semidirect
170. #3799C22×C3semidirect
176. #3755C22×C3semidirect
177. #3753C22×C3semidirect
178. #3748C22×C3semidirect
180. C3×#216C2×D3semidirect
181. C3×#216C22×C3semidirect
187. C3×#215C2×D3semidirect
188. C3×#215C22×C3semidirect
191. C3×#214C2×D3semidirect
192. C3×#214C22×C3semidirect
201. C3×#213C2×D3semidirect
202. C3×#213C22×C3semidirect
209. C2×C3×C3⋊C8C2×D3semidirect
210. C2×C3×C3⋊C8C22×C3semidirect
215. #3715C22×C3semidirect
216. #3714C22×C3semidirect
217. #3714C22×C3semidirect
218. #3713C22×C3semidirect
219. #3711C22×C3semidirect
220. D3×C3⋊C8C22×C3semidirect
242. #1009C3×D3semidirect
255. #950C3×D3semidirect
429. C3×#41D32semidirect
430. C3×#41C2×C3×D3semidirect
431. C3×#41C2×C3×D3semidirect
450. #239C2×C3×D3semidirect
456. D3×D4C2×C3×D3semidirect
461. #235C2×C3×D3semidirect
468. C2×D12C2×C3×D3semidirect
493. #216C2×C3×D3semidirect
498. #215C2×C3×D3semidirect
500. #214C2×C3×D3semidirect
508. #213C2×C3×D3semidirect
514. C2×C3⋊C8C2×C3×D3semidirect
604. C33#576semidirect
779. #41C3×D32semidirect
880. C32#5769semidirect
881. C32#5835semidirect
882. C32C3×#576semidirect
969. C3#10595456direct (N × H)
970. C3C3×#5769semidirect
971. C3C3×#5835semidirect

Maximal subgroups

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

subgroupindex
C32×#10092
C3×#643082
C3×#641582
C32×#9502
C3×#639492
C3×#639392
C3×#639342
C3×D3×#2132
C2×C3×#37142
C3×#638232
C3×#638142
C3×#58353
C3×#57693
#105954563