Finite Group Databasebeta

← C3×#10595096 #13174791

Subgroups — C3×#10595096 #13174791

Order 1728.

1436 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#1004C211yesmaximal, characteristic, complemented
2C3×#64307C211yesmaximal, characteristic, complemented
3C3×#64141C211yesmaximal, characteristic, complemented
4C2×C32×#213C211yesmaximal, characteristic, complemented
5C3×#63933C212yesmaximal, complemented
6C3×#63932C212yesmaximal, complemented
7C3×#63925C212yesmaximal, complemented
8C3×D3×#213C212yesmaximal, complemented
9C3×#63829C211yesmaximal, characteristic, complemented
10C3×#63823C211yesmaximal, characteristic, complemented
11C3×#63814C211yesmaximal, characteristic, complemented
12C3×#5835—31nomaximal
13C3×#5757—31nomaximal
14#10595096C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic, complemented
16C3×#3828C2211yescharacteristic, complemented
17C2×C32×#67—22no—
18C32×#237—21no—
19C32×#237C2212yescomplemented
20C32×D3×D4—21no—
21C32×D3×D4C2212yescomplemented
22C32×#235C2211yescharacteristic
23C32×#235C2211yescharacteristic, complemented
24C2×C32×D12C2211yescharacteristic, complemented
25C3×D3×#67—22no—
26C3×#3802—21no—
27C3×D3×D12C2212yescomplemented
28C3×#3796—21no—
29C3×#3795C2212yescomplemented
30C3×#3754C2212yescomplemented
31C3×#3753C2212yescomplemented
32C3×#3748C2211yescharacteristic, complemented
33C32×#213C2212yescomplemented
34C32×#213C2212yescomplemented
35C2×C32×C3⋊C8C2211yescharacteristic, complemented
36C3×#3719C2211yescharacteristic, complemented
37C3×#3717C2211yescharacteristic, complemented
38C3×#3716C2211yescharacteristic, complemented
39C3×#3715C2212yescomplemented
40C3×#3714C2211yescharacteristic, complemented
41C3×#3713C2212yescomplemented
42C3×#3711C2212yescomplemented
43C3×D3×C3⋊C8C2212yescomplemented
44C32×H(5,𝔽2)—31no—
45C3×#1009—31no—
46C3×#1004—21no—
47C3×#1004—31no—
48C3×#1004D311yescharacteristic, complemented
49C3×#1004C2×C311yescharacteristic, complemented
50#64307C2×C311yescharacteristic, complemented
51C2×C32×D8—31no—
52#64141C2×C311yescharacteristic, complemented
53C3×#950—32no—
54C3×#950—31no—
55C3×#949—31no—
56C3×#949—32no—
57C3×#948—31no—
58C3×#932—31no—
59C3×#932—31no—
60C3×#932—31no—
61C3×#932—32no—
62C3×#932—61no—
63C2×C3×#213—21no—
64C2×C3×#213—32no—
65C2×C3×#213D311yescharacteristic, complemented
66C2×C3×#213C2×C311yescharacteristic, complemented
67C3×#912—32no—
68C3×#911—32no—
69C3×#911—32no—
70C3×D3×D8—32no—
71C3×#904—31no—
72C3×#901—31no—
73#63933C2×C312yescomplemented
74#63932C2×C312yescomplemented
75#63925C2×C312yescomplemented
76D3×#213C2×C312yescomplemented
77#63829C2×C311yescharacteristic, complemented
78#63823C2×C311yescharacteristic, complemented
79#63814C2×C311yescharacteristic, complemented
80C23×C33—21no—
81C22×C32×D3—21no—
82C22×C32×D3—22no—
83C2×C3×D32—22no—
84C33×D4—21no—
85C33×D4C2312yes—
86C2×C33×C4C2311yescharacteristic
87C3×#638—21no—
88C3×C4⋊(C3⋊D3)C2311yescharacteristic
89C3×C4×C3⋊D3—21no—
90C3×#634C2311yescharacteristic
91C32×#67—21no—
92C32×#67—22no—
93C32×#67—22no—
94C32×#67D412yes—
95C2×C32×Dic3—22no—
96C32×D12—21no—
97C32×D12D411yescharacteristic
98C32×D12C2312yes—
99C32×D12C2311yescharacteristic
100C32×C4×D3—21no—
101C32×C4×D3C2312yes—
102C32×Dic6D411yescharacteristic
103C32×Dic6C2311yescharacteristic
104C3×#626—22no—
105C3×#625—22no—
106C3×D3×Dic3—22no—
107C3×C3⋊(C3⋊C8)C2312yes—
108C32×C3⋊C8C2311yescharacteristic
109C32×C3⋊C8C2311yescharacteristic
110C3×#576—91no—
111#5835—31no—
112#5757—31no—
113C32×#41—31no—
114C32×#41—32no—
115C32×#41—31no—
116C32×#41—61no—
117C2×C32×D4—21no—
118C2×C32×D4—21no—
119C2×C32×D4—21no—
120C2×C32×D4—32no—
121C2×C32×D4—31no—
122C2×C32×D4—41no—
123C2×C32×D4—61no—
124C2×C32×D4—62no—
125C2×C32×D4C2×D311yescharacteristic, complemented
126C2×C32×D4C2×D311yescharacteristic, complemented
127C2×C32×D4C22×C311yescharacteristic, complemented
128#3828C22×C311yescharacteristic, complemented
129C2×C3×#67—24no—
130C2×C3×#67—22no—
131C2×C3×#67—22no—
132C2×C3×#67—62no—
133C3×#239—61no—
134C3×#237—22no—
135C3×#237—22no—
136C3×#237—21no—
137C3×#237—21no—
138C3×#237—32no—
139C3×#237—61no—
140C3×#237C2×D312yescomplemented
141C3×#237C22×C312yescomplemented
142C3×D3×D4—22no—
143C3×D3×D4—22no—
144C3×D3×D4—21no—
145C3×D3×D4—21no—
146C3×D3×D4—32no—
147C3×D3×D4—61no—
148C3×D3×D4—62no—
149C3×D3×D4—61no—
150C3×D3×D4C2×D312yescomplemented
151C3×D3×D4C22×C312yescomplemented
152C3×#235—21no—
153C3×#235—21no—
154C3×#235—31no—
155C3×#235—31no—
156C3×#235—32no—
157C3×#235—61no—
158C3×#235C2×D311yescharacteristic
159C3×#235C2×D311yescharacteristic, complemented
160C3×#235C22×C311yescharacteristic
161C3×#235C22×C311yescharacteristic, complemented
162C2×C3×D12—21no—
163C2×C3×D12—32no—
164C2×C3×D12C2×D311yescharacteristic, complemented
165C2×C3×D12C22×C311yescharacteristic, complemented
166D3×#67—22no—
167#3802—21no—
168D3×D12C22×C312yescomplemented
169#3796—21no—
170#3795C22×C312yescomplemented
171C32×D8—32no—
172C32×D8—32no—
173C2×C32×C8—31no—
174#3754C22×C312yescomplemented
175#3753C22×C312yescomplemented
176#3748C22×C311yescharacteristic, complemented
177C3×#216—31no—
178C3×#215—32no—
179C3×#215—31no—
180C3×#214—32no—
181C3×#214—32no—
182C3×#214—32no—
183C3×#214—31no—
184C3×#214—62no—
185C3×#213—22no—
186C3×#213—22no—
187C3×#213—32no—
188C3×#213—32no—
189C3×#213—32no—
190C3×#213—32no—
191C3×#213—31no—
192C3×#213—62no—
193C3×#213C2×D312yescomplemented
194C3×#213C2×D312yescomplemented
195C3×#213C22×C312yescomplemented
196C3×#213C22×C312yescomplemented
197C3×#208—31no—
198C3×#208—31no—
199C3×#208—32no—
200C3×#208—61no—
201C2×C3×C3⋊C8—21no—
202C2×C3×C3⋊C8—32no—
203C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
204C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
205C3×Dic12—31no—
206C3×D24—31no—
207C3×#204—31no—
208C3×#204—31no—
209C3×ΓL(1,𝔽25)—32no—
210C3×D3×C8—32no—
211#3719C22×C311yescharacteristic, complemented
212#3717C22×C311yescharacteristic, complemented
213#3716C22×C311yescharacteristic, complemented
214#3715C22×C312yescomplemented
215#3714C22×C311yescharacteristic, complemented
216#3713C22×C312yescomplemented
217#3711C22×C312yescomplemented
218D3×C3⋊C8C22×C312yescomplemented
219C22×C33—22no—
220C22×C33—81no—
221C22×C33C2×D411yescharacteristic
222C2×C3×C3⋊D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—22no—
225C2×C32×D3—82no—
226C2×C32×D3—81no—
227C2×C32×D3C2×D412yes—
228C3×D32—82no—
229C33×C4C2×D411yescharacteristic
230C33×C4C2411yescharacteristic
231C3×C3⋊Dic3—21no—
232C32×Dic3—21no—
233C32×Dic3C2×D412yes—
234C3×H(5,𝔽2)—31no—
235C3×H(5,𝔽2)—31no—
236C3×H(5,𝔽2)—61no—
237C3×H(5,𝔽2)—91no—
238#1009—31no—
239#1004—31no—
240#1004C3×D311yescharacteristic, complemented
241C3×AGL(1,ℤ/8)—92no—
242C3×AGL(1,ℤ/8)—92no—
243C3×AGL(1,ℤ/8)—91no—
244C3×AGL(1,ℤ/8)—91no—
245C3×#135—91no—
246C3×#135—92no—
247C2×C3×D8—31no—
248C2×C3×D8—31no—
249C2×C3×D8—61no—
250C2×C3×D8—92no—
251C3×#131—91no—
252#950—32no—
253#950—31no—
254#949—31no—
255#949—32no—
256#948—31no—
257#932—31no—
258#932—31no—
259#932—31no—
260#932—32no—
261#932—61no—
262C2×#213—32no—
263C2×#213C3×D311yescharacteristic, complemented
264#912—32no—
265#911—32no—
266#911—32no—
267D3×D8—32no—
268#904—31no—
269#901—31no—
270C23×C32—21no—
271C23×C32—22no—
272C23×C32—21no—
273C23×C32—21no—
274C23×C32—41no—
275C23×C32—41no—
276C23×C32—42no—
277C23×C32—62no—
278C23×C32—61no—
279C22×C3×D3—24no—
280C22×C3×D3—21no—
281C22×C3×D3—21no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—41no—
285C22×C3×D3—62no—
286C22×C3×D3—62no—
287C2×D32—22no—
288C32×Q8—31no—
289C32×Q8—31no—
290C32×D4—21no—
291C32×D4—22no—
292C32×D4—21no—
293C32×D4—21no—
294C32×D4—22no—
295C32×D4—22no—
296C32×D4—22no—
297C32×D4—32no—
298C32×D4—31no—
299C32×D4—31no—
300C32×D4—32no—
301C32×D4—42no—
302C32×D4—41no—
303C32×D4—41no—
304C32×D4—42no—
305C32×D4—62no—
306C32×D4—62no—
307C32×D4—61no—
308C32×D4—61no—
309C32×D4C22×D312yes—
310C32×D4C22×D312yes—
311C32×D4C23×C312yes—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—32no—
316C2×C32×C4—41no—
317C2×C32×C4—62no—
318C2×C32×C4—61no—
319C2×C32×C4C22×D311yescharacteristic
320C2×C32×C4C22×D311yescharacteristic
321C2×C32×C4C23×C311yescharacteristic
322#638—21no—
323C4⋊(C3⋊D3)C23×C311yescharacteristic
324C4×C3⋊D3—21no—
325#634C23×C311yescharacteristic
326C3×#67—22no—
327C3×#67—24no—
328C3×#67—24no—
329C3×#67—21no—
330C3×#67—21no—
331C3×#67—22no—
332C3×#67—22no—
333C3×#67—22no—
334C3×#67—22no—
335C3×#67—22no—
336C3×#67—62no—
337C3×#67—61no—
338C3×#67—61no—
339C3×#67—62no—
340C3×#67—62no—
341C3×#67—121no—
342C3×#67#6712yes—
343C3×#67C3×D412yes—
344C2×C3×Dic3—24no—
345C2×C3×Dic3—22no—
346C2×C3×Dic3—22no—
347C2×C3×Dic3—62no—
348C3×D12—21no—
349C3×D12—21no—
350C3×D12—21no—
351C3×D12—21no—
352C3×D12—22no—
353C3×D12—31no—
354C3×D12—31no—
355C3×D12—41no—
356C3×D12—61no—
357C3×D12—62no—
358C3×D12#6711yescharacteristic
359C3×D12C3×D411yescharacteristic
360C3×D12C22×D311yescharacteristic
361C3×D12C22×D312yes—
362C3×D12C23×C311yescharacteristic
363C3×D12C23×C312yes—
364C3×C4×D3—22no—
365C3×C4×D3—21no—
366C3×C4×D3—21no—
367C3×C4×D3—22no—
368C3×C4×D3—62no—
369C3×C4×D3—61no—
370C3×C4×D3—61no—
371C3×C4×D3—121no—
372C3×C4×D3C22×D312yes—
373C3×C4×D3C23×C312yes—
374C3×Dic6—21no—
375C3×Dic6—21no—
376C3×Dic6—31no—
377C3×Dic6—31no—
378C3×Dic6—61no—
379C3×Dic6#6711yescharacteristic
380C3×Dic6C3×D411yescharacteristic
381C3×Dic6C22×D311yescharacteristic
382C3×Dic6C23×C311yescharacteristic
383#626—22no—
384#625—22no—
385D3×Dic3—22no—
386C32×C8—31no—
387C32×C8—31no—
388C3⋊(C3⋊C8)C23×C312yes—
389C3×C3⋊C8—21no—
390C3×C3⋊C8—21no—
391C3×C3⋊C8—32no—
392C3×C3⋊C8—32no—
393C3×C3⋊C8—62no—
394C3×C3⋊C8C22×D311yescharacteristic
395C3×C3⋊C8C22×D311yescharacteristic
396C3×C3⋊C8C23×C311yescharacteristic
397C3×C3⋊C8C23×C311yescharacteristic
398#576—91noSylow
399C2×C33—21no—
400C2×C33—42no—
401C2×C33C22×D411yescharacteristic
402C3×C3⋊D3—41no—
403C32×D3—22no—
404C32×D3—41no—
405C32×D3—42no—
406C3×#41—31no—
407C3×#41—31no—
408C3×#41—32no—
409C3×#41—32no—
410C3×#41—31no—
411C3×#41—31no—
412C3×#41—61no—
413C3×#41—61no—
414C3×#41—62no—
415C3×#41—61no—
416C3×#41—61no—
417C3×#41—62no—
418C3×#41—92no—
419C3×#41—91no—
420C3×#41—181no—
421C2×C3×D4—21no—
422C2×C3×D4—21no—
423C2×C3×D4—21no—
424C2×C3×D4—32no—
425C2×C3×D4—32no—
426C2×C3×D4—31no—
427C2×C3×D4—31no—
428C2×C3×D4—41no—
429C2×C3×D4—61no—
430C2×C3×D4—62no—
431C2×C3×D4—61no—
432C2×C3×D4—61no—
433C2×C3×D4—62no—
434C2×C3×D4—62no—
435C2×C3×D4—62no—
436C2×C3×D4—64no—
437C2×C3×D4—92no—
438C2×C3×D4—181no—
439C2×C3×D4—182no—
440C2×C3×D4D3211yescharacteristic, complemented
441C2×C3×D4C2×C3×D311yescharacteristic, complemented
442C2×C3×D4C2×C3×D311yescharacteristic, complemented
443C2×#67—22no—
444C2×#67—62no—
445#239—61no—
446#237—21no—
447#237—32no—
448#237—61no—
449#237C2×C3×D312yescomplemented
450D3×D4—21no—
451D3×D4—32no—
452D3×D4—61no—
453D3×D4—62no—
454D3×D4—61no—
455D3×D4C2×C3×D312yescomplemented
456#235—31no—
457#235—31no—
458#235—32no—
459#235—61no—
460#235C2×C3×D311yescharacteristic
461#235C2×C3×D311yescharacteristic, complemented
462C2×D12—32no—
463C2×D12C2×C3×D311yescharacteristic, complemented
464C3×Q16—91no—
465C3×SD16—91no—
466C3×SD16—91no—
467C3×SD16—92no—
468C3×SD16—92no—
469C3×D8—32no—
470C3×D8—32no—
471C3×D8—32no—
472C3×D8—32no—
473C3×D8—62no—
474C3×D8—62no—
475C3×D8—91no—
476C3×D8—92no—
477C3×D8—92no—
478C3×M16—92no—
479C3×M16—91no—
480C2×C3×C8—31no—
481C2×C3×C8—31no—
482C2×C3×C8—61no—
483C2×C3×C8—92no—
484#216—31no—
485#215—32no—
486#215—31no—
487#214—32no—
488#214—32no—
489#214—32no—
490#214—31no—
491#214—62no—
492#213—32no—
493#213—32no—
494#213—32no—
495#213—32no—
496#213—31no—
497#213—62no—
498#213C2×C3×D312yescomplemented
499#213C2×C3×D312yescomplemented
500#208—31no—
501#208—31no—
502#208—32no—
503#208—61no—
504C2×C3⋊C8—32no—
505C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
506Dic12—31no—
507D24—31no—
508#204—31no—
509#204—31no—
510ΓL(1,𝔽25)—32no—
511D3×C8—32no—
512C22×C32—22no—
513C22×C32—24no—
514C22×C32—22no—
515C22×C32—22no—
516C22×C32—21no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32—32no—
520C22×C32—41no—
521C22×C32—42no—
522C22×C32—42no—
523C22×C32—44no—
524C22×C32—61no—
525C22×C32—62no—
526C22×C32—81no—
527C22×C32—81no—
528C22×C32—81no—
529C22×C32—82no—
530C22×C32—82no—
531C22×C32—82no—
532C22×C32—84no—
533C22×C32—241no—
534C22×C32—242no—
535C22×C32D3×D411yescharacteristic
536C22×C32C2×#6711yescharacteristic
537C22×C32C2×C3×D411yescharacteristic
538C2×C3⋊D3—21no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—21no—
542C2×C3×D3—22no—
543C2×C3×D3—21no—
544C2×C3×D3—22no—
545C2×C3×D3—42no—
546C2×C3×D3—61no—
547C2×C3×D3—61no—
548C2×C3×D3—82no—
549C2×C3×D3—82no—
550C2×C3×D3—81no—
551C2×C3×D3—81no—
552C2×C3×D3—84no—
553C2×C3×D3—82no—
554C2×C3×D3—121no—
555C2×C3×D3—242no—
556C2×C3×D3—242no—
557C2×C3×D3C2×#6712yes—
558C2×C3×D3C2×C3×D412yes—
559D32—82no—
560C32×C4—21no—
561C32×C4—21no—
562C32×C4—21no—
563C32×C4—21no—
564C32×C4—21no—
565C32×C4—21no—
566C32×C4—32no—
567C32×C4—41no—
568C32×C4—41no—
569C32×C4—61no—
570C32×C4D3×D411yescharacteristic
571C32×C4C2×#6711yescharacteristic
572C32×C4C2×C3×D411yescharacteristic
573C32×C4C23×D311yescharacteristic
574C32×C4C23×D311yescharacteristic
575C32×C4C24×C311yescharacteristic
576C3⋊Dic3—21no—
577C3×Dic3—22no—
578C3×Dic3—21no—
579C3×Dic3—21no—
580C3×Dic3—22no—
581C3×Dic3—61no—
582C3×Dic3—61no—
583C3×Dic3—121no—
584C3×Dic3C2×#6712yes—
585C3×Dic3C2×C3×D412yes—
586H(5,𝔽2)—31no—
587H(5,𝔽2)—91no—
588AGL(1,ℤ/8)—92no—
589AGL(1,ℤ/8)—92no—
590AGL(1,ℤ/8)—91no—
591AGL(1,ℤ/8)—91no—
592#135—91no—
593#135—92no—
594C2×D8—31no—
595C2×D8—92no—
596#131—91no—
597C33#57611yescharacteristic, complemented, Sylow
598C23×C3—22no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—42no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—64no—
608C23×C3—61no—
609C23×C3—61no—
610C23×C3—121no—
611C23×C3—182no—
612C22×D3—21no—
613C22×D3—22no—
614C22×D3—62no—
615C22×D3—62no—
616C3×Q8—31no—
617C3×Q8—31no—
618C3×Q8—31no—
619C3×Q8—31no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×Q8—91no—
623C3×D4—22no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—22no—
628C3×D4—22no—
629C3×D4—22no—
630C3×D4—32no—
631C3×D4—32no—
632C3×D4—32no—
633C3×D4—31no—
634C3×D4—31no—
635C3×D4—32no—
636C3×D4—31no—
637C3×D4—31no—
638C3×D4—41no—
639C3×D4—41no—
640C3×D4—42no—
641C3×D4—42no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—62no—
645C3×D4—62no—
646C3×D4—62no—
647C3×D4—62no—
648C3×D4—62no—
649C3×D4—62no—
650C3×D4—64no—
651C3×D4—64no—
652C3×D4—62no—
653C3×D4—61no—
654C3×D4—61no—
655C3×D4—61no—
656C3×D4—61no—
657C3×D4—91no—
658C3×D4—121no—
659C3×D4—182no—
660C3×D4—182no—
661C3×D4—181no—
662C3×D4C2×D3212yes—
663C3×D4C22×C3×D312yes—
664C3×D4C22×C3×D312yes—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—41no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—62no—
675C2×C3×C4—64no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—182no—
679C2×C3×C4—181no—
680C2×C3×C4C2×D3211yescharacteristic
681C2×C3×C4C22×C3×D311yescharacteristic
682C2×C3×C4C22×C3×D311yescharacteristic
683#67—21no—
684#67—22no—
685#67—22no—
686#67—62no—
687#67—61no—
688#67—61no—
689#67—62no—
690#67—62no—
691#67—121no—
692#67C3×#6712yes—
693C2×Dic3—22no—
694C2×Dic3—62no—
695D12—21no—
696D12—31no—
697D12—31no—
698D12—61no—
699D12—62no—
700D12C3×#6711yescharacteristic
701D12C22×C3×D311yescharacteristic
702D12C22×C3×D312yes—
703C4×D3—21no—
704C4×D3—62no—
705C4×D3—61no—
706C4×D3—61no—
707C4×D3—121no—
708C4×D3C22×C3×D312yes—
709Dic6—31no—
710Dic6—31no—
711Dic6—61no—
712Dic6C3×#6711yescharacteristic
713Dic6C22×C3×D311yescharacteristic
714C3×C8—31no—
715C3×C8—31no—
716C3×C8—31no—
717C3×C8—31no—
718C3×C8—61no—
719C3×C8—61no—
720C3×C8—92no—
721C3⋊C8—32no—
722C3⋊C8—32no—
723C3⋊C8—62no—
724C3⋊C8C22×C3×D311yescharacteristic
725C3⋊C8C22×C3×D311yescharacteristic
726C2×C32—21no—
727C2×C32—22no—
728C2×C32—21no—
729C2×C32—21no—
730C2×C32—21no—
731C2×C32—21no—
732C2×C32—21no—
733C2×C32—41no—
734C2×C32—41no—
735C2×C32—41no—
736C2×C32—42no—
737C2×C32—42no—
738C2×C32—44no—
739C2×C32—42no—
740C2×C32—42no—
741C2×C32—62no—
742C2×C32—82no—
743C2×C32—82no—
744C2×C32—84no—
745C2×C32—121no—
746C2×C32—122no—
747C2×C32C2×D3×D411yescharacteristic
748C2×C32C22×#6711yescharacteristic
749C2×C32C22×C3×D411yescharacteristic
750C3⋊D3—41no—
751C3×D3—22no—
752C3×D3—22no—
753C3×D3—42no—
754C3×D3—42no—
755C3×D3—42no—
756C3×D3—41no—
757C3×D3—42no—
758C3×D3—41no—
759C3×D3—82no—
760C3×D3—121no—
761C3×D3—121no—
762C3×D3—241no—
763#41—31no—
764#41—32no—
765#41—31no—
766#41—61no—
767#41—92no—
768#41—91no—
769#41—181no—
770C2×D4—32no—
771C2×D4—31no—
772C2×D4—61no—
773C2×D4—62no—
774C2×D4—92no—
775C2×D4—181no—
776C2×D4—182no—
777C2×D4C3×D3211yescharacteristic, complemented
778Q16—91no—
779SD16—91no—
780SD16—91no—
781SD16—92no—
782SD16—92no—
783D8—32no—
784D8—32no—
785D8—91no—
786D8—92no—
787D8—92no—
788M16—92no—
789M16—91no—
790C2×C8—31no—
791C2×C8—92no—
792C22×C3—24no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—32no—
800C22×C3—32no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—44no—
804C22×C3—41no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—61no—
808C22×C3—62no—
809C22×C3—61no—
810C22×C3—62no—
811C22×C3—81no—
812C22×C3—81no—
813C22×C3—81no—
814C22×C3—82no—
815C22×C3—82no—
816C22×C3—82no—
817C22×C3—84no—
818C22×C3—122no—
819C22×C3—181no—
820C22×C3—241no—
821C22×C3—241no—
822C22×C3—242no—
823C22×C3—242no—
824C22×C3—242no—
825C22×C3—244no—
826C22×C3—722no—
827C22×C3D3×#6711yescharacteristic
828C22×C3C3×D3×D411yescharacteristic
829C22×C3C2×C3×#6711yescharacteristic
830C2×D3—22no—
831C2×D3—21no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—82no—
835C2×D3—81no—
836C2×D3—121no—
837C2×D3—242no—
838C2×D3—242no—
839C2×D3C2×C3×#6712yes—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—32no—
847C3×C4—32no—
848C3×C4—41no—
849C3×C4—41no—
850C3×C4—62no—
851C3×C4—62no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—181no—
855C3×C4D3×#6711yescharacteristic
856C3×C4C3×D3×D411yescharacteristic
857C3×C4C2×C3×#6711yescharacteristic
858C3×C4C22×D3211yescharacteristic
859C3×C4C23×C3×D311yescharacteristic
860C3×C4C23×C3×D311yescharacteristic
861Dic3—21no—
862Dic3—61no—
863Dic3—61no—
864Dic3—121no—
865Dic3C2×C3×#6712yes—
866C32—21no—
867C32—21no—
868C32—21no—
869C32—41no—
870C32#575711yescharacteristic, complemented
871C32#583511yescharacteristic, complemented
872C32C3×#57611yescharacteristic, complemented
873C23—21no—
874C23—62no—
875C23—61no—
876C23—182no—
877Q8—31no—
878Q8—31no—
879Q8—91no—
880D4—21no—
881D4—32no—
882D4—32no—
883D4—31no—
884D4—31no—
885D4—62no—
886D4—62no—
887D4—61no—
888D4—61no—
889D4—91no—
890D4—182no—
891D4—182no—
892D4—181no—
893D4C2×C3×D3212yes—
894C2×C4—32no—
895C2×C4—62no—
896C2×C4—61no—
897C2×C4—182no—
898C2×C4—181no—
899C2×C4C2×C3×D3211yescharacteristic
900C8—31no—
901C8—31no—
902C8—92no—
903C2×C3—22no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—41no—
911C2×C3—41no—
912C2×C3—42no—
913C2×C3—44no—
914C2×C3—42no—
915C2×C3—42no—
916C2×C3—42no—
917C2×C3—41no—
918C2×C3—62no—
919C2×C3—62no—
920C2×C3—82no—
921C2×C3—82no—
922C2×C3—84no—
923C2×C3—122no—
924C2×C3—122no—
925C2×C3—121no—
926C2×C3—121no—
927C2×C3—122no—
928C2×C3—122no—
929C2×C3—242no—
930C2×C3—361no—
931C2×C3C2×D3×#6711yescharacteristic
932C2×C3C2×C3×D3×D411yescharacteristic
933C2×C3C22×C3×#6711yescharacteristic
934D3—22no—
935D3—42no—
936D3—41no—
937D3—121no—
938D3—121no—
939D3—241no—
940C22—22no—
941C22—32no—
942C22—61no—
943C22—62no—
944C22—81no—
945C22—181no—
946C22—241no—
947C22—242no—
948C22—722no—
949C22C3×D3×#6711yescharacteristic
950C4—32no—
951C4—61no—
952C4—181no—
953C4C3×D3×#6711yescharacteristic
954C4C22×C3×D3211yescharacteristic
955C3—21no—
956C3—21no—
957C3—21no—
958C3—41no—
959C3#1059509611yescharacteristic, direct product factor
960C3C3×#575711yescharacteristic, complemented
961C3C3×#583511yescharacteristic, complemented
962C2—21no—
963C2—42no—
964C2—62no—
965C2—121no—
966C2—122no—
967C2—361no—
968C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC2×C3C2×D3×#67
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC2×C33×D4C22
socleC2×C33C22×D4
hypercenterC2×C3×D4D32
hypocenterC32C3×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C32×#1004C2semidirect
2. C3×#64307C2semidirect
3. C3×#64141C2semidirect
4. C2×C32×#213C2semidirect
5. C3×#63933C2semidirect
6. C3×#63932C2semidirect
7. C3×#63925C2semidirect
8. C3×D3×#213C2semidirect
9. C3×#63829C2semidirect
10. C3×#63823C2semidirect
11. C3×#63814C2semidirect
14. #10595096C3direct (N × H)
15. C2×C33×D4C22semidirect
16. C3×#3828C22semidirect
19. C32×#237C22semidirect
21. C32×D3×D4C22semidirect
23. C32×#235C22semidirect
24. C2×C32×D12C22semidirect
27. C3×D3×D12C22semidirect
29. C3×#3795C22semidirect
30. C3×#3754C22semidirect
31. C3×#3753C22semidirect
32. C3×#3748C22semidirect
33. C32×#213C22semidirect
34. C32×#213C22semidirect
35. C2×C32×C3⋊C8C22semidirect
36. C3×#3719C22semidirect
37. C3×#3717C22semidirect
38. C3×#3716C22semidirect
39. C3×#3715C22semidirect
40. C3×#3714C22semidirect
41. C3×#3713C22semidirect
42. C3×#3711C22semidirect
43. C3×D3×C3⋊C8C22semidirect
48. C3×#1004D3semidirect
49. C3×#1004C2×C3semidirect
50. #64307C2×C3semidirect
52. #64141C2×C3semidirect
65. C2×C3×#213D3semidirect
66. C2×C3×#213C2×C3semidirect
73. #63933C2×C3semidirect
74. #63932C2×C3semidirect
75. #63925C2×C3semidirect
76. D3×#213C2×C3semidirect
77. #63829C2×C3semidirect
78. #63823C2×C3semidirect
79. #63814C2×C3semidirect
125. C2×C32×D4C2×D3semidirect
126. C2×C32×D4C2×D3semidirect
127. C2×C32×D4C22×C3semidirect
128. #3828C22×C3semidirect
140. C3×#237C2×D3semidirect
141. C3×#237C22×C3semidirect
150. C3×D3×D4C2×D3semidirect
151. C3×D3×D4C22×C3semidirect
159. C3×#235C2×D3semidirect
161. C3×#235C22×C3semidirect
164. C2×C3×D12C2×D3semidirect
165. C2×C3×D12C22×C3semidirect
168. D3×D12C22×C3semidirect
170. #3795C22×C3semidirect
174. #3754C22×C3semidirect
175. #3753C22×C3semidirect
176. #3748C22×C3semidirect
193. C3×#213C2×D3semidirect
194. C3×#213C2×D3semidirect
195. C3×#213C22×C3semidirect
196. C3×#213C22×C3semidirect
203. C2×C3×C3⋊C8C2×D3semidirect
204. C2×C3×C3⋊C8C22×C3semidirect
211. #3719C22×C3semidirect
212. #3717C22×C3semidirect
213. #3716C22×C3semidirect
214. #3715C22×C3semidirect
215. #3714C22×C3semidirect
216. #3713C22×C3semidirect
217. #3711C22×C3semidirect
218. D3×C3⋊C8C22×C3semidirect
240. #1004C3×D3semidirect
263. C2×#213C3×D3semidirect
440. C2×C3×D4D32semidirect
441. C2×C3×D4C2×C3×D3semidirect
442. C2×C3×D4C2×C3×D3semidirect
449. #237C2×C3×D3semidirect
455. D3×D4C2×C3×D3semidirect
461. #235C2×C3×D3semidirect
463. C2×D12C2×C3×D3semidirect
498. #213C2×C3×D3semidirect
499. #213C2×C3×D3semidirect
505. C2×C3⋊C8C2×C3×D3semidirect
597. C33#576semidirect
777. C2×D4C3×D32semidirect
870. C32#5757semidirect
871. C32#5835semidirect
872. C32C3×#576semidirect
959. C3#10595096direct (N × H)
960. C3C3×#5757semidirect
961. C3C3×#5835semidirect

Maximal subgroups

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

subgroupindex
C32×#10042
C3×#643072
C3×#641412
C2×C32×#2132
C3×#639332
C3×#639322
C3×#639252
C3×D3×#2132
C3×#638292
C3×#638232
C3×#638142
C3×#58353
C3×#57573
#105950963