Finite Group Databasebeta

← C3×#10595097 #13174792

Subgroups — C3×#10595097 #13174792

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×#64308C211yesmaximal, characteristic, complemented
3C2×C3×#3753C211yesmaximal, characteristic, complemented
4C32×#932C211yesmaximal, characteristic, complemented
5C3×#63935C212yesmaximal, complemented
6C3×#63934C212yesmaximal, complemented
7C3×#63925C212yesmaximal, complemented
8C3×D3×#213C212yesmaximal, complemented
9C3×#63825C211yesmaximal, characteristic, complemented
10C3×#63822C211yesmaximal, characteristic, complemented
11C3×#63815C211yesmaximal, characteristic, complemented
12C3×#5835—31nomaximal
13C3×#5774—31nomaximal
14#10595097C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic, complemented
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C2×C32×#67—22no—
18C32×#237—21no—
19C32×#237C2212yescomplemented
20C32×D3×D4—21no—
21C32×D3×D4C2212yescomplemented
22C32×#235C2211yescharacteristic
23C32×#235C2211yescharacteristic, complemented
24C32×#235C2211yescharacteristic, complemented
25C3×#3811—22no—
26C3×D3×D12—21no—
27C3×D3×D12C2212yescomplemented
28C3×#3799—21no—
29C3×#3799C2212yescomplemented
30C3×#3753C2212yescomplemented
31C3×#3753C2212yescomplemented
32C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
33C32×#214C2212yescomplemented
34C32×#213C2212yescomplemented
35C32×#208C2211yescharacteristic, complemented
36C3×#3718C2211yescharacteristic, complemented
37C3×#3717C2212yescomplemented
38C3×#3715C2211yescharacteristic, complemented
39C3×#3715C2211yescharacteristic, complemented
40C3×#3714C2212yescomplemented
41C3×#3713C2211yescharacteristic, complemented
42C3×#3711C2212yescomplemented
43C3×D3×C3⋊C8C2212yescomplemented
44C32×H(5,𝔽2)—31no—
45C3×#1009—31no—
46C3×#1009—31no—
47C3×#1004—21no—
48C3×#1004D311yescharacteristic, complemented
49C3×#1004C2×C311yescharacteristic, complemented
50#64308C2×C311yescharacteristic, complemented
51C32×AGL(1,ℤ/8)—31no—
52C2×#3753C2×C311yescharacteristic, complemented
53C3×#950—31no—
54C3×#950—31no—
55C3×#950—32no—
56C3×#949—32no—
57C3×#949—31no—
58C3×#948—31no—
59C3×#932—21no—
60C3×#932—32no—
61C3×#932D311yescharacteristic, complemented
62C3×#932C2×C311yescharacteristic, complemented
63C2×C3×#213—31no—
64C2×C3×#213—31no—
65C2×C3×#213—32no—
66C2×C3×#213—61no—
67C3×#916—32no—
68C3×#914—32no—
69C3×#911—32no—
70C3×D3×D8—32no—
71C3×#908—31no—
72C3×#907—31no—
73#63935C2×C312yescomplemented
74#63934C2×C312yescomplemented
75#63925C2×C312yescomplemented
76D3×#213C2×C312yescomplemented
77#63825C2×C311yescharacteristic, complemented
78#63822C2×C311yescharacteristic, complemented
79#63815C2×C311yescharacteristic, complemented
80C23×C33—21no—
81C22×C3×C3⋊D3—21no—
82C22×C32×D3—22no—
83C2×C3×D32—22no—
84C33×D4—21no—
85C33×D4C2312yes—
86C2×C33×C4C2311yescharacteristic
87C3×C4⋊(C3⋊D3)—21no—
88C3×C4⋊(C3⋊D3)C2312yes—
89C32×#67—21no—
90C32×#67—21no—
91C32×#67—22no—
92C32×#67—22no—
93C32×#67D412yes—
94C2×C32×Dic3—22no—
95C32×D12D411yescharacteristic
96C32×D12C2311yescharacteristic
97C32×D12C2311yescharacteristic
98C32×C4×D3—21no—
99C32×C4×D3—21no—
100C32×C4×D3C2312yes—
101C32×Dic6D411yescharacteristic
102C32×Dic6C2311yescharacteristic
103C32×Dic6C2311yescharacteristic
104C3×#626—22no—
105C3×#626—22no—
106C3×#624—22no—
107C3×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×C3⋊(C3⋊C8)C2311yescharacteristic
109C32×C3⋊C8C2312yes—
110C3×#576—91no—
111#5835—31no—
112#5774—31no—
113C32×#41—31no—
114C32×#41—32no—
115C32×#41—31no—
116C32×#41—31no—
117C32×#41—61no—
118C2×C32×D4—21no—
119C2×C32×D4—21no—
120C2×C32×D4—21no—
121C2×C32×D4—32no—
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
128C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
129C2×C3×#67—24no—
130C2×C3×#67—22no—
131C2×C3×#67—22no—
132C3×#239—32no—
133C3×#239—61no—
134C3×#237—22no—
135C3×#237—22no—
136C3×#237—21no—
137C3×#237—21no—
138C3×#237C2×D312yescomplemented
139C3×#237C22×C312yescomplemented
140C3×D3×D4—22no—
141C3×D3×D4—22no—
142C3×D3×D4—21no—
143C3×D3×D4—21no—
144C3×D3×D4—32no—
145C3×D3×D4—61no—
146C3×D3×D4—62no—
147C3×D3×D4—62no—
148C3×D3×D4C2×D312yescomplemented
149C3×D3×D4C22×C312yescomplemented
150C3×#235—21no—
151C3×#235—21no—
152C3×#235—21no—
153C3×#235—32no—
154C3×#235—61no—
155C3×#235C2×D311yescharacteristic
156C3×#235C2×D311yescharacteristic, complemented
157C3×#235C2×D311yescharacteristic, complemented
158C3×#235C22×C311yescharacteristic
159C3×#235C22×C311yescharacteristic, complemented
160C3×#235C22×C311yescharacteristic, complemented
161C2×C3×D12—31no—
162C2×C3×D12—31no—
163C2×C3×D12—32no—
164C2×C3×D12—61no—
165C2×C3×D12—61no—
166#3811—22no—
167D3×D12—21no—
168D3×D12C22×C312yescomplemented
169#3799—21no—
170#3799C22×C312yescomplemented
171C32×SD16—32no—
172C32×D8—32no—
173C32×M16—31no—
174#3753C22×C312yescomplemented
175#3753C22×C312yescomplemented
176C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
177C3×#216—31no—
178C3×#216—31no—
179C3×#215—31no—
180C3×#215—31no—
181C3×#215—32no—
182C3×#214—22no—
183C3×#214—31no—
184C3×#214—31no—
185C3×#214C2×D312yescomplemented
186C3×#214C22×C312yescomplemented
187C3×#213—22no—
188C3×#213—32no—
189C3×#213—32no—
190C3×#213—32no—
191C3×#213—32no—
192C3×#213—31no—
193C3×#213—31no—
194C3×#213—32no—
195C3×#213—62no—
196C3×#213—62no—
197C3×#213C2×D312yescomplemented
198C3×#213C22×C312yescomplemented
199C3×#208—21no—
200C3×#208—32no—
201C3×#208C2×D311yescharacteristic, complemented
202C3×#208C22×C311yescharacteristic, complemented
203C2×C3×C3⋊C8—31no—
204C2×C3×C3⋊C8—31no—
205C2×C3×C3⋊C8—32no—
206C2×C3×C3⋊C8—61no—
207C3×D24—32no—
208C3×#204—32no—
209C3×ΓL(1,𝔽25)—32no—
210C3×D3×C8—32no—
211#3718C22×C311yescharacteristic, complemented
212#3717C22×C312yescomplemented
213#3715C22×C311yescharacteristic, complemented
214#3715C22×C311yescharacteristic, complemented
215#3714C22×C312yescomplemented
216#3713C22×C311yescharacteristic, complemented
217#3711C22×C312yescomplemented
218D3×C3⋊C8C22×C312yescomplemented
219C22×C33—22no—
220C22×C33—81no—
221C22×C33C2×D411yescharacteristic
222C2×C3×C3⋊D3—22no—
223C2×C3×C3⋊D3—81no—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226C2×C32×D3—82no—
227C2×C32×D3C2×D412yes—
228C3×D32—82no—
229C33×C4C2×D411yescharacteristic
230C33×C4C2411yescharacteristic
231C32×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#1009—31no—
240#1004C3×D311yescharacteristic, complemented
241C3×AGL(1,ℤ/8)—31no—
242C3×AGL(1,ℤ/8)—31no—
243C3×AGL(1,ℤ/8)—61no—
244C3×AGL(1,ℤ/8)—91no—
245C3×AGL(1,ℤ/8)—92no—
246C3×AGL(1,ℤ/8)—92no—
247C3×#135—92no—
248C3×#135—91no—
249C2×C3×D8—92no—
250C2×C3×D8—91no—
251C3×#131—91no—
252#950—31no—
253#950—31no—
254#950—32no—
255#949—32no—
256#949—31no—
257#948—31no—
258#932—32no—
259#932C3×D311yescharacteristic, complemented
260C2×#213—31no—
261C2×#213—31no—
262C2×#213—32no—
263C2×#213—61no—
264#916—32no—
265#914—32no—
266#911—32no—
267D3×D8—32no—
268#908—31no—
269#907—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—
278C22×C3⋊D3—21no—
279C22×C3×D3—24no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—62no—
283C22×C3×D3—61no—
284C22×C3×D3—61no—
285C22×C3×D3—62no—
286C22×C3×D3—121no—
287C2×D32—22no—
288C32×Q8—31no—
289C32×Q8—31no—
290C32×Q8—31no—
291C32×D4—21no—
292C32×D4—22no—
293C32×D4—21no—
294C32×D4—21no—
295C32×D4—22no—
296C32×D4—22no—
297C32×D4—22no—
298C32×D4—32no—
299C32×D4—31no—
300C32×D4—31no—
301C32×D4—31no—
302C32×D4—42no—
303C32×D4—41no—
304C32×D4—41no—
305C32×D4—42no—
306C32×D4—62no—
307C32×D4—62no—
308C32×D4—61no—
309C32×D4—61no—
310C32×D4C22×D312yes—
311C32×D4C22×D312yes—
312C32×D4C23×C312yes—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4—32no—
317C2×C32×C4—41no—
318C2×C32×C4—62no—
319C2×C32×C4—61no—
320C2×C32×C4—61no—
321C2×C32×C4C22×D311yescharacteristic
322C2×C32×C4C22×D311yescharacteristic
323C2×C32×C4C23×C311yescharacteristic
324C4⋊(C3⋊D3)—21no—
325C4⋊(C3⋊D3)C23×C312yes—
326C3×#67—22no—
327C3×#67—24no—
328C3×#67—24no—
329C3×#67—21no—
330C3×#67—21no—
331C3×#67—21no—
332C3×#67—21no—
333C3×#67—22no—
334C3×#67—22no—
335C3×#67—22no—
336C3×#67—22no—
337C3×#67—22no—
338C3×#67—41no—
339C3×#67—62no—
340C3×#67—62no—
341C3×#67#6712yes—
342C3×#67C3×D412yes—
343C2×C3×Dic3—24no—
344C2×C3×Dic3—22no—
345C2×C3×Dic3—22no—
346C3×D12—21no—
347C3×D12—21no—
348C3×D12—21no—
349C3×D12—32no—
350C3×D12—32no—
351C3×D12—62no—
352C3×D12—62no—
353C3×D12—62no—
354C3×D12—61no—
355C3×D12—61no—
356C3×D12—121no—
357C3×D12#6711yescharacteristic
358C3×D12C3×D411yescharacteristic
359C3×D12C22×D311yescharacteristic
360C3×D12C22×D311yescharacteristic
361C3×D12C23×C311yescharacteristic
362C3×D12C23×C311yescharacteristic
363C3×C4×D3—22no—
364C3×C4×D3—21no—
365C3×C4×D3—21no—
366C3×C4×D3—21no—
367C3×C4×D3—21no—
368C3×C4×D3—22no—
369C3×C4×D3—41no—
370C3×C4×D3—62no—
371C3×C4×D3—62no—
372C3×C4×D3C22×D312yes—
373C3×C4×D3C23×C312yes—
374C3×Dic6—21no—
375C3×Dic6—21no—
376C3×Dic6—21no—
377C3×Dic6#6711yescharacteristic
378C3×Dic6C3×D411yescharacteristic
379C3×Dic6C22×D311yescharacteristic
380C3×Dic6C22×D311yescharacteristic
381C3×Dic6C23×C311yescharacteristic
382C3×Dic6C23×C311yescharacteristic
383#626—22no—
384#626—22no—
385#624—22no—
386C32×C8—32no—
387C3⋊(C3⋊C8)C23×C311yescharacteristic
388C3⋊(C3⋊C8)C23×C311yescharacteristic
389C3×C3⋊C8—22no—
390C3×C3⋊C8—31no—
391C3×C3⋊C8—31no—
392C3×C3⋊C8—31no—
393C3×C3⋊C8—31no—
394C3×C3⋊C8—61no—
395C3×C3⋊C8—61no—
396C3×C3⋊C8C22×D312yes—
397C3×C3⋊C8C23×C312yes—
398#576—91noSylow
399C2×C33—21no—
400C2×C33—42no—
401C2×C33C22×D411yescharacteristic
402C3×C3⋊D3—42no—
403C32×D3—22no—
404C32×D3—41no—
405C32×D3—41no—
406C3×#41—31no—
407C3×#41—31no—
408C3×#41—32no—
409C3×#41—32no—
410C3×#41—31no—
411C3×#41—31no—
412C3×#41—31no—
413C3×#41—31no—
414C3×#41—61no—
415C3×#41—61no—
416C3×#41—61no—
417C3×#41—62no—
418C3×#41—61no—
419C3×#41—61no—
420C3×#41—62no—
421C3×#41—92no—
422C3×#41—181no—
423C2×C3×D4—21no—
424C2×C3×D4—21no—
425C2×C3×D4—21no—
426C2×C3×D4—32no—
427C2×C3×D4—32no—
428C2×C3×D4—41no—
429C2×C3×D4—62no—
430C2×C3×D4—61no—
431C2×C3×D4—61no—
432C2×C3×D4—62no—
433C2×C3×D4—62no—
434C2×C3×D4—62no—
435C2×C3×D4—64no—
436C2×C3×D4—92no—
437C2×C3×D4—91no—
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—
444#239—32no—
445#239—61no—
446#237—21no—
447#237C2×C3×D312yescomplemented
448D3×D4—21no—
449D3×D4—32no—
450D3×D4—61no—
451D3×D4—62no—
452D3×D4—62no—
453D3×D4C2×C3×D312yescomplemented
454#235—32no—
455#235—61no—
456#235C2×C3×D311yescharacteristic
457#235C2×C3×D311yescharacteristic, complemented
458#235C2×C3×D311yescharacteristic, complemented
459C2×D12—31no—
460C2×D12—31no—
461C2×D12—32no—
462C2×D12—61no—
463C2×D12—61no—
464C3×Q16—91no—
465C3×SD16—32no—
466C3×SD16—32no—
467C3×SD16—62no—
468C3×SD16—92no—
469C3×SD16—91no—
470C3×SD16—91no—
471C3×D8—32no—
472C3×D8—32no—
473C3×D8—62no—
474C3×D8—92no—
475C3×D8—91no—
476C3×D8—92no—
477C3×D8—92no—
478C3×M16—31no—
479C3×M16—31no—
480C3×M16—61no—
481C3×M16—92no—
482C2×C3×C8—92no—
483C2×C3×C8—91no—
484#216—31no—
485#216—31no—
486#215—31no—
487#215—31no—
488#215—32no—
489#214—31no—
490#214—31no—
491#214C2×C3×D312yescomplemented
492#213—32no—
493#213—32no—
494#213—32no—
495#213—32no—
496#213—31no—
497#213—31no—
498#213—32no—
499#213—62no—
500#213—62no—
501#213C2×C3×D312yescomplemented
502#208—32no—
503#208C2×C3×D311yescharacteristic, complemented
504C2×C3⋊C8—31no—
505C2×C3⋊C8—31no—
506C2×C3⋊C8—32no—
507C2×C3⋊C8—61no—
508D24—32no—
509#204—32no—
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—61no—
526C22×C32—81no—
527C22×C32—81no—
528C22×C32—81no—
529C22×C32—82no—
530C22×C32—82no—
531C22×C32—82no—
532C22×C32—84no—
533C22×C32—242no—
534C22×C32D3×D411yescharacteristic
535C22×C32C2×#6711yescharacteristic
536C22×C32C2×C3×D411yescharacteristic
537C2×C3⋊D3—22no—
538C2×C3⋊D3—81no—
539C2×C3×D3—22no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—21no—
544C2×C3×D3—22no—
545C2×C3×D3—41no—
546C2×C3×D3—62no—
547C2×C3×D3—62no—
548C2×C3×D3—82no—
549C2×C3×D3—82no—
550C2×C3×D3—84no—
551C2×C3×D3—122no—
552C2×C3×D3—242no—
553C2×C3×D3—242no—
554C2×C3×D3—241no—
555C2×C3×D3—241no—
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×C4—61no—
571C32×C4D3×D411yescharacteristic
572C32×C4C2×#6711yescharacteristic
573C32×C4C2×C3×D411yescharacteristic
574C32×C4C23×D311yescharacteristic
575C32×C4C23×D311yescharacteristic
576C32×C4C24×C311yescharacteristic
577C3×Dic3—22no—
578C3×Dic3—21no—
579C3×Dic3—21no—
580C3×Dic3—21no—
581C3×Dic3—21no—
582C3×Dic3—22no—
583C3×Dic3—41no—
584C3×Dic3C2×#6712yes—
585C3×Dic3C2×C3×D412yes—
586H(5,𝔽2)—31no—
587H(5,𝔽2)—91no—
588AGL(1,ℤ/8)—31no—
589AGL(1,ℤ/8)—91no—
590AGL(1,ℤ/8)—92no—
591AGL(1,ℤ/8)—92no—
592#135—92no—
593#135—91no—
594C2×D8—92no—
595C2×D8—91no—
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—182no—
609C23×C3—181no—
610C22×D3—22no—
611C22×D3—62no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—62no—
615C22×D3—121no—
616C3×Q8—31no—
617C3×Q8—31no—
618C3×Q8—31no—
619C3×Q8—31no—
620C3×Q8—31no—
621C3×Q8—31no—
622C3×Q8—61no—
623C3×Q8—61no—
624C3×Q8—61no—
625C3×D4—22no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—22no—
630C3×D4—22no—
631C3×D4—22no—
632C3×D4—32no—
633C3×D4—32no—
634C3×D4—31no—
635C3×D4—31no—
636C3×D4—31no—
637C3×D4—31no—
638C3×D4—31no—
639C3×D4—31no—
640C3×D4—41no—
641C3×D4—41no—
642C3×D4—42no—
643C3×D4—42no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—61no—
647C3×D4—62no—
648C3×D4—62no—
649C3×D4—62no—
650C3×D4—62no—
651C3×D4—62no—
652C3×D4—64no—
653C3×D4—64no—
654C3×D4—62no—
655C3×D4—61no—
656C3×D4—61no—
657C3×D4—61no—
658C3×D4—61no—
659C3×D4—92no—
660C3×D4—121no—
661C3×D4—182no—
662C3×D4—182no—
663C3×D4—181no—
664C3×D4C2×D3212yes—
665C3×D4C22×C3×D312yes—
666C3×D4C22×C3×D312yes—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—41no—
673C2×C3×C4—62no—
674C2×C3×C4—62no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—64no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—121no—
683C2×C3×C4—182no—
684C2×C3×C4C2×D3211yescharacteristic
685C2×C3×C4C22×C3×D311yescharacteristic
686C2×C3×C4C22×C3×D311yescharacteristic
687#67—21no—
688#67—21no—
689#67—22no—
690#67—22no—
691#67—62no—
692#67—62no—
693#67C3×#6712yes—
694C2×Dic3—22no—
695D12—32no—
696D12—32no—
697D12—62no—
698D12—62no—
699D12—62no—
700D12—61no—
701D12—61no—
702D12—121no—
703D12C3×#6711yescharacteristic
704D12C22×C3×D311yescharacteristic
705D12C22×C3×D311yescharacteristic
706C4×D3—21no—
707C4×D3—21no—
708C4×D3—62no—
709C4×D3—62no—
710C4×D3C22×C3×D312yes—
711Dic6C3×#6711yescharacteristic
712Dic6C22×C3×D311yescharacteristic
713Dic6C22×C3×D311yescharacteristic
714C3×C8—32no—
715C3×C8—32no—
716C3×C8—62no—
717C3×C8—91no—
718C3×C8—91no—
719C3⋊C8—31no—
720C3⋊C8—31no—
721C3⋊C8—31no—
722C3⋊C8—31no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8C22×C3×D312yes—
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—121no—
747C2×C32C2×D3×D411yescharacteristic
748C2×C32C22×#6711yescharacteristic
749C2×C32C22×C3×D411yescharacteristic
750C3⋊D3—42no—
751C3×D3—22no—
752C3×D3—22no—
753C3×D3—42no—
754C3×D3—42no—
755C3×D3—41no—
756C3×D3—41no—
757C3×D3—41no—
758C3×D3—41no—
759C3×D3—81no—
760C3×D3—122no—
761C3×D3—122no—
762C3×D3—242no—
763#41—31no—
764#41—32no—
765#41—31no—
766#41—31no—
767#41—61no—
768#41—92no—
769#41—181no—
770C2×D4—32no—
771C2×D4—61no—
772C2×D4—62no—
773C2×D4—92no—
774C2×D4—91no—
775C2×D4—181no—
776C2×D4—182no—
777C2×D4C3×D3211yescharacteristic, complemented
778Q16—91no—
779SD16—32no—
780SD16—92no—
781SD16—91no—
782SD16—91no—
783D8—32no—
784D8—92no—
785D8—91no—
786D8—92no—
787D8—92no—
788M16—31no—
789M16—92no—
790C2×C8—92no—
791C2×C8—91no—
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—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—81no—
812C22×C3—81no—
813C22×C3—81no—
814C22×C3—82no—
815C22×C3—82no—
816C22×C3—82no—
817C22×C3—84no—
818C22×C3—121no—
819C22×C3—182no—
820C22×C3—242no—
821C22×C3—242no—
822C22×C3—244no—
823C22×C3—721no—
824C22×C3—722no—
825C22×C3D3×#6711yescharacteristic
826C22×C3C3×D3×D411yescharacteristic
827C22×C3C2×C3×#6711yescharacteristic
828C2×D3—21no—
829C2×D3—21no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—82no—
833C2×D3—122no—
834C2×D3—242no—
835C2×D3—242no—
836C2×D3—241no—
837C2×D3—241no—
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—61no—
855C3×C4—61no—
856C3×C4—121no—
857C3×C4D3×#6711yescharacteristic
858C3×C4C3×D3×D411yescharacteristic
859C3×C4C2×C3×#6711yescharacteristic
860C3×C4C22×D3211yescharacteristic
861C3×C4C23×C3×D311yescharacteristic
862C3×C4C23×C3×D311yescharacteristic
863Dic3—21no—
864Dic3—21no—
865Dic3C2×C3×#6712yes—
866C32—21no—
867C32—21no—
868C32—21no—
869C32—41no—
870C32#577411yescharacteristic, complemented
871C32#583511yescharacteristic, complemented
872C32C3×#57611yescharacteristic, complemented
873C23—21no—
874C23—62no—
875C23—182no—
876C23—181no—
877Q8—31no—
878Q8—31no—
879Q8—31no—
880D4—21no—
881D4—32no—
882D4—31no—
883D4—31no—
884D4—31no—
885D4—62no—
886D4—62no—
887D4—61no—
888D4—61no—
889D4—92no—
890D4—182no—
891D4—182no—
892D4—181no—
893D4C2×C3×D3212yes—
894C2×C4—32no—
895C2×C4—62no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—182no—
899C2×C4C2×C3×D3211yescharacteristic
900C8—32no—
901C8—91no—
902C8—91no—
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—121no—
928C2×C3—121no—
929C2×C3—241no—
930C2×C3—362no—
931C2×C3C2×D3×#6711yescharacteristic
932C2×C3C2×C3×D3×D411yescharacteristic
933C2×C3C22×C3×#6711yescharacteristic
934D3—22no—
935D3—41no—
936D3—41no—
937D3—122no—
938D3—122no—
939D3—242no—
940C22—22no—
941C22—32no—
942C22—61no—
943C22—61no—
944C22—81no—
945C22—182no—
946C22—242no—
947C22—721no—
948C22—722no—
949C22C3×D3×#6711yescharacteristic
950C4—32no—
951C4—61no—
952C4—61no—
953C4C3×D3×#6711yescharacteristic
954C4C22×C3×D3211yescharacteristic
955C3—21no—
956C3—21no—
957C3—21no—
958C3—41no—
959C3#1059509711yescharacteristic, direct product factor
960C3C3×#577411yescharacteristic, complemented
961C3C3×#583511yescharacteristic, complemented
962C2—21no—
963C2—42no—
964C2—62no—
965C2—121no—
966C2—121no—
967C2—362no—
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×#64308C2semidirect
3. C2×C3×#3753C2semidirect
4. C32×#932C2semidirect
5. C3×#63935C2semidirect
6. C3×#63934C2semidirect
7. C3×#63925C2semidirect
8. C3×D3×#213C2semidirect
9. C3×#63825C2semidirect
10. C3×#63822C2semidirect
11. C3×#63815C2semidirect
14. #10595097C3direct (N × H)
15. C2×C33×D4C22semidirect
16. C2×C3×C4⋊(C3⋊D3)C22semidirect
19. C32×#237C22semidirect
21. C32×D3×D4C22semidirect
23. C32×#235C22semidirect
24. C32×#235C22semidirect
27. C3×D3×D12C22semidirect
29. C3×#3799C22semidirect
30. C3×#3753C22semidirect
31. C3×#3753C22semidirect
32. C2×C3×C3⋊(C3⋊C8)C22semidirect
33. C32×#214C22semidirect
34. C32×#213C22semidirect
35. C32×#208C22semidirect
36. C3×#3718C22semidirect
37. C3×#3717C22semidirect
38. C3×#3715C22semidirect
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. #64308C2×C3semidirect
52. C2×#3753C2×C3semidirect
61. C3×#932D3semidirect
62. C3×#932C2×C3semidirect
73. #63935C2×C3semidirect
74. #63934C2×C3semidirect
75. #63925C2×C3semidirect
76. D3×#213C2×C3semidirect
77. #63825C2×C3semidirect
78. #63822C2×C3semidirect
79. #63815C2×C3semidirect
125. C2×C32×D4C2×D3semidirect
126. C2×C32×D4C2×D3semidirect
127. C2×C32×D4C22×C3semidirect
128. C2×C4⋊(C3⋊D3)C22×C3semidirect
138. C3×#237C2×D3semidirect
139. C3×#237C22×C3semidirect
148. C3×D3×D4C2×D3semidirect
149. C3×D3×D4C22×C3semidirect
156. C3×#235C2×D3semidirect
157. C3×#235C2×D3semidirect
159. C3×#235C22×C3semidirect
160. C3×#235C22×C3semidirect
168. D3×D12C22×C3semidirect
170. #3799C22×C3semidirect
174. #3753C22×C3semidirect
175. #3753C22×C3semidirect
176. C2×C3⋊(C3⋊C8)C22×C3semidirect
185. C3×#214C2×D3semidirect
186. C3×#214C22×C3semidirect
197. C3×#213C2×D3semidirect
198. C3×#213C22×C3semidirect
201. C3×#208C2×D3semidirect
202. C3×#208C22×C3semidirect
211. #3718C22×C3semidirect
212. #3717C22×C3semidirect
213. #3715C22×C3semidirect
214. #3715C22×C3semidirect
215. #3714C22×C3semidirect
216. #3713C22×C3semidirect
217. #3711C22×C3semidirect
218. D3×C3⋊C8C22×C3semidirect
240. #1004C3×D3semidirect
259. #932C3×D3semidirect
440. C2×C3×D4D32semidirect
441. C2×C3×D4C2×C3×D3semidirect
442. C2×C3×D4C2×C3×D3semidirect
447. #237C2×C3×D3semidirect
453. D3×D4C2×C3×D3semidirect
457. #235C2×C3×D3semidirect
458. #235C2×C3×D3semidirect
491. #214C2×C3×D3semidirect
501. #213C2×C3×D3semidirect
503. #208C2×C3×D3semidirect
597. C33#576semidirect
777. C2×D4C3×D32semidirect
870. C32#5774semidirect
871. C32#5835semidirect
872. C32C3×#576semidirect
959. C3#10595097direct (N × H)
960. C3C3×#5774semidirect
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×#643082
C2×C3×#37532
C32×#9322
C3×#639352
C3×#639342
C3×#639252
C3×D3×#2132
C3×#638252
C3×#638222
C3×#638152
C3×#58353
C3×#57743
#105950973