Finite Group Databasebeta

← C3×#10595029 #13174604

Subgroups — C3×#10595029 #13174604

Order 1728.

1730 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C2×C32×C4×Dic3C211yesmaximal, characteristic, complemented
4C3×#63978C214yesmaximal, complemented
5C3×#63911C211yesmaximal, characteristic, complemented
6C3×C4×#626C214yesmaximal, complemented
7C3×#63866C211yesmaximal, characteristic, complemented
8C3×#63864C211yesmaximal, characteristic, complemented
9C3×#63860C211yesmaximal, characteristic, complemented
10C3×#5832—31nomaximal
11C3×#5477—31nomaximal
12#10595029C311yesmaximal, characteristic, direct product factor
13C22×C33×C4C2211yescharacteristic
14C2×C3×#638C2212yes—
15C3×#3828—24no—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2212yes—
18C2×C3×#634C2211yescharacteristic
19C2×C32×#67C2212yes—
20C22×C32×Dic3C2212yes—
21C32×#235—24no—
22C2×C32×D12C2211yescharacteristic
23C2×C32×C4×D3C2212yes—
24C2×C32×Dic6C2211yescharacteristic
25C2×C3×#626C2214yes—
26C32×C4×Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28C32×C4×Dic3C2212yes—
29C3×Dic3⋊Dic3C2214yes—
30C3×#3722C2214yes—
31C3×(C2×D3)⋊Dic3C2214yes—
32C2×C32×#41—31no—
33C2×#3828C2×C311yescharacteristic, complemented
34C2×C3×#235—21no—
35C2×C3×#235—31no—
36C2×C3×#235—31no—
37C2×C3×#235—61no—
38C2×C3×#235D311yescharacteristic, complemented
39C2×C3×#235C2×C311yescharacteristic, complemented
40C2×C32×C42—31no—
41C3×#947—31no—
42C3×#944—31no—
43C3×#940—31no—
44C3×#939—34no—
45C3×#936—31no—
46C3×#930—34no—
47C3×C4×#67—34no—
48C2×C3×C4×Dic3—21no—
49C2×C3×C4×Dic3D311yescharacteristic, complemented
50C2×C3×C4×Dic3C2×C311yescharacteristic, complemented
51C3×#875—31no—
52C3×#875—31no—
53C3×#874—31no—
54C3×C4×D12—34no—
55C3×#869—31no—
56#63978C2×C314yescomplemented
57#63911C2×C311yescharacteristic, complemented
58C4×#626C2×C314yescomplemented
59#63866C2×C311yescharacteristic, complemented
60#63864C2×C311yescharacteristic, complemented
61#63860C2×C311yescharacteristic, complemented
62C23×C33C2311yescharacteristic
63C22×C3×C3⋊D3C2312yes—
64C22×C32×D3C2312yes—
65C2×C33×C4D414yescomplemented
66C2×C33×C4C2311yescharacteristic
67C2×C33×C4C2311yescharacteristic
68C3×#638—24no—
69C2×C3×C3⋊Dic3C2312yes—
70C3×C4⋊(C3⋊D3)—22no—
71C3×C4×C3⋊D3—24no—
72C3×#634—22no—
73C32×#67—24no—
74C2×C32×Dic3—24no—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78C32×D12—22no—
79C32×C4×D3—24no—
80C32×Dic6—22no—
81C3×#626—28no—
82C3×#532—91no—
83#5832—31no—
84#5477—31no—
85C32×#41—64no—
86C2×C32×Q8—31no—
87C2×C32×D4—32no—
88C2×C32×D4—31no—
89C22×C32×C4—21no—
90C22×C32×C4—21no—
91C22×C32×C4—21no—
92C22×C32×C4—32no—
93C22×C32×C4—32no—
94C22×C32×C4—41no—
95C22×C32×C4C2×D311yescharacteristic
96C22×C32×C4C2×D311yescharacteristic
97C22×C32×C4C22×C311yescharacteristic
98C2×#638C22×C312yes—
99#3828—24no—
100C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
101C2×C4×C3⋊D3C22×C312yes—
102C2×#634C22×C311yescharacteristic
103C2×C3×#67—22no—
104C2×C3×#67—32no—
105C2×C3×#67—32no—
106C2×C3×#67—34no—
107C2×C3×#67—62no—
108C2×C3×#67C2×D312yes—
109C2×C3×#67C22×C312yes—
110C22×C3×Dic3—22no—
111C22×C3×Dic3C2×D312yes—
112C22×C3×Dic3C22×C312yes—
113C3×#235—28no—
114C3×#235—24no—
115C3×#235—24no—
116C3×#235—68no—
117C3×#235—64no—
118C3×#235—64no—
119C2×C3×D12—21no—
120C2×C3×D12—34no—
121C2×C3×D12—31no—
122C2×C3×D12—31no—
123C2×C3×D12—61no—
124C2×C3×D12C2×D311yescharacteristic
125C2×C3×D12C22×C311yescharacteristic
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—62no—
130C2×C3×C4×D3C2×D312yes—
131C2×C3×C4×D3C22×C312yes—
132C2×C3×Dic6—21no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—61no—
136C2×C3×Dic6C2×D311yescharacteristic
137C2×C3×Dic6C22×C311yescharacteristic
138C2×#626C22×C314yes—
139C32×C42—31no—
140C32×C42—32no—
141C32×C42—31no—
142C3×#217—34no—
143C3×(C2×D3)⋊C4—34no—
144C3×(C2×D3)⋊C4—34no—
145C3×(C2×D3)⋊C4—34no—
146C3×C4⋊Dic3—34no—
147C3×Dic3⋊C4—34no—
148C3×C4×Dic3—22no—
149C3×C4×Dic3—21no—
150C3×C4×Dic3—21no—
151C3×C4×Dic3C2×D312yes—
152C3×C4×Dic3C2×D311yescharacteristic
153C3×C4×Dic3C2×D311yescharacteristic
154C3×C4×Dic3C22×C311yescharacteristic
155C3×C4×Dic3C22×C311yescharacteristic
156C3×C4×Dic3C22×C312yes—
157Dic3⋊Dic3C22×C314yes—
158#3722C22×C314yes—
159(C2×D3)⋊Dic3C22×C314yes—
160C22×C33—22no—
161C22×C33C2×D412yes—
162C22×C33C2411yescharacteristic
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—24no—
165C2×C32×D3—22no—
166C2×C32×D3—24no—
167C33×C4C2×D412yes—
168C33×C4C2×D412yes—
169C3×C3⋊Dic3—22no—
170C32×Dic3—22no—
171C32×Dic3—22no—
172C32×Dic3#4114yescomplemented
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—61no—
176C2×C3×#41—91no—
177C2×#235—31no—
178C2×#235—31no—
179C2×#235—61no—
180C2×#235C3×D311yescharacteristic, complemented
181C3×C4⋊Q8—91no—
182C3×#127—91no—
183C3×#124—91no—
184C3×#124—91no—
185C3×#121—94no—
186C3×C4×D4—94no—
187C2×C3×C42—31no—
188C2×C3×C42—31no—
189C2×C3×C42—61no—
190#947—31no—
191#944—31no—
192#940—31no—
193#939—34no—
194#936—31no—
195#930—34no—
196C4×#67—34no—
197C2×C4×Dic3C3×D311yescharacteristic, complemented
198#875—31no—
199#875—31no—
200#874—31no—
201C4×D12—34no—
202#869—31no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—32no—
207C23×C32—41no—
208C23×C32C22×D311yescharacteristic
209C23×C32C22×D311yescharacteristic
210C23×C32C23×C311yescharacteristic
211C22×C3⋊D3C23×C312yes—
212C22×C3×D3—22no—
213C22×C3×D3—32no—
214C22×C3×D3—32no—
215C22×C3×D3—62no—
216C22×C3×D3C22×D312yes—
217C22×C3×D3C23×C312yes—
218C32×Q8—62no—
219C32×D4—64no—
220C32×D4—62no—
221C2×C32×C4—24no—
222C2×C32×C4—24no—
223C2×C32×C4—24no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—32no—
231C2×C32×C4—32no—
232C2×C32×C4—32no—
233C2×C32×C4—44no—
234C2×C32×C4—41no—
235C2×C32×C4—41no—
236C2×C32×C4—64no—
237C2×C32×C4—64no—
238C2×C32×C4D1214yescomplemented
239C2×C32×C4#6714yescomplemented
240C2×C32×C4C3×D414yescomplemented
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C23×C311yescharacteristic
246C2×C32×C4C23×C311yescharacteristic
247#638—24no—
248C2×C3⋊Dic3C23×C312yes—
249C4⋊(C3⋊D3)—22no—
250C4×C3⋊D3—24no—
251#634—22no—
252C3×#67—28no—
253C3×#67—24no—
254C3×#67—24no—
255C3×#67—68no—
256C3×#67—64no—
257C3×#67—64no—
258C3×#67—68no—
259C2×C3×Dic3—28no—
260C2×C3×Dic3—24no—
261C2×C3×Dic3—24no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3C22×D312yes—
269C2×C3×Dic3C22×D312yes—
270C2×C3×Dic3C22×D312yes—
271C2×C3×Dic3C23×C312yes—
272C2×C3×Dic3C23×C312yes—
273C2×C3×Dic3C23×C312yes—
274C3×D12—24no—
275C3×D12—22no—
276C3×D12—22no—
277C3×D12—64no—
278C3×D12—68no—
279C3×D12—62no—
280C3×D12—62no—
281C3×C4×D3—28no—
282C3×C4×D3—24no—
283C3×C4×D3—24no—
284C3×C4×D3—68no—
285C3×C4×D3—64no—
286C3×C4×D3—64no—
287C3×Dic6—24no—
288C3×Dic6—22no—
289C3×Dic6—22no—
290C3×Dic6—64no—
291C3×Dic6—62no—
292C3×Dic6—62no—
293#626—28no—
294#532—91noSylow
295C2×C33—22no—
296C2×C33C22×D411yescharacteristic
297C2×C33C2×#4112yes—
298C3×C3⋊D3—42no—
299C32×D3—42no—
300C3×#41—68no—
301C3×#41—64no—
302C3×#41—64no—
303C3×#41—184no—
304C2×C3×Q8—31no—
305C2×C3×Q8—31no—
306C2×C3×Q8—61no—
307C2×C3×Q8—91no—
308C2×C3×D4—32no—
309C2×C3×D4—32no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—61no—
313C2×C3×D4—62no—
314C2×C3×D4—94no—
315C2×C3×D4—92no—
316C2×C3×D4—91no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—32no—
321C22×C3×C4—32no—
322C22×C3×C4—32no—
323C22×C3×C4—32no—
324C22×C3×C4—41no—
325C22×C3×C4—62no—
326C22×C3×C4—62no—
327C22×C3×C4—92no—
328C22×C3×C4D3211yescharacteristic
329C22×C3×C4C2×C3×D311yescharacteristic
330C22×C3×C4C2×C3×D311yescharacteristic
331C2×#67—32no—
332C2×#67—32no—
333C2×#67—34no—
334C2×#67—62no—
335C2×#67C2×C3×D312yes—
336C22×Dic3C2×C3×D312yes—
337#235—24no—
338#235—68no—
339#235—64no—
340#235—64no—
341C2×D12—34no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—61no—
345C2×D12C2×C3×D311yescharacteristic
346C2×C4×D3—32no—
347C2×C4×D3—32no—
348C2×C4×D3—62no—
349C2×C4×D3C2×C3×D312yes—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—61no—
353C2×Dic6C2×C3×D311yescharacteristic
354C3×C4⋊C4—94no—
355C3×C22⋊C4—94no—
356C3×C22⋊C4—94no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—32no—
360C3×C42—31no—
361C3×C42—32no—
362C3×C42—31no—
363C3×C42—62no—
364C3×C42—61no—
365C3×C42—61no—
366#217—34no—
367(C2×D3)⋊C4—34no—
368(C2×D3)⋊C4—34no—
369(C2×D3)⋊C4—34no—
370C4⋊Dic3—34no—
371Dic3⋊C4—34no—
372C4×Dic3C2×C3×D312yes—
373C4×Dic3C2×C3×D311yescharacteristic
374C4×Dic3C2×C3×D311yescharacteristic
375C22×C32—22no—
376C22×C32—24no—
377C22×C32—22no—
378C22×C32—22no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—42no—
386C22×C32—41no—
387C22×C32—42no—
388C22×C32—42no—
389C22×C32—44no—
390C22×C32—62no—
391C22×C32—64no—
392C22×C32C2×D1212yes—
393C22×C32C2×#6712yes—
394C22×C32C2×C3×D412yes—
395C22×C32C23×D311yescharacteristic
396C22×C32C23×D311yescharacteristic
397C22×C32C24×C311yescharacteristic
398C2×C3⋊D3—22no—
399C2×C3⋊D3—24no—
400C2×C3×D3—24no—
401C2×C3×D3—24no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—24no—
405C2×C3×D3—44no—
406C2×C3×D3—64no—
407C2×C3×D3—62no—
408C2×C3×D3—64no—
409C2×C3×D3—64no—
410C2×C3×D3—62no—
411C2×C3×D3—124no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—22no—
417C32×C4—22no—
418C32×C4—34no—
419C32×C4—42no—
420C32×C4—42no—
421C32×C4—62no—
422C32×C4—62no—
423C32×C4C2×D1212yes—
424C32×C4C2×D1212yes—
425C32×C4C2×#6712yes—
426C32×C4C2×#6712yes—
427C32×C4C2×C3×D412yes—
428C32×C4C2×C3×D412yes—
429C3⋊Dic3—22no—
430C3×Dic3—24no—
431C3×Dic3—24no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—24no—
437C3×Dic3—64no—
438C3×Dic3—62no—
439C3×Dic3—62no—
440C3×Dic3#23514yescomplemented
441C3×Dic3C3×#4114yescomplemented
442C2×#41—31no—
443C2×#41—91no—
444C4⋊Q8—91no—
445#127—91no—
446#124—91no—
447#124—91no—
448#121—94no—
449C4×D4—94no—
450C2×C42—31no—
451C33#53211yescharacteristic, complemented, Sylow
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—32no—
456C23×C3—32no—
457C23×C3—41no—
458C23×C3—62no—
459C23×C3—92no—
460C23×C3C2×D3211yescharacteristic
461C23×C3C22×C3×D311yescharacteristic
462C23×C3C22×C3×D311yescharacteristic
463C22×D3—32no—
464C22×D3—32no—
465C22×D3—62no—
466C22×D3C22×C3×D312yes—
467C3×Q8—64no—
468C3×Q8—62no—
469C3×Q8—62no—
470C3×Q8—182no—
471C3×D4—64no—
472C3×D4—68no—
473C3×D4—64no—
474C3×D4—64no—
475C3×D4—62no—
476C3×D4—62no—
477C3×D4—188no—
478C3×D4—184no—
479C3×D4—182no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—44no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—68no—
502C2×C3×C4—64no—
503C2×C3×C4—64no—
504C2×C3×C4—68no—
505C2×C3×C4—64no—
506C2×C3×C4—64no—
507C2×C3×C4—92no—
508C2×C3×C4—184no—
509C2×C3×C4#62614yescomplemented
510C2×C3×C4C3×D1214yescomplemented
511C2×C3×C4C3×#6714yescomplemented
512C2×C3×C4C2×D3211yescharacteristic
513C2×C3×C4C2×D3211yescharacteristic
514C2×C3×C4C22×C3×D311yescharacteristic
515C2×C3×C4C22×C3×D311yescharacteristic
516C2×C3×C4C22×C3×D311yescharacteristic
517C2×C3×C4C22×C3×D311yescharacteristic
518#67—24no—
519#67—68no—
520#67—64no—
521#67—64no—
522#67—68no—
523C2×Dic3—24no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—62no—
527C2×Dic3C22×C3×D312yes—
528C2×Dic3C22×C3×D312yes—
529C2×Dic3C22×C3×D312yes—
530D12—22no—
531D12—64no—
532D12—68no—
533D12—62no—
534D12—62no—
535C4×D3—24no—
536C4×D3—68no—
537C4×D3—64no—
538C4×D3—64no—
539Dic6—22no—
540Dic6—64no—
541Dic6—62no—
542Dic6—62no—
543C2×C32—22no—
544C2×C32—24no—
545C2×C32—22no—
546C2×C32—22no—
547C2×C32—22no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—22no—
551C2×C32—22no—
552C2×C32—21no—
553C2×C32—41no—
554C2×C32—42no—
555C2×C32—42no—
556C2×C32—42no—
557C2×C32—44no—
558C2×C32—122no—
559C2×C32C22×D1211yescharacteristic
560C2×C32C2×#23512yes—
561C2×C32D3×#4112yes—
562C2×C32C22×#6711yescharacteristic
563C2×C32C22×C3×D411yescharacteristic
564C2×C32C2×C3×#4112yes—
565C3⋊D3—42no—
566C3×D3—44no—
567C3×D3—42no—
568C3×D3—42no—
569C3×D3—124no—
570C3×D3—122no—
571C3×D3—122no—
572#41—64no—
573#41—184no—
574C2×Q8—31no—
575C2×Q8—91no—
576C2×D4—32no—
577C2×D4—31no—
578C2×D4—94no—
579C2×D4—92no—
580C2×D4—91no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—92no—
584C22×C4C3×D3211yescharacteristic
585C4⋊C4—94no—
586C22⋊C4—94no—
587C22⋊C4—94no—
588C42—32no—
589C42—31no—
590C42—31no—
591C22×C3—24no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—44no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—64no—
607C22×C3—64no—
608C22×C3—62no—
609C22×C3—62no—
610C22×C3—64no—
611C22×C3—124no—
612C22×C3—184no—
613C22×C3—182no—
614C22×C3C2×#62612yes—
615C22×C3C2×C3×D1212yes—
616C22×C3C2×C3×#6712yes—
617C22×C3C22×D3211yescharacteristic
618C22×C3C23×C3×D311yescharacteristic
619C22×C3C23×C3×D311yescharacteristic
620C2×D3—24no—
621C2×D3—22no—
622C2×D3—64no—
623C2×D3—62no—
624C2×D3—64no—
625C2×D3—64no—
626C2×D3—62no—
627C2×D3—124no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—34no—
635C3×C4—34no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—64no—
639C3×C4—64no—
640C3×C4—64no—
641C3×C4—62no—
642C3×C4—62no—
643C3×C4—62no—
644C3×C4—62no—
645C3×C4—182no—
646C3×C4C2×#62612yes—
647C3×C4C2×#62612yes—
648C3×C4C2×C3×D1212yes—
649C3×C4C2×C3×D1212yes—
650C3×C4C2×C3×#6712yes—
651C3×C4C2×C3×#6712yes—
652Dic3—22no—
653Dic3—22no—
654Dic3—64no—
655Dic3—62no—
656Dic3—62no—
657Dic3C3×#23514yescomplemented
658C32—21no—
659C32—21no—
660C32—21no—
661C32—41no—
662C32#547711yescharacteristic, complemented
663C32#583211yescharacteristic, complemented
664C32C3×#53211yescharacteristic, complemented
665C23—32no—
666C23—92no—
667C23C2×C3×D3211yescharacteristic
668Q8—62no—
669Q8—182no—
670D4—64no—
671D4—62no—
672D4—188no—
673D4—184no—
674D4—182no—
675C2×C4—32no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—64no—
679C2×C4—64no—
680C2×C4—92no—
681C2×C4—184no—
682C2×C4C3×#62614yescomplemented
683C2×C4C2×C3×D3211yescharacteristic
684C2×C4C2×C3×D3211yescharacteristic
685C2×C3—24no—
686C2×C3—22no—
687C2×C3—22no—
688C2×C3—22no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—22no—
693C2×C3—22no—
694C2×C3—22no—
695C2×C3—42no—
696C2×C3—42no—
697C2×C3—44no—
698C2×C3—41no—
699C2×C3—42no—
700C2×C3—124no—
701C2×C3—122no—
702C2×C3—122no—
703C2×C3—362no—
704C2×C3D3×#23512yes—
705C2×C3C22×#62611yescharacteristic
706C2×C3C22×C3×D1211yescharacteristic
707C2×C3C2×C3×#23512yes—
708C2×C3C3×D3×#4112yes—
709C2×C3C22×C3×#6711yescharacteristic
710D3—42no—
711D3—124no—
712D3—122no—
713D3—122no—
714C22—22no—
715C22—62no—
716C22—64no—
717C22—182no—
718C22—184no—
719C22C2×C3×#62612yes—
720C22C22×C3×D3211yescharacteristic
721C4—34no—
722C4—62no—
723C4—62no—
724C4—182no—
725C4C2×C3×#62612yes—
726C4C2×C3×#62612yes—
727C3—21no—
728C3—21no—
729C3—21no—
730C3—41no—
731C3#1059502911yescharacteristic, direct product factor
732C3C3×#547711yescharacteristic, complemented
733C3C3×#583211yescharacteristic, complemented
734C2—22no—
735C2—122no—
736C2—362no—
737C2C3×D3×#23512yes—
738C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×C32×#235C2semidirect
3. C2×C32×C4×Dic3C2semidirect
4. C3×#63978C2semidirect
5. C3×#63911C2semidirect
6. C3×C4×#626C2semidirect
7. C3×#63866C2semidirect
8. C3×#63864C2semidirect
9. C3×#63860C2semidirect
12. #10595029C3direct (N × H)
33. C2×#3828C2×C3semidirect
38. C2×C3×#235D3semidirect
39. C2×C3×#235C2×C3semidirect
49. C2×C3×C4×Dic3D3semidirect
50. C2×C3×C4×Dic3C2×C3semidirect
56. #63978C2×C3semidirect
57. #63911C2×C3semidirect
58. C4×#626C2×C3semidirect
59. #63866C2×C3semidirect
60. #63864C2×C3semidirect
61. #63860C2×C3semidirect
65. C2×C33×C4D4semidirect
172. C32×Dic3#41semidirect
180. C2×#235C3×D3semidirect
197. C2×C4×Dic3C3×D3semidirect
238. C2×C32×C4D12semidirect
239. C2×C32×C4#67semidirect
240. C2×C32×C4C3×D4semidirect
440. C3×Dic3#235semidirect
441. C3×Dic3C3×#41semidirect
451. C33#532semidirect
509. C2×C3×C4#626semidirect
510. C2×C3×C4C3×D12semidirect
511. C2×C3×C4C3×#67semidirect
657. Dic3C3×#235semidirect
662. C32#5477semidirect
663. C32#5832semidirect
664. C32C3×#532semidirect
682. C2×C4C3×#626semidirect
731. C3#10595029direct (N × H)
732. C3C3×#5477semidirect
733. C3C3×#5832semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C32×#2352
C2×C32×C4×Dic32
C3×#639782
C3×#639112
C3×C4×#6262
C3×#638662
C3×#638642
C3×#638602
C3×#58323
C3×#54773
#105950293