Finite Group Databasebeta

← C3×#78930 #11867120

Subgroups — C3×#78930 #11867120

Order 1152.

1191 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×C3×D3×M16C211yesmaximal, characteristic, complemented
4C3×#5524C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6C3×#5133C211yesmaximal, characteristic, complemented
7C3×#4995C211yesmaximal, characteristic, complemented
8C3×#4782C212yesmaximal, complemented
9C3×#4780C212yesmaximal, complemented
10C3×#4778C212yesmaximal, complemented
11C3×#4775C212yesmaximal, complemented
12C3×#3055—31nomaximal
13#78930C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67—21no—
16C2×C3×#235C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×M16C2211yescharacteristic
19C32×#117C2211yescharacteristic
20C2×C3×#217—21no—
21C3×#938—21no—
22C3×#938—21no—
23C3×#938C2212yes—
24C3×#938C2212yes—
25C2×C3×#214C2212yescomplemented
26C3×#932—24no—
27C2×C3×#213C2212yescomplemented
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×D3×M16—24no—
31C2×C3×ΓL(1,𝔽25)C2212yescomplemented
32C2×C3×D3×C8C2212yescomplemented
33C3×#897C2211yescharacteristic, complemented
34C3×#897C2211yescharacteristic, complemented
35C3×#895C2211yescharacteristic, complemented
36C3×#895C2211yescharacteristic, complemented
37C3×#886—21no—
38C3×#882—21no—
39C3×C4×D12—21no—
40C3×C4×D12—21no—
41C32×#102C2212yescomplemented
42C32×#102C2212yescomplemented
43C3×#821C2212yescomplemented
44C3×#816C2212yescomplemented
45C3×#808C2212yescomplemented
46C3×#807C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—31no—
48C22×C3×M16—31no—
49C3×#525—31no—
50C2×C3×#121—31no—
51C2×#938C2×C311yescharacteristic, complemented
52C2×#932C2×C311yescharacteristic, complemented
53C2×D3×M16C2×C311yescharacteristic, complemented
54#5524C2×C311yescharacteristic, complemented
55C3×#469—32no—
56C3×#468—32no—
57C3×#466—32no—
58C3×#465—32no—
59C3×#428—31no—
60C3×#418—21no—
61C3×#418D311yescharacteristic, complemented
62C3×#418C2×C311yescharacteristic, complemented
63C3×#417—31no—
64#5133C2×C311yescharacteristic, complemented
65#4995C2×C311yescharacteristic, complemented
66#4782C2×C312yescomplemented
67#4780C2×C312yescomplemented
68#4778C2×C312yescomplemented
69#4775C2×C312yescomplemented
70C24×C32—21no—
71C23×C3×D3D411yescharacteristic
72C2×C32×D4—22no—
73C2×C32×D4—21no—
74C2×C32×D4—22no—
75C2×C32×D4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C2×C3×#67—21no—
78C2×C3×#67—22no—
79C2×C3×#67—22no—
80C2×C3×#67—44no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3D411yescharacteristic
83C3×#235—22no—
84C3×#235—22no—
85C2×C3×D12—21no—
86C2×C3×D12—21no—
87C2×C3×D12C2311yescharacteristic
88C2×C3×C4×D3—22no—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3—21no—
91C2×C3×C4×D3D411yescharacteristic
92C2×C3×C4×D3D411yescharacteristic
93C2×C3×C4×D3C2311yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C32×M16—22no—
97C2×C32×C8C2312yes—
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101C32×C42—21no—
102C3×#217—22no—
103C3×#217—22no—
104C3×#214—24no—
105C3×#213—24no—
106C3×(C2×D3)⋊C4—21no—
107C3×(C2×D3)⋊C4—21no—
108C3×(C2×D3)⋊C4—21no—
109C3×(C2×D3)⋊C4—21no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3C2312yes—
114C3×#208D414yescomplemented
115C2×C3×C3⋊C8C2312yes—
116C3×ΓL(1,𝔽25)—24no—
117C3×D3×C8—24no—
118#3055—31noSylow
119C2×C3×#41—31no—
120C22×C3×D4—21no—
121C22×C3×D4—61no—
122C22×C3×D4C2×D311yescharacteristic
123C22×C3×D4C22×C311yescharacteristic
124C23×C3×C4—31no—
125C22×#67—21no—
126C2×#235C22×C311yescharacteristic
127C22×C4×D3C22×C311yescharacteristic
128C3×AGL(1,ℤ/8)—64no—
129C2×C3×SD16—32no—
130C2×C3×D8—32no—
131C2×C3×M16—21no—
132C2×C3×M16—31no—
133C2×C3×M16—32no—
134C2×C3×M16—64no—
135C2×C3×M16C2×D311yescharacteristic
136C2×C3×M16C22×C311yescharacteristic
137C22×C3×C8—32no—
138C3×#123—61no—
139C3×C22⋊Q8—31no—
140C3×C22⋊Q8—31no—
141C3×#121—32no—
142C3×#121—32no—
143C3×#121—31no—
144C3×#121—31no—
145C3×#121—61no—
146C3×#121—61no—
147C3×#120—61no—
148C3×C4×D4—61no—
149C3×C4×D4—61no—
150C3×#117—21no—
151C3×#117C2×D311yescharacteristic
152C3×#117C22×C311yescharacteristic
153C2×C3×C4⋊C4—31no—
154C2×C3×C22⋊C4—61no—
155C2×#217—21no—
156#938—21no—
157#938—21no—
158#938C22×C312yes—
159#938C22×C312yes—
160C2×#214C22×C312yescomplemented
161#932—24no—
162C2×#213C22×C312yescomplemented
163C2×C4⋊Dic3C22×C311yescharacteristic
164C2×#208C22×C311yescharacteristic
165D3×M16—24no—
166C2×ΓL(1,𝔽25)C22×C312yescomplemented
167C2×D3×C8C22×C312yescomplemented
168#897C22×C311yescharacteristic, complemented
169#897C22×C311yescharacteristic, complemented
170#895C22×C311yescharacteristic, complemented
171#895C22×C311yescharacteristic, complemented
172#886—21no—
173#882—21no—
174C4×D12—21no—
175C4×D12—21no—
176C3×#107—32no—
177C3×#106—32no—
178C3×#103—32no—
179C3×#102—22no—
180C3×#102—22no—
181C3×#102—32no—
182C3×#102C2×D312yescomplemented
183C3×#102C2×D312yescomplemented
184C3×#102C22×C312yescomplemented
185C3×#102C22×C312yescomplemented
186#821C22×C312yescomplemented
187#816C22×C312yescomplemented
188#808C22×C312yescomplemented
189#807C22×C312yescomplemented
190C23×C32—22no—
191C23×C32—42no—
192C23×C32—42no—
193C23×C32—42no—
194C23×C32C2×D411yescharacteristic
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3—21no—
198C22×C3×D3—41no—
199C22×C3×D3C2×D411yescharacteristic
200C22×C3×D3C2×D411yescharacteristic
201C32×D4—22no—
202C32×D4—22no—
203C32×D4—42no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D412yes—
208C2×C32×C4#4112yes—
209C2×C32×C4C2411yescharacteristic
210C3×#67—44no—
211C3×#67—42no—
212C3×#67—44no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—42no—
217C2×C3×Dic3C2×D411yescharacteristic
218C2×C3×Dic3C2×D411yescharacteristic
219C3×D12—21no—
220C3×D12—21no—
221C3×D12—42no—
222C3×D12—42no—
223C3×C4×D3—22no—
224C3×C4×D3—22no—
225C3×C4×D3—21no—
226C3×C4×D3—21no—
227C3×C4×D3—21no—
228C3×C4×D3—21no—
229C3×C4×D3—42no—
230C3×Dic6—21no—
231C3×Dic6—21no—
232C32×C8—22no—
233C3×C3⋊C8C2×D414yescomplemented
234C2×AGL(1,ℤ/8)—31no—
235C22×M16—31no—
236#525—31no—
237C2×#121—31no—
238#469—32no—
239#468—32no—
240#466—32no—
241#465—32no—
242#428—31no—
243#418C3×D311yescharacteristic, complemented
244#417—31no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—31no—
248C24×C3—41no—
249C23×D3C3×D411yescharacteristic
250C3×#41—62no—
251C3×#41—62no—
252C2×C3×Q8—31no—
253C2×C3×D4—24no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4—21no—
257C2×C3×D4—22no—
258C2×C3×D4—21no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—31no—
262C2×C3×D4—42no—
263C2×C3×D4—41no—
264C2×C3×D4—61no—
265C2×C3×D4—61no—
266C2×C3×D4—62no—
267C2×C3×D4—62no—
268C2×C3×D4—61no—
269C2×C3×D4—124no—
270C2×C3×D4C22×D312yes—
271C2×C3×D4C23×C312yes—
272C22×C3×C4—21no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—62no—
279C22×C3×C4—62no—
280C22×C3×C4—61no—
281C22×C3×C4—61no—
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C23×C311yescharacteristic
284C2×#67—21no—
285C2×#67—22no—
286C2×#67—22no—
287C2×#67—44no—
288C22×Dic3—21no—
289C22×Dic3C3×D411yescharacteristic
290#235—22no—
291#235—22no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12C23×C311yescharacteristic
295C2×C4×D3—22no—
296C2×C4×D3—22no—
297C2×C4×D3—21no—
298C2×C4×D3C3×D411yescharacteristic
299C2×C4×D3C3×D411yescharacteristic
300C2×C4×D3C23×C311yescharacteristic
301C2×C4×D3C23×C311yescharacteristic
302C2×Dic6C23×C311yescharacteristic
303C3×SD16—64no—
304C3×D8—64no—
305C3×M16—22no—
306C3×M16—22no—
307C3×M16—34no—
308C3×M16—42no—
309C3×M16—64no—
310C2×C3×C8—22no—
311C2×C3×C8—32no—
312C2×C3×C8—64no—
313C2×C3×C8C22×D312yes—
314C2×C3×C8C23×C312yes—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—32no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C23×C311yescharacteristic
324C3×C4⋊C4C23×C311yescharacteristic
325C3×C22⋊C4—21no—
326C3×C22⋊C4—21no—
327C3×C22⋊C4—41no—
328C3×C22⋊C4—61no—
329C3×C22⋊C4—61no—
330C3×C22⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—62no—
333C3×C22⋊C4—62no—
334C3×C42—21no—
335C3×C42—21no—
336C3×C42—41no—
337#217—22no—
338#217—22no—
339#214—24no—
340#213—24no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—21no—
344(C2×D3)⋊C4—21no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3C23×C312yes—
349#208C3×D414yescomplemented
350C2×C3⋊C8C23×C312yes—
351ΓL(1,𝔽25)—24no—
352D3×C8—24no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—42no—
356C22×C32—42no—
357C22×C32—42no—
358C22×C32—84no—
359C22×C32#12112yes—
360C22×C32C22×D411yescharacteristic
361C2×C3×D3—21no—
362C2×C3×D3—21no—
363C2×C3×D3—21no—
364C2×C3×D3—21no—
365C2×C3×D3—21no—
366C2×C3×D3—44no—
367C2×C3×D3—41no—
368C2×C3×D3—41no—
369C2×C3×D3—41no—
370C2×C3×D3AGL(1,ℤ/8)12yescomplemented
371C32×C4—41no—
372C32×C4—41no—
373C32×C4#12112yes—
374C32×C4C22×D411yescharacteristic
375C32×C4C2×#4111yescharacteristic
376C3×Dic3—21no—
377C3×Dic3—21no—
378C3×Dic3—41no—
379C3×Dic3—42no—
380C2×#41—31no—
381C22×D4—61no—
382C22×D4C2×C3×D311yescharacteristic
383C23×C4—31no—
384AGL(1,ℤ/8)—64no—
385C2×SD16—32no—
386C2×D8—32no—
387C2×M16—31no—
388C2×M16—32no—
389C2×M16—64no—
390C2×M16C2×C3×D311yescharacteristic
391C22×C8—32no—
392#123—61no—
393C22⋊Q8—31no—
394C22⋊Q8—31no—
395#121—32no—
396#121—32no—
397#121—31no—
398#121—31no—
399#121—61no—
400#121—61no—
401#120—61no—
402C4×D4—61no—
403C4×D4—61no—
404#117C2×C3×D311yescharacteristic
405C2×C4⋊C4—31no—
406C2×C22⋊C4—61no—
407#107—32no—
408#106—32no—
409#103—32no—
410#102—32no—
411#102C2×C3×D312yescomplemented
412#102C2×C3×D312yescomplemented
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—31no—
417C23×C3—31no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—44no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—62no—
427C23×C3—62no—
428C23×C3—61no—
429C23×C3—82no—
430C23×C3—82no—
431C23×C3—121no—
432C23×C3D3×D411yescharacteristic
433C23×C3C2×C3×D411yescharacteristic
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—21no—
437C22×D3—41no—
438C22×D3C2×C3×D411yescharacteristic
439C22×D3C2×C3×D411yescharacteristic
440C3×Q8—61no—
441C3×Q8—61no—
442C3×D4—24no—
443C3×D4—22no—
444C3×D4—22no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—42no—
448C3×D4—44no—
449C3×D4—42no—
450C3×D4—42no—
451C3×D4—61no—
452C3×D4—61no—
453C3×D4—122no—
454C3×D4—122no—
455C3×D4—124no—
456C3×D4—124no—
457C3×D4—122no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—62no—
478C2×C3×C4—61no—
479C2×C3×C4—122no—
480C2×C3×C4—122no—
481C2×C3×C4#23512yes—
482C2×C3×C4D3×D411yescharacteristic
483C2×C3×C4D3×D412yes—
484C2×C3×C4C2×C3×D411yescharacteristic
485C2×C3×C4C2×C3×D412yes—
486C2×C3×C4C3×#4112yes—
487C2×C3×C4C23×D311yescharacteristic
488C2×C3×C4C24×C311yescharacteristic
489#67—44no—
490#67—42no—
491#67—44no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—42no—
496C2×Dic3C2×C3×D411yescharacteristic
497C2×Dic3C2×C3×D411yescharacteristic
498D12—21no—
499D12—21no—
500D12—42no—
501D12—42no—
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—21no—
505C4×D3—21no—
506C4×D3—21no—
507C4×D3—21no—
508C4×D3—42no—
509Dic6—21no—
510Dic6—21no—
511C3×C8—22no—
512C3×C8—22no—
513C3×C8—34no—
514C3×C8—42no—
515C3⋊C8C2×C3×D414yescomplemented
516C2×C32—22no—
517C2×C32—82no—
518C2×C32C2×#12111yescharacteristic
519C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
520C2×C32#57511yescharacteristic
521C3×D3—22no—
522C3×D3—41no—
523C3×D3—81no—
524C24—21no—
525C24—31no—
526#41—62no—
527#41—62no—
528C2×Q8—31no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—21no—
532C2×D4—31no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—61no—
538C2×D4—124no—
539C2×D4C22×C3×D312yes—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4C22×C3×D311yescharacteristic
550SD16—64no—
551D8—64no—
552M16—22no—
553M16—34no—
554M16—64no—
555C2×C8—32no—
556C2×C8—64no—
557C2×C8C22×C3×D312yes—
558C4⋊C4—32no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4C22×C3×D311yescharacteristic
563C4⋊C4C22×C3×D311yescharacteristic
564C22⋊C4—21no—
565C22⋊C4—61no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—62no—
570C22⋊C4—62no—
571C42—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—22no—
577C22×C3—21no—
578C22×C3—32no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—44no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—61no—
589C22×C3—61no—
590C22×C3—61no—
591C22×C3—61no—
592C22×C3—61no—
593C22×C3—82no—
594C22×C3—82no—
595C22×C3—84no—
596C22×C3—84no—
597C22×C3—88no—
598C22×C3—124no—
599C22×C3—121no—
600C22×C3—121no—
601C22×C3—121no—
602C22×C3#88412yes—
603C22×C3C3×#12112yes—
604C22×C3C2×D3×D411yescharacteristic
605C22×C3C22×C3×D411yescharacteristic
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—44no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3C3×AGL(1,ℤ/8)12yescomplemented
616C3×C4—22no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—61no—
624C3×C4—61no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—121no—
628C3×C4—122no—
629C3×C4#88412yes—
630C3×C4C3×#12112yes—
631C3×C4C2×#23511yescharacteristic
632C3×C4C2×D3×D411yescharacteristic
633C3×C4C22×C3×D411yescharacteristic
634C3×C4C2×C3×#4111yescharacteristic
635Dic3—21no—
636Dic3—21no—
637Dic3—42no—
638Dic3—41no—
639C32#305511yescharacteristic, complemented, Sylow
640C23—22no—
641C23—31no—
642C23—31no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—62no—
647C23—62no—
648C23—61no—
649C23—121no—
650C23C3×D3×D411yescharacteristic
651Q8—61no—
652Q8—61no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—61no—
657D4—61no—
658D4—122no—
659D4—122no—
660D4—124no—
661D4—124no—
662D4—122no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—62no—
675C2×C4—61no—
676C2×C4—122no—
677C2×C4—122no—
678C2×C4C3×#23512yes—
679C2×C4C3×D3×D411yescharacteristic
680C2×C4C3×D3×D412yes—
681C2×C4C23×C3×D311yescharacteristic
682C8—22no—
683C8—34no—
684C2×C3—22no—
685C2×C3—22no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—42no—
690C2×C3—62no—
691C2×C3—84no—
692C2×C3—82no—
693C2×C3—82no—
694C2×C3—121no—
695C2×C3—241no—
696C2×C3C2×#88411yescharacteristic
697C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
698C2×C3#577311yescharacteristic
699C2×C3C2×C3×#12111yescharacteristic
700C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
701C2×C3C3×#57511yescharacteristic
702D3—22no—
703D3—41no—
704D3—81no—
705C22—21no—
706C22—21no—
707C22—32no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—61no—
712C22—61no—
713C22—61no—
714C22—61no—
715C22—61no—
716C22—84no—
717C22—124no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22C3×#88412yes—
722C22C2×C3×D3×D411yescharacteristic
723C4—41no—
724C4—41no—
725C4—61no—
726C4—61no—
727C4—121no—
728C4—122no—
729C4C3×#88412yes—
730C4C2×C3×#23511yescharacteristic
731C4C2×C3×D3×D411yescharacteristic
732C3—21no—
733C3#7893011yescharacteristic, direct product factor
734C3C3×#305511yescharacteristic, complemented
735C2—22no—
736C2—62no—
737C2—82no—
738C2—121no—
739C2—241no—
740C2C2×C3×#88411yescharacteristic
741C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
742C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#418C2
socleC22×C32C22×D4
hypercenterC3×#418D3
hypocenterC3C3×#3055
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
1. C2×C3×#938C2semidirect
2. C2×C3×#932C2semidirect
3. C2×C3×D3×M16C2semidirect
4. C3×#5524C2semidirect
5. C32×#418C2semidirect
6. C3×#5133C2semidirect
7. C3×#4995C2semidirect
8. C3×#4782C2semidirect
9. C3×#4780C2semidirect
10. C3×#4778C2semidirect
11. C3×#4775C2semidirect
13. #78930C3direct (N × H)
25. C2×C3×#214C22semidirect
27. C2×C3×#213C22semidirect
31. C2×C3×ΓL(1,𝔽25)C22semidirect
32. C2×C3×D3×C8C22semidirect
33. C3×#897C22semidirect
34. C3×#897C22semidirect
35. C3×#895C22semidirect
36. C3×#895C22semidirect
41. C32×#102C22semidirect
42. C32×#102C22semidirect
43. C3×#821C22semidirect
44. C3×#816C22semidirect
45. C3×#808C22semidirect
46. C3×#807C22semidirect
51. C2×#938C2×C3semidirect
52. C2×#932C2×C3semidirect
53. C2×D3×M16C2×C3semidirect
54. #5524C2×C3semidirect
61. C3×#418D3semidirect
62. C3×#418C2×C3semidirect
64. #5133C2×C3semidirect
65. #4995C2×C3semidirect
66. #4782C2×C3semidirect
67. #4780C2×C3semidirect
68. #4778C2×C3semidirect
69. #4775C2×C3semidirect
114. C3×#208D4semidirect
160. C2×#214C22×C3semidirect
162. C2×#213C22×C3semidirect
166. C2×ΓL(1,𝔽25)C22×C3semidirect
167. C2×D3×C8C22×C3semidirect
168. #897C22×C3semidirect
169. #897C22×C3semidirect
170. #895C22×C3semidirect
171. #895C22×C3semidirect
182. C3×#102C2×D3semidirect
183. C3×#102C2×D3semidirect
184. C3×#102C22×C3semidirect
185. C3×#102C22×C3semidirect
186. #821C22×C3semidirect
187. #816C22×C3semidirect
188. #808C22×C3semidirect
189. #807C22×C3semidirect
233. C3×C3⋊C8C2×D4semidirect
243. #418C3×D3semidirect
349. #208C3×D4semidirect
370. C2×C3×D3AGL(1,ℤ/8)semidirect
411. #102C2×C3×D3semidirect
412. #102C2×C3×D3semidirect
515. C3⋊C8C2×C3×D4semidirect
615. C2×D3C3×AGL(1,ℤ/8)semidirect
639. C32#3055semidirect
733. C3#78930direct (N × H)
734. C3C3×#3055semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C3×#9322
C2×C3×D3×M162
C3×#55242
C32×#4182
C3×#51332
C3×#49952
C3×#47822
C3×#47802
C3×#47782
C3×#47752
C3×#30553
#789303