Finite Group Databasebeta

← C3×#79211 #11867129

Subgroups — C3×#79211 #11867129

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3C3×#5524C211yesmaximal, characteristic, complemented
4C2×C3×#895C211yesmaximal, characteristic, complemented
5C32×#428C211yesmaximal, characteristic, complemented
6C3×#5001C211yesmaximal, characteristic, complemented
7C3×#4966C211yesmaximal, characteristic, complemented
8C3×#4886C212yesmaximal, complemented
9C3×#4883C212yesmaximal, complemented
10C3×#4865C212yesmaximal, complemented
11C3×#4864C212yesmaximal, complemented
12C3×#3055—31nomaximal
13#79211C311yesmaximal, characteristic, direct product factor
14C2×C3×#235C2211yescharacteristic
15C22×C3×D12—21no—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×M16C2211yescharacteristic
19C32×#117C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4—21no—
22C2×C3×#208C2211yescharacteristic
23C3×#908—24no—
24C3×D3×M16—24no—
25C2×C3×D24C2212yescomplemented
26C2×C3×#204C2212yescomplemented
27C2×C3×ΓL(1,𝔽25)C2212yescomplemented
28C2×C3×D3×C8C2212yescomplemented
29C3×#897C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×#895—21no—
32C3×#895—21no—
33C3×#895C2212yes—
34C3×#895C2212yes—
35C3×#895C2211yescharacteristic, complemented
36C3×#895C2211yescharacteristic, complemented
37C3×#886—21no—
38C3×#882—21no—
39C3×C4×D12—21no—
40C3×C4×D12—21no—
41C32×#107C2212yescomplemented
42C32×#106C2212yescomplemented
43C3×#810C2212yescomplemented
44C3×#809C2212yescomplemented
45C3×#809C2212yescomplemented
46C3×#809C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—31no—
48C22×C3×M16—31no—
49C3×#525—31no—
50C2×C3×#121—31no—
51C2×#908C2×C311yescharacteristic, complemented
52C2×D3×M16C2×C311yescharacteristic, complemented
53#5524C2×C311yescharacteristic, complemented
54C2×#895C2×C311yescharacteristic, complemented
55C3×#469—32no—
56C3×#468—32no—
57C3×#466—32no—
58C3×#465—32no—
59C3×#428—21no—
60C3×#428D311yescharacteristic, complemented
61C3×#428C2×C311yescharacteristic, complemented
62C3×#418—31no—
63C3×#417—31no—
64#5001C2×C311yescharacteristic, complemented
65#4966C2×C311yescharacteristic, complemented
66#4886C2×C312yescomplemented
67#4883C2×C312yescomplemented
68#4865C2×C312yescomplemented
69#4864C2×C312yescomplemented
70C23×C3×D3—21no—
71C23×C3×D3D411yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—21no—
75C22×C3×Dic3D411yescharacteristic
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12—22no—
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12—21no—
82C2×C3×D12—22no—
83C2×C3×D12—22no—
84C2×C3×D12—21no—
85C2×C3×D12—44no—
86C2×C3×D12C2312yes—
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×M16D414yescomplemented
97C2×C32×C8C2312yes—
98C32×C4⋊C4—21no—
99C32×C4⋊C4C2312yes—
100C32×C4⋊C4C2311yescharacteristic
101C32×C4⋊C4C2311yescharacteristic
102C32×C22⋊C4—21no—
103C32×C42—21no—
104C3×(C2×D3)⋊C4—21no—
105C3×(C2×D3)⋊C4—21no—
106C3×(C2×D3)⋊C4—21no—
107C3×(C2×D3)⋊C4—21no—
108C3×(C2×D3)⋊C4—22no—
109C3×(C2×D3)⋊C4—22no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3—21no—
112C3×#208—22no—
113C2×C3×C3⋊C8C2312yes—
114C3×D24—24no—
115C3×#204—24no—
116C3×ΓL(1,𝔽25)—24no—
117C3×D3×C8—24no—
118#3055—31noSylow
119C2×C3×#41—31no—
120C22×C3×D4—31no—
121C22×C3×D4—61no—
122C23×C3×C4—31no—
123C2×#235C22×C311yescharacteristic
124C22×D12—21no—
125C22×D12C22×C311yescharacteristic
126C22×C4×D3C22×C311yescharacteristic
127C3×AGL(1,ℤ/8)—64no—
128C2×C3×SD16—32no—
129C2×C3×D8—32no—
130C2×C3×M16—21no—
131C2×C3×M16—31no—
132C2×C3×M16—32no—
133C2×C3×M16—64no—
134C2×C3×M16C2×D311yescharacteristic
135C2×C3×M16C22×C311yescharacteristic
136C22×C3×C8—32no—
137C3×#123—61no—
138C3×C22⋊Q8—31no—
139C3×C22⋊Q8—31no—
140C3×#121—32no—
141C3×#121—32no—
142C3×#121—31no—
143C3×#121—31no—
144C3×#121—61no—
145C3×#121—61no—
146C3×#120—61no—
147C3×C4×D4—61no—
148C3×C4×D4—61no—
149C3×#117—21no—
150C3×#117C2×D311yescharacteristic
151C3×#117C22×C311yescharacteristic
152C2×C3×C4⋊C4—21no—
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C22×C311yescharacteristic
155C2×C3×C22⋊C4—61no—
156C2×(C2×D3)⋊C4—21no—
157C2×#208C22×C311yescharacteristic
158#908—24no—
159D3×M16—24no—
160C2×D24C22×C312yescomplemented
161C2×#204C22×C312yescomplemented
162C2×ΓL(1,𝔽25)C22×C312yescomplemented
163C2×D3×C8C22×C312yescomplemented
164#897C22×C311yescharacteristic, complemented
165#897C22×C311yescharacteristic, complemented
166#895—21no—
167#895—21no—
168#895C22×C312yes—
169#895C22×C312yes—
170#895C22×C311yescharacteristic, complemented
171#895C22×C311yescharacteristic, complemented
172#886—21no—
173#882—21no—
174C4×D12—21no—
175C4×D12—21no—
176C3×#107—22no—
177C3×#107C2×D312yescomplemented
178C3×#107C22×C312yescomplemented
179C3×#106—22no—
180C3×#106C2×D312yescomplemented
181C3×#106C22×C312yescomplemented
182C3×#103—32no—
183C3×#102—32no—
184C3×#102—32no—
185C3×#102—32no—
186#810C22×C312yescomplemented
187#809C22×C312yescomplemented
188#809C22×C312yescomplemented
189#809C22×C312yescomplemented
190C23×C32C2×D411yescharacteristic
191C22×C3×D3—22no—
192C22×C3×D3—22no—
193C22×C3×D3—22no—
194C22×C3×D3—21no—
195C22×C3×D3—41no—
196C22×C3×D3—42no—
197C22×C3×D3—42no—
198C22×C3×D3—42no—
199C22×C3×D3C2×D411yescharacteristic
200C22×C3×D3C2×D411yescharacteristic
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—22no—
204C2×C32×C4—42no—
205C2×C32×C4C2×D412yes—
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4#4112yes—
208C2×C32×C4C2411yescharacteristic
209C3×#67—42no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3C2×D411yescharacteristic
213C2×C3×Dic3C2×D411yescharacteristic
214C3×D12—22no—
215C3×D12—21no—
216C3×D12—22no—
217C3×D12—21no—
218C3×D12—42no—
219C3×D12—44no—
220C3×D12—42no—
221C3×D12—44no—
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×C8C2×D414yescomplemented
233C3×C3⋊C8—22no—
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#428C3×D311yescharacteristic, complemented
243#418—31no—
244#417—31no—
245C24×C3—31no—
246C24×C3—61no—
247C23×D3—21no—
248C23×D3C3×D411yescharacteristic
249C3×#41—62no—
250C3×#41—62no—
251C2×C3×Q8—31no—
252C2×C3×D4—31no—
253C2×C3×D4—32no—
254C2×C3×D4—61no—
255C2×C3×D4—61no—
256C2×C3×D4—62no—
257C2×C3×D4—62no—
258C2×C3×D4—61no—
259C2×C3×D4—62no—
260C2×C3×D4—61no—
261C2×C3×D4—62no—
262C2×C3×D4—124no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—41no—
272C22×C3×C4—62no—
273C22×C3×C4—62no—
274C22×C3×C4—61no—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C23×C311yescharacteristic
277C2×#67—21no—
278C22×Dic3C3×D411yescharacteristic
279#235—22no—
280#235—22no—
281C2×D12—22no—
282C2×D12—22no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—22no—
286C2×D12—22no—
287C2×D12—21no—
288C2×D12—44no—
289C2×D12C23×C312yes—
290C2×D12C23×C311yescharacteristic
291C2×C4×D3—22no—
292C2×C4×D3—22no—
293C2×C4×D3—21no—
294C2×C4×D3C3×D411yescharacteristic
295C2×C4×D3C3×D411yescharacteristic
296C2×C4×D3C23×C311yescharacteristic
297C2×C4×D3C23×C311yescharacteristic
298C2×Dic6C23×C311yescharacteristic
299C3×SD16—64no—
300C3×D8—64no—
301C3×M16—24no—
302C3×M16—62no—
303C3×M16—64no—
304C3×M16D1214yescomplemented
305C3×M16C3×D414yescomplemented
306C2×C3×C8—22no—
307C2×C3×C8—32no—
308C2×C3×C8—64no—
309C2×C3×C8C22×D312yes—
310C2×C3×C8C23×C312yes—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—41no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C4⋊C4C22×D312yes—
322C3×C4⋊C4C23×C311yescharacteristic
323C3×C4⋊C4C23×C311yescharacteristic
324C3×C4⋊C4C23×C312yes—
325C3×C22⋊C4—21no—
326C3×C22⋊C4—21no—
327C3×C22⋊C4—41no—
328C3×C22⋊C4—62no—
329C3×C22⋊C4—62no—
330C3×C22⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C42—21no—
335C3×C42—21no—
336C3×C42—41no—
337(C2×D3)⋊C4—21no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—22no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345#208—22no—
346C2×C3⋊C8C23×C312yes—
347D24—24no—
348#204—24no—
349ΓL(1,𝔽25)—24no—
350D3×C8—24no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32#12112yes—
354C22×C32C22×D411yescharacteristic
355C2×C3×D3—21no—
356C2×C3×D3—21no—
357C2×C3×D3—21no—
358C2×C3×D3—21no—
359C2×C3×D3—21no—
360C2×C3×D3—44no—
361C2×C3×D3—41no—
362C2×C3×D3—42no—
363C2×C3×D3—42no—
364C2×C3×D3—41no—
365C2×C3×D3—41no—
366C2×C3×D3—42no—
367C2×C3×D3—84no—
368C2×C3×D3AGL(1,ℤ/8)12yescomplemented
369C32×C4—42no—
370C32×C4—41no—
371C32×C4—41no—
372C32×C4#12112yes—
373C32×C4C22×D411yescharacteristic
374C32×C4C2×#4111yescharacteristic
375C3×Dic3—21no—
376C3×Dic3—21no—
377C3×Dic3—41no—
378C2×#41—31no—
379C22×D4—31no—
380C22×D4—61no—
381C23×C4—31no—
382AGL(1,ℤ/8)—64no—
383C2×SD16—32no—
384C2×D8—32no—
385C2×M16—31no—
386C2×M16—32no—
387C2×M16—64no—
388C2×M16C2×C3×D311yescharacteristic
389C22×C8—32no—
390#123—61no—
391C22⋊Q8—31no—
392C22⋊Q8—31no—
393#121—32no—
394#121—32no—
395#121—31no—
396#121—31no—
397#121—61no—
398#121—61no—
399#120—61no—
400C4×D4—61no—
401C4×D4—61no—
402#117C2×C3×D311yescharacteristic
403C2×C4⋊C4C2×C3×D311yescharacteristic
404C2×C22⋊C4—61no—
405#107C2×C3×D312yescomplemented
406#106C2×C3×D312yescomplemented
407#103—32no—
408#102—32no—
409#102—32no—
410#102—32no—
411C23×C3—21no—
412C23×C3—31no—
413C23×C3—31no—
414C23×C3—62no—
415C23×C3—62no—
416C23×C3—61no—
417C23×C3—62no—
418C23×C3—121no—
419C23×C3—122no—
420C23×C3—122no—
421C23×C3—122no—
422C23×C3D3×D411yescharacteristic
423C23×C3C2×C3×D411yescharacteristic
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—21no—
427C22×D3—22no—
428C22×D3—41no—
429C22×D3—42no—
430C22×D3—42no—
431C22×D3—42no—
432C22×D3C2×C3×D411yescharacteristic
433C22×D3C2×C3×D411yescharacteristic
434C3×Q8—61no—
435C3×Q8—61no—
436C3×D4—61no—
437C3×D4—62no—
438C3×D4—62no—
439C3×D4—61no—
440C3×D4—122no—
441C3×D4—124no—
442C3×D4—122no—
443C3×D4—124no—
444C3×D4—122no—
445C3×D4—122no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—42no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—82no—
472C2×C3×C4—122no—
473C2×C3×C4C2×D1212yes—
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4#23912yes—
476C2×C3×C4C2×C3×D412yes—
477C2×C3×C4C2×C3×D411yescharacteristic
478C2×C3×C4C3×#4112yes—
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C24×C311yescharacteristic
481#67—42no—
482C2×Dic3—22no—
483C2×Dic3—21no—
484C2×Dic3C2×C3×D411yescharacteristic
485C2×Dic3C2×C3×D411yescharacteristic
486D12—22no—
487D12—21no—
488D12—22no—
489D12—21no—
490D12—42no—
491D12—44no—
492D12—42no—
493D12—44no—
494D12—42no—
495C4×D3—22no—
496C4×D3—22no—
497C4×D3—21no—
498C4×D3—21no—
499C4×D3—21no—
500C4×D3—21no—
501C4×D3—42no—
502Dic6—21no—
503Dic6—21no—
504C3×C8—24no—
505C3×C8—62no—
506C3×C8C2×D1214yescomplemented
507C3×C8C2×C3×D414yescomplemented
508C3⋊C8—22no—
509C2×C32—22no—
510C2×C32C2×#12111yescharacteristic
511C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
512C2×C32#57511yescharacteristic
513C3×D3—22no—
514C3×D3—41no—
515C3×D3—81no—
516C3×D3—82no—
517C24—31no—
518C24—61no—
519#41—62no—
520#41—62no—
521C2×Q8—31no—
522C2×D4—31no—
523C2×D4—32no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—62no—
527C2×D4—62no—
528C2×D4—61no—
529C2×D4—62no—
530C2×D4—61no—
531C2×D4—62no—
532C2×D4—124no—
533C22×C4—21no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—61no—
542C22×C4C22×C3×D311yescharacteristic
543SD16—64no—
544D8—64no—
545M16—62no—
546M16—64no—
547M16C3×D1214yescomplemented
548C2×C8—32no—
549C2×C8—64no—
550C2×C8C22×C3×D312yes—
551C4⋊C4—21no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4C22×C3×D311yescharacteristic
555C4⋊C4C22×C3×D311yescharacteristic
556C4⋊C4C22×C3×D312yes—
557C22⋊C4—21no—
558C22⋊C4—62no—
559C22⋊C4—62no—
560C22⋊C4—61no—
561C22⋊C4—61no—
562C22⋊C4—61no—
563C22⋊C4—61no—
564C42—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—22no—
570C22×C3—21no—
571C22×C3—32no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—61no—
575C22×C3—61no—
576C22×C3—61no—
577C22×C3—61no—
578C22×C3—61no—
579C22×C3—124no—
580C22×C3—121no—
581C22×C3—122no—
582C22×C3—122no—
583C22×C3—121no—
584C22×C3—121no—
585C22×C3—122no—
586C22×C3—244no—
587C22×C3#89512yes—
588C22×C3C3×#12112yes—
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C22×C3×D411yescharacteristic
591C2×D3—21no—
592C2×D3—21no—
593C2×D3—21no—
594C2×D3—21no—
595C2×D3—21no—
596C2×D3—44no—
597C2×D3—42no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—42no—
601C2×D3—41no—
602C2×D3—42no—
603C2×D3—84no—
604C2×D3C3×AGL(1,ℤ/8)12yescomplemented
605C3×C4—22no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—42no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—42no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—61no—
615C3×C4—61no—
616C3×C4—82no—
617C3×C4—81no—
618C3×C4—81no—
619C3×C4—121no—
620C3×C4#89512yes—
621C3×C4C3×#12112yes—
622C3×C4C22×D1211yescharacteristic
623C3×C4C2×#23911yescharacteristic
624C3×C4C22×C3×D411yescharacteristic
625C3×C4C2×C3×#4111yescharacteristic
626Dic3—21no—
627Dic3—21no—
628Dic3—41no—
629C32#305511yescharacteristic, complemented, Sylow
630C23—31no—
631C23—31no—
632C23—62no—
633C23—62no—
634C23—61no—
635C23—62no—
636C23—121no—
637C23—122no—
638C23—122no—
639C23—122no—
640C23C3×D3×D411yescharacteristic
641Q8—61no—
642Q8—61no—
643D4—61no—
644D4—62no—
645D4—62no—
646D4—61no—
647D4—124no—
648D4—122no—
649D4—124no—
650D4—122no—
651D4—122no—
652D4—122no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—42no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—122no—
668C2×C4C2×C3×D1212yes—
669C2×C4C3×D3×D411yescharacteristic
670C2×C4C3×#23912yes—
671C2×C4C23×C3×D311yescharacteristic
672C8—62no—
673C8C2×C3×D1214yescomplemented
674C2×C3—22no—
675C2×C3—22no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—42no—
680C2×C3—62no—
681C2×C3—121no—
682C2×C3—242no—
683C2×C3—241no—
684C2×C3C2×#89511yescharacteristic
685C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
686C2×C3#577711yescharacteristic
687C2×C3C2×C3×#12111yescharacteristic
688C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
689C2×C3C3×#57511yescharacteristic
690D3—22no—
691D3—41no—
692D3—82no—
693D3—81no—
694C22—21no—
695C22—21no—
696C22—32no—
697C22—61no—
698C22—61no—
699C22—61no—
700C22—61no—
701C22—61no—
702C22—124no—
703C22—121no—
704C22—122no—
705C22—122no—
706C22—121no—
707C22—121no—
708C22—122no—
709C22—244no—
710C22C3×#89512yes—
711C22C2×C3×D3×D411yescharacteristic
712C4—42no—
713C4—41no—
714C4—41no—
715C4—61no—
716C4—61no—
717C4—121no—
718C4C3×#89512yes—
719C4C22×C3×D1211yescharacteristic
720C4C2×C3×#23911yescharacteristic
721C3—21no—
722C3#7921111yescharacteristic, direct product factor
723C3C3×#305511yescharacteristic, complemented
724C2—22no—
725C2—62no—
726C2—121no—
727C2—242no—
728C2—241no—
729C2C2×C3×#89511yescharacteristic
730C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
731C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#428C2
socleC22×C32C22×D4
hypercenterC3×#428D3
hypocenterC3C3×#3055
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#428

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. C2×C3×D3×M16C2semidirect
3. C3×#5524C2semidirect
4. C2×C3×#895C2semidirect
5. C32×#428C2semidirect
6. C3×#5001C2semidirect
7. C3×#4966C2semidirect
8. C3×#4886C2semidirect
9. C3×#4883C2semidirect
10. C3×#4865C2semidirect
11. C3×#4864C2semidirect
13. #79211C3direct (N × H)
25. C2×C3×D24C22semidirect
26. C2×C3×#204C22semidirect
27. C2×C3×ΓL(1,𝔽25)C22semidirect
28. C2×C3×D3×C8C22semidirect
29. C3×#897C22semidirect
30. C3×#897C22semidirect
35. C3×#895C22semidirect
36. C3×#895C22semidirect
41. C32×#107C22semidirect
42. C32×#106C22semidirect
43. C3×#810C22semidirect
44. C3×#809C22semidirect
45. C3×#809C22semidirect
46. C3×#809C22semidirect
51. C2×#908C2×C3semidirect
52. C2×D3×M16C2×C3semidirect
53. #5524C2×C3semidirect
54. C2×#895C2×C3semidirect
60. C3×#428D3semidirect
61. C3×#428C2×C3semidirect
64. #5001C2×C3semidirect
65. #4966C2×C3semidirect
66. #4886C2×C3semidirect
67. #4883C2×C3semidirect
68. #4865C2×C3semidirect
69. #4864C2×C3semidirect
96. C32×M16D4semidirect
160. C2×D24C22×C3semidirect
161. C2×#204C22×C3semidirect
162. C2×ΓL(1,𝔽25)C22×C3semidirect
163. C2×D3×C8C22×C3semidirect
164. #897C22×C3semidirect
165. #897C22×C3semidirect
170. #895C22×C3semidirect
171. #895C22×C3semidirect
177. C3×#107C2×D3semidirect
178. C3×#107C22×C3semidirect
180. C3×#106C2×D3semidirect
181. C3×#106C22×C3semidirect
186. #810C22×C3semidirect
187. #809C22×C3semidirect
188. #809C22×C3semidirect
189. #809C22×C3semidirect
232. C32×C8C2×D4semidirect
242. #428C3×D3semidirect
304. C3×M16D12semidirect
305. C3×M16C3×D4semidirect
368. C2×C3×D3AGL(1,ℤ/8)semidirect
405. #107C2×C3×D3semidirect
406. #106C2×C3×D3semidirect
506. C3×C8C2×D12semidirect
507. C3×C8C2×C3×D4semidirect
547. M16C3×D12semidirect
604. C2×D3C3×AGL(1,ℤ/8)semidirect
629. C32#3055semidirect
673. C8C2×C3×D12semidirect
722. C3#79211direct (N × H)
723. C3C3×#3055semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×C3×D3×M162
C3×#55242
C2×C3×#8952
C32×#4282
C3×#50012
C3×#49662
C3×#48862
C3×#48832
C3×#48652
C3×#48642
C3×#30553
#792113