Finite Group Databasebeta

← C3×#78888 #11867135

Subgroups — C3×#78888 #11867135

Order 1152.

1177 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
1C3×#5828C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×C3×D3×M16C211yesmaximal, characteristic, complemented
4C2×C3×#895C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6C3×#5131C211yesmaximal, characteristic, complemented
7C3×#4964C211yesmaximal, characteristic, complemented
8C3×#4812C212yesmaximal, complemented
9C3×#4807C212yesmaximal, complemented
10C3×#4782C212yesmaximal, complemented
11C3×#4775C212yesmaximal, complemented
12C3×#3055—31nomaximal
13#78888C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C3×D12—21no—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×M16C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C3×#949—24no—
21C3×#946C2211yescharacteristic, complemented
22C3×#946C2211yescharacteristic, complemented
23C2×C3×#215C2212yescomplemented
24C3×#938C2211yescharacteristic, complemented
25C3×#938C2211yescharacteristic, complemented
26C3×#937—21no—
27C3×#935—21no—
28C2×C3×#213C2212yescomplemented
29C3×C4×#67—21no—
30C3×C4×#67—21no—
31C2×C3×(C2×D3)⋊C4—21no—
32C3×#926C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C3×D3×M16—24no—
35C2×C3×ΓL(1,𝔽25)C2212yescomplemented
36C2×C3×D3×C8C2212yescomplemented
37C3×#895—21no—
38C3×#895—21no—
39C3×#895C2212yes—
40C3×#895C2212yes—
41C32×#103C2212yescomplemented
42C32×#102C2212yescomplemented
43C3×#821C2212yescomplemented
44C3×#821C2212yescomplemented
45C3×#808C2212yescomplemented
46C3×#807C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—31no—
48C22×C3×M16—31no—
49C3×#525—31no—
50C2×C3×#121—31no—
51#5828C2×C311yescharacteristic, complemented
52C2×#949C2×C311yescharacteristic, complemented
53C2×D3×M16C2×C311yescharacteristic, complemented
54C2×#895C2×C311yescharacteristic, complemented
55C3×#469—32no—
56C3×#468—32no—
57C3×#466—32no—
58C3×#465—32no—
59C3×#428—31no—
60C3×#418—31no—
61C3×#417—21no—
62C3×#417D311yescharacteristic, complemented
63C3×#417C2×C311yescharacteristic, complemented
64#5131C2×C311yescharacteristic, complemented
65#4964C2×C311yescharacteristic, complemented
66#4812C2×C312yescomplemented
67#4807C2×C312yescomplemented
68#4782C2×C312yescomplemented
69#4775C2×C312yescomplemented
70C23×C3×D3—21no—
71C23×C3×D3D411yescharacteristic
72C32×#41—22no—
73C32×#41—22no—
74C2×C32×Q8C2311yescharacteristic
75C2×C32×D4—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C32×C4C2311yescharacteristic
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C22×C3×Dic3D411yescharacteristic
83C2×C3×D12—22no—
84C2×C3×D12—22no—
85C2×C3×D12—22no—
86C2×C3×D12—22no—
87C2×C3×D12—21no—
88C2×C3×D12—44no—
89C2×C3×D12C2312yes—
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3D411yescharacteristic
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C32×M16—22no—
97C2×C32×C8C2312yes—
98C32×C4⋊C4—21no—
99C32×C4⋊C4C2312yes—
100C3×#217—21no—
101C3×#217—21no—
102C3×#217—21no—
103C3×#215—24no—
104C3×#213—24no—
105C3×(C2×D3)⋊C4—21no—
106C3×(C2×D3)⋊C4—21no—
107C3×(C2×D3)⋊C4—22no—
108C3×(C2×D3)⋊C4—22no—
109C3×C4⋊Dic3C2311yescharacteristic
110C3×C4⋊Dic3C2311yescharacteristic
111C3×Dic3⋊C4—21no—
112C3×Dic3⋊C4—21no—
113C3×C4×Dic3—21no—
114C3×#208D414yescomplemented
115C2×C3×C3⋊C8C2312yes—
116C3×ΓL(1,𝔽25)—24no—
117C3×D3×C8—24no—
118#3055—31noSylow
119C2×C3×#41—21no—
120C2×C3×#41C2×D311yescharacteristic
121C2×C3×#41C22×C311yescharacteristic
122C22×C3×D4—31no—
123C22×C3×D4—61no—
124C23×C3×C4—31no—
125C22×D12—21no—
126C22×D12C22×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—31no—
142C3×#121—31no—
143C3×#121—32no—
144C3×#121—32no—
145C3×#121—61no—
146C3×#121—61no—
147C3×#120—61no—
148C3×C4×D4—61no—
149C3×C4×D4—61no—
150C3×#117—31no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C22×C311yescharacteristic
154C2×C3×C22⋊C4—61no—
155#949—24no—
156#946C22×C311yescharacteristic, complemented
157#946C22×C311yescharacteristic, complemented
158C2×#215C22×C312yescomplemented
159#938C22×C311yescharacteristic, complemented
160#938C22×C311yescharacteristic, complemented
161#937—21no—
162#935—21no—
163C2×#213C22×C312yescomplemented
164C4×#67—21no—
165C4×#67—21no—
166C2×(C2×D3)⋊C4—21no—
167#926C22×C311yescharacteristic
168C2×#208C22×C311yescharacteristic
169D3×M16—24no—
170C2×ΓL(1,𝔽25)C22×C312yescomplemented
171C2×D3×C8C22×C312yescomplemented
172#895—21no—
173#895—21no—
174#895C22×C312yes—
175#895C22×C312yes—
176C3×#107—32no—
177C3×#106—32no—
178C3×#103—22no—
179C3×#103C2×D312yescomplemented
180C3×#103C22×C312yescomplemented
181C3×#102—22no—
182C3×#102—32no—
183C3×#102—32no—
184C3×#102C2×D312yescomplemented
185C3×#102C22×C312yescomplemented
186#821C22×C312yescomplemented
187#821C22×C312yescomplemented
188#808C22×C312yescomplemented
189#807C22×C312yescomplemented
190C23×C32—21no—
191C23×C32C2×D411yescharacteristic
192C22×C3×D3—22no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—41no—
196C22×C3×D3—42no—
197C22×C3×D3—42no—
198C22×C3×D3—42no—
199C22×C3×D3C2×D411yescharacteristic
200C22×C3×D3C2×D411yescharacteristic
201C32×Q8—21no—
202C32×Q8—21no—
203C32×D4—21no—
204C32×D4—21no—
205C32×D4—42no—
206C2×C32×C4—21no—
207C2×C32×C4—22no—
208C2×C32×C4—42no—
209C2×C32×C4—42no—
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D412yes—
212C2×C32×C4#4112yes—
213C2×C32×C4C2411yescharacteristic
214C3×#67—42no—
215C3×#67—42no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3—21no—
219C2×C3×Dic3C2×D411yescharacteristic
220C2×C3×Dic3C2×D411yescharacteristic
221C3×D12—22no—
222C3×D12—22no—
223C3×D12—44no—
224C3×D12—44no—
225C3×D12—42no—
226C3×C4×D3—22no—
227C3×C4×D3—22no—
228C3×C4×D3—21no—
229C3×C4×D3—21no—
230C3×C4×D3—21no—
231C3×C4×D3—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#418—31no—
244#417C3×D311yescharacteristic, complemented
245C24×C3—31no—
246C24×C3—61no—
247C23×D3—21no—
248C23×D3C3×D411yescharacteristic
249C3×#41—24no—
250C3×#41—22no—
251C3×#41—22no—
252C3×#41—22no—
253C3×#41—22no—
254C3×#41—42no—
255C2×C3×Q8—21no—
256C2×C3×Q8C22×D311yescharacteristic
257C2×C3×Q8C23×C311yescharacteristic
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—32no—
262C2×C3×D4—41no—
263C2×C3×D4—62no—
264C2×C3×D4—62no—
265C2×C3×D4—61no—
266C2×C3×D4—61no—
267C2×C3×D4—62no—
268C2×C3×D4—62no—
269C2×C3×D4—61no—
270C2×C3×D4—124no—
271C2×C3×D4C22×D311yescharacteristic
272C2×C3×D4C23×C311yescharacteristic
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—41no—
284C22×C3×C4—41no—
285C22×C3×C4—62no—
286C22×C3×C4—62no—
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C23×C311yescharacteristic
289C2×#67—21no—
290C2×#67—21no—
291C22×Dic3C3×D411yescharacteristic
292C2×D12—22no—
293C2×D12—22no—
294C2×D12—22no—
295C2×D12—22no—
296C2×D12—21no—
297C2×D12—44no—
298C2×D12C23×C312yes—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3C3×D411yescharacteristic
302C2×C4×D3C3×D411yescharacteristic
303C2×C4×D3C23×C311yescharacteristic
304C2×C4×D3C23×C311yescharacteristic
305C3×SD16—64no—
306C3×D8—64no—
307C3×M16—22no—
308C3×M16—22no—
309C3×M16—34no—
310C3×M16—42no—
311C3×M16—64no—
312C2×C3×C8—22no—
313C2×C3×C8—32no—
314C2×C3×C8—64no—
315C2×C3×C8C22×D312yes—
316C2×C3×C8C23×C312yes—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—41no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4C22×D312yes—
326C3×C4⋊C4C23×C312yes—
327C3×C22⋊C4—62no—
328C3×C22⋊C4—62no—
329C3×C22⋊C4—61no—
330C3×C22⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C42—61no—
335#217—21no—
336#217—21no—
337#217—21no—
338#215—24no—
339#213—24no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—22no—
344C4⋊Dic3C23×C311yescharacteristic
345C4⋊Dic3C23×C311yescharacteristic
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348C4×Dic3—21no—
349#208C3×D414yescomplemented
350C2×C3⋊C8C23×C312yes—
351ΓL(1,𝔽25)—24no—
352D3×C8—24no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—41no—
358C22×C32#12112yes—
359C22×C32C22×D411yescharacteristic
360C2×C3×D3—21no—
361C2×C3×D3—21no—
362C2×C3×D3—21no—
363C2×C3×D3—21no—
364C2×C3×D3—21no—
365C2×C3×D3—44no—
366C2×C3×D3—42no—
367C2×C3×D3—42no—
368C2×C3×D3—42no—
369C2×C3×D3—84no—
370C2×C3×D3AGL(1,ℤ/8)12yescomplemented
371C32×C4—41no—
372C32×C4—42no—
373C32×C4#12112yes—
374C32×C4C22×D411yescharacteristic
375C32×C4C2×#4111yescharacteristic
376C3×Dic3—21no—
377C3×Dic3—21no—
378C3×Dic3—41no—
379C3×Dic3—41no—
380C2×#41C2×C3×D311yescharacteristic
381C22×D4—31no—
382C22×D4—61no—
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—31no—
396#121—31no—
397#121—32no—
398#121—32no—
399#121—61no—
400#121—61no—
401#120—61no—
402C4×D4—61no—
403C4×D4—61no—
404#117—31no—
405C2×C4⋊C4C2×C3×D311yescharacteristic
406C2×C22⋊C4—61no—
407#107—32no—
408#106—32no—
409#103C2×C3×D312yescomplemented
410#102—32no—
411#102—32no—
412#102C2×C3×D312yescomplemented
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—31no—
417C23×C3—31no—
418C23×C3—41no—
419C23×C3—62no—
420C23×C3—62no—
421C23×C3—62no—
422C23×C3—121no—
423C23×C3—122no—
424C23×C3—122no—
425C23×C3—122no—
426C23×C3D3×D411yescharacteristic
427C23×C3C2×C3×D411yescharacteristic
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—41no—
432C22×D3—42no—
433C22×D3—42no—
434C22×D3—42no—
435C22×D3C2×C3×D411yescharacteristic
436C22×D3C2×C3×D411yescharacteristic
437C3×Q8—22no—
438C3×Q8—21no—
439C3×Q8—21no—
440C3×Q8—21no—
441C3×Q8—21no—
442C3×Q8—41no—
443C3×D4—22no—
444C3×D4—21no—
445C3×D4—21no—
446C3×D4—21no—
447C3×D4—21no—
448C3×D4—41no—
449C3×D4—44no—
450C3×D4—42no—
451C3×D4—42no—
452C3×D4—62no—
453C3×D4—62no—
454C3×D4—124no—
455C3×D4—124no—
456C3×D4—122no—
457C3×D4—122no—
458C3×D4—122no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—41no—
470C2×C3×C4—42no—
471C2×C3×C4—44no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—82no—
486C2×C3×C4#23512yes—
487C2×C3×C4D3×D411yescharacteristic
488C2×C3×C4D3×D412yes—
489C2×C3×C4C2×C3×D411yescharacteristic
490C2×C3×C4C2×C3×D412yes—
491C2×C3×C4C3×#4112yes—
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C24×C311yescharacteristic
494#67—42no—
495#67—42no—
496C2×Dic3—22no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3C2×C3×D411yescharacteristic
500C2×Dic3C2×C3×D411yescharacteristic
501D12—22no—
502D12—22no—
503D12—44no—
504D12—44no—
505D12—42no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—21no—
509C4×D3—21no—
510C4×D3—21no—
511C4×D3—21no—
512C3×C8—22no—
513C3×C8—22no—
514C3×C8—34no—
515C3×C8—42no—
516C3⋊C8C2×C3×D414yescomplemented
517C2×C32—22no—
518C2×C32—81no—
519C2×C32C2×#12111yescharacteristic
520C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
521C2×C32#57511yescharacteristic
522C3×D3—22no—
523C3×D3—41no—
524C3×D3—82no—
525C24—31no—
526C24—61no—
527#41—22no—
528#41—22no—
529C2×Q8C22×C3×D311yescharacteristic
530C2×D4—21no—
531C2×D4—32no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—62no—
537C2×D4—62no—
538C2×D4—61no—
539C2×D4—124no—
540C2×D4C22×C3×D311yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4C22×C3×D311yescharacteristic
551SD16—64no—
552D8—64no—
553M16—22no—
554M16—34no—
555M16—64no—
556C2×C8—32no—
557C2×C8—64no—
558C2×C8C22×C3×D312yes—
559C4⋊C4—21no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4C22×C3×D312yes—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C42—61no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—32no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—42no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—61no—
590C22×C3—61no—
591C22×C3—61no—
592C22×C3—61no—
593C22×C3—61no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—124no—
597C22×C3—122no—
598C22×C3—122no—
599C22×C3—122no—
600C22×C3—244no—
601C22×C3#88412yes—
602C22×C3C3×#12112yes—
603C22×C3C2×D3×D411yescharacteristic
604C22×C3C22×C3×D411yescharacteristic
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—44no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—84no—
615C2×D3C3×AGL(1,ℤ/8)12yescomplemented
616C3×C4—22no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—82no—
627C3×C4—121no—
628C3×C4—121no—
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—41no—
638Dic3—41no—
639C32#305511yescharacteristic, complemented, Sylow
640C23—21no—
641C23—31no—
642C23—31no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23—121no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23C3×D3×D411yescharacteristic
651Q8—21no—
652Q8—21no—
653D4—21no—
654D4—21no—
655D4—42no—
656D4—62no—
657D4—62no—
658D4—124no—
659D4—124no—
660D4—122no—
661D4—122no—
662D4—122no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
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—82no—
692C2×C3—81no—
693C2×C3—81no—
694C2×C3—121no—
695C2×C3—242no—
696C2×C3C2×#88411yescharacteristic
697C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
698C2×C3#577711yescharacteristic
699C2×C3C2×C3×#12111yescharacteristic
700C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
701C2×C3C3×#57511yescharacteristic
702D3—22no—
703D3—41no—
704D3—82no—
705C22—21no—
706C22—21no—
707C22—32no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—61no—
712C22—61no—
713C22—61no—
714C22—61no—
715C22—61no—
716C22—124no—
717C22—122no—
718C22—122no—
719C22—122no—
720C22—244no—
721C22C3×#88412yes—
722C22C2×C3×D3×D411yescharacteristic
723C4—41no—
724C4—42no—
725C4—61no—
726C4—61no—
727C4—121no—
728C4—121no—
729C4C3×#88412yes—
730C4C2×C3×#23511yescharacteristic
731C4C2×C3×D3×D411yescharacteristic
732C3—21no—
733C3#7888811yescharacteristic, direct product factor
734C3C3×#305511yescharacteristic, complemented
735C2—22no—
736C2—62no—
737C2—81no—
738C2—121no—
739C2—242no—
740C2C2×C3×#88411yescharacteristic
741C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
742C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#417C2
socleC22×C32C22×D4
hypercenterC3×#417D3
hypocenterC3C3×#3055
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
1. C3×#5828C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×D3×M16C2semidirect
4. C2×C3×#895C2semidirect
5. C32×#417C2semidirect
6. C3×#5131C2semidirect
7. C3×#4964C2semidirect
8. C3×#4812C2semidirect
9. C3×#4807C2semidirect
10. C3×#4782C2semidirect
11. C3×#4775C2semidirect
13. #78888C3direct (N × H)
21. C3×#946C22semidirect
22. C3×#946C22semidirect
23. C2×C3×#215C22semidirect
24. C3×#938C22semidirect
25. C3×#938C22semidirect
28. C2×C3×#213C22semidirect
35. C2×C3×ΓL(1,𝔽25)C22semidirect
36. C2×C3×D3×C8C22semidirect
41. C32×#103C22semidirect
42. C32×#102C22semidirect
43. C3×#821C22semidirect
44. C3×#821C22semidirect
45. C3×#808C22semidirect
46. C3×#807C22semidirect
51. #5828C2×C3semidirect
52. C2×#949C2×C3semidirect
53. C2×D3×M16C2×C3semidirect
54. C2×#895C2×C3semidirect
62. C3×#417D3semidirect
63. C3×#417C2×C3semidirect
64. #5131C2×C3semidirect
65. #4964C2×C3semidirect
66. #4812C2×C3semidirect
67. #4807C2×C3semidirect
68. #4782C2×C3semidirect
69. #4775C2×C3semidirect
114. C3×#208D4semidirect
156. #946C22×C3semidirect
157. #946C22×C3semidirect
158. C2×#215C22×C3semidirect
159. #938C22×C3semidirect
160. #938C22×C3semidirect
163. C2×#213C22×C3semidirect
170. C2×ΓL(1,𝔽25)C22×C3semidirect
171. C2×D3×C8C22×C3semidirect
179. C3×#103C2×D3semidirect
180. C3×#103C22×C3semidirect
184. C3×#102C2×D3semidirect
185. C3×#102C22×C3semidirect
186. #821C22×C3semidirect
187. #821C22×C3semidirect
188. #808C22×C3semidirect
189. #807C22×C3semidirect
233. C3×C3⋊C8C2×D4semidirect
244. #417C3×D3semidirect
349. #208C3×D4semidirect
370. C2×C3×D3AGL(1,ℤ/8)semidirect
409. #103C2×C3×D3semidirect
412. #102C2×C3×D3semidirect
516. C3⋊C8C2×C3×D4semidirect
615. C2×D3C3×AGL(1,ℤ/8)semidirect
639. C32#3055semidirect
733. C3#78888direct (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
C3×#58282
C2×C3×#9492
C2×C3×D3×M162
C2×C3×#8952
C32×#4172
C3×#51312
C3×#49642
C3×#48122
C3×#48072
C3×#47822
C3×#47752
C3×#30553
#788883