Finite Group Databasebeta

← C3×#84052 #11808984

Subgroups — C3×#84052 #11808984

Order 1152.

3809 conjugacy classes of subgroups.

The subgroup lattice has 775 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×D4C211yesmaximal, characteristic, complemented
2C23×C3×#67C211yesmaximal, characteristic, complemented
3C2×C3×#953C212yesmaximal, complemented
4C2×C3×#937C212yesmaximal, complemented
5C3×#5247C211yesmaximal, characteristic, complemented
6C3×#5223C214yesmaximal, complemented
7C3×#5220C212yesmaximal, complemented
8C3×#5213C212yesmaximal, complemented
9C3×#2403—31nomaximal
10#84052C311yesmaximal, characteristic, direct product factor
11C25×C32C2211yescharacteristic
12C25×C32C2211yescharacteristic, complemented
13C24×C3×D3C2211yescharacteristic, complemented
14C22×C32×D4—28no—
15C22×C32×D4—24no—
16C22×C32×D4C2212yes—
17C22×C32×D4C2212yescomplemented
18C23×C32×C4C2211yescharacteristic, complemented
19C22×C3×#67—28no—
20C22×C3×#67—24no—
21C22×C3×#67C2212yes—
22C22×C3×#67C2212yescomplemented
23C22×C3×#67C2214yescomplemented
24C23×C3×Dic3C2211yescharacteristic, complemented
25C3×#953—28no—
26C2×C3×#217C2212yescomplemented
27C2×C3×#217C2212yescomplemented
28C2×C3×#217C2214yescomplemented
29C2×C3×#217C2212yescomplemented
30C3×#937—28no—
31C2×C3×(C2×D3)⋊C4C2214yescomplemented
32C3×C3⋊#95C2214yescomplemented
33C23×C3×D4—21no—
34C23×C3×D4—31no—
35C23×C3×D4D311yescharacteristic, complemented
36C23×C3×D4C2×C311yescharacteristic, complemented
37C23×#67C2×C311yescharacteristic, complemented
38C2×C3×#120—32no—
39C2×C3×#120—32no—
40C2×#953C2×C312yescomplemented
41C2×#937C2×C312yescomplemented
42C3×#392—34no—
43C3×#386—32no—
44C3×#386—32no—
45C3×#379—31no—
46#5247C2×C311yescharacteristic, complemented
47#5223C2×C314yescomplemented
48#5220C2×C312yescomplemented
49#5213C2×C312yescomplemented
50C24×C32—24no—
51C24×C32—22no—
52C24×C32—24no—
53C24×C32—24no—
54C24×C32—24no—
55C24×C32—42no—
56C24×C32—42no—
57C24×C32D414yescomplemented
58C24×C32C2311yescharacteristic
59C24×C32C2312yes—
60C24×C32C2311yescharacteristic
61C24×C32C2311yescharacteristic
62C23×C3×D3—22no—
63C23×C3×D3—24no—
64C23×C3×D3—24no—
65C23×C3×D3—42no—
66C23×C3×D3C2312yes—
67C2×C32×D4—232no—
68C2×C32×D4—24no—
69C2×C32×D4—24no—
70C2×C32×D4—24no—
71C2×C32×D4—24no—
72C2×C32×D4—24no—
73C2×C32×D4D418yescomplemented
74C22×C32×C4—22no—
75C22×C32×C4—24no—
76C22×C32×C4C2312yes—
77C2×C3×#67—232no—
78C2×C3×#67—24no—
79C2×C3×#67—24no—
80C2×C3×#67—24no—
81C2×C3×#67—24no—
82C2×C3×#67—28no—
83C2×C3×#67—28no—
84C2×C3×#67—24no—
85C2×C3×#67—44no—
86C2×C3×#67D418yescomplemented
87C22×C3×Dic3—22no—
88C22×C3×Dic3—24no—
89C22×C3×Dic3C2314yes—
90C22×C3×Dic3C2312yes—
91C3×#217—24no—
92C3×#217—24no—
93C3×#217—28no—
94C3×#217—42no—
95C3×(C2×D3)⋊C4—28no—
96#2403—31noSylow
97C25×C3—21no—
98C25×C3—21no—
99C25×C3—31no—
100C25×C3C2×D311yescharacteristic
101C25×C3C2×D311yescharacteristic, complemented
102C25×C3C22×C311yescharacteristic
103C25×C3C22×C311yescharacteristic, complemented
104C24×D3C22×C311yescharacteristic, complemented
105C22×C3×D4—28no—
106C22×C3×D4—216no—
107C22×C3×D4—24no—
108C22×C3×D4—24no—
109C22×C3×D4—28no—
110C22×C3×D4—28no—
111C22×C3×D4—22no—
112C22×C3×D4—22no—
113C22×C3×D4—32no—
114C22×C3×D4—32no—
115C22×C3×D4—34no—
116C22×C3×D4—68no—
117C22×C3×D4—64no—
118C22×C3×D4C2×D312yes—
119C22×C3×D4C2×D312yescomplemented
120C22×C3×D4C22×C312yes—
121C22×C3×D4C22×C312yescomplemented
122C23×C3×C4—21no—
123C23×C3×C4—31no—
124C23×C3×C4C2×D311yescharacteristic, complemented
125C23×C3×C4C22×C311yescharacteristic, complemented
126C22×#67—24no—
127C22×#67—28no—
128C22×#67C22×C312yes—
129C22×#67C22×C312yescomplemented
130C22×#67C22×C314yescomplemented
131C23×Dic3C22×C311yescharacteristic, complemented
132C3×#120—68no—
133C3×#120—68no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—34no—
137C2×C3×C22⋊C4—34no—
138C2×C3×C22⋊C4—32no—
139#953—28no—
140C2×#217C22×C312yescomplemented
141C2×#217C22×C314yescomplemented
142C2×#217C22×C312yescomplemented
143C2×#217C22×C312yescomplemented
144#937—28no—
145C2×(C2×D3)⋊C4C22×C314yescomplemented
146C3×#95—34no—
147C3⋊#95C22×C314yescomplemented
148C23×C32—22no—
149C23×C32—22no—
150C23×C32—28no—
151C23×C32—28no—
152C23×C32—22no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32—28no—
158C23×C32—24no—
159C23×C32—22no—
160C23×C32—22no—
161C23×C32—24no—
162C23×C32—44no—
163C23×C32—416no—
164C23×C32—416no—
165C23×C32—44no—
166C23×C32—44no—
167C23×C32C2×D414yes—
168C23×C32C2×D412yes—
169C23×C32C2×D414yes—
170C23×C32C2×D412yes—
171C23×C32C2×D412yes—
172C23×C32C2×D414yescomplemented
173C23×C32C2411yescharacteristic
174C22×C3×D3—28no—
175C22×C3×D3—24no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—24no—
179C22×C3×D3—416no—
180C22×C3×D3—44no—
181C22×C3×D3—44no—
182C22×C3×D3C2×D414yescomplemented
183C32×D4—216no—
184C32×D4—216no—
185C2×C32×C4—28no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4C2×D414yescomplemented
189C3×#67—216no—
190C3×#67—216no—
191C3×#67—416no—
192C2×C3×Dic3—28no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—24no—
196C2×C3×Dic3—24no—
197C2×C3×Dic3—24no—
198C2×C3×Dic3C2×D414yescomplemented
199C23×D4—31no—
200C23×D4C3×D311yescharacteristic, complemented
201C2×#120—32no—
202C2×#120—32no—
203#392—34no—
204#386—32no—
205#386—32no—
206#379—31no—
207C24×C3—28no—
208C24×C3—24no—
209C24×C3—28no—
210C24×C3—24no—
211C24×C3—24no—
212C24×C3—22no—
213C24×C3—24no—
214C24×C3—24no—
215C24×C3—24no—
216C24×C3—22no—
217C24×C3—24no—
218C24×C3—24no—
219C24×C3—24no—
220C24×C3—24no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—22no—
224C24×C3—21no—
225C24×C3—32no—
226C24×C3—44no—
227C24×C3—44no—
228C24×C3—42no—
229C24×C3—42no—
230C24×C3—42no—
231C24×C3—42no—
232C24×C3—44no—
233C24×C3—44no—
234C24×C3—64no—
235C24×C3—62no—
236C24×C3—64no—
237C24×C3—122no—
238C24×C3#6714yescomplemented
239C24×C3C3×D414yescomplemented
240C24×C3C22×D311yescharacteristic
241C24×C3C22×D312yes—
242C24×C3C22×D311yescharacteristic
243C24×C3C22×D311yescharacteristic
244C24×C3C23×C311yescharacteristic
245C24×C3C23×C312yes—
246C24×C3C23×C311yescharacteristic
247C24×C3C23×C311yescharacteristic
248C23×D3—22no—
249C23×D3—24no—
250C23×D3—24no—
251C23×D3—42no—
252C23×D3C23×C312yes—
253C2×C3×D4—264no—
254C2×C3×D4—232no—
255C2×C3×D4—232no—
256C2×C3×D4—28no—
257C2×C3×D4—28no—
258C2×C3×D4—28no—
259C2×C3×D4—28no—
260C2×C3×D4—28no—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—24no—
266C2×C3×D4—24no—
267C2×C3×D4—24no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—24no—
271C2×C3×D4—28no—
272C2×C3×D4—38no—
273C2×C3×D4—64no—
274C2×C3×D4—64no—
275C2×C3×D4—632no—
276C2×C3×D4—64no—
277C2×C3×D4—64no—
278C2×C3×D4—64no—
279C2×C3×D4—68no—
280C2×C3×D4—68no—
281C2×C3×D4—124no—
282C2×C3×D4#6718yescomplemented
283C2×C3×D4C3×D418yescomplemented
284C22×C3×C4—24no—
285C22×C3×C4—28no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—24no—
289C22×C3×C4—24no—
290C22×C3×C4—22no—
291C22×C3×C4—32no—
292C22×C3×C4—34no—
293C22×C3×C4—64no—
294C22×C3×C4—62no—
295C22×C3×C4C22×D312yes—
296C22×C3×C4C23×C312yes—
297C2×#67—232no—
298C2×#67—24no—
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—28no—
303C2×#67—28no—
304C2×#67—24no—
305C2×#67—44no—
306C2×#67C3×D418yescomplemented
307C22×Dic3—22no—
308C22×Dic3—24no—
309C22×Dic3C23×C314yes—
310C22×Dic3C23×C312yes—
311C3×C22⋊C4—68no—
312C3×C22⋊C4—64no—
313C3×C22⋊C4—64no—
314C3×C22⋊C4—68no—
315C3×C22⋊C4—122no—
316#217—24no—
317#217—24no—
318#217—28no—
319#217—42no—
320(C2×D3)⋊C4—28no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—28no—
324C22×C32—22no—
325C22×C32—24no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—28no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—28no—
332C22×C32—416no—
333C22×C32—416no—
334C22×C32—42no—
335C22×C32—42no—
336C22×C32—44no—
337C22×C32—44no—
338C22×C32#12014yescomplemented
339C22×C32#12014yescomplemented
340C22×C32C22×D412yes—
341C22×C32C22×D411yescharacteristic
342C22×C32C22×D412yes—
343C22×C32H(5,𝔽2)12yes—
344C2×C3×D3—24no—
345C2×C3×D3—28no—
346C2×C3×D3—416no—
347C2×C3×D3—42no—
348C2×C3×D3—42no—
349C2×C3×D3—44no—
350C32×C4—24no—
351C3×Dic3—24no—
352C3×Dic3—44no—
353C25—31no—
354C25C2×C3×D311yescharacteristic
355C25C2×C3×D311yescharacteristic, complemented
356C22×D4—24no—
357C22×D4—28no—
358C22×D4—32no—
359C22×D4—32no—
360C22×D4—34no—
361C22×D4—68no—
362C22×D4—64no—
363C22×D4C2×C3×D312yes—
364C22×D4C2×C3×D312yescomplemented
365C23×C4—31no—
366C23×C4C2×C3×D311yescharacteristic, complemented
367#120—68no—
368#120—68no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—34no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—32no—
374#95—34no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—216no—
386C23×C3—28no—
387C23×C3—28no—
388C23×C3—216no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—28no—
393C23×C3—28no—
394C23×C3—28no—
395C23×C3—28no—
396C23×C3—24no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—24no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—24no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—24no—
410C23×C3—21no—
411C23×C3—24no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—24no—
417C23×C3—34no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—48no—
421C23×C3—44no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—416no—
428C23×C3—416no—
429C23×C3—416no—
430C23×C3—416no—
431C23×C3—48no—
432C23×C3—432no—
433C23×C3—432no—
434C23×C3—48no—
435C23×C3—44no—
436C23×C3—44no—
437C23×C3—48no—
438C23×C3—44no—
439C23×C3—44no—
440C23×C3—68no—
441C23×C3—62no—
442C23×C3—64no—
443C23×C3—64no—
444C23×C3—62no—
445C23×C3—1216no—
446C23×C3—124no—
447C23×C3—124no—
448C23×C3D3×D414yes—
449C23×C3C2×#6712yes—
450C23×C3C2×#6712yes—
451C23×C3C2×#6714yes—
452C23×C3C2×#6712yes—
453C23×C3C2×#6714yescomplemented
454C23×C3C2×C3×D414yes—
455C23×C3C2×C3×D412yes—
456C23×C3C2×C3×D414yes—
457C23×C3C2×C3×D412yes—
458C23×C3C2×C3×D412yes—
459C23×C3C2×C3×D414yescomplemented
460C23×C3C23×D311yescharacteristic
461C23×C3C24×C311yescharacteristic
462C22×D3—28no—
463C22×D3—24no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—24no—
467C22×D3—416no—
468C22×D3—44no—
469C22×D3—44no—
470C22×D3C2×C3×D414yescomplemented
471C3×D4—232no—
472C3×D4—216no—
473C3×D4—216no—
474C3×D4—232no—
475C3×D4—216no—
476C3×D4—216no—
477C3×D4—616no—
478C3×D4—616no—
479C3×D4—1216no—
480C2×C3×C4—216no—
481C2×C3×C4—28no—
482C2×C3×C4—28no—
483C2×C3×C4—24no—
484C2×C3×C4—24no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—24no—
490C2×C3×C4—34no—
491C2×C3×C4—68no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—64no—
495C2×C3×C4—64no—
496C2×C3×C4—64no—
497C2×C3×C4C2×#6714yescomplemented
498C2×C3×C4C2×C3×D414yescomplemented
499#67—216no—
500#67—216no—
501#67—416no—
502C2×Dic3—28no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—24no—
506C2×Dic3—24no—
507C2×Dic3—24no—
508C2×Dic3C2×C3×D414yescomplemented
509C2×C32—24no—
510C2×C32—24no—
511C2×C32—42no—
512C2×C32—44no—
513C2×C32C2×#12011yescharacteristic
514C2×C32C2×#12011yescharacteristic
515C2×C32#53411yescharacteristic
516C2×C32D4214yes—
517C3×D3—44no—
518C24—24no—
519C24—24no—
520C24—22no—
521C24—24no—
522C24—24no—
523C24—32no—
524C24—42no—
525C24—42no—
526C24—64no—
527C24—62no—
528C24—64no—
529C24—122no—
530C24C3×#6714yescomplemented
531C24C22×C3×D311yescharacteristic
532C24C22×C3×D312yes—
533C24C22×C3×D311yescharacteristic
534C24C22×C3×D311yescharacteristic
535C2×D4—232no—
536C2×D4—24no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—38no—
542C2×D4—64no—
543C2×D4—64no—
544C2×D4—632no—
545C2×D4—64no—
546C2×D4—64no—
547C2×D4—64no—
548C2×D4—68no—
549C2×D4—68no—
550C2×D4—124no—
551C2×D4C3×#6718yescomplemented
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—32no—
555C22×C4—34no—
556C22×C4—64no—
557C22×C4—62no—
558C22×C4C22×C3×D312yes—
559C22⋊C4—68no—
560C22⋊C4—64no—
561C22⋊C4—64no—
562C22⋊C4—68no—
563C22⋊C4—122no—
564C22×C3—24no—
565C22×C3—216no—
566C22×C3—24no—
567C22×C3—22no—
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—28no—
578C22×C3—28no—
579C22×C3—24no—
580C22×C3—28no—
581C22×C3—22no—
582C22×C3—28no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—24no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—24no—
589C22×C3—22no—
590C22×C3—28no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—21no—
596C22×C3—22no—
597C22×C3—42no—
598C22×C3—48no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—48no—
602C22×C3—42no—
603C22×C3—416no—
604C22×C3—416no—
605C22×C3—432no—
606C22×C3—432no—
607C22×C3—416no—
608C22×C3—416no—
609C22×C3—44no—
610C22×C3—48no—
611C22×C3—48no—
612C22×C3—44no—
613C22×C3—42no—
614C22×C3—44no—
615C22×C3—44no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—64no—
622C22×C3—68no—
623C22×C3—1216no—
624C22×C3—124no—
625C22×C3—122no—
626C22×C3—122no—
627C22×C3#93714yescomplemented
628C22×C3#95314yescomplemented
629C22×C3C3×#12014yescomplemented
630C22×C3C3×#12014yescomplemented
631C22×C3C2×D3×D412yes—
632C22×C3#100412yes—
633C22×C3C22×#6711yescharacteristic
634C22×C3C22×#6712yes—
635C22×C3C22×C3×D412yes—
636C22×C3C22×C3×D411yescharacteristic
637C22×C3C22×C3×D412yes—
638C22×C3C3×H(5,𝔽2)12yes—
639C2×D3—24no—
640C2×D3—28no—
641C2×D3—416no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—44no—
645C3×C4—28no—
646C3×C4—24no—
647C3×C4—24no—
648C3×C4—64no—
649C3×C4—124no—
650Dic3—24no—
651Dic3—44no—
652C32#240311yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—34no—
668C23—44no—
669C23—416no—
670C23—416no—
671C23—44no—
672C23—44no—
673C23—68no—
674C23—62no—
675C23—64no—
676C23—64no—
677C23—62no—
678C23—1216no—
679C23—124no—
680C23—124no—
681C23C3×D3×D414yes—
682C23C2×C3×#6712yes—
683C23C2×C3×#6712yes—
684C23C2×C3×#6714yes—
685C23C2×C3×#6712yes—
686C23C2×C3×#6714yescomplemented
687C23C23×C3×D311yescharacteristic
688D4—216no—
689D4—216no—
690D4—616no—
691D4—616no—
692D4—1216no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—34no—
697C2×C4—68no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—64no—
702C2×C4—64no—
703C2×C4C2×C3×#6714yescomplemented
704C2×C3—28no—
705C2×C3—24no—
706C2×C3—24no—
707C2×C3—24no—
708C2×C3—24no—
709C2×C3—21no—
710C2×C3—24no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—44no—
714C2×C3—44no—
715C2×C3—48no—
716C2×C3—42no—
717C2×C3—44no—
718C2×C3—42no—
719C2×C3—44no—
720C2×C3—124no—
721C2×C3C2×#93711yescharacteristic
722C2×C3D4×#6714yes—
723C2×C3#580411yescharacteristic
724C2×C3C2×#95311yescharacteristic
725C2×C3C2×C3×#12011yescharacteristic
726C2×C3C2×C3×#12011yescharacteristic
727C2×C3C3×#53411yescharacteristic
728C2×C3C3×D4214yes—
729D3—44no—
730C22—22no—
731C22—28no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—28no—
738C22—22no—
739C22—22no—
740C22—24no—
741C22—416no—
742C22—416no—
743C22—42no—
744C22—44no—
745C22—44no—
746C22—42no—
747C22—64no—
748C22—68no—
749C22—1216no—
750C22—124no—
751C22—122no—
752C22—122no—
753C22C3×#93714yescomplemented
754C22C3×#95314yescomplemented
755C22C2×C3×D3×D412yes—
756C22C3×#100412yes—
757C22C22×C3×#6711yescharacteristic
758C22C22×C3×#6712yes—
759C4—24no—
760C4—64no—
761C4—124no—
762C3—21no—
763C3#8405211yescharacteristic, direct product factor
764C3C3×#240311yescharacteristic, complemented
765C2—24no—
766C2—24no—
767C2—42no—
768C2—44no—
769C2—124no—
770C2C2×C3×#93711yescharacteristic
771C2C3×D4×#6714yes—
772C2C3×#580411yescharacteristic
773C2C2×C3×#95311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC23×C32×D4C2
socleC23×C32C24
hypercenterC23×C3×D4D3
hypocenterC3C3×#2403
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C32×D4C2semidirect
2. C23×C3×#67C2semidirect
3. C2×C3×#953C2semidirect
4. C2×C3×#937C2semidirect
5. C3×#5247C2semidirect
6. C3×#5223C2semidirect
7. C3×#5220C2semidirect
8. C3×#5213C2semidirect
10. #84052C3direct (N × H)
12. C25×C32C22semidirect
13. C24×C3×D3C22semidirect
17. C22×C32×D4C22semidirect
18. C23×C32×C4C22semidirect
22. C22×C3×#67C22semidirect
23. C22×C3×#67C22semidirect
24. C23×C3×Dic3C22semidirect
26. C2×C3×#217C22semidirect
27. C2×C3×#217C22semidirect
28. C2×C3×#217C22semidirect
29. C2×C3×#217C22semidirect
31. C2×C3×(C2×D3)⋊C4C22semidirect
32. C3×C3⋊#95C22semidirect
35. C23×C3×D4D3semidirect
36. C23×C3×D4C2×C3semidirect
37. C23×#67C2×C3semidirect
40. C2×#953C2×C3semidirect
41. C2×#937C2×C3semidirect
46. #5247C2×C3semidirect
47. #5223C2×C3semidirect
48. #5220C2×C3semidirect
49. #5213C2×C3semidirect
57. C24×C32D4semidirect
73. C2×C32×D4D4semidirect
86. C2×C3×#67D4semidirect
101. C25×C3C2×D3semidirect
103. C25×C3C22×C3semidirect
104. C24×D3C22×C3semidirect
119. C22×C3×D4C2×D3semidirect
121. C22×C3×D4C22×C3semidirect
124. C23×C3×C4C2×D3semidirect
125. C23×C3×C4C22×C3semidirect
129. C22×#67C22×C3semidirect
130. C22×#67C22×C3semidirect
131. C23×Dic3C22×C3semidirect
140. C2×#217C22×C3semidirect
141. C2×#217C22×C3semidirect
142. C2×#217C22×C3semidirect
143. C2×#217C22×C3semidirect
145. C2×(C2×D3)⋊C4C22×C3semidirect
147. C3⋊#95C22×C3semidirect
172. C23×C32C2×D4semidirect
182. C22×C3×D3C2×D4semidirect
188. C2×C32×C4C2×D4semidirect
198. C2×C3×Dic3C2×D4semidirect
200. C23×D4C3×D3semidirect
238. C24×C3#67semidirect
239. C24×C3C3×D4semidirect
282. C2×C3×D4#67semidirect
283. C2×C3×D4C3×D4semidirect
306. C2×#67C3×D4semidirect
338. C22×C32#120semidirect
339. C22×C32#120semidirect
355. C25C2×C3×D3semidirect
364. C22×D4C2×C3×D3semidirect
366. C23×C4C2×C3×D3semidirect
453. C23×C3C2×#67semidirect
459. C23×C3C2×C3×D4semidirect
470. C22×D3C2×C3×D4semidirect
497. C2×C3×C4C2×#67semidirect
498. C2×C3×C4C2×C3×D4semidirect
508. C2×Dic3C2×C3×D4semidirect
530. C24C3×#67semidirect
551. C2×D4C3×#67semidirect
627. C22×C3#937semidirect
628. C22×C3#953semidirect
629. C22×C3C3×#120semidirect
630. C22×C3C3×#120semidirect
652. C32#2403semidirect
686. C23C2×C3×#67semidirect
703. C2×C4C2×C3×#67semidirect
753. C22C3×#937semidirect
754. C22C3×#953semidirect
763. C3#84052direct (N × H)
764. C3C3×#2403semidirect

Maximal subgroups

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

subgroupindex
C23×C32×D42
C23×C3×#672
C2×C3×#9532
C2×C3×#9372
C3×#52472
C3×#52232
C3×#52202
C3×#52132
C3×#24033
#840523