Finite Group Databasebeta

← C3×#83175 #11811940

Subgroups — C3×#83175 #11811940

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 737 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C2×C32×#127C211yesmaximal, characteristic, complemented
3C2×C3×#940C211yesmaximal, characteristic, complemented
4C2×C3×#938C211yesmaximal, characteristic, complemented
5C2×C3×#937C214yesmaximal, complemented
6C3×#5223C214yesmaximal, complemented
7C3×#5221C211yesmaximal, characteristic, complemented
8C3×#4939C211yesmaximal, characteristic, complemented
9C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C3×#2433—31nomaximal
11#83175C311yesmaximal, characteristic, direct product factor
12C24×C3×D3C2212yes—
13C22×C32×D4C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic, complemented
15C22×C32×D4C2214yescomplemented
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2214yescomplemented
19C2×C3×D3×D4—24no—
20C2×C3×D3×D4—24no—
21C2×C3×D3×D4—24no—
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C32×#127—24no—
25C2×C32×C42C2211yescharacteristic, complemented
26C2×C3×#217C2214yescomplemented
27C2×C3×#217C2212yescomplemented
28C3×#940—24no—
29C3×#938—24no—
30C3×#937—216no—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2214yescomplemented
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35C3×C3⋊#95C2212yescomplemented
36C23×C3×D4—31no—
37C22×D3×D4C2×C311yescharacteristic, complemented
38C2×C3×#127—21no—
39C2×C3×#127—31no—
40C2×C3×#127D311yescharacteristic, complemented
41C2×C3×#127C2×C311yescharacteristic, complemented
42C2×C3×#121—31no—
43C2×C3×#120—34no—
44C2×#940C2×C311yescharacteristic, complemented
45C2×#938C2×C311yescharacteristic, complemented
46C2×#937C2×C314yescomplemented
47C3×#392—34no—
48C3×#390—31no—
49C3×#390—31no—
50C3×C4×C22⋊C4—31no—
51#5223C2×C314yescomplemented
52#5221C2×C311yescharacteristic, complemented
53#4939C2×C311yescharacteristic, complemented
54C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
55C24×C32C2312yes—
56C24×C32C2312yes—
57C23×C3×D3—24no—
58C23×C3×D3—24no—
59C23×C3×D3—24no—
60C23×C3×D3—28no—
61C23×C3×D3—44no—
62C23×C3×D3C2312yes—
63C23×C3×D3C2311yescharacteristic
64C2×C32×D4—28no—
65C2×C32×D4—22no—
66C2×C32×D4—22no—
67C2×C32×D4—22no—
68C2×C32×D4—22no—
69C2×C32×D4—22no—
70C2×C32×D4—28no—
71C2×C32×D4—44no—
72C2×C32×D4D414yescomplemented
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C2×C3×#67—24no—
76C2×C3×#67—24no—
77C2×C3×#67—28no—
78C2×C3×#67—24no—
79C2×C3×#67—28no—
80C2×C3×#67—24no—
81C2×C3×#67—28no—
82C2×C3×#67—44no—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C3×D3×D4—232no—
87C2×C3×D12—22no—
88C2×C3×D12—22no—
89C2×C3×D12D414yescomplemented
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3D414yescomplemented
93C32×C42—22no—
94C3×#217—24no—
95C3×#217—28no—
96C3×(C2×D3)⋊C4—28no—
97C3×(C2×D3)⋊C4D418yescomplemented
98C3×C4⋊Dic3—22no—
99C3×C4×Dic3—22no—
100#2433—31noSylow
101C25×C3—32no—
102C24×D3C22×C312yes—
103C22×C3×D4—21no—
104C22×C3×D4—21no—
105C22×C3×D4—24no—
106C22×C3×D4—32no—
107C22×C3×D4—32no—
108C22×C3×D4—34no—
109C22×C3×D4—31no—
110C22×C3×D4—64no—
111C22×C3×D4—64no—
112C22×C3×D4—64no—
113C22×C3×D4C2×D311yescharacteristic
114C22×C3×D4C2×D311yescharacteristic, complemented
115C22×C3×D4C2×D314yescomplemented
116C22×C3×D4C22×C311yescharacteristic
117C22×C3×D4C22×C311yescharacteristic, complemented
118C22×C3×D4C22×C314yescomplemented
119C23×C3×C4—31no—
120C22×#67C22×C312yes—
121C22×#67C22×C312yes—
122C22×#67C22×C314yescomplemented
123C2×D3×D4—24no—
124C2×D3×D4—24no—
125C2×D3×D4—24no—
126C22×D12C22×C311yescharacteristic
127C22×C4×D3C22×C311yescharacteristic
128C3×#127—28no—
129C3×#127—24no—
130C3×#127—24no—
131C3×#127—64no—
132C3×#121—64no—
133C3×#120—616no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—34no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—34no—
139C2×C3×C42—21no—
140C2×C3×C42—31no—
141C2×C3×C42C2×D311yescharacteristic, complemented
142C2×C3×C42C22×C311yescharacteristic, complemented
143C2×#217C22×C314yescomplemented
144C2×#217C22×C312yescomplemented
145#940—24no—
146#938—24no—
147#937—216no—
148C2×(C2×D3)⋊C4C22×C312yes—
149C2×(C2×D3)⋊C4C22×C314yescomplemented
150C2×C4⋊Dic3C22×C311yescharacteristic, complemented
151C2×C4×Dic3C22×C311yescharacteristic, complemented
152C3×#95—32no—
153C3⋊#95C22×C312yescomplemented
154C23×C32—22no—
155C23×C32—24no—
156C23×C32—22no—
157C23×C32—22no—
158C23×C32—24no—
159C23×C32—22no—
160C23×C32—22no—
161C23×C32—24no—
162C23×C32—24no—
163C23×C32C2×D414yes—
164C23×C32C2411yescharacteristic
165C22×C3×D3—21no—
166C22×C3×D3—21no—
167C22×C3×D3—22no—
168C22×C3×D3—216no—
169C22×C3×D3—24no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—24no—
173C22×C3×D3—416no—
174C22×C3×D3—416no—
175C22×C3×D3—48no—
176C22×C3×D3—48no—
177C22×C3×D3C2×D414yes—
178C22×C3×D3C2×D414yes—
179C22×C3×D3C2×D412yes—
180C32×D4—28no—
181C32×D4—416no—
182C32×D4—44no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4C2×D412yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4C2×D412yes—
188C2×C32×C4C2×D414yescomplemented
189C3×#67—216no—
190C3×#67—416no—
191C3×#67—48no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—24no—
198C2×C3×Dic3C2×D412yes—
199C2×C3×Dic3C2×D414yescomplemented
200C3×D12—28no—
201C3×C4×D3—28no—
202C23×D4—31no—
203C2×#127—31no—
204C2×#127C3×D311yescharacteristic, complemented
205C2×#121—31no—
206C2×#120—34no—
207#392—34no—
208#390—31no—
209#390—31no—
210C4×C22⋊C4—31no—
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—31no—
214C24×C3—32no—
215C24×C3—64no—
216C24×C3—64no—
217C24×C3—68no—
218C24×C3—64no—
219C24×C3—124no—
220C24×C3C22×D312yes—
221C24×C3C22×D312yes—
222C24×C3C23×C312yes—
223C24×C3C23×C312yes—
224C23×D3—24no—
225C23×D3—24no—
226C23×D3—24no—
227C23×D3—28no—
228C23×D3—44no—
229C23×D3C23×C312yes—
230C23×D3C23×C311yescharacteristic
231C2×C3×D4—216no—
232C2×C3×D4—24no—
233C2×C3×D4—28no—
234C2×C3×D4—28no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—22no—
239C2×C3×D4—28no—
240C2×C3×D4—22no—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—22no—
245C2×C3×D4—22no—
246C2×C3×D4—28no—
247C2×C3×D4—24no—
248C2×C3×D4—34no—
249C2×C3×D4—42no—
250C2×C3×D4—42no—
251C2×C3×D4—42no—
252C2×C3×D4—42no—
253C2×C3×D4—48no—
254C2×C3×D4—44no—
255C2×C3×D4—44no—
256C2×C3×D4—48no—
257C2×C3×D4—64no—
258C2×C3×D4—68no—
259C2×C3×D4—632no—
260C2×C3×D4—64no—
261C2×C3×D4—64no—
262C2×C3×D4—68no—
263C2×C3×D4—64no—
264C2×C3×D4—68no—
265C2×C3×D4—62no—
266C2×C3×D4—62no—
267C2×C3×D4—124no—
268C2×C3×D4#6714yescomplemented
269C2×C3×D4C3×D414yescomplemented
270C22×C3×C4—22no—
271C22×C3×C4—21no—
272C22×C3×C4—31no—
273C22×C3×C4—32no—
274C22×C3×C4—34no—
275C22×C3×C4—32no—
276C22×C3×C4—62no—
277C22×C3×C4—62no—
278C22×C3×C4C22×D312yes—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C23×C312yes—
281C22×C3×C4C23×C311yescharacteristic
282C2×#67—24no—
283C2×#67—24no—
284C2×#67—28no—
285C2×#67—24no—
286C2×#67—28no—
287C2×#67—24no—
288C2×#67—28no—
289C2×#67—44no—
290C22×Dic3C23×C312yes—
291C22×Dic3C23×C311yescharacteristic
292C22×Dic3C23×C312yes—
293D3×D4—232no—
294C2×D12—22no—
295C2×D12—22no—
296C2×D12C3×D414yescomplemented
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3C3×D414yescomplemented
300C3×C4⋊C4—62no—
301C3×C22⋊C4—38no—
302C3×C22⋊C4—68no—
303C3×C22⋊C4—64no—
304C3×C22⋊C4—68no—
305C3×C42—24no—
306C3×C42—22no—
307C3×C42—22no—
308C3×C42—62no—
309#217—24no—
310#217—28no—
311(C2×D3)⋊C4—28no—
312(C2×D3)⋊C4C3×D418yescomplemented
313C4⋊Dic3—22no—
314C4×Dic3—22no—
315C22×C32—24no—
316C22×C32—28no—
317C22×C32—42no—
318C22×C32—44no—
319C22×C32—42no—
320C22×C32—42no—
321C22×C32—44no—
322C22×C32—42no—
323C22×C32—42no—
324C22×C32—44no—
325C22×C32C22×D411yescharacteristic
326C22×C32C22×D411yescharacteristic
327C22×C32C22×D412yes—
328C22×C32C22×D411yescharacteristic
329C22×C32H(5,𝔽2)12yes—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—24no—
333C2×C3×D3—24no—
334C2×C3×D3—24no—
335C2×C3×D3—28no—
336C2×C3×D3—432no—
337C2×C3×D3—42no—
338C2×C3×D3—42no—
339C2×C3×D3—44no—
340C2×C3×D3#12714yescomplemented
341C32×C4—24no—
342C32×C4#12014yescomplemented
343C3×Dic3—22no—
344C3×Dic3—24no—
345C3×Dic3—42no—
346C25—32no—
347C22×D4—32no—
348C22×D4—32no—
349C22×D4—34no—
350C22×D4—31no—
351C22×D4—64no—
352C22×D4—64no—
353C22×D4—64no—
354C22×D4C2×C3×D311yescharacteristic
355C22×D4C2×C3×D311yescharacteristic, complemented
356C22×D4C2×C3×D314yescomplemented
357C23×C4—31no—
358#127—24no—
359#127—64no—
360#121—64no—
361#120—616no—
362C2×C4⋊C4—31no—
363C2×C22⋊C4—32no—
364C2×C22⋊C4—34no—
365C2×C22⋊C4—32no—
366C2×C22⋊C4—34no—
367C2×C42—31no—
368C2×C42C2×C3×D311yescharacteristic, complemented
369#95—32no—
370C23×C3—24no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—22no—
380C23×C3—24no—
381C23×C3—22no—
382C23×C3—24no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—24no—
387C23×C3—22no—
388C23×C3—24no—
389C23×C3—21no—
390C23×C3—24no—
391C23×C3—34no—
392C23×C3—32no—
393C23×C3—34no—
394C23×C3—44no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—44no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—44no—
401C23×C3—44no—
402C23×C3—616no—
403C23×C3—61no—
404C23×C3—62no—
405C23×C3—61no—
406C23×C3—64no—
407C23×C3—62no—
408C23×C3—64no—
409C23×C3—62no—
410C23×C3—1216no—
411C23×C3—128no—
412C23×C3—1216no—
413C23×C3—128no—
414C23×C3C2×#6714yes—
415C23×C3C2×C3×D414yes—
416C23×C3C23×D311yescharacteristic
417C23×C3C24×C311yescharacteristic
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—22no—
421C22×D3—216no—
422C22×D3—24no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—24no—
426C22×D3—416no—
427C22×D3—416no—
428C22×D3—48no—
429C22×D3—48no—
430C22×D3C2×C3×D414yes—
431C22×D3C2×C3×D414yes—
432C22×D3C2×C3×D412yes—
433C3×D4—28no—
434C3×D4—28no—
435C3×D4—48no—
436C3×D4—416no—
437C3×D4—416no—
438C3×D4—432no—
439C3×D4—48no—
440C3×D4—44no—
441C3×D4—44no—
442C3×D4—616no—
443C3×D4—68no—
444C3×D4—1216no—
445C3×D4—128no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—24no—
455C2×C3×C4—22no—
456C2×C3×C4—32no—
457C2×C3×C4—34no—
458C2×C3×C4—62no—
459C2×C3×C4—61no—
460C2×C3×C4—62no—
461C2×C3×C4—61no—
462C2×C3×C4—68no—
463C2×C3×C4—64no—
464C2×C3×C4—62no—
465C2×C3×C4D3×D412yes—
466C2×C3×C4D3×D412yes—
467C2×C3×C4D3×D414yescomplemented
468C2×C3×C4C2×#6712yes—
469C2×C3×C4C2×C3×D412yes—
470C2×C3×C4C2×C3×D412yes—
471C2×C3×C4C2×C3×D412yes—
472C2×C3×C4C2×C3×D414yescomplemented
473#67—216no—
474#67—416no—
475#67—48no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—24no—
482C2×Dic3C2×C3×D412yes—
483C2×Dic3C2×C3×D414yescomplemented
484D12—28no—
485C4×D3—28no—
486C2×C32—44no—
487C2×C32—82no—
488C2×C32C2×#12011yescharacteristic
489C2×C32C2×#12711yescharacteristic
490C2×C32#53511yescharacteristic
491C2×C32D4212yes—
492C2×C32D4212yes—
493C3×D3—24no—
494C3×D3—44no—
495C24—31no—
496C24—32no—
497C24—64no—
498C24—64no—
499C24—68no—
500C24—64no—
501C24—124no—
502C24C22×C3×D312yes—
503C24C22×C3×D312yes—
504C2×D4—28no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—28no—
510C2×D4—22no—
511C2×D4—34no—
512C2×D4—44no—
513C2×D4—64no—
514C2×D4—68no—
515C2×D4—632no—
516C2×D4—64no—
517C2×D4—64no—
518C2×D4—68no—
519C2×D4—64no—
520C2×D4—68no—
521C2×D4—62no—
522C2×D4—62no—
523C2×D4—124no—
524C2×D4C3×#6714yescomplemented
525C22×C4—31no—
526C22×C4—32no—
527C22×C4—34no—
528C22×C4—32no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4C22×C3×D312yes—
532C22×C4C22×C3×D311yescharacteristic
533C4⋊C4—62no—
534C22⋊C4—38no—
535C22⋊C4—68no—
536C22⋊C4—64no—
537C22⋊C4—68no—
538C42—22no—
539C42—62no—
540C22×C3—24no—
541C22×C3—28no—
542C22×C3—24no—
543C22×C3—28no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—21no—
549C22×C3—34no—
550C22×C3—44no—
551C22×C3—48no—
552C22×C3—44no—
553C22×C3—48no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—44no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—44no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—44no—
563C22×C3—42no—
564C22×C3—44no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—62no—
571C22×C3—64no—
572C22×C3—62no—
573C22×C3—64no—
574C22×C3—68no—
575C22×C3—64no—
576C22×C3—82no—
577C22×C3—82no—
578C22×C3—84no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—84no—
582C22×C3—1232no—
583C22×C3—122no—
584C22×C3—122no—
585C22×C3—124no—
586C22×C3C2×D3×D411yescharacteristic
587C22×C3C2×D3×D412yes—
588C22×C3C2×D3×D411yescharacteristic
589C22×C3#100412yes—
590C22×C3C22×#6711yescharacteristic
591C22×C3C22×C3×D411yescharacteristic
592C22×C3C22×C3×D411yescharacteristic
593C22×C3C22×C3×D412yes—
594C22×C3C22×C3×D411yescharacteristic
595C22×C3C3×H(5,𝔽2)12yes—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—24no—
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—28no—
602C2×D3—432no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—44no—
606C2×D3C3×#12714yescomplemented
607C3×C4—28no—
608C3×C4—24no—
609C3×C4—24no—
610C3×C4—24no—
611C3×C4—64no—
612C3×C4—62no—
613C3×C4—122no—
614C3×C4#93714yescomplemented
615C3×C4C3×#12014yescomplemented
616Dic3—22no—
617Dic3—24no—
618Dic3—42no—
619C32#243311yescharacteristic, complemented, Sylow
620C23—24no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—34no—
630C23—32no—
631C23—34no—
632C23—616no—
633C23—61no—
634C23—62no—
635C23—61no—
636C23—64no—
637C23—62no—
638C23—64no—
639C23—62no—
640C23—1216no—
641C23—128no—
642C23—1216no—
643C23—128no—
644C23C2×C3×#6714yes—
645C23C23×C3×D311yescharacteristic
646D4—28no—
647D4—416no—
648D4—44no—
649D4—616no—
650D4—68no—
651D4—1216no—
652D4—128no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—34no—
656C2×C4—32no—
657C2×C4—62no—
658C2×C4—61no—
659C2×C4—62no—
660C2×C4—61no—
661C2×C4—68no—
662C2×C4—64no—
663C2×C4—62no—
664C2×C4C3×D3×D412yes—
665C2×C4C3×D3×D412yes—
666C2×C4C3×D3×D414yescomplemented
667C2×C4C2×C3×#6712yes—
668C2×C3—21no—
669C2×C3—22no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—22no—
673C2×C3—44no—
674C2×C3—44no—
675C2×C3—64no—
676C2×C3—84no—
677C2×C3—84no—
678C2×C3—82no—
679C2×C3—82no—
680C2×C3—124no—
681C2×C3D3×#12711yescharacteristic
682C2×C3#571511yescharacteristic
683C2×C3#571712yes—
684C2×C3C2×#93711yescharacteristic
685C2×C3D4×#6712yes—
686C2×C3C2×C3×#12011yescharacteristic
687C2×C3C2×C3×#12711yescharacteristic
688C2×C3C3×#53511yescharacteristic
689C2×C3C3×D4212yes—
690C2×C3C3×D4212yes—
691D3—24no—
692D3—44no—
693C22—24no—
694C22—28no—
695C22—34no—
696C22—42no—
697C22—42no—
698C22—44no—
699C22—42no—
700C22—44no—
701C22—42no—
702C22—42no—
703C22—44no—
704C22—62no—
705C22—64no—
706C22—62no—
707C22—64no—
708C22—64no—
709C22—68no—
710C22—1232no—
711C22—124no—
712C22—122no—
713C22—122no—
714C22C2×C3×D3×D411yescharacteristic
715C22C2×C3×D3×D411yescharacteristic
716C22C2×C3×D3×D412yes—
717C22C3×#100412yes—
718C22C22×C3×#6711yescharacteristic
719C4—24no—
720C4—62no—
721C4—64no—
722C4—122no—
723C4C3×#93714yescomplemented
724C3—21no—
725C3#8317511yescharacteristic, direct product factor
726C3C3×#243311yescharacteristic, complemented
727C2—44no—
728C2—64no—
729C2—82no—
730C2—124no—
731C2C3×D3×#12711yescharacteristic
732C2C3×#571511yescharacteristic
733C2C3×#571712yes—
734C2C2×C3×#93711yescharacteristic
735C2C3×D4×#6712yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#127C2
socleC23×C32C24
hypercenterC2×C3×#127D3
hypocenterC3C3×#2433
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#127

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C2×C32×#127C2semidirect
3. C2×C3×#940C2semidirect
4. C2×C3×#938C2semidirect
5. C2×C3×#937C2semidirect
6. C3×#5223C2semidirect
7. C3×#5221C2semidirect
8. C3×#4939C2semidirect
9. C3×C4×(C2×D3)⋊C4C2semidirect
11. #83175C3direct (N × H)
14. C22×C32×D4C22semidirect
15. C22×C32×D4C22semidirect
18. C22×C3×#67C22semidirect
25. C2×C32×C42C22semidirect
26. C2×C3×#217C22semidirect
27. C2×C3×#217C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C3×C3⋊#95C22semidirect
37. C22×D3×D4C2×C3semidirect
40. C2×C3×#127D3semidirect
41. C2×C3×#127C2×C3semidirect
44. C2×#940C2×C3semidirect
45. C2×#938C2×C3semidirect
46. C2×#937C2×C3semidirect
51. #5223C2×C3semidirect
52. #5221C2×C3semidirect
53. #4939C2×C3semidirect
54. C4×(C2×D3)⋊C4C2×C3semidirect
72. C2×C32×D4D4semidirect
89. C2×C3×D12D4semidirect
92. C2×C3×C4×D3D4semidirect
97. C3×(C2×D3)⋊C4D4semidirect
114. C22×C3×D4C2×D3semidirect
115. C22×C3×D4C2×D3semidirect
117. C22×C3×D4C22×C3semidirect
118. C22×C3×D4C22×C3semidirect
122. C22×#67C22×C3semidirect
141. C2×C3×C42C2×D3semidirect
142. C2×C3×C42C22×C3semidirect
143. C2×#217C22×C3semidirect
144. C2×#217C22×C3semidirect
149. C2×(C2×D3)⋊C4C22×C3semidirect
150. C2×C4⋊Dic3C22×C3semidirect
151. C2×C4×Dic3C22×C3semidirect
153. C3⋊#95C22×C3semidirect
188. C2×C32×C4C2×D4semidirect
199. C2×C3×Dic3C2×D4semidirect
204. C2×#127C3×D3semidirect
268. C2×C3×D4#67semidirect
269. C2×C3×D4C3×D4semidirect
296. C2×D12C3×D4semidirect
299. C2×C4×D3C3×D4semidirect
312. (C2×D3)⋊C4C3×D4semidirect
340. C2×C3×D3#127semidirect
342. C32×C4#120semidirect
355. C22×D4C2×C3×D3semidirect
356. C22×D4C2×C3×D3semidirect
368. C2×C42C2×C3×D3semidirect
467. C2×C3×C4D3×D4semidirect
472. C2×C3×C4C2×C3×D4semidirect
483. C2×Dic3C2×C3×D4semidirect
524. C2×D4C3×#67semidirect
606. C2×D3C3×#127semidirect
614. C3×C4#937semidirect
615. C3×C4C3×#120semidirect
619. C32#2433semidirect
666. C2×C4C3×D3×D4semidirect
723. C4C3×#937semidirect
725. C3#83175direct (N × H)
726. C3C3×#2433semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×C32×#1272
C2×C3×#9402
C2×C3×#9382
C2×C3×#9372
C3×#52232
C3×#52212
C3×#49392
C3×C4×(C2×D3)⋊C42
C3×#24333
#831753