Finite Group Databasebeta

← C3×#83190 #11836018

Subgroups — C3×#83190 #11836018

Order 1152.

2113 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#127C211yesmaximal, characteristic, complemented
2C2×C3×#939C212yesmaximal, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×C3×#937C212yesmaximal, complemented
5C3×#5223C212yesmaximal, complemented
6C3×#5223C212yesmaximal, complemented
7C3×#5222C212yesmaximal, complemented
8C3×#5220C211yesmaximal, characteristic, complemented
9C3×#4940C212yesmaximal, complemented
10C3×#2669—31nomaximal
11#83190C311yesmaximal, characteristic, direct product factor
12C24×C3×D3C2211yescharacteristic
13C22×C32×D4C2212yes—
14C22×C32×D4C2211yescharacteristic
15C22×C32×D4C2212yescomplemented
16C22×C32×D4C2211yescharacteristic, complemented
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C23×C3×Dic3C2211yescharacteristic, complemented
21C32×#127—24no—
22C2×C32×C42C2211yescharacteristic, complemented
23C2×C3×#217C2212yes—
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2212yescomplemented
26C2×C3×#217C2211yescharacteristic, complemented
27C2×C3×#217C2212yescomplemented
28C3×#939—28no—
29C3×#937—24no—
30C3×#937—28no—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×Dic3⋊C4C2212yescomplemented
35C3×C3⋊#95C2212yescomplemented
36C3×C3⋊#95C2212yescomplemented
37C2×C3×#127—21no—
38C2×C3×#127D311yescharacteristic, complemented
39C2×C3×#127C2×C311yescharacteristic, complemented
40C2×C3×#121—32no—
41C2×C3×#120—32no—
42C2×C3×#120—31no—
43C2×#939C2×C312yescomplemented
44C2×#937C2×C311yescharacteristic, complemented
45C2×#937C2×C312yescomplemented
46C3×#394—32no—
47C3×#392—32no—
48C3×#392—32no—
49C3×#388—32no—
50C3×#386—31no—
51#5223C2×C312yescomplemented
52#5223C2×C312yescomplemented
53#5222C2×C312yescomplemented
54#5220C2×C311yescharacteristic, complemented
55#4940C2×C312yescomplemented
56C24×C32C2312yes—
57C24×C32C2311yescharacteristic
58C24×C32C2311yescharacteristic
59C23×C3×D3—22no—
60C23×C3×D3—24no—
61C23×C3×D3—41no—
62C23×C3×D3—42no—
63C23×C3×D3—41no—
64C23×C3×D3C2312yes—
65C2×C32×D4—24no—
66C2×C32×D4—24no—
67C2×C32×D4—22no—
68C2×C32×D4—24no—
69C2×C32×D4—24no—
70C2×C32×D4—41no—
71C2×C32×D4—41no—
72C2×C32×D4—42no—
73C2×C32×D4—42no—
74C2×C32×D4—41no—
75C2×C32×D4—41no—
76C2×C32×D4D414yescomplemented
77C22×C32×C4C2312yes—
78C22×C32×C4C2311yescharacteristic
79C2×C3×#67—24no—
80C2×C3×#67—24no—
81C2×C3×#67—24no—
82C2×C3×#67—24no—
83C2×C3×#67—24no—
84C2×C3×#67—42no—
85C2×C3×#67—42no—
86C2×C3×#67—42no—
87C2×C3×#67—42no—
88C22×C3×Dic3—24no—
89C22×C3×Dic3—41no—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2312yes—
93C32×C42—22no—
94C3×#217—22no—
95C3×#217—24no—
96C3×#217—24no—
97C3×#217—41no—
98C3×#217—42no—
99C3×(C2×D3)⋊C4—24no—
100C3×(C2×D3)⋊C4—24no—
101C3×(C2×D3)⋊C4D418yescomplemented
102C3×Dic3⋊C4—24no—
103#2669—31noSylow
104C25×C3—31no—
105C24×D3C22×C311yescharacteristic
106C22×C3×D4—22no—
107C22×C3×D4—21no—
108C22×C3×D4—22no—
109C22×C3×D4—21no—
110C22×C3×D4—32no—
111C22×C3×D4—32no—
112C22×C3×D4—32no—
113C22×C3×D4C2×D312yes—
114C22×C3×D4C2×D311yescharacteristic
115C22×C3×D4C2×D312yescomplemented
116C22×C3×D4C2×D311yescharacteristic, complemented
117C22×C3×D4C22×C312yes—
118C22×C3×D4C22×C311yescharacteristic
119C22×C3×D4C22×C312yescomplemented
120C22×C3×D4C22×C311yescharacteristic, complemented
121C23×C3×C4—31no—
122C22×#67C22×C312yes—
123C22×#67C22×C312yes—
124C22×#67C22×C312yes—
125C23×Dic3C22×C311yescharacteristic, complemented
126C3×#127—28no—
127C3×#127—24no—
128C3×#127—24no—
129C3×#121—68no—
130C3×#120—68no—
131C3×#120—64no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—32no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C42—21no—
142C2×C3×C42C2×D311yescharacteristic, complemented
143C2×C3×C42C22×C311yescharacteristic, complemented
144C2×#217C22×C312yes—
145C2×#217C22×C311yescharacteristic
146C2×#217C22×C312yescomplemented
147C2×#217C22×C311yescharacteristic, complemented
148C2×#217C22×C312yescomplemented
149#939—28no—
150#937—24no—
151#937—28no—
152C2×(C2×D3)⋊C4C22×C312yes—
153C2×(C2×D3)⋊C4C22×C312yes—
154C2×(C2×D3)⋊C4C22×C312yes—
155C2×Dic3⋊C4C22×C312yescomplemented
156C3×#95—32no—
157C3×#95—32no—
158C3⋊#95C22×C312yescomplemented
159C3⋊#95C22×C312yescomplemented
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—22no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32—22no—
175C23×C32C2×D412yes—
176C23×C32C2×D412yes—
177C23×C32C2411yescharacteristic
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—44no—
185C22×C3×D3—48no—
186C22×C3×D3—48no—
187C22×C3×D3—44no—
188C22×C3×D3—44no—
189C22×C3×D3C2×D414yes—
190C32×D4—44no—
191C32×D4—48no—
192C32×D4—48no—
193C32×D4—44no—
194C2×C32×C4—22no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—22no—
198C2×C32×C4C2×D414yes—
199C2×C32×C4C2×D412yes—
200C3×#67—48no—
201C3×#67—48no—
202C3×#67—48no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—44no—
212C2×C3×Dic3C2×D414yes—
213C2×#127C3×D311yescharacteristic, complemented
214C2×#121—32no—
215C2×#120—32no—
216C2×#120—31no—
217#394—32no—
218#392—32no—
219#392—32no—
220#388—32no—
221#386—31no—
222C24×C3—22no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—32no—
226C24×C3—64no—
227C24×C3—62no—
228C24×C3—122no—
229C24×C3—121no—
230C24×C3—121no—
231C24×C3C22×D312yes—
232C24×C3C22×D311yescharacteristic
233C24×C3C22×D311yescharacteristic
234C24×C3C23×C312yes—
235C24×C3C23×C311yescharacteristic
236C24×C3C23×C311yescharacteristic
237C23×D3—22no—
238C23×D3—24no—
239C23×D3—41no—
240C23×D3—42no—
241C23×D3—41no—
242C23×D3C23×C312yes—
243C2×C3×D4—28no—
244C2×C3×D4—28no—
245C2×C3×D4—24no—
246C2×C3×D4—24no—
247C2×C3×D4—24no—
248C2×C3×D4—24no—
249C2×C3×D4—24no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—22no—
253C2×C3×D4—24no—
254C2×C3×D4—24no—
255C2×C3×D4—22no—
256C2×C3×D4—24no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
259C2×C3×D4—41no—
260C2×C3×D4—41no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—41no—
264C2×C3×D4—41no—
265C2×C3×D4—41no—
266C2×C3×D4—41no—
267C2×C3×D4—42no—
268C2×C3×D4—42no—
269C2×C3×D4—41no—
270C2×C3×D4—41no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—64no—
278C2×C3×D4—64no—
279C2×C3×D4—64no—
280C2×C3×D4—64no—
281C2×C3×D4—64no—
282C2×C3×D4—122no—
283C2×C3×D4—122no—
284C2×C3×D4—122no—
285C2×C3×D4—122no—
286C2×C3×D4#6714yescomplemented
287C2×C3×D4C3×D414yescomplemented
288C22×C3×C4—22no—
289C22×C3×C4—21no—
290C22×C3×C4—32no—
291C22×C3×C4—32no—
292C22×C3×C4—32no—
293C22×C3×C4—64no—
294C22×C3×C4—121no—
295C22×C3×C4C22×D312yes—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C23×C311yescharacteristic
298C22×C3×C4C23×C312yes—
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—42no—
305C2×#67—42no—
306C2×#67—42no—
307C2×#67—42no—
308C22×Dic3—24no—
309C22×Dic3—41no—
310C22×Dic3C23×C312yes—
311C22×Dic3C23×C312yes—
312C22×Dic3C23×C312yes—
313C3×C4⋊C4—64no—
314C3×C22⋊C4—38no—
315C3×C22⋊C4—64no—
316C3×C22⋊C4—64no—
317C3×C22⋊C4—62no—
318C3×C22⋊C4—64no—
319C3×C22⋊C4—64no—
320C3×C22⋊C4—121no—
321C3×C22⋊C4—122no—
322C3×C42—24no—
323C3×C42—22no—
324C3×C42—22no—
325#217—22no—
326#217—24no—
327#217—24no—
328#217—41no—
329#217—42no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4C3×D418yescomplemented
333Dic3⋊C4—24no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—24no—
337C22×C32—24no—
338C22×C32—42no—
339C22×C32—42no—
340C22×C32—42no—
341C22×C32—42no—
342C22×C32—42no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—42no—
348C22×C32—42no—
349C22×C32—42no—
350C22×C32—42no—
351C22×C32C22×D412yes—
352C22×C32C22×D411yescharacteristic
353C22×C32H(5,𝔽2)11yescharacteristic
354C22×C32H(5,𝔽2)11yescharacteristic
355C22×C32H(5,𝔽2)12yes—
356C2×C3×D3—24no—
357C2×C3×D3—24no—
358C2×C3×D3—24no—
359C2×C3×D3—416no—
360C2×C3×D3—42no—
361C2×C3×D3—42no—
362C2×C3×D3—42no—
363C2×C3×D3—42no—
364C32×C4—22no—
365C32×C4—24no—
366C3×Dic3—24no—
367C3×Dic3—42no—
368C3×Dic3—42no—
369C25—31no—
370C22×D4—32no—
371C22×D4—32no—
372C22×D4—32no—
373C22×D4C2×C3×D312yes—
374C22×D4C2×C3×D311yescharacteristic
375C22×D4C2×C3×D312yescomplemented
376C22×D4C2×C3×D311yescharacteristic, complemented
377C23×C4—31no—
378#127—24no—
379#121—68no—
380#120—68no—
381#120—64no—
382C2×C4⋊C4—32no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—32no—
387C2×C22⋊C4—32no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—32no—
391C2×C42C2×C3×D311yescharacteristic, complemented
392#95—32no—
393#95—32no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—22no—
410C23×C3—24no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—21no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—34no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—62no—
444C23×C3—62no—
445C23×C3—62no—
446C23×C3—62no—
447C23×C3—62no—
448C23×C3—62no—
449C23×C3—128no—
450C23×C3—124no—
451C23×C3—124no—
452C23×C3—128no—
453C23×C3—124no—
454C23×C3C2×#6712yes—
455C23×C3C2×#6712yes—
456C23×C3C2×C3×D412yes—
457C23×C3C2×C3×D412yes—
458C23×C3C23×D311yescharacteristic
459C23×C3C24×C311yescharacteristic
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—44no—
467C22×D3—48no—
468C22×D3—48no—
469C22×D3—44no—
470C22×D3—44no—
471C22×D3C2×C3×D414yes—
472C3×D4—44no—
473C3×D4—44no—
474C3×D4—48no—
475C3×D4—48no—
476C3×D4—48no—
477C3×D4—48no—
478C3×D4—48no—
479C3×D4—416no—
480C3×D4—416no—
481C3×D4—48no—
482C3×D4—44no—
483C3×D4—44no—
484C3×D4—128no—
485C3×D4—128no—
486C3×D4—128no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—22no—
499C2×C3×C4—24no—
500C2×C3×C4—22no—
501C2×C3×C4—34no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—124no—
511C2×C3×C4D3×D414yes—
512C2×C3×C4C2×#6712yes—
513C2×C3×C4C2×C3×D414yes—
514C2×C3×C4C2×C3×D412yes—
515#67—48no—
516#67—48no—
517#67—48no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—44no—
527C2×Dic3C2×C3×D414yes—
528C2×C32—42no—
529C2×C32—42no—
530C2×C32—82no—
531C2×C32#53411yescharacteristic
532C2×C32#53512yes—
533C2×C32D4211yescharacteristic
534C2×C32D4212yes—
535C2×C32#56011yescharacteristic
536C3×D3—44no—
537C24—32no—
538C24—64no—
539C24—62no—
540C24—122no—
541C24—121no—
542C24—121no—
543C24C22×C3×D312yes—
544C24C22×C3×D311yescharacteristic
545C24C22×C3×D311yescharacteristic
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—64no—
560C2×D4—64no—
561C2×D4—64no—
562C2×D4—122no—
563C2×D4—122no—
564C2×D4—122no—
565C2×D4—122no—
566C2×D4C3×#6714yescomplemented
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—64no—
571C22×C4—121no—
572C22×C4C22×C3×D312yes—
573C22×C4C22×C3×D311yescharacteristic
574C4⋊C4—64no—
575C22⋊C4—38no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—62no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—121no—
582C22⋊C4—122no—
583C42—22no—
584C22×C3—24no—
585C22×C3—24no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—64no—
631C22×C3—64no—
632C22×C3—64no—
633C22×C3—82no—
634C22×C3—82no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—82no—
640C22×C3—82no—
641C22×C3—82no—
642C22×C3—82no—
643C22×C3—1216no—
644C22×C3—122no—
645C22×C3—122no—
646C22×C3—122no—
647C22×C3—122no—
648C22×C3C2×D3×D412yes—
649C22×C3#100411yescharacteristic
650C22×C3#100412yes—
651C22×C3#100411yescharacteristic
652C22×C3C22×#6711yescharacteristic
653C22×C3C22×C3×D412yes—
654C22×C3C22×C3×D411yescharacteristic
655C22×C3C3×H(5,𝔽2)11yescharacteristic
656C22×C3C3×H(5,𝔽2)12yes—
657C22×C3C3×H(5,𝔽2)11yescharacteristic
658C2×D3—24no—
659C2×D3—24no—
660C2×D3—24no—
661C2×D3—416no—
662C2×D3—42no—
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C3×C4—28no—
667C3×C4—24no—
668C3×C4—24no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—24no—
672C3×C4—64no—
673C3×C4—122no—
674C3×C4—122no—
675Dic3—24no—
676Dic3—42no—
677Dic3—42no—
678C32#266911yescharacteristic, complemented, Sylow
679C23—22no—
680C23—22no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—22no—
685C23—21no—
686C23—21no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—34no—
695C23—62no—
696C23—62no—
697C23—62no—
698C23—62no—
699C23—62no—
700C23—62no—
701C23—128no—
702C23—124no—
703C23—124no—
704C23—128no—
705C23—124no—
706C23C2×C3×#6712yes—
707C23C2×C3×#6712yes—
708C23C23×C3×D311yescharacteristic
709D4—44no—
710D4—48no—
711D4—48no—
712D4—44no—
713D4—128no—
714D4—128no—
715D4—128no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—34no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—124no—
730C2×C4C3×D3×D414yes—
731C2×C4C2×C3×#6712yes—
732C2×C3—22no—
733C2×C3—21no—
734C2×C3—22no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—42no—
741C2×C3—82no—
742C2×C3—82no—
743C2×C3—84no—
744C2×C3—82no—
745C2×C3—82no—
746C2×C3—124no—
747C2×C3#571512yes—
748C2×C3#571711yescharacteristic
749C2×C3#572011yescharacteristic
750C2×C3D4×#6712yes—
751C2×C3#580411yescharacteristic
752C2×C3C3×#53411yescharacteristic
753C2×C3C3×#53512yes—
754C2×C3C3×D4212yes—
755C2×C3C3×D4211yescharacteristic
756C2×C3C3×#56011yescharacteristic
757D3—44no—
758C22—24no—
759C22—24no—
760C22—22no—
761C22—22no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—64no—
776C22—64no—
777C22—64no—
778C22—1216no—
779C22—122no—
780C22—122no—
781C22—122no—
782C22—122no—
783C22C2×C3×D3×D412yes—
784C22C3×#100412yes—
785C22C3×#100411yescharacteristic
786C22C3×#100411yescharacteristic
787C22C22×C3×#6711yescharacteristic
788C4—24no—
789C4—22no—
790C4—64no—
791C4—122no—
792C4—122no—
793C3—21no—
794C3#8319011yescharacteristic, direct product factor
795C3C3×#266911yescharacteristic, complemented
796C2—42no—
797C2—42no—
798C2—82no—
799C2—124no—
800C2C3×#571512yes—
801C2C3×#571711yescharacteristic
802C2C3×#572011yescharacteristic
803C2C3×D4×#6712yes—
804C2C3×#580411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#127C2
socleC23×C32C24
hypercenterC2×C3×#127D3
hypocenterC3C3×#2669
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. C2×C32×#127C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#937C2semidirect
4. C2×C3×#937C2semidirect
5. C3×#5223C2semidirect
6. C3×#5223C2semidirect
7. C3×#5222C2semidirect
8. C3×#5220C2semidirect
9. C3×#4940C2semidirect
11. #83190C3direct (N × H)
15. C22×C32×D4C22semidirect
16. C22×C32×D4C22semidirect
20. C23×C3×Dic3C22semidirect
22. C2×C32×C42C22semidirect
25. C2×C3×#217C22semidirect
26. C2×C3×#217C22semidirect
27. C2×C3×#217C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
35. C3×C3⋊#95C22semidirect
36. C3×C3⋊#95C22semidirect
38. C2×C3×#127D3semidirect
39. C2×C3×#127C2×C3semidirect
43. C2×#939C2×C3semidirect
44. C2×#937C2×C3semidirect
45. C2×#937C2×C3semidirect
51. #5223C2×C3semidirect
52. #5223C2×C3semidirect
53. #5222C2×C3semidirect
54. #5220C2×C3semidirect
55. #4940C2×C3semidirect
76. C2×C32×D4D4semidirect
101. C3×(C2×D3)⋊C4D4semidirect
115. C22×C3×D4C2×D3semidirect
116. C22×C3×D4C2×D3semidirect
119. C22×C3×D4C22×C3semidirect
120. C22×C3×D4C22×C3semidirect
125. C23×Dic3C22×C3semidirect
142. C2×C3×C42C2×D3semidirect
143. C2×C3×C42C22×C3semidirect
146. C2×#217C22×C3semidirect
147. C2×#217C22×C3semidirect
148. C2×#217C22×C3semidirect
155. C2×Dic3⋊C4C22×C3semidirect
158. C3⋊#95C22×C3semidirect
159. C3⋊#95C22×C3semidirect
213. C2×#127C3×D3semidirect
286. C2×C3×D4#67semidirect
287. C2×C3×D4C3×D4semidirect
332. (C2×D3)⋊C4C3×D4semidirect
375. C22×D4C2×C3×D3semidirect
376. C22×D4C2×C3×D3semidirect
391. C2×C42C2×C3×D3semidirect
566. C2×D4C3×#67semidirect
678. C32#2669semidirect
794. C3#83190direct (N × H)
795. C3C3×#2669semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1272
C2×C3×#9392
C2×C3×#9372
C3×#52232
C3×#52222
C3×#52202
C3×#49402
C3×#26693
#831903