Finite Group Databasebeta

← C3×#82594 #11836030

Subgroups — C3×#82594 #11836030

Order 1152.

2195 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#120C211yesmaximal, characteristic, complemented
2C2×C3×#953C212yesmaximal, complemented
3C2×C3×#940C211yesmaximal, characteristic, complemented
4C2×C3×#939C212yesmaximal, complemented
5C3×#5223C212yesmaximal, complemented
6C3×#5220C211yesmaximal, characteristic, complemented
7C3×#4960C212yesmaximal, complemented
8C3×#4959C212yesmaximal, complemented
9C3×#4944C212yesmaximal, complemented
10C3×#2669—31nomaximal
11#82594C311yesmaximal, characteristic, direct product factor
12C25×C32C2211yescharacteristic
13C22×C32×D4C2212yes—
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yescomplemented
19C23×C3×Dic3C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic, complemented
21C32×#120—24no—
22C2×C32×C22⋊C4C2212yes—
23C2×C32×C22⋊C4C2211yescharacteristic
24C3×#953—28no—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28C2×C3×#217C2211yescharacteristic, complemented
29C3×#940—24no—
30C3×#939—28no—
31C2×C3×(C2×D3)⋊C4C2212yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yescomplemented
33C2×C3×Dic3⋊C4C2212yescomplemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35C3×C3⋊#95C2212yescomplemented
36C3×C3⋊#95C2212yescomplemented
37C2×C3×#127—31no—
38C2×C3×#121—32no—
39C2×C3×#120—21no—
40C2×C3×#120—32no—
41C2×C3×#120D311yescharacteristic, complemented
42C2×C3×#120C2×C311yescharacteristic, complemented
43C2×#953C2×C312yescomplemented
44C2×#940C2×C311yescharacteristic, complemented
45C2×#939C2×C312yescomplemented
46C3×#394—32no—
47C3×#392—32no—
48C3×#392—32no—
49C3×#388—32no—
50C3×#386—31no—
51#5223C2×C312yescomplemented
52#5220C2×C311yescharacteristic, complemented
53#4960C2×C312yescomplemented
54#4959C2×C312yescomplemented
55#4944C2×C312yescomplemented
56C24×C32—22no—
57C24×C32—24no—
58C24×C32—41no—
59C24×C32—42no—
60C24×C32—41no—
61C24×C32C2312yes—
62C24×C32C2311yescharacteristic
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C2×C32×D4—24no—
66C2×C32×D4—24no—
67C2×C32×D4—41no—
68C2×C32×D4—41no—
69C2×C32×D4—42no—
70C2×C32×D4D414yescomplemented
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—24no—
74C2×C3×#67—24no—
75C2×C3×#67—24no—
76C2×C3×#67—24no—
77C2×C3×#67—24no—
78C2×C3×#67—24no—
79C2×C3×#67—24no—
80C2×C3×#67—42no—
81C2×C3×#67—42no—
82C2×C3×#67—42no—
83C2×C3×#67—42no—
84C2×C3×#67—42no—
85C22×C3×Dic3—24no—
86C22×C3×Dic3—41no—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C2×C3×D12—22no—
91C2×C3×D12—41no—
92C2×C3×D12—41no—
93C32×C22⋊C4—22no—
94C32×C22⋊C4—24no—
95C3×#217—24no—
96C3×#217—24no—
97C3×#217—41no—
98C3×#217D418yescomplemented
99C3×(C2×D3)⋊C4—24no—
100C3×(C2×D3)⋊C4—42no—
101C3×Dic3⋊C4—24no—
102C3×C4×Dic3—22no—
103#2669—31noSylow
104C25×C3—21no—
105C25×C3C2×D311yescharacteristic
106C25×C3C22×C311yescharacteristic
107C22×C3×D4—22no—
108C22×C3×D4—21no—
109C22×C3×D4—32no—
110C22×C3×D4—32no—
111C22×C3×D4—32no—
112C22×C3×D4—32no—
113C22×C3×D4—31no—
114C22×C3×D4C2×D312yes—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C22×C312yes—
117C22×C3×D4C22×C311yescharacteristic
118C23×C3×C4—31no—
119C22×#67C22×C312yes—
120C22×#67C22×C312yes—
121C22×#67C22×C312yes—
122C22×#67C22×C312yescomplemented
123C23×Dic3C22×C311yescharacteristic, complemented
124C22×D12C22×C311yescharacteristic, complemented
125C3×#127—64no—
126C3×#121—68no—
127C3×#120—28no—
128C3×#120—24no—
129C3×#120—24no—
130C3×#120—68no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—32no—
140C2×C3×C22⋊C4C2×D312yes—
141C2×C3×C22⋊C4C2×D311yescharacteristic
142C2×C3×C22⋊C4C22×C312yes—
143C2×C3×C22⋊C4C22×C311yescharacteristic
144C2×C3×C42—31no—
145#953—28no—
146C2×#217C22×C312yes—
147C2×#217C22×C312yes—
148C2×#217C22×C312yes—
149C2×#217C22×C311yescharacteristic, complemented
150#940—24no—
151#939—28no—
152C2×(C2×D3)⋊C4C22×C312yescomplemented
153C2×(C2×D3)⋊C4C22×C312yescomplemented
154C2×Dic3⋊C4C22×C312yescomplemented
155C2×C4×Dic3C22×C311yescharacteristic, complemented
156C3×#95—32no—
157C3×#95—32no—
158C3⋊#95C22×C312yescomplemented
159C3⋊#95C22×C312yescomplemented
160C23×C32—22no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—22no—
174C23×C32—48no—
175C23×C32—44no—
176C23×C32—44no—
177C23×C32—48no—
178C23×C32—44no—
179C23×C32C2×D414yes—
180C23×C32C2×D412yes—
181C23×C32C2×D412yes—
182C23×C32C2411yescharacteristic
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—22no—
190C32×D4—44no—
191C32×D4—48no—
192C2×C32×C4—22no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4C2×D412yes—
198C3×#67—48no—
199C3×#67—48no—
200C3×#67—48no—
201C3×#67—48no—
202C2×C3×Dic3—22no—
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—44no—
210C2×C3×Dic3C2×D414yes—
211C2×C3×Dic3C2×D414yes—
212C3×D12—44no—
213C2×#127—31no—
214C2×#121—32no—
215C2×#120—32no—
216C2×#120C3×D311yescharacteristic, complemented
217#394—32no—
218#392—32no—
219#392—32no—
220#388—32no—
221#386—31no—
222C24×C3—24no—
223C24×C3—24no—
224C24×C3—22no—
225C24×C3—24no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—32no—
231C24×C3—44no—
232C24×C3—42no—
233C24×C3—41no—
234C24×C3—41no—
235C24×C3—42no—
236C24×C3—41no—
237C24×C3—41no—
238C24×C3—44no—
239C24×C3—42no—
240C24×C3—42no—
241C24×C3C22×D312yes—
242C24×C3C22×D311yescharacteristic
243C24×C3C22×D311yescharacteristic
244C24×C3C23×C312yes—
245C24×C3C23×C311yescharacteristic
246C24×C3C23×C311yescharacteristic
247C23×D3C23×C312yes—
248C2×C3×D4—28no—
249C2×C3×D4—24no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4—44no—
255C2×C3×D4—41no—
256C2×C3×D4—41no—
257C2×C3×D4—42no—
258C2×C3×D4—41no—
259C2×C3×D4—41no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—44no—
264C2×C3×D4—64no—
265C2×C3×D4—64no—
266C2×C3×D4—64no—
267C2×C3×D4—64no—
268C2×C3×D4—64no—
269C2×C3×D4—64no—
270C2×C3×D4—64no—
271C2×C3×D4—62no—
272C2×C3×D4—121no—
273C2×C3×D4—121no—
274C2×C3×D4—122no—
275C2×C3×D4—122no—
276C2×C3×D4—122no—
277C2×C3×D4—122no—
278C2×C3×D4—122no—
279C2×C3×D4#6714yescomplemented
280C2×C3×D4C3×D414yescomplemented
281C22×C3×C4—22no—
282C22×C3×C4—21no—
283C22×C3×C4—32no—
284C22×C3×C4—32no—
285C22×C3×C4—32no—
286C22×C3×C4—64no—
287C22×C3×C4—121no—
288C22×C3×C4C22×D312yes—
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C23×C312yes—
291C22×C3×C4C23×C311yescharacteristic
292C2×#67—24no—
293C2×#67—24no—
294C2×#67—24no—
295C2×#67—24no—
296C2×#67—24no—
297C2×#67—24no—
298C2×#67—24no—
299C2×#67—42no—
300C2×#67—42no—
301C2×#67—42no—
302C2×#67—42no—
303C2×#67—42no—
304C22×Dic3—24no—
305C22×Dic3—41no—
306C22×Dic3C23×C312yes—
307C22×Dic3C23×C312yes—
308C22×Dic3C23×C312yes—
309C2×D12—22no—
310C2×D12—41no—
311C2×D12—41no—
312C3×C4⋊C4—64no—
313C3×C22⋊C4—24no—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—38no—
320C3×C22⋊C4—64no—
321C3×C22⋊C4—64no—
322C3×C22⋊C4—64no—
323C3×C22⋊C4—122no—
324C3×C22⋊C4—121no—
325C3×C42—62no—
326#217—24no—
327#217—24no—
328#217—41no—
329#217C3×D418yescomplemented
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—42no—
332Dic3⋊C4—24no—
333C4×Dic3—22no—
334C22×C32—22no—
335C22×C32—24no—
336C22×C32—22no—
337C22×C32—24no—
338C22×C32—24no—
339C22×C32—24no—
340C22×C32—24no—
341C22×C32—416no—
342C22×C32—42no—
343C22×C32—42no—
344C22×C32—42no—
345C22×C32—42no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—42no—
349C22×C32—42no—
350C22×C32—41no—
351C22×C32—41no—
352C22×C32C22×D412yes—
353C22×C32C22×D411yescharacteristic
354C22×C32H(5,𝔽2)11yescharacteristic
355C22×C32H(5,𝔽2)11yescharacteristic
356C22×C32H(5,𝔽2)12yes—
357C2×C3×D3—42no—
358C2×C3×D3—42no—
359C2×C3×D3—42no—
360C2×C3×D3—42no—
361C2×C3×D3—42no—
362C2×C3×D3—42no—
363C2×C3×D3—42no—
364C32×C4—22no—
365C32×C4—42no—
366C3×Dic3—24no—
367C3×Dic3—24no—
368C3×Dic3—42no—
369C25C2×C3×D311yescharacteristic
370C22×D4—32no—
371C22×D4—32no—
372C22×D4—32no—
373C22×D4—32no—
374C22×D4—31no—
375C22×D4C2×C3×D312yes—
376C22×D4C2×C3×D311yescharacteristic
377C23×C4—31no—
378#127—64no—
379#121—68no—
380#120—24no—
381#120—68no—
382C2×C4⋊C4—32no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—32no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4C2×C3×D312yes—
390C2×C22⋊C4C2×C3×D311yescharacteristic
391C2×C42—31no—
392#95—32no—
393#95—32no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—22no—
426C23×C3—21no—
427C23×C3—24no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—42no—
440C23×C3—48no—
441C23×C3—44no—
442C23×C3—44no—
443C23×C3—48no—
444C23×C3—416no—
445C23×C3—48no—
446C23×C3—44no—
447C23×C3—48no—
448C23×C3—44no—
449C23×C3—48no—
450C23×C3—48no—
451C23×C3—416no—
452C23×C3—48no—
453C23×C3—44no—
454C23×C3—44no—
455C23×C3—62no—
456C23×C3—62no—
457C23×C3—62no—
458C23×C3—62no—
459C23×C3—62no—
460C23×C3—62no—
461C23×C3—62no—
462C23×C3D3×D414yes—
463C23×C3C2×#6712yes—
464C23×C3C2×#6712yes—
465C23×C3C2×C3×D414yes—
466C23×C3C2×C3×D412yes—
467C23×C3C2×C3×D412yes—
468C23×C3C23×D311yescharacteristic
469C23×C3C24×C311yescharacteristic
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C3×D4—44no—
478C3×D4—44no—
479C3×D4—48no—
480C3×D4—48no—
481C3×D4—48no—
482C3×D4—416no—
483C3×D4—124no—
484C3×D4—128no—
485C3×D4—128no—
486C3×D4—128no—
487C3×D4—128no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—24no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—34no—
501C2×C3×C4—34no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—42no—
505C2×C3×C4—42no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—124no—
514C2×C3×C4C2×#6712yes—
515C2×C3×C4C2×C3×D412yes—
516#67—48no—
517#67—48no—
518#67—48no—
519#67—48no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—44no—
528C2×Dic3C2×C3×D414yes—
529C2×Dic3C2×C3×D414yes—
530D12—44no—
531C2×C32—42no—
532C2×C32—44no—
533C2×C32—42no—
534C2×C32#53411yescharacteristic
535C2×C32#53512yes—
536C2×C32D4212yes—
537C2×C32D4211yescharacteristic
538C2×C32#56011yescharacteristic
539C3×D3—82no—
540C24—24no—
541C24—22no—
542C24—32no—
543C24—42no—
544C24—41no—
545C24—41no—
546C24C22×C3×D312yes—
547C24C22×C3×D311yescharacteristic
548C24C22×C3×D311yescharacteristic
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4—64no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—64no—
560C2×D4—64no—
561C2×D4—62no—
562C2×D4—121no—
563C2×D4—121no—
564C2×D4—122no—
565C2×D4—122no—
566C2×D4—122no—
567C2×D4—122no—
568C2×D4—122no—
569C2×D4C3×#6714yescomplemented
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—64no—
574C22×C4—121no—
575C22×C4C22×C3×D312yes—
576C22×C4C22×C3×D311yescharacteristic
577C4⋊C4—64no—
578C22⋊C4—22no—
579C22⋊C4—24no—
580C22⋊C4—38no—
581C22⋊C4—64no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—122no—
585C22⋊C4—121no—
586C42—62no—
587C22×C3—28no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—44no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—44no—
612C22×C3—42no—
613C22×C3—44no—
614C22×C3—44no—
615C22×C3—42no—
616C22×C3—44no—
617C22×C3—44no—
618C22×C3—44no—
619C22×C3—42no—
620C22×C3—432no—
621C22×C3—416no—
622C22×C3—416no—
623C22×C3—41no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3—42no—
642C22×C3—41no—
643C22×C3—81no—
644C22×C3—82no—
645C22×C3—81no—
646C22×C3—122no—
647C22×C3—122no—
648C22×C3—122no—
649C22×C3—122no—
650C22×C3—122no—
651C22×C3—122no—
652C22×C3—122no—
653C22×C3C2×D3×D412yes—
654C22×C3#100412yes—
655C22×C3#100411yescharacteristic
656C22×C3#100411yescharacteristic
657C22×C3C22×#6711yescharacteristic
658C22×C3C22×C3×D412yes—
659C22×C3C22×C3×D411yescharacteristic
660C22×C3C3×H(5,𝔽2)11yescharacteristic
661C22×C3C3×H(5,𝔽2)12yes—
662C22×C3C3×H(5,𝔽2)11yescharacteristic
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C2×D3—42no—
669C2×D3—42no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—42no—
673C3×C4—44no—
674C3×C4—42no—
675C3×C4—42no—
676C3×C4—64no—
677C3×C4—64no—
678C3×C4—122no—
679Dic3—24no—
680Dic3—24no—
681Dic3—42no—
682C32#266911yescharacteristic, complemented, Sylow
683C23—22no—
684C23—22no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—22no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—48no—
698C23—44no—
699C23—44no—
700C23—48no—
701C23—44no—
702C23—62no—
703C23—62no—
704C23—62no—
705C23—62no—
706C23—62no—
707C23—62no—
708C23—62no—
709C23C3×D3×D414yes—
710C23C2×C3×#6712yes—
711C23C2×C3×#6712yes—
712C23C23×C3×D311yescharacteristic
713D4—44no—
714D4—48no—
715D4—124no—
716D4—128no—
717D4—128no—
718D4—128no—
719D4—128no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—34no—
726C2×C4—34no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—124no—
735C2×C4C2×C3×#6712yes—
736C2×C3—22no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—22no—
740C2×C3—21no—
741C2×C3—48no—
742C2×C3—44no—
743C2×C3—42no—
744C2×C3—44no—
745C2×C3—42no—
746C2×C3—44no—
747C2×C3—42no—
748C2×C3—42no—
749C2×C3—82no—
750C2×C3—242no—
751C2×C3#559011yescharacteristic
752C2×C3#559212yes—
753C2×C3#559511yescharacteristic
754C2×C3D4×#6712yes—
755C2×C3#580411yescharacteristic
756C2×C3C3×#53411yescharacteristic
757C2×C3C3×#53512yes—
758C2×C3C3×D4212yes—
759C2×C3C3×D4211yescharacteristic
760C2×C3C3×#56011yescharacteristic
761D3—82no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—22no—
766C22—22no—
767C22—24no—
768C22—24no—
769C22—416no—
770C22—42no—
771C22—42no—
772C22—41no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—41no—
779C22—41no—
780C22—122no—
781C22—122no—
782C22—122no—
783C22—122no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22C2×C3×D3×D412yes—
788C22C3×#100412yes—
789C22C3×#100411yescharacteristic
790C22C3×#100411yescharacteristic
791C22C22×C3×#6711yescharacteristic
792C4—22no—
793C4—42no—
794C4—64no—
795C4—64no—
796C4—122no—
797C3—21no—
798C3#8259411yescharacteristic, direct product factor
799C3C3×#266911yescharacteristic, complemented
800C2—44no—
801C2—42no—
802C2—42no—
803C2—242no—
804C2C3×#559011yescharacteristic
805C2C3×#559212yes—
806C2C3×#559511yescharacteristic
807C2C3×D4×#6712yes—
808C2C3×#580411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#120C2
socleC23×C32C24
hypercenterC2×C3×#120D3
hypocenterC3C3×#2669
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
1. C2×C32×#120C2semidirect
2. C2×C3×#953C2semidirect
3. C2×C3×#940C2semidirect
4. C2×C3×#939C2semidirect
5. C3×#5223C2semidirect
6. C3×#5220C2semidirect
7. C3×#4960C2semidirect
8. C3×#4959C2semidirect
9. C3×#4944C2semidirect
11. #82594C3direct (N × H)
18. C22×C3×#67C22semidirect
19. C23×C3×Dic3C22semidirect
20. C22×C3×D12C22semidirect
28. C2×C3×#217C22semidirect
31. C2×C3×(C2×D3)⋊C4C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
33. C2×C3×Dic3⋊C4C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C3×C3⋊#95C22semidirect
36. C3×C3⋊#95C22semidirect
41. C2×C3×#120D3semidirect
42. C2×C3×#120C2×C3semidirect
43. C2×#953C2×C3semidirect
44. C2×#940C2×C3semidirect
45. C2×#939C2×C3semidirect
51. #5223C2×C3semidirect
52. #5220C2×C3semidirect
53. #4960C2×C3semidirect
54. #4959C2×C3semidirect
55. #4944C2×C3semidirect
70. C2×C32×D4D4semidirect
98. C3×#217D4semidirect
122. C22×#67C22×C3semidirect
123. C23×Dic3C22×C3semidirect
124. C22×D12C22×C3semidirect
149. C2×#217C22×C3semidirect
152. C2×(C2×D3)⋊C4C22×C3semidirect
153. C2×(C2×D3)⋊C4C22×C3semidirect
154. C2×Dic3⋊C4C22×C3semidirect
155. C2×C4×Dic3C22×C3semidirect
158. C3⋊#95C22×C3semidirect
159. C3⋊#95C22×C3semidirect
216. C2×#120C3×D3semidirect
279. C2×C3×D4#67semidirect
280. C2×C3×D4C3×D4semidirect
329. #217C3×D4semidirect
569. C2×D4C3×#67semidirect
682. C32#2669semidirect
798. C3#82594direct (N × H)
799. C3C3×#2669semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1202
C2×C3×#9532
C2×C3×#9402
C2×C3×#9392
C3×#52232
C3×#52202
C3×#49602
C3×#49592
C3×#49442
C3×#26693
#825943