Finite Group Databasebeta

← C3×#82588 #11811943

Subgroups — C3×#82588 #11811943

Order 1152.

3027 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic, complemented
2C2×C32×#120C211yesmaximal, characteristic, complemented
3C2×C3×#953C211yesmaximal, characteristic, complemented
4C2×C3×#940C212yesmaximal, complemented
5C2×C3×#939C211yesmaximal, characteristic, complemented
6C2×C3×#937C211yesmaximal, characteristic, complemented
7C2×C3×#882C211yesmaximal, characteristic, complemented
8C3×#5223C212yesmaximal, complemented
9C3×#4960C212yesmaximal, complemented
10C3×#4957C212yesmaximal, complemented
11C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
12C3×#2433—31nomaximal
13#82588C311yesmaximal, characteristic, direct product factor
14C25×C32C2211yescharacteristic
15C24×C3×D3C2211yescharacteristic
16C22×C32×D4C2211yescharacteristic
17C22×C32×D4C2212yescomplemented
18C22×C3×#67—28no—
19C22×C3×#67—24no—
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2212yes—
22C22×C3×#67C2212yes—
23C22×C3×#67C2211yescharacteristic, complemented
24C22×C3×#67C2212yescomplemented
25C22×C3×#67C2212yescomplemented
26C23×C3×Dic3C2211yescharacteristic
27C22×C3×D12C2212yescomplemented
28C32×#120—24no—
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2212yescomplemented
31C3×#953—24no—
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2212yescomplemented
34C2×C3×#217C2211yescharacteristic, complemented
35C3×#940—28no—
36C3×#939—24no—
37C3×#937—24no—
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×(C2×D3)⋊C4C2212yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×C4×Dic3C2212yescomplemented
43C3×#882—24no—
44C3×C3⋊#95C2212yescomplemented
45C23×C3×D4—31no—
46C23×#67C2×C311yescharacteristic, complemented
47C2×C3×#127—32no—
48C2×C3×#121—31no—
49C2×C3×#120—21no—
50C2×C3×#120—31no—
51C2×C3×#120—31no—
52C2×C3×#120—31no—
53C2×C3×#120D311yescharacteristic, complemented
54C2×C3×#120C2×C311yescharacteristic, complemented
55C2×#953C2×C311yescharacteristic, complemented
56C2×#940C2×C312yescomplemented
57C2×#939C2×C311yescharacteristic, complemented
58C2×#937C2×C311yescharacteristic, complemented
59C2×#882C2×C311yescharacteristic, complemented
60C3×#392—32no—
61C3×#392—32no—
62C3×#390—32no—
63C3×C4×C22⋊C4—31no—
64#5223C2×C312yescomplemented
65#4960C2×C312yescomplemented
66#4957C2×C312yescomplemented
67Dic3×C22⋊C4C2×C311yescharacteristic, complemented
68C24×C32—24no—
69C24×C32—22no—
70C24×C32—22no—
71C24×C32—22no—
72C24×C32—42no—
73C24×C32C2311yescharacteristic
74C24×C32C2312yes—
75C24×C32C2311yescharacteristic
76C23×C3×D3—22no—
77C23×C3×D3—24no—
78C23×C3×D3—22no—
79C23×C3×D3—22no—
80C23×C3×D3—42no—
81C23×C3×D3C2311yescharacteristic
82C23×C3×D3C2312yes—
83C2×C32×D4—22no—
84C2×C32×D4—22no—
85C2×C32×D4—22no—
86C2×C32×D4—24no—
87C2×C32×D4—24no—
88C2×C32×D4—42no—
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2312yes—
91C2×C3×#67—232no—
92C2×C3×#67—24no—
93C2×C3×#67—24no—
94C2×C3×#67—22no—
95C2×C3×#67—22no—
96C2×C3×#67—24no—
97C2×C3×#67—22no—
98C2×C3×#67—24no—
99C2×C3×#67—24no—
100C2×C3×#67—24no—
101C2×C3×#67—24no—
102C2×C3×#67—22no—
103C2×C3×#67—24no—
104C2×C3×#67—24no—
105C2×C3×#67—24no—
106C2×C3×#67—42no—
107C2×C3×#67—42no—
108C2×C3×#67D418yescomplemented
109C22×C3×Dic3—24no—
110C22×C3×Dic3D414yescomplemented
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2312yes—
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×D12—24no—
116C2×C3×D12—24no—
117C2×C3×D12—42no—
118C32×C22⋊C4—24no—
119C32×C22⋊C4D414yescomplemented
120C3×#217—22no—
121C3×#217—24no—
122C3×#217D414yescomplemented
123C3×(C2×D3)⋊C4—24no—
124C3×(C2×D3)⋊C4—22no—
125C3×(C2×D3)⋊C4—24no—
126C3×Dic3⋊C4—22no—
127C3×C4×Dic3—24no—
128#2433—31noSylow
129C25×C3—21no—
130C25×C3—31no—
131C25×C3C2×D311yescharacteristic
132C25×C3C22×C311yescharacteristic
133C24×D3C22×C311yescharacteristic
134C22×C3×D4—21no—
135C22×C3×D4—22no—
136C22×C3×D4—32no—
137C22×C3×D4—32no—
138C22×C3×D4—31no—
139C22×C3×D4—31no—
140C22×C3×D4—32no—
141C22×C3×D4—32no—
142C22×C3×D4—32no—
143C22×C3×D4—64no—
144C22×C3×D4—68no—
145C22×C3×D4C2×D311yescharacteristic
146C22×C3×D4C2×D312yescomplemented
147C22×C3×D4C22×C311yescharacteristic
148C22×C3×D4C22×C312yescomplemented
149C23×C3×C4—31no—
150C22×#67—28no—
151C22×#67—24no—
152C22×#67C22×C312yes—
153C22×#67C22×C311yescharacteristic
154C22×#67C22×C312yes—
155C22×#67C22×C311yescharacteristic, complemented
156C22×#67C22×C312yescomplemented
157C22×#67C22×C312yescomplemented
158C23×Dic3C22×C311yescharacteristic
159C22×D12C22×C312yescomplemented
160C3×#127—68no—
161C3×#121—64no—
162C3×#120—28no—
163C3×#120—24no—
164C3×#120—24no—
165C3×#120—64no—
166C3×#120—64no—
167C3×#120—64no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—21no—
170C2×C3×C22⋊C4—22no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—32no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—32no—
175C2×C3×C22⋊C4—32no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4C2×D311yescharacteristic
178C2×C3×C22⋊C4C2×D312yescomplemented
179C2×C3×C22⋊C4C22×C311yescharacteristic
180C2×C3×C22⋊C4C22×C312yescomplemented
181C2×C3×C42—32no—
182#953—24no—
183C2×#217C22×C311yescharacteristic
184C2×#217C22×C312yescomplemented
185C2×#217C22×C311yescharacteristic, complemented
186#940—28no—
187#939—24no—
188#937—24no—
189C2×(C2×D3)⋊C4C22×C312yescomplemented
190C2×(C2×D3)⋊C4C22×C312yescomplemented
191C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
192C2×Dic3⋊C4C22×C311yescharacteristic, complemented
193C2×C4×Dic3C22×C312yescomplemented
194#882—24no—
195C3×#95—32no—
196C3⋊#95C22×C312yescomplemented
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—21no—
200C23×C32—22no—
201C23×C32—22no—
202C23×C32—28no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—22no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—22no—
210C23×C32—22no—
211C23×C32—48no—
212C23×C32—48no—
213C23×C32—44no—
214C23×C32—44no—
215C23×C32C2×D414yes—
216C23×C32C2×D412yes—
217C23×C32C2×D412yes—
218C23×C32C2×D412yes—
219C23×C32C2411yescharacteristic
220C22×C3×D3—28no—
221C22×C3×D3—22no—
222C22×C3×D3—22no—
223C22×C3×D3—22no—
224C22×C3×D3—22no—
225C22×C3×D3—22no—
226C22×C3×D3—22no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—22no—
230C22×C3×D3—21no—
231C22×C3×D3—22no—
232C22×C3×D3—48no—
233C22×C3×D3—48no—
234C22×C3×D3—44no—
235C22×C3×D3—44no—
236C22×C3×D3C2×D414yes—
237C32×D4—48no—
238C32×D4—44no—
239C2×C32×C4—21no—
240C2×C32×C4—22no—
241C2×C32×C4—22no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D414yescomplemented
245C3×#67—216no—
246C3×#67—216no—
247C3×#67—48no—
248C3×#67—48no—
249C3×#67—44no—
250C3×#67—44no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—28no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D412yes—
259C2×C3×Dic3C2×D414yes—
260C2×C3×Dic3C2×D412yes—
261C2×C3×Dic3C2×D414yescomplemented
262C3×D12—48no—
263C23×D4—31no—
264C2×#127—32no—
265C2×#121—31no—
266C2×#120—31no—
267C2×#120—31no—
268C2×#120—31no—
269C2×#120C3×D311yescharacteristic, complemented
270#392—32no—
271#392—32no—
272#390—32no—
273C4×C22⋊C4—31no—
274C24×C3—24no—
275C24×C3—22no—
276C24×C3—24no—
277C24×C3—22no—
278C24×C3—24no—
279C24×C3—22no—
280C24×C3—22no—
281C24×C3—22no—
282C24×C3—22no—
283C24×C3—22no—
284C24×C3—21no—
285C24×C3—21no—
286C24×C3—32no—
287C24×C3—31no—
288C24×C3—44no—
289C24×C3—42no—
290C24×C3—42no—
291C24×C3—42no—
292C24×C3—42no—
293C24×C3—44no—
294C24×C3—64no—
295C24×C3—62no—
296C24×C3—62no—
297C24×C3—62no—
298C24×C3—122no—
299C24×C3C22×D311yescharacteristic
300C24×C3C22×D312yes—
301C24×C3C22×D311yescharacteristic
302C24×C3C23×C311yescharacteristic
303C24×C3C23×C312yes—
304C24×C3C23×C311yescharacteristic
305C23×D3—22no—
306C23×D3—24no—
307C23×D3—22no—
308C23×D3—22no—
309C23×D3—42no—
310C23×D3C23×C311yescharacteristic
311C23×D3C23×C312yes—
312C2×C3×D4—24no—
313C2×C3×D4—28no—
314C2×C3×D4—22no—
315C2×C3×D4—22no—
316C2×C3×D4—24no—
317C2×C3×D4—22no—
318C2×C3×D4—22no—
319C2×C3×D4—22no—
320C2×C3×D4—24no—
321C2×C3×D4—22no—
322C2×C3×D4—24no—
323C2×C3×D4—24no—
324C2×C3×D4—38no—
325C2×C3×D4—42no—
326C2×C3×D4—42no—
327C2×C3×D4—44no—
328C2×C3×D4—42no—
329C2×C3×D4—42no—
330C2×C3×D4—44no—
331C2×C3×D4—64no—
332C2×C3×D4—64no—
333C2×C3×D4—64no—
334C2×C3×D4—64no—
335C2×C3×D4—64no—
336C2×C3×D4—64no—
337C2×C3×D4—62no—
338C2×C3×D4—64no—
339C2×C3×D4—64no—
340C2×C3×D4—632no—
341C2×C3×D4—64no—
342C2×C3×D4—64no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—64no—
346C2×C3×D4—62no—
347C2×C3×D4—64no—
348C2×C3×D4—122no—
349C2×C3×D4—122no—
350C2×C3×D4—122no—
351C22×C3×C4—21no—
352C22×C3×C4—22no—
353C22×C3×C4—31no—
354C22×C3×C4—34no—
355C22×C3×C4—31no—
356C22×C3×C4—32no—
357C22×C3×C4—31no—
358C22×C3×C4—64no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D312yes—
361C22×C3×C4C23×C311yescharacteristic
362C22×C3×C4C23×C312yes—
363C2×#67—232no—
364C2×#67—24no—
365C2×#67—24no—
366C2×#67—22no—
367C2×#67—22no—
368C2×#67—24no—
369C2×#67—22no—
370C2×#67—24no—
371C2×#67—24no—
372C2×#67—24no—
373C2×#67—24no—
374C2×#67—22no—
375C2×#67—24no—
376C2×#67—24no—
377C2×#67—24no—
378C2×#67—42no—
379C2×#67—42no—
380C2×#67C3×D418yescomplemented
381C22×Dic3—24no—
382C22×Dic3C3×D414yescomplemented
383C22×Dic3C23×C311yescharacteristic
384C22×Dic3C23×C311yescharacteristic
385C22×Dic3C23×C312yes—
386C22×Dic3C23×C311yescharacteristic
387C2×D12—24no—
388C2×D12—24no—
389C2×D12—42no—
390C3×C4⋊C4—62no—
391C3×C22⋊C4—28no—
392C3×C22⋊C4—24no—
393C3×C22⋊C4—24no—
394C3×C22⋊C4—24no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—64no—
397C3×C22⋊C4—62no—
398C3×C22⋊C4—64no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—64no—
401C3×C22⋊C4#6714yescomplemented
402C3×C22⋊C4C3×D414yescomplemented
403C3×C42—64no—
404#217—22no—
405#217—24no—
406#217C3×D414yescomplemented
407(C2×D3)⋊C4—24no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—24no—
410Dic3⋊C4—22no—
411C4×Dic3—24no—
412C22×C32—24no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—416no—
420C22×C32—42no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—41no—
425C22×C32—42no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—42no—
429C22×C32#12714yescomplemented
430C22×C32C22×D411yescharacteristic
431C22×C32C22×D412yes—
432C22×C32C22×D411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32H(5,𝔽2)12yes—
435C2×C3×D3—24no—
436C2×C3×D3—24no—
437C2×C3×D3—24no—
438C2×C3×D3—416no—
439C2×C3×D3—42no—
440C2×C3×D3—42no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—42no—
447C2×C3×D3—42no—
448C32×C4—24no—
449C32×C4—41no—
450C3×Dic3—22no—
451C3×Dic3—24no—
452C3×Dic3—41no—
453C3×Dic3#12014yescomplemented
454C25—31no—
455C25C2×C3×D311yescharacteristic
456C22×D4—32no—
457C22×D4—31no—
458C22×D4—31no—
459C22×D4—32no—
460C22×D4—32no—
461C22×D4—32no—
462C22×D4—32no—
463C22×D4—64no—
464C22×D4—68no—
465C22×D4C2×C3×D311yescharacteristic
466C22×D4C2×C3×D312yescomplemented
467C23×C4—31no—
468#127—68no—
469#121—64no—
470#120—24no—
471#120—64no—
472#120—64no—
473#120—64no—
474C2×C4⋊C4—31no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4—32no—
477C2×C22⋊C4—31no—
478C2×C22⋊C4—32no—
479C2×C22⋊C4—32no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4C2×C3×D311yescharacteristic
482C2×C22⋊C4C2×C3×D312yescomplemented
483C2×C42—32no—
484#95—32no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—24no—
490C23×C3—28no—
491C23×C3—24no—
492C23×C3—28no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—21no—
507C23×C3—22no—
508C23×C3—21no—
509C23×C3—22no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—22no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—22no—
516C23×C3—21no—
517C23×C3—24no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—34no—
522C23×C3—42no—
523C23×C3—42no—
524C23×C3—42no—
525C23×C3—42no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—41no—
529C23×C3—42no—
530C23×C3—41no—
531C23×C3—42no—
532C23×C3—48no—
533C23×C3—48no—
534C23×C3—48no—
535C23×C3—48no—
536C23×C3—48no—
537C23×C3—416no—
538C23×C3—44no—
539C23×C3—44no—
540C23×C3—48no—
541C23×C3—416no—
542C23×C3—48no—
543C23×C3—44no—
544C23×C3—44no—
545C23×C3—68no—
546C23×C3—62no—
547C23×C3—62no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—62no—
552C23×C3—61no—
553C23×C3—62no—
554C23×C3—61no—
555C23×C3—62no—
556C23×C3—61no—
557C23×C3—128no—
558C23×C3—128no—
559C23×C3—124no—
560C23×C3—124no—
561C23×C3D3×D414yes—
562C23×C3D3×D412yes—
563C23×C3D3×D412yes—
564C23×C3C2×#6712yes—
565C23×C3C2×C3×D414yes—
566C23×C3C2×C3×D412yes—
567C23×C3C2×C3×D412yes—
568C23×C3C2×C3×D412yes—
569C23×C3C23×D311yescharacteristic
570C23×C3C24×C311yescharacteristic
571C22×D3—28no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—22no—
581C22×D3—21no—
582C22×D3—22no—
583C22×D3—48no—
584C22×D3—48no—
585C22×D3—44no—
586C22×D3—44no—
587C22×D3C2×C3×D414yes—
588C3×D4—48no—
589C3×D4—48no—
590C3×D4—416no—
591C3×D4—48no—
592C3×D4—44no—
593C3×D4—44no—
594C3×D4—616no—
595C3×D4—616no—
596C3×D4—128no—
597C3×D4—124no—
598C3×D4—128no—
599C3×D4—128no—
600C3×D4—124no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—24no—
613C2×C3×C4—34no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—34no—
617C2×C3×C4—42no—
618C2×C3×C4—42no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—68no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4C2×#6714yescomplemented
629C2×C3×C4C2×C3×D414yescomplemented
630#67—216no—
631#67—216no—
632#67—48no—
633#67—48no—
634#67—44no—
635#67—44no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—28no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3C2×C3×D412yes—
644C2×Dic3C2×C3×D414yes—
645C2×Dic3C2×C3×D412yes—
646C2×Dic3C2×C3×D414yescomplemented
647D12—48no—
648C2×C32—24no—
649C2×C32—44no—
650C2×C32—81no—
651C2×C32C2×#12011yescharacteristic
652C2×C32C2×#12711yescharacteristic
653C2×C32#53511yescharacteristic
654C2×C32D4212yes—
655C2×C32D4212yes—
656C3×D3—44no—
657C3×D3—81no—
658C24—24no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—32no—
663C24—31no—
664C24—42no—
665C24—64no—
666C24—62no—
667C24—62no—
668C24—62no—
669C24—122no—
670C24C22×C3×D311yescharacteristic
671C24C22×C3×D312yes—
672C24C22×C3×D311yescharacteristic
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—24no—
678C2×D4—38no—
679C2×D4—42no—
680C2×D4—64no—
681C2×D4—64no—
682C2×D4—64no—
683C2×D4—64no—
684C2×D4—64no—
685C2×D4—64no—
686C2×D4—62no—
687C2×D4—64no—
688C2×D4—64no—
689C2×D4—632no—
690C2×D4—64no—
691C2×D4—64no—
692C2×D4—62no—
693C2×D4—62no—
694C2×D4—64no—
695C2×D4—62no—
696C2×D4—64no—
697C2×D4—122no—
698C2×D4—122no—
699C2×D4—122no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—32no—
703C22×C4—34no—
704C22×C4—31no—
705C22×C4—64no—
706C22×C4C22×C3×D311yescharacteristic
707C22×C4C22×C3×D312yes—
708C4⋊C4—62no—
709C22⋊C4—24no—
710C22⋊C4—34no—
711C22⋊C4—64no—
712C22⋊C4—62no—
713C22⋊C4—64no—
714C22⋊C4—62no—
715C22⋊C4—64no—
716C22⋊C4C3×#6714yescomplemented
717C42—64no—
718C22×C3—24no—
719C22×C3—22no—
720C22×C3—24no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—24no—
725C22×C3—24no—
726C22×C3—28no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—24no—
730C22×C3—24no—
731C22×C3—24no—
732C22×C3—24no—
733C22×C3—24no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—22no—
738C22×C3—21no—
739C22×C3—44no—
740C22×C3—42no—
741C22×C3—44no—
742C22×C3—42no—
743C22×C3—44no—
744C22×C3—44no—
745C22×C3—416no—
746C22×C3—416no—
747C22×C3—44no—
748C22×C3—44no—
749C22×C3—44no—
750C22×C3—44no—
751C22×C3—44no—
752C22×C3—42no—
753C22×C3—432no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—42no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—64no—
773C22×C3—64no—
774C22×C3—64no—
775C22×C3—81no—
776C22×C3—82no—
777C22×C3—81no—
778C22×C3—1216no—
779C22×C3—122no—
780C22×C3—122no—
781C22×C3—122no—
782C22×C3—122no—
783C22×C3—122no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3—122no—
787C22×C3—121no—
788C22×C3#94014yescomplemented
789C22×C3C3×#12714yescomplemented
790C22×C3C2×D3×D412yes—
791C22×C3C2×D3×D411yescharacteristic
792C22×C3C2×D3×D411yescharacteristic
793C22×C3#100412yes—
794C22×C3C22×#6711yescharacteristic
795C22×C3C22×C3×D411yescharacteristic
796C22×C3C22×C3×D412yes—
797C22×C3C22×C3×D411yescharacteristic
798C22×C3C22×C3×D411yescharacteristic
799C22×C3C3×H(5,𝔽2)12yes—
800C2×D3—24no—
801C2×D3—24no—
802C2×D3—24no—
803C2×D3—416no—
804C2×D3—42no—
805C2×D3—42no—
806C2×D3—42no—
807C2×D3—42no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—42no—
812C2×D3—42no—
813C3×C4—24no—
814C3×C4—24no—
815C3×C4—34no—
816C3×C4—44no—
817C3×C4—42no—
818C3×C4—41no—
819C3×C4—41no—
820C3×C4—62no—
821C3×C4—64no—
822C3×C4—121no—
823Dic3—22no—
824Dic3—24no—
825Dic3—41no—
826Dic3C3×#12014yescomplemented
827C32#243311yescharacteristic, complemented, Sylow
828C23—22no—
829C23—22no—
830C23—28no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—34no—
843C23—48no—
844C23—48no—
845C23—44no—
846C23—44no—
847C23—68no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—61no—
855C23—62no—
856C23—61no—
857C23—62no—
858C23—61no—
859C23—128no—
860C23—128no—
861C23—124no—
862C23—124no—
863C23C3×D3×D414yes—
864C23C3×D3×D412yes—
865C23C3×D3×D412yes—
866C23C2×C3×#6712yes—
867C23C23×C3×D311yescharacteristic
868D4—48no—
869D4—44no—
870D4—616no—
871D4—616no—
872D4—128no—
873D4—124no—
874D4—128no—
875D4—128no—
876D4—124no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—34no—
883C2×C4—32no—
884C2×C4—34no—
885C2×C4—32no—
886C2×C4—68no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4C2×C3×#6714yescomplemented
894C2×C3—24no—
895C2×C3—24no—
896C2×C3—22no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—22no—
900C2×C3—21no—
901C2×C3—44no—
902C2×C3—48no—
903C2×C3—44no—
904C2×C3—44no—
905C2×C3—82no—
906C2×C3—81no—
907C2×C3—81no—
908C2×C3—124no—
909C2×C3—241no—
910C2×C3D3×#12011yescharacteristic
911C2×C3#559012yes—
912C2×C3#559211yescharacteristic
913C2×C3D4×#6712yes—
914C2×C3C2×#94011yescharacteristic
915C2×C3C2×C3×#12011yescharacteristic
916C2×C3C2×C3×#12711yescharacteristic
917C2×C3C3×#53511yescharacteristic
918C2×C3C3×D4212yes—
919C2×C3C3×D4212yes—
920D3—44no—
921D3—81no—
922C22—24no—
923C22—22no—
924C22—24no—
925C22—22no—
926C22—24no—
927C22—24no—
928C22—24no—
929C22—416no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—41no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—64no—
940C22—64no—
941C22—64no—
942C22—1216no—
943C22—122no—
944C22—122no—
945C22—122no—
946C22—122no—
947C22—122no—
948C22—121no—
949C22—121no—
950C22—122no—
951C22—121no—
952C22C3×#94014yescomplemented
953C22C2×C3×D3×D412yes—
954C22C2×C3×D3×D411yescharacteristic
955C22C2×C3×D3×D411yescharacteristic
956C22C3×#100412yes—
957C22C22×C3×#6711yescharacteristic
958C4—24no—
959C4—34no—
960C4—41no—
961C4—62no—
962C4—64no—
963C4—121no—
964C3—21no—
965C3#8258811yescharacteristic, direct product factor
966C3C3×#243311yescharacteristic, complemented
967C2—24no—
968C2—44no—
969C2—81no—
970C2—124no—
971C2—241no—
972C2C3×D3×#12011yescharacteristic
973C2C3×#559012yes—
974C2C3×#559211yescharacteristic
975C2C3×D4×#6712yes—
976C2C2×C3×#94011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#120C2
socleC23×C32C24
hypercenterC2×C3×#120D3
hypocenterC3C3×#2433
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. C23×C3×#67C2semidirect
2. C2×C32×#120C2semidirect
3. C2×C3×#953C2semidirect
4. C2×C3×#940C2semidirect
5. C2×C3×#939C2semidirect
6. C2×C3×#937C2semidirect
7. C2×C3×#882C2semidirect
8. C3×#5223C2semidirect
9. C3×#4960C2semidirect
10. C3×#4957C2semidirect
11. C3×Dic3×C22⋊C4C2semidirect
13. #82588C3direct (N × H)
17. C22×C32×D4C22semidirect
23. C22×C3×#67C22semidirect
24. C22×C3×#67C22semidirect
25. C22×C3×#67C22semidirect
27. C22×C3×D12C22semidirect
30. C2×C32×C22⋊C4C22semidirect
33. C2×C3×#217C22semidirect
34. C2×C3×#217C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C2×C3×C4×Dic3C22semidirect
44. C3×C3⋊#95C22semidirect
46. C23×#67C2×C3semidirect
53. C2×C3×#120D3semidirect
54. C2×C3×#120C2×C3semidirect
55. C2×#953C2×C3semidirect
56. C2×#940C2×C3semidirect
57. C2×#939C2×C3semidirect
58. C2×#937C2×C3semidirect
59. C2×#882C2×C3semidirect
64. #5223C2×C3semidirect
65. #4960C2×C3semidirect
66. #4957C2×C3semidirect
67. Dic3×C22⋊C4C2×C3semidirect
108. C2×C3×#67D4semidirect
110. C22×C3×Dic3D4semidirect
119. C32×C22⋊C4D4semidirect
122. C3×#217D4semidirect
146. C22×C3×D4C2×D3semidirect
148. C22×C3×D4C22×C3semidirect
155. C22×#67C22×C3semidirect
156. C22×#67C22×C3semidirect
157. C22×#67C22×C3semidirect
159. C22×D12C22×C3semidirect
178. C2×C3×C22⋊C4C2×D3semidirect
180. C2×C3×C22⋊C4C22×C3semidirect
184. C2×#217C22×C3semidirect
185. C2×#217C22×C3semidirect
189. C2×(C2×D3)⋊C4C22×C3semidirect
190. C2×(C2×D3)⋊C4C22×C3semidirect
191. C2×(C2×D3)⋊C4C22×C3semidirect
192. C2×Dic3⋊C4C22×C3semidirect
193. C2×C4×Dic3C22×C3semidirect
196. C3⋊#95C22×C3semidirect
244. C2×C32×C4C2×D4semidirect
261. C2×C3×Dic3C2×D4semidirect
269. C2×#120C3×D3semidirect
380. C2×#67C3×D4semidirect
382. C22×Dic3C3×D4semidirect
401. C3×C22⋊C4#67semidirect
402. C3×C22⋊C4C3×D4semidirect
406. #217C3×D4semidirect
429. C22×C32#127semidirect
453. C3×Dic3#120semidirect
466. C22×D4C2×C3×D3semidirect
482. C2×C22⋊C4C2×C3×D3semidirect
628. C2×C3×C4C2×#67semidirect
629. C2×C3×C4C2×C3×D4semidirect
646. C2×Dic3C2×C3×D4semidirect
716. C22⋊C4C3×#67semidirect
788. C22×C3#940semidirect
789. C22×C3C3×#127semidirect
826. Dic3C3×#120semidirect
827. C32#2433semidirect
893. C2×C4C2×C3×#67semidirect
952. C22C3×#940semidirect
965. C3#82588direct (N × H)
966. C3C3×#2433semidirect

Maximal subgroups

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

subgroupindex
C23×C3×#672
C2×C32×#1202
C2×C3×#9532
C2×C3×#9402
C2×C3×#9392
C2×C3×#9372
C2×C3×#8822
C3×#52232
C3×#49602
C3×#49572
C3×Dic3×C22⋊C42
C3×#24333
#825883