Finite Group Databasebeta

← C3×#82669 #11824419

Subgroups — C3×#82669 #11824419

Order 1152.

2109 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×C3×#940C212yesmaximal, complemented
3C2×C3×#940C211yesmaximal, characteristic, complemented
4C2×C3×#938C211yesmaximal, characteristic, complemented
5C2×C3×#930C211yesmaximal, characteristic, complemented
6C2×C3×C4×#67C211yesmaximal, characteristic, complemented
7C2×C3×#895C211yesmaximal, characteristic, complemented
8C3×#5223C212yesmaximal, complemented
9C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
10C3×#4960C212yesmaximal, complemented
11C3×#4957C212yesmaximal, complemented
12C3×#2541—31nomaximal
13#82669C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C22×C32×D4C2212yes—
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2212yes—
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2212yes—
24C22×C3×C4×D3C2211yescharacteristic
25C32×#121—24no—
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2212yes—
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2212yes—
30C3×#940—28no—
31C3×#940—24no—
32C3×#938—24no—
33C3×#930—24no—
34C3×C4×#67—24no—
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2212yes—
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×#895—24no—
43C3×C3⋊#95C2212yes—
44C2×C3×#127—31no—
45C2×C3×#127—32no—
46C2×C3×#121—21no—
47C2×C3×#121—31no—
48C2×C3×#121—31no—
49C2×C3×#121—31no—
50C2×C3×#121D311yescharacteristic, complemented
51C2×C3×#121C2×C311yescharacteristic, complemented
52C2×C3×C4×D4—31no—
53C2×#940C2×C312yescomplemented
54C2×#940C2×C311yescharacteristic, complemented
55C2×#938C2×C311yescharacteristic, complemented
56C2×#930C2×C311yescharacteristic, complemented
57C2×C4×#67C2×C311yescharacteristic, complemented
58C2×#895C2×C311yescharacteristic, complemented
59C3×#392—32no—
60C3×#392—32no—
61C3×#390—32no—
62C3×C4×C4⋊C4—31no—
63#5223C2×C312yescomplemented
64Dic3×C4⋊C4C2×C311yescharacteristic, complemented
65#4960C2×C312yescomplemented
66#4957C2×C312yescomplemented
67C24×C32C2312yes—
68C24×C32C2311yescharacteristic
69C23×C3×D3C2312yes—
70C23×C3×D3C2311yescharacteristic
71C2×C32×D4—24no—
72C2×C32×D4—24no—
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4—22no—
76C2×C32×D4—42no—
77C22×C32×C4—22no—
78C22×C32×C4—22no—
79C22×C32×C4—22no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2312yes—
82C22×C32×C4C2311yescharacteristic
83C2×C3×#67—24no—
84C2×C3×#67—24no—
85C2×C3×#67—22no—
86C2×C3×#67—24no—
87C2×C3×#67—24no—
88C2×C3×#67—24no—
89C2×C3×#67—24no—
90C2×C3×#67—24no—
91C2×C3×#67—22no—
92C2×C3×#67—24no—
93C2×C3×#67—42no—
94C2×C3×#67—42no—
95C2×C3×#67—42no—
96C2×C3×#67—42no—
97C2×C3×#67D414yescomplemented
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2312yes—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×D12—24no—
103C2×C3×D12—24no—
104C2×C3×D12—22no—
105C2×C3×D12—22no—
106C2×C3×D12—22no—
107C2×C3×D12—42no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C32×C4⋊C4D414yescomplemented
112C32×C22⋊C4—24no—
113C3×#217—22no—
114C3×#217—24no—
115C3×(C2×D3)⋊C4—24no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—24no—
118C3×C4⋊Dic3D414yescomplemented
119C3×Dic3⋊C4—22no—
120C3×C4×Dic3—24no—
121C3×C4×Dic3D414yescomplemented
122#2541—31noSylow
123C22×C3×D4—21no—
124C22×C3×D4—22no—
125C22×C3×D4—31no—
126C22×C3×D4—32no—
127C22×C3×D4—32no—
128C22×C3×D4—32no—
129C22×C3×D4—32no—
130C22×C3×D4—31no—
131C22×C3×D4—32no—
132C22×C3×D4C2×D311yescharacteristic
133C22×C3×D4C2×D312yes—
134C22×C3×D4C22×C311yescharacteristic
135C22×C3×D4C22×C312yes—
136C23×C3×C4—21no—
137C23×C3×C4—31no—
138C23×C3×C4C2×D311yescharacteristic
139C23×C3×C4C22×C311yescharacteristic
140C22×#67C22×C312yes—
141C22×#67C22×C312yes—
142C22×#67C22×C312yes—
143C22×#67C22×C311yescharacteristic
144C22×#67C22×C312yes—
145C22×D12C22×C311yescharacteristic
146C22×D12C22×C312yes—
147C22×C4×D3C22×C311yescharacteristic
148C3×#127—64no—
149C3×#127—68no—
150C3×#121—28no—
151C3×#121—24no—
152C3×#121—24no—
153C3×#121—64no—
154C3×#121—64no—
155C3×#121—64no—
156C3×C4×D4—64no—
157C2×C3×C4⋊C4—21no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4C2×D311yescharacteristic
161C2×C3×C4⋊C4C22×C311yescharacteristic
162C2×C3×C22⋊C4—22no—
163C2×C3×C22⋊C4—32no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—32no—
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4C2×D312yes—
169C2×C3×C22⋊C4C22×C312yes—
170C2×C3×C42—31no—
171C2×C3×C42—32no—
172C2×#217C22×C312yes—
173C2×#217C22×C311yescharacteristic
174#940—28no—
175#940—24no—
176#938—24no—
177#930—24no—
178C4×#67—24no—
179C2×(C2×D3)⋊C4C22×C312yes—
180C2×(C2×D3)⋊C4C22×C312yes—
181C2×(C2×D3)⋊C4C22×C311yescharacteristic
182C2×C4⋊Dic3C22×C311yescharacteristic
183C2×Dic3⋊C4C22×C311yescharacteristic
184C2×C4×Dic3C22×C312yes—
185C2×C4×Dic3C22×C311yescharacteristic
186#895—24no—
187C3×#95—32no—
188C3⋊#95C22×C312yes—
189C23×C32—21no—
190C23×C32—21no—
191C23×C32—22no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—22no—
200C23×C32—22no—
201C23×C32—22no—
202C23×C32C2×D412yes—
203C23×C32C2411yescharacteristic
204C22×C3×D3—21no—
205C22×C3×D3—21no—
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3C2×D412yes—
218C32×D4—48no—
219C32×D4—44no—
220C2×C32×C4—21no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—44no—
226C2×C32×C4C2×D412yes—
227C2×C32×C4C2×D412yes—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2×D412yes—
230C3×#67—28no—
231C3×#67—48no—
232C3×#67—48no—
233C3×#67—48no—
234C3×#67—48no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3C2×D412yes—
243C2×C3×Dic3C2×D414yes—
244C2×C3×Dic3C2×D412yes—
245C2×C3×Dic3C2×D412yes—
246C2×C3×Dic3#4112yes—
247C3×D12—48no—
248C3×D12—44no—
249C3×C4×D3—44no—
250C2×#127—31no—
251C2×#127—32no—
252C2×#121—31no—
253C2×#121—31no—
254C2×#121—31no—
255C2×#121C3×D311yescharacteristic, complemented
256C2×C4×D4—31no—
257#392—32no—
258#392—32no—
259#390—32no—
260C4×C4⋊C4—31no—
261C24×C3—21no—
262C24×C3—22no—
263C24×C3—31no—
264C24×C3—32no—
265C24×C3C22×D312yes—
266C24×C3C22×D311yescharacteristic
267C24×C3C23×C312yes—
268C24×C3C23×C311yescharacteristic
269C23×D3C23×C312yes—
270C23×D3C23×C311yescharacteristic
271C2×C3×D4—24no—
272C2×C3×D4—28no—
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—22no—
276C2×C3×D4—22no—
277C2×C3×D4—24no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—24no—
282C2×C3×D4—22no—
283C2×C3×D4—34no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—44no—
287C2×C3×D4—42no—
288C2×C3×D4—42no—
289C2×C3×D4—44no—
290C2×C3×D4—64no—
291C2×C3×D4—62no—
292C2×C3×D4—62no—
293C2×C3×D4—64no—
294C2×C3×D4—64no—
295C2×C3×D4—64no—
296C2×C3×D4—64no—
297C2×C3×D4—64no—
298C2×C3×D4—64no—
299C2×C3×D4—64no—
300C2×C3×D4—64no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C2×C3×D4—64no—
304C2×C3×D4—62no—
305C2×C3×D4—122no—
306C2×C3×D4—122no—
307C2×C3×D4—122no—
308C2×C3×D4—122no—
309C2×C3×D4—122no—
310C22×C3×C4—24no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—22no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—32no—
323C22×C3×C4—31no—
324C22×C3×C4—42no—
325C22×C3×C4—42no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D312yes—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C23×C311yescharacteristic
333C22×C3×C4C23×C312yes—
334C22×C3×C4C23×C311yescharacteristic
335C2×#67—24no—
336C2×#67—24no—
337C2×#67—22no—
338C2×#67—24no—
339C2×#67—24no—
340C2×#67—24no—
341C2×#67—24no—
342C2×#67—24no—
343C2×#67—22no—
344C2×#67—24no—
345C2×#67—42no—
346C2×#67—42no—
347C2×#67—42no—
348C2×#67—42no—
349C2×#67C3×D414yescomplemented
350C22×Dic3C23×C311yescharacteristic
351C22×Dic3C23×C311yescharacteristic
352C22×Dic3C23×C312yes—
353C22×Dic3C23×C311yescharacteristic
354C2×D12—24no—
355C2×D12—24no—
356C2×D12—22no—
357C2×D12—22no—
358C2×D12—22no—
359C2×D12—42no—
360C2×C4×D3—22no—
361C2×C4×D3—22no—
362C2×C4×D3—22no—
363C3×C4⋊C4—24no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4—62no—
366C3×C4⋊C4#6714yescomplemented
367C3×C4⋊C4C3×D414yescomplemented
368C3×C22⋊C4—28no—
369C3×C22⋊C4—24no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—62no—
372C3×C22⋊C4—64no—
373C3×C22⋊C4—62no—
374C3×C22⋊C4—64no—
375C3×C22⋊C4—64no—
376C3×C42—34no—
377C3×C42—64no—
378#217—22no—
379#217—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—24no—
383C4⋊Dic3C3×D414yescomplemented
384Dic3⋊C4—22no—
385C4×Dic3—24no—
386C4×Dic3C3×D414yescomplemented
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—42no—
395C22×C32—42no—
396C22×C32—42no—
397C22×C32—42no—
398C22×C32—42no—
399C22×C32—42no—
400C22×C32—42no—
401C22×C32C22×D411yescharacteristic
402C22×C32C22×D411yescharacteristic
403C22×C32C22×D411yescharacteristic
404C22×C32C22×D411yescharacteristic
405C22×C32C2×#4111yescharacteristic
406C22×C32H(5,𝔽2)11yescharacteristic
407C22×C32H(5,𝔽2)11yescharacteristic
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—42no—
416C2×C3×D3—42no—
417C2×C3×D3—42no—
418C2×C3×D3—42no—
419C2×C3×D3—42no—
420C2×C3×D3—42no—
421C2×C3×D3—42no—
422C32×C4—24no—
423C32×C4—41no—
424C32×C4#12714yescomplemented
425C3×Dic3—22no—
426C3×Dic3—24no—
427C3×Dic3—41no—
428C3×Dic3#12114yescomplemented
429C22×D4—31no—
430C22×D4—32no—
431C22×D4—32no—
432C22×D4—32no—
433C22×D4—32no—
434C22×D4—31no—
435C22×D4—32no—
436C22×D4C2×C3×D311yescharacteristic
437C22×D4C2×C3×D312yes—
438C23×C4—31no—
439C23×C4C2×C3×D311yescharacteristic
440#127—64no—
441#127—68no—
442#121—24no—
443#121—64no—
444#121—64no—
445#121—64no—
446C4×D4—64no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4C2×C3×D311yescharacteristic
450C2×C22⋊C4—31no—
451C2×C22⋊C4—32no—
452C2×C22⋊C4—31no—
453C2×C22⋊C4—32no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4C2×C3×D312yes—
456C2×C42—31no—
457C2×C42—32no—
458#95—32no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—24no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—21no—
489C23×C3—22no—
490C23×C3—32no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—42no—
496C23×C3—42no—
497C23×C3—42no—
498C23×C3—42no—
499C23×C3—42no—
500C23×C3—42no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—62no—
508C23×C3—62no—
509C23×C3—62no—
510C23×C3—62no—
511C23×C3—62no—
512C23×C3—62no—
513C23×C3—62no—
514C23×C3D3×D412yes—
515C23×C3C2×C3×D412yes—
516C23×C3C23×D311yescharacteristic
517C23×C3C24×C311yescharacteristic
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3C2×C3×D412yes—
532C3×D4—48no—
533C3×D4—48no—
534C3×D4—48no—
535C3×D4—416no—
536C3×D4—44no—
537C3×D4—44no—
538C3×D4—68no—
539C3×D4—128no—
540C3×D4—128no—
541C3×D4—128no—
542C3×D4—128no—
543C3×D4—128no—
544C3×D4—124no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—24no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—34no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—42no—
568C2×C3×C4—42no—
569C2×C3×C4—48no—
570C2×C3×C4—44no—
571C2×C3×C4—44no—
572C2×C3×C4—62no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—62no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—124no—
580C2×C3×C4D3×D412yes—
581C2×C3×C4D3×D412yes—
582C2×C3×C4C2×#6714yes—
583C2×C3×C4C2×#6712yes—
584C2×C3×C4C2×C3×D412yes—
585C2×C3×C4C2×C3×D412yes—
586C2×C3×C4C2×C3×D414yes—
587C2×C3×C4C2×C3×D412yes—
588#67—28no—
589#67—48no—
590#67—48no—
591#67—48no—
592#67—48no—
593C2×Dic3—22no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—22no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3C2×C3×D412yes—
601C2×Dic3C2×C3×D414yes—
602C2×Dic3C2×C3×D412yes—
603C2×Dic3C2×C3×D412yes—
604C2×Dic3C3×#4112yes—
605D12—48no—
606D12—44no—
607C4×D3—44no—
608C2×C32—42no—
609C2×C32—82no—
610C2×C32C2×#12111yescharacteristic
611C2×C32C2×#12711yescharacteristic
612C2×C32#53511yescharacteristic
613C2×C32D4211yescharacteristic
614C2×C32D4211yescharacteristic
615C2×C32#55011yescharacteristic
616C2×C32#55011yescharacteristic
617C3×D3—42no—
618C3×D3—82no—
619C24—31no—
620C24—32no—
621C24C22×C3×D312yes—
622C24C22×C3×D311yescharacteristic
623C2×D4—24no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—24no—
627C2×D4—22no—
628C2×D4—34no—
629C2×D4—42no—
630C2×D4—64no—
631C2×D4—62no—
632C2×D4—62no—
633C2×D4—64no—
634C2×D4—64no—
635C2×D4—64no—
636C2×D4—64no—
637C2×D4—64no—
638C2×D4—64no—
639C2×D4—64no—
640C2×D4—64no—
641C2×D4—62no—
642C2×D4—62no—
643C2×D4—64no—
644C2×D4—62no—
645C2×D4—122no—
646C2×D4—122no—
647C2×D4—122no—
648C2×D4—122no—
649C2×D4—122no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—32no—
656C22×C4—31no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4C22×C3×D311yescharacteristic
661C22×C4C22×C3×D312yes—
662C22×C4C22×C3×D311yescharacteristic
663C4⋊C4—34no—
664C4⋊C4—62no—
665C4⋊C4C3×#6714yescomplemented
666C22⋊C4—24no—
667C22⋊C4—62no—
668C22⋊C4—64no—
669C22⋊C4—62no—
670C22⋊C4—64no—
671C22⋊C4—64no—
672C42—34no—
673C42—64no—
674C22×C3—24no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—44no—
695C22×C3—44no—
696C22×C3—44no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—82no—
723C22×C3—82no—
724C22×C3—82no—
725C22×C3—82no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—122no—
731C22×C3—122no—
732C22×C3—122no—
733C22×C3—122no—
734C22×C3—122no—
735C22×C3—122no—
736C22×C3—122no—
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C2×D3×D411yescharacteristic
739C22×C3C2×D3×D411yescharacteristic
740C22×C3#100411yescharacteristic
741C22×C3D3×#4111yescharacteristic
742C22×C3#100911yescharacteristic
743C22×C3C22×#6711yescharacteristic
744C22×C3C22×C3×D411yescharacteristic
745C22×C3C22×C3×D411yescharacteristic
746C22×C3C22×C3×D411yescharacteristic
747C22×C3C22×C3×D411yescharacteristic
748C22×C3C2×C3×#4111yescharacteristic
749C22×C3C3×H(5,𝔽2)11yescharacteristic
750C22×C3C3×H(5,𝔽2)11yescharacteristic
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—42no—
759C2×D3—42no—
760C2×D3—42no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C3×C4—24no—
766C3×C4—24no—
767C3×C4—24no—
768C3×C4—34no—
769C3×C4—44no—
770C3×C4—42no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—62no—
774C3×C4—64no—
775C3×C4—121no—
776C3×C4#94014yescomplemented
777C3×C4C3×#12714yescomplemented
778Dic3—22no—
779Dic3—24no—
780Dic3—41no—
781Dic3C3×#12114yescomplemented
782C32#254111yescharacteristic, complemented, Sylow
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—32no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23C3×D3×D412yes—
811C23C23×C3×D311yescharacteristic
812D4—48no—
813D4—44no—
814D4—68no—
815D4—128no—
816D4—128no—
817D4—128no—
818D4—128no—
819D4—128no—
820D4—124no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—34no—
831C2×C4—44no—
832C2×C4—62no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—62no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—124no—
840C2×C4C3×D3×D412yes—
841C2×C4C3×D3×D412yes—
842C2×C4C2×C3×#6714yes—
843C2×C4C2×C3×#6712yes—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—44no—
852C2×C3—42no—
853C2×C3—42no—
854C2×C3—84no—
855C2×C3—82no—
856C2×C3—82no—
857C2×C3—122no—
858C2×C3—242no—
859C2×C3#559911yescharacteristic
860C2×C3D3×#12111yescharacteristic
861C2×C3#560711yescharacteristic
862C2×C3#560911yescharacteristic
863C2×C3D4×#6711yescharacteristic
864C2×C3C2×#94011yescharacteristic
865C2×C3#583411yescharacteristic
866C2×C3C2×C3×#12111yescharacteristic
867C2×C3C2×C3×#12711yescharacteristic
868C2×C3C3×#53511yescharacteristic
869C2×C3C3×D4211yescharacteristic
870C2×C3C3×D4211yescharacteristic
871C2×C3C3×#55011yescharacteristic
872C2×C3C3×#55011yescharacteristic
873D3—42no—
874D3—82no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—122no—
897C22—122no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22C2×C3×D3×D411yescharacteristic
904C22C2×C3×D3×D411yescharacteristic
905C22C2×C3×D3×D411yescharacteristic
906C22C3×#100411yescharacteristic
907C22C3×D3×#4111yescharacteristic
908C22C3×#100911yescharacteristic
909C22C22×C3×#6711yescharacteristic
910C4—24no—
911C4—34no—
912C4—41no—
913C4—62no—
914C4—64no—
915C4—121no—
916C4C3×#94014yescomplemented
917C3—21no—
918C3#8266911yescharacteristic, direct product factor
919C3C3×#254111yescharacteristic, complemented
920C2—42no—
921C2—82no—
922C2—122no—
923C2—242no—
924C2C3×#559911yescharacteristic
925C2C3×D3×#12111yescharacteristic
926C2C3×#560711yescharacteristic
927C2C3×#560911yescharacteristic
928C2C3×D4×#6711yescharacteristic
929C2C2×C3×#94011yescharacteristic
930C2C3×#583411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C3×#2541
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#940C2semidirect
4. C2×C3×#938C2semidirect
5. C2×C3×#930C2semidirect
6. C2×C3×C4×#67C2semidirect
7. C2×C3×#895C2semidirect
8. C3×#5223C2semidirect
9. C3×Dic3×C4⋊C4C2semidirect
10. C3×#4960C2semidirect
11. C3×#4957C2semidirect
13. #82669C3direct (N × H)
50. C2×C3×#121D3semidirect
51. C2×C3×#121C2×C3semidirect
53. C2×#940C2×C3semidirect
54. C2×#940C2×C3semidirect
55. C2×#938C2×C3semidirect
56. C2×#930C2×C3semidirect
57. C2×C4×#67C2×C3semidirect
58. C2×#895C2×C3semidirect
63. #5223C2×C3semidirect
64. Dic3×C4⋊C4C2×C3semidirect
65. #4960C2×C3semidirect
66. #4957C2×C3semidirect
97. C2×C3×#67D4semidirect
111. C32×C4⋊C4D4semidirect
118. C3×C4⋊Dic3D4semidirect
121. C3×C4×Dic3D4semidirect
255. C2×#121C3×D3semidirect
349. C2×#67C3×D4semidirect
366. C3×C4⋊C4#67semidirect
367. C3×C4⋊C4C3×D4semidirect
383. C4⋊Dic3C3×D4semidirect
386. C4×Dic3C3×D4semidirect
424. C32×C4#127semidirect
428. C3×Dic3#121semidirect
665. C4⋊C4C3×#67semidirect
776. C3×C4#940semidirect
777. C3×C4C3×#127semidirect
781. Dic3C3×#121semidirect
782. C32#2541semidirect
916. C4C3×#940semidirect
918. C3#82669direct (N × H)
919. C3C3×#2541semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×#9402
C2×C3×#9382
C2×C3×#9302
C2×C3×C4×#672
C2×C3×#8952
C3×#52232
C3×Dic3×C4⋊C42
C3×#49602
C3×#49572
C3×#25413
#826693