Finite Group Databasebeta

← D3×#4660 #11808513

Subgroups — D3×#4660 #11808513

Order 1152.

1275 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2C2×D3×Dic3⋊C4C211yesmaximal, characteristic
3#10592359C211yesmaximal, characteristic, complemented
4C3×D3×#95C211yesmaximal, characteristic
5C3×#4660C211yesmaximal, characteristic, complemented
6D3×C3⋊#95C211yesmaximal, characteristic
7D3×C3⋊#95C211yesmaximal, characteristic
8D3×C3⋊#95C211yesmaximal, characteristic
9D3×C3⋊#95C211yesmaximal, characteristic
10#10591343C211yesmaximal, characteristic, complemented
11#10591218C211yesmaximal, characteristic, complemented
12#10591211C211yesmaximal, characteristic, complemented
13#10591210C211yesmaximal, characteristic, complemented
14#10591207C211yesmaximal, characteristic, complemented
15#10591196C211yesmaximal, characteristic, complemented
16D3×#400—31nomaximal
17C2×#4660—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33D3×C4⋊Dic3—24no—
34D3×Dic3⋊C4—24no—
35C32×#95C2211yescharacteristic
36#63658C2211yescharacteristic
37#63658C2211yescharacteristic
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C22×C4⋊Dic3—31no—
56C22×Dic3⋊C4—31no—
57C2×D3×C4⋊C4—31no—
58C2×D3×C4⋊C4—31no—
59C3×#400—31no—
60C2×C3×#95—31no—
61C2×C3⋊#95—31no—
62C2×C3⋊#95—31no—
63C2×C3⋊#95—31no—
64C2×C3⋊#95—31no—
65#4986—31no—
66#4985—31no—
67D3×#95—31no—
68D3×#95—31no—
69D3×#95—31no—
70D3×#95—31no—
71D3×#95D311yescharacteristic
72#4660—31no—
73#4660—31no—
74#4660—31no—
75#4660—31no—
76#4660—31no—
77#4660—31no—
78#4660—31no—
79#4660—31no—
80#4660—31no—
81#4660—61no—
82#4660D311yescharacteristic, direct product factor
83#4659—31no—
84#4658—31no—
85#4658—31no—
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3Q814yes—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3D414yes—
122C4⋊(C3⋊Dic3)—22no—
123#3750—22no—
124C3×C4⋊Dic3—22no—
125C3×Dic3⋊C4—22no—
126#3724—22no—
127Dic3⋊Dic3—22no—
128Dic3⋊Dic3—22no—
129Dic3⋊Dic3—22no—
130C2×#400—91noSylow
131C23×C3×C4—31no—
132C23×C3×C4—31no—
133C23×C3×C4—31no—
134C23×Dic3—31no—
135C23×Dic3—31no—
136C23×Dic3—31no—
137C23×Dic3—31no—
138C22×C4×D3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×C4×D3—31no—
142C22×C4×D3C2×D311yescharacteristic
143C22×C4×D3C2×D311yescharacteristic
144C22×C4×D3C2×D311yescharacteristic
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—61no—
153C2×C4⋊Dic3—64no—
154C2×C4⋊Dic3C2×D311yescharacteristic
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—61no—
163C2×Dic3⋊C4—64no—
164C2×Dic3⋊C4C2×D311yescharacteristic
165D3×C4⋊C4—64no—
166D3×C4⋊C4—64no—
167C3×#95—21no—
168C3×#95—31no—
169C3×#95—31no—
170C3×#95—31no—
171C3×#95—31no—
172C3×#95—31no—
173C3×#95—31no—
174C3×#95—31no—
175C3×#95C2×D311yescharacteristic
176C3×#95C2×D311yescharacteristic
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—61no—
202C3⋊#95—61no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C23×C32C2411yescharacteristic
213C22×C3×D3C2×D412yes—
214C22×C3×D3C2×Q812yes—
215C22×C3×D3#4112yes—
216C22×C3×D3#4112yes—
217C22×C3×D3#4112yes—
218C22×C3×D3#4112yes—
219C22×C3×D3#4112yes—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4C2×Q812yes—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D412yes—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D412yes—
261C2×C3×Dic3C2×Q812yes—
262C3×C4×D3—28no—
263C3×C4×D3—44no—
264C3×C4×D3—44no—
265D3×Dic3—28no—
266D3×Dic3—44no—
267D3×Dic3—44no—
268D3×Dic3—44no—
269C22×C4⋊C4—91no—
270C22×C4⋊C4—91no—
271#400—31no—
272#400—91no—
273#400—91no—
274#400—91no—
275#400—91no—
276#400—91no—
277#400—91no—
278#400—91no—
279C2×#95—31no—
280C2×#95—91no—
281C2×#95—91no—
282C2×#95—91no—
283C2×#95—91no—
284C24×C3—31no—
285C23×D3C22×D311yescharacteristic
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—34no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—62no—
298C22×C3×C4—62no—
299C22×C3×C4—62no—
300C22×C3×C4—62no—
301C22×C3×C4—62no—
302C22×C3×C4—62no—
303C22×C3×C4—62no—
304C22×C3×C4—62no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—34no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—62no—
325C22×Dic3—62no—
326C22×Dic3—62no—
327C22×Dic3—62no—
328C22×Dic3—62no—
329C22×Dic3—62no—
330C22×Dic3—62no—
331C22×Dic3—62no—
332C22×Dic3—62no—
333C22×Dic3—62no—
334C22×Dic3—62no—
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C2×C4×D3—22no—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—22no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×C4×D3—22no—
349C2×C4×D3—22no—
350C2×C4×D3—34no—
351C2×C4×D3—62no—
352C2×C4×D3—62no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3Dic614yes—
363C3×C4⋊C4—62no—
364C3×C4⋊C4—62no—
365C4⋊Dic3—22no—
366C4⋊Dic3—62no—
367C4⋊Dic3—62no—
368C4⋊Dic3—62no—
369C4⋊Dic3—62no—
370C4⋊Dic3—62no—
371C4⋊Dic3—122no—
372Dic3⋊C4—22no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—122no—
381C22×C32C22×D411yescharacteristic
382C22×C32C22×Q811yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32C2×#4111yescharacteristic
387C22×C32C2×#4111yescharacteristic
388C2×C3×D3C22⋊Q814yes—
389C2×C3×D3#12314yes—
390C2×C3×D3#12414yes—
391C2×C3×D3#12514yes—
392C2×C3×D3#12514yes—
393C2×C3×D3#12614yes—
394C2×C3×D3#12614yes—
395C32×C4—22no—
396C32×C4—41no—
397C32×C4—41no—
398C3⋊Dic3—22no—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—91no—
413C23×C4—91no—
414C23×C4—91no—
415C23×C4—91no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—184no—
425C2×C4⋊C4—184no—
426#95—31no—
427#95—31no—
428#95—31no—
429#95—31no—
430#95—31no—
431#95—31no—
432#95—31no—
433#95—91no—
434#95—91no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95—91no—
445#95D3211yescharacteristic
446C23×C3—21no—
447C23×C3—32no—
448C23×C3—32no—
449C23×C3—32no—
450C23×C3—32no—
451C23×C3—32no—
452C23×C3—32no—
453C23×C3—32no—
454C23×C3C23×D311yescharacteristic
455C23×C3C23×D311yescharacteristic
456C22×D3C2×Dic612yes—
457C22×D3#23512yes—
458C22×D3#23512yes—
459C22×D3D3×D412yes—
460C22×D3#23712yes—
461C22×D3#23712yes—
462C22×D3#23912yes—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—68no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—124no—
511C2×C3×C4—124no—
512C2×C3×C4C2×Dic612yes—
513C2×C3×C4D3×Q812yes—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—62no—
536C2×Dic3—68no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—124no—
571C2×Dic3—124no—
572C2×Dic3—124no—
573C2×Dic3C2×Dic612yes—
574C2×Dic3D3×D412yes—
575C4×D3—28no—
576C4×D3—44no—
577C4×D3—44no—
578C4×D3—68no—
579C4×D3—124no—
580C4×D3—124no—
581C4×D3—124no—
582C2×C32C2×C22⋊Q811yescharacteristic
583C2×C32C2×#12311yescharacteristic
584C2×C32C2×#12411yescharacteristic
585C2×C32C2×#12511yescharacteristic
586C2×C32C2×#12511yescharacteristic
587C2×C32C2×#12611yescharacteristic
588C2×C32C2×#12611yescharacteristic
589C3×D3#40018yescomplemented
590C24—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—34no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—94no—
608C22×C4—91no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—91no—
612C22×C4—182no—
613C22×C4—182no—
614C22×C4—182no—
615C22×C4—182no—
616C22×C4—182no—
617C22×C4—182no—
618C22×C4—182no—
619C22×C4—182no—
620C22×C4—182no—
621C22×C4—182no—
622C22×C4—182no—
623C22×C4C2×D3211yescharacteristic
624C22×C4C2×D3211yescharacteristic
625C22×C4C2×D3211yescharacteristic
626C4⋊C4—62no—
627C4⋊C4—62no—
628C4⋊C4—182no—
629C4⋊C4—182no—
630C4⋊C4—182no—
631C4⋊C4—182no—
632C4⋊C4—182no—
633C4⋊C4—182no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—34no—
642C22×C3—34no—
643C22×C3—34no—
644C22×C3—34no—
645C22×C3—34no—
646C22×C3—34no—
647C22×C3—34no—
648C22×C3C22×Dic611yescharacteristic
649C22×C3C2×#23511yescharacteristic
650C22×C3C2×#23511yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×#23711yescharacteristic
654C22×C3C2×#23711yescharacteristic
655C22×C3C2×D3×Q811yescharacteristic
656C22×C3C2×#23911yescharacteristic
657C22×C3D3×#4111yescharacteristic
658C22×C3D3×#4111yescharacteristic
659C22×C3D3×#4111yescharacteristic
660C22×C3D3×#4111yescharacteristic
661C22×C3D3×#4111yescharacteristic
662C2×D3#87014yes—
663C2×D3#87814yes—
664C2×D3#87914yes—
665C2×D3#88514yes—
666C2×D3#89014yes—
667C2×D3#89414yes—
668C2×D3#89814yes—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—42no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—62no—
677C3×C4—62no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685Dic3—22no—
686Dic3—22no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—62no—
693Dic3—62no—
694Dic3—122no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—241no—
702Dic3—241no—
703Dic3—241no—
704C32C2×#40011yescharacteristic, complemented, Sylow
705C23—32no—
706C23—32no—
707C23—32no—
708C23—32no—
709C23—32no—
710C23—32no—
711C23—32no—
712C23C22×D3211yescharacteristic
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—68no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—92no—
744C2×C4—124no—
745C2×C4—124no—
746C2×C4—188no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—364no—
759C2×C4—364no—
760C2×C4—364no—
761C2×C4D3×Dic612yes—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—38no—
770C2×C3C2×#87011yescharacteristic
771C2×C3C2×#87811yescharacteristic
772C2×C3C2×#87911yescharacteristic
773C2×C3C2×#88511yescharacteristic
774C2×C3C2×#89011yescharacteristic
775C2×C3C2×#89411yescharacteristic
776C2×C3C2×#89811yescharacteristic
777C2×C3D3×C22⋊Q811yescharacteristic
778C2×C3D3×#12311yescharacteristic
779C2×C3D3×#12411yescharacteristic
780C2×C3D3×#12511yescharacteristic
781C2×C3D3×#12511yescharacteristic
782C2×C3D3×#12611yescharacteristic
783C2×C3D3×#12611yescharacteristic
784D3#466018yesdirect product factor
785C22—34no—
786C22—34no—
787C22—34no—
788C22—34no—
789C22—34no—
790C22—34no—
791C22—34no—
792C22C2×D3×Dic611yescharacteristic
793C22D3×#23511yescharacteristic
794C22D3×#23511yescharacteristic
795C22D32×D411yescharacteristic
796C22D3×#23711yescharacteristic
797C22D3×#23711yescharacteristic
798C22D3×#23911yescharacteristic
799C4—22no—
800C4—41no—
801C4—41no—
802C4—62no—
803C4—62no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4—182no—
810C4—361no—
811C4—361no—
812C4—361no—
813C3—21no—
814C3C2×#466011yescharacteristic, complemented
815C3D3×#40011yescharacteristic, complemented
816C2—38no—
817C2D3×#87011yescharacteristic
818C2D3×#87811yescharacteristic
819C2D3×#87911yescharacteristic
820C2D3×#88511yescharacteristic
821C2D3×#89011yescharacteristic
822C2D3×#89411yescharacteristic
823C2D3×#89811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32C2×#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #10592359C2semidirect
5. C3×#4660C2semidirect
10. #10591343C2semidirect
11. #10591218C2semidirect
12. #10591211C2semidirect
13. #10591210C2semidirect
14. #10591207C2semidirect
15. #10591196C2semidirect
82. #4660D3direct (N × H)
589. C3×D3#400semidirect
704. C32C2×#400semidirect
784. D3#4660direct (N × H)
814. C3C2×#4660semidirect
815. C3D3×#400semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C2×D3×Dic3⋊C42
#105923592
C3×D3×#952
C3×#46602
D3×C3⋊#952
#105913432
#105912182
#105912112
#105912102
#105912072
#105911962
D3×#4003
C2×#46603