Finite Group Databasebeta

← D3×#4655 #11801390

Subgroups — D3×#4655 #11801390

Order 1152.

1501 conjugacy classes of subgroups.

The subgroup lattice has 846 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
3C2×C4×D3×Dic3C211yesmaximal, characteristic
4#10592354C211yesmaximal, characteristic, complemented
5C3×D3×#95C211yesmaximal, characteristic
6C3×#4655C211yesmaximal, characteristic, complemented
7D3×C3⋊#95C211yesmaximal, characteristic
8D3×C3⋊#95C211yesmaximal, characteristic
9D3×C3⋊#95C211yesmaximal, characteristic
10#10591335C211yesmaximal, characteristic, complemented
11#10591333C211yesmaximal, characteristic, complemented
12#10591272C211yesmaximal, characteristic, complemented
13#10591263C211yesmaximal, characteristic, complemented
14#10591253C211yesmaximal, characteristic, complemented
15#10591249C211yesmaximal, characteristic, complemented
16D3×#387—31nomaximal
17C2×#4655—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×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37D3×C4⋊Dic3—24no—
38D3×Dic3⋊C4C418yescomplemented
39C4×D3×Dic3—24no—
40C32×#95C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C22×C4⋊Dic3—31no—
57C22×Dic3⋊C4—31no—
58C22×C4×Dic3—31no—
59C2×D3×C4⋊C4—31no—
60C2×D3×C4⋊C4—31no—
61C2×C42×D3—31no—
62C3×#387—31no—
63C2×C3×#95—31no—
64C2×C3⋊#95—31no—
65C2×C3⋊#95—31no—
66C2×C3⋊#95—31no—
67#4980—31no—
68#4978—31no—
69#4933—31no—
70D3×#95—31no—
71D3×#95—31no—
72D3×#95—31no—
73D3×#95D311yescharacteristic
74#4655—31no—
75#4655—31no—
76#4655—31no—
77#4655—31no—
78#4655—31no—
79#4655—31no—
80#4655—31no—
81#4655—31no—
82#4655—61no—
83#4655D311yescharacteristic, direct product factor
84#4654—31no—
85#4653—31no—
86#4652—31no—
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
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
101C22×C3×Dic3C2311yescharacteristic
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×D3C2×C414yes—
110C2×C3×C4×D3Q814yes—
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×Dic3C2×C414yes—
121C2×D3×Dic3C2×C414yes—
122C2×D3×Dic3D414yes—
123C4⋊(C3⋊Dic3)—22no—
124#3750C2×C414yescomplemented
125C4×C3⋊Dic3—22no—
126C3×C4⋊Dic3—22no—
127C3×Dic3⋊C4C2×C414yescomplemented
128C3×C4×Dic3—22no—
129#3724C2×C414yescomplemented
130Dic3⋊Dic3—22no—
131Dic3⋊Dic3—22no—
132Dic3⋊Dic3C2×C414yescomplemented
133Dic32—22no—
134Dic32—22no—
135C2×#387—91noSylow
136C23×C3×C4—31no—
137C23×C3×C4—31no—
138C23×C3×C4—31no—
139C23×Dic3—31no—
140C23×Dic3—31no—
141C23×Dic3—31no—
142C23×Dic3—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3C2×D311yescharacteristic
148C22×C4×D3C2×D311yescharacteristic
149C22×C4×D3C2×D311yescharacteristic
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C42—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—61no—
159C2×C4⋊Dic3—64no—
160C2×C4⋊Dic3C2×D311yescharacteristic
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—38no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—61no—
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—61no—
178C2×C4×Dic3—64no—
179C2×C4×Dic3C2×D311yescharacteristic
180D3×C4⋊C4—38no—
181D3×C4⋊C4—64no—
182C42×D3—64no—
183C3×#95—21no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95—31no—
190C3×#95C2×D311yescharacteristic
191C3×#95C2×D311yescharacteristic
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—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—61no—
211C3⋊#95—61no—
212C3⋊#95—61no—
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C23×C32C2411yescharacteristic
220C22×C3×D3C22×C412yes—
221C22×C3×D3C2×D412yes—
222C22×C3×D3C2×Q812yes—
223C22×C3×D3#4112yes—
224C22×C3×D3#4112yes—
225C22×C3×D3#4112yes—
226C22×C3×D3#4112yes—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4C22×C412yes—
235C2×C32×C4C2×Q812yes—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C22×C412yes—
246C2×C3⋊Dic3C22×C412yes—
247C2×C3⋊Dic3C2×D412yes—
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×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C2×D412yes—
268C2×C3×Dic3C2×Q812yes—
269C3×C4×D3—28no—
270C3×C4×D3—28no—
271C3×C4×D3—44no—
272D3×Dic3—28no—
273D3×Dic3—28no—
274D3×Dic3—28no—
275D3×Dic3—44no—
276C22×C4⋊C4—91no—
277C22×C4⋊C4—91no—
278C22×C42—91no—
279#387—31no—
280#387—91no—
281#387—91no—
282#387—91no—
283#387—91no—
284#387—91no—
285#387—91no—
286#387—91no—
287C2×#95—31no—
288C2×#95—91no—
289C2×#95—91no—
290C2×#95—91no—
291C24×C3—31no—
292C23×D3C22×D311yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—34no—
302C22×C3×C4—34no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—62no—
306C22×C3×C4—62no—
307C22×C3×C4—62no—
308C22×C3×C4—62no—
309C22×C3×C4—62no—
310C22×C3×C4—62no—
311C22×C3×C4—62no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—34no—
325C22×Dic3—34no—
326C22×Dic3—34no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—62no—
334C22×Dic3—62no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337C22×Dic3—62no—
338C22×Dic3—62no—
339C22×Dic3—62no—
340C22×Dic3—62no—
341C22×Dic3—62no—
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—22no—
354C2×C4×D3—22no—
355C2×C4×D3—22no—
356C2×C4×D3—34no—
357C2×C4×D3—34no—
358C2×C4×D3—34no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—62no—
367C2×C4×D3—62no—
368C2×C4×D3Dic614yes—
369C2×C4×D3C4×D314yes—
370C3×C4⋊C4—34no—
371C3×C4⋊C4—62no—
372C3×C42—62no—
373C4⋊Dic3—22no—
374C4⋊Dic3—34no—
375C4⋊Dic3—62no—
376C4⋊Dic3—62no—
377C4⋊Dic3—62no—
378C4⋊Dic3—62no—
379C4⋊Dic3—122no—
380Dic3⋊C4—34no—
381Dic3⋊C4—34no—
382Dic3⋊C4—34no—
383Dic3⋊C4—34no—
384Dic3⋊C4—34no—
385Dic3⋊C4—64no—
386Dic3⋊C4—62no—
387Dic3⋊C4—62no—
388Dic3⋊C4C4×D314yescomplemented
389C4×Dic3—22no—
390C4×Dic3—62no—
391C4×Dic3—62no—
392C4×Dic3—62no—
393C4×Dic3—62no—
394C4×Dic3—62no—
395C4×Dic3—62no—
396C4×Dic3—122no—
397C22×C32C23×C411yescharacteristic
398C22×C32C22×D411yescharacteristic
399C22×C32C22×Q811yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C2×C3×D3#11714yes—
405C2×C3×D3C4×D414yes—
406C2×C3×D3C4×Q814yes—
407C2×C3×D3C22⋊Q814yes—
408C2×C3×D3#12314yes—
409C2×C3×D3#12514yes—
410C2×C3×D3#12614yes—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—41no—
414C3⋊Dic3—22no—
415C3⋊Dic3—22no—
416C3⋊Dic3—22no—
417C3⋊Dic3—41no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—91no—
429C23×C4—91no—
430C23×C4—91no—
431C23×C4—91no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—98no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4—91no—
440C2×C4⋊C4—91no—
441C2×C4⋊C4—184no—
442C2×C42—31no—
443C2×C42—91no—
444C2×C42—91no—
445C2×C42—91no—
446C2×C42—184no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—31no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95D3211yescharacteristic
463C23×C3—21no—
464C23×C3—32no—
465C23×C3—32no—
466C23×C3—32no—
467C23×C3—32no—
468C23×C3—32no—
469C23×C3—32no—
470C23×C3—32no—
471C23×C3C23×D311yescharacteristic
472C23×C3C23×D311yescharacteristic
473C22×D3C2×Dic612yes—
474C22×D3C2×C4×D312yes—
475C22×D3#23512yes—
476C22×D3D3×D412yes—
477C22×D3#23712yes—
478C22×D3#23712yes—
479C22×D3#23912yes—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—68no—
509C2×C3×C4—68no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—124no—
527C2×C3×C4C2×Dic612yes—
528C2×C3×C4C2×C4×D312yes—
529C2×C3×C4C2×C4×D312yes—
530C2×C3×C4D3×Q812yes—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—32no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—68no—
557C2×Dic3—68no—
558C2×Dic3—68no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3—121no—
580C2×Dic3—121no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—124no—
587C2×Dic3C2×Dic612yes—
588C2×Dic3C2×C4×D312yes—
589C2×Dic3C2×C4×D312yes—
590C2×Dic3C2×C4×D312yes—
591C2×Dic3D3×D412yes—
592C4×D3—28no—
593C4×D3—28no—
594C4×D3—44no—
595C4×D3—68no—
596C4×D3—68no—
597C4×D3—68no—
598C4×D3—124no—
599C2×C32C2×#11711yescharacteristic
600C2×C32C2×C4×D411yescharacteristic
601C2×C32C2×C4×Q811yescharacteristic
602C2×C32C2×C22⋊Q811yescharacteristic
603C2×C32C2×#12311yescharacteristic
604C2×C32C2×#12511yescharacteristic
605C2×C32C2×#12611yescharacteristic
606C3×D3#38718yescomplemented
607C24—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—34no—
614C22×C4—34no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—94no—
625C22×C4—94no—
626C22×C4—94no—
627C22×C4—91no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—182no—
632C22×C4—182no—
633C22×C4—182no—
634C22×C4—182no—
635C22×C4—182no—
636C22×C4—182no—
637C22×C4—182no—
638C22×C4—182no—
639C22×C4—182no—
640C22×C4C2×D3211yescharacteristic
641C22×C4C2×D3211yescharacteristic
642C22×C4C2×D3211yescharacteristic
643C4⋊C4—34no—
644C4⋊C4—62no—
645C4⋊C4—94no—
646C4⋊C4—94no—
647C4⋊C4—94no—
648C4⋊C4—182no—
649C4⋊C4—182no—
650C4⋊C4—182no—
651C42—62no—
652C42—182no—
653C42—182no—
654C42—182no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—34no—
663C22×C3—34no—
664C22×C3—34no—
665C22×C3—34no—
666C22×C3—34no—
667C22×C3—34no—
668C22×C3—34no—
669C22×C3C22×Dic611yescharacteristic
670C22×C3C22×C4×D311yescharacteristic
671C22×C3C22×C4×D311yescharacteristic
672C22×C3C2×#23511yescharacteristic
673C22×C3C2×D3×D411yescharacteristic
674C22×C3C2×D3×D411yescharacteristic
675C22×C3C2×#23711yescharacteristic
676C22×C3C2×#23711yescharacteristic
677C22×C3C2×D3×Q811yescharacteristic
678C22×C3C2×#23911yescharacteristic
679C22×C3D3×#4111yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C2×D3C4×Dic614yes—
684C2×D3#87814yes—
685C2×D3#87914yes—
686C2×D3#67⋊C414yes—
687C2×D3#89014yes—
688C2×D3#89214yes—
689C2×D3#89414yes—
690C3×C4—22no—
691C3×C4—22no—
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—42no—
695C3×C4—42no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—62no—
699C3×C4—62no—
700C3×C4—62no—
701C3×C4—62no—
702C3×C4—62no—
703C3×C4—81no—
704C3×C4—121no—
705C3×C4—121no—
706Dic3—22no—
707Dic3—22no—
708Dic3—22no—
709Dic3—22no—
710Dic3—22no—
711Dic3—41no—
712Dic3—41no—
713Dic3—62no—
714Dic3—62no—
715Dic3—62no—
716Dic3—62no—
717Dic3—62no—
718Dic3—62no—
719Dic3—122no—
720Dic3—122no—
721Dic3—122no—
722Dic3—121no—
723Dic3—121no—
724Dic3—241no—
725C32C2×#38711yescharacteristic, complemented, Sylow
726C23—32no—
727C23—32no—
728C23—32no—
729C23—32no—
730C23—32no—
731C23—32no—
732C23—32no—
733C23C22×D3211yescharacteristic
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—32no—
742C2×C4—32no—
743C2×C4—32no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—68no—
747C2×C4—68no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—92no—
765C2×C4—92no—
766C2×C4—92no—
767C2×C4—124no—
768C2×C4—188no—
769C2×C4—188no—
770C2×C4—188no—
771C2×C4—181no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—364no—
781C2×C4D3×Dic612yes—
782C2×C4C4×D3212yes—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—38no—
791C2×C3C2×C4×Dic611yescharacteristic
792C2×C3C2×#87811yescharacteristic
793C2×C3C2×#87911yescharacteristic
794C2×C3C2×#67⋊C411yescharacteristic
795C2×C3C2×#89011yescharacteristic
796C2×C3C2×#89211yescharacteristic
797C2×C3C2×#89411yescharacteristic
798C2×C3D3×#11711yescharacteristic
799C2×C3C4×D3×D411yescharacteristic
800C2×C3C4×D3×Q811yescharacteristic
801C2×C3D3×C22⋊Q811yescharacteristic
802C2×C3D3×#12311yescharacteristic
803C2×C3D3×#12511yescharacteristic
804C2×C3D3×#12611yescharacteristic
805D3#465518yesdirect product factor
806C22—34no—
807C22—34no—
808C22—34no—
809C22—34no—
810C22—34no—
811C22—34no—
812C22—34no—
813C22C2×D3×Dic611yescharacteristic
814C22C2×C4×D3211yescharacteristic
815C22D3×#23511yescharacteristic
816C22D32×D411yescharacteristic
817C22D3×#23711yescharacteristic
818C22D3×#23711yescharacteristic
819C22D3×#23911yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—62no—
824C4—62no—
825C4—62no—
826C4—62no—
827C4—62no—
828C4—121no—
829C4—121no—
830C4—182no—
831C4—182no—
832C4—182no—
833C4—361no—
834C3—21no—
835C3C2×#465511yescharacteristic, complemented
836C3D3×#38711yescharacteristic, complemented
837C2—38no—
838C2C4×D3×Dic611yescharacteristic
839C2D3×#87811yescharacteristic
840C2D3×#87911yescharacteristic
841C2D3×#67⋊C411yescharacteristic
842C2D3×#89011yescharacteristic
843C2D3×#89211yescharacteristic
844C2D3×#89411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32C2×#387
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #10592354C2semidirect
6. C3×#4655C2semidirect
10. #10591335C2semidirect
11. #10591333C2semidirect
12. #10591272C2semidirect
13. #10591263C2semidirect
14. #10591253C2semidirect
15. #10591249C2semidirect
38. D3×Dic3⋊C4C4semidirect
83. #4655D3direct (N × H)
124. #3750C2×C4semidirect
127. C3×Dic3⋊C4C2×C4semidirect
129. #3724C2×C4semidirect
132. Dic3⋊Dic3C2×C4semidirect
388. Dic3⋊C4C4×D3semidirect
606. C3×D3#387semidirect
725. C32C2×#387semidirect
805. D3#4655direct (N × H)
835. C3C2×#4655semidirect
836. C3D3×#387semidirect

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
C2×C4×D3×Dic32
#105923542
C3×D3×#952
C3×#46552
D3×C3⋊#952
#105913352
#105913332
#105912722
#105912632
#105912532
#105912492
D3×#3873
C2×#46553