Finite Group Databasebeta

← D3×#4928 #11801579

Subgroups — D3×#4928 #11801579

Order 1152.

1685 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C42×D3C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C2×D3×C4⋊Dic3C211yesmaximal, characteristic
4C2×D3×Dic3⋊C4C212yesmaximal
5#10592627C211yesmaximal, characteristic, complemented
6C3×#4928C211yesmaximal, characteristic, complemented
7D3×C3⋊#95C212yesmaximal
8#10591352C211yesmaximal, characteristic, complemented
9#10591330C212yesmaximal, complemented
10#10591327C212yesmaximal, complemented
11#10591212C211yesmaximal, characteristic, complemented
12C2×#4928—31nomaximal
13D3×#389—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C22×D3×Dic3C2212yes—
19C2×C32×C42C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×C42×D3—24no—
30C2×#3724C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34D3×C4⋊Dic3—24no—
35D3×C4⋊Dic3C418yescomplemented
36D3×Dic3⋊C4—28no—
37#63658C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41C22×C3×C42—31no—
42C22×C4⋊Dic3—31no—
43C22×C4⋊Dic3—31no—
44C22×Dic3⋊C4—32no—
45C2×D3×C4⋊C4—31no—
46C2×D3×C4⋊C4—32no—
47C2×D3×C4⋊C4—31no—
48C2×C42×D3D311yescharacteristic
49C3×#389—31no—
50C2×C3⋊#95—32no—
51#4984—31no—
52#4976—32no—
53#4972—31no—
54#4928—31no—
55#4928—31no—
56#4928—31no—
57#4928—31no—
58#4928—32no—
59#4928—32no—
60#4928—61no—
61#4928D311yescharacteristic, direct product factor
62D3×#95—32no—
63#4647—32no—
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3C2×C414yes—
80C2×C3×C4×D3D414yes—
81C2×C3×C4×D3D414yes—
82C2×C3×C4×D3Q814yes—
83C2×C3×C4×D3Q814yes—
84C2×D3×Dic3—24no—
85C2×D3×Dic3—24no—
86C2×D3×Dic3—24no—
87C2×D3×Dic3—24no—
88C2×D3×Dic3—24no—
89C2×D3×Dic3C2×C418yes—
90C32×C42—22no—
91C4⋊(C3⋊Dic3)—22no—
92C4⋊(C3⋊Dic3)C2×C414yescomplemented
93#3750—24no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3C2×C414yescomplemented
96C3×Dic3⋊C4—24no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3—22no—
100#3724—24no—
101Dic3⋊Dic3—24no—
102Dic3⋊Dic3—24no—
103Dic3⋊Dic3C2×C418yescomplemented
104C2×#389—91noSylow
105C23×C3×C4—31no—
106C23×C3×C4—31no—
107C23×C3×C4—31no—
108C23×Dic3—32no—
109C23×Dic3—32no—
110C22×C4×D3—32no—
111C22×C4×D3—32no—
112C22×C4×D3C2×D311yescharacteristic
113C22×C4×D3C2×D311yescharacteristic
114C22×C4×D3C2×D311yescharacteristic
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C42—21no—
119C2×C3×C42—31no—
120C2×C3×C42—31no—
121C2×C3×C42—31no—
122C2×C3×C42—64no—
123C2×C3×C42C2×D311yescharacteristic
124C2×C3×C42C2×D311yescharacteristic
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3—38no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3—64no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4—62no—
146C2×Dic3⋊C4—68no—
147C2×Dic3⋊C4C2×D312yes—
148C2×C4×Dic3C2×D311yescharacteristic
149C2×C4×Dic3C2×D311yescharacteristic
150C2×C4×Dic3C2×D311yescharacteristic
151D3×C4⋊C4—38no—
152D3×C4⋊C4—68no—
153D3×C4⋊C4—64no—
154C42×D3—24no—
155C3×#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95—62no—
163C3⋊#95C2×D312yes—
164C23×C32C2411yescharacteristic
165C22×C3×D3C22×C412yes—
166C22×C3×D3C2×D412yes—
167C22×C3×D3C2×D412yes—
168C22×C3×D3C2×Q812yes—
169C22×C3×D3C2×Q812yes—
170C22×C3×D3#4112yes—
171C22×C3×D3#4112yes—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×Q812yes—
180C2×C32×C4C2×Q812yes—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C22×C414yes—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3C22×C414yes—
197C2×C3×Dic3C22×C412yes—
198C2×C3×Dic3C2×D412yes—
199C2×C3×Dic3C2×D412yes—
200C2×C3×Dic3C2×Q812yes—
201C2×C3×Dic3C2×Q812yes—
202C3×C4×D3—28no—
203C3×C4×D3—28no—
204C3×C4×D3C4⋊C4116yescomplemented
205D3×Dic3—216no—
206D3×Dic3—48no—
207C22×C4⋊C4—91no—
208C22×C4⋊C4—92no—
209C22×C4⋊C4—91no—
210C22×C42—31no—
211#389—31no—
212#389—92no—
213#389—91no—
214#389—92no—
215#389—91no—
216#389—91no—
217C2×#95—92no—
218C24×C3—31no—
219C23×D3C22×D311yescharacteristic
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—31no—
224C22×C3×C4—34no—
225C22×C3×C4—34no—
226C22×C3×C4—34no—
227C22×C3×C4—31no—
228C22×C3×C4—32no—
229C22×C3×C4—31no—
230C22×C3×C4—34no—
231C22×C3×C4—34no—
232C22×C3×C4—32no—
233C22×C3×C4—62no—
234C22×C3×C4—62no—
235C22×C3×C4—62no—
236C22×C3×C4—62no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—38no—
246C22×Dic3—32no—
247C22×Dic3—32no—
248C22×Dic3—62no—
249C22×Dic3—62no—
250C22×Dic3—64no—
251C22×Dic3—64no—
252C22×Dic3—64no—
253C22×Dic3—64no—
254C22×Dic3—64no—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D311yescharacteristic
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D311yescharacteristic
259C22×Dic3C22×D311yescharacteristic
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3—38no—
265C2×C4×D3—64no—
266C2×C4×D3—64no—
267C2×C4×D3—64no—
268C2×C4×D3—64no—
269C2×C4×D3—64no—
270C2×C4×D3Dic614yes—
271C2×C4×D3Dic614yes—
272C2×C4×D3C4×D314yes—
273C2×C4×D3D1214yes—
274C2×C4×D3#6714yes—
275C3×C4⋊C4—34no—
276C3×C4⋊C4—64no—
277C3×C4⋊C4—62no—
278C3×C42—22no—
279C3×C42—22no—
280C3×C42—42no—
281C3×C42—62no—
282C3×C42—62no—
283C3×C42—62no—
284C4⋊Dic3—22no—
285C4⋊Dic3—34no—
286C4⋊Dic3—34no—
287C4⋊Dic3—38no—
288C4⋊Dic3—64no—
289C4⋊Dic3—64no—
290C4⋊Dic3—62no—
291C4⋊Dic3—62no—
292C4⋊Dic3—64no—
293C4⋊Dic3—122no—
294C4⋊Dic3C4×D314yescomplemented
295Dic3⋊C4—24no—
296Dic3⋊C4—38no—
297Dic3⋊C4—64no—
298Dic3⋊C4—64no—
299Dic3⋊C4—64no—
300Dic3⋊C4—64no—
301Dic3⋊C4—64no—
302Dic3⋊C4—64no—
303Dic3⋊C4—124no—
304C4×Dic3—22no—
305C4×Dic3—22no—
306C4×Dic3—22no—
307C22×C32C23×C411yescharacteristic
308C22×C32C22×D411yescharacteristic
309C22×C32C22×D411yescharacteristic
310C22×C32C22×Q811yescharacteristic
311C22×C32C22×Q811yescharacteristic
312C22×C32C2×#4111yescharacteristic
313C22×C32C2×#4111yescharacteristic
314C2×C3×D3C2×C4⋊C414yes—
315C2×C3×D3C4×D414yes—
316C2×C3×D3C4×Q814yes—
317C2×C3×D3#12114yes—
318C2×C3×D3C22⋊Q814yes—
319C2×C3×D3#12514yes—
320C2×C3×D3C4⋊Q814yes—
321C32×C4—22no—
322C32×C4—22no—
323C32×C4C2×C4⋊C414yescomplemented
324C3⋊Dic3—24no—
325C3⋊Dic3—42no—
326C3×Dic3—24no—
327C3×Dic3—22no—
328C3×Dic3—22no—
329C3×Dic3—42no—
330C3×Dic3C2×C4⋊C414yescomplemented
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—92no—
335C23×C4—92no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—32no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—98no—
340C2×C4⋊C4—92no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—92no—
343C2×C4⋊C4—92no—
344C2×C4⋊C4—92no—
345C2×C4⋊C4—92no—
346C2×C4⋊C4—91no—
347C2×C4⋊C4—188no—
348C2×C4⋊C4—184no—
349C2×C42—31no—
350C2×C42—31no—
351C2×C42—31no—
352C2×C42—64no—
353C2×C42D3211yescharacteristic
354#95—32no—
355#95—92no—
356#95—92no—
357#95—92no—
358C23×C3—21no—
359C23×C3—32no—
360C23×C3—32no—
361C23×C3—32no—
362C23×C3—32no—
363C23×C3—32no—
364C23×C3—32no—
365C23×C3—32no—
366C23×C3C23×D311yescharacteristic
367C23×C3C23×D311yescharacteristic
368C22×D3C2×Dic612yes—
369C22×D3C2×Dic612yes—
370C22×D3C2×C4×D312yes—
371C22×D3C2×D1212yes—
372C22×D3#23512yes—
373C22×D3#23512yes—
374C22×D3C2×#6712yes—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—32no—
389C2×C3×C4—32no—
390C2×C3×C4—32no—
391C2×C3×C4—316no—
392C2×C3×C4—34no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—68no—
400C2×C3×C4—68no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4C2×Dic612yes—
411C2×C3×C4C2×Dic612yes—
412C2×C3×C4C2×C4×D312yes—
413C2×C3×C4C2×C4×D312yes—
414C2×C3×C4C2×D1212yes—
415C2×C3×C4D3×D412yes—
416C2×C3×C4D3×D412yes—
417C2×C3×C4D3×Q812yes—
418C2×C3×C4D3×Q812yes—
419C2×C3×C4C2×#6712yes—
420C2×Dic3—21no—
421C2×Dic3—21no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—21no—
425C2×Dic3—21no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—34no—
430C2×Dic3—34no—
431C2×Dic3—64no—
432C2×Dic3—616no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—122no—
444C2×Dic3—122no—
445C2×Dic3—122no—
446C2×Dic3—122no—
447C2×Dic3—122no—
448C2×Dic3—128no—
449C2×Dic3C2×Dic612yes—
450C2×Dic3C2×Dic612yes—
451C2×Dic3C2×C4×D314yes—
452C2×Dic3C2×C4×D312yes—
453C2×Dic3C2×D1212yes—
454C2×Dic3C2×#6712yes—
455C4×D3—28no—
456C4×D3—28no—
457C4×D3—616no—
458C4×D3—128no—
459C4×D3Dic3⋊C4116yescomplemented
460C2×C32C22×C4⋊C411yescharacteristic
461C2×C32C2×C4×D411yescharacteristic
462C2×C32C2×C4×Q811yescharacteristic
463C2×C32C2×#12111yescharacteristic
464C2×C32C2×C22⋊Q811yescharacteristic
465C2×C32C2×#12511yescharacteristic
466C2×C32C2×C4⋊Q811yescharacteristic
467C3×D3#38918yescomplemented
468C24—31no—
469C22×C4—31no—
470C22×C4—34no—
471C22×C4—34no—
472C22×C4—34no—
473C22×C4—32no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—34no—
477C22×C4—34no—
478C22×C4—32no—
479C22×C4—62no—
480C22×C4—62no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—98no—
484C22×C4—92no—
485C22×C4—92no—
486C22×C4—184no—
487C22×C4—184no—
488C22×C4—184no—
489C22×C4—184no—
490C22×C4—184no—
491C22×C4C2×D3211yescharacteristic
492C22×C4C2×D3211yescharacteristic
493C22×C4C2×D3211yescharacteristic
494C4⋊C4—34no—
495C4⋊C4—64no—
496C4⋊C4—62no—
497C4⋊C4—98no—
498C4⋊C4—94no—
499C4⋊C4—184no—
500C4⋊C4—184no—
501C4⋊C4—184no—
502C4⋊C4—184no—
503C4⋊C4—182no—
504C42—22no—
505C42—62no—
506C42—62no—
507C42—62no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—34no—
516C22×C3—34no—
517C22×C3—34no—
518C22×C3—34no—
519C22×C3—34no—
520C22×C3—34no—
521C22×C3—34no—
522C22×C3C22×Dic611yescharacteristic
523C22×C3C22×Dic611yescharacteristic
524C22×C3C22×C4×D311yescharacteristic
525C22×C3C22×C4×D311yescharacteristic
526C22×C3C22×D1211yescharacteristic
527C22×C3C2×#23511yescharacteristic
528C22×C3C2×#23511yescharacteristic
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C2×D3×D411yescharacteristic
531C22×C3C2×D3×Q811yescharacteristic
532C22×C3C2×D3×Q811yescharacteristic
533C22×C3D3×#4111yescharacteristic
534C22×C3D3×#4111yescharacteristic
535C22×C3C22×#6711yescharacteristic
536C2×D3C4×Dic614yes—
537C2×D3#86914yes—
538C2×D3#87014yes—
539C2×D3C4×D1214yes—
540C2×D3C2×Dic3⋊C414yes—
541C2×D3#92414yes—
542C2×D3#93014yes—
543C3×C4—22no—
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—24no—
548C3×C4—34no—
549C3×C4—42no—
550C3×C4—42no—
551C3×C4—64no—
552C3×C4—62no—
553C3×C4—62no—
554C3×C4—122no—
555C3×C4D3×C4⋊C414yescomplemented
556C3×C4C2×Dic3⋊C414yescomplemented
557Dic3—22no—
558Dic3—22no—
559Dic3—24no—
560Dic3—42no—
561Dic3—64no—
562Dic3—64no—
563Dic3—124no—
564Dic3—122no—
565Dic3—122no—
566Dic3—242no—
567Dic3C2×Dic3⋊C414yescomplemented
568C32C2×#38911yescharacteristic, complemented, Sylow
569C23—32no—
570C23—32no—
571C23—32no—
572C23—32no—
573C23—32no—
574C23—32no—
575C23—32no—
576C23C22×D3211yescharacteristic
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—32no—
582C2×C4—32no—
583C2×C4—32no—
584C2×C4—316no—
585C2×C4—32no—
586C2×C4—34no—
587C2×C4—32no—
588C2×C4—68no—
589C2×C4—68no—
590C2×C4—62no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—62no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—94no—
600C2×C4—1816no—
601C2×C4—182no—
602C2×C4—182no—
603C2×C4—182no—
604C2×C4—182no—
605C2×C4—182no—
606C2×C4—368no—
607C2×C4D3×Dic612yes—
608C2×C4D3×Dic612yes—
609C2×C4C4×D3212yes—
610C2×C4D3×D1212yes—
611C2×C4D3×#6712yes—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—38no—
620C2×C3C2×C4×Dic611yescharacteristic
621C2×C3C2×#86911yescharacteristic
622C2×C3C2×#87011yescharacteristic
623C2×C3C2×C4×D1211yescharacteristic
624C2×C3C2×D3×C4⋊C411yescharacteristic
625C2×C3C4×D3×D411yescharacteristic
626C2×C3C4×D3×Q811yescharacteristic
627C2×C3D3×#12111yescharacteristic
628C2×C3D3×C22⋊Q811yescharacteristic
629C2×C3D3×#12511yescharacteristic
630C2×C3D3×C4⋊Q811yescharacteristic
631C2×C3C22×Dic3⋊C411yescharacteristic
632C2×C3C2×#92411yescharacteristic
633C2×C3C2×#93011yescharacteristic
634D3#492818yesdirect product factor
635C22—34no—
636C22—34no—
637C22—34no—
638C22—34no—
639C22—34no—
640C22—34no—
641C22—34no—
642C22C2×D3×Dic611yescharacteristic
643C22C2×D3×Dic611yescharacteristic
644C22C2×C4×D3211yescharacteristic
645C22C2×D3×D1211yescharacteristic
646C22D3×#23511yescharacteristic
647C22D3×#23511yescharacteristic
648C22C2×D3×#6711yescharacteristic
649C4—22no—
650C4—22no—
651C4—34no—
652C4—62no—
653C4—64no—
654C4—62no—
655C4—122no—
656C4—184no—
657C4—362no—
658C4D3×Dic3⋊C414yescomplemented
659C3—21no—
660C3D3×#38911yescharacteristic, complemented
661C3C2×#492811yescharacteristic, complemented
662C2—38no—
663C2C4×D3×Dic611yescharacteristic
664C2D3×#86911yescharacteristic
665C2D3×#87011yescharacteristic
666C2C4×D3×D1211yescharacteristic
667C2C2×D3×Dic3⋊C411yescharacteristic
668C2D3×#92411yescharacteristic
669C2D3×#93011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C2×#389
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
5. #10592627C2semidirect
6. C3×#4928C2semidirect
8. #10591352C2semidirect
9. #10591330C2semidirect
10. #10591327C2semidirect
11. #10591212C2semidirect
35. D3×C4⋊Dic3C4semidirect
61. #4928D3direct (N × H)
92. C4⋊(C3⋊Dic3)C2×C4semidirect
95. C3×C4⋊Dic3C2×C4semidirect
103. Dic3⋊Dic3C2×C4semidirect
204. C3×C4×D3C4⋊C4semidirect
294. C4⋊Dic3C4×D3semidirect
323. C32×C4C2×C4⋊C4semidirect
330. C3×Dic3C2×C4⋊C4semidirect
459. C4×D3Dic3⋊C4semidirect
467. C3×D3#389semidirect
555. C3×C4D3×C4⋊C4semidirect
556. C3×C4C2×Dic3⋊C4semidirect
567. Dic3C2×Dic3⋊C4semidirect
568. C32C2×#389semidirect
634. D3#4928direct (N × H)
658. C4D3×Dic3⋊C4semidirect
660. C3D3×#389semidirect
661. C3C2×#4928semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D32
C2×D3×C4⋊Dic32
C2×D3×Dic3⋊C42
#105926272
C3×#49282
D3×C3⋊#952
#105913522
#105913302
#105913272
#105912122
C2×#49283
D3×#3893