Finite Group Databasebeta

← D3×#4993 #11808479

Subgroups — D3×#4993 #11808479

Order 1152.

1909 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×D3×(C2×D3)⋊C4C212yesmaximal
3C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×D3×Dic3⋊C4C212yesmaximal, complemented
5#10592692C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8#10591350C211yesmaximal, characteristic, complemented
9#10591324C211yesmaximal, characteristic, complemented
10#10591303C212yesmaximal, complemented
11#10591203C212yesmaximal, complemented
12C2×#4993—31nomaximal
13D3×#399—31nomaximal
14C23×D32C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic, complemented
20C2×#3752C2211yescharacteristic
21C2×#3752C2212yes—
22C2×#3750C2212yescomplemented
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
26C2×C3×Dic3⋊C4C2212yescomplemented
27C2×C3×Dic3⋊C4C2212yescomplemented
28C3×D3×C4⋊C4—24no—
29C2×#3724C2212yescomplemented
30C2×Dic3⋊Dic3C2212yescomplemented
31C2×#3722C2212yes—
32C2×#3722C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2212yes—
35D3×(C2×D3)⋊C4—24no—
36D3×(C2×D3)⋊C4—28no—
37D3×Dic3⋊C4—28no—
38#63658C2211yescharacteristic, complemented
39C3×C3⋊#95C2211yescharacteristic, complemented
40#63579C2212yescomplemented
41C22×C3×C4⋊C4—31no—
42C22×(C2×D3)⋊C4—32no—
43C22×(C2×D3)⋊C4—31no—
44C22×Dic3⋊C4—32no—
45C2×D3×C4⋊C4—32no—
46C2×D3×C4⋊C4D311yescharacteristic, complemented
47C2×D3×C22⋊C4—32no—
48C2×D3×C22⋊C4—31no—
49C3×#399—31no—
50C2×C3⋊#95—31no—
51#4993—31no—
52#4993—31no—
53#4993—32no—
54#4993—31no—
55#4993—32no—
56#4993—32no—
57#4993—31no—
58#4993—61no—
59#4993D311yescharacteristic, direct product factor
60#4949—31no—
61#4949—32no—
62#4677—31no—
63D3×#95—31no—
64C23×C3⋊D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C23×C3×D3C2311yescharacteristic
67C22×D32—24no—
68C22×D32—22no—
69C22×D32—24no—
70C22×D32—22no—
71C22×D32Q814yes—
72C22×C32×C4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3—24no—
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3D414yes—
85C2×D3×Dic3—24no—
86C2×D3×Dic3—24no—
87C2×D3×Dic3—24no—
88C2×D3×Dic3—22no—
89C2×D3×Dic3D418yes—
90C32×C4⋊C4—22no—
91#3752—22no—
92#3752—24no—
93#3750—24no—
94C3×(C2×D3)⋊C4—22no—
95C3×(C2×D3)⋊C4—24no—
96C3×C4⋊Dic3—22no—
97C3×Dic3⋊C4—24no—
98C3×Dic3⋊C4—24no—
99#3724—24no—
100Dic3⋊Dic3—24no—
101#3722—24no—
102#3722—22no—
103(C2×D3)⋊Dic3—24no—
104(C2×D3)⋊Dic3—22no—
105C2×#399—91noSylow
106C24×D3—31no—
107C24×D3—31no—
108C23×C3×C4—31no—
109C23×C3×C4—32no—
110C23×Dic3—32no—
111C23×Dic3—31no—
112C22×C4×D3—32no—
113C22×C4×D3—31no—
114C22×C4×D3C2×D312yes—
115C22×C4×D3C2×D311yescharacteristic
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—32no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—64no—
121C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
122C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—31no—
125C2×#217—32no—
126C2×#217—31no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—31no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—62no—
138C2×(C2×D3)⋊C4—61no—
139C2×(C2×D3)⋊C4—68no—
140C2×(C2×D3)⋊C4—64no—
141C2×(C2×D3)⋊C4C2×D311yescharacteristic
142C2×(C2×D3)⋊C4C2×D312yes—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3C2×D311yescharacteristic, complemented
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4—32no—
148C2×Dic3⋊C4—32no—
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—62no—
151C2×Dic3⋊C4—68no—
152C2×Dic3⋊C4C2×D312yescomplemented
153C2×Dic3⋊C4C2×D312yescomplemented
154D3×C4⋊C4—24no—
155D3×C4⋊C4—68no—
156D3×C22⋊C4—68no—
157D3×C22⋊C4—64no—
158C3×#95—31no—
159C3⋊#95—31no—
160C3⋊#95—31no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—61no—
164C3⋊#95C2×D311yescharacteristic, complemented
165C23×C32C2411yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3C2×Q812yes—
171C22×C3×D3—22no—
172C22×C3×D3—21no—
173C22×C3×D3—22no—
174C22×C3×D3—21no—
175C22×C3×D3C2×D414yes—
176C22×C3×D3C2×D412yes—
177C22×C3×D3C2×Q812yes—
178C22×C3×D3C2×Q812yes—
179C22×C3×D3#4114yes—
180C22×C3×D3#4112yes—
181C2×D32—216no—
182C2×D32—28no—
183C2×D32—48no—
184C2×D32—44no—
185C2×D32—44no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4C2×D412yes—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3C2×D414yes—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3C2×D414yes—
205C2×C3×Dic3C2×D412yes—
206C3×C4×D3—28no—
207C3×C4×D3—48no—
208D3×Dic3—216no—
209D3×Dic3—44no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—92no—
212C22×C22⋊C4—91no—
213C22×C22⋊C4—92no—
214#399—31no—
215#399—91no—
216#399—92no—
217#399—91no—
218#399—92no—
219#399—91no—
220C2×#95—91no—
221C24×C3—31no—
222C24×C3—31no—
223C23×D3—31no—
224C23×D3—31no—
225C23×D3—34no—
226C23×D3—34no—
227C23×D3—61no—
228C23×D3—64no—
229C23×D3—62no—
230C23×D3—62no—
231C23×D3—64no—
232C23×D3—64no—
233C23×D3—64no—
234C23×D3—62no—
235C23×D3—62no—
236C23×D3C22×D311yescharacteristic
237C23×D3C22×D311yescharacteristic
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—34no—
243C22×C3×C4—32no—
244C22×C3×C4—31no—
245C22×C3×C4—64no—
246C22×C3×C4—64no—
247C22×C3×C4—64no—
248C22×C3×C4—64no—
249C22×C3×C4C22×D312yes—
250C22×C3×C4C22×D312yes—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—38no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—62no—
259C22×Dic3—61no—
260C22×Dic3—64no—
261C22×Dic3—64no—
262C22×Dic3—64no—
263C22×Dic3—62no—
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D312yes—
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D311yescharacteristic
268C2×C4×D3—24no—
269C2×C4×D3—24no—
270C2×C4×D3—24no—
271C2×C4×D3—24no—
272C2×C4×D3—38no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—62no—
277C2×C4×D3#6714yes—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—42no—
281C3×C4⋊C4—64no—
282C3×C4⋊C4—64no—
283C3×C4⋊C4—62no—
284C3×C22⋊C4—64no—
285C3×C22⋊C4—62no—
286#217—64no—
287#217—62no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—64no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—64no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—124no—
301(C2×D3)⋊C4—122no—
302C4⋊Dic3—22no—
303C4⋊Dic3—64no—
304Dic3⋊C4—24no—
305Dic3⋊C4—24no—
306Dic3⋊C4—64no—
307Dic3⋊C4—64no—
308Dic3⋊C4—64no—
309Dic3⋊C4—64no—
310Dic3⋊C4—64no—
311Dic3⋊C4—124no—
312C22×C32C22×D412yes—
313C22×C32C22×D411yescharacteristic
314C22×C32C22×Q811yescharacteristic
315C22×C32C2×#4112yes—
316C22×C32C2×#4111yescharacteristic
317C2×C3⋊D3—24no—
318C2×C3⋊D3—22no—
319C2×C3⋊D3—42no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3×D3—24no—
323C2×C3×D3—22no—
324C2×C3×D3—42no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3C22⋊Q818yes—
328C2×C3×D3C22⋊Q814yes—
329C2×C3×D3#12318yes—
330C2×C3×D3#12314yes—
331C2×C3×D3#12714yes—
332D32—416no—
333C32×C4—22no—
334C32×C4—42no—
335C3⋊Dic3—24no—
336C3⋊Dic3—41no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3—41no—
340C3×Dic3—42no—
341C25—91no—
342C23×C4—31no—
343C23×C4—32no—
344C23×C4—92no—
345C23×C4—91no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—32no—
349C2×C4⋊C4—64no—
350C2×C4⋊C4—92no—
351C2×C4⋊C4—92no—
352C2×C4⋊C4—92no—
353C2×C4⋊C4—188no—
354C2×C4⋊C4D3211yescharacteristic, complemented
355C2×C22⋊C4—32no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—92no—
358C2×C22⋊C4—91no—
359C2×C22⋊C4—91no—
360C2×C22⋊C4—92no—
361C2×C22⋊C4—92no—
362C2×C22⋊C4—91no—
363C2×C22⋊C4—184no—
364C2×C22⋊C4—188no—
365#95—31no—
366#95—92no—
367#95—91no—
368C23×C3—21no—
369C23×C3—34no—
370C23×C3—32no—
371C23×C3—32no—
372C23×C3—32no—
373C23×C3—34no—
374C23×C3—32no—
375C23×C3—62no—
376C23×C3—62no—
377C23×C3—61no—
378C23×C3—61no—
379C23×C3C23×D311yescharacteristic
380C23×C3C23×D311yescharacteristic
381C22×D3—22no—
382C22×D3—21no—
383C22×D3—22no—
384C22×D3—21no—
385C22×D3—32no—
386C22×D3—32no—
387C22×D3—62no—
388C22×D3—616no—
389C22×D3—68no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—62no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—616no—
399C22×D3—68no—
400C22×D3—122no—
401C22×D3—121no—
402C22×D3—122no—
403C22×D3—121no—
404C22×D3—128no—
405C22×D3—124no—
406C22×D3—124no—
407C22×D3—128no—
408C22×D3—124no—
409C22×D3—124no—
410C22×D3#23514yes—
411C22×D3D3×D414yes—
412C22×D3D3×Q812yes—
413C22×D3D3×Q812yes—
414C22×D3#23912yes—
415C22×D3C2×#6712yes—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—34no—
426C2×C3×C4—32no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—68no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—62no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4—61no—
440C2×C3×C4—128no—
441C2×C3×C4D3×D412yes—
442C2×C3×C4C2×#6712yes—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—21no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—34no—
452C2×Dic3—34no—
453C2×Dic3—64no—
454C2×Dic3—616no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—122no—
464C2×Dic3—122no—
465C2×Dic3—122no—
466C2×Dic3—121no—
467C2×Dic3—124no—
468C2×Dic3D3×D414yes—
469C2×Dic3C2×#6712yes—
470C4×D3—28no—
471C4×D3—48no—
472C4×D3—616no—
473C4×D3—124no—
474C2×C32C2×C22⋊Q812yes—
475C2×C32C2×C22⋊Q811yescharacteristic
476C2×C32C2×#12312yes—
477C2×C32C2×#12311yescharacteristic
478C2×C32C2×#12711yescharacteristic
479C3⋊D3—42no—
480C3×D3—42no—
481C3×D3#39918yescomplemented
482C24—31no—
483C24—31no—
484C24—94no—
485C24—91no—
486C24—184no—
487C24—182no—
488C24—184no—
489C24—182no—
490C22×C4—32no—
491C22×C4—31no—
492C22×C4—34no—
493C22×C4—31no—
494C22×C4—32no—
495C22×C4—64no—
496C22×C4—64no—
497C22×C4—64no—
498C22×C4—64no—
499C22×C4—98no—
500C22×C4—92no—
501C22×C4—91no—
502C22×C4—184no—
503C22×C4—184no—
504C22×C4—182no—
505C22×C4—184no—
506C22×C4C2×D3212yes—
507C22×C4C2×D3211yescharacteristic
508C4⋊C4—22no—
509C4⋊C4—64no—
510C4⋊C4—64no—
511C4⋊C4—62no—
512C4⋊C4—184no—
513C4⋊C4—184no—
514C4⋊C4—184no—
515C22⋊C4—64no—
516C22⋊C4—62no—
517C22⋊C4—184no—
518C22⋊C4—184no—
519C22⋊C4—182no—
520C22⋊C4—182no—
521C22⋊C4—184no—
522C22⋊C4—182no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—38no—
529C22×C3—34no—
530C22×C3—34no—
531C22×C3—38no—
532C22×C3—34no—
533C22×C3—64no—
534C22×C3—62no—
535C22×C3—122no—
536C22×C3—121no—
537C22×C3—121no—
538C22×C3C2×#23512yes—
539C22×C3C2×D3×D412yes—
540C22×C3C2×D3×D412yes—
541C22×C3C2×D3×D411yescharacteristic
542C22×C3C2×D3×Q811yescharacteristic
543C22×C3C2×D3×Q811yescharacteristic
544C22×C3C2×#23911yescharacteristic
545C22×C3D3×#4112yes—
546C22×C3D3×#4111yescharacteristic
547C22×C3C22×#6711yescharacteristic
548C2×D3—24no—
549C2×D3—22no—
550C2×D3—42no—
551C2×D3—41no—
552C2×D3—41no—
553C2×D3—64no—
554C2×D3—62no—
555C2×D3—64no—
556C2×D3—62no—
557C2×D3—124no—
558C2×D3—122no—
559C2×D3—1216no—
560C2×D3—122no—
561C2×D3—121no—
562C2×D3—121no—
563C2×D3—122no—
564C2×D3—121no—
565C2×D3—121no—
566C2×D3—1216no—
567C2×D3—242no—
568C2×D3—241no—
569C2×D3—241no—
570C2×D3#89418yes—
571C2×D3#89618yes—
572C2×D3#92914yes—
573C2×D3#94014yes—
574C2×D3#94614yes—
575C3×C4—22no—
576C3×C4—22no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—42no—
580C3×C4—62no—
581C3×C4—64no—
582C3×C4—82no—
583C3×C4—122no—
584C3×C4—121no—
585Dic3—24no—
586Dic3—22no—
587Dic3—41no—
588Dic3—42no—
589Dic3—64no—
590Dic3—64no—
591Dic3—124no—
592Dic3—121no—
593Dic3—121no—
594Dic3—241no—
595C32C2×#39911yescharacteristic, complemented, Sylow
596C23—34no—
597C23—34no—
598C23—32no—
599C23—32no—
600C23—32no—
601C23—32no—
602C23—62no—
603C23—62no—
604C23—61no—
605C23—61no—
606C23—92no—
607C23—1816no—
608C23—188no—
609C23—182no—
610C23—182no—
611C23—181no—
612C23—181no—
613C23—368no—
614C23—364no—
615C23—364no—
616C23C22×D3211yescharacteristic
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—34no—
622C2×C4—32no—
623C2×C4—68no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—61no—
631C2×C4—62no—
632C2×C4—94no—
633C2×C4—128no—
634C2×C4—1816no—
635C2×C4—182no—
636C2×C4—182no—
637C2×C4—182no—
638C2×C4—181no—
639C2×C4—364no—
640C2×C4D3×#6712yes—
641C2×C3—22no—
642C2×C3—22no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—38no—
647C2×C3—122no—
648C2×C3C2×#89412yes—
649C2×C3C2×#89612yes—
650C2×C3D3×C22⋊Q812yes—
651C2×C3D3×C22⋊Q811yescharacteristic
652C2×C3D3×#12312yes—
653C2×C3D3×#12311yescharacteristic
654C2×C3D3×#12711yescharacteristic
655C2×C3C2×#92911yescharacteristic
656C2×C3C2×#94011yescharacteristic
657C2×C3C2×#94611yescharacteristic
658D3—42no—
659D3—122no—
660D3—122no—
661D3—242no—
662D3#499318yesdirect product factor
663C22—38no—
664C22—38no—
665C22—34no—
666C22—34no—
667C22—34no—
668C22—64no—
669C22—62no—
670C22—122no—
671C22—121no—
672C22—121no—
673C22—184no—
674C22—182no—
675C22—3616no—
676C22—362no—
677C22—361no—
678C22—361no—
679C22D3×#23512yes—
680C22D32×D412yes—
681C22D32×Q811yescharacteristic
682C22D3×#23911yescharacteristic
683C22C2×D3×#6711yescharacteristic
684C4—22no—
685C4—42no—
686C4—64no—
687C4—62no—
688C4—122no—
689C4—121no—
690C4—184no—
691C4—361no—
692C3—21no—
693C3D3×#39911yescharacteristic, complemented
694C3C2×#499311yescharacteristic, complemented
695C2—38no—
696C2—122no—
697C2—362no—
698C2D3×#89412yes—
699C2D3×#89612yes—
700C2D3×#92911yescharacteristic
701C2D3×#94011yescharacteristic
702C2D3×#94611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
4. C2×D3×Dic3⋊C4C2semidirect
5. #10592692C2semidirect
6. C3×#4993C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591350C2semidirect
9. #10591324C2semidirect
10. #10591303C2semidirect
11. #10591203C2semidirect
19. C2×C32×C4⋊C4C22semidirect
22. C2×#3750C22semidirect
25. C2×C3×C4⋊Dic3C22semidirect
26. C2×C3×Dic3⋊C4C22semidirect
27. C2×C3×Dic3⋊C4C22semidirect
29. C2×#3724C22semidirect
30. C2×Dic3⋊Dic3C22semidirect
38. #63658C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
46. C2×D3×C4⋊C4D3semidirect
59. #4993D3direct (N × H)
121. C2×C3×C4⋊C4C2×D3semidirect
122. C2×C3×C4⋊C4C2×D3semidirect
144. C2×C4⋊Dic3C2×D3semidirect
152. C2×Dic3⋊C4C2×D3semidirect
153. C2×Dic3⋊C4C2×D3semidirect
164. C3⋊#95C2×D3semidirect
354. C2×C4⋊C4D32semidirect
481. C3×D3#399semidirect
595. C32C2×#399semidirect
662. D3#4993direct (N × H)
693. C3D3×#399semidirect
694. C3C2×#4993semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×D3×(C2×D3)⋊C42
C2×D3×Dic3⋊C42
#105926922
C3×#49932
D3×C3⋊#952
#105913502
#105913242
#105913032
#105912032
C2×#49933
D3×#3993