Finite Group Databasebeta

← D4×((C3⋊D3)⋊C3)⋊C4 #13151365

Subgroups — D4×((C3⋊D3)⋊C3)⋊C4 #13151365

Order 1728.

1585 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
2C22×((C3⋊D3)⋊C3)⋊C4C212yesmaximal, complemented
3D4×#1084C211yesmaximal, characteristic, complemented
4D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
5#11721315C212yesmaximal, complemented
6#11721314C212yesmaximal, complemented
7#11721310C212yesmaximal, complemented
8#11721136C211yesmaximal, characteristic, complemented
9#11721132C211yesmaximal, characteristic, complemented
10#11721129C211yesmaximal, characteristic, complemented
11C4×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
12D4×#624—31nomaximal
13D3×D4×Dic3—31nomaximal
14C23×(C3⋊D3)⋊C3C2212yes—
15C2×D4×H(3,𝔽3)C2211yescharacteristic
16C22×#1084C2212yescomplemented
17C2×#638⋊C3C2212yes—
18C22×(C3⋊Dic3)⋊C3C2212yescomplemented
19D4×(C3⋊D3)⋊C3C418yescomplemented
20C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×((C3⋊D3)⋊C3)⋊C4—28no—
23C2×((C3⋊D3)⋊C3)⋊C4C2212yes—
24C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
25C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
27C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
28#88552C2212yescomplemented
29C4⋊#1084C2211yescharacteristic, complemented
30C4×#1084C2211yescharacteristic, complemented
31#3757⋊C3C2212yescomplemented
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
33C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
34#88450C2212yescomplemented
35#88450C2212yescomplemented
36#88448C2212yescomplemented
37#88447C2211yescharacteristic, complemented
38#88447C2211yescharacteristic, complemented
39C2×D4×C3⋊D3D311yescharacteristic
40C2×C3×D3×D4—31no—
41C22×#624—32no—
42C22×D3×Dic3—32no—
43D4×C3⋊Dic3D311yescharacteristic, complemented
44C3×D4×Dic3—31no—
45C3×D4×Dic3—31no—
46C3×D4×Dic3—31no—
47C3×D4×Dic3—61no—
48#63974—32no—
49#67⋊Dic3—32no—
50Dic3×#67—32no—
51D3×#217—32no—
52#63952—32no—
53#63952—32no—
54#63900—31no—
55#63898—31no—
56#63894—31no—
57#63894—31no—
58Dic3×D12—31no—
59D3×C4⋊Dic3—31no—
60C4×#624—31no—
61C4×D3×Dic3—31no—
62C23×H(3,𝔽3)C2312yes—
63C22×(C3⋊D3)⋊C3—24no—
64C22×(C3⋊D3)⋊C3—24no—
65C22×(C3⋊D3)⋊C3C2×C418yescomplemented
66C22×(C3⋊D3)⋊C3C2312yes—
67C22×(C3⋊D3)⋊C3C2311yescharacteristic
68D4×H(3,𝔽3)C2×C414yescomplemented
69C2×C4×H(3,𝔽3)C2311yescharacteristic
70C2×#1084—24no—
71C2×#1084C2312yes—
72C2×#1084C2311yescharacteristic
73C2×#1084C2311yescharacteristic
74#638⋊C3C2×C418yescomplemented
75C2×(C3⋊Dic3)⋊C3—24no—
76C2×(C3⋊Dic3)⋊C3C2312yes—
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
80C4⋊((C3⋊D3)⋊C3)C2×C414yescomplemented
81C4×(C3⋊D3)⋊C3C2×C414yescomplemented
82((C3⋊D3)⋊C3)⋊C4—24no—
83((C3⋊D3)⋊C3)⋊C4—22no—
84((C3⋊D3)⋊C3)⋊C4—24no—
85((C3⋊D3)⋊C3)⋊C4—24no—
86((C3⋊D3)⋊C3)⋊C4D414yesdirect product factor
87C2×D4×Dic3—91no—
88C4×D3×D4—91no—
89C4×D3×D4—91no—
90C23×C3⋊D3C2×D312yes—
91C23×C3×D3—32no—
92C2×C32×D4—21no—
93C2×C32×D4C2×D311yescharacteristic
94C2×C32×D4C2×D311yescharacteristic
95C2×#638C2×D312yes—
96C22×C3⋊Dic3C2×D312yescomplemented
97D4×C3⋊D3Dic318yescomplemented
98C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
99C2×C4×C3⋊D3C2×D311yescharacteristic
100C2×C3×#67—32no—
101C22×C3×Dic3—32no—
102C22×C3×Dic3—32no—
103C22×C3×Dic3—32no—
104C22×C3×Dic3—62no—
105C3×D3×D4—38no—
106C2×C3×D12—31no—
107C2×C3×C4×D3—31no—
108C2×#624—31no—
109C2×#624—32no—
110C2×#624—32no—
111C2×#624—32no—
112C2×#624—31no—
113C2×#624—68no—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—32no—
116C2×D3×Dic3—32no—
117C2×D3×Dic3—32no—
118C2×D3×Dic3—31no—
119C2×D3×Dic3—68no—
120#3757C2×D312yescomplemented
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
122C4×C3⋊Dic3C2×D311yescharacteristic, complemented
123C3×#217—32no—
124C3×#217—32no—
125C3×#217—32no—
126C3×#217—62no—
127C3×C4⋊Dic3—31no—
128C3×C4⋊Dic3—31no—
129C3×C4⋊Dic3—31no—
130C3×C4⋊Dic3—61no—
131C3×C4×Dic3—31no—
132C3×C4×Dic3—31no—
133C3×C4×Dic3—31no—
134C3×C4×Dic3—61no—
135#3724—32no—
136Dic3⋊Dic3—32no—
137#3722—32no—
138#3722—32no—
139(C2×D3)⋊Dic3—32no—
140(C2×D3)⋊Dic3—32no—
141Dic32—31no—
142Dic32—31no—
143Dic32—31no—
144Dic32—31no—
145C22×H(3,𝔽3)—22no—
146C22×H(3,𝔽3)—22no—
147C22×H(3,𝔽3)C22×C414yescomplemented
148C22×H(3,𝔽3)C2411yescharacteristic
149C2×(C3⋊D3)⋊C3—22no—
150C2×(C3⋊D3)⋊C3—22no—
151C2×(C3⋊D3)⋊C3—216no—
152C2×(C3⋊D3)⋊C3C22×C412yes—
153C2×(C3⋊D3)⋊C3C22×C414yescomplemented
154C2×(C3⋊D3)⋊C3C2×D412yes—
155C2×(C3⋊D3)⋊C3#4112yes—
156C4×H(3,𝔽3)C22×C412yescomplemented
157#1084—22no—
158#1084—21no—
159#1084C2×D412yescomplemented
160(C3⋊Dic3)⋊C3—22no—
161(C3⋊Dic3)⋊C3—21no—
162(C3⋊Dic3)⋊C3C22×C412yescomplemented
163(C3⋊Dic3)⋊C3C2×D412yescomplemented
164C22×C3×D4—91no—
165C23×Dic3—92no—
166C2×D3×D4—31no—
167C2×D3×D4—91no—
168C22×C4×D3—92no—
169C22×C4×D3—92no—
170C3×C4×D4—91no—
171C3×C4×D4—91no—
172C2×#217—92no—
173D4×Dic3—31no—
174D4×Dic3—31no—
175D4×Dic3—31no—
176D4×Dic3—61no—
177D4×Dic3—91no—
178D4×Dic3—91no—
179D4×Dic3—91no—
180D4×Dic3—92no—
181D4×Dic3—92no—
182C4×#67—92no—
183C4×#67—92no—
184C2×C4⋊Dic3—91no—
185C2×C4×Dic3—91no—
186#893—91no—
187#893—91no—
188D3×C4⋊C4—91no—
189D3×C4⋊C4—91no—
190#67⋊C4—92no—
191#67⋊C4—92no—
192D3×C22⋊C4—92no—
193D3×C22⋊C4—92no—
194C4×D12—91no—
195C4×D12—91no—
196C42×D3—91no—
197C42×D3—91no—
198C23×C32—22no—
199C23×C32C22×D312yes—
200C23×C32C22×D312yes—
201C22×C3⋊D3—24no—
202C22×C3⋊D3—24no—
203C22×C3⋊D3C2×Dic318yescomplemented
204C22×C3⋊D3C22×D312yes—
205C22×C3⋊D3C22×D311yescharacteristic
206C22×C3×D3—31no—
207C22×C3×D3—38no—
208C22×C3×D3—32no—
209C22×C3×D3—64no—
210C22×C3×D3—64no—
211C32×D4—24no—
212C32×D4C4×D314yescomplemented
213C32×D4C2×Dic314yescomplemented
214C2×C32×C4—21no—
215C2×C32×C4C22×D311yescharacteristic
216C2×C32×C4C22×D311yescharacteristic
217#638C2×Dic318yescomplemented
218C2×C3⋊Dic3—24no—
219C2×C3⋊Dic3C22×D311yescharacteristic
220C2×C3⋊Dic3C22×D312yes—
221C2×C3⋊Dic3C22×D311yescharacteristic
222C2×C3⋊Dic3C22×D311yescharacteristic
223C4⋊(C3⋊D3)C2×Dic314yescomplemented
224C4×C3⋊D3C2×Dic314yescomplemented
225C3×#67—38no—
226C2×C3×Dic3—31no—
227C2×C3×Dic3—31no—
228C2×C3×Dic3—31no—
229C2×C3×Dic3—31no—
230C2×C3×Dic3—31no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—31no—
233C2×C3×Dic3—31no—
234C2×C3×Dic3—32no—
235C2×C3×Dic3—32no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—62no—
239C2×C3×Dic3—64no—
240C2×C3×Dic3—64no—
241C2×C3×Dic3—64no—
242C2×C3×Dic3—124no—
243C3×D12—34no—
244C3×C4×D3—34no—
245#624—34no—
246#624—64no—
247#624—64no—
248#624—64no—
249#624—62no—
250D3×Dic3—34no—
251D3×Dic3—64no—
252D3×Dic3—62no—
253D3×Dic3—64no—
254D3×Dic3—64no—
255C2×C4×D4—271noSylow
256C2×H(3,𝔽3)—24no—
257C2×H(3,𝔽3)C23×C411yescharacteristic
258C2×H(3,𝔽3)C22×D411yescharacteristic
259C2×H(3,𝔽3)C2×#4111yescharacteristic
260(C3⋊D3)⋊C3—24no—
261(C3⋊D3)⋊C3C4×D414yescomplemented
262C24×C3—92no—
263C23×D3—32no—
264C23×D3—92no—
265C2×C3×D4—31no—
266C2×C3×D4—31no—
267C2×C3×D4—61no—
268C2×C3×D4—91no—
269C2×C3×D4—98no—
270C2×C3×D4—92no—
271C2×C3×D4D3211yescharacteristic
272C22×C3×C4—91no—
273C22×C3×C4—92no—
274C22×C3×C4—92no—
275C2×#67—32no—
276C2×#67—92no—
277C22×Dic3—32no—
278C22×Dic3—32no—
279C22×Dic3—32no—
280C22×Dic3—62no—
281C22×Dic3—92no—
282C22×Dic3—91no—
283C22×Dic3—91no—
284C22×Dic3—92no—
285C22×Dic3—92no—
286C22×Dic3—92no—
287C22×Dic3—188no—
288D3×D4—38no—
289D3×D4—98no—
290C2×D12—31no—
291C2×D12—91no—
292C2×C4×D3—31no—
293C2×C4×D3—91no—
294C2×C4×D3—91no—
295C2×C4×D3—91no—
296C2×C4×D3—91no—
297C2×C4×D3—92no—
298C2×C4×D3—92no—
299C2×C4×D3—92no—
300C2×C4×D3—91no—
301C2×C4×D3—92no—
302C2×C4×D3—92no—
303C2×C4×D3—92no—
304C2×C4×D3—188no—
305C2×C4×D3—188no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4—91no—
308C3×C22⋊C4—92no—
309C3×C22⋊C4—92no—
310C3×C42—91no—
311C3×C42—91no—
312#217—32no—
313#217—32no—
314#217—32no—
315#217—62no—
316#217—92no—
317#217—92no—
318#217—92no—
319(C2×D3)⋊C4—92no—
320(C2×D3)⋊C4—92no—
321(C2×D3)⋊C4—92no—
322(C2×D3)⋊C4—92no—
323C4⋊Dic3—31no—
324C4⋊Dic3—31no—
325C4⋊Dic3—31no—
326C4⋊Dic3—61no—
327C4⋊Dic3—91no—
328C4⋊Dic3—92no—
329Dic3⋊C4—92no—
330Dic3⋊C4—92no—
331C4×Dic3—31no—
332C4×Dic3—31no—
333C4×Dic3—31no—
334C4×Dic3—61no—
335C4×Dic3—91no—
336C4×Dic3—91no—
337C4×Dic3—91no—
338C4×Dic3—91no—
339C4×Dic3—91no—
340C4×Dic3—91no—
341C4×Dic3—91no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32—21no—
347C22×C32—24no—
348C22×C32—42no—
349C22×C32—42no—
350C22×C32C2×C4×D314yescomplemented
351C22×C32C22×Dic314yescomplemented
352C22×C32C23×D311yescharacteristic
353C22×C32C23×D311yescharacteristic
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—216no—
357C2×C3⋊D3D3×D412yes—
358C2×C3⋊D3#23712yes—
359C2×C3⋊D3C22×Dic312yes—
360C2×C3⋊D3C22×Dic314yescomplemented
361C2×C3×D3—32no—
362C2×C3×D3—32no—
363C2×C3×D3—32no—
364C2×C3×D3—34no—
365C2×C3×D3—616no—
366C2×C3×D3—62no—
367C2×C3×D3—62no—
368C32×C4—22no—
369C32×C4C2×C4×D312yescomplemented
370C32×C4C22×Dic312yescomplemented
371C3⋊Dic3—22no—
372C3⋊Dic3—21no—
373C3⋊Dic3D3×D412yescomplemented
374C3⋊Dic3C22×Dic312yescomplemented
375C3×Dic3—32no—
376C3×Dic3—32no—
377C3×Dic3—32no—
378C3×Dic3—32no—
379C3×Dic3—62no—
380C3×Dic3—62no—
381C3×Dic3—62no—
382C3×Dic3—62no—
383C3×Dic3—61no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3—121no—
387C3×Dic3—122no—
388C22×D4—91no—
389C23×C4—272no—
390C4×D4—91no—
391C4×D4—91no—
392C4×D4—271no—
393C4×D4—271no—
394C4×D4—272no—
395C4×D4—272no—
396C2×C4⋊C4—271no—
397C2×C22⋊C4—272no—
398C2×C42—271no—
399H(3,𝔽3)C2×C4×D411yescharacteristic, complemented, Sylow
400C23×C3—32no—
401C23×C3—32no—
402C23×C3—62no—
403C23×C3—91no—
404C23×C3—92no—
405C23×C3—98no—
406C23×C3—184no—
407C23×C3—184no—
408C23×C3C2×D3212yes—
409C22×D3—31no—
410C22×D3—32no—
411C22×D3—38no—
412C22×D3—64no—
413C22×D3—64no—
414C22×D3—91no—
415C22×D3—98no—
416C22×D3—92no—
417C22×D3—184no—
418C22×D3—184no—
419C3×D4—34no—
420C3×D4—34no—
421C3×D4—64no—
422C3×D4—94no—
423C3×D4—98no—
424C3×D4D3×Dic314yes—
425C2×C3×C4—31no—
426C2×C3×C4—31no—
427C2×C3×C4—61no—
428C2×C3×C4—94no—
429C2×C3×C4—91no—
430C2×C3×C4—91no—
431C2×C3×C4—91no—
432C2×C3×C4—91no—
433C2×C3×C4—92no—
434C2×C3×C4—91no—
435C2×C3×C4—92no—
436C2×C3×C4—184no—
437C2×C3×C4—184no—
438C2×C3×C4C2×D3211yescharacteristic
439#67—38no—
440#67—98no—
441C2×Dic3—31no—
442C2×Dic3—31no—
443C2×Dic3—31no—
444C2×Dic3—31no—
445C2×Dic3—31no—
446C2×Dic3—31no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—31no—
450C2×Dic3—32no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—62no—
454C2×Dic3—64no—
455C2×Dic3—64no—
456C2×Dic3—64no—
457C2×Dic3—91no—
458C2×Dic3—91no—
459C2×Dic3—91no—
460C2×Dic3—92no—
461C2×Dic3—94no—
462C2×Dic3—124no—
463C2×Dic3—184no—
464C2×Dic3—184no—
465C2×Dic3—184no—
466C2×Dic3—182no—
467C2×Dic3—184no—
468D12—34no—
469D12—94no—
470C4×D3—34no—
471C4×D3—94no—
472C4×D3—94no—
473C4×D3—94no—
474C4×D3—184no—
475C4×D3—184no—
476C4×D3—184no—
477C4×D3—184no—
478C4×D3—182no—
479C4×D3—184no—
480C4×D3—182no—
481C4×D3—184no—
482C2×C32—24no—
483C2×C32—24no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—44no—
488C2×C32C22×C4×D311yescharacteristic
489C2×C32C2×D3×D411yescharacteristic
490C2×C32C2×D3×D411yescharacteristic
491C2×C32C2×#23711yescharacteristic
492C2×C32D3×#4111yescharacteristic
493C2×C32C23×Dic311yescharacteristic
494C3⋊D3—24no—
495C3⋊D3D4×Dic314yescomplemented
496C3×D3—34no—
497C3×D3—64no—
498C24—92no—
499C2×D4—92no—
500C2×D4—98no—
501C2×D4—91no—
502C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic
503C22×C4—91no—
504C22×C4—92no—
505C22×C4—92no—
506C22×C4—271no—
507C22×C4—271no—
508C22×C4—272no—
509C22×C4—272no—
510C22×C4—272no—
511C22×C4—548no—
512C4⋊C4—91no—
513C4⋊C4—91no—
514C4⋊C4—272no—
515C22⋊C4—92no—
516C22⋊C4—92no—
517C22⋊C4—272no—
518C22⋊C4—272no—
519C42—91no—
520C42—91no—
521C42—271no—
522C42—271no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—31no—
526C22×C3—31no—
527C22×C3—34no—
528C22×C3—34no—
529C22×C3—62no—
530C22×C3—62no—
531C22×C3—62no—
532C22×C3—62no—
533C22×C3—61no—
534C22×C3—64no—
535C22×C3—92no—
536C22×C3—92no—
537C22×C3—92no—
538C22×C3—94no—
539C22×C3—122no—
540C22×C3—122no—
541C22×C3—182no—
542C22×C3—182no—
543C22×C3—1816no—
544C22×C3C2×D3×Dic314yes—
545C22×C3C22×D3211yescharacteristic
546C2×D3—32no—
547C2×D3—32no—
548C2×D3—32no—
549C2×D3—34no—
550C2×D3—616no—
551C2×D3—62no—
552C2×D3—62no—
553C2×D3—92no—
554C2×D3—92no—
555C2×D3—92no—
556C2×D3—94no—
557C2×D3—1816no—
558C2×D3—182no—
559C2×D3—182no—
560C3×C4—32no—
561C3×C4—32no—
562C3×C4—62no—
563C3×C4—92no—
564C3×C4—92no—
565C3×C4—92no—
566C3×C4—182no—
567C3×C4—181no—
568C3×C4—182no—
569C3×C4—181no—
570C3×C4C2×D3×Dic312yes—
571Dic3—32no—
572Dic3—32no—
573Dic3—32no—
574Dic3—32no—
575Dic3—62no—
576Dic3—62no—
577Dic3—61no—
578Dic3—62no—
579Dic3—61no—
580Dic3—62no—
581Dic3—61no—
582Dic3—92no—
583Dic3—92no—
584Dic3—122no—
585Dic3—121no—
586Dic3—182no—
587Dic3—181no—
588C32—21no—
589C32C4×D3×D411yescharacteristic, complemented
590C32C2×D4×Dic311yescharacteristic, complemented
591C23—91no—
592C23—92no—
593C23—98no—
594C23—184no—
595C23—184no—
596C23C2×((C3⋊D3)⋊C3)⋊C212yes—
597D4—98no—
598D4—94no—
599D4((C3⋊D3)⋊C3)⋊C414yesdirect product factor
600C2×C4—91no—
601C2×C4—91no—
602C2×C4—91no—
603C2×C4—94no—
604C2×C4—91no—
605C2×C4—91no—
606C2×C4—92no—
607C2×C4—92no—
608C2×C4—184no—
609C2×C4—184no—
610C2×C4—274no—
611C2×C4—544no—
612C2×C4—544no—
613C2×C4—544no—
614C2×C4—542no—
615C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
616C2×C3—24no—
617C2×C3—31no—
618C2×C3—31no—
619C2×C3—31no—
620C2×C3—31no—
621C2×C3—31no—
622C2×C3—31no—
623C2×C3—64no—
624C2×C3—64no—
625C2×C3—61no—
626C2×C3—61no—
627C2×C3—61no—
628C2×C3—94no—
629C2×C3—124no—
630C2×C3—184no—
631C2×C3D32×D411yescharacteristic
632C2×C3D3×#23711yescharacteristic
633C2×C3C22×D3×Dic311yescharacteristic
634D3—34no—
635D3—64no—
636D3—94no—
637D3—184no—
638C22—22no—
639C22—22no—
640C22—92no—
641C22—92no—
642C22—92no—
643C22—94no—
644C22—1816no—
645C22—182no—
646C22—182no—
647C22C2×((C3⋊D3)⋊C3)⋊C414yescomplemented
648C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
649C4—92no—
650C4—92no—
651C4—92no—
652C4—182no—
653C4—182no—
654C4—181no—
655C4—181no—
656C4C2×((C3⋊D3)⋊C3)⋊C412yescomplemented
657C3—31no—
658C3—31no—
659C3—61no—
660C3D3×D4×Dic311yescharacteristic
661C2—24no—
662C2—94no—
663C2—184no—
664C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
665C2#1172250411yescharacteristic
666C2C22×((C3⋊D3)⋊C3)⋊C411yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C22×D32
FittingC2×D4×H(3,𝔽3)C22
prime radicalC2×D4×(C3⋊D3)⋊C3C2
cosocleC22×H(3,𝔽3)C24
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×C4×D4
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×((C3⋊D3)⋊C3)⋊C4C2semidirect
3. D4×#1084C2semidirect
4. D4×(C3⋊Dic3)⋊C3C2semidirect
5. #11721315C2semidirect
6. #11721314C2semidirect
7. #11721310C2semidirect
8. #11721136C2semidirect
9. #11721132C2semidirect
10. #11721129C2semidirect
11. C4×((C3⋊D3)⋊C3)⋊C4C2semidirect
16. C22×#1084C22semidirect
18. C22×(C3⋊Dic3)⋊C3C22semidirect
19. D4×(C3⋊D3)⋊C3C4semidirect
26. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
27. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
28. #88552C22semidirect
29. C4⋊#1084C22semidirect
30. C4×#1084C22semidirect
31. #3757⋊C3C22semidirect
32. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
33. C4×(C3⋊Dic3)⋊C3C22semidirect
34. #88450C22semidirect
35. #88450C22semidirect
36. #88448C22semidirect
37. #88447C22semidirect
38. #88447C22semidirect
43. D4×C3⋊Dic3D3semidirect
65. C22×(C3⋊D3)⋊C3C2×C4semidirect
68. D4×H(3,𝔽3)C2×C4semidirect
74. #638⋊C3C2×C4semidirect
80. C4⋊((C3⋊D3)⋊C3)C2×C4semidirect
81. C4×(C3⋊D3)⋊C3C2×C4semidirect
86. ((C3⋊D3)⋊C3)⋊C4D4direct (N × H)
96. C22×C3⋊Dic3C2×D3semidirect
97. D4×C3⋊D3Dic3semidirect
120. #3757C2×D3semidirect
121. C4⋊(C3⋊Dic3)C2×D3semidirect
122. C4×C3⋊Dic3C2×D3semidirect
147. C22×H(3,𝔽3)C22×C4semidirect
153. C2×(C3⋊D3)⋊C3C22×C4semidirect
156. C4×H(3,𝔽3)C22×C4semidirect
159. #1084C2×D4semidirect
162. (C3⋊Dic3)⋊C3C22×C4semidirect
163. (C3⋊Dic3)⋊C3C2×D4semidirect
203. C22×C3⋊D3C2×Dic3semidirect
212. C32×D4C4×D3semidirect
213. C32×D4C2×Dic3semidirect
217. #638C2×Dic3semidirect
223. C4⋊(C3⋊D3)C2×Dic3semidirect
224. C4×C3⋊D3C2×Dic3semidirect
261. (C3⋊D3)⋊C3C4×D4semidirect
350. C22×C32C2×C4×D3semidirect
351. C22×C32C22×Dic3semidirect
360. C2×C3⋊D3C22×Dic3semidirect
369. C32×C4C2×C4×D3semidirect
370. C32×C4C22×Dic3semidirect
373. C3⋊Dic3D3×D4semidirect
374. C3⋊Dic3C22×Dic3semidirect
399. H(3,𝔽3)C2×C4×D4semidirect
495. C3⋊D3D4×Dic3semidirect
589. C32C4×D3×D4semidirect
590. C32C2×D4×Dic3semidirect
599. D4((C3⋊D3)⋊C3)⋊C4direct (N × H)
647. C22C2×((C3⋊D3)⋊C3)⋊C4semidirect
656. C4C2×((C3⋊D3)⋊C3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×(C3⋊D3)⋊C32
C22×((C3⋊D3)⋊C3)⋊C42
D4×#10842
D4×(C3⋊Dic3)⋊C32
#117213152
#117213142
#117213102
#117211362
#117211322
#117211292
C4×((C3⋊D3)⋊C3)⋊C42
D4×#6243
D3×D4×Dic33