Finite Group Databasebeta

← C2×C4×#638⋊C3 #13153555

Subgroups — C2×C4×#638⋊C3 #13153555

Order 1728.

1727 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C22×#638⋊C3C211yesmaximal, characteristic
3C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
4C2×#3757⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C218yesmaximal, direct product factor
6C2×#3752⋊C3C211yesmaximal, characteristic, complemented
7C2×#3750⋊C3C211yesmaximal, characteristic, complemented
8C2×C4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
9C2×C4×#638C311yesmaximal, characteristic, complemented
10C2×C3×C4×#67—31nomaximal
11C24×H(3,𝔽3)C2211yescharacteristic
12C23×(C3⋊D3)⋊C3C2211yescharacteristic
13C22×C4×H(3,𝔽3)—24no—
14C22×C4×H(3,𝔽3)C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C22×C4×H(3,𝔽3)C2214yescomplemented
17C2×#638⋊C3C418yesdirect product factor
18C2×#638⋊C3C2214yes—
19C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3—24no—
23C2×C4×(C3⋊D3)⋊C3C2214yescomplemented
24#3757⋊C3C2214yescomplemented
25#3752⋊C3C2214yescomplemented
26#3750⋊C3C2214yescomplemented
27C4×(C3⋊Dic3)⋊C3C2214yescomplemented
28C23×C32×C4—21no—
29C23×C32×C4D311yescharacteristic, complemented
30C23×C32×C4C2×C311yescharacteristic, complemented
31C22×#638C2×C311yescharacteristic
32C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
33C22×C3×#67—31no—
34C22×C3×C4×D3—31no—
35C2×#3757C2×C311yescharacteristic, complemented
36C4×#638C2×C318yescomplemented
37C2×#3752C2×C311yescharacteristic, complemented
38C2×#3750C2×C311yescharacteristic, complemented
39C2×C4×C3⋊Dic3C2×C311yescharacteristic, complemented
40C2×C3×#217—31no—
41C3×C4×#67—38no—
42C2×C3×(C2×D3)⋊C4—31no—
43C2×C3×Dic3⋊C4—31no—
44C2×C3×C4×Dic3—31no—
45C23×H(3,𝔽3)—22no—
46C23×H(3,𝔽3)—22no—
47C23×H(3,𝔽3)C2×C414yescomplemented
48C23×H(3,𝔽3)C2312yes—
49C23×H(3,𝔽3)C2311yescharacteristic
50C22×(C3⋊D3)⋊C3—22no—
51C22×(C3⋊D3)⋊C3—22no—
52C22×(C3⋊D3)⋊C3C2×C414yescomplemented
53C22×(C3⋊D3)⋊C3C2312yes—
54C2×C4×H(3,𝔽3)—22no—
55C2×C4×H(3,𝔽3)—28no—
56C2×C4×H(3,𝔽3)D414yescomplemented
57C2×C4×H(3,𝔽3)C2312yes—
58C2×C4×H(3,𝔽3)C2312yes—
59#638⋊C3C2×C4116yesdirect product factor
60C2×(C3⋊Dic3)⋊C3—22no—
61C2×(C3⋊Dic3)⋊C3—22no—
62C2×(C3⋊Dic3)⋊C3C2×C414yescomplemented
63C2×(C3⋊Dic3)⋊C3C2312yes—
64C2×(C3⋊Dic3)⋊C3C2312yes—
65C2×(C3⋊Dic3)⋊C3C2312yes—
66C4×(C3⋊D3)⋊C3—28no—
67C2×C3×C4×D4—91no—
68C2×C4×#67—31no—
69C2×C4×#67—91no—
70C24×C32—21no—
71C24×C32C2×D311yescharacteristic
72C24×C32C22×C311yescharacteristic
73C23×C3⋊D3C22×C311yescharacteristic
74C23×C3×D3—31no—
75C22×C32×C4—28no—
76C22×C32×C4—21no—
77C22×C32×C4—21no—
78C22×C32×C4—24no—
79C22×C32×C4—24no—
80C22×C32×C4—24no—
81C22×C32×C4C2×D311yescharacteristic
82C22×C32×C4C2×D311yescharacteristic
83C22×C32×C4C2×D314yescomplemented
84C22×C32×C4C22×C311yescharacteristic
85C22×C32×C4C22×C311yescharacteristic
86C22×C32×C4C22×C314yescomplemented
87C2×#638C3×C418yescomplemented
88C2×#638C22×C314yes—
89C22×C3⋊Dic3C22×C311yescharacteristic
90C22×C3⋊Dic3C22×C311yescharacteristic
91C22×C3⋊Dic3C22×C311yescharacteristic
92C2×C4×C3⋊D3—24no—
93C2×C4×C3⋊D3C22×C314yescomplemented
94C2×C3×#67—38no—
95C2×C3×#67—34no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C2×C3×C4×D3—34no—
100C2×C3×C4×D3—64no—
101#3757C22×C314yescomplemented
102#3752C22×C314yescomplemented
103#3750C22×C314yescomplemented
104C4×C3⋊Dic3C22×C314yescomplemented
105C3×#217—34no—
106C3×(C2×D3)⋊C4—34no—
107C3×Dic3⋊C4—34no—
108C3×C4×Dic3—34no—
109C22×H(3,𝔽3)—28no—
110C22×H(3,𝔽3)—22no—
111C22×H(3,𝔽3)—22no—
112C22×H(3,𝔽3)C22×C412yes—
113C22×H(3,𝔽3)C22×C414yescomplemented
114C22×H(3,𝔽3)C2×D412yes—
115C22×H(3,𝔽3)#4112yes—
116C22×H(3,𝔽3)C2411yescharacteristic
117C2×(C3⋊D3)⋊C3—28no—
118C2×(C3⋊D3)⋊C3—22no—
119C2×(C3⋊D3)⋊C3—22no—
120C2×(C3⋊D3)⋊C3C22×C414yescomplemented
121C4×H(3,𝔽3)—22no—
122C4×H(3,𝔽3)C2×D414yescomplemented
123(C3⋊Dic3)⋊C3—22no—
124(C3⋊Dic3)⋊C3—22no—
125(C3⋊Dic3)⋊C3C22×C414yescomplemented
126C22×C3×D4—91no—
127C23×C3×C4—31no—
128C23×C3×C4—31no—
129C23×C3×C4—61no—
130C23×C3×C4—91no—
131C23×C3×C4C3×D311yescharacteristic
132C22×#67—31no—
133C22×#67—91no—
134C22×C4×D3—31no—
135C22×C4×D3—91no—
136C3×C4×D4—98no—
137C2×C3×C4⋊C4—91no—
138C2×C3×C22⋊C4—91no—
139C2×C3×C22⋊C4—91no—
140C2×C3×C42—91no—
141C2×#217—31no—
142C2×#217—91no—
143C4×#67—38no—
144C4×#67—98no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—91no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—91no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3—91no—
151C23×C32—24no—
152C23×C32—24no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32—24no—
158C23×C32—22no—
159C23×C32—21no—
160C23×C32C4×D314yescomplemented
161C23×C32C2×C3×C414yescomplemented
162C23×C32C22×D312yes—
163C23×C32C22×D311yescharacteristic
164C23×C32C23×C312yes—
165C23×C32C23×C311yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3C2×C3×C414yescomplemented
169C22×C3⋊D3C23×C312yes—
170C22×C3×D3—34no—
171C22×C3×D3—32no—
172C22×C3×D3—62no—
173C22×C3×D3—62no—
174C2×C32×C4—24no—
175C2×C32×C4—216no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—28no—
179C2×C32×C4—28no—
180C2×C32×C4—24no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4#6714yescomplemented
184C2×C32×C4C3×D414yescomplemented
185C2×C32×C4C22×D312yes—
186C2×C32×C4C22×D312yes—
187C2×C32×C4C23×C312yes—
188C2×C32×C4C23×C312yes—
189#638C2×C3×C4116yescomplemented
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3C2×C3×C414yescomplemented
193C2×C3⋊Dic3C23×C312yes—
194C2×C3⋊Dic3C23×C312yes—
195C2×C3⋊Dic3C23×C312yes—
196C4×C3⋊D3—28no—
197C3×#67—316no—
198C2×C3×Dic3—34no—
199C2×C3×Dic3—32no—
200C2×C3×Dic3—32no—
201C2×C3×Dic3—32no—
202C2×C3×Dic3—62no—
203C2×C3×Dic3—62no—
204C3×C4×D3—68no—
205C2×C4×D4—91noSylow
206C2×H(3,𝔽3)—24no—
207C2×H(3,𝔽3)C4×D414yescomplemented
208C2×H(3,𝔽3)C23×C411yescharacteristic
209C2×H(3,𝔽3)C22×D411yescharacteristic
210C2×H(3,𝔽3)C2×#4111yescharacteristic
211(C3⋊D3)⋊C3—24no—
212C24×C3—31no—
213C24×C3—31no—
214C24×C3—61no—
215C24×C3—91no—
216C24×C3C2×C3×D311yescharacteristic
217C23×D3—31no—
218C23×D3—91no—
219C2×C3×D4—94no—
220C2×C3×D4—98no—
221C22×C3×C4—24no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—34no—
227C22×C3×C4—34no—
228C22×C3×C4—64no—
229C22×C3×C4—64no—
230C22×C3×C4—68no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C22×C3×C4—64no—
234C22×C3×C4—94no—
235C22×C3×C4—91no—
236C22×C3×C4—91no—
237C22×C3×C4—91no—
238C22×C3×C4—184no—
239C22×C3×C4C2×C3×D311yescharacteristic
240C22×C3×C4C2×C3×D311yescharacteristic
241C22×C3×C4C2×C3×D314yes—
242C2×#67—38no—
243C2×#67—34no—
244C2×#67—94no—
245C2×#67—98no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—31no—
249C22×Dic3—91no—
250C22×Dic3—91no—
251C22×Dic3—91no—
252C2×C4×D3—34no—
253C2×C4×D3—64no—
254C2×C4×D3—94no—
255C2×C4×D3—184no—
256C3×C4⋊C4—94no—
257C3×C22⋊C4—94no—
258C3×C22⋊C4—94no—
259C3×C42—94no—
260#217—34no—
261#217—94no—
262(C2×D3)⋊C4—34no—
263(C2×D3)⋊C4—94no—
264Dic3⋊C4—34no—
265Dic3⋊C4—94no—
266C4×Dic3—34no—
267C4×Dic3—94no—
268C22×C32—24no—
269C22×C32—216no—
270C22×C32—24no—
271C22×C32—28no—
272C22×C32—28no—
273C22×C32—22no—
274C22×C32—22no—
275C22×C32—22no—
276C22×C32—22no—
277C22×C32—21no—
278C22×C32—22no—
279C22×C32—24no—
280C22×C32—22no—
281C22×C32—22no—
282C22×C32C2×C4×D312yes—
283C22×C32C2×C4×D314yescomplemented
284C22×C32#23512yes—
285C22×C32C2×#6712yes—
286C22×C32C22×C3×C412yes—
287C22×C32C22×C3×C414yescomplemented
288C22×C32C2×C3×D412yes—
289C22×C32C3×#4112yes—
290C22×C32C23×D311yescharacteristic
291C22×C32C24×C311yescharacteristic
292C2×C3⋊D3—28no—
293C2×C3⋊D3—22no—
294C2×C3⋊D3—22no—
295C2×C3⋊D3C22×C3×C414yescomplemented
296C2×C3×D3—34no—
297C2×C3×D3—68no—
298C2×C3×D3—62no—
299C2×C3×D3—62no—
300C32×C4—24no—
301C32×C4—22no—
302C32×C4—22no—
303C32×C4—24no—
304C32×C4C2×#6714yescomplemented
305C32×C4C2×C3×D414yescomplemented
306C3⋊Dic3—22no—
307C3⋊Dic3—22no—
308C3⋊Dic3C22×C3×C414yescomplemented
309C3×Dic3—34no—
310C3×Dic3—62no—
311C3×Dic3—62no—
312C22×D4—91no—
313C23×C4—91no—
314C23×C4(C3⋊D3)⋊C311yescharacteristic, complemented
315C4×D4—98no—
316C2×C4⋊C4—91no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—91no—
319C2×C42—91no—
320H(3,𝔽3)C2×C4×D411yescharacteristic, complemented, Sylow
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—34no—
324C23×C3—34no—
325C23×C3—31no—
326C23×C3—31no—
327C23×C3—32no—
328C23×C3—32no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—64no—
334C23×C3—64no—
335C23×C3—64no—
336C23×C3—62no—
337C23×C3—61no—
338C23×C3—92no—
339C23×C3—94no—
340C23×C3—182no—
341C23×C3—182no—
342C23×C3C3×C4×D314yes—
343C23×C3C22×C3×D312yes—
344C23×C3C22×C3×D311yescharacteristic
345C22×D3—32no—
346C22×D3—34no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—94no—
350C22×D3—92no—
351C22×D3—182no—
352C22×D3—182no—
353C3×D4—916no—
354C2×C3×C4—22no—
355C2×C3×C4—28no—
356C2×C3×C4—34no—
357C2×C3×C4—34no—
358C2×C3×C4—32no—
359C2×C3×C4—32no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—68no—
363C2×C3×C4—68no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—64no—
367C2×C3×C4—616no—
368C2×C3×C4—64no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—92no—
372C2×C3×C4—94no—
373C2×C3×C4—92no—
374C2×C3×C4—92no—
375C2×C3×C4—188no—
376C2×C3×C4—182no—
377C2×C3×C4—182no—
378C2×C3×C4C3×#6714yes—
379C2×C3×C4C22×C3×D312yes—
380C2×C3×C4C22×C3×D312yes—
381#67—316no—
382#67—916no—
383C2×Dic3—32no—
384C2×Dic3—34no—
385C2×Dic3—32no—
386C2×Dic3—32no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—94no—
390C2×Dic3—92no—
391C2×Dic3—92no—
392C2×Dic3—92no—
393C2×Dic3—182no—
394C2×Dic3—182no—
395C4×D3—68no—
396C4×D3—188no—
397C2×C32—28no—
398C2×C32—24no—
399C2×C32—24no—
400C2×C32—24no—
401C2×C32—21no—
402C2×C32—21no—
403C2×C32—21no—
404C2×C32C4×#6714yescomplemented
405C2×C32C3×C4×D414yescomplemented
406C2×C32C22×C4×D311yescharacteristic
407C2×C32C2×#23511yescharacteristic
408C2×C32C22×#6711yescharacteristic
409C2×C32C23×C3×C411yescharacteristic
410C2×C32C22×C3×D411yescharacteristic
411C2×C32C2×C3×#4111yescharacteristic
412C3⋊D3—24no—
413C3×D3—64no—
414C24—91no—
415C24C2×(C3⋊D3)⋊C311yescharacteristic
416C2×D4—98no—
417C2×D4—94no—
418C22×C4—24no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—94no—
423C22×C4—184no—
424C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
425C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
426C22×C4C2×(C3⋊D3)⋊C314yescomplemented
427C4⋊C4—94no—
428C22⋊C4—94no—
429C22⋊C4—94no—
430C42—94no—
431C22×C3—28no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—31no—
435C22×C3—31no—
436C22×C3—32no—
437C22×C3—32no—
438C22×C3—34no—
439C22×C3—34no—
440C22×C3—32no—
441C22×C3—32no—
442C22×C3—32no—
443C22×C3—32no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—68no—
449C22×C3—68no—
450C22×C3—64no—
451C22×C3—64no—
452C22×C3—616no—
453C22×C3—61no—
454C22×C3—62no—
455C22×C3—64no—
456C22×C3—62no—
457C22×C3—62no—
458C22×C3—94no—
459C22×C3—182no—
460C22×C3—182no—
461C22×C3—188no—
462C22×C3C2×C3×C4×D312yes—
463C22×C3C2×C3×C4×D314yes—
464C22×C3C3×#23512yes—
465C22×C3C2×C3×#6712yes—
466C22×C3C23×C3×D311yescharacteristic
467C2×D3—34no—
468C2×D3—68no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—94no—
472C2×D3—182no—
473C2×D3—182no—
474C2×D3—188no—
475C3×C4—22no—
476C3×C4—34no—
477C3×C4—34no—
478C3×C4—62no—
479C3×C4—62no—
480C3×C4—64no—
481C3×C4—64no—
482C3×C4—94no—
483C3×C4—182no—
484C3×C4—182no—
485C3×C4C2×C3×#6714yes—
486Dic3—34no—
487Dic3—62no—
488Dic3—62no—
489Dic3—94no—
490Dic3—182no—
491Dic3—182no—
492C32—21no—
493C32C2×C4×#6711yescharacteristic, complemented
494C32C2×C3×C4×D411yescharacteristic, complemented
495C23—22no—
496C23—22no—
497C23—92no—
498C23—94no—
499C23—182no—
500C23—182no—
501C23C4×(C3⋊D3)⋊C314yescomplemented
502C23C22×(C3⋊D3)⋊C312yes—
503C23C22×(C3⋊D3)⋊C311yescharacteristic
504D4—916no—
505C2×C4—22no—
506C2×C4—28no—
507C2×C4—92no—
508C2×C4—94no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4—188no—
514C2×C4#638⋊C314yesdirect product factor
515C2×C4C22×(C3⋊D3)⋊C312yes—
516C2×C4C22×(C3⋊D3)⋊C312yes—
517C2×C3—24no—
518C2×C3—31no—
519C2×C3—31no—
520C2×C3—31no—
521C2×C3—31no—
522C2×C3—34no—
523C2×C3—34no—
524C2×C3—31no—
525C2×C3—31no—
526C2×C3—64no—
527C2×C3—64no—
528C2×C3—68no—
529C2×C3—61no—
530C2×C3—61no—
531C2×C3—64no—
532C2×C3—61no—
533C2×C3—184no—
534C2×C3C3×C4×#6714yes—
535C2×C3C22×C3×C4×D311yescharacteristic
536C2×C3C2×C3×#23511yescharacteristic
537C2×C3C22×C3×#6711yescharacteristic
538D3—64no—
539D3—184no—
540C22—22no—
541C22—28no—
542C22—22no—
543C22—94no—
544C22—182no—
545C22—188no—
546C22—182no—
547C22C2×C4×(C3⋊D3)⋊C312yes—
548C22C2×C4×(C3⋊D3)⋊C314yescomplemented
549C22#3828⋊C312yes—
550C22C2×#638⋊C312yes—
551C22C23×(C3⋊D3)⋊C311yescharacteristic
552C4—22no—
553C4—94no—
554C4—182no—
555C4—182no—
556C4C2×#638⋊C314yesdirect product factor
557C3—31no—
558C3—31no—
559C3—61no—
560C3C2×C3×C4×#6711yescharacteristic
561C2—24no—
562C2—184no—
563C2C4×#638⋊C314yesdirect product factor
564C2C22×C4×(C3⋊D3)⋊C311yescharacteristic
565C2C2×#3828⋊C311yescharacteristic
566C2C22×#638⋊C311yescharacteristic
subgroupG/H
centerC22×C4C2×(C3⋊D3)⋊C3
commutatorC2×C32C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC23×C4×H(3,𝔽3)C2
socleC23×C3C22×C3×D3
prime radicalC22×#638⋊C3C2
cosocleC22×C32C24×C3
hypercenterC23×C4(C3⋊D3)⋊C3
hypocenterC32C2×C3×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4×H(3,𝔽3)C2semidirect
3. C22×C4×(C3⋊D3)⋊C3C2semidirect
4. C2×#3757⋊C3C2semidirect
5. C4×#638⋊C3C2direct (N × H)
6. C2×#3752⋊C3C2semidirect
7. C2×#3750⋊C3C2semidirect
8. C2×C4×(C3⋊Dic3)⋊C3C2semidirect
9. C2×C4×#638C3semidirect
16. C22×C4×H(3,𝔽3)C22semidirect
17. C2×#638⋊C3C4direct (N × H)
23. C2×C4×(C3⋊D3)⋊C3C22semidirect
24. #3757⋊C3C22semidirect
25. #3752⋊C3C22semidirect
26. #3750⋊C3C22semidirect
27. C4×(C3⋊Dic3)⋊C3C22semidirect
29. C23×C32×C4D3semidirect
30. C23×C32×C4C2×C3semidirect
32. C22×C4×C3⋊D3C2×C3semidirect
35. C2×#3757C2×C3semidirect
36. C4×#638C2×C3semidirect
37. C2×#3752C2×C3semidirect
38. C2×#3750C2×C3semidirect
39. C2×C4×C3⋊Dic3C2×C3semidirect
47. C23×H(3,𝔽3)C2×C4semidirect
52. C22×(C3⋊D3)⋊C3C2×C4semidirect
56. C2×C4×H(3,𝔽3)D4semidirect
59. #638⋊C3C2×C4direct (N × H)
62. C2×(C3⋊Dic3)⋊C3C2×C4semidirect
83. C22×C32×C4C2×D3semidirect
86. C22×C32×C4C22×C3semidirect
87. C2×#638C3×C4semidirect
93. C2×C4×C3⋊D3C22×C3semidirect
101. #3757C22×C3semidirect
102. #3752C22×C3semidirect
103. #3750C22×C3semidirect
104. C4×C3⋊Dic3C22×C3semidirect
113. C22×H(3,𝔽3)C22×C4semidirect
120. C2×(C3⋊D3)⋊C3C22×C4semidirect
122. C4×H(3,𝔽3)C2×D4semidirect
125. (C3⋊Dic3)⋊C3C22×C4semidirect
160. C23×C32C4×D3semidirect
161. C23×C32C2×C3×C4semidirect
168. C22×C3⋊D3C2×C3×C4semidirect
183. C2×C32×C4#67semidirect
184. C2×C32×C4C3×D4semidirect
189. #638C2×C3×C4semidirect
192. C2×C3⋊Dic3C2×C3×C4semidirect
207. C2×H(3,𝔽3)C4×D4semidirect
283. C22×C32C2×C4×D3semidirect
287. C22×C32C22×C3×C4semidirect
295. C2×C3⋊D3C22×C3×C4semidirect
304. C32×C4C2×#67semidirect
305. C32×C4C2×C3×D4semidirect
308. C3⋊Dic3C22×C3×C4semidirect
314. C23×C4(C3⋊D3)⋊C3semidirect
320. H(3,𝔽3)C2×C4×D4semidirect
404. C2×C32C4×#67semidirect
405. C2×C32C3×C4×D4semidirect
426. C22×C4C2×(C3⋊D3)⋊C3semidirect
493. C32C2×C4×#67semidirect
494. C32C2×C3×C4×D4semidirect
501. C23C4×(C3⋊D3)⋊C3semidirect
514. C2×C4#638⋊C3direct (N × H)
548. C22C2×C4×(C3⋊D3)⋊C3semidirect
556. C4C2×#638⋊C3direct (N × H)
563. C2C4×#638⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×H(3,𝔽3)2
C22×#638⋊C32
C22×C4×(C3⋊D3)⋊C32
C2×#3757⋊C32
C4×#638⋊C32
C2×#3752⋊C32
C2×#3750⋊C32
C2×C4×(C3⋊Dic3)⋊C32
C2×C4×#6383
C2×C3×C4×#673