Finite Group Databasebeta

← C2×#64093⋊C3 #13152365

Subgroups — C2×#64093⋊C3 #13152365

Order 1728.

1623 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#638⋊C3C211yesmaximal, characteristic, complemented
2C22×#638⋊C3C211yesmaximal, characteristic, complemented
3C22×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
4C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
6C2×#3752⋊C3C211yesmaximal, characteristic, complemented
7C2×#3750⋊C3C211yesmaximal, characteristic, complemented
8#64093⋊C3C218yesmaximal, direct product factor
9C2×#64093C311yesmaximal, characteristic, complemented
10C2×C3×#884—31nomaximal
11C24×H(3,𝔽3)C2211yescharacteristic
12C23×(C3⋊D3)⋊C3C2211yescharacteristic
13C23×(C3⋊D3)⋊C3C2211yescharacteristic
14C22×C4×H(3,𝔽3)C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#638⋊C3—24no—
17C2×#638⋊C3—24no—
18C2×#638⋊C3C2214yescomplemented
19C2×#638⋊C3C2214yescomplemented
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×C4⋊((C3⋊D3)⋊C3)—24no—
23C2×C4⋊((C3⋊D3)⋊C3)C2214yescomplemented
24C2×C4×(C3⋊D3)⋊C3—24no—
25C2×C4×(C3⋊D3)⋊C3C2214yescomplemented
26C22⋊C4×H(3,𝔽3)C2214yescomplemented
27#3752⋊C3C2214yescomplemented
28#3750⋊C3C2214yescomplemented
29C22×#638C2×C311yescharacteristic, complemented
30C22×#638C2×C311yescharacteristic, complemented
31C22×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
32C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
33C22×C3×#67—31no—
34C22×C3×#67—31no—
35C22×C3×D12—31no—
36C22×C3×C4×D3—31no—
37C2×C32×C22⋊C4—21no—
38C2×C32×C22⋊C4D311yescharacteristic, complemented
39C2×C32×C22⋊C4C2×C311yescharacteristic, complemented
40C2×#3752C2×C311yescharacteristic, complemented
41C2×#3750C2×C311yescharacteristic, complemented
42#64093C2×C318yescomplemented
43C2×C3×(C2×D3)⋊C4—31no—
44C2×C3×Dic3⋊C4—31no—
45C3×#884—38no—
46C23×H(3,𝔽3)—22no—
47C23×H(3,𝔽3)—22no—
48C23×H(3,𝔽3)—22no—
49C23×H(3,𝔽3)C2312yes—
50C23×H(3,𝔽3)C2311yescharacteristic
51C22×(C3⋊D3)⋊C3—22no—
52C22×(C3⋊D3)⋊C3—22no—
53C22×(C3⋊D3)⋊C3—22no—
54C22×(C3⋊D3)⋊C3—22no—
55C22×(C3⋊D3)⋊C3—22no—
56C22×(C3⋊D3)⋊C3D414yescomplemented
57C22×(C3⋊D3)⋊C3C2312yes—
58C22×(C3⋊D3)⋊C3C2312yes—
59C2×C4×H(3,𝔽3)—22no—
60C2×C4×H(3,𝔽3)—22no—
61C2×C4×H(3,𝔽3)C2312yes—
62C2×C4×H(3,𝔽3)C2312yes—
63#638⋊C3—28no—
64#638⋊C3—28no—
65C2×(C3⋊Dic3)⋊C3—22no—
66C2×(C3⋊Dic3)⋊C3D414yescomplemented
67C2×(C3⋊Dic3)⋊C3C2312yes—
68C2×(C3⋊Dic3)⋊C3C2312yes—
69C4⋊((C3⋊D3)⋊C3)—28no—
70C4×(C3⋊D3)⋊C3—28no—
71C2×C3×#121—91no—
72C2×#884—31no—
73C2×#884—91no—
74C24×C32—21no—
75C24×C32C2×D311yescharacteristic
76C24×C32C22×C311yescharacteristic
77C23×C3⋊D3C22×C311yescharacteristic
78C23×C3⋊D3C22×C311yescharacteristic
79C23×C3×D3—31no—
80C23×C3×D3—31no—
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4C2×D311yescharacteristic
84C22×C32×C4C2×D311yescharacteristic
85C22×C32×C4C22×C311yescharacteristic
86C22×C32×C4C22×C311yescharacteristic
87C2×#638—24no—
88C2×#638—24no—
89C2×#638C22×C314yescomplemented
90C2×#638C22×C314yescomplemented
91C22×C3⋊Dic3C22×C311yescharacteristic
92C22×C3⋊Dic3C22×C311yescharacteristic
93C2×C4⋊(C3⋊D3)—24no—
94C2×C4⋊(C3⋊D3)C22×C314yescomplemented
95C2×C4×C3⋊D3—24no—
96C2×C4×C3⋊D3C22×C314yescomplemented
97C2×C3×#67—34no—
98C2×C3×#67—34no—
99C2×C3×#67—64no—
100C2×C3×#67—64no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C2×C3×D12—34no—
104C2×C3×D12—64no—
105C2×C3×C4×D3—34no—
106C2×C3×C4×D3—64no—
107C32×C22⋊C4—24no—
108C32×C22⋊C4C2×D314yescomplemented
109C32×C22⋊C4C22×C314yescomplemented
110#3752C22×C314yescomplemented
111#3750C22×C314yescomplemented
112C3×(C2×D3)⋊C4—34no—
113C3×Dic3⋊C4—34no—
114C22×H(3,𝔽3)—22no—
115C22×H(3,𝔽3)—22no—
116C22×H(3,𝔽3)—22no—
117C22×H(3,𝔽3)—44no—
118C22×H(3,𝔽3)C2×D412yes—
119C22×H(3,𝔽3)C2×D412yes—
120C22×H(3,𝔽3)#4112yes—
121C22×H(3,𝔽3)C2411yescharacteristic
122C2×(C3⋊D3)⋊C3—28no—
123C2×(C3⋊D3)⋊C3—22no—
124C2×(C3⋊D3)⋊C3—22no—
125C2×(C3⋊D3)⋊C3—22no—
126C2×(C3⋊D3)⋊C3—22no—
127C2×(C3⋊D3)⋊C3—22no—
128C2×(C3⋊D3)⋊C3—44no—
129C2×(C3⋊D3)⋊C3C2×D414yescomplemented
130C4×H(3,𝔽3)—22no—
131C4×H(3,𝔽3)—22no—
132(C3⋊Dic3)⋊C3—22no—
133(C3⋊Dic3)⋊C3C2×D414yescomplemented
134C22×C3×D4—91no—
135C22×C3×D4—91no—
136C22×C3×D4—91no—
137C23×C3×C4—91no—
138C22×#67—31no—
139C22×#67—31no—
140C22×#67—91no—
141C22×#67—91no—
142C22×D12—31no—
143C22×D12—91no—
144C22×C4×D3—31no—
145C22×C4×D3—91no—
146C3×#121—98no—
147C2×C3×C4⋊C4—91no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—61no—
151C2×C3×C22⋊C4—91no—
152C2×C3×C22⋊C4C3×D311yescharacteristic
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—91no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—91no—
157#884—38no—
158#884—98no—
159C23×C32—24no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—21no—
167C23×C32—22no—
168C23×C32—42no—
169C23×C32—42no—
170C23×C32C22×D312yes—
171C23×C32C22×D311yescharacteristic
172C23×C32C23×C312yes—
173C23×C32C23×C311yescharacteristic
174C22×C3⋊D3—22no—
175C22×C3⋊D3—22no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3C3×D414yescomplemented
180C22×C3⋊D3C23×C312yes—
181C22×C3⋊D3C23×C312yes—
182C22×C3×D3—34no—
183C22×C3×D3—32no—
184C22×C3×D3—32no—
185C22×C3×D3—62no—
186C22×C3×D3—62no—
187C22×C3×D3—62no—
188C22×C3×D3—62no—
189C22×C3×D3—62no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4—22no—
193C2×C32×C4—22no—
194C2×C32×C4—22no—
195C2×C32×C4—22no—
196C2×C32×C4—42no—
197C2×C32×C4—42no—
198C2×C32×C4C22×D312yes—
199C2×C32×C4C22×D312yes—
200C2×C32×C4C23×C312yes—
201C2×C32×C4C23×C312yes—
202#638—28no—
203#638—28no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3C3×D414yescomplemented
206C2×C3⋊Dic3C23×C312yes—
207C2×C3⋊Dic3C23×C312yes—
208C4⋊(C3⋊D3)—28no—
209C4×C3⋊D3—28no—
210C3×#67—68no—
211C3×#67—68no—
212C2×C3×Dic3—34no—
213C2×C3×Dic3—32no—
214C2×C3×Dic3—32no—
215C2×C3×Dic3—62no—
216C3×D12—68no—
217C3×C4×D3—68no—
218C2×#121—91noSylow
219C2×H(3,𝔽3)—42no—
220C2×H(3,𝔽3)#12114yescomplemented
221C2×H(3,𝔽3)C22×D411yescharacteristic
222C2×H(3,𝔽3)C22×D411yescharacteristic
223C2×H(3,𝔽3)C2×#4111yescharacteristic
224(C3⋊D3)⋊C3—24no—
225(C3⋊D3)⋊C3—42no—
226C24×C3—31no—
227C24×C3—31no—
228C24×C3—61no—
229C24×C3—91no—
230C24×C3—91no—
231C24×C3C2×C3×D311yescharacteristic
232C23×D3—31no—
233C23×D3—31no—
234C23×D3—91no—
235C23×D3—91no—
236C2×C3×D4—94no—
237C2×C3×D4—94no—
238C2×C3×D4—94no—
239C2×C3×D4—184no—
240C2×C3×D4—184no—
241C2×C3×D4—184no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—61no—
247C22×C3×C4—61no—
248C22×C3×C4—94no—
249C22×C3×C4—91no—
250C22×C3×C4—91no—
251C22×C3×C4—184no—
252C22×C3×C4C2×C3×D311yescharacteristic
253C22×C3×C4C2×C3×D311yescharacteristic
254C2×#67—34no—
255C2×#67—34no—
256C2×#67—64no—
257C2×#67—64no—
258C2×#67—94no—
259C2×#67—94no—
260C2×#67—184no—
261C2×#67—184no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—91no—
265C22×Dic3—91no—
266C2×D12—34no—
267C2×D12—64no—
268C2×D12—94no—
269C2×D12—184no—
270C2×C4×D3—34no—
271C2×C4×D3—64no—
272C2×C4×D3—94no—
273C2×C4×D3—184no—
274C3×C4⋊C4—94no—
275C3×C22⋊C4—34no—
276C3×C22⋊C4—34no—
277C3×C22⋊C4—64no—
278C3×C22⋊C4—94no—
279C3×C22⋊C4C2×C3×D314yes—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—94no—
282Dic3⋊C4—34no—
283Dic3⋊C4—94no—
284C22×C32—24no—
285C22×C32—22no—
286C22×C32—22no—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32—22no—
291C22×C32—21no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—22no—
295C22×C32—42no—
296C22×C32—42no—
297C22×C32—48no—
298C22×C32—44no—
299C22×C32—44no—
300C22×C32#23512yes—
301C22×C32D3×D412yes—
302C22×C32D3×D412yes—
303C22×C32C2×C3×D412yes—
304C22×C32C2×C3×D412yes—
305C22×C32C3×#4112yes—
306C22×C32C23×D311yescharacteristic
307C22×C32C24×C311yescharacteristic
308C2×C3⋊D3—28no—
309C2×C3⋊D3—22no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3—22no—
314C2×C3⋊D3—44no—
315C2×C3⋊D3C2×C3×D414yescomplemented
316C2×C3×D3—34no—
317C2×C3×D3—68no—
318C2×C3×D3—62no—
319C2×C3×D3—62no—
320C2×C3×D3—62no—
321C2×C3×D3—62no—
322C2×C3×D3—62no—
323C2×C3×D3—124no—
324C32×C4—22no—
325C32×C4—22no—
326C32×C4—22no—
327C32×C4—22no—
328C32×C4—42no—
329C32×C4—42no—
330C3⋊Dic3—22no—
331C3⋊Dic3C2×C3×D414yescomplemented
332C3×Dic3—34no—
333C3×Dic3—62no—
334C22×D4—91no—
335C22×D4—91no—
336C22×D4—91no—
337C23×C4—91no—
338#121—98no—
339C2×C4⋊C4—91no—
340C2×C22⋊C4—91no—
341C2×C22⋊C4(C3⋊D3)⋊C311yescharacteristic, complemented
342H(3,𝔽3)C2×#12111yescharacteristic, complemented, Sylow
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—32no—
347C23×C3—32no—
348C23×C3—31no—
349C23×C3—31no—
350C23×C3—62no—
351C23×C3—62no—
352C23×C3—62no—
353C23×C3—62no—
354C23×C3—62no—
355C23×C3—62no—
356C23×C3—64no—
357C23×C3—62no—
358C23×C3—61no—
359C23×C3—92no—
360C23×C3—94no—
361C23×C3—92no—
362C23×C3—122no—
363C23×C3—122no—
364C23×C3—182no—
365C23×C3—182no—
366C23×C3—182no—
367C23×C3—182no—
368C23×C3—182no—
369C23×C3C22×C3×D312yes—
370C23×C3C22×C3×D311yescharacteristic
371C22×D3—32no—
372C22×D3—34no—
373C22×D3—32no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—94no—
380C22×D3—92no—
381C22×D3—92no—
382C22×D3—182no—
383C22×D3—182no—
384C22×D3—182no—
385C22×D3—182no—
386C22×D3—182no—
387C3×D4—188no—
388C3×D4—188no—
389C3×D4—188no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—92no—
403C2×C3×C4—94no—
404C2×C3×C4—92no—
405C2×C3×C4—122no—
406C2×C3×C4—122no—
407C2×C3×C4—188no—
408C2×C3×C4—182no—
409C2×C3×C4C22×C3×D312yes—
410C2×C3×C4C22×C3×D312yes—
411#67—68no—
412#67—68no—
413#67—188no—
414#67—188no—
415C2×Dic3—32no—
416C2×Dic3—34no—
417C2×Dic3—32no—
418C2×Dic3—62no—
419C2×Dic3—94no—
420C2×Dic3—92no—
421C2×Dic3—92no—
422C2×Dic3—182no—
423D12—68no—
424D12—188no—
425C4×D3—68no—
426C4×D3—188no—
427C2×C32—24no—
428C2×C32—21no—
429C2×C32—21no—
430C2×C32—21no—
431C2×C32—44no—
432C2×C32—42no—
433C2×C32—42no—
434C2×C32#88414yescomplemented
435C2×C32C3×#12114yescomplemented
436C2×C32C2×#23511yescharacteristic
437C2×C32C2×D3×D411yescharacteristic
438C2×C32C2×D3×D411yescharacteristic
439C2×C32C22×C3×D411yescharacteristic
440C2×C32C22×C3×D411yescharacteristic
441C2×C32C2×C3×#4111yescharacteristic
442C3⋊D3—24no—
443C3⋊D3—42no—
444C3×D3—64no—
445C3×D3—122no—
446C24—91no—
447C24—91no—
448C24C2×(C3⋊D3)⋊C311yescharacteristic
449C2×D4—94no—
450C2×D4—94no—
451C2×D4—94no—
452C2×D4—184no—
453C2×D4—184no—
454C2×D4—184no—
455C22×C4—91no—
456C22×C4—91no—
457C22×C4—94no—
458C22×C4—184no—
459C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
460C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
461C4⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4C2×(C3⋊D3)⋊C314yescomplemented
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—31no—
468C22×C3—31no—
469C22×C3—32no—
470C22×C3—32no—
471C22×C3—32no—
472C22×C3—32no—
473C22×C3—32no—
474C22×C3—32no—
475C22×C3—44no—
476C22×C3—62no—
477C22×C3—62no—
478C22×C3—62no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—64no—
483C22×C3—61no—
484C22×C3—62no—
485C22×C3—62no—
486C22×C3—62no—
487C22×C3—94no—
488C22×C3—122no—
489C22×C3—122no—
490C22×C3—124no—
491C22×C3—124no—
492C22×C3—128no—
493C22×C3—182no—
494C22×C3—182no—
495C22×C3—188no—
496C22×C3—182no—
497C22×C3—182no—
498C22×C3—182no—
499C22×C3—364no—
500C22×C3C3×#23512yes—
501C22×C3C3×D3×D412yes—
502C22×C3C3×D3×D412yes—
503C22×C3C23×C3×D311yescharacteristic
504C2×D3—34no—
505C2×D3—68no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—62no—
510C2×D3—62no—
511C2×D3—94no—
512C2×D3—124no—
513C2×D3—182no—
514C2×D3—182no—
515C2×D3—188no—
516C2×D3—182no—
517C2×D3—182no—
518C2×D3—182no—
519C2×D3—364no—
520C3×C4—22no—
521C3×C4—22no—
522C3×C4—62no—
523C3×C4—62no—
524C3×C4—62no—
525C3×C4—62no—
526C3×C4—94no—
527C3×C4—122no—
528C3×C4—122no—
529C3×C4—182no—
530Dic3—34no—
531Dic3—62no—
532Dic3—94no—
533Dic3—182no—
534C32—21no—
535C32C2×#88411yescharacteristic, complemented
536C32C2×C3×#12111yescharacteristic, complemented
537C23—22no—
538C23—22no—
539C23—22no—
540C23—92no—
541C23—94no—
542C23—92no—
543C23—182no—
544C23—182no—
545C23—182no—
546C23—182no—
547C23—182no—
548C23C22×(C3⋊D3)⋊C312yes—
549C23C22×(C3⋊D3)⋊C311yescharacteristic
550D4—188no—
551D4—188no—
552D4—188no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—92no—
556C2×C4—94no—
557C2×C4—92no—
558C2×C4—188no—
559C2×C4—182no—
560C2×C4C22×(C3⋊D3)⋊C312yes—
561C2×C4C22×(C3⋊D3)⋊C312yes—
562C2×C3—31no—
563C2×C3—31no—
564C2×C3—31no—
565C2×C3—31no—
566C2×C3—31no—
567C2×C3—31no—
568C2×C3—34no—
569C2×C3—34no—
570C2×C3—42no—
571C2×C3—61no—
572C2×C3—61no—
573C2×C3—61no—
574C2×C3—64no—
575C2×C3—122no—
576C2×C3—122no—
577C2×C3—124no—
578C2×C3—184no—
579C2×C3—362no—
580C2×C3C3×#88414yes—
581C2×C3C2×C3×#23511yescharacteristic
582C2×C3C2×C3×D3×D411yescharacteristic
583C2×C3C2×C3×D3×D411yescharacteristic
584D3—64no—
585D3—122no—
586D3—184no—
587D3—362no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—44no—
592C22—94no—
593C22—182no—
594C22—182no—
595C22—188no—
596C22—182no—
597C22—182no—
598C22—182no—
599C22—364no—
600C22#3828⋊C312yes—
601C22D4×(C3⋊D3)⋊C312yes—
602C22D4×(C3⋊D3)⋊C312yes—
603C22C23×(C3⋊D3)⋊C311yescharacteristic
604C4—22no—
605C4—22no—
606C4—94no—
607C4—182no—
608C3—31no—
609C3—31no—
610C3—61no—
611C3C2×C3×#88411yescharacteristic
612C2—42no—
613C2—184no—
614C2—362no—
615C2#64093⋊C314yesdirect product factor
616C2C2×#3828⋊C311yescharacteristic
617C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
618C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC23C22×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
FrattiniC22×C3C23×C3×D3
FittingC2×C22⋊C4×H(3,𝔽3)C2
socleC23×C3C22×C3×D3
hypercenterC2×C22⋊C4(C3⋊D3)⋊C3
hypocenterC32C2×C3×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#638⋊C3C2semidirect
2. C22×#638⋊C3C2semidirect
3. C22×C4⋊((C3⋊D3)⋊C3)C2semidirect
4. C22×C4×(C3⋊D3)⋊C3C2semidirect
5. C2×C22⋊C4×H(3,𝔽3)C2semidirect
6. C2×#3752⋊C3C2semidirect
7. C2×#3750⋊C3C2semidirect
8. #64093⋊C3C2direct (N × H)
9. C2×#64093C3semidirect
18. C2×#638⋊C3C22semidirect
19. C2×#638⋊C3C22semidirect
23. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
26. C22⋊C4×H(3,𝔽3)C22semidirect
27. #3752⋊C3C22semidirect
28. #3750⋊C3C22semidirect
29. C22×#638C2×C3semidirect
30. C22×#638C2×C3semidirect
31. C22×C4⋊(C3⋊D3)C2×C3semidirect
32. C22×C4×C3⋊D3C2×C3semidirect
38. C2×C32×C22⋊C4D3semidirect
39. C2×C32×C22⋊C4C2×C3semidirect
40. C2×#3752C2×C3semidirect
41. C2×#3750C2×C3semidirect
42. #64093C2×C3semidirect
56. C22×(C3⋊D3)⋊C3D4semidirect
66. C2×(C3⋊Dic3)⋊C3D4semidirect
89. C2×#638C22×C3semidirect
90. C2×#638C22×C3semidirect
94. C2×C4⋊(C3⋊D3)C22×C3semidirect
96. C2×C4×C3⋊D3C22×C3semidirect
108. C32×C22⋊C4C2×D3semidirect
109. C32×C22⋊C4C22×C3semidirect
110. #3752C22×C3semidirect
111. #3750C22×C3semidirect
129. C2×(C3⋊D3)⋊C3C2×D4semidirect
133. (C3⋊Dic3)⋊C3C2×D4semidirect
179. C22×C3⋊D3C3×D4semidirect
205. C2×C3⋊Dic3C3×D4semidirect
220. C2×H(3,𝔽3)#121semidirect
315. C2×C3⋊D3C2×C3×D4semidirect
331. C3⋊Dic3C2×C3×D4semidirect
341. C2×C22⋊C4(C3⋊D3)⋊C3semidirect
342. H(3,𝔽3)C2×#121semidirect
434. C2×C32#884semidirect
435. C2×C32C3×#121semidirect
463. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
535. C32C2×#884semidirect
536. C32C2×C3×#121semidirect
615. C2#64093⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#638⋊C32
C22×C4⋊((C3⋊D3)⋊C3)2
C22×C4×(C3⋊D3)⋊C32
C2×C22⋊C4×H(3,𝔽3)2
C2×#3752⋊C32
C2×#3750⋊C32
#64093⋊C32
C2×#640933
C2×C3×#8843