Finite Group Databasebeta

← #10596067⋊C3 #13152839

Subgroups — #10596067⋊C3 #13152839

Order 1728.

1179 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3830⋊C3C212yesmaximal, complemented
2H(3,𝔽3)×#121C211yesmaximal, characteristic, complemented
3#64149⋊C3C211yesmaximal, characteristic, complemented
4#64148⋊C3C212yesmaximal, complemented
5D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
6#64139⋊C3C211yesmaximal, characteristic, complemented
7C2×C4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
8#64102⋊C3C211yesmaximal, characteristic, complemented
9#64097⋊C3C211yesmaximal, characteristic, complemented
10#64094⋊C3C212yesmaximal, complemented
11#64090⋊C3C212yesmaximal, complemented
12#10596067C311yesmaximal, characteristic, complemented
13C3×#5596—31nomaximal
14C2×D4×H(3,𝔽3)C2212yes—
15C2×D4×H(3,𝔽3)C2211yescharacteristic
16C22×C4×H(3,𝔽3)C2211yescharacteristic
17C2×#638⋊C3C2212yes—
18C2×#638⋊C3C2212yes—
19C2×#638⋊C3C2212yes—
20C22×(C3⋊Dic3)⋊C3C2212yes—
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23#3830⋊C3—28no—
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2212yes—
26C2×#634⋊C3C2212yes—
27C4⋊C4×H(3,𝔽3)C2211yescharacteristic
28C22⋊C4×H(3,𝔽3)C2212yes—
29#3757⋊C3C2212yes—
30#3752⋊C3C2212yes—
31#3752⋊C3C2212yes—
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
33#3750⋊C3C2212yes—
34C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
35C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
36C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
37C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
38C2×#3830C2×C312yescomplemented
39C2×C3×#237—32no—
40C32×#121—21no—
41C32×#121D311yescharacteristic, complemented
42C32×#121C2×C311yescharacteristic, complemented
43#64149C2×C311yescharacteristic, complemented
44#64148C2×C312yescomplemented
45D4×C3⋊Dic3C2×C311yescharacteristic, complemented
46#64139C2×C311yescharacteristic, complemented
47C2×C4×C3⋊Dic3C2×C311yescharacteristic, complemented
48#64102C2×C311yescharacteristic, complemented
49#64097C2×C311yescharacteristic, complemented
50#64094C2×C312yescomplemented
51#64090C2×C312yescomplemented
52C3×#940—31no—
53C3×#939—32no—
54C3×D4×Dic3—31no—
55C3×#930—31no—
56C2×C3×C4×Dic3—31no—
57C3×#893—31no—
58C3×#888—31no—
59C3×#885—32no—
60C3×#67⋊C4—32no—
61C23×H(3,𝔽3)C2312yes—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3C2312yes—
64D4×H(3,𝔽3)—24no—
65D4×H(3,𝔽3)—22no—
66C2×C4×H(3,𝔽3)—22no—
67C2×C4×H(3,𝔽3)C2312yes—
68C2×C4×H(3,𝔽3)C2311yescharacteristic
69C2×C4×H(3,𝔽3)C2311yescharacteristic
70#638⋊C3—24no—
71#638⋊C3—24no—
72#638⋊C3—24no—
73C2×(C3⋊Dic3)⋊C3—24no—
74C2×(C3⋊Dic3)⋊C3—22no—
75C2×(C3⋊Dic3)⋊C3D414yescomplemented
76C2×(C3⋊Dic3)⋊C3C2312yes—
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
80C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
81C4⋊((C3⋊D3)⋊C3)—22no—
82C4×(C3⋊D3)⋊C3—24no—
83#634⋊C3—24no—
84C3×#532—91no—
85#5596—31no—
86#5596—91no—
87C2×C32×D4—21no—
88C2×C32×D4—22no—
89C2×C32×D4C2×D311yescharacteristic
90C2×C32×D4C2×D312yes—
91C2×C32×D4C22×C312yes—
92C2×C32×D4C22×C311yescharacteristic
93C22×C32×C4—21no—
94C22×C32×C4C2×D311yescharacteristic
95C22×C32×C4C22×C311yescharacteristic
96C2×#638C22×C312yes—
97C2×#638C22×C312yes—
98C2×#638C22×C312yes—
99C22×C3⋊Dic3C22×C312yes—
100C22×C3⋊Dic3C22×C311yescharacteristic
101C22×C3⋊Dic3C22×C311yescharacteristic
102#3830—28no—
103C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
104C2×C4×C3⋊D3C22×C312yes—
105C2×#634C22×C312yes—
106C2×C3×#67—32no—
107C2×C3×#67—32no—
108C2×C3×#67—32no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—32no—
111C22×C3×Dic3—31no—
112C3×#237—68no—
113C2×C3×D12—31no—
114C2×C3×C4×D3—32no—
115C2×C3×Dic6—32no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2×D311yescharacteristic
118C32×C4⋊C4C22×C311yescharacteristic
119C32×C22⋊C4—22no—
120C32×C22⋊C4C2×D312yes—
121C32×C22⋊C4C22×C312yes—
122#3757C22×C312yes—
123#3752C22×C312yes—
124#3752C22×C312yes—
125C4⋊(C3⋊Dic3)C22×C311yescharacteristic
126#3750C22×C312yes—
127C4×C3⋊Dic3C22×C311yescharacteristic
128C4×C3⋊Dic3C22×C311yescharacteristic
129C4×C3⋊Dic3C22×C311yescharacteristic
130C4×C3⋊Dic3C22×C311yescharacteristic
131C3×#217—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×C4⋊Dic3—31no—
135C3×Dic3⋊C4—32no—
136C3×C4×Dic3—31no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—31no—
140C22×H(3,𝔽3)—21no—
141C22×H(3,𝔽3)—21no—
142C22×H(3,𝔽3)—22no—
143C22×H(3,𝔽3)—22no—
144C22×H(3,𝔽3)—22no—
145C22×H(3,𝔽3)C2×D412yes—
146C22×H(3,𝔽3)C2411yescharacteristic
147C2×(C3⋊D3)⋊C3—22no—
148C2×(C3⋊D3)⋊C3—22no—
149C2×(C3⋊D3)⋊C3—22no—
150C4×H(3,𝔽3)—22no—
151C4×H(3,𝔽3)—21no—
152C4×H(3,𝔽3)#4112yescomplemented
153(C3⋊Dic3)⋊C3—22no—
154(C3⋊Dic3)⋊C3—21no—
155(C3⋊Dic3)⋊C3C2×D412yes—
156(C3⋊Dic3)⋊C3C2×D412yes—
157(C3⋊Dic3)⋊C3#4112yescomplemented
158C2×C3×#41—92no—
159C2×#237—32no—
160C2×#237—92no—
161C3×C4⋊Q8—91no—
162C3×#127—91no—
163C3×#124—92no—
164C3×#121—31no—
165C3×#121—31no—
166C3×#121—61no—
167C3×#121—91no—
168C3×#121—92no—
169C3×#121C3×D311yescharacteristic
170C3×C4×D4—92no—
171C3×C4×D4—91no—
172C3×C4×D4—91no—
173C2×C3×C42—91no—
174#940—31no—
175#940—91no—
176#939—32no—
177#939—92no—
178D4×Dic3—31no—
179D4×Dic3—91no—
180#930—31no—
181#930—91no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—91no—
184#893—31no—
185#893—91no—
186#888—31no—
187#888—91no—
188#885—32no—
189#885—92no—
190#67⋊C4—32no—
191#67⋊C4—92no—
192C23×C32—21no—
193C23×C32—22no—
194C23×C32C22×D312yes—
195C23×C32C22×D311yescharacteristic
196C23×C32C23×C312yes—
197C23×C32C23×C311yescharacteristic
198C22×C3⋊D3C23×C312yes—
199C22×C3×D3—32no—
200C32×D4—24no—
201C32×D4—24no—
202C32×D4—22no—
203C32×D4—22no—
204C32×D4—42no—
205C32×D4—44no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—22no—
211C2×C32×C4—42no—
212C2×C32×C4C22×D311yescharacteristic
213C2×C32×C4C22×D312yes—
214C2×C32×C4C22×D311yescharacteristic
215C2×C32×C4C23×C311yescharacteristic
216C2×C32×C4C23×C312yes—
217C2×C32×C4C23×C311yescharacteristic
218#638—24no—
219#638—24no—
220#638—24no—
221C2×C3⋊Dic3—24no—
222C2×C3⋊Dic3—22no—
223C2×C3⋊Dic3C3×D414yescomplemented
224C2×C3⋊Dic3C23×C311yescharacteristic
225C2×C3⋊Dic3C23×C312yes—
226C2×C3⋊Dic3C23×C311yescharacteristic
227C2×C3⋊Dic3C23×C311yescharacteristic
228C2×C3⋊Dic3C23×C311yescharacteristic
229C4⋊(C3⋊D3)—22no—
230C4×C3⋊D3—24no—
231#634—24no—
232C3×#67—64no—
233C3×#67—64no—
234C3×#67—64no—
235C2×C3×Dic3—34no—
236C2×C3×Dic3—31no—
237C2×C3×Dic3—31no—
238C2×C3×Dic3—31no—
239C2×C3×Dic3—31no—
240C2×C3×Dic3—32no—
241C2×C3×Dic3—64no—
242C2×C3×Dic3—62no—
243C3×D12—62no—
244C3×C4×D3—64no—
245C3×Dic6—64no—
246#532—91noSylow
247C2×H(3,𝔽3)—22no—
248C2×H(3,𝔽3)—42no—
249C2×H(3,𝔽3)C22×D411yescharacteristic
250C2×H(3,𝔽3)C2×#4111yescharacteristic
251C2×H(3,𝔽3)C2×#4111yescharacteristic
252(C3⋊D3)⋊C3—42no—
253C3×#41—188no—
254C2×C3×Q8—92no—
255C2×C3×D4—31no—
256C2×C3×D4—32no—
257C2×C3×D4—31no—
258C2×C3×D4—32no—
259C2×C3×D4—61no—
260C2×C3×D4—62no—
261C2×C3×D4—91no—
262C2×C3×D4—92no—
263C2×C3×D4—92no—
264C2×C3×D4—92no—
265C2×C3×D4C2×C3×D311yescharacteristic
266C2×C3×D4C2×C3×D312yes—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—61no—
270C22×C3×C4—92no—
271C22×C3×C4—91no—
272C22×C3×C4—91no—
273C22×C3×C4—92no—
274C22×C3×C4C2×C3×D311yescharacteristic
275C2×#67—32no—
276C2×#67—32no—
277C2×#67—32no—
278C2×#67—92no—
279C2×#67—92no—
280C2×#67—92no—
281C22×Dic3—31no—
282C22×Dic3—32no—
283C22×Dic3—31no—
284C22×Dic3—91no—
285C22×Dic3—92no—
286C22×Dic3—91no—
287#237—68no—
288#237—188no—
289C2×D12—31no—
290C2×D12—91no—
291C2×C4×D3—32no—
292C2×C4×D3—92no—
293C2×Dic6—32no—
294C2×Dic6—92no—
295C3×C4⋊C4—31no—
296C3×C4⋊C4—31no—
297C3×C4⋊C4—61no—
298C3×C4⋊C4—92no—
299C3×C4⋊C4—91no—
300C3×C4⋊C4C2×C3×D311yescharacteristic
301C3×C22⋊C4—32no—
302C3×C22⋊C4—32no—
303C3×C22⋊C4—62no—
304C3×C22⋊C4—92no—
305C3×C22⋊C4—92no—
306C3×C22⋊C4—92no—
307C3×C22⋊C4C2×C3×D312yes—
308C3×C42—91no—
309C3×C42—91no—
310C3×C42—91no—
311C3×C42—91no—
312#217—32no—
313#217—92no—
314(C2×D3)⋊C4—32no—
315(C2×D3)⋊C4—32no—
316(C2×D3)⋊C4—92no—
317(C2×D3)⋊C4—92no—
318C4⋊Dic3—31no—
319C4⋊Dic3—91no—
320Dic3⋊C4—32no—
321Dic3⋊C4—92no—
322C4×Dic3—31no—
323C4×Dic3—31no—
324C4×Dic3—31no—
325C4×Dic3—31no—
326C4×Dic3—91no—
327C4×Dic3—91no—
328C4×Dic3—91no—
329C4×Dic3—91no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—22no—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—22no—
340C22×C32—21no—
341C22×C32—22no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—42no—
345C22×C32—42no—
346C22×C32—42no—
347C22×C32D3×D412yes—
348C22×C32C2×C3×D412yes—
349C22×C32C23×D311yescharacteristic
350C22×C32C24×C311yescharacteristic
351C2×C3⋊D3—22no—
352C2×C3⋊D3—22no—
353C2×C3⋊D3—22no—
354C2×C3×D3—62no—
355C2×C3×D3—62no—
356C2×C3×D3—62no—
357C32×C4—22no—
358C32×C4—21no—
359C32×C4—22no—
360C32×C4—21no—
361C32×C4—22no—
362C32×C4—41no—
363C32×C4—42no—
364C32×C4#23712yescomplemented
365C32×C4C3×#4112yescomplemented
366C3⋊Dic3—22no—
367C3⋊Dic3—21no—
368C3⋊Dic3C2×C3×D412yes—
369C3⋊Dic3C2×C3×D412yes—
370C3⋊Dic3C3×#4112yescomplemented
371C3×Dic3—32no—
372C3×Dic3—32no—
373C3×Dic3—32no—
374C3×Dic3—62no—
375C3×Dic3—61no—
376C2×#41—92no—
377C4⋊Q8—91no—
378#127—91no—
379#124—92no—
380#121—92no—
381#121—91no—
382#121(C3⋊D3)⋊C311yescharacteristic, complemented
383C4×D4—91no—
384C4×D4—91no—
385C4×D4—92no—
386C2×C42—91no—
387H(3,𝔽3)#53211yescharacteristic, complemented, Sylow
388C23×C3—31no—
389C23×C3—31no—
390C23×C3—32no—
391C23×C3—32no—
392C23×C3—61no—
393C23×C3—62no—
394C23×C3—92no—
395C23×C3C22×C3×D312yes—
396C23×C3C22×C3×D311yescharacteristic
397C22×D3—32no—
398C22×D3—92no—
399C3×Q8—184no—
400C3×D4—24no—
401C3×D4—22no—
402C3×D4—62no—
403C3×D4—62no—
404C3×D4—64no—
405C3×D4—64no—
406C3×D4—122no—
407C3×D4—124no—
408C3×D4—182no—
409C3×D4—184no—
410C3×D4—184no—
411C3×D4—184no—
412C2×C3×C4—22no—
413C2×C3×C4—31no—
414C2×C3×C4—31no—
415C2×C3×C4—31no—
416C2×C3×C4—32no—
417C2×C3×C4—31no—
418C2×C3×C4—32no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—62no—
424C2×C3×C4—91no—
425C2×C3×C4—91no—
426C2×C3×C4—91no—
427C2×C3×C4—94no—
428C2×C3×C4—91no—
429C2×C3×C4—92no—
430C2×C3×C4—122no—
431C2×C3×C4—184no—
432C2×C3×C4—182no—
433C2×C3×C4—184no—
434C2×C3×C4C22×C3×D311yescharacteristic
435C2×C3×C4C22×C3×D312yes—
436C2×C3×C4C22×C3×D311yescharacteristic
437#67—64no—
438#67—64no—
439#67—64no—
440#67—184no—
441#67—184no—
442#67—184no—
443C2×Dic3—31no—
444C2×Dic3—31no—
445C2×Dic3—31no—
446C2×Dic3—34no—
447C2×Dic3—31no—
448C2×Dic3—32no—
449C2×Dic3—64no—
450C2×Dic3—62no—
451C2×Dic3—94no—
452C2×Dic3—91no—
453C2×Dic3—91no—
454C2×Dic3—91no—
455C2×Dic3—91no—
456C2×Dic3—92no—
457C2×Dic3—184no—
458C2×Dic3—182no—
459D12—62no—
460D12—182no—
461C4×D3—64no—
462C4×D3—184no—
463Dic6—64no—
464Dic6—184no—
465C2×C32—22no—
466C2×C32—22no—
467C2×C32—21no—
468C2×C32—21no—
469C2×C32—21no—
470C2×C32—42no—
471C2×C32—42no—
472C2×C32—42no—
473C2×C32—82no—
474C2×C32C2×D3×D411yescharacteristic
475C2×C32C2×#23711yescharacteristic
476C2×C32D3×#4111yescharacteristic
477C2×C32C22×C3×D411yescharacteristic
478C2×C32C2×C3×#4111yescharacteristic
479C2×C32C2×C3×#4111yescharacteristic
480C3⋊D3—42no—
481C3×D3—122no—
482#41—188no—
483C2×Q8—92no—
484C2×D4—92no—
485C2×D4—92no—
486C2×D4—92no—
487C2×D4—91no—
488C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
489C2×D4C2×(C3⋊D3)⋊C312yes—
490C22×C4—91no—
491C22×C4—91no—
492C22×C4—92no—
493C22×C4—92no—
494C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
495C4⋊C4—92no—
496C4⋊C4—91no—
497C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
498C22⋊C4—92no—
499C22⋊C4—92no—
500C22⋊C4—92no—
501C22⋊C4C2×(C3⋊D3)⋊C312yes—
502C42—91no—
503C42—91no—
504C42—91no—
505C42—91no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—31no—
512C22×C3—31no—
513C22×C3—32no—
514C22×C3—32no—
515C22×C3—61no—
516C22×C3—61no—
517C22×C3—61no—
518C22×C3—61no—
519C22×C3—62no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—62no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—61no—
526C22×C3—62no—
527C22×C3—121no—
528C22×C3—121no—
529C22×C3—122no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3—182no—
533C22×C3—182no—
534C22×C3—182no—
535C22×C3C3×D3×D412yes—
536C22×C3C23×C3×D311yescharacteristic
537C2×D3—62no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—182no—
541C2×D3—182no—
542C2×D3—182no—
543C3×C4—22no—
544C3×C4—21no—
545C3×C4—32no—
546C3×C4—32no—
547C3×C4—62no—
548C3×C4—61no—
549C3×C4—61no—
550C3×C4—62no—
551C3×C4—62no—
552C3×C4—92no—
553C3×C4—92no—
554C3×C4—92no—
555C3×C4—121no—
556C3×C4—122no—
557C3×C4—182no—
558C3×C4—181no—
559C3×C4C3×#23712yes—
560Dic3—32no—
561Dic3—32no—
562Dic3—32no—
563Dic3—62no—
564Dic3—61no—
565Dic3—92no—
566Dic3—92no—
567Dic3—92no—
568Dic3—182no—
569Dic3—181no—
570C32—21no—
571C32#559611yescharacteristic, complemented
572C32C3×#53211yescharacteristic, complemented
573C23—92no—
574C23C22×(C3⋊D3)⋊C312yes—
575C23C22×(C3⋊D3)⋊C311yescharacteristic
576Q8—184no—
577D4—24no—
578D4—22no—
579D4—184no—
580D4—184no—
581D4—184no—
582D4—182no—
583C2×C4—22no—
584C2×C4—91no—
585C2×C4—91no—
586C2×C4—91no—
587C2×C4—94no—
588C2×C4—91no—
589C2×C4—92no—
590C2×C4—184no—
591C2×C4—184no—
592C2×C4—182no—
593C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
594C2×C4C22×(C3⋊D3)⋊C312yes—
595C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
596C2×C3—22no—
597C2×C3—31no—
598C2×C3—31no—
599C2×C3—31no—
600C2×C3—31no—
601C2×C3—31no—
602C2×C3—31no—
603C2×C3—42no—
604C2×C3—62no—
605C2×C3—62no—
606C2×C3—61no—
607C2×C3—61no—
608C2×C3—61no—
609C2×C3—122no—
610C2×C3—122no—
611C2×C3—122no—
612C2×C3—242no—
613C2×C3—362no—
614C2×C3C2×C3×D3×D411yescharacteristic
615C2×C3C2×C3×#23711yescharacteristic
616C2×C3C3×D3×#4111yescharacteristic
617D3—122no—
618D3—362no—
619C22—21no—
620C22—21no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—182no—
625C22—182no—
626C22—182no—
627C22D4×(C3⋊D3)⋊C312yes—
628C22C23×(C3⋊D3)⋊C311yescharacteristic
629C4—22no—
630C4—21no—
631C4—92no—
632C4—92no—
633C4—92no—
634C4—182no—
635C4—181no—
636C4#3830⋊C312yescomplemented
637C3—31no—
638C3—31no—
639C3—61no—
640C3C3×#559611yescharacteristic
641C2—22no—
642C2—42no—
643C2—362no—
644C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
645C2C2×#3830⋊C311yescharacteristic
646C2#41×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#121C2
hypercenter#121(C3⋊D3)⋊C3
hypocenterC32C3×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#3830⋊C3C2semidirect
2. H(3,𝔽3)×#121C2semidirect
3. #64149⋊C3C2semidirect
4. #64148⋊C3C2semidirect
5. D4×(C3⋊Dic3)⋊C3C2semidirect
6. #64139⋊C3C2semidirect
7. C2×C4×(C3⋊Dic3)⋊C3C2semidirect
8. #64102⋊C3C2semidirect
9. #64097⋊C3C2semidirect
10. #64094⋊C3C2semidirect
11. #64090⋊C3C2semidirect
12. #10596067C3semidirect
38. C2×#3830C2×C3semidirect
41. C32×#121D3semidirect
42. C32×#121C2×C3semidirect
43. #64149C2×C3semidirect
44. #64148C2×C3semidirect
45. D4×C3⋊Dic3C2×C3semidirect
46. #64139C2×C3semidirect
47. C2×C4×C3⋊Dic3C2×C3semidirect
48. #64102C2×C3semidirect
49. #64097C2×C3semidirect
50. #64094C2×C3semidirect
51. #64090C2×C3semidirect
75. C2×(C3⋊Dic3)⋊C3D4semidirect
152. C4×H(3,𝔽3)#41semidirect
157. (C3⋊Dic3)⋊C3#41semidirect
223. C2×C3⋊Dic3C3×D4semidirect
364. C32×C4#237semidirect
365. C32×C4C3×#41semidirect
370. C3⋊Dic3C3×#41semidirect
382. #121(C3⋊D3)⋊C3semidirect
387. H(3,𝔽3)#532semidirect
571. C32#5596semidirect
572. C32C3×#532semidirect
636. C4#3830⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#3830⋊C32
H(3,𝔽3)×#1212
#64149⋊C32
#64148⋊C32
D4×(C3⋊Dic3)⋊C32
#64139⋊C32
C2×C4×(C3⋊Dic3)⋊C32
#64102⋊C32
#64097⋊C32
#64094⋊C32
#64090⋊C32
#105960673
C3×#55963