Finite Group Databasebeta

← #10596069⋊C3 #13152841

Subgroups — #10596069⋊C3 #13152841

Order 1728.

1109 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⋊C3C211yesmaximal, characteristic, complemented
2C22×#634⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#121C211yesmaximal, characteristic, complemented
4#64148⋊C3C212yesmaximal, complemented
5#64145⋊C3C211yesmaximal, characteristic, complemented
6D4×(C3⋊Dic3)⋊C3C212yesmaximal, complemented
7C4×#638⋊C3C211yesmaximal, characteristic, complemented
8#64106⋊C3C211yesmaximal, characteristic, complemented
9#64096⋊C3C211yesmaximal, characteristic, complemented
10#64094⋊C3C212yesmaximal, complemented
11#64087⋊C3C212yesmaximal, complemented
12#10596069C311yesmaximal, characteristic, complemented
13C3×#5598—31nomaximal
14C2×D4×H(3,𝔽3)C2211yescharacteristic
15C2×D4×H(3,𝔽3)C2212yes—
16C22×C4×H(3,𝔽3)C2211yescharacteristic
17C2×#638⋊C3C2212yes—
18C2×#638⋊C3C2211yescharacteristic
19C22×(C3⋊Dic3)⋊C3C2212yes—
20C22×(C3⋊Dic3)⋊C3C2212yes—
21#3830⋊C3—24no—
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×#634⋊C3—24no—
24C2×#634⋊C3C2211yescharacteristic
25C2×#634⋊C3C2212yes—
26C2×#634⋊C3C2211yescharacteristic
27C4⋊C4×H(3,𝔽3)C2211yescharacteristic
28C22⋊C4×H(3,𝔽3)C2212yes—
29#3757⋊C3C2211yescharacteristic
30#3757⋊C3C2212yes—
31#3757⋊C3C2212yes—
32#3752⋊C3C2211yescharacteristic
33#3752⋊C3C2212yes—
34C4⋊((C3⋊Dic3)⋊C3)C2212yes—
35#3750⋊C3C2211yescharacteristic
36#3750⋊C3C2212yes—
37C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
38C4×(C3⋊Dic3)⋊C3C2212yes—
39C2×#3830C2×C311yescharacteristic, complemented
40C22×#634C2×C311yescharacteristic, complemented
41C2×C3×#237—31no—
42C22×C3×Dic6—31no—
43C32×#121—21no—
44C32×#121D311yescharacteristic, complemented
45C32×#121C2×C311yescharacteristic, complemented
46#64148C2×C312yescomplemented
47#64145C2×C311yescharacteristic, complemented
48D4×C3⋊Dic3C2×C312yescomplemented
49C4×#638C2×C311yescharacteristic, complemented
50#64106C2×C311yescharacteristic, complemented
51#64096C2×C311yescharacteristic, complemented
52#64094C2×C312yescomplemented
53#64087C2×C312yescomplemented
54C3×#939—32no—
55C3×#936—31no—
56C3×D4×Dic3—32no—
57C3×C4×#67—31no—
58C3×#897—31no—
59C3×#887—31no—
60C3×#885—32no—
61C3×#878—32no—
62C23×H(3,𝔽3)C2312yes—
63C23×H(3,𝔽3)C2311yescharacteristic
64C22×(C3⋊D3)⋊C3C2311yescharacteristic
65D4×H(3,𝔽3)—24no—
66D4×H(3,𝔽3)—22no—
67C2×C4×H(3,𝔽3)—22no—
68C2×C4×H(3,𝔽3)C2311yescharacteristic
69C2×C4×H(3,𝔽3)C2312yes—
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71#638⋊C3—22no—
72#638⋊C3—24no—
73C2×(C3⋊Dic3)⋊C3—24no—
74C2×(C3⋊Dic3)⋊C3—24no—
75C2×(C3⋊Dic3)⋊C3C2312yes—
76C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C2×(C3⋊Dic3)⋊C3C2312yes—
80C4×(C3⋊D3)⋊C3—22no—
81#634⋊C3—22no—
82#634⋊C3—24no—
83#634⋊C3D414yescomplemented
84C3×#548—91no—
85#5598—31no—
86#5598—91no—
87C2×C32×D4—21no—
88C2×C32×D4—22no—
89C2×C32×D4C2×D312yes—
90C2×C32×D4C2×D311yescharacteristic
91C2×C32×D4C22×C311yescharacteristic
92C2×C32×D4C22×C312yes—
93C22×C32×C4—21no—
94C22×C32×C4C2×D311yescharacteristic
95C22×C32×C4C22×C311yescharacteristic
96C2×#638C22×C312yes—
97C2×#638C22×C311yescharacteristic
98C22×C3⋊Dic3C22×C312yes—
99C22×C3⋊Dic3C22×C312yes—
100#3830—24no—
101C2×C4×C3⋊D3C22×C311yescharacteristic
102C2×#634—24no—
103C2×#634C22×C312yes—
104C2×#634C22×C311yescharacteristic
105C2×#634C22×C311yescharacteristic
106C2×C3×#67—32no—
107C2×C3×#67—31no—
108C22×C3×Dic3—32no—
109C22×C3×Dic3—32no—
110C3×#237—64no—
111C2×C3×C4×D3—31no—
112C2×C3×Dic6—31no—
113C2×C3×Dic6—32no—
114C2×C3×Dic6—31no—
115C2×C3×Dic6—64no—
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#3757C22×C312yes—
124#3757C22×C311yescharacteristic
125#3752C22×C311yescharacteristic
126#3752C22×C312yes—
127C4⋊(C3⋊Dic3)C22×C312yes—
128#3750C22×C311yescharacteristic
129#3750C22×C312yes—
130C4×C3⋊Dic3C22×C312yes—
131C4×C3⋊Dic3C22×C311yescharacteristic
132C3×#217—32no—
133C3×#217—32no—
134C3×#217—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—32no—
137C3×C4⋊Dic3—32no—
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4—32no—
140C3×C4×Dic3—32no—
141C3×C4×Dic3—31no—
142C22×H(3,𝔽3)—21no—
143C22×H(3,𝔽3)—21no—
144C22×H(3,𝔽3)—22no—
145C22×H(3,𝔽3)—22no—
146C22×H(3,𝔽3)—22no—
147C22×H(3,𝔽3)#4112yescomplemented
148C22×H(3,𝔽3)C2411yescharacteristic
149C2×(C3⋊D3)⋊C3—21no—
150C2×(C3⋊D3)⋊C3—21no—
151C2×(C3⋊D3)⋊C3—21no—
152C4×H(3,𝔽3)—21no—
153C4×H(3,𝔽3)—22no—
154C4×H(3,𝔽3)C2×D412yes—
155(C3⋊Dic3)⋊C3—22no—
156(C3⋊Dic3)⋊C3—21no—
157(C3⋊Dic3)⋊C3—21no—
158(C3⋊Dic3)⋊C3—21no—
159(C3⋊Dic3)⋊C3C2×D414yes—
160C2×C3×#41—91no—
161C22×C3×Q8—91no—
162C2×#237—31no—
163C2×#237—91no—
164C22×Dic6—31no—
165C22×Dic6—91no—
166C3×#124—92no—
167C3×#124—91no—
168C3×C22⋊Q8—92no—
169C3×C22⋊Q8—91no—
170C3×#121—31no—
171C3×#121—31no—
172C3×#121—61no—
173C3×#121—92no—
174C3×#121C3×D311yescharacteristic
175C3×C4×Q8—91no—
176C3×C4×D4—91no—
177C3×C4×D4—92no—
178#939—32no—
179#939—92no—
180#936—31no—
181#936—91no—
182D4×Dic3—32no—
183D4×Dic3—92no—
184C4×#67—31no—
185C4×#67—91no—
186#897—31no—
187#897—91no—
188#887—31no—
189#887—91no—
190#885—32no—
191#885—92no—
192#878—32no—
193#878—92no—
194C23×C32—21no—
195C23×C32—22no—
196C23×C32C22×D312yes—
197C23×C32C22×D311yescharacteristic
198C23×C32C23×C312yes—
199C23×C32C23×C311yescharacteristic
200C22×C3⋊D3C23×C311yescharacteristic
201C22×C3×D3—31no—
202C32×D4—24no—
203C32×D4—24no—
204C32×D4—22no—
205C32×D4—22no—
206C32×D4—42no—
207C32×D4—44no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—22no—
213C2×C32×C4—42no—
214C2×C32×C4C22×D312yes—
215C2×C32×C4C22×D311yescharacteristic
216C2×C32×C4C22×D311yescharacteristic
217C2×C32×C4C23×C312yes—
218C2×C32×C4C23×C311yescharacteristic
219C2×C32×C4C23×C311yescharacteristic
220#638—22no—
221#638—24no—
222C2×C3⋊Dic3—24no—
223C2×C3⋊Dic3—24no—
224C2×C3⋊Dic3C23×C311yescharacteristic
225C2×C3⋊Dic3C23×C311yescharacteristic
226C2×C3⋊Dic3C23×C311yescharacteristic
227C2×C3⋊Dic3C23×C312yes—
228C2×C3⋊Dic3C23×C312yes—
229C4×C3⋊D3—22no—
230#634—22no—
231#634—24no—
232#634C3×D414yescomplemented
233C3×#67—64no—
234C3×#67—62no—
235C2×C3×Dic3—32no—
236C2×C3×Dic3—31no—
237C2×C3×Dic3—31no—
238C2×C3×Dic3—31no—
239C2×C3×Dic3—32no—
240C2×C3×Dic3—64no—
241C2×C3×Dic3—64no—
242C3×C4×D3—62no—
243C3×Dic6—34no—
244C3×Dic6—64no—
245C3×Dic6—62no—
246#548—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)2−1+411yescharacteristic
252(C3⋊D3)⋊C3—41no—
253C3×#41—184no—
254C2×C3×Q8—91no—
255C2×C3×Q8—91no—
256C2×C3×Q8—92no—
257C2×C3×Q8—184no—
258C2×C3×D4—32no—
259C2×C3×D4—31no—
260C2×C3×D4—32no—
261C2×C3×D4—31no—
262C2×C3×D4—62no—
263C2×C3×D4—61no—
264C2×C3×D4—91no—
265C2×C3×D4—92no—
266C2×C3×D4C2×C3×D312yes—
267C2×C3×D4C2×C3×D311yescharacteristic
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—61no—
271C22×C3×C4—91no—
272C22×C3×C4—92no—
273C22×C3×C4—92no—
274C22×C3×C4C2×C3×D311yescharacteristic
275C2×#67—32no—
276C2×#67—31no—
277C2×#67—92no—
278C2×#67—91no—
279C22×Dic3—32no—
280C22×Dic3—32no—
281C22×Dic3—92no—
282C22×Dic3—92no—
283#237—64no—
284#237—184no—
285C2×C4×D3—31no—
286C2×C4×D3—91no—
287C2×Dic6—31no—
288C2×Dic6—32no—
289C2×Dic6—31no—
290C2×Dic6—64no—
291C2×Dic6—91no—
292C2×Dic6—92no—
293C2×Dic6—91no—
294C2×Dic6—184no—
295C3×C4⋊C4—31no—
296C3×C4⋊C4—31no—
297C3×C4⋊C4—61no—
298C3×C4⋊C4—91no—
299C3×C4⋊C4—92no—
300C3×C4⋊C4—92no—
301C3×C4⋊C4C2×C3×D311yescharacteristic
302C3×C22⋊C4—32no—
303C3×C22⋊C4—32no—
304C3×C22⋊C4—62no—
305C3×C22⋊C4—91no—
306C3×C22⋊C4—92no—
307C3×C22⋊C4—91no—
308C3×C22⋊C4—92no—
309C3×C22⋊C4—92no—
310C3×C22⋊C4C2×C3×D312yes—
311C3×C42—91no—
312C3×C42—92no—
313#217—32no—
314#217—32no—
315#217—31no—
316#217—92no—
317#217—92no—
318#217—91no—
319(C2×D3)⋊C4—31no—
320(C2×D3)⋊C4—32no—
321(C2×D3)⋊C4—91no—
322(C2×D3)⋊C4—92no—
323C4⋊Dic3—32no—
324C4⋊Dic3—92no—
325Dic3⋊C4—31no—
326Dic3⋊C4—32no—
327Dic3⋊C4—91no—
328Dic3⋊C4—92no—
329C4×Dic3—32no—
330C4×Dic3—31no—
331C4×Dic3—92no—
332C4×Dic3—91no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32—21no—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—21no—
344C22×C32—22no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—42no—
348C22×C32—42no—
349C22×C32—42no—
350C22×C32#23712yescomplemented
351C22×C32C3×#4112yescomplemented
352C22×C32C23×D311yescharacteristic
353C22×C32C24×C311yescharacteristic
354C2×C3⋊D3—21no—
355C2×C3⋊D3—21no—
356C2×C3⋊D3—21no—
357C2×C3×D3—61no—
358C2×C3×D3—61no—
359C2×C3×D3—61no—
360C32×C4—21no—
361C32×C4—22no—
362C32×C4—21no—
363C32×C4—22no—
364C32×C4—22no—
365C32×C4—41no—
366C32×C4—42no—
367C32×C4D3×D412yes—
368C32×C4C2×C3×D412yes—
369C3⋊Dic3—22no—
370C3⋊Dic3—21no—
371C3⋊Dic3—21no—
372C3⋊Dic3—21no—
373C3⋊Dic3C2×C3×D414yes—
374C3×Dic3—34no—
375C3×Dic3—62no—
376C3×Dic3—61no—
377C3×Dic3—61no—
378C3×Dic3—61no—
379C2×#41—91no—
380C22×Q8—91no—
381#124—91no—
382#124—92no—
383C22⋊Q8—91no—
384C22⋊Q8—92no—
385#121—92no—
386#121(C3⋊D3)⋊C311yescharacteristic, complemented
387C4×Q8—91no—
388C4×D4—92no—
389C4×D4—91no—
390H(3,𝔽3)#54811yescharacteristic, complemented, Sylow
391C23×C3—31no—
392C23×C3—31no—
393C23×C3—32no—
394C23×C3—32no—
395C23×C3—61no—
396C23×C3—62no—
397C23×C3—91no—
398C23×C3C22×C3×D312yes—
399C23×C3C22×C3×D311yescharacteristic
400C22×D3—31no—
401C22×D3—91no—
402C3×Q8—94no—
403C3×Q8—182no—
404C3×Q8—184no—
405C3×D4—24no—
406C3×D4—22no—
407C3×D4—62no—
408C3×D4—62no—
409C3×D4—64no—
410C3×D4—64no—
411C3×D4—122no—
412C3×D4—124no—
413C3×D4—184no—
414C3×D4—182no—
415C2×C3×C4—22no—
416C2×C3×C4—31no—
417C2×C3×C4—31no—
418C2×C3×C4—32no—
419C2×C3×C4—31no—
420C2×C3×C4—32no—
421C2×C3×C4—31no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—62no—
427C2×C3×C4—92no—
428C2×C3×C4—91no—
429C2×C3×C4—91no—
430C2×C3×C4—92no—
431C2×C3×C4—91no—
432C2×C3×C4—122no—
433C2×C3×C4—182no—
434C2×C3×C4—184no—
435C2×C3×C4—184no—
436C2×C3×C4C22×C3×D312yes—
437C2×C3×C4C22×C3×D311yescharacteristic
438C2×C3×C4C22×C3×D311yescharacteristic
439#67—64no—
440#67—62no—
441#67—184no—
442#67—182no—
443C2×Dic3—32no—
444C2×Dic3—31no—
445C2×Dic3—31no—
446C2×Dic3—31no—
447C2×Dic3—32no—
448C2×Dic3—64no—
449C2×Dic3—64no—
450C2×Dic3—92no—
451C2×Dic3—91no—
452C2×Dic3—91no—
453C2×Dic3—91no—
454C2×Dic3—92no—
455C2×Dic3—184no—
456C2×Dic3—184no—
457C4×D3—62no—
458C4×D3—182no—
459Dic6—34no—
460Dic6—64no—
461Dic6—62no—
462Dic6—94no—
463Dic6—184no—
464Dic6—182no—
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×C32#101011yescharacteristic
477C2×C32C22×C3×D411yescharacteristic
478C2×C32C2×C3×#4111yescharacteristic
479C2×C32C3×2−1+411yescharacteristic
480C3⋊D3—41no—
481C3×D3—121no—
482#41—184no—
483C2×Q8—91no—
484C2×Q8—92no—
485C2×Q8—91no—
486C2×Q8—184no—
487C2×D4—91no—
488C2×D4—92no—
489C2×D4C2×(C3⋊D3)⋊C312yes—
490C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
491C22×C4—92no—
492C22×C4—92no—
493C22×C4—91no—
494C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
495C4⋊C4—91no—
496C4⋊C4—92no—
497C4⋊C4—92no—
498C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
499C22⋊C4—91no—
500C22⋊C4—92no—
501C22⋊C4—92no—
502C22⋊C4—91no—
503C22⋊C4—92no—
504C22⋊C4C2×(C3⋊D3)⋊C312yes—
505C42—92no—
506C42—91no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—31no—
513C22×C3—31no—
514C22×C3—32no—
515C22×C3—32no—
516C22×C3—61no—
517C22×C3—61no—
518C22×C3—61no—
519C22×C3—61no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—62no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—62no—
526C22×C3—61no—
527C22×C3—62no—
528C22×C3—121no—
529C22×C3—121no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3—122no—
533C22×C3—181no—
534C22×C3—181no—
535C22×C3—181no—
536C22×C3C3×#23712yes—
537C22×C3C23×C3×D311yescharacteristic
538C2×D3—61no—
539C2×D3—61no—
540C2×D3—61no—
541C2×D3—181no—
542C2×D3—181no—
543C2×D3—181no—
544C3×C4—21no—
545C3×C4—22no—
546C3×C4—32no—
547C3×C4—32no—
548C3×C4—61no—
549C3×C4—61no—
550C3×C4—62no—
551C3×C4—62no—
552C3×C4—62no—
553C3×C4—94no—
554C3×C4—121no—
555C3×C4—122no—
556C3×C4—181no—
557C3×C4—182no—
558C3×C4—181no—
559C3×C4—181no—
560C3×C4C3×D3×D412yes—
561Dic3—34no—
562Dic3—62no—
563Dic3—61no—
564Dic3—61no—
565Dic3—61no—
566Dic3—94no—
567Dic3—182no—
568Dic3—181no—
569Dic3—181no—
570Dic3—181no—
571C32—21no—
572C32#559811yescharacteristic, complemented
573C32C3×#54811yescharacteristic, complemented
574C23—91no—
575C23C22×(C3⋊D3)⋊C312yes—
576C23C22×(C3⋊D3)⋊C311yescharacteristic
577Q8—94no—
578Q8—184no—
579Q8—182no—
580D4—24no—
581D4—22no—
582D4—184no—
583D4—182no—
584C2×C4—22no—
585C2×C4—92no—
586C2×C4—91no—
587C2×C4—91no—
588C2×C4—92no—
589C2×C4—91no—
590C2×C4—184no—
591C2×C4—184no—
592C2×C4—182no—
593C2×C4C22×(C3⋊D3)⋊C312yes—
594C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
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—361no—
614C2×C3C2×C3×D3×D411yescharacteristic
615C2×C3C2×C3×#23711yescharacteristic
616C2×C3C3×#101011yescharacteristic
617D3—121no—
618D3—361no—
619C22—21no—
620C22—21no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—181no—
625C22—181no—
626C22—181no—
627C22#3830⋊C312yescomplemented
628C22C23×(C3⋊D3)⋊C311yescharacteristic
629C4—21no—
630C4—22no—
631C4—94no—
632C4—181no—
633C4—182no—
634C4—181no—
635C4—181no—
636C4D4×(C3⋊D3)⋊C312yes—
637C3—31no—
638C3—31no—
639C3—61no—
640C3C3×#559811yescharacteristic
641C2—22no—
642C2—42no—
643C2—361no—
644C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
645C2C2×#3830⋊C311yescharacteristic
646C2#1172263911yescharacteristic
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×#548
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. C22×#634⋊C3C2semidirect
3. H(3,𝔽3)×#121C2semidirect
4. #64148⋊C3C2semidirect
5. #64145⋊C3C2semidirect
6. D4×(C3⋊Dic3)⋊C3C2semidirect
7. C4×#638⋊C3C2semidirect
8. #64106⋊C3C2semidirect
9. #64096⋊C3C2semidirect
10. #64094⋊C3C2semidirect
11. #64087⋊C3C2semidirect
12. #10596069C3semidirect
39. C2×#3830C2×C3semidirect
40. C22×#634C2×C3semidirect
44. C32×#121D3semidirect
45. C32×#121C2×C3semidirect
46. #64148C2×C3semidirect
47. #64145C2×C3semidirect
48. D4×C3⋊Dic3C2×C3semidirect
49. C4×#638C2×C3semidirect
50. #64106C2×C3semidirect
51. #64096C2×C3semidirect
52. #64094C2×C3semidirect
53. #64087C2×C3semidirect
83. #634⋊C3D4semidirect
147. C22×H(3,𝔽3)#41semidirect
232. #634C3×D4semidirect
350. C22×C32#237semidirect
351. C22×C32C3×#41semidirect
386. #121(C3⋊D3)⋊C3semidirect
390. H(3,𝔽3)#548semidirect
572. C32#5598semidirect
573. C32C3×#548semidirect
627. C22#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
C22×#634⋊C32
H(3,𝔽3)×#1212
#64148⋊C32
#64145⋊C32
D4×(C3⋊Dic3)⋊C32
C4×#638⋊C32
#64106⋊C32
#64096⋊C32
#64094⋊C32
#64087⋊C32
#105960693
C3×#55983