Finite Group Databasebeta

← #10592367⋊C3 #13141356

Subgroups — #10592367⋊C3 #13141356

Order 1728.

895 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
2C2×#3752⋊C3C211yesmaximal, characteristic
3C2×#3752⋊C3C211yesmaximal, characteristic
4C2×C4⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
5C2×#3750⋊C3C211yesmaximal, characteristic, complemented
6H(3,𝔽3)×#95C211yesmaximal, characteristic, complemented
7#63658⋊C3C211yesmaximal, characteristic, complemented
8#10592367C311yesmaximal, characteristic, complemented
9C3×#4668—31nomaximal
10C23×(C3⋊D3)⋊C3C2211yescharacteristic
11C22×C4×H(3,𝔽3)C2211yescharacteristic
12C22×C4×H(3,𝔽3)C2211yescharacteristic
13C22×C4×H(3,𝔽3)C2211yescharacteristic
14C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
15C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
16C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
17C2×C4×(C3⋊D3)⋊C3—22no—
18C2×C4×(C3⋊D3)⋊C3—22no—
19C2×C4×(C3⋊D3)⋊C3—22no—
20#3752⋊C3—22no—
21#3752⋊C3C414yescomplemented
22C4⋊((C3⋊Dic3)⋊C3)—22no—
23#3750⋊C3—22no—
24C22×C4×C3⋊D3C2×C311yescharacteristic
25C22×C3×C4×D3—31no—
26C2×#3752C2×C311yescharacteristic
27C2×#3752C2×C311yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
29C2×#3750C2×C311yescharacteristic, complemented
30C2×C3×(C2×D3)⋊C4—31no—
31C2×C3×(C2×D3)⋊C4—31no—
32C2×C3×C4⋊Dic3—31no—
33C2×C3×Dic3⋊C4—31no—
34C32×#95—21no—
35C32×#95D311yescharacteristic, complemented
36C32×#95C2×C311yescharacteristic, complemented
37#63658C2×C311yescharacteristic, complemented
38C3×C3⋊#95—31no—
39C23×H(3,𝔽3)C2311yescharacteristic
40C22×(C3⋊D3)⋊C3—21no—
41C22×(C3⋊D3)⋊C3—21no—
42C22×(C3⋊D3)⋊C3—21no—
43C22×(C3⋊D3)⋊C3—21no—
44C22×(C3⋊D3)⋊C3C2×C412yes—
45C22×(C3⋊D3)⋊C3D412yes—
46C22×(C3⋊D3)⋊C3Q812yes—
47C2×C4×H(3,𝔽3)—21no—
48C2×C4×H(3,𝔽3)—21no—
49C2×C4×H(3,𝔽3)—21no—
50C2×C4×H(3,𝔽3)—21no—
51C2×C4×H(3,𝔽3)—21no—
52C2×C4×H(3,𝔽3)—21no—
53C2×C4×H(3,𝔽3)—21no—
54C2×C4×H(3,𝔽3)C2×C412yescomplemented
55C2×C4×H(3,𝔽3)D412yes—
56C2×(C3⋊Dic3)⋊C3—21no—
57C2×(C3⋊Dic3)⋊C3—21no—
58C2×(C3⋊Dic3)⋊C3—21no—
59C2×(C3⋊Dic3)⋊C3—21no—
60C2×(C3⋊Dic3)⋊C3—21no—
61C2×(C3⋊Dic3)⋊C3—21no—
62C2×(C3⋊Dic3)⋊C3—21no—
63C2×(C3⋊Dic3)⋊C3C2×C412yescomplemented
64C2×(C3⋊Dic3)⋊C3D412yes—
65C4×(C3⋊D3)⋊C3—28no—
66C3×#385—91no—
67#4668—31no—
68#4668—91no—
69C23×C3⋊D3C22×C311yescharacteristic
70C23×C3×D3—31no—
71C22×C32×C4—21no—
72C22×C32×C4—21no—
73C22×C32×C4—21no—
74C22×C32×C4C2×D311yescharacteristic
75C22×C32×C4C2×D311yescharacteristic
76C22×C32×C4C2×D311yescharacteristic
77C22×C32×C4C22×C311yescharacteristic
78C22×C32×C4C22×C311yescharacteristic
79C22×C32×C4C22×C311yescharacteristic
80C22×C3⋊Dic3C22×C311yescharacteristic
81C22×C3⋊Dic3C22×C311yescharacteristic
82C22×C3⋊Dic3C22×C311yescharacteristic
83C2×C4×C3⋊D3—22no—
84C2×C4×C3⋊D3—22no—
85C2×C4×C3⋊D3—22no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C2×C3×C4×D3—62no—
90C2×C3×C4×D3—62no—
91C2×C3×C4×D3—62no—
92#3752—22no—
93#3752C3×C414yescomplemented
94C4⋊(C3⋊Dic3)—22no—
95#3750—22no—
96C3×(C2×D3)⋊C4—34no—
97C3×(C2×D3)⋊C4—62no—
98C3×C4⋊Dic3—62no—
99C3×Dic3⋊C4—62no—
100C22×H(3,𝔽3)C22×C411yescharacteristic
101C22×H(3,𝔽3)C2×D411yescharacteristic
102C22×H(3,𝔽3)C2×D411yescharacteristic
103C22×H(3,𝔽3)C2×D411yescharacteristic
104C22×H(3,𝔽3)C2×Q811yescharacteristic
105C22×H(3,𝔽3)#4111yescharacteristic
106C22×H(3,𝔽3)#4111yescharacteristic
107C2×(C3⋊D3)⋊C3—22no—
108C2×(C3⋊D3)⋊C3—22no—
109C2×(C3⋊D3)⋊C3—22no—
110C2×(C3⋊D3)⋊C3—22no—
111C2×(C3⋊D3)⋊C3—22no—
112C2×(C3⋊D3)⋊C3—22no—
113C2×(C3⋊D3)⋊C3C4⋊C414yescomplemented
114C4×H(3,𝔽3)—22no—
115C4×H(3,𝔽3)—22no—
116C4×H(3,𝔽3)—41no—
117(C3⋊Dic3)⋊C3—22no—
118(C3⋊Dic3)⋊C3—22no—
119(C3⋊Dic3)⋊C3—41no—
120C23×C3×C4—91no—
121C22×C4×D3—31no—
122C22×C4×D3—91no—
123C2×C3×C4⋊C4—91no—
124C2×C3×C4⋊C4—91no—
125C2×C3×C22⋊C4—91no—
126C2×C3×C22⋊C4—91no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—91no—
130C2×(C2×D3)⋊C4—91no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—91no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—91no—
135C3×#95—31no—
136C3×#95—31no—
137C3×#95—61no—
138C3×#95—91no—
139C3×#95C3×D311yescharacteristic
140C3⋊#95—31no—
141C3⋊#95—91no—
142C23×C32—21no—
143C23×C32C22×D311yescharacteristic
144C23×C32C23×C311yescharacteristic
145C22×C3⋊D3—21no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3C2×C3×C412yes—
150C22×C3⋊D3C3×D412yes—
151C22×C3⋊D3C3×Q812yes—
152C22×C3×D3—32no—
153C22×C3×D3—32no—
154C22×C3×D3—32no—
155C22×C3×D3—61no—
156C22×C3×D3—61no—
157C22×C3×D3—61no—
158C22×C3×D3—61no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—22no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—41no—
177C2×C32×C4—41no—
178C2×C32×C4—41no—
179C2×C32×C4—41no—
180C2×C32×C4—41no—
181C2×C32×C4—41no—
182C2×C32×C4C4×D312yescomplemented
183C2×C32×C4D1212yes—
184C2×C32×C4C2×C3×C412yescomplemented
185C2×C32×C4C3×D412yes—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3C2×C3×C412yescomplemented
194C2×C3⋊Dic3C3×D412yes—
195C4×C3⋊D3—28no—
196C2×C3×Dic3—32no—
197C2×C3×Dic3—32no—
198C2×C3×Dic3—61no—
199C2×C3×Dic3—61no—
200C2×C3×Dic3—61no—
201C2×C3×Dic3—61no—
202C2×C3×Dic3—61no—
203C2×C3×Dic3—61no—
204C2×C3×Dic3—61no—
205C3×C4×D3—68no—
206#385—91noSylow
207C2×H(3,𝔽3)C2×C4⋊C411yescharacteristic
208C2×H(3,𝔽3)C4×D411yescharacteristic
209C2×H(3,𝔽3)C4×D411yescharacteristic
210C2×H(3,𝔽3)#12011yescharacteristic
211C2×H(3,𝔽3)C22⋊Q811yescharacteristic
212C2×H(3,𝔽3)C22⋊Q811yescharacteristic
213C2×H(3,𝔽3)#12311yescharacteristic
214(C3⋊D3)⋊C3—24no—
215C24×C3—91no—
216C23×D3—31no—
217C23×D3—91no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4—91no—
228C22×C3×C4—91no—
229C22×C3×C4—91no—
230C22×C3×C4—182no—
231C22×C3×C4—182no—
232C22×C3×C4—182no—
233C22×C3×C4C2×C3×D311yescharacteristic
234C22×C3×C4C2×C3×D311yescharacteristic
235C22×C3×C4C2×C3×D311yescharacteristic
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—91no—
240C22×Dic3—91no—
241C22×Dic3—91no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—182no—
246C2×C4×D3—182no—
247C2×C4×D3—182no—
248C3×C4⋊C4—182no—
249C3×C4⋊C4—182no—
250C3×C22⋊C4—94no—
251C3×C22⋊C4—182no—
252(C2×D3)⋊C4—34no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—94no—
255(C2×D3)⋊C4—182no—
256C4⋊Dic3—62no—
257C4⋊Dic3—182no—
258Dic3⋊C4—62no—
259Dic3⋊C4—182no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32C2×C4×D311yescharacteristic
268C22×C32C2×D1211yescharacteristic
269C22×C32#23511yescharacteristic
270C22×C32D3×D411yescharacteristic
271C22×C32D3×D411yescharacteristic
272C22×C32#23711yescharacteristic
273C22×C32D3×Q811yescharacteristic
274C22×C32C22×C3×C411yescharacteristic
275C22×C32C2×C3×D411yescharacteristic
276C22×C32C2×C3×D411yescharacteristic
277C22×C32C2×C3×D411yescharacteristic
278C22×C32C2×C3×Q811yescharacteristic
279C22×C32C3×#4111yescharacteristic
280C22×C32C3×#4111yescharacteristic
281C2×C3⋊D3—22no—
282C2×C3⋊D3—22no—
283C2×C3⋊D3—22no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3C3×C4⋊C414yescomplemented
288C2×C3×D3—34no—
289C2×C3×D3—62no—
290C2×C3×D3—62no—
291C2×C3×D3—62no—
292C2×C3×D3—62no—
293C2×C3×D3—62no—
294C2×C3×D3—62no—
295C32×C4—22no—
296C32×C4—22no—
297C32×C4—22no—
298C32×C4—22no—
299C32×C4—42no—
300C32×C4—42no—
301C32×C4—42no—
302C32×C4—41no—
303C32×C4—41no—
304C3⋊Dic3—22no—
305C3⋊Dic3—22no—
306C3⋊Dic3—41no—
307C3×Dic3—62no—
308C3×Dic3—62no—
309C3×Dic3—121no—
310C23×C4—91no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—91no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4—91no—
315#95—91no—
316#95(C3⋊D3)⋊C311yescharacteristic, complemented
317H(3,𝔽3)#38511yescharacteristic, complemented, Sylow
318C23×C3—31no—
319C23×C3—31no—
320C23×C3—61no—
321C23×C3—92no—
322C23×C3—92no—
323C23×C3—92no—
324C23×C3—181no—
325C23×C3—181no—
326C23×C3—181no—
327C23×C3—181no—
328C23×C3C22×C3×D311yescharacteristic
329C22×D3—32no—
330C22×D3—32no—
331C22×D3—32no—
332C22×D3—61no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—92no—
337C22×D3—92no—
338C22×D3—92no—
339C22×D3—181no—
340C22×D3—181no—
341C22×D3—181no—
342C22×D3—181no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—92no—
372C2×C3×C4—92no—
373C2×C3×C4—121no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—188no—
380C2×C3×C4—181no—
381C2×C3×C4—181no—
382C2×C3×C4—181no—
383C2×C3×C4—181no—
384C2×C3×C4—181no—
385C2×C3×C4—181no—
386C2×C3×C4—181no—
387C2×C3×C4C3×C4×D312yes—
388C2×C3×C4C3×D1212yes—
389C2×Dic3—32no—
390C2×Dic3—32no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—92no—
399C2×Dic3—92no—
400C2×Dic3—181no—
401C2×Dic3—181no—
402C2×Dic3—181no—
403C2×Dic3—181no—
404C2×Dic3—181no—
405C2×Dic3—181no—
406C2×Dic3—181no—
407C4×D3—68no—
408C4×D3—188no—
409C2×C32—21no—
410C2×C32—21no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—21no—
416C2×C32C4×D1211yescharacteristic
417C2×C32#67⋊C411yescharacteristic
418C2×C32#88211yescharacteristic
419C2×C32#88311yescharacteristic
420C2×C32D3×C4⋊C411yescharacteristic
421C2×C32#89611yescharacteristic
422C2×C32#89711yescharacteristic
423C2×C32C2×C3×C4⋊C411yescharacteristic
424C2×C32C3×C4×D411yescharacteristic
425C2×C32C3×C4×D411yescharacteristic
426C2×C32C3×#12011yescharacteristic
427C2×C32C3×C22⋊Q811yescharacteristic
428C2×C32C3×C22⋊Q811yescharacteristic
429C2×C32C3×#12311yescharacteristic
430C3⋊D3—24no—
431C3×D3—64no—
432C24—91no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—182no—
437C22×C4—182no—
438C22×C4—182no—
439C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
440C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
441C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
442C4⋊C4—182no—
443C4⋊C4—182no—
444C22⋊C4—94no—
445C22⋊C4—182no—
446C22×C3—31no—
447C22×C3—31no—
448C22×C3—31no—
449C22×C3—31no—
450C22×C3—31no—
451C22×C3—31no—
452C22×C3—31no—
453C22×C3—31no—
454C22×C3—31no—
455C22×C3—31no—
456C22×C3—31no—
457C22×C3—31no—
458C22×C3—31no—
459C22×C3—31no—
460C22×C3—61no—
461C22×C3—61no—
462C22×C3—61no—
463C22×C3—61no—
464C22×C3—61no—
465C22×C3—61no—
466C22×C3—61no—
467C22×C3—94no—
468C22×C3—182no—
469C22×C3—182no—
470C22×C3—182no—
471C22×C3—182no—
472C22×C3—182no—
473C22×C3—182no—
474C22×C3C2×C3×C4×D311yescharacteristic
475C22×C3C2×C3×D1211yescharacteristic
476C22×C3C3×#23511yescharacteristic
477C22×C3C3×D3×D411yescharacteristic
478C22×C3C3×D3×D411yescharacteristic
479C22×C3C3×#23711yescharacteristic
480C22×C3C3×D3×Q811yescharacteristic
481C2×D3—34no—
482C2×D3—62no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—94no—
489C2×D3—182no—
490C2×D3—182no—
491C2×D3—182no—
492C2×D3—182no—
493C2×D3—182no—
494C2×D3—182no—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—41no—
498C3×C4—62no—
499C3×C4—62no—
500C3×C4—62no—
501C3×C4—62no—
502C3×C4—122no—
503C3×C4—122no—
504C3×C4—121no—
505C3×C4—121no—
506C3×C4—122no—
507C3×C4—182no—
508C3×C4—182no—
509C3×C4—361no—
510Dic3—62no—
511Dic3—62no—
512Dic3—121no—
513Dic3—182no—
514Dic3—182no—
515Dic3—361no—
516C32—21no—
517C32#466811yescharacteristic, complemented
518C32C3×#38511yescharacteristic, complemented
519C23—92no—
520C23—92no—
521C23—92no—
522C23—181no—
523C23—181no—
524C23—181no—
525C23—181no—
526C23C22×(C3⋊D3)⋊C311yescharacteristic
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—92no—
535C2×C4—92no—
536C2×C4—188no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4C4×(C3⋊D3)⋊C312yescomplemented
545C2×C4C4⋊((C3⋊D3)⋊C3)12yes—
546C2×C3—31no—
547C2×C3—31no—
548C2×C3—31no—
549C2×C3—31no—
550C2×C3—31no—
551C2×C3—31no—
552C2×C3—31no—
553C2×C3—31no—
554C2×C3—31no—
555C2×C3—31no—
556C2×C3—31no—
557C2×C3—31no—
558C2×C3—31no—
559C2×C3—31no—
560C2×C3—61no—
561C2×C3—61no—
562C2×C3—61no—
563C2×C3—61no—
564C2×C3—61no—
565C2×C3—61no—
566C2×C3—61no—
567C2×C3—184no—
568C2×C3C3×C4×D1211yescharacteristic
569C2×C3C3×#67⋊C411yescharacteristic
570C2×C3C3×#88211yescharacteristic
571C2×C3C3×#88311yescharacteristic
572C2×C3C3×D3×C4⋊C411yescharacteristic
573C2×C3C3×#89611yescharacteristic
574C2×C3C3×#89711yescharacteristic
575D3—64no—
576D3—184no—
577C22—94no—
578C22—182no—
579C22—182no—
580C22—182no—
581C22—182no—
582C22—182no—
583C22—182no—
584C22C2×C4×(C3⋊D3)⋊C311yescharacteristic
585C22C2×C4⋊((C3⋊D3)⋊C3)11yescharacteristic
586C22#3828⋊C311yescharacteristic
587C22D4×(C3⋊D3)⋊C311yescharacteristic
588C22D4×(C3⋊D3)⋊C311yescharacteristic
589C22#3830⋊C311yescharacteristic
590C22Q8×(C3⋊D3)⋊C311yescharacteristic
591C4—22no—
592C4—22no—
593C4—41no—
594C4—182no—
595C4—182no—
596C4—361no—
597C3—31no—
598C3—31no—
599C3—61no—
600C3C3×#466811yescharacteristic
601C2—184no—
602C2C4×C4⋊((C3⋊D3)⋊C3)11yescharacteristic
603C2#64090⋊C311yescharacteristic
604C2#64091⋊C311yescharacteristic
605C2#64092⋊C311yescharacteristic
606C2C4⋊C4×(C3⋊D3)⋊C311yescharacteristic
607C2#64105⋊C311yescharacteristic
608C2#64106⋊C311yescharacteristic
subgroupG/H
centerC23C22×(C3⋊D3)⋊C3
commutatorC22×C32C22×C3×C4
Frattini, socleC23×C3C22×C3×D3
FittingH(3,𝔽3)×#95C2
prime radicalC23×(C3⋊D3)⋊C3C22
cosocleC23×C32C23×C3
hypercenter#95(C3⋊D3)⋊C3
hypocenterC32C3×#385
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊((C3⋊Dic3)⋊C3)C2semidirect
5. C2×#3750⋊C3C2semidirect
6. H(3,𝔽3)×#95C2semidirect
7. #63658⋊C3C2semidirect
8. #10592367C3semidirect
21. #3752⋊C3C4semidirect
28. C2×C4⋊(C3⋊Dic3)C2×C3semidirect
29. C2×#3750C2×C3semidirect
35. C32×#95D3semidirect
36. C32×#95C2×C3semidirect
37. #63658C2×C3semidirect
54. C2×C4×H(3,𝔽3)C2×C4semidirect
63. C2×(C3⋊Dic3)⋊C3C2×C4semidirect
93. #3752C3×C4semidirect
113. C2×(C3⋊D3)⋊C3C4⋊C4semidirect
182. C2×C32×C4C4×D3semidirect
184. C2×C32×C4C2×C3×C4semidirect
193. C2×C3⋊Dic3C2×C3×C4semidirect
287. C2×C3⋊D3C3×C4⋊C4semidirect
316. #95(C3⋊D3)⋊C3semidirect
317. H(3,𝔽3)#385semidirect
517. C32#4668semidirect
518. C32C3×#385semidirect
544. C2×C4C4×(C3⋊D3)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C4×(C3⋊D3)⋊C32
C2×#3752⋊C32
C2×C4⋊((C3⋊Dic3)⋊C3)2
C2×#3750⋊C32
H(3,𝔽3)×#952
#63658⋊C32
#105923673
C3×#46683