Finite Group Databasebeta

← #10596295⋊C3 #13153724

Subgroups — #10596295⋊C3 #13153724

Order 1728.

1186 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×#3830⋊C3C211yesmaximal, characteristic, complemented
3#64155⋊C3C211yesmaximal, characteristic, complemented
4#64153⋊C3C211yesmaximal, characteristic, complemented
5#64148⋊C3C212yesmaximal, complemented
6#64144⋊C3C212yesmaximal, complemented
7D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
8#64138⋊C3C212yesmaximal, complemented
9C4×#638⋊C3C211yesmaximal, characteristic, complemented
10#64133⋊C3C211yesmaximal, characteristic, complemented
11C2×#3750⋊C3C212yesmaximal, complemented
12#10596295C311yesmaximal, characteristic, complemented
13C3×#5824—31nomaximal
14#41×H(3,𝔽3)—24no—
15C2×Q8×H(3,𝔽3)C2211yescharacteristic
16C2×D4×H(3,𝔽3)C2212yes—
17C2×D4×H(3,𝔽3)C2211yescharacteristic
18C22×C4×H(3,𝔽3)C2212yes—
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2212yes—
21C2×#638⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2212yes—
23C22×(C3⋊Dic3)⋊C3C2212yes—
24#3830⋊C3—24no—
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×#634⋊C3C2211yescharacteristic
27#3757⋊C3C2212yes—
28#3757⋊C3C2211yescharacteristic
29#3757⋊C3C2212yes—
30#3752⋊C3C2211yescharacteristic
31#3752⋊C3C2212yes—
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
33#3750⋊C3C2211yescharacteristic
34#3750⋊C3C2212yes—
35#3750⋊C3C2212yes—
36#3750⋊C3C2212yes—
37#3750⋊C3C2212yes—
38C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
39C2×C32×#41—21no—
40C2×C32×#41D311yescharacteristic, complemented
41C2×C32×#41C2×C311yescharacteristic, complemented
42C2×#3830C2×C311yescharacteristic, complemented
43C2×C3×#237—31no—
44#64155C2×C311yescharacteristic, complemented
45#64153C2×C311yescharacteristic, complemented
46#64148C2×C312yescomplemented
47#64144C2×C312yescomplemented
48D4×C3⋊Dic3C2×C311yescharacteristic, complemented
49#64138C2×C312yescomplemented
50C4×#638C2×C311yescharacteristic, complemented
51#64133C2×C311yescharacteristic, complemented
52C2×#3750C2×C312yescomplemented
53C3×#946—31no—
54C3×#944—31no—
55C3×#939—32no—
56C3×#935—32no—
57C3×D4×Dic3—31no—
58C3×#929—32no—
59C3×C4×#67—31no—
60C3×#924—31no—
61C2×C3×Dic3⋊C4—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C23×H(3,𝔽3)C2312yes—
64C22×(C3⋊D3)⋊C3C2311yescharacteristic
65Q8×H(3,𝔽3)—22no—
66D4×H(3,𝔽3)—24no—
67D4×H(3,𝔽3)D414yescomplemented
68C2×C4×H(3,𝔽3)—24no—
69C2×C4×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×C4×H(3,𝔽3)C2312yes—
72C2×C4×H(3,𝔽3)C2311yescharacteristic
73#638⋊C3—24no—
74#638⋊C3—22no—
75C2×(C3⋊Dic3)⋊C3—24no—
76C2×(C3⋊Dic3)⋊C3—24no—
77C2×(C3⋊Dic3)⋊C3C2312yes—
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C2×(C3⋊Dic3)⋊C3C2312yes—
80C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
81C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
82C4×(C3⋊D3)⋊C3—22no—
83#634⋊C3—22no—
84C3×#547—91no—
85#5824—31no—
86#5824—91no—
87C32×#41—28no—
88C32×#41—24no—
89C32×#41—24no—
90C2×C32×Q8—21no—
91C2×C32×Q8C2×D311yescharacteristic
92C2×C32×Q8C22×C311yescharacteristic
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4C2×D312yes—
96C2×C32×D4C2×D311yescharacteristic
97C2×C32×D4C22×C312yes—
98C2×C32×D4C22×C311yescharacteristic
99C22×C32×C4—22no—
100C22×C32×C4—21no—
101C22×C32×C4C2×D312yes—
102C22×C32×C4C2×D311yescharacteristic
103C22×C32×C4C22×C312yes—
104C22×C32×C4C22×C311yescharacteristic
105C2×#638C22×C312yes—
106C2×#638C22×C311yescharacteristic
107C22×C3⋊Dic3C22×C312yes—
108C22×C3⋊Dic3C22×C312yes—
109#3830—24no—
110C2×C4×C3⋊D3C22×C311yescharacteristic
111C2×#634C22×C311yescharacteristic
112C2×C3×#67—31no—
113C2×C3×#67—32no—
114C22×C3×Dic3—32no—
115C22×C3×Dic3—32no—
116C3×#237—64no—
117C2×C3×C4×D3—31no—
118C2×C3×Dic6—31no—
119#3757C22×C312yes—
120#3757C22×C311yescharacteristic
121#3757C22×C312yes—
122#3752C22×C311yescharacteristic
123#3752C22×C312yes—
124C4⋊(C3⋊Dic3)C22×C311yescharacteristic
125#3750C22×C311yescharacteristic
126#3750C22×C312yes—
127#3750C22×C312yes—
128#3750C22×C312yes—
129#3750C22×C312yes—
130C4×C3⋊Dic3C22×C311yescharacteristic
131C3×#217—32no—
132C3×#217—31no—
133C3×#217—32no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—32no—
136C3×C4⋊Dic3—31no—
137C3×Dic3⋊C4—31no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—32no—
142C3×C4×Dic3—31no—
143C22×H(3,𝔽3)—22no—
144C22×H(3,𝔽3)—22no—
145C22×H(3,𝔽3)—21no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)—21no—
148C22×H(3,𝔽3)C2×D414yes—
149C22×H(3,𝔽3)C2411yescharacteristic
150C2×(C3⋊D3)⋊C3—21no—
151C2×(C3⋊D3)⋊C3—21no—
152C2×(C3⋊D3)⋊C3—21no—
153C4×H(3,𝔽3)—21no—
154C4×H(3,𝔽3)—22no—
155C4×H(3,𝔽3)C2×D412yes—
156(C3⋊Dic3)⋊C3—22no—
157(C3⋊Dic3)⋊C3—21no—
158(C3⋊Dic3)⋊C3—22no—
159(C3⋊Dic3)⋊C3—21no—
160(C3⋊Dic3)⋊C3#4112yescomplemented
161C2×C3×#41—31no—
162C2×C3×#41—31no—
163C2×C3×#41—61no—
164C2×C3×#41—91no—
165C2×C3×#41C3×D311yescharacteristic
166C2×#237—31no—
167C2×#237—91no—
168C3×C4⋊Q8—91no—
169C3×#123—92no—
170C3×#123—92no—
171C3×C22⋊Q8—91no—
172C3×C22⋊Q8—91no—
173C3×#121—92no—
174C3×C4×D4—91no—
175C3×C4×D4—91no—
176C2×C3×C4⋊C4—92no—
177#946—31no—
178#946—91no—
179#944—31no—
180#944—91no—
181#939—32no—
182#939—92no—
183#935—32no—
184#935—92no—
185D4×Dic3—31no—
186D4×Dic3—91no—
187#929—32no—
188#929—92no—
189C4×#67—31no—
190C4×#67—91no—
191#924—31no—
192#924—91no—
193C2×Dic3⋊C4—32no—
194C2×Dic3⋊C4—92no—
195C23×C32—21no—
196C23×C32—22no—
197C23×C32C22×D311yescharacteristic
198C23×C32C22×D312yes—
199C23×C32C23×C311yescharacteristic
200C23×C32C23×C312yes—
201C22×C3⋊D3C23×C311yescharacteristic
202C22×C3×D3—31no—
203C32×Q8—24no—
204C32×Q8—22no—
205C32×Q8—22no—
206C32×D4—28no—
207C32×D4—24no—
208C32×D4—24no—
209C32×D4—24no—
210C32×D4#6714yescomplemented
211C32×D4C3×D414yescomplemented
212C2×C32×C4—28no—
213C2×C32×C4—24no—
214C2×C32×C4—24no—
215C2×C32×C4—24no—
216C2×C32×C4—22no—
217C2×C32×C4—22no—
218C2×C32×C4—21no—
219C2×C32×C4—22no—
220C2×C32×C4—21no—
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C22×D312yes—
223C2×C32×C4C22×D311yescharacteristic
224C2×C32×C4C23×C311yescharacteristic
225C2×C32×C4C23×C312yes—
226C2×C32×C4C23×C311yescharacteristic
227#638—24no—
228#638—22no—
229C2×C3⋊Dic3—24no—
230C2×C3⋊Dic3—24no—
231C2×C3⋊Dic3C23×C311yescharacteristic
232C2×C3⋊Dic3C23×C312yes—
233C2×C3⋊Dic3C23×C311yescharacteristic
234C2×C3⋊Dic3C23×C312yes—
235C2×C3⋊Dic3C23×C311yescharacteristic
236C4×C3⋊D3—22no—
237#634—22no—
238C3×#67—62no—
239C3×#67—64no—
240C2×C3×Dic3—31no—
241C2×C3×Dic3—31no—
242C2×C3×Dic3—32no—
243C2×C3×Dic3—31no—
244C2×C3×Dic3—32no—
245C2×C3×Dic3—64no—
246C2×C3×Dic3—64no—
247C3×C4×D3—62no—
248C3×Dic6—62no—
249#547—91noSylow
250C2×H(3,𝔽3)—24no—
251C2×H(3,𝔽3)—41no—
252C2×H(3,𝔽3)C22×D411yescharacteristic
253C2×H(3,𝔽3)C2×#4111yescharacteristic
254C2×H(3,𝔽3)2−1+411yescharacteristic
255(C3⋊D3)⋊C3—41no—
256C3×#41—24no—
257C3×#41—64no—
258C3×#41—64no—
259C3×#41—68no—
260C3×#41—184no—
261C2×C3×Q8—31no—
262C2×C3×Q8—31no—
263C2×C3×Q8—61no—
264C2×C3×Q8—91no—
265C2×C3×Q8C2×C3×D311yescharacteristic
266C2×C3×D4—31no—
267C2×C3×D4—31no—
268C2×C3×D4—32no—
269C2×C3×D4—32no—
270C2×C3×D4—62no—
271C2×C3×D4—61no—
272C2×C3×D4—91no—
273C2×C3×D4—92no—
274C2×C3×D4C2×C3×D312yes—
275C2×C3×D4C2×C3×D311yescharacteristic
276C22×C3×C4—32no—
277C22×C3×C4—31no—
278C22×C3×C4—32no—
279C22×C3×C4—31no—
280C22×C3×C4—62no—
281C22×C3×C4—61no—
282C22×C3×C4—91no—
283C22×C3×C4—92no—
284C22×C3×C4—92no—
285C22×C3×C4C2×C3×D312yes—
286C22×C3×C4C2×C3×D311yescharacteristic
287C2×#67—31no—
288C2×#67—32no—
289C2×#67—91no—
290C2×#67—92no—
291C22×Dic3—32no—
292C22×Dic3—32no—
293C22×Dic3—92no—
294C22×Dic3—92no—
295#237—64no—
296#237—184no—
297C2×C4×D3—31no—
298C2×C4×D3—91no—
299C2×Dic6—31no—
300C2×Dic6—91no—
301C3×C4⋊C4—91no—
302C3×C4⋊C4—92no—
303C3×C4⋊C4—92no—
304C3×C4⋊C4—92no—
305C3×C4⋊C4—92no—
306C3×C4⋊C4—91no—
307C3×C22⋊C4—91no—
308C3×C22⋊C4—92no—
309C3×C22⋊C4—92no—
310C3×C22⋊C4—91no—
311C3×C22⋊C4—92no—
312C3×C42—91no—
313#217—32no—
314#217—31no—
315#217—32no—
316#217—92no—
317#217—91no—
318#217—92no—
319(C2×D3)⋊C4—31no—
320(C2×D3)⋊C4—32no—
321(C2×D3)⋊C4—91no—
322(C2×D3)⋊C4—92no—
323C4⋊Dic3—31no—
324C4⋊Dic3—91no—
325Dic3⋊C4—31no—
326Dic3⋊C4—32no—
327Dic3⋊C4—32no—
328Dic3⋊C4—32no—
329Dic3⋊C4—32no—
330Dic3⋊C4—91no—
331Dic3⋊C4—92no—
332Dic3⋊C4—92no—
333Dic3⋊C4—92no—
334Dic3⋊C4—92no—
335C4×Dic3—31no—
336C4×Dic3—91no—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—24no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32C2×#6714yes—
355C22×C32C2×C3×D414yes—
356C22×C32C23×D311yescharacteristic
357C22×C32C24×C311yescharacteristic
358C2×C3⋊D3—21no—
359C2×C3⋊D3—21no—
360C2×C3⋊D3—21no—
361C2×C3×D3—61no—
362C2×C3×D3—61no—
363C2×C3×D3—61no—
364C32×C4—22no—
365C32×C4—24no—
366C32×C4—21no—
367C32×C4—22no—
368C32×C4—21no—
369C32×C4—22no—
370C32×C4—22no—
371C32×C4C2×#6712yes—
372C32×C4C2×C3×D412yes—
373C3⋊Dic3—22no—
374C3⋊Dic3—21no—
375C3⋊Dic3—22no—
376C3⋊Dic3—21no—
377C3⋊Dic3C3×#4112yescomplemented
378C3×Dic3—32no—
379C3×Dic3—62no—
380C3×Dic3—61no—
381C3×Dic3—62no—
382C3×Dic3—61no—
383C2×#41—91no—
384C2×#41(C3⋊D3)⋊C311yescharacteristic, complemented
385C4⋊Q8—91no—
386#123—92no—
387#123—92no—
388C22⋊Q8—91no—
389C22⋊Q8—91no—
390#121—92no—
391C4×D4—91no—
392C4×D4—91no—
393C2×C4⋊C4—92no—
394H(3,𝔽3)#54711yescharacteristic, complemented, Sylow
395C23×C3—32no—
396C23×C3—32no—
397C23×C3—31no—
398C23×C3—31no—
399C23×C3—61no—
400C23×C3—62no—
401C23×C3—91no—
402C23×C3C22×C3×D311yescharacteristic
403C23×C3C22×C3×D312yes—
404C22×D3—31no—
405C22×D3—91no—
406C3×Q8—22no—
407C3×Q8—62no—
408C3×Q8—62no—
409C3×Q8—64no—
410C3×Q8—182no—
411C3×D4—24no—
412C3×D4—34no—
413C3×D4—34no—
414C3×D4—64no—
415C3×D4—64no—
416C3×D4—68no—
417C3×D4—64no—
418C3×D4—182no—
419C3×D4—184no—
420C3×D4C3×#6714yes—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—31no—
424C2×C3×C4—31no—
425C2×C3×C4—31no—
426C2×C3×C4—32no—
427C2×C3×C4—31no—
428C2×C3×C4—32no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—64no—
432C2×C3×C4—64no—
433C2×C3×C4—68no—
434C2×C3×C4—64no—
435C2×C3×C4—61no—
436C2×C3×C4—62no—
437C2×C3×C4—61no—
438C2×C3×C4—91no—
439C2×C3×C4—91no—
440C2×C3×C4—92no—
441C2×C3×C4—91no—
442C2×C3×C4—92no—
443C2×C3×C4—182no—
444C2×C3×C4—184no—
445C2×C3×C4—184no—
446C2×C3×C4C22×C3×D311yescharacteristic
447C2×C3×C4C22×C3×D312yes—
448C2×C3×C4C22×C3×D311yescharacteristic
449#67—62no—
450#67—64no—
451#67—182no—
452#67—184no—
453C2×Dic3—31no—
454C2×Dic3—31no—
455C2×Dic3—32no—
456C2×Dic3—31no—
457C2×Dic3—32no—
458C2×Dic3—64no—
459C2×Dic3—64no—
460C2×Dic3—91no—
461C2×Dic3—91no—
462C2×Dic3—92no—
463C2×Dic3—91no—
464C2×Dic3—92no—
465C2×Dic3—184no—
466C2×Dic3—184no—
467C4×D3—62no—
468C4×D3—182no—
469Dic6—62no—
470Dic6—182no—
471C2×C32—24no—
472C2×C32—24no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—44no—
477C2×C32—42no—
478C2×C32—41no—
479C2×C32—41no—
480C2×C32D3×#4111yescharacteristic
481C2×C32#101011yescharacteristic
482C2×C32C22×#6711yescharacteristic
483C2×C32C22×C3×D411yescharacteristic
484C2×C32C2×C3×#4111yescharacteristic
485C2×C32C3×2−1+411yescharacteristic
486C3⋊D3—41no—
487C3×D3—121no—
488#41—24no—
489#41—184no—
490C2×Q8—91no—
491C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic
492C2×D4—91no—
493C2×D4—92no—
494C2×D4C2×(C3⋊D3)⋊C312yes—
495C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
496C22×C4—92no—
497C22×C4—92no—
498C22×C4—91no—
499C22×C4C2×(C3⋊D3)⋊C312yes—
500C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
501C4⋊C4—91no—
502C4⋊C4—92no—
503C4⋊C4—92no—
504C4⋊C4—92no—
505C4⋊C4—91no—
506C4⋊C4—92no—
507C22⋊C4—92no—
508C22⋊C4—91no—
509C22⋊C4—92no—
510C22⋊C4—91no—
511C22⋊C4—92no—
512C42—91no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—31no—
519C22×C3—31no—
520C22×C3—34no—
521C22×C3—34no—
522C22×C3—62no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—62no—
526C22×C3—61no—
527C22×C3—61no—
528C22×C3—61no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—62no—
533C22×C3—61no—
534C22×C3—64no—
535C22×C3—122no—
536C22×C3—122no—
537C22×C3—121no—
538C22×C3—121no—
539C22×C3—181no—
540C22×C3—181no—
541C22×C3—181no—
542C22×C3C2×C3×#6714yes—
543C22×C3C23×C3×D311yescharacteristic
544C2×D3—61no—
545C2×D3—61no—
546C2×D3—61no—
547C2×D3—181no—
548C2×D3—181no—
549C2×D3—181no—
550C3×C4—21no—
551C3×C4—22no—
552C3×C4—32no—
553C3×C4—32no—
554C3×C4—61no—
555C3×C4—61no—
556C3×C4—62no—
557C3×C4—62no—
558C3×C4—62no—
559C3×C4—64no—
560C3×C4—62no—
561C3×C4—92no—
562C3×C4—181no—
563C3×C4—182no—
564C3×C4—182no—
565C3×C4—181no—
566C3×C4C2×C3×#6712yes—
567Dic3—32no—
568Dic3—62no—
569Dic3—61no—
570Dic3—62no—
571Dic3—61no—
572Dic3—92no—
573Dic3—182no—
574Dic3—181no—
575Dic3—182no—
576Dic3—181no—
577C32—21no—
578C32#582411yescharacteristic, complemented
579C32C3×#54711yescharacteristic, complemented
580C23—91no—
581C23C22×(C3⋊D3)⋊C311yescharacteristic
582C23C22×(C3⋊D3)⋊C312yes—
583Q8—22no—
584Q8—182no—
585D4—24no—
586D4—182no—
587D4—184no—
588D4#638⋊C314yescomplemented
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—91no—
592C2×C4—91no—
593C2×C4—92no—
594C2×C4—91no—
595C2×C4—92no—
596C2×C4—184no—
597C2×C4—184no—
598C2×C4—182no—
599C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
600C2×C4C22×(C3⋊D3)⋊C312yes—
601C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
602C2×C3—24no—
603C2×C3—31no—
604C2×C3—31no—
605C2×C3—31no—
606C2×C3—31no—
607C2×C3—31no—
608C2×C3—31no—
609C2×C3—41no—
610C2×C3—64no—
611C2×C3—64no—
612C2×C3—61no—
613C2×C3—61no—
614C2×C3—61no—
615C2×C3—124no—
616C2×C3—121no—
617C2×C3—121no—
618C2×C3—122no—
619C2×C3—361no—
620C2×C3C3×D3×#4111yescharacteristic
621C2×C3C3×#101011yescharacteristic
622C2×C3C22×C3×#6711yescharacteristic
623D3—121no—
624D3—361no—
625C22—22no—
626C22—22no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—181no—
631C22—181no—
632C22—181no—
633C22C2×#638⋊C314yes—
634C22C23×(C3⋊D3)⋊C311yescharacteristic
635C4—21no—
636C4—22no—
637C4—92no—
638C4—182no—
639C4—181no—
640C4—181no—
641C4—182no—
642C4C2×#638⋊C312yes—
643C3—31no—
644C3—31no—
645C3—61no—
646C3C3×#582411yescharacteristic
647C2—24no—
648C2—41no—
649C2—361no—
650C2#41×(C3⋊D3)⋊C311yescharacteristic
651C2#1172263911yescharacteristic
652C2C22×#638⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingC2×#41×H(3,𝔽3)C2
hypercenterC2×#41(C3⋊D3)⋊C3
hypocenterC32C3×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×H(3,𝔽3)C2semidirect
2. C2×#3830⋊C3C2semidirect
3. #64155⋊C3C2semidirect
4. #64153⋊C3C2semidirect
5. #64148⋊C3C2semidirect
6. #64144⋊C3C2semidirect
7. D4×(C3⋊Dic3)⋊C3C2semidirect
8. #64138⋊C3C2semidirect
9. C4×#638⋊C3C2semidirect
10. #64133⋊C3C2semidirect
11. C2×#3750⋊C3C2semidirect
12. #10596295C3semidirect
40. C2×C32×#41D3semidirect
41. C2×C32×#41C2×C3semidirect
42. C2×#3830C2×C3semidirect
44. #64155C2×C3semidirect
45. #64153C2×C3semidirect
46. #64148C2×C3semidirect
47. #64144C2×C3semidirect
48. D4×C3⋊Dic3C2×C3semidirect
49. #64138C2×C3semidirect
50. C4×#638C2×C3semidirect
51. #64133C2×C3semidirect
52. C2×#3750C2×C3semidirect
67. D4×H(3,𝔽3)D4semidirect
160. (C3⋊Dic3)⋊C3#41semidirect
210. C32×D4#67semidirect
211. C32×D4C3×D4semidirect
377. C3⋊Dic3C3×#41semidirect
384. C2×#41(C3⋊D3)⋊C3semidirect
394. H(3,𝔽3)#547semidirect
578. C32#5824semidirect
579. C32C3×#547semidirect
588. D4#638⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#41×H(3,𝔽3)2
C2×#3830⋊C32
#64155⋊C32
#64153⋊C32
#64148⋊C32
#64144⋊C32
D4×(C3⋊Dic3)⋊C32
#64138⋊C32
C4×#638⋊C32
#64133⋊C32
C2×#3750⋊C32
#105962953
C3×#58243