Finite Group Databasebeta

← C3×#10591005 #13158022

Subgroups — C3×#10591005 #13158022

Order 1728.

792 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#235C211yesmaximal, characteristic
2C32×D3×M16C211yesmaximal, characteristic, complemented
3C3×#63855C211yesmaximal, characteristic, complemented
4C3×#63652C211yesmaximal, characteristic, complemented
5C32×#825C211yesmaximal, characteristic, complemented
6C3×#63570C211yesmaximal, characteristic, complemented
7C3×#63568C211yesmaximal, characteristic, complemented
8C3×#5139—31nomaximal
9C3×#4821—31nomaximal
10#10591005C311yesmaximal, characteristic, direct product factor
11C3×#3828C2211yescharacteristic
12C32×#235C2211yescharacteristic
13C2×C32×C4×D3C2211yescharacteristic
14C3×D3×#67—21no—
15C3×#3804—21no—
16C3×D3×D12C411yescharacteristic, complemented
17C3×C4×D32—21no—
18C3×#3799C411yescharacteristic, complemented
19C3×#3798—21no—
20C3×#3795C411yescharacteristic, complemented
21C3×D3×Dic6C411yescharacteristic, complemented
22C33×M16C2211yescharacteristic, complemented
23C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
24C32×C4×Dic3C2211yescharacteristic, complemented
25C32×#208C2211yescharacteristic, complemented
26C32×ΓL(1,𝔽25)—21no—
27C32×D3×C8—21no—
28C3×Dic3⋊Dic3—21no—
29C3×(C2×D3)⋊Dic3—21no—
30C3×D3×#41—31no—
31C2×C3×#235—31no—
32D3×#235C2×C311yescharacteristic
33C2×C32×M16—31no—
34C3×#926—31no—
35C3×D3×M16—21no—
36C3×D3×M16D311yescharacteristic, complemented
37C3×D3×M16C2×C311yescharacteristic, complemented
38C3×#872—31no—
39#63855C2×C311yescharacteristic, complemented
40C32×#104—31no—
41#63652C2×C311yescharacteristic, complemented
42C3×#837—31no—
43C3×#825—21no—
44C3×#825—31no—
45C3×#825—31no—
46C3×#825—31no—
47C3×#825—31no—
48C3×#825—61no—
49C3×#825D311yescharacteristic, complemented
50C3×#825C2×C311yescharacteristic, complemented
51C3×#805—31no—
52#63570C2×C311yescharacteristic, complemented
53#63568C2×C311yescharacteristic, complemented
54C22×C32×D3D411yescharacteristic
55C2×C3×D32—21no—
56C2×C33×C4C2311yescharacteristic
57C3×#638—21no—
58C2×C3×C3⋊Dic3—21no—
59C3×C4⋊(C3⋊D3)C2×C411yescharacteristic
60C3×C4×C3⋊D3—21no—
61C3×#634C2×C411yescharacteristic
62C32×#67—21no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3D411yescharacteristic
65C32×D12C2×C411yescharacteristic
66C32×C4×D3—21no—
67C32×C4×D3C2×C411yescharacteristic
68C32×C4×D3C2×C411yescharacteristic
69C32×C4×D3D411yescharacteristic
70C32×C4×D3D411yescharacteristic
71C32×Dic6C2×C411yescharacteristic
72C3×#627—21no—
73C3×#626—21no—
74C3×#626—21no—
75C3×#625—21no—
76C3×#624—21no—
77C3×D3×Dic3—21no—
78C3×D3×Dic3—21no—
79C33×C8—21no—
80C32×C3⋊C8—21no—
81C3×#421—91no—
82#5139—31no—
83#4821—31no—
84C32×#41—31no—
85C22×C32×C4—31no—
86#3828C22×C311yescharacteristic
87C2×C3×#67—61no—
88C3×#239—31no—
89C3×D3×Q8—31no—
90C3×#237—31no—
91C3×#237—61no—
92C3×D3×D4—31no—
93C3×D3×D4—61no—
94C3×#235—21no—
95C3×#235—31no—
96C3×#235—31no—
97C3×#235—31no—
98C3×#235—31no—
99C3×#235—61no—
100C3×#235—61no—
101C3×#235—61no—
102C3×#235—61no—
103C3×#235C2×D311yescharacteristic
104C3×#235C22×C311yescharacteristic
105C2×C3×D12—31no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—61no—
108C2×C3×C4×D3—61no—
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×C4×D3C22×C311yescharacteristic
111C2×C3×Dic6—31no—
112D3×#67—21no—
113#3804—21no—
114D3×D12C3×C411yescharacteristic, complemented
115C4×D32—21no—
116#3799C3×C411yescharacteristic, complemented
117#3798—21no—
118#3795C3×C411yescharacteristic, complemented
119D3×Dic6C3×C411yescharacteristic, complemented
120C32×M16—21no—
121C32×M16—21no—
122C32×M16—21no—
123C32×M16—31no—
124C32×M16—41no—
125C32×M16—61no—
126C32×M16C2×D311yescharacteristic, complemented
127C32×M16C2×D311yescharacteristic, complemented
128C32×M16C22×C311yescharacteristic, complemented
129C2×C32×C8—61no—
130C32×C42—31no—
131C4×C3⋊Dic3C22×C311yescharacteristic, complemented
132C3×#217—61no—
133C3×(C2×D3)⋊C4—61no—
134C3×C4⋊Dic3—61no—
135C3×Dic3⋊C4—61no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—61no—
140C3×C4×Dic3C2×D311yescharacteristic, complemented
141C3×C4×Dic3C22×C311yescharacteristic, complemented
142C3×#208—21no—
143C3×#208C2×D311yescharacteristic, complemented
144C3×#208C22×C311yescharacteristic, complemented
145C3×ΓL(1,𝔽25)—22no—
146C3×ΓL(1,𝔽25)—21no—
147C3×ΓL(1,𝔽25)—21no—
148C3×D3×C8—22no—
149C3×D3×C8—21no—
150C3×D3×C8—21no—
151Dic3⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153C22×C33C2×D411yescharacteristic
154C2×C3×C3⋊D3—21no—
155C2×C32×D3—21no—
156C2×C32×D3—41no—
157C2×C32×D3C22⋊C411yescharacteristic
158C2×C32×D3C22⋊C411yescharacteristic
159C3×D32—42no—
160C33×C4C22×C411yescharacteristic
161C33×C4C2×D411yescharacteristic
162C3×C3⋊Dic3—21no—
163C3×C3⋊Dic3—41no—
164C32×Dic3—21no—
165C32×Dic3—41no—
166C32×Dic3C22⋊C411yescharacteristic
167C32×Dic3C22⋊C411yescharacteristic
168C2×C3×#41—91no—
169D3×#41—31no—
170C2×#235—31no—
171C2×C3×M16—31no—
172C2×C3×M16—31no—
173C2×C3×M16—61no—
174C3×#117—91no—
175#926—31no—
176D3×M16C3×D311yescharacteristic, complemented
177#872—31no—
178C3×#104—31no—
179C3×#104—31no—
180C3×#104—61no—
181C3×#104—91no—
182C3×#104—91no—
183C3×#104—91no—
184#837—31no—
185#825—31no—
186#825—31no—
187#825—31no—
188#825—31no—
189#825—61no—
190#825C3×D311yescharacteristic, complemented
191#805—31no—
192C23×C32—31no—
193C22×C3×D3—21no—
194C22×C3×D3—61no—
195C22×C3×D3—61no—
196C22×C3×D3D1211yescharacteristic
197C22×C3×D3C3×D411yescharacteristic
198C2×D32—21no—
199C32×Q8—31no—
200C32×D4—31no—
201C32×D4—61no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—31no—
206C2×C32×C4—31no—
207C2×C32×C4—31no—
208C2×C32×C4—31no—
209C2×C32×C4—31no—
210C2×C32×C4—41no—
211C2×C32×C4—61no—
212C2×C32×C4—61no—
213C2×C32×C4C22×D311yescharacteristic
214C2×C32×C4C22×D311yescharacteristic
215C2×C32×C4C23×C311yescharacteristic
216#638—21no—
217C2×C3⋊Dic3—21no—
218C4⋊(C3⋊D3)C2×C3×C411yescharacteristic
219C4×C3⋊D3—21no—
220#634C2×C3×C411yescharacteristic
221C3×#67—21no—
222C3×#67—21no—
223C3×#67—41no—
224C3×#67—61no—
225C3×#67—61no—
226C3×#67—61no—
227C3×#67—61no—
228C3×#67—61no—
229C3×#67—61no—
230C3×#67—121no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—41no—
235C2×C3×Dic3—61no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—121no—
240C2×C3×Dic3D1211yescharacteristic
241C2×C3×Dic3C3×D411yescharacteristic
242C3×D12—21no—
243C3×D12—31no—
244C3×D12—31no—
245C3×D12—61no—
246C3×D12—61no—
247C3×D12—61no—
248C3×D12C4×D311yescharacteristic
249C3×D12C2×C3×C411yescharacteristic
250C3×C4×D3—21no—
251C3×C4×D3—21no—
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—41no—
257C3×C4×D3—61no—
258C3×C4×D3—61no—
259C3×C4×D3—61no—
260C3×C4×D3—61no—
261C3×C4×D3—61no—
262C3×C4×D3—61no—
263C3×C4×D3—121no—
264C3×C4×D3C4×D311yescharacteristic
265C3×C4×D3C4×D311yescharacteristic
266C3×C4×D3#6711yescharacteristic
267C3×C4×D3#6711yescharacteristic
268C3×C4×D3C2×C3×C411yescharacteristic
269C3×C4×D3C2×C3×C411yescharacteristic
270C3×C4×D3C3×D411yescharacteristic
271C3×C4×D3C3×D411yescharacteristic
272C3×Dic6—21no—
273C3×Dic6—31no—
274C3×Dic6—31no—
275C3×Dic6—61no—
276C3×Dic6—61no—
277C3×Dic6—61no—
278C3×Dic6C4×D311yescharacteristic
279C3×Dic6C2×C3×C411yescharacteristic
280#627—21no—
281#626—21no—
282#626—21no—
283#625—21no—
284#624—21no—
285D3×Dic3—21no—
286D3×Dic3—21no—
287C32×C8—21no—
288C32×C8—22no—
289C32×C8—21no—
290C32×C8—21no—
291C32×C8—41no—
292C32×C8—41no—
293C32×C8—42no—
294C32×C8—61no—
295C3×C3⋊C8—22no—
296C3×C3⋊C8—21no—
297C3×C3⋊C8—21no—
298#421—91noSylow
299C2×C33—21no—
300C2×C33C2×C22⋊C411yescharacteristic
301C3×C3⋊D3—41no—
302C32×D3—21no—
303C32×D3—21no—
304C32×D3—41no—
305C3×#41—31no—
306C3×#41—31no—
307C3×#41—61no—
308C3×#41—91no—
309C3×#41—91no—
310C3×#41—91no—
311C3×#41—181no—
312C3×#41—181no—
313C2×C3×Q8—91no—
314C2×C3×D4—91no—
315C2×C3×D4—181no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—181no—
320C2×#67—61no—
321#239—31no—
322D3×Q8—31no—
323#237—31no—
324#237—61no—
325D3×D4—31no—
326D3×D4—61no—
327#235—31no—
328#235—31no—
329#235—31no—
330#235—31no—
331#235—61no—
332#235—61no—
333#235—61no—
334#235—61no—
335#235C2×C3×D311yescharacteristic
336C2×D12—31no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3C2×C3×D311yescharacteristic
340C2×Dic6—31no—
341C3×M16—21no—
342C3×M16—21no—
343C3×M16—21no—
344C3×M16—31no—
345C3×M16—31no—
346C3×M16—41no—
347C3×M16—61no—
348C3×M16—61no—
349C3×M16—61no—
350C3×M16—62no—
351C3×M16D3211yescharacteristic, complemented
352C3×M16C2×C3×D311yescharacteristic, complemented
353C3×M16C2×C3×D311yescharacteristic, complemented
354C2×C3×C8—61no—
355C2×C3×C8—61no—
356C2×C3×C8—62no—
357C3×C4⋊C4—181no—
358C3×C22⋊C4—181no—
359C3×C42—31no—
360C3×C42—31no—
361C3×C42—61no—
362C3×C42—91no—
363#217—61no—
364(C2×D3)⋊C4—61no—
365C4⋊Dic3—61no—
366Dic3⋊C4—61no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—61no—
370C4×Dic3C2×C3×D311yescharacteristic, complemented
371#208C2×C3×D311yescharacteristic, complemented
372ΓL(1,𝔽25)—21no—
373D3×C8—21no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—31no—
378C22×C32—31no—
379C22×C32—41no—
380C22×C32—61no—
381C22×C32—121no—
382C22×C32C2×D1211yescharacteristic
383C22×C32D3×D411yescharacteristic
384C22×C32C2×C3×D411yescharacteristic
385C2×C3⋊D3—21no—
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3—21no—
389C2×C3×D3—21no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—42no—
394C2×C3×D3—61no—
395C2×C3×D3—61no—
396C2×C3×D3—121no—
397C2×C3×D3—122no—
398C2×C3×D3—122no—
399C2×C3×D3(C2×D3)⋊C411yescharacteristic
400C2×C3×D3(C2×D3)⋊C411yescharacteristic
401C2×C3×D3C3×C22⋊C411yescharacteristic
402C2×C3×D3C3×C22⋊C411yescharacteristic
403D32—42no—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—31no—
411C32×C4—31no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4—61no—
415C32×C4—121no—
416C32×C4C2×C4×D311yescharacteristic
417C32×C4C2×C4×D311yescharacteristic
418C32×C4D3×D411yescharacteristic
419C32×C4C2×#6711yescharacteristic
420C32×C4C22×C3×C411yescharacteristic
421C32×C4C2×C3×D411yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—41no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—42no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C3×Dic3—121no—
435C3×Dic3—121no—
436C3×Dic3—121no—
437C3×Dic3—122no—
438C3×Dic3(C2×D3)⋊C411yescharacteristic
439C3×Dic3(C2×D3)⋊C411yescharacteristic
440C3×Dic3C3×C22⋊C411yescharacteristic
441C3×Dic3C3×C22⋊C411yescharacteristic
442C2×#41—91no—
443C2×M16—31no—
444#117—91no—
445#104—31no—
446#104—91no—
447#104—91no—
448#104—91no—
449C33#42111yescharacteristic, complemented, Sylow
450C23×C3—31no—
451C23×C3—31no—
452C23×C3—61no—
453C23×C3—181no—
454C22×D3—61no—
455C22×D3—61no—
456C22×D3C3×D1211yescharacteristic
457C3×Q8—31no—
458C3×Q8—31no—
459C3×Q8—61no—
460C3×Q8—91no—
461C3×Q8—181no—
462C3×D4—31no—
463C3×D4—31no—
464C3×D4—61no—
465C3×D4—61no—
466C3×D4—61no—
467C3×D4—91no—
468C3×D4—121no—
469C3×D4—181no—
470C3×D4—181no—
471C3×D4—181no—
472C3×D4—181no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—121no—
497C2×C3×C4—121no—
498C2×C3×C4—181no—
499C2×C3×C4—181no—
500C2×C3×C4—181no—
501C2×C3×C4—181no—
502C2×C3×C4—181no—
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C22×C3×D311yescharacteristic
505C2×C3×C4C22×C3×D311yescharacteristic
506#67—21no—
507#67—61no—
508#67—61no—
509#67—61no—
510#67—61no—
511#67—61no—
512#67—61no—
513#67—121no—
514C2×Dic3—21no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—121no—
520C2×Dic3C3×D1211yescharacteristic
521D12—31no—
522D12—31no—
523D12—61no—
524D12—61no—
525D12—61no—
526D12C3×C4×D311yescharacteristic
527C4×D3—21no—
528C4×D3—61no—
529C4×D3—61no—
530C4×D3—61no—
531C4×D3—61no—
532C4×D3—61no—
533C4×D3—61no—
534C4×D3—121no—
535C4×D3C3×C4×D311yescharacteristic
536C4×D3C3×C4×D311yescharacteristic
537C4×D3C3×#6711yescharacteristic
538C4×D3C3×#6711yescharacteristic
539Dic6—31no—
540Dic6—31no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6C3×C4×D311yescharacteristic
545C3×C8—22no—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—41no—
550C3×C8—41no—
551C3×C8—42no—
552C3×C8—62no—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—41no—
563C2×C32—41no—
564C2×C32—41no—
565C2×C32—41no—
566C2×C32—61no—
567C2×C32—61no—
568C2×C32—81no—
569C2×C32—121no—
570C2×C32D3×C22⋊C411yescharacteristic
571C2×C32C2×(C2×D3)⋊C411yescharacteristic
572C2×C32C2×C3×C22⋊C411yescharacteristic
573C3⋊D3—41no—
574C3×D3—22no—
575C3×D3—21no—
576C3×D3—21no—
577C3×D3—21no—
578C3×D3—21no—
579C3×D3—41no—
580C3×D3—41no—
581C3×D3—41no—
582C3×D3—81no—
583C3×D3—121no—
584C3×D3—121no—
585C3×D3—241no—
586#41—31no—
587#41—91no—
588#41—91no—
589#41—91no—
590#41—181no—
591#41—181no—
592C2×Q8—91no—
593C2×D4—91no—
594C2×D4—181no—
595C22×C4—31no—
596C22×C4—181no—
597M16—31no—
598M16—61no—
599M16C3×D3211yescharacteristic, complemented
600C2×C8—61no—
601C4⋊C4—181no—
602C22⋊C4—181no—
603C42—31no—
604C42—91no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—31no—
609C22×C3—31no—
610C22×C3—31no—
611C22×C3—31no—
612C22×C3—41no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—122no—
621C22×C3—181no—
622C22×C3—362no—
623C22×C3D3×D1211yescharacteristic
624C22×C3C2×C3×D1211yescharacteristic
625C22×C3C3×D3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—41no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—121no—
631C2×D3—122no—
632C2×D3—122no—
633C2×D3C3×(C2×D3)⋊C411yescharacteristic
634C2×D3C3×(C2×D3)⋊C411yescharacteristic
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—31no—
642C3×C4—31no—
643C3×C4—31no—
644C3×C4—31no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—122no—
655C3×C4—181no—
656C3×C4—361no—
657C3×C4C4×D3211yescharacteristic
658C3×C4D3×#6711yescharacteristic
659C3×C4C2×C3×C4×D311yescharacteristic
660C3×C4C2×C3×C4×D311yescharacteristic
661C3×C4C3×D3×D411yescharacteristic
662C3×C4C2×C3×#6711yescharacteristic
663Dic3—21no—
664Dic3—41no—
665Dic3—61no—
666Dic3—61no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—122no—
671Dic3C3×(C2×D3)⋊C411yescharacteristic
672Dic3C3×(C2×D3)⋊C411yescharacteristic
673C32—21no—
674C32—21no—
675C32—21no—
676C32—41no—
677C32#482111yescharacteristic, complemented
678C32#513911yescharacteristic, complemented
679C32C3×#42111yescharacteristic, complemented
680C23—31no—
681C23—181no—
682Q8—31no—
683Q8—91no—
684Q8—181no—
685D4—31no—
686D4—61no—
687D4—91no—
688D4—181no—
689D4—181no—
690D4—181no—
691D4—181no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—181no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4C2×C3×D3211yescharacteristic
705C8—21no—
706C8—61no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—41no—
714C2×C3—41no—
715C2×C3—41no—
716C2×C3—41no—
717C2×C3—62no—
718C2×C3—61no—
719C2×C3—61no—
720C2×C3—61no—
721C2×C3—61no—
722C2×C3—81no—
723C2×C3—121no—
724C2×C3—121no—
725C2×C3—121no—
726C2×C3—241no—
727C2×C3—361no—
728C2×C3D3×(C2×D3)⋊C411yescharacteristic
729C2×C3C3×D3×C22⋊C411yescharacteristic
730C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
731D3—21no—
732D3—21no—
733D3—41no—
734D3—121no—
735D3—121no—
736D3—241no—
737C22—31no—
738C22—31no—
739C22—61no—
740C22—121no—
741C22—181no—
742C22—362no—
743C22C3×D3×D1211yescharacteristic
744C4—31no—
745C4—31no—
746C4—61no—
747C4—121no—
748C4—181no—
749C4—361no—
750C4C3×C4×D3211yescharacteristic
751C4C3×D3×#6711yescharacteristic
752C3—21no—
753C3—21no—
754C3—21no—
755C3—41no—
756C3#1059100511yescharacteristic, direct product factor
757C3C3×#482111yescharacteristic, complemented
758C3C3×#513911yescharacteristic, complemented
759C2—21no—
760C2—61no—
761C2—61no—
762C2—121no—
763C2—361no—
764C2C3×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC3×C4D3×#67
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC33×M16C22
socleC2×C33C2×C22⋊C4
prime radicalC3×D3×#235C2
cosocleC2×C32×C4C23×C3
hypercenterC3×M16D32
hypocenterC32C3×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×M16

Complements

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

NH ≅ G/Ntype
2. C32×D3×M16C2semidirect
3. C3×#63855C2semidirect
4. C3×#63652C2semidirect
5. C32×#825C2semidirect
6. C3×#63570C2semidirect
7. C3×#63568C2semidirect
10. #10591005C3direct (N × H)
16. C3×D3×D12C4semidirect
18. C3×#3799C4semidirect
20. C3×#3795C4semidirect
21. C3×D3×Dic6C4semidirect
22. C33×M16C22semidirect
23. C3×C4×C3⋊Dic3C22semidirect
24. C32×C4×Dic3C22semidirect
25. C32×#208C22semidirect
36. C3×D3×M16D3semidirect
37. C3×D3×M16C2×C3semidirect
39. #63855C2×C3semidirect
41. #63652C2×C3semidirect
49. C3×#825D3semidirect
50. C3×#825C2×C3semidirect
52. #63570C2×C3semidirect
53. #63568C2×C3semidirect
114. D3×D12C3×C4semidirect
116. #3799C3×C4semidirect
118. #3795C3×C4semidirect
119. D3×Dic6C3×C4semidirect
126. C32×M16C2×D3semidirect
127. C32×M16C2×D3semidirect
128. C32×M16C22×C3semidirect
131. C4×C3⋊Dic3C22×C3semidirect
140. C3×C4×Dic3C2×D3semidirect
141. C3×C4×Dic3C22×C3semidirect
143. C3×#208C2×D3semidirect
144. C3×#208C22×C3semidirect
176. D3×M16C3×D3semidirect
190. #825C3×D3semidirect
351. C3×M16D32semidirect
352. C3×M16C2×C3×D3semidirect
353. C3×M16C2×C3×D3semidirect
370. C4×Dic3C2×C3×D3semidirect
371. #208C2×C3×D3semidirect
449. C33#421semidirect
599. M16C3×D32semidirect
677. C32#4821semidirect
678. C32#5139semidirect
679. C32C3×#421semidirect
756. C3#10591005direct (N × H)
757. C3C3×#4821semidirect
758. C3C3×#5139semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#2352
C32×D3×M162
C3×#638552
C3×#636522
C32×#8252
C3×#635702
C3×#635682
C3×#51393
C3×#48213
#105910053