Finite Group Databasebeta

← C3×D3×#825 #13158021

Subgroups — C3×D3×#825 #13158021

Order 1728.

856 conjugacy classes of subgroups.

The subgroup lattice has 774 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×C4×D3×Dic3C211yesmaximal, characteristic, complemented
4C3×#63652C211yesmaximal, characteristic, complemented
5C32×#825C211yesmaximal, characteristic, complemented
6C3×#63570C211yesmaximal, characteristic, complemented
7C3×#63568C211yesmaximal, characteristic, complemented
8C2×C3×#825—31nomaximal
9C3×D3×#104—31nomaximal
10D3×#825C311yesmaximal, characteristic, direct product factor
11C3×#3828C2211yescharacteristic
12C32×#235C2211yescharacteristic
13C2×C32×C4×D3C2211yescharacteristic
14C3×D3×#67—21no—
15C3×#3804—21no—
16C2×C3×D3×Dic3—21no—
17C3×D3×D12C411yescharacteristic, complemented
18C3×C4×D32—21no—
19C3×#3799C411yescharacteristic, complemented
20C3×#3798—21no—
21C3×#3795C411yescharacteristic, complemented
22C3×D3×Dic6C411yescharacteristic, complemented
23C33×M16C2211yescharacteristic, complemented
24C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
25C32×C4×Dic3C2211yescharacteristic, complemented
26C32×#208C2211yescharacteristic, complemented
27C32×ΓL(1,𝔽25)—21no—
28C32×D3×C8—21no—
29C3×Dic32—21no—
30C3×D3×#41—31no—
31C2×C3×#235—31no—
32D3×#235C2×C311yescharacteristic
33C2×C32×M16—31no—
34C2×C3×C4×Dic3—31no—
35C3×D3×M16—21no—
36C3×D3×M16D311yescharacteristic, complemented
37C3×D3×M16C2×C311yescharacteristic, complemented
38C3×C42×D3—31no—
39C4×D3×Dic3C2×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, direct product factor
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, complemented
60C3×C4×C3⋊D3—21no—
61C3×#634C2×C411yescharacteristic, complemented
62C32×#67—21no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3D411yescharacteristic
65C32×D12C2×C411yescharacteristic, complemented
66C32×C4×D3—21no—
67C32×C4×D3C2×C411yescharacteristic
68C32×C4×D3C2×C411yescharacteristic
69C32×C4×D3D411yescharacteristic
70C32×C4×D3D411yescharacteristic
71C32×Dic6C2×C411yescharacteristic, complemented
72C3×#627—21no—
73C3×#626—21no—
74C3×#626—21no—
75C3×#625—21no—
76C3×#624—21no—
77C3×D3×Dic3—24no—
78C3×D3×Dic3—21no—
79C3×D3×Dic3—21no—
80C33×C8—21no—
81C32×C3⋊C8—21no—
82C2×C3×#104—91no—
83C2×#825—31no—
84D3×#104—31no—
85C32×#41—31no—
86C22×C32×C4—31no—
87#3828C22×C311yescharacteristic
88C2×C3×#67—61no—
89C22×C3×Dic3—61no—
90C3×#239—31no—
91C3×D3×Q8—31no—
92C3×#237—31no—
93C3×#237—61no—
94C3×D3×D4—31no—
95C3×D3×D4—61no—
96C3×#235—21no—
97C3×#235—31no—
98C3×#235—31no—
99C3×#235—31no—
100C3×#235—31no—
101C3×#235—61no—
102C3×#235—61no—
103C3×#235—61no—
104C3×#235—61no—
105C3×#235C2×D311yescharacteristic
106C3×#235C22×C311yescharacteristic
107C2×C3×D12—31no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—61no—
110C2×C3×C4×D3—61no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3C2×D311yescharacteristic
113C2×C3×C4×D3C22×C311yescharacteristic
114C2×C3×Dic6—31no—
115D3×#67—21no—
116#3804—21no—
117C2×D3×Dic3—21no—
118D3×D12C3×C411yescharacteristic, complemented
119C4×D32—21no—
120#3799C3×C411yescharacteristic, complemented
121#3798—21no—
122#3795C3×C411yescharacteristic, complemented
123D3×Dic6C3×C411yescharacteristic, complemented
124C32×M16—21no—
125C32×M16—21no—
126C32×M16—21no—
127C32×M16—31no—
128C32×M16—41no—
129C32×M16—61no—
130C32×M16C2×D311yescharacteristic, complemented
131C32×M16C2×D311yescharacteristic, complemented
132C32×M16C22×C311yescharacteristic, complemented
133C2×C32×C8—61no—
134C32×C42—31no—
135C4×C3⋊Dic3C22×C311yescharacteristic, complemented
136C3×C4×Dic3—21no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—61no—
140C3×C4×Dic3—61no—
141C3×C4×Dic3—61no—
142C3×C4×Dic3C2×D311yescharacteristic, complemented
143C3×C4×Dic3C22×C311yescharacteristic, complemented
144C3×#208—21no—
145C3×#208C2×D311yescharacteristic, complemented
146C3×#208C22×C311yescharacteristic, complemented
147C3×ΓL(1,𝔽25)—22no—
148C3×ΓL(1,𝔽25)—21no—
149C3×ΓL(1,𝔽25)—21no—
150C3×D3×C8—22no—
151C3×D3×C8—21no—
152C3×D3×C8—21no—
153Dic32—21no—
154C22×C33C2×D411yescharacteristic
155C2×C3×C3⋊D3—21no—
156C2×C32×D3—22no—
157C2×C32×D3—21no—
158C2×C32×D3C22⋊C411yescharacteristic
159C2×C32×D3C22⋊C411yescharacteristic
160C3×D32—42no—
161C33×C4C22×C411yescharacteristic
162C33×C4C2×D411yescharacteristic
163C3×C3⋊Dic3—22no—
164C3×C3⋊Dic3—21no—
165C32×Dic3—22no—
166C32×Dic3—21no—
167C32×Dic3C22⋊C411yescharacteristic
168C32×Dic3C22⋊C411yescharacteristic
169C2×C3×#41—91no—
170D3×#41—31no—
171C2×#235—31no—
172C2×C3×M16—31no—
173C2×C3×M16—31no—
174C2×C3×M16—61no—
175C2×C3×C42—91no—
176C2×C4×Dic3—31no—
177D3×M16C3×D311yescharacteristic, complemented
178C42×D3—31no—
179C3×#104—31no—
180C3×#104—31no—
181C3×#104—61no—
182C3×#104—91no—
183C3×#104—91no—
184C3×#104—91no—
185#837—31no—
186#825—31no—
187#825—31no—
188#825—31no—
189#825—31no—
190#825—61no—
191#825C3×D311yescharacteristic, direct product factor
192#805—31no—
193C23×C32—31no—
194C22×C3×D3—21no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197C22×C3×D3D1211yescharacteristic
198C22×C3×D3C3×D411yescharacteristic
199C2×D32—21no—
200C32×Q8—31no—
201C32×D4—31no—
202C32×D4—61no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—31no—
207C2×C32×C4—31no—
208C2×C32×C4—31no—
209C2×C32×C4—31no—
210C2×C32×C4—31no—
211C2×C32×C4—41no—
212C2×C32×C4—61no—
213C2×C32×C4—61no—
214C2×C32×C4C22×D311yescharacteristic
215C2×C32×C4C22×D311yescharacteristic
216C2×C32×C4C23×C311yescharacteristic
217#638—21no—
218C2×C3⋊Dic3—21no—
219C4⋊(C3⋊D3)C2×C3×C411yescharacteristic, complemented
220C4×C3⋊D3—21no—
221#634C2×C3×C411yescharacteristic, complemented
222C3×#67—21no—
223C3×#67—21no—
224C3×#67—41no—
225C3×#67—61no—
226C3×#67—61no—
227C3×#67—61no—
228C3×#67—61no—
229C3×#67—61no—
230C3×#67—61no—
231C3×#67—121no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—41no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—64no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—121no—
242C2×C3×Dic3D1211yescharacteristic
243C2×C3×Dic3C3×D411yescharacteristic
244C3×D12—21no—
245C3×D12—31no—
246C3×D12—31no—
247C3×D12—61no—
248C3×D12—61no—
249C3×D12—61no—
250C3×D12C4×D311yescharacteristic, complemented
251C3×D12C2×C3×C411yescharacteristic, complemented
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—41no—
259C3×C4×D3—61no—
260C3×C4×D3—61no—
261C3×C4×D3—64no—
262C3×C4×D3—61no—
263C3×C4×D3—61no—
264C3×C4×D3—61no—
265C3×C4×D3—61no—
266C3×C4×D3—121no—
267C3×C4×D3C4×D311yescharacteristic
268C3×C4×D3C4×D311yescharacteristic
269C3×C4×D3#6711yescharacteristic
270C3×C4×D3#6711yescharacteristic
271C3×C4×D3C2×C3×C411yescharacteristic
272C3×C4×D3C2×C3×C411yescharacteristic
273C3×C4×D3C3×D411yescharacteristic
274C3×C4×D3C3×D411yescharacteristic
275C3×Dic6—21no—
276C3×Dic6—31no—
277C3×Dic6—31no—
278C3×Dic6—61no—
279C3×Dic6—61no—
280C3×Dic6—61no—
281C3×Dic6C4×D311yescharacteristic, complemented
282C3×Dic6C2×C3×C411yescharacteristic, complemented
283#627—21no—
284#626—21no—
285#626—21no—
286#625—21no—
287#624—21no—
288D3×Dic3—24no—
289D3×Dic3—21no—
290D3×Dic3—21no—
291C32×C8—21no—
292C32×C8—22no—
293C32×C8—21no—
294C32×C8—21no—
295C32×C8—41no—
296C32×C8—41no—
297C32×C8—42no—
298C32×C8—61no—
299C3×C3⋊C8—22no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#104—91noSylow
303C2×C33—21no—
304C2×C33C2×C22⋊C411yescharacteristic
305C3×C3⋊D3—41no—
306C32×D3—21no—
307C32×D3—41no—
308C32×D3#10412yescomplemented
309C3×#41—31no—
310C3×#41—31no—
311C3×#41—61no—
312C3×#41—91no—
313C3×#41—91no—
314C3×#41—91no—
315C3×#41—181no—
316C3×#41—181no—
317C2×C3×Q8—91no—
318C2×C3×D4—91no—
319C2×C3×D4—181no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C22×C3×C4—181no—
324C22×C3×C4—181no—
325C2×#67—61no—
326C22×Dic3—61no—
327#239—31no—
328D3×Q8—31no—
329#237—31no—
330#237—61no—
331D3×D4—31no—
332D3×D4—61no—
333#235—31no—
334#235—31no—
335#235—31no—
336#235—31no—
337#235—61no—
338#235—61no—
339#235—61no—
340#235—61no—
341#235C2×C3×D311yescharacteristic
342C2×D12—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3C2×C3×D311yescharacteristic
347C2×Dic6—31no—
348C3×M16—21no—
349C3×M16—21no—
350C3×M16—21no—
351C3×M16—31no—
352C3×M16—31no—
353C3×M16—41no—
354C3×M16—61no—
355C3×M16—61no—
356C3×M16—61no—
357C3×M16—62no—
358C3×M16D3211yescharacteristic, complemented
359C3×M16C2×C3×D311yescharacteristic, complemented
360C3×M16C2×C3×D311yescharacteristic, complemented
361C2×C3×C8—61no—
362C2×C3×C8—61no—
363C2×C3×C8—62no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—61no—
367C3×C42—91no—
368C3×C42—181no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3C2×C3×D311yescharacteristic, complemented
375#208C2×C3×D311yescharacteristic, complemented
376ΓL(1,𝔽25)—21no—
377D3×C8—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—31no—
382C22×C32—31no—
383C22×C32—41no—
384C22×C32—62no—
385C22×C32—61no—
386C22×C32C2×D1211yescharacteristic
387C22×C32D3×D411yescharacteristic
388C22×C32C2×C3×D411yescharacteristic
389C2×C3⋊D3—21no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C2×C3×D3—21no—
396C2×C3×D3—42no—
397C2×C3×D3—41no—
398C2×C3×D3—61no—
399C2×C3×D3—61no—
400C2×C3×D3—121no—
401C2×C3×D3—122no—
402C2×C3×D3—122no—
403C2×C3×D3(C2×D3)⋊C411yescharacteristic
404C2×C3×D3(C2×D3)⋊C411yescharacteristic
405C2×C3×D3C3×C22⋊C411yescharacteristic
406C2×C3×D3C3×C22⋊C411yescharacteristic
407D32—42no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—31no—
415C32×C4—31no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—62no—
419C32×C4—61no—
420C32×C4C2×C4×D311yescharacteristic
421C32×C4C2×C4×D311yescharacteristic
422C32×C4D3×D411yescharacteristic
423C32×C4C2×#6711yescharacteristic
424C32×C4C22×C3×C411yescharacteristic
425C32×C4C2×C3×D411yescharacteristic
426C3⋊Dic3—22no—
427C3⋊Dic3—21no—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—42no—
436C3×Dic3—62no—
437C3×Dic3—62no—
438C3×Dic3—61no—
439C3×Dic3—61no—
440C3×Dic3—121no—
441C3×Dic3—122no—
442C3×Dic3(C2×D3)⋊C411yescharacteristic
443C3×Dic3(C2×D3)⋊C411yescharacteristic
444C3×Dic3C3×C22⋊C411yescharacteristic
445C3×Dic3C3×C22⋊C411yescharacteristic
446C2×#41—91no—
447C2×M16—31no—
448C2×C42—91no—
449#104—31no—
450#104—91no—
451#104—91no—
452#104—91no—
453C33C2×#10411yescharacteristic, complemented, Sylow
454C23×C3—31no—
455C23×C3—31no—
456C23×C3—61no—
457C23×C3—181no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3C3×D1211yescharacteristic
461C3×Q8—31no—
462C3×Q8—31no—
463C3×Q8—61no—
464C3×Q8—91no—
465C3×Q8—181no—
466C3×D4—31no—
467C3×D4—31no—
468C3×D4—61no—
469C3×D4—61no—
470C3×D4—61no—
471C3×D4—91no—
472C3×D4—121no—
473C3×D4—181no—
474C3×D4—181no—
475C3×D4—181no—
476C3×D4—181no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
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—31no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—121no—
501C2×C3×C4—121no—
502C2×C3×C4—181no—
503C2×C3×C4—181no—
504C2×C3×C4—181no—
505C2×C3×C4—184no—
506C2×C3×C4—181no—
507C2×C3×C4—181no—
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C22×C3×D311yescharacteristic
510C2×C3×C4C22×C3×D311yescharacteristic
511#67—21no—
512#67—61no—
513#67—61no—
514#67—61no—
515#67—61no—
516#67—61no—
517#67—61no—
518#67—121no—
519C2×Dic3—21no—
520C2×Dic3—61no—
521C2×Dic3—64no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3C3×D1211yescharacteristic
527D12—31no—
528D12—31no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12C3×C4×D311yescharacteristic, complemented
533C4×D3—21no—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—64no—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—121no—
542C4×D3C3×C4×D311yescharacteristic
543C4×D3C3×C4×D311yescharacteristic
544C4×D3C3×#6711yescharacteristic
545C4×D3C3×#6711yescharacteristic
546Dic6—31no—
547Dic6—31no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6C3×C4×D311yescharacteristic, complemented
552C3×C8—22no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—41no—
558C3×C8—42no—
559C3×C8—62no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—32no—
570C2×C32—41no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32—41no—
574C2×C32—61no—
575C2×C32—81no—
576C2×C32—121no—
577C2×C32D3×C22⋊C411yescharacteristic
578C2×C32C2×(C2×D3)⋊C411yescharacteristic
579C2×C32C2×C3×C22⋊C411yescharacteristic
580C3⋊D3—41no—
581C3×D3—21no—
582C3×D3—21no—
583C3×D3—22no—
584C3×D3—41no—
585C3×D3—41no—
586C3×D3—41no—
587C3×D3—81no—
588C3×D3—121no—
589C3×D3—121no—
590C3×D3—241no—
591C3×D3#82512yesdirect product factor
592C3×D3C3×#10412yescomplemented
593#41—31no—
594#41—91no—
595#41—91no—
596#41—91no—
597#41—181no—
598#41—181no—
599C2×Q8—91no—
600C2×D4—91no—
601C2×D4—181no—
602C22×C4—31no—
603C22×C4—181no—
604C22×C4—181no—
605M16—31no—
606M16—61no—
607M16C3×D3211yescharacteristic, complemented
608C2×C8—61no—
609C42—31no—
610C42—91no—
611C42—181no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—31no—
616C22×C3—31no—
617C22×C3—31no—
618C22×C3—31no—
619C22×C3—41no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—62no—
623C22×C3—62no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—121no—
627C22×C3—122no—
628C22×C3—181no—
629C22×C3—362no—
630C22×C3D3×D1211yescharacteristic
631C22×C3C2×C3×D1211yescharacteristic
632C22×C3C3×D3×D411yescharacteristic
633C2×D3—22no—
634C2×D3—21no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—121no—
638C2×D3—122no—
639C2×D3—122no—
640C2×D3C3×(C2×D3)⋊C411yescharacteristic
641C2×D3C3×(C2×D3)⋊C411yescharacteristic
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—31no—
649C3×C4—31no—
650C3×C4—31no—
651C3×C4—31no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—62no—
657C3×C4—62no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—121no—
661C3×C4—122no—
662C3×C4—182no—
663C3×C4—181no—
664C3×C4C4×D3211yescharacteristic
665C3×C4D3×#6711yescharacteristic
666C3×C4C2×C3×C4×D311yescharacteristic
667C3×C4C2×C3×C4×D311yescharacteristic
668C3×C4C3×D3×D411yescharacteristic
669C3×C4C2×C3×#6711yescharacteristic
670Dic3—22no—
671Dic3—21no—
672Dic3—62no—
673Dic3—62no—
674Dic3—61no—
675Dic3—61no—
676Dic3—121no—
677Dic3—122no—
678Dic3C3×(C2×D3)⋊C411yescharacteristic
679Dic3C3×(C2×D3)⋊C411yescharacteristic
680C32—21no—
681C32—21no—
682C32—21no—
683C32—41no—
684C32D3×#10411yescharacteristic, complemented
685C32C2×#82511yescharacteristic, complemented
686C32C2×C3×#10411yescharacteristic, complemented
687C23—31no—
688C23—181no—
689Q8—31no—
690Q8—91no—
691Q8—181no—
692D4—31no—
693D4—61no—
694D4—91no—
695D4—181no—
696D4—181no—
697D4—181no—
698D4—181no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—184no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4C2×C3×D3211yescharacteristic
713C8—21no—
714C8—61no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—32no—
722C2×C3—32no—
723C2×C3—41no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—62no—
728C2×C3—61no—
729C2×C3—61no—
730C2×C3—81no—
731C2×C3—121no—
732C2×C3—121no—
733C2×C3—121no—
734C2×C3—241no—
735C2×C3—361no—
736C2×C3D3×(C2×D3)⋊C411yescharacteristic
737C2×C3C3×D3×C22⋊C411yescharacteristic
738C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
739D3—21no—
740D3—41no—
741D3—121no—
742D3—121no—
743D3—241no—
744D3C3×#82512yesdirect product factor
745C22—31no—
746C22—31no—
747C22—62no—
748C22—61no—
749C22—181no—
750C22—362no—
751C22C3×D3×D1211yescharacteristic
752C4—31no—
753C4—31no—
754C4—62no—
755C4—61no—
756C4—182no—
757C4—181no—
758C4C3×C4×D3211yescharacteristic
759C4C3×D3×#6711yescharacteristic
760C3—21no—
761C3—21no—
762C3—21no—
763C3—41no—
764C3D3×#82511yescharacteristic, direct product factor
765C3C3×D3×#10411yescharacteristic, complemented
766C3C2×C3×#82511yescharacteristic, complemented
767C2—21no—
768C2—32no—
769C2—61no—
770C2—121no—
771C2—361no—
772C2C3×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
hypocenterC32C2×C3×#104
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×C4×D3×Dic3C2semidirect
4. C3×#63652C2semidirect
5. C32×#825C2semidirect
6. C3×#63570C2semidirect
7. C3×#63568C2semidirect
10. D3×#825C3direct (N × H)
17. C3×D3×D12C4semidirect
19. C3×#3799C4semidirect
21. C3×#3795C4semidirect
22. C3×D3×Dic6C4semidirect
23. C33×M16C22semidirect
24. C3×C4×C3⋊Dic3C22semidirect
25. C32×C4×Dic3C22semidirect
26. C32×#208C22semidirect
36. C3×D3×M16D3semidirect
37. C3×D3×M16C2×C3semidirect
39. C4×D3×Dic3C2×C3semidirect
41. #63652C2×C3semidirect
49. C3×#825D3direct (N × H)
50. C3×#825C2×C3semidirect
52. #63570C2×C3semidirect
53. #63568C2×C3semidirect
59. C3×C4⋊(C3⋊D3)C2×C4semidirect
61. C3×#634C2×C4semidirect
65. C32×D12C2×C4semidirect
71. C32×Dic6C2×C4semidirect
118. D3×D12C3×C4semidirect
120. #3799C3×C4semidirect
122. #3795C3×C4semidirect
123. D3×Dic6C3×C4semidirect
130. C32×M16C2×D3semidirect
131. C32×M16C2×D3semidirect
132. C32×M16C22×C3semidirect
135. C4×C3⋊Dic3C22×C3semidirect
142. C3×C4×Dic3C2×D3semidirect
143. C3×C4×Dic3C22×C3semidirect
145. C3×#208C2×D3semidirect
146. C3×#208C22×C3semidirect
177. D3×M16C3×D3semidirect
191. #825C3×D3direct (N × H)
219. C4⋊(C3⋊D3)C2×C3×C4semidirect
221. #634C2×C3×C4semidirect
250. C3×D12C4×D3semidirect
251. C3×D12C2×C3×C4semidirect
281. C3×Dic6C4×D3semidirect
282. C3×Dic6C2×C3×C4semidirect
308. C32×D3#104semidirect
358. C3×M16D32semidirect
359. C3×M16C2×C3×D3semidirect
360. C3×M16C2×C3×D3semidirect
374. C4×Dic3C2×C3×D3semidirect
375. #208C2×C3×D3semidirect
453. C33C2×#104semidirect
532. D12C3×C4×D3semidirect
551. Dic6C3×C4×D3semidirect
591. C3×D3#825direct (N × H)
592. C3×D3C3×#104semidirect
607. M16C3×D32semidirect
684. C32D3×#104semidirect
685. C32C2×#825semidirect
686. C32C2×C3×#104semidirect
744. D3C3×#825direct (N × H)
764. C3D3×#825direct (N × H)
765. C3C3×D3×#104semidirect
766. C3C2×C3×#825semidirect

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×C4×D3×Dic32
C3×#636522
C32×#8252
C3×#635702
C3×#635682
C2×C3×#8253
C3×D3×#1043
D3×#8253