Finite Group Databasebeta

← C3×#81750 #11889805

Subgroups — C3×#81750 #11889805

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5726C211yesmaximal, characteristic
2C3×#5694C211yesmaximal, characteristic, complemented
3C32×#491C211yesmaximal, characteristic, complemented
4C3×#5090C211yesmaximal, characteristic, complemented
5C3×#5066C211yesmaximal, characteristic, complemented
6C3×#4816C211yesmaximal, characteristic, complemented
7C3×#4814C211yesmaximal, characteristic, complemented
8C3×#4813C211yesmaximal, characteristic, complemented
9C3×#4811C211yesmaximal, characteristic, complemented
10C3×#4808C211yesmaximal, characteristic, complemented
11C3×#4808C211yesmaximal, characteristic, complemented
12C3×#4804C211yesmaximal, characteristic, complemented
13C3×#4803C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4706C211yesmaximal, characteristic, complemented
16C3×#3315—31nomaximal
17#81750C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic
21C32×#125C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#898—21no—
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#895—21no—
33C3×#894—21no—
34C3×#894—21no—
35C3×#894—21no—
36C3×#892—21no—
37C3×#892C2211yescharacteristic
38C3×D3×C4⋊C4—21no—
39C3×D3×C4⋊C4C2211yescharacteristic
40C3×#890—21no—
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#97C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#818C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#552—31no—
62C3×#547—31no—
63#5726C2×C311yescharacteristic
64#5694C2×C311yescharacteristic, complemented
65C3×#491—21no—
66C3×#491D311yescharacteristic, complemented
67C3×#491C2×C311yescharacteristic, complemented
68C3×#485—31no—
69C3×#484—31no—
70C3×#478—31no—
71C3×#470—31no—
72C3×#467—31no—
73C3×#462—31no—
74C3×#452—31no—
75C3×#452—31no—
76C3×#440—31no—
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5090C2×C311yescharacteristic, complemented
81#5066C2×C311yescharacteristic, complemented
82#4816C2×C311yescharacteristic, complemented
83#4814C2×C311yescharacteristic, complemented
84#4813C2×C311yescharacteristic, complemented
85#4811C2×C311yescharacteristic, complemented
86#4808C2×C311yescharacteristic, complemented
87#4808C2×C311yescharacteristic, complemented
88#4804C2×C311yescharacteristic, complemented
89#4803C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4706C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C3×#239—22no—
95C3×#239—22no—
96C3×#239—41no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12D411yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C42C2311yescharacteristic
118C3×#216—41no—
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3315—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C22×C311yescharacteristic
148C2×#239C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—21no—
155C3×C4⋊Q8C2×D311yescharacteristic
156C3×C4⋊Q8C22×C311yescharacteristic
157C3×#126—61no—
158C3×#125—21no—
159C3×#125—61no—
160C3×#125C2×D311yescharacteristic
161C3×#125C22×C311yescharacteristic
162C3×#123—61no—
163C3×#123—61no—
164C3×#123—61no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×#121—61no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×#117—31no—
174C3×#117—61no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—61no—
177#946C22×C311yescharacteristic
178#946C22×C311yescharacteristic
179C2×#216C22×C311yescharacteristic
180C2×#216C22×C311yescharacteristic
181C2×#204C22×C311yescharacteristic
182C2×ΓL(1,𝔽25)C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic
184#898—21no—
185#897C22×C311yescharacteristic
186#897C22×C311yescharacteristic
187#895—21no—
188#894—21no—
189#894—21no—
190#894—21no—
191#892—21no—
192#892C22×C311yescharacteristic
193D3×C4⋊C4—21no—
194D3×C4⋊C4C22×C311yescharacteristic
195#890—21no—
196C4×D12C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C4×Dic6C22×C311yescharacteristic
199C3×#107—31no—
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#103C2×D311yescharacteristic
213C3×#103C2×D311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#103C22×C311yescharacteristic
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×#97—21no—
224C3×#97C2×D311yescharacteristic
225C3×#97C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230(C2×D3)⋊C8C22×C311yescharacteristic
231#818C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#809C22×C311yescharacteristic
234#809C22×C311yescharacteristic
235#808C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237C4⋊(C3⋊C8)C22×C311yescharacteristic
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—41no—
259C3×D12—42no—
260C3×D12—42no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—31no—
277#547—31no—
278#491C3×D311yescharacteristic, complemented
279#485—31no—
280#484—31no—
281#478—31no—
282#470—31no—
283#467—31no—
284#462—31no—
285#452—31no—
286#452—31no—
287#440—31no—
288#435—31no—
289#417—31no—
290#416—31no—
291C3×#41—62no—
292C3×#41—62no—
293C3×#41—121no—
294C3×#41—121no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C23×C311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312#239—22no—
313#239—22no—
314#239—41no—
315#239—41no—
316C2×D12—21no—
317C2×D12—21no—
318C2×D12C3×D411yescharacteristic
319C2×D12C23×C311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3C23×C311yescharacteristic
325C2×C4×D3C23×C311yescharacteristic
326C2×Dic6C23×C311yescharacteristic
327C3×Q16—121no—
328C3×Q16—121no—
329C3×SD16—62no—
330C3×M16—121no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—121no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C23×C311yescharacteristic
339C2×C3×C8C23×C311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4—41no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C23×C311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C22⋊C4—31no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42—61no—
377C3×C42—61no—
378C3×C42C22×D311yescharacteristic
379C3×C42C23×C311yescharacteristic
380#216—41no—
381#216—41no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4C3×D411yescharacteristic
389(C2×D3)⋊C4C3×D411yescharacteristic
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3C3×D411yescharacteristic
393C4⋊Dic3C23×C311yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399C4×Dic3—21no—
400C4×Dic3—21no—
401C2×C3⋊C8C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403#204—22no—
404ΓL(1,𝔽25)—41no—
405D3×C8—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4H(5,𝔽2)11yescharacteristic
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—31no—
430C2×#41—31no—
431C2×Q16—31no—
432C2×Q16—31no—
433C2×SD16—31no—
434C2×M16—31no—
435C22×C8—31no—
436C4⋊Q8C2×C3×D311yescharacteristic
437#126—61no—
438#125—61no—
439#125C2×C3×D311yescharacteristic
440#123—61no—
441#123—61no—
442#123—61no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—31no—
447#121—61no—
448C4×Q8—31no—
449C4×D4—31no—
450C4×D4—31no—
451#117—31no—
452#117—61no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—61no—
455#107—31no—
456#107—31no—
457#106—31no—
458C4⋊C8—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103C2×C3×D311yescharacteristic
463#103C2×C3×D311yescharacteristic
464#103C2×C3×D311yescharacteristic
465#103C2×C3×D311yescharacteristic
466#102—31no—
467#102—31no—
468#102—31no—
469C22⋊C8—31no—
470C22⋊C8—31no—
471#97C2×C3×D311yescharacteristic
472C23×C3—31no—
473C23×C3—31no—
474C23×C3—61no—
475C22×D3—21no—
476C22×D3C2×C3×D411yescharacteristic
477C22×D3C2×C3×D411yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—32no—
493C3×D4—61no—
494C3×D4—121no—
495C3×D4—122no—
496C3×D4—122no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—122no—
522C2×C3×C4—122no—
523C2×C3×C4—122no—
524C2×C3×C4—122no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C2×C3×D411yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C24×C311yescharacteristic
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3C2×C3×D411yescharacteristic
535C2×Dic3C2×C3×D411yescharacteristic
536D12—21no—
537D12—41no—
538D12—42no—
539D12—42no—
540D12C3×#4112yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—42no—
546C4×D3—42no—
547C4×D3—42no—
548C4×D3—42no—
549Dic6—21no—
550Dic6—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—41no—
556C3×C8—41no—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C2×C32#54611yescharacteristic
562C2×C32#57511yescharacteristic
563C2×C32#57811yescharacteristic
564C3×D3—41no—
565C3×D3—41no—
566C3×D3—42no—
567#41—62no—
568#41—62no—
569#41—121no—
570#41—121no—
571C2×Q8—31no—
572C2×Q8C22×C3×D311yescharacteristic
573C2×Q8C22×C3×D311yescharacteristic
574C2×D4—31no—
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—61no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584Q16—121no—
585Q16—121no—
586SD16—62no—
587M16—121no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—121no—
591C2×C8C22×C3×D311yescharacteristic
592C2×C8C22×C3×D311yescharacteristic
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4C22×C3×D311yescharacteristic
607C4⋊C4C22×C3×D311yescharacteristic
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C42—61no—
617C42—61no—
618C42C22×C3×D311yescharacteristic
619C22×C3—21no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—62no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C22×C3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—22no—
638C2×D3—41no—
639C2×D3—41no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4D3×#4111yescharacteristic
666C3×C4#100911yescharacteristic
667C3×C4C2×C3×#4111yescharacteristic
668C3×C4C3×H(5,𝔽2)11yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674C32#331511yescharacteristic, complemented, Sylow
675C23—31no—
676C23—31no—
677C23—61no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—61no—
683Q8—61no—
684D4—32no—
685D4—61no—
686D4—121no—
687D4—122no—
688D4—122no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4C3×D3×D411yescharacteristic
707C2×C4C3×D3×D411yescharacteristic
708C2×C4C23×C3×D311yescharacteristic
709C8—21no—
710C8—21no—
711C8—61no—
712C8—61no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—121no—
717C2×C3—121no—
718C2×C3—122no—
719C2×C3#567611yescharacteristic
720C2×C3#577711yescharacteristic
721C2×C3#577911yescharacteristic
722C2×C3C3×#54611yescharacteristic
723C2×C3C3×#57511yescharacteristic
724C2×C3C3×#57811yescharacteristic
725D3—41no—
726D3—41no—
727D3—42no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—62no—
735C22—121no—
736C22—121no—
737C22C2×C3×D3×D411yescharacteristic
738C4—21no—
739C4—21no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—61no—
745C4—61no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4C3×D3×#4111yescharacteristic
750C4C3×#100911yescharacteristic
751C3—21no—
752C3#8175011yescharacteristic, direct product factor
753C3C3×#331511yescharacteristic, complemented
754C2—121no—
755C2—121no—
756C2—122no—
757C2C3×#567611yescharacteristic
758C2C3×#577711yescharacteristic
759C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#491C2
socleC22×C32C22×D4
prime radicalC3×#5726C2
hypercenterC3×#491D3
hypocenterC3C3×#3315
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#491

Complements

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

NH ≅ G/Ntype
2. C3×#5694C2semidirect
3. C32×#491C2semidirect
4. C3×#5090C2semidirect
5. C3×#5066C2semidirect
6. C3×#4816C2semidirect
7. C3×#4814C2semidirect
8. C3×#4813C2semidirect
9. C3×#4811C2semidirect
10. C3×#4808C2semidirect
11. C3×#4808C2semidirect
12. C3×#4804C2semidirect
13. C3×#4803C2semidirect
14. C3×#4710C2semidirect
15. C3×#4706C2semidirect
17. #81750C3direct (N × H)
64. #5694C2×C3semidirect
66. C3×#491D3semidirect
67. C3×#491C2×C3semidirect
80. #5090C2×C3semidirect
81. #5066C2×C3semidirect
82. #4816C2×C3semidirect
83. #4814C2×C3semidirect
84. #4813C2×C3semidirect
85. #4811C2×C3semidirect
86. #4808C2×C3semidirect
87. #4808C2×C3semidirect
88. #4804C2×C3semidirect
89. #4803C2×C3semidirect
90. #4710C2×C3semidirect
91. #4706C2×C3semidirect
278. #491C3×D3semidirect
674. C32#3315semidirect
752. C3#81750direct (N × H)
753. C3C3×#3315semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C3×#56942
C32×#4912
C3×#50902
C3×#50662
C3×#48162
C3×#48142
C3×#48132
C3×#48112
C3×#48082
C3×#48042
C3×#48032
C3×#47102
C3×#47062
C3×#33153
#817503