Finite Group Databasebeta

← C3×#81245 #11887701

Subgroups — C3×#81245 #11887701

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 759 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic, complemented
2C3×#5576C211yesmaximal, characteristic
3C32×#479C211yesmaximal, characteristic, complemented
4C3×#5068C211yesmaximal, characteristic, complemented
5C3×C4×#216C211yesmaximal, characteristic, complemented
6C3×#4887C211yesmaximal, characteristic, complemented
7C3×#4882C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×#4864C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4834C211yesmaximal, characteristic, complemented
12C3×#4809C211yesmaximal, characteristic, complemented
13C3×#4808C211yesmaximal, characteristic, complemented
14C3×#4804C211yesmaximal, characteristic, complemented
15C3×D3×#103C211yesmaximal, characteristic, complemented
16C3×#3300—31nomaximal
17#81245C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C32×#125C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×#898—21no—
28C3×#897—21no—
29C3×#897C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#895—21no—
33C3×#895C2211yescharacteristic
34C3×#894—21no—
35C3×#892—21no—
36C3×#892C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#890—21no—
39C3×#875—21no—
40C3×#875C2211yescharacteristic
41C3×C4×D12—21no—
42C3×C4×D12C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×C4⋊C8C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#103C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#552—31no—
62C3×#548—31no—
63#5694C2×C311yescharacteristic, complemented
64#5576C2×C311yescharacteristic
65C3×#488—31no—
66C3×#485—31no—
67C3×#480—31no—
68C3×#479—21no—
69C3×#479D311yescharacteristic, complemented
70C3×#479C2×C311yescharacteristic, complemented
71C3×#467—31no—
72C3×#465—31no—
73C3×#464—31no—
74C3×#452—31no—
75C3×#451—31no—
76C3×C4×Q16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#103—31no—
80#5068C2×C311yescharacteristic, complemented
81C4×#216C2×C311yescharacteristic, complemented
82#4887C2×C311yescharacteristic, complemented
83#4882C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85#4864C2×C311yescharacteristic, complemented
86#4845C2×C311yescharacteristic, complemented
87#4834C2×C311yescharacteristic, complemented
88#4809C2×C311yescharacteristic, complemented
89#4808C2×C311yescharacteristic, complemented
90#4804C2×C311yescharacteristic, complemented
91D3×#103C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C3×#239—22no—
94C3×#239—41no—
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C42—21no—
118C32×C42C2311yescharacteristic
119C3×#216—22no—
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)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×Dic12—41no—
141C3×#204—41no—
142C3×D3×C8—41no—
143C3×D3×C8—41no—
144#3300—31noSylow
145C2×C3×#41—31no—
146C22×C3×Q8—31no—
147C2×#239C22×C311yescharacteristic
148C2×D3×Q8C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×#126—61no—
155C3×#125—21no—
156C3×#125—61no—
157C3×#125C2×D311yescharacteristic
158C3×#125C22×C311yescharacteristic
159C3×#124—31no—
160C3×#124—61no—
161C3×#123—61no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—61no—
166C3×#121—31no—
167C3×#121—61no—
168C3×C4×Q8—21no—
169C3×C4×Q8—31no—
170C3×C4×Q8C2×D311yescharacteristic
171C3×C4×Q8C22×C311yescharacteristic
172C3×C4×D4—31no—
173C3×C4×D4—61no—
174C3×#117—31no—
175C3×#117—61no—
176C2×C3×C4⋊C4—31no—
177C2×#216C22×C311yescharacteristic
178C2×Dic12C22×C311yescharacteristic
179C2×#204C22×C311yescharacteristic
180C2×D3×C8C22×C311yescharacteristic
181C2×D3×C8C22×C311yescharacteristic
182#898—21no—
183#897—21no—
184#897C22×C311yescharacteristic
185#897C22×C311yescharacteristic
186#897C22×C311yescharacteristic
187#895—21no—
188#895C22×C311yescharacteristic
189#894—21no—
190#892—21no—
191#892C22×C311yescharacteristic
192D3×C4⋊C4C22×C311yescharacteristic
193#890—21no—
194#875—21no—
195#875C22×C311yescharacteristic
196C4×D12—21no—
197C4×D12C22×C311yescharacteristic
198C4×Dic6C22×C311yescharacteristic
199C3×#107—21no—
200C3×#107—31no—
201C3×#107C2×D311yescharacteristic
202C3×#107C22×C311yescharacteristic
203C3×#106—21no—
204C3×#106C2×D311yescharacteristic
205C3×#106C22×C311yescharacteristic
206C3×C4⋊C8—21no—
207C3×C4⋊C8C2×D311yescharacteristic
208C3×C4⋊C8C22×C311yescharacteristic
209C3×#103—21no—
210C3×#103—21no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103C2×D311yescharacteristic
217C3×#103C2×D311yescharacteristic
218C3×#103C22×C311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#102—31no—
221C3×#102—31no—
222C3×#102—31no—
223C3×C22⋊C8—31no—
224C3×C22⋊C8—31no—
225C3×C4×C8—31no—
226#835C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#809C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237C4×C3⋊C8C22×C311yescharacteristic
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—22no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—42no—
259C3×D12—42no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—31no—
277#548—31no—
278#488—31no—
279#485—31no—
280#480—31no—
281#479C3×D311yescharacteristic, complemented
282#467—31no—
283#465—31no—
284#464—31no—
285#452—31no—
286#451—31no—
287C4×Q16—31no—
288C8×D4—31no—
289#416—31no—
290C2×#103—31no—
291C3×#41—62no—
292C3×#41—121no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C23×C311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310#239—22no—
311#239—41no—
312D3×Q8—22no—
313D3×Q8—41no—
314C2×D12—21no—
315C2×D12—21no—
316C2×D12C3×D411yescharacteristic
317C2×D12C23×C311yescharacteristic
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3C23×C311yescharacteristic
322C2×C4×D3C23×C311yescharacteristic
323C2×Dic6—21no—
324C2×Dic6C23×C311yescharacteristic
325C2×Dic6C23×C311yescharacteristic
326C3×Q16—62no—
327C3×Q16—121no—
328C3×SD16—121no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—121no—
334C2×C3×C8—121no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C23×C311yescharacteristic
338C2×C3×C8C23×C311yescharacteristic
339C3×C4⋊C4—21no—
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—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—41no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—41no—
377C3×C42—61no—
378C3×C42—61no—
379C3×C42C22×D311yescharacteristic
380C3×C42C23×C311yescharacteristic
381#216—22no—
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)⋊C4—21no—
389(C2×D3)⋊C4C3×D411yescharacteristic
390(C2×D3)⋊C4C3×D411yescharacteristic
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3C3×D411yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398C4×Dic3—21no—
399C4×Dic3—21no—
400C2×C3⋊C8C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402Dic12—41no—
403#204—41no—
404D3×C8—41no—
405D3×C8—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3#13512yes—
416C32×C4—22no—
417C32×C4—21no—
418C32×C4—21no—
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—
430C22×Q8—31no—
431C2×Q16—31no—
432C2×Q16—31no—
433C2×SD16—31no—
434C22×C8—31no—
435C22×C8—31no—
436#126—61no—
437#125—61no—
438#125C2×C3×D311yescharacteristic
439#124—31no—
440#124—61no—
441#123—61no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446#121—31no—
447#121—61no—
448C4×Q8—31no—
449C4×Q8C2×C3×D311yescharacteristic
450C4×D4—31no—
451C4×D4—61no—
452#117—31no—
453#117—61no—
454C2×C4⋊C4—31no—
455#107—31no—
456#107C2×C3×D311yescharacteristic
457#106C2×C3×D311yescharacteristic
458C4⋊C8C2×C3×D311yescharacteristic
459#103—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103C2×C3×D311yescharacteristic
465#103C2×C3×D311yescharacteristic
466#102—31no—
467#102—31no—
468#102—31no—
469C22⋊C8—31no—
470C22⋊C8—31no—
471C4×C8—31no—
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—22no—
481C3×Q8—41no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—122no—
487C3×Q8#23912yes—
488C3×Q8C3×#4112yes—
489C3×D4—62no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—122no—
493C3×D4—122no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
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—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—122no—
519C2×C3×C4—122no—
520C2×C3×C4—122no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×C3×D411yescharacteristic
524C2×C3×C4C2×C3×D411yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C24×C311yescharacteristic
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3C2×C3×D411yescharacteristic
531C2×Dic3C2×C3×D411yescharacteristic
532D12—22no—
533D12—21no—
534D12—21no—
535D12—42no—
536D12—42no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—42no—
542C4×D3—42no—
543C4×D3—42no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6—42no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C2×C32#54611yescharacteristic
560C2×C32C2×#13511yescharacteristic
561C2×C32#57811yescharacteristic
562C3×D3—22no—
563C3×D3—41no—
564C3×D3—81no—
565#41—62no—
566#41—121no—
567C2×Q8—31no—
568C2×Q8—31no—
569C2×Q8—61no—
570C2×Q8—62no—
571C2×Q8—121no—
572C2×Q8C22×C3×D311yescharacteristic
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—61no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582Q16—62no—
583Q16—121no—
584SD16—121no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—121no—
588C2×C8—121no—
589C2×C8C22×C3×D311yescharacteristic
590C2×C8C22×C3×D311yescharacteristic
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4C22×C3×D311yescharacteristic
602C4⋊C4C22×C3×D311yescharacteristic
603C4⋊C4C22×C3×D311yescharacteristic
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C42—21no—
614C42—61no—
615C42—61no—
616C42C22×C3×D311yescharacteristic
617C22×C3—21no—
618C22×C3—32no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C22×C3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3C3×#13512yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—42no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—81no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23911yescharacteristic
664C3×C4#100911yescharacteristic
665C3×C4C2×C3×#4111yescharacteristic
666C3×C4C3×H(5,𝔽2)11yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672C32#330011yescharacteristic, complemented, Sylow
673C23—31no—
674C23—31no—
675C23—61no—
676Q8—21no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—122no—
682Q8C3×#23912yes—
683D4—62no—
684D4—61no—
685D4—61no—
686D4—122no—
687D4—122no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4C3×D3×D411yescharacteristic
705C2×C4C3×D3×D411yescharacteristic
706C2×C4C23×C3×D311yescharacteristic
707C8—21no—
708C8—21no—
709C8—61no—
710C8—61no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—62no—
715C2×C3—121no—
716C2×C3—241no—
717C2×C3#563011yescharacteristic
718C2×C3D3×#13511yescharacteristic
719C2×C3#577911yescharacteristic
720C2×C3C3×#54611yescharacteristic
721C2×C3C2×C3×#13511yescharacteristic
722C2×C3C3×#57811yescharacteristic
723D3—22no—
724D3—41no—
725D3—81no—
726C22—32no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—121no—
733C22—121no—
734C22—121no—
735C22C2×C3×D3×D411yescharacteristic
736C4—21no—
737C4—21no—
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—61no—
743C4—61no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4C2×C3×#23911yescharacteristic
748C4C3×#100911yescharacteristic
749C3—21no—
750C3#8124511yescharacteristic, direct product factor
751C3C3×#330011yescharacteristic, complemented
752C2—62no—
753C2—121no—
754C2—241no—
755C2C3×#563011yescharacteristic
756C2C3×D3×#13511yescharacteristic
757C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radicalC3×#5576C2
hypercenterC3×#479D3
hypocenterC3C3×#3300
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#479

Complements

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

NH ≅ G/Ntype
1. C3×#5694C2semidirect
3. C32×#479C2semidirect
4. C3×#5068C2semidirect
5. C3×C4×#216C2semidirect
6. C3×#4887C2semidirect
7. C3×#4882C2semidirect
8. C3×#4868C2semidirect
9. C3×#4864C2semidirect
10. C3×#4845C2semidirect
11. C3×#4834C2semidirect
12. C3×#4809C2semidirect
13. C3×#4808C2semidirect
14. C3×#4804C2semidirect
15. C3×D3×#103C2semidirect
17. #81245C3direct (N × H)
63. #5694C2×C3semidirect
69. C3×#479D3semidirect
70. C3×#479C2×C3semidirect
80. #5068C2×C3semidirect
81. C4×#216C2×C3semidirect
82. #4887C2×C3semidirect
83. #4882C2×C3semidirect
84. #4868C2×C3semidirect
85. #4864C2×C3semidirect
86. #4845C2×C3semidirect
87. #4834C2×C3semidirect
88. #4809C2×C3semidirect
89. #4808C2×C3semidirect
90. #4804C2×C3semidirect
91. D3×#103C2×C3semidirect
281. #479C3×D3semidirect
672. C32#3300semidirect
750. C3#81245direct (N × H)
751. C3C3×#3300semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
C3×#55762
C32×#4792
C3×#50682
C3×C4×#2162
C3×#48872
C3×#48822
C3×#48682
C3×#48642
C3×#48452
C3×#48342
C3×#48092
C3×#48082
C3×#48042
C3×D3×#1032
C3×#33003
#812453