Finite Group Databasebeta

← C3×#81445 #11887193

Subgroups — C3×#81445 #11887193

Order 1152.

868 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic
2C3×#5513C211yesmaximal, characteristic, complemented
3C32×#483C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C3×#4871C211yesmaximal, characteristic, complemented
7C3×#4866C211yesmaximal, characteristic, complemented
8C3×#4864C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4808C211yesmaximal, characteristic, complemented
11C3×#4804C211yesmaximal, characteristic, complemented
12C3×#4800C211yesmaximal, characteristic, complemented
13C3×#4798C211yesmaximal, characteristic, complemented
14C3×#4731C211yesmaximal, characteristic, complemented
15C3×#67⋊C8C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#81445C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic, complemented
24C3×#929—21no—
25C3×C4×#67C2211yescharacteristic
26C3×#926—21no—
27C3×#924C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic, complemented
32C3×#898—21no—
33C3×#897C2211yescharacteristic, complemented
34C3×#895—21no—
35C3×#895C2211yescharacteristic
36C3×#894—21no—
37C3×#893C2211yescharacteristic
38C3×#892C2211yescharacteristic, complemented
39C3×#890C2211yescharacteristic, complemented
40C3×#889—21no—
41C3×#887C2211yescharacteristic, complemented
42C3×#882—21no—
43C3×D3×C22⋊C4—21no—
44C32×#106C2211yescharacteristic, complemented
45C32×#106C2211yescharacteristic, complemented
46C32×#103C2211yescharacteristic, complemented
47C32×#103C2211yescharacteristic, complemented
48C32×C22⋊C8C2211yescharacteristic
49C3×#835C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×#807C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5630C2×C311yescharacteristic
64#5513C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#483—21no—
67C3×#483D311yescharacteristic, complemented
68C3×#483C2×C311yescharacteristic, complemented
69C3×#482—31no—
70C3×#478—31no—
71C3×#467—31no—
72C3×#465—31no—
73C3×#464—31no—
74C3×#452—31no—
75C3×#450—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80#5051C2×C311yescharacteristic, complemented
81C2×#809C2×C311yescharacteristic, complemented
82#4871C2×C311yescharacteristic, complemented
83#4866C2×C311yescharacteristic, complemented
84#4864C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4808C2×C311yescharacteristic, complemented
87#4804C2×C311yescharacteristic, complemented
88#4800C2×C311yescharacteristic, complemented
89#4798C2×C311yescharacteristic, complemented
90#4731C2×C311yescharacteristic, complemented
91#67⋊C8C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C3×#239—22no—
98C3×#239—41no—
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—41no—
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×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142C3×#204—41no—
143C3×D3×C8—41no—
144#3296—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C22×C311yescharacteristic
148C22×D12C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×#126—61no—
155C3×#125—31no—
156C3×#125—61no—
157C3×#124—31no—
158C3×#123—61no—
159C3×#123—61no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8C2×D311yescharacteristic
164C3×C22⋊Q8C22×C311yescharacteristic
165C3×#121—31no—
166C3×#121—61no—
167C3×#120—61no—
168C3×C4×Q8—31no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×#117—31no—
172C3×#117—61no—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4C2×D311yescharacteristic
175C2×C3×C4⋊C4C22×C311yescharacteristic
176C2×C3×C22⋊C4—61no—
177#947C22×C311yescharacteristic
178C2×#216C22×C311yescharacteristic, complemented
179#929—21no—
180C4×#67C22×C311yescharacteristic
181#926—21no—
182#924C22×C311yescharacteristic
183C22×C3⋊C8C22×C311yescharacteristic
184C2×#204C22×C311yescharacteristic
185C2×#204C22×C311yescharacteristic
186C2×D3×C8C22×C311yescharacteristic, complemented
187#898—21no—
188#897C22×C311yescharacteristic, complemented
189#895—21no—
190#895C22×C311yescharacteristic
191#894—21no—
192#893C22×C311yescharacteristic
193#892C22×C311yescharacteristic, complemented
194#890C22×C311yescharacteristic, complemented
195#889—21no—
196#887C22×C311yescharacteristic, complemented
197#882—21no—
198D3×C22⋊C4—21no—
199C3×#107—31no—
200C3×#106—21no—
201C3×#106—21no—
202C3×#106C2×D311yescharacteristic, complemented
203C3×#106C2×D311yescharacteristic, complemented
204C3×#106C22×C311yescharacteristic, complemented
205C3×#106C22×C311yescharacteristic, complemented
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103C2×D311yescharacteristic, complemented
212C3×#103C2×D311yescharacteristic, complemented
213C3×#103C22×C311yescharacteristic, complemented
214C3×#103C22×C311yescharacteristic, complemented
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×C22⋊C8—21no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8C2×D311yescharacteristic
224C3×C22⋊C8C22×C311yescharacteristic
225C3×C4×C8—31no—
226#835C22×C311yescharacteristic, complemented
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic, complemented
230Dic3⋊C8C22×C311yescharacteristic, complemented
231C8×Dic3C22×C311yescharacteristic, complemented
232#810C22×C311yescharacteristic, complemented
233#809C22×C311yescharacteristic
234#809C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#809C22×C311yescharacteristic
237#807C22×C311yescharacteristic, complemented
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12—42no—
267C3×D12—81no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—31no—
281#488—31no—
282#483C3×D311yescharacteristic, complemented
283#482—31no—
284#478—31no—
285#467—31no—
286#465—31no—
287#464—31no—
288#452—31no—
289#450—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C2×#67C3×D411yescharacteristic
320#239—22no—
321#239—41no—
322C2×D12—22no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12—41no—
327C2×D12C23×C311yescharacteristic
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3C23×C311yescharacteristic
332C2×Dic6C23×C311yescharacteristic
333C3×Q16—121no—
334C3×SD16—62no—
335C3×SD16—121no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C23×C311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
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⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C23×C311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C4⋊C4C23×C311yescharacteristic
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—31no—
372C3×C22⋊C4—41no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C42—31no—
381C3×C42—61no—
382C3×C42—61no—
383#217—21no—
384#217C3×D411yescharacteristic
385#216—41no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4C3×D411yescharacteristic
393C4⋊Dic3—21no—
394C4⋊Dic3—21no—
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4C3×D411yescharacteristic
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3C23×C311yescharacteristic
403C2×C3⋊C8—41no—
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406#204—22no—
407#204—41no—
408D3×C8—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32#13512yes—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—31no—
440C22×C8—31no—
441C22×C8—31no—
442#126—61no—
443#125—31no—
444#125—61no—
445#124—31no—
446#123—61no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8C2×C3×D311yescharacteristic
451#121—31no—
452#121—61no—
453#120—61no—
454C4×Q8—31no—
455C4×D4—31no—
456C4×D4—31no—
457#117—31no—
458#117—61no—
459C2×C4⋊C4C2×C3×D311yescharacteristic
460C2×C22⋊C4—61no—
461#107—31no—
462#106C2×C3×D311yescharacteristic, complemented
463#106C2×C3×D311yescharacteristic, complemented
464C4⋊C8—31no—
465#103—31no—
466#103—31no—
467#103C2×C3×D311yescharacteristic, complemented
468#103C2×C3×D311yescharacteristic, complemented
469#102—31no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475C22⋊C8—31no—
476C22⋊C8C2×C3×D311yescharacteristic
477C4×C8—31no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—122no—
483C23×C3—122no—
484C23×C3—241no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×C3×D411yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—81no—
492C22×D3C2×C3×D411yescharacteristic
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×D4—32no—
502C3×D4—62no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—122no—
507C3×D4—122no—
508C3×D4—241no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—42no—
533C2×C3×C4—42no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—82no—
539C2×C3×C4—122no—
540C2×C3×C4—241no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C24×C311yescharacteristic
545#67—22no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550C2×Dic3C2×C3×D411yescharacteristic
551D12—21no—
552D12—21no—
553D12—21no—
554D12—42no—
555D12—42no—
556D12—81no—
557D12C3×#4112yes—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—42no—
561C4×D3—81no—
562Dic6—21no—
563Dic6—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—41no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C2×C32—22no—
575C2×C32#54611yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32#57711yescharacteristic
578C3×D3—41no—
579C3×D3—42no—
580C3×D3—81no—
581C24—61no—
582#41—62no—
583#41—121no—
584C2×Q8—31no—
585C2×Q8C22×C3×D311yescharacteristic
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—62no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—121no—
594C22×C4—21no—
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4C22×C3×D311yescharacteristic
599Q16—121no—
600SD16—62no—
601SD16—121no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—121no—
605C2×C8—121no—
606C2×C8C22×C3×D311yescharacteristic
607C2×C8C22×C3×D311yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4C22×C3×D311yescharacteristic
618C4⋊C4C22×C3×D311yescharacteristic
619C4⋊C4C22×C3×D311yescharacteristic
620C22⋊C4—21no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C42—31no—
631C42—61no—
632C42—61no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—61no—
642C22×C3—62no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—244no—
651C22×C3#91612yes—
652C22×C3C3×#13512yes—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C22×C3×D411yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—22no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—84no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689C3×C4C2×C3×#4111yescharacteristic
690C3×C4C3×H(5,𝔽2)11yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696C32#329611yescharacteristic, complemented, Sylow
697C23—31no—
698C23—61no—
699C23—61no—
700C23—122no—
701C23—122no—
702C23—241no—
703C23C3×D3×D411yescharacteristic
704Q8—21no—
705Q8—21no—
706Q8—61no—
707Q8—61no—
708D4—32no—
709D4—62no—
710D4—61no—
711D4—61no—
712D4—61no—
713D4—122no—
714D4—122no—
715D4—241no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—42no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—122no—
731C2×C4—241no—
732C2×C4C3×D3×D411yescharacteristic
733C2×C4C23×C3×D311yescharacteristic
734C8—21no—
735C8—21no—
736C8—61no—
737C8—61no—
738C2×C3—22no—
739C2×C3—22no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—42no—
744C2×C3—121no—
745C2×C3—122no—
746C2×C3—241no—
747C2×C3#565411yescharacteristic
748C2×C3C2×#91611yescharacteristic
749C2×C3#577811yescharacteristic
750C2×C3C3×#54611yescharacteristic
751C2×C3C2×C3×#13511yescharacteristic
752C2×C3C3×#57711yescharacteristic
753D3—41no—
754D3—42no—
755D3—81no—
756C22—21no—
757C22—21no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—62no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—244no—
768C22C3×#91612yes—
769C22C2×C3×D3×D411yescharacteristic
770C4—21no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4C3×D3×#4111yescharacteristic
781C4C3×#100911yescharacteristic
782C3—21no—
783C3#8144511yescharacteristic, direct product factor
784C3C3×#329611yescharacteristic, complemented
785C2—22no—
786C2—121no—
787C2—122no—
788C2—241no—
789C2C3×#565411yescharacteristic
790C2C2×C3×#91611yescharacteristic
791C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#483C2
socleC22×C32C22×D4
prime radicalC3×#5630C2
hypercenterC3×#483D3
hypocenterC3C3×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#483

Complements

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

NH ≅ G/Ntype
2. C3×#5513C2semidirect
3. C32×#483C2semidirect
4. C3×#5051C2semidirect
5. C2×C3×#809C2semidirect
6. C3×#4871C2semidirect
7. C3×#4866C2semidirect
8. C3×#4864C2semidirect
9. C3×#4852C2semidirect
10. C3×#4808C2semidirect
11. C3×#4804C2semidirect
12. C3×#4800C2semidirect
13. C3×#4798C2semidirect
14. C3×#4731C2semidirect
15. C3×#67⋊C8C2semidirect
17. #81445C3direct (N × H)
23. C2×C3×#216C22semidirect
31. C2×C3×D3×C8C22semidirect
33. C3×#897C22semidirect
38. C3×#892C22semidirect
39. C3×#890C22semidirect
41. C3×#887C22semidirect
44. C32×#106C22semidirect
45. C32×#106C22semidirect
46. C32×#103C22semidirect
47. C32×#103C22semidirect
49. C3×#835C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. C3×#810C22semidirect
60. C3×#807C22semidirect
64. #5513C2×C3semidirect
67. C3×#483D3semidirect
68. C3×#483C2×C3semidirect
80. #5051C2×C3semidirect
81. C2×#809C2×C3semidirect
82. #4871C2×C3semidirect
83. #4866C2×C3semidirect
84. #4864C2×C3semidirect
85. #4852C2×C3semidirect
86. #4808C2×C3semidirect
87. #4804C2×C3semidirect
88. #4800C2×C3semidirect
89. #4798C2×C3semidirect
90. #4731C2×C3semidirect
91. #67⋊C8C2×C3semidirect
178. C2×#216C22×C3semidirect
186. C2×D3×C8C22×C3semidirect
188. #897C22×C3semidirect
193. #892C22×C3semidirect
194. #890C22×C3semidirect
196. #887C22×C3semidirect
202. C3×#106C2×D3semidirect
203. C3×#106C2×D3semidirect
204. C3×#106C22×C3semidirect
205. C3×#106C22×C3semidirect
211. C3×#103C2×D3semidirect
212. C3×#103C2×D3semidirect
213. C3×#103C22×C3semidirect
214. C3×#103C22×C3semidirect
226. #835C22×C3semidirect
229. (C2×D3)⋊C8C22×C3semidirect
230. Dic3⋊C8C22×C3semidirect
231. C8×Dic3C22×C3semidirect
232. #810C22×C3semidirect
237. #807C22×C3semidirect
282. #483C3×D3semidirect
462. #106C2×C3×D3semidirect
463. #106C2×C3×D3semidirect
467. #103C2×C3×D3semidirect
468. #103C2×C3×D3semidirect
696. C32#3296semidirect
783. C3#81445direct (N × H)
784. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
C3×#55132
C32×#4832
C3×#50512
C2×C3×#8092
C3×#48712
C3×#48662
C3×#48642
C3×#48522
C3×#48082
C3×#48042
C3×#48002
C3×#47982
C3×#47312
C3×#67⋊C82
C3×#32963
#814453