Finite Group Databasebeta

← C3×#80568 #11870560

Subgroups — C3×#80568 #11870560

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5680C211yesmaximal, characteristic, complemented
2C3×C4×#239C211yesmaximal, characteristic, complemented
3C32×#464C211yesmaximal, characteristic, complemented
4C3×#5187C211yesmaximal, characteristic, complemented
5C3×Dic3×Q16C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic
7C3×Dic3×SD16C211yesmaximal, characteristic, complemented
8C3×#5057C211yesmaximal, characteristic, complemented
9C3×#5022C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4833C211yesmaximal, characteristic, complemented
12C3×#4815C211yesmaximal, characteristic, complemented
13C3×#4788C211yesmaximal, characteristic, complemented
14C3×#4784C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#80568C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#893—21no—
31C3×#893C2211yescharacteristic
32C3×#892—21no—
33C3×#892C2211yescharacteristic
34C3×#883—21no—
35C3×#67⋊C4—21no—
36C3×#879—21no—
37C3×#877—21no—
38C3×C4×D12—21no—
39C3×C4×D12C2211yescharacteristic
40C3×C42×D3—21no—
41C3×C42×D3C2211yescharacteristic
42C3×#870C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#818C2211yescharacteristic
55C3×#817C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5680C2×C311yescharacteristic, complemented
64C4×#239C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#464—21no—
70C3×#464D311yescharacteristic, complemented
71C3×#464C2×C311yescharacteristic, complemented
72C3×#463—31no—
73C3×#452—31no—
74C3×#449—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#431—31no—
80#5187C2×C311yescharacteristic, complemented
81Dic3×Q16C2×C311yescharacteristic, complemented
82#5172C2×C311yescharacteristic
83Dic3×SD16C2×C311yescharacteristic, complemented
84#5057C2×C311yescharacteristic, complemented
85#5022C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4833C2×C311yescharacteristic, complemented
88#4815C2×C311yescharacteristic, complemented
89#4788C2×C311yescharacteristic, complemented
90#4784C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×#239—22no—
98C3×#239—22no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C32×Q16—22no—
108C32×SD16—22no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C42—21no—
116C32×C42C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#215—22no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#239C22×C311yescharacteristic
144C2×C3×Q16—21no—
145C2×C3×Q16C2×D311yescharacteristic
146C2×C3×Q16C22×C311yescharacteristic
147C2×C3×SD16—21no—
148C2×C3×SD16—31no—
149C2×C3×SD16C2×D311yescharacteristic
150C2×C3×SD16C22×C311yescharacteristic
151C2×C3×D8—31no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#124—21no—
155C3×#124C2×D311yescharacteristic
156C3×#124C22×C311yescharacteristic
157C3×#123—61no—
158C3×C22⋊Q8—31no—
159C3×#121—31no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8C2×D311yescharacteristic
164C3×C4×Q8C22×C311yescharacteristic
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—61no—
169C3×C4×D4—61no—
170C3×C4×D4—61no—
171C3×#117—31no—
172C3×#117—61no—
173C3×#117—61no—
174C2×C3×C42—31no—
175C2×C3×C42—61no—
176#946C22×C311yescharacteristic
177Q8×Dic3C22×C311yescharacteristic
178Q8×Dic3C22×C311yescharacteristic
179C2×#215C22×C311yescharacteristic
180#938C22×C311yescharacteristic
181D4×Dic3C22×C311yescharacteristic
182C2×#213C22×C311yescharacteristic
183#893—21no—
184#893C22×C311yescharacteristic
185#892—21no—
186#892C22×C311yescharacteristic
187#883—21no—
188#67⋊C4—21no—
189#879—21no—
190#877—21no—
191C4×D12—21no—
192C4×D12C22×C311yescharacteristic
193C42×D3—21no—
194C42×D3C22×C311yescharacteristic
195#870C22×C311yescharacteristic
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—21no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8C2×D311yescharacteristic
203C3×C4⋊C8C22×C311yescharacteristic
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic
209C3×#103C22×C311yescharacteristic
210C3×#102—21no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C22×C311yescharacteristic
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C4×C8—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228#818C22×C311yescharacteristic
229#817C22×C311yescharacteristic
230C8×Dic3C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C32×Q8#4112yes—
242C32×D4—21no—
243C32×D4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—42no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—42no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—24no—
259C3×D12—21no—
260C3×D12#4112yes—
261C3×C4×D3—24no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—22no—
265C3×C4×D3—41no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#529—31no—
273C4×#41—31no—
274#485—31no—
275#482—31no—
276#479—31no—
277#478—31no—
278#464C3×D311yescharacteristic, complemented
279#463—31no—
280#452—31no—
281#449—31no—
282C4×Q16—31no—
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8—31no—
286#431—31no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—21no—
290C2×C3×Q8—21no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×Q8C23×C311yescharacteristic
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C23×C311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C22×Dic3—21no—
310#239—22no—
311#239—22no—
312C2×D12—21no—
313C2×D12C23×C311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3C3×D411yescharacteristic
318C2×C4×D3C3×D411yescharacteristic
319C2×C4×D3C23×C311yescharacteristic
320C3×Q16—22no—
321C3×Q16—22no—
322C3×Q16—42no—
323C3×SD16—22no—
324C3×SD16—22no—
325C3×SD16—42no—
326C3×SD16—62no—
327C3×D8—62no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C23×C311yescharacteristic
335C2×C3×C8C23×C311yescharacteristic
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—41no—
369C3×C42—61no—
370C3×C42—61no—
371C3×C42—61no—
372C3×C42C22×D311yescharacteristic
373C3×C42C23×C311yescharacteristic
374#217—21no—
375#217—21no—
376#215—22no—
377#213—22no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3C23×C311yescharacteristic
385C4⋊Dic3C23×C311yescharacteristic
386C4⋊Dic3C23×C311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3C3×D411yescharacteristic
394C4×Dic3C3×D411yescharacteristic
395C4×Dic3C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397C2×C3⋊C8C23×C311yescharacteristic
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C2×C3×D3—21no—
403C2×C3×D3—22no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C32×C4—22no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—41no—
412C32×C4—41no—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3#13512yes—
421C2×#41—31no—
422C2×Q16C2×C3×D311yescharacteristic
423C2×SD16—31no—
424C2×SD16C2×C3×D311yescharacteristic
425C2×D8—31no—
426#126—61no—
427#125—31no—
428#124C2×C3×D311yescharacteristic
429#123—61no—
430C22⋊Q8—31no—
431#121—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×Q8C2×C3×D311yescharacteristic
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4—61no—
441#117—31no—
442#117—61no—
443#117—61no—
444C2×C42—31no—
445C2×C42—61no—
446#107—31no—
447#107—31no—
448#106—31no—
449#106—31no—
450C4⋊C8—31no—
451C4⋊C8C2×C3×D311yescharacteristic
452#103—31no—
453#103—31no—
454#103—31no—
455#103C2×C3×D311yescharacteristic
456#102—31no—
457#102—31no—
458#102—31no—
459#102C2×C3×D311yescharacteristic
460C22⋊C8—31no—
461C22⋊C8—31no—
462C4×C8—31no—
463C4×C8—31no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—31no—
467C23×C3—41no—
468C23×C3—61no—
469C22×D3—21no—
470C22×D3C2×C3×D411yescharacteristic
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8#23712yes—
482C3×Q8C3×#4112yes—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—32no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4—122no—
493C2×C3×C4—21no—
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—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—62no—
509C2×C3×C4—64no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—121no—
516C2×C3×C4—122no—
517C2×C3×C4—122no—
518C2×C3×C4—122no—
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C2×C3×D411yescharacteristic
522C2×C3×C4C2×C3×D411yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C24×C311yescharacteristic
525#67—42no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—42no—
530C2×Dic3C2×C3×D411yescharacteristic
531C2×Dic3C2×C3×D411yescharacteristic
532C2×Dic3C2×C3×D411yescharacteristic
533D12—24no—
534D12—21no—
535D12C3×#4112yes—
536C4×D3—24no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—22no—
540C4×D3—41no—
541C4×D3—42no—
542C4×D3—42no—
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—41no—
548C3×C8—41no—
549C3×C8—61no—
550C3×C8—61no—
551C3⋊C8—21no—
552C3⋊C8—21no—
553C2×C32—81no—
554C2×C32#52511yescharacteristic
555C2×C32C2×#13511yescharacteristic
556C2×C32#57511yescharacteristic
557C3×D3—41no—
558C3×D3—42no—
559#41—62no—
560#41—62no—
561C2×Q8C22×C3×D311yescharacteristic
562C2×Q8C22×C3×D311yescharacteristic
563C2×D4—31no—
564C2×D4—61no—
565C2×D4—61no—
566C2×D4C22×C3×D311yescharacteristic
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574Q16—22no—
575SD16—22no—
576SD16—62no—
577D8—62no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8C22×C3×D311yescharacteristic
581C2×C8C22×C3×D311yescharacteristic
582C4⋊C4—21no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4C22×C3×D311yescharacteristic
592C22⋊C4—21no—
593C22⋊C4—21no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C42—21no—
601C42—31no—
602C42—31no—
603C42—31no—
604C42—61no—
605C42—61no—
606C42—61no—
607C42C22×C3×D311yescharacteristic
608C22×C3—21no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—62no—
618C22×C3—61no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×C3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—22no—
630C2×D3—41no—
631C2×D3—41no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—32no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—42no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—81no—
651C3×C4—81no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4C2×#23711yescharacteristic
656C3×C4D3×#4111yescharacteristic
657C3×C4C2×C3×#4111yescharacteristic
658C3×C4C2×C3×#4111yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3C3×#13512yes—
665C32#310211yescharacteristic, complemented, Sylow
666C23—21no—
667C23—31no—
668C23—61no—
669Q8—21no—
670Q8—21no—
671Q8—21no—
672Q8C3×#23712yes—
673D4—21no—
674D4—21no—
675D4—32no—
676D4—64no—
677D4—61no—
678D4—122no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—62no—
686C2×C4—64no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—121no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4C3×D3×D411yescharacteristic
697C2×C4C3×D3×D411yescharacteristic
698C2×C4C23×C3×D311yescharacteristic
699C8—21no—
700C8—21no—
701C8—61no—
702C8—61no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—81no—
707C2×C3—81no—
708C2×C3—121no—
709C2×C3—122no—
710C2×C3—161no—
711C2×C3#560611yescharacteristic
712C2×C3D3×#13511yescharacteristic
713C2×C3#577711yescharacteristic
714C2×C3C3×#52511yescharacteristic
715C2×C3C2×C3×#13511yescharacteristic
716C2×C3C3×#57511yescharacteristic
717D3—41no—
718D3—42no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—61no—
723C22—61no—
724C22—62no—
725C22—61no—
726C22—121no—
727C22—121no—
728C22C2×C3×D3×D411yescharacteristic
729C4—21no—
730C4—21no—
731C4—22no—
732C4—32no—
733C4—41no—
734C4—41no—
735C4—61no—
736C4—61no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4C2×C3×#23711yescharacteristic
741C4C3×D3×#4111yescharacteristic
742C3—21no—
743C3#8056811yescharacteristic, direct product factor
744C3C3×#310211yescharacteristic, complemented
745C2—81no—
746C2—121no—
747C2—122no—
748C2C3×#560611yescharacteristic
749C2C3×D3×#13511yescharacteristic
750C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radicalC3×#5172C2
hypercenterC3×#464D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#464

Complements

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

NH ≅ G/Ntype
1. C3×#5680C2semidirect
2. C3×C4×#239C2semidirect
3. C32×#464C2semidirect
4. C3×#5187C2semidirect
5. C3×Dic3×Q16C2semidirect
7. C3×Dic3×SD16C2semidirect
8. C3×#5057C2semidirect
9. C3×#5022C2semidirect
10. C3×#4847C2semidirect
11. C3×#4833C2semidirect
12. C3×#4815C2semidirect
13. C3×#4788C2semidirect
14. C3×#4784C2semidirect
15. C3×#4756C2semidirect
17. #80568C3direct (N × H)
63. #5680C2×C3semidirect
64. C4×#239C2×C3semidirect
70. C3×#464D3semidirect
71. C3×#464C2×C3semidirect
80. #5187C2×C3semidirect
81. Dic3×Q16C2×C3semidirect
83. Dic3×SD16C2×C3semidirect
84. #5057C2×C3semidirect
85. #5022C2×C3semidirect
86. #4847C2×C3semidirect
87. #4833C2×C3semidirect
88. #4815C2×C3semidirect
89. #4788C2×C3semidirect
90. #4784C2×C3semidirect
91. #4756C2×C3semidirect
278. #464C3×D3semidirect
665. C32#3102semidirect
743. C3#80568direct (N × H)
744. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×#56802
C3×C4×#2392
C32×#4642
C3×#51872
C3×Dic3×Q162
C3×#51722
C3×Dic3×SD162
C3×#50572
C3×#50222
C3×#48472
C3×#48332
C3×#48152
C3×#47882
C3×#47842
C3×#47562
C3×#31023
#805683