Finite Group Databasebeta

← C3×#80517 #11895296

Subgroups — C3×#80517 #11895296

Order 1152.

786 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5681C211yesmaximal, characteristic, complemented
2C3×#5539C211yesmaximal, characteristic, complemented
3C32×#463C211yesmaximal, characteristic, complemented
4C3×#5165C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6C3×#5150C211yesmaximal, characteristic
7C3×Dic3×D8C211yesmaximal, characteristic, complemented
8C3×#5056C211yesmaximal, characteristic, complemented
9C3×C4×#213C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4830C211yesmaximal, characteristic, complemented
12C3×#4800C211yesmaximal, characteristic, complemented
13C3×#4793C211yesmaximal, characteristic, complemented
14C3×#4763C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic, complemented
16C3×#3361—31nomaximal
17#80517C311yesmaximal, characteristic, direct product factor
18C2×C32×SD16C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#940C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×#924—21no—
30C2×C3×Dic3⋊C4—21no—
31C3×#890C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#886—21no—
34C3×#885—21no—
35C3×#883—21no—
36C3×#67⋊C4—21no—
37C3×#878—21no—
38C3×#878—21no—
39C3×C4×D12C2211yescharacteristic
40C3×#870C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#559—31no—
62C3×#554—31no—
63#5681C2×C311yescharacteristic, complemented
64#5539C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#488—31no—
67C3×#486—31no—
68C3×#478—31no—
69C3×#478—31no—
70C3×#477—31no—
71C3×#463—21no—
72C3×#463—31no—
73C3×#463D311yescharacteristic, complemented
74C3×#463C2×C311yescharacteristic, complemented
75C3×#459—31no—
76C3×C8×Q8—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×C4×D8—31no—
80#5165C2×C311yescharacteristic, complemented
81Dic3×SD16C2×C311yescharacteristic, complemented
82#5150C2×C311yescharacteristic
83Dic3×D8C2×C311yescharacteristic, complemented
84#5056C2×C311yescharacteristic, complemented
85C4×#213C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4830C2×C311yescharacteristic, complemented
88#4800C2×C311yescharacteristic, complemented
89#4793C2×C311yescharacteristic, complemented
90#4763C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6D411yescharacteristic
105C32×SD16—22no—
106C32×D8—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#213—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3361—31noSylow
139C2×C3×SD16—21no—
140C2×C3×SD16C2×D311yescharacteristic
141C2×C3×SD16C22×C311yescharacteristic
142C2×C3×D8—21no—
143C2×C3×D8—31no—
144C2×C3×D8C2×D311yescharacteristic
145C2×C3×D8C22×C311yescharacteristic
146C3×C4⋊Q8—31no—
147C3×#127—31no—
148C3×#125—31no—
149C3×#125—31no—
150C3×#124—21no—
151C3×#124—31no—
152C3×#124—61no—
153C3×#124C2×D311yescharacteristic
154C3×#124C22×C311yescharacteristic
155C3×#123—61no—
156C3×#123—61no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×D4—21no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—61no—
168C3×C4×D4C2×D311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic
170C2×C3×C4⋊C4—61no—
171#947C22×C311yescharacteristic
172Q8×Dic3C22×C311yescharacteristic
173#940C22×C311yescharacteristic
174D4×Dic3C22×C311yescharacteristic
175D4×Dic3C22×C311yescharacteristic
176D4×Dic3C22×C311yescharacteristic
177C2×#213C22×C311yescharacteristic
178#924—21no—
179C2×Dic3⋊C4—21no—
180#890C22×C311yescharacteristic
181#888C22×C311yescharacteristic
182#886—21no—
183#885—21no—
184#883—21no—
185#67⋊C4—21no—
186#878—21no—
187#878—21no—
188C4×D12C22×C311yescharacteristic
189#870C22×C311yescharacteristic
190C4×Dic6C22×C311yescharacteristic
191C3×#107—31no—
192C3×#107—31no—
193C3×#106—31no—
194C3×C4⋊C8—21no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8C2×D311yescharacteristic
198C3×C4⋊C8C22×C311yescharacteristic
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C22×C311yescharacteristic
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×C4×C8—31no—
214C3×C4×C8—31no—
215C3×C4×C8—31no—
216#835C22×C311yescharacteristic
217#835C22×C311yescharacteristic
218#832C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#821C22×C311yescharacteristic
223#818C22×C311yescharacteristic
224#817C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228C8×Dic3C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231C4×C3⋊C8C22×C311yescharacteristic
232C23×C32—21no—
233C23×C32—21no—
234C22×C3×D3—21no—
235C32×Q8—21no—
236C32×Q8—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—81no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C3×#67—42no—
248C3×#67—81no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—42no—
253C2×C3×Dic3—81no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×C4×D3—81no—
262C3×Dic6—22no—
263C3×Dic6—81no—
264C32×C8—21no—
265C32×C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#559—31no—
269#554—31no—
270#488—31no—
271#488—31no—
272#486—31no—
273#478—31no—
274#478—31no—
275#477—31no—
276#463—31no—
277#463C3×D311yescharacteristic, complemented
278#459—31no—
279C8×Q8—31no—
280C4×SD16—31no—
281C4×D8—31no—
282C4×D8—31no—
283C2×C3×Q8—21no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C23×C311yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—31no—
291C2×C3×D4—61no—
292C2×C3×D4—61no—
293C2×C3×D4C22×D311yescharacteristic
294C2×C3×D4C22×D311yescharacteristic
295C2×C3×D4C23×C311yescharacteristic
296C2×C3×D4C23×C311yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—41no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C2×D12C23×C311yescharacteristic
310C2×C4×D3—21no—
311C2×Dic6—21no—
312C2×Dic6C3×D411yescharacteristic
313C3×SD16—22no—
314C3×SD16—22no—
315C3×SD16—42no—
316C3×D8—22no—
317C3×D8—22no—
318C3×D8—42no—
319C3×D8—62no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C22×D311yescharacteristic
326C2×C3×C8C23×C311yescharacteristic
327C2×C3×C8C23×C311yescharacteristic
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C23×C311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—41no—
351C3×C22⋊C4—41no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—21no—
359C3×C42—31no—
360C3×C42—31no—
361C3×C42—61no—
362C3×C42C22×D311yescharacteristic
363C3×C42C23×C311yescharacteristic
364#217—21no—
365#217—21no—
366#217—21no—
367#213—22no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3C3×D411yescharacteristic
374C4⋊Dic3C23×C311yescharacteristic
375C4⋊Dic3C23×C311yescharacteristic
376C4⋊Dic3C23×C311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4C3×D411yescharacteristic
382Dic3⋊C4C3×D411yescharacteristic
383C4×Dic3—21no—
384C4×Dic3C23×C311yescharacteristic
385C4×Dic3C23×C311yescharacteristic
386C2×C3⋊C8C23×C311yescharacteristic
387C2×C3⋊C8C23×C311yescharacteristic
388C22×C32—22no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32C22×D411yescharacteristic
395C2×C3×D3—41no—
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C32×C4—21no—
399C32×C4—21no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4C2×#4111yescharacteristic
403C32×C42−1+411yescharacteristic
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3#13512yes—
411C2×SD16C2×C3×D311yescharacteristic
412C2×D8—31no—
413C2×D8C2×C3×D311yescharacteristic
414C4⋊Q8—31no—
415#127—31no—
416#125—31no—
417#125—31no—
418#124—31no—
419#124—61no—
420#124C2×C3×D311yescharacteristic
421#123—61no—
422#123—61no—
423C22⋊Q8—61no—
424C22⋊Q8—61no—
425C22⋊Q8—61no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×D4—31no—
429C4×D4—31no—
430C4×D4—31no—
431C4×D4—31no—
432C4×D4—61no—
433C4×D4C2×C3×D311yescharacteristic
434C2×C4⋊C4—61no—
435#107—31no—
436#107—31no—
437#106—31no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440C4⋊C8C2×C3×D311yescharacteristic
441#103—31no—
442#103—31no—
443#103C2×C3×D311yescharacteristic
444#102—31no—
445#102—31no—
446#102—31no—
447#102—31no—
448#102—31no—
449#102—31no—
450#102C2×C3×D311yescharacteristic
451C4×C8—31no—
452C4×C8—31no—
453C4×C8—31no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—61no—
461C22×D3—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—62no—
469C3×Q8—241no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—21no—
473C3×D4—21no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—22no—
477C3×D4—41no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4—122no—
483C3×D4—241no—
484C3×D4#23712yes—
485C3×D4C3×#4112yes—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—81no—
503C2×C3×C4—81no—
504C2×C3×C4—82no—
505C2×C3×C4—122no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C2×C3×D411yescharacteristic
512C2×C3×C4C2×C3×D411yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C24×C311yescharacteristic
515#67—42no—
516#67—81no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—42no—
521C2×Dic3—81no—
522C2×Dic3—81no—
523C2×Dic3C2×C3×D411yescharacteristic
524C2×Dic3C2×C3×D411yescharacteristic
525C2×Dic3C2×C3×D411yescharacteristic
526C2×Dic3C2×C3×D411yescharacteristic
527D12—21no—
528D12—21no—
529C4×D3—81no—
530Dic6—22no—
531Dic6—81no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—21no—
535C3×C8—21no—
536C3×C8—41no—
537C3×C8—41no—
538C3×C8—61no—
539C3×C8—61no—
540C3⋊C8—21no—
541C3⋊C8—21no—
542C2×C32—42no—
543C2×C32—81no—
544C2×C32#54811yescharacteristic
545C2×C32C2×#13511yescharacteristic
546C2×C32#57611yescharacteristic
547C3×D3—81no—
548C2×Q8—31no—
549C2×Q8—61no—
550C2×Q8C22×C3×D311yescharacteristic
551C2×D4—31no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4C22×C3×D311yescharacteristic
555C2×D4C22×C3×D311yescharacteristic
556C22×C4—21no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561SD16—22no—
562D8—22no—
563D8—62no—
564C2×C8—31no—
565C2×C8—31no—
566C2×C8C22×C3×D311yescharacteristic
567C2×C8C22×C3×D311yescharacteristic
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4C22×C3×D311yescharacteristic
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C22⋊C4—61no—
588C22⋊C4—61no—
589C22⋊C4—61no—
590C42—31no—
591C42—31no—
592C42—61no—
593C42C22×C3×D311yescharacteristic
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—21no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3C2×D3×D411yescharacteristic
617C22×C3C22×C3×D411yescharacteristic
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—32no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—81no—
638C3×C4—81no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4C2×#23711yescharacteristic
643C3×C4#101011yescharacteristic
644C3×C4C2×C3×#4111yescharacteristic
645C3×C4C3×2−1+411yescharacteristic
646Dic3—21no—
647Dic3—21no—
648Dic3—21no—
649Dic3—41no—
650Dic3—41no—
651Dic3—41no—
652Dic3C3×#13512yes—
653C32#336111yescharacteristic, complemented, Sylow
654C23—21no—
655C23—21no—
656C23—61no—
657Q8—21no—
658Q8—21no—
659Q8—62no—
660Q8—241no—
661D4—21no—
662D4—21no—
663D4—21no—
664D4—61no—
665D4—61no—
666D4—122no—
667D4—241no—
668D4C3×#23712yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—31no—
674C2×C4—31no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—81no—
679C2×C4—122no—
680C2×C4—241no—
681C2×C4—241no—
682C2×C4—241no—
683C2×C4C3×D3×D411yescharacteristic
684C2×C4C3×D3×D411yescharacteristic
685C2×C4C23×C3×D311yescharacteristic
686C8—21no—
687C8—21no—
688C8—61no—
689C8—61no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—42no—
694C2×C3—42no—
695C2×C3—82no—
696C2×C3—81no—
697C2×C3—81no—
698C2×C3—161no—
699C2×C3—241no—
700C2×C3#559811yescharacteristic
701C2×C3D3×#13511yescharacteristic
702C2×C3#577411yescharacteristic
703C2×C3C3×#54811yescharacteristic
704C2×C3C2×C3×#13511yescharacteristic
705C2×C3C3×#57611yescharacteristic
706D3—81no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22C2×C3×D3×D411yescharacteristic
717C4—21no—
718C4—21no—
719C4—32no—
720C4—41no—
721C4—41no—
722C4—61no—
723C4—61no—
724C4—61no—
725C4—121no—
726C4—121no—
727C4—121no—
728C4C2×C3×#23711yescharacteristic
729C4C3×#101011yescharacteristic
730C3—21no—
731C3#8051711yescharacteristic, direct product factor
732C3C3×#336111yescharacteristic, complemented
733C2—42no—
734C2—81no—
735C2—241no—
736C2C3×#559811yescharacteristic
737C2C3×D3×#13511yescharacteristic
738C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
prime radicalC3×#5150C2
hypercenterC3×#463D3
hypocenterC3C3×#3361
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C3×#5681C2semidirect
2. C3×#5539C2semidirect
3. C32×#463C2semidirect
4. C3×#5165C2semidirect
5. C3×Dic3×SD16C2semidirect
7. C3×Dic3×D8C2semidirect
8. C3×#5056C2semidirect
9. C3×C4×#213C2semidirect
10. C3×#4847C2semidirect
11. C3×#4830C2semidirect
12. C3×#4800C2semidirect
13. C3×#4793C2semidirect
14. C3×#4763C2semidirect
15. C3×#4760C2semidirect
17. #80517C3direct (N × H)
63. #5681C2×C3semidirect
64. #5539C2×C3semidirect
73. C3×#463D3semidirect
74. C3×#463C2×C3semidirect
80. #5165C2×C3semidirect
81. Dic3×SD16C2×C3semidirect
83. Dic3×D8C2×C3semidirect
84. #5056C2×C3semidirect
85. C4×#213C2×C3semidirect
86. #4847C2×C3semidirect
87. #4830C2×C3semidirect
88. #4800C2×C3semidirect
89. #4793C2×C3semidirect
90. #4763C2×C3semidirect
91. #4760C2×C3semidirect
277. #463C3×D3semidirect
653. C32#3361semidirect
731. C3#80517direct (N × H)
732. C3C3×#3361semidirect

Maximal subgroups

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

subgroupindex
C3×#56812
C3×#55392
C32×#4632
C3×#51652
C3×Dic3×SD162
C3×#51502
C3×Dic3×D82
C3×#50562
C3×C4×#2132
C3×#48472
C3×#48302
C3×#48002
C3×#47932
C3×#47632
C3×#47602
C3×#33613
#805173