Finite Group Databasebeta

← C3×#80573 #11872561

Subgroups — C3×#80573 #11872561

Order 1152.

796 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5682C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic, complemented
3C32×#464C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic, complemented
5C3×Dic3×Q16C211yesmaximal, characteristic, complemented
6C3×#5170C211yesmaximal, characteristic
7C3×#5164C211yesmaximal, characteristic, complemented
8C3×#5054C211yesmaximal, characteristic, complemented
9C3×#5020C211yesmaximal, characteristic, complemented
10C3×#4850C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4814C211yesmaximal, characteristic, complemented
13C3×#4789C211yesmaximal, characteristic, complemented
14C3×#4784C211yesmaximal, characteristic
15C3×#4758C211yesmaximal, characteristic, complemented
16C3×#3121—31nomaximal
17#80573C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×#892—21no—
31C3×#892C2211yescharacteristic
32C3×#887—21no—
33C3×#887C2211yescharacteristic
34C3×#886—21no—
35C3×#885—21no—
36C3×#879—21no—
37C3×#878—21no—
38C3×#872—21no—
39C3×#872C2211yescharacteristic
40C3×#869C2211yescharacteristic
41C3×C4×Dic6—21no—
42C3×C4×Dic6C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#815C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#542—31no—
62C3×#519—31no—
63#5682C2×C311yescharacteristic
64#5572C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#477—31no—
68C3×#475—31no—
69C3×#464—21no—
70C3×#464—31no—
71C3×#464D311yescharacteristic, complemented
72C3×#464C2×C311yescharacteristic, complemented
73C3×#451—31no—
74C3×#448—31no—
75C3×#441—31no—
76C3×#440—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5186C2×C311yescharacteristic, complemented
81Dic3×Q16C2×C311yescharacteristic, complemented
82#5170C2×C311yescharacteristic
83#5164C2×C311yescharacteristic, complemented
84#5054C2×C311yescharacteristic, complemented
85#5020C2×C311yescharacteristic, complemented
86#4850C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4814C2×C311yescharacteristic, complemented
89#4789C2×C311yescharacteristic, complemented
90#4784C2×C311yescharacteristic
91#4758C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8—22no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C32×Q16—22no—
105C32×SD16—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#216—22no—
117C3×#214—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3121—31noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C22×C311yescharacteristic
144C2×C3×Q16—21no—
145C2×C3×Q16—31no—
146C2×C3×Q16C2×D311yescharacteristic
147C2×C3×Q16C22×C311yescharacteristic
148C2×C3×SD16—21no—
149C2×C3×SD16—31no—
150C2×C3×SD16C2×D311yescharacteristic
151C2×C3×SD16C22×C311yescharacteristic
152C3×C4⋊Q8—31no—
153C3×#126—61no—
154C3×#124—21no—
155C3×#124—61no—
156C3×#124C2×D311yescharacteristic
157C3×#124C22×C311yescharacteristic
158C3×#123—61no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—61no—
161C3×#121—31no—
162C3×C4×Q8—21no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—31no—
167C3×C4×Q8—61no—
168C3×C4×Q8—61no—
169C3×C4×Q8C2×D311yescharacteristic
170C3×C4×Q8C22×C311yescharacteristic
171C3×C4×D4—31no—
172C3×#117—31no—
173C3×#117—31no—
174C3×#117—61no—
175C3×#117—61no—
176#946C22×C311yescharacteristic
177Q8×Dic3C22×C311yescharacteristic
178Q8×Dic3C22×C311yescharacteristic
179C2×#216C22×C311yescharacteristic
180#938C22×C311yescharacteristic
181D4×Dic3C22×C311yescharacteristic
182C2×#214C22×C311yescharacteristic
183#892—21no—
184#892C22×C311yescharacteristic
185#887—21no—
186#887C22×C311yescharacteristic
187#886—21no—
188#885—21no—
189#879—21no—
190#878—21no—
191#872—21no—
192#872C22×C311yescharacteristic
193#869C22×C311yescharacteristic
194C4×Dic6—21no—
195C4×Dic6C22×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×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C22×C311yescharacteristic
212C3×#102—21no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C22×C311yescharacteristic
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×#97—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#818C22×C311yescharacteristic
227#818C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#815C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C23×C32—21no—
236C22×C3×D3C2×D411yescharacteristic
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8#4112yes—
241C32×D4—21no—
242C32×D4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C3×#67—81no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×C4×D3—24no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×Dic6—24no—
262C3×Dic6—21no—
263C3×Dic6—81no—
264C3×Dic6#4112yes—
265C32×C8—21no—
266C32×C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—31no—
270#519—31no—
271#485—31no—
272#482—31no—
273#477—31no—
274#475—31no—
275#464—31no—
276#464C3×D311yescharacteristic, complemented
277#451—31no—
278#448—31no—
279#441—31no—
280#440—31no—
281C4×Q16—31no—
282C4×SD16—31no—
283#433—31no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—31no—
287C2×C3×Q8—61no—
288C2×C3×Q8—62no—
289C2×C3×Q8—62no—
290C2×C3×Q8—61no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×Q8C23×C311yescharacteristic
295C2×C3×D4—21no—
296C2×C3×D4—61no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C23×C311yescharacteristic
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—21no—
303C22×Dic3—21no—
304D3×Q8—22no—
305D3×Q8—22no—
306C2×C4×D3—21no—
307C2×C4×D3C23×C311yescharacteristic
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6C23×C311yescharacteristic
311C3×Q16—22no—
312C3×Q16—22no—
313C3×Q16—42no—
314C3×Q16—62no—
315C3×SD16—22no—
316C3×SD16—22no—
317C3×SD16—42no—
318C3×SD16—62no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C2×C3×C8C22×D311yescharacteristic
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C23×C311yescharacteristic
326C2×C3×C8C23×C311yescharacteristic
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
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×C42—21no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—31no—
360C3×C42—41no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42—61no—
365C3×C42—61no—
366C3×C42C22×D311yescharacteristic
367C3×C42C23×C311yescharacteristic
368#217—21no—
369#217—21no—
370#216—22no—
371#214—22no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4C3×D411yescharacteristic
375(C2×D3)⋊C4C3×D411yescharacteristic
376C4⋊Dic3—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3C23×C311yescharacteristic
380C4⋊Dic3C23×C311yescharacteristic
381C4⋊Dic3C23×C311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4C3×D411yescharacteristic
386Dic3⋊C4C3×D411yescharacteristic
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3C23×C311yescharacteristic
393C2×C3⋊C8C23×C311yescharacteristic
394C2×C3⋊C8C23×C311yescharacteristic
395C22×C32—41no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32C22×D411yescharacteristic
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C32×C4—22no—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4C2×#4111yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3×Dic3—21no—
410C3×Dic3—22no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C22×Q8—31no—
417C2×Q16—31no—
418C2×Q16C2×C3×D311yescharacteristic
419C2×SD16—31no—
420C2×SD16C2×C3×D311yescharacteristic
421C4⋊Q8—31no—
422#126—61no—
423#124—61no—
424#124C2×C3×D311yescharacteristic
425#123—61no—
426C22⋊Q8—31no—
427C22⋊Q8—61no—
428#121—31no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—61no—
434C4×Q8—61no—
435C4×Q8C2×C3×D311yescharacteristic
436C4×D4—31no—
437#117—31no—
438#117—31no—
439#117—61no—
440#117—61no—
441#107—31no—
442#107—31no—
443#106—31no—
444#106—31no—
445C4⋊C8—31no—
446C4⋊C8C2×C3×D311yescharacteristic
447#103—31no—
448#103—31no—
449#103—31no—
450#103—31no—
451#103—31no—
452#103C2×C3×D311yescharacteristic
453#102—31no—
454#102C2×C3×D311yescharacteristic
455C22⋊C8—31no—
456C22⋊C8—31no—
457#97—31no—
458C4×C8—31no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—31no—
462C23×C3—41no—
463C22×D3C2×C3×D411yescharacteristic
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—22no—
471C3×Q8—32no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—64no—
476C3×Q8—61no—
477C3×Q8—241no—
478C3×Q8#23712yes—
479C3×Q8C3×#4112yes—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—241no—
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—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—64no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—241no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×C3×D411yescharacteristic
513C2×C3×C4C2×C3×D411yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C24×C311yescharacteristic
516#67—81no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—81no—
522C2×Dic3C2×C3×D411yescharacteristic
523C2×Dic3C2×C3×D411yescharacteristic
524C2×Dic3C2×C3×D411yescharacteristic
525C4×D3—24no—
526C4×D3—21no—
527C4×D3—21no—
528Dic6—24no—
529Dic6—21no—
530Dic6—81no—
531Dic6C3×#4112yes—
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—81no—
543C2×C32#52511yescharacteristic
544C2×C32#57711yescharacteristic
545C2×C32#57811yescharacteristic
546C3×D3—41no—
547C2×Q8—31no—
548C2×Q8—61no—
549C2×Q8—62no—
550C2×Q8—62no—
551C2×Q8—61no—
552C2×Q8C22×C3×D311yescharacteristic
553C2×Q8C22×C3×D311yescharacteristic
554C2×D4—61no—
555C2×D4C22×C3×D311yescharacteristic
556C22×C4—31no—
557C22×C4—61no—
558C22×C4—61no—
559Q16—22no—
560Q16—62no—
561SD16—22no—
562SD16—62no—
563C2×C8—31no—
564C2×C8—31no—
565C2×C8C22×C3×D311yescharacteristic
566C2×C8C22×C3×D311yescharacteristic
567C4⋊C4—21no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4C22×C3×D311yescharacteristic
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C22⋊C4—61no—
588C42—21no—
589C42—31no—
590C42—61no—
591C42—61no—
592C42—61no—
593C42—61no—
594C42—61no—
595C42C22×C3×D311yescharacteristic
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3C2×D3×D411yescharacteristic
610C22×C3C22×C3×D411yescharacteristic
611C2×D3—21no—
612C2×D3—21no—
613C2×D3—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—61no—
632C3×C4—62no—
633C3×C4—81no—
634C3×C4—81no—
635C3×C4—121no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4C2×#23711yescharacteristic
639C3×C4D3×#4111yescharacteristic
640C3×C4C2×C3×#4111yescharacteristic
641C3×C4C2×C3×#4111yescharacteristic
642Dic3—21no—
643Dic3—21no—
644Dic3—21no—
645Dic3—22no—
646Dic3—41no—
647Dic3—41no—
648Dic3—41no—
649C32#312111yescharacteristic, complemented, Sylow
650C23—21no—
651C23—31no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8—32no—
656Q8—64no—
657Q8—61no—
658Q8—241no—
659Q8C3×#23712yes—
660D4—21no—
661D4—21no—
662D4—241no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—64no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—241no—
677C2×C4C3×D3×D411yescharacteristic
678C2×C4C3×D3×D411yescharacteristic
679C2×C4C23×C3×D311yescharacteristic
680C8—21no—
681C8—21no—
682C8—61no—
683C8—61no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—81no—
688C2×C3—81no—
689C2×C3—121no—
690C2×C3—161no—
691C2×C3#560611yescharacteristic
692C2×C3#577111yescharacteristic
693C2×C3#577811yescharacteristic
694C2×C3C3×#52511yescharacteristic
695C2×C3C3×#57711yescharacteristic
696C2×C3C3×#57811yescharacteristic
697D3—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—61no—
702C22—61no—
703C22—61no—
704C22C2×C3×D3×D411yescharacteristic
705C4—21no—
706C4—21no—
707C4—22no—
708C4—41no—
709C4—41no—
710C4—61no—
711C4—61no—
712C4—61no—
713C4—62no—
714C4—121no—
715C4—121no—
716C4—121no—
717C4C2×C3×#23711yescharacteristic
718C4C3×D3×#4111yescharacteristic
719C3—21no—
720C3#8057311yescharacteristic, direct product factor
721C3C3×#312111yescharacteristic, complemented
722C2—81no—
723C2—121no—
724C2C3×#560611yescharacteristic
725C2C3×#577111yescharacteristic
726C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radicalC3×#938C22
hypercenterC3×#464D3
hypocenterC3C3×#3121
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
2. C3×#5572C2semidirect
3. C32×#464C2semidirect
4. C3×#5186C2semidirect
5. C3×Dic3×Q16C2semidirect
7. C3×#5164C2semidirect
8. C3×#5054C2semidirect
9. C3×#5020C2semidirect
10. C3×#4850C2semidirect
11. C3×#4840C2semidirect
12. C3×#4814C2semidirect
13. C3×#4789C2semidirect
15. C3×#4758C2semidirect
17. #80573C3direct (N × H)
64. #5572C2×C3semidirect
71. C3×#464D3semidirect
72. C3×#464C2×C3semidirect
80. #5186C2×C3semidirect
81. Dic3×Q16C2×C3semidirect
83. #5164C2×C3semidirect
84. #5054C2×C3semidirect
85. #5020C2×C3semidirect
86. #4850C2×C3semidirect
87. #4840C2×C3semidirect
88. #4814C2×C3semidirect
89. #4789C2×C3semidirect
91. #4758C2×C3semidirect
276. #464C3×D3semidirect
649. C32#3121semidirect
720. C3#80573direct (N × H)
721. C3C3×#3121semidirect

Maximal subgroups

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

subgroupindex
C3×#56822
C3×#55722
C32×#4642
C3×#51862
C3×Dic3×Q162
C3×#51702
C3×#51642
C3×#50542
C3×#50202
C3×#48502
C3×#48402
C3×#48142
C3×#47892
C3×#47842
C3×#47582
C3×#31213
#805733