Finite Group Databasebeta

← C3×#81497 #11872573

Subgroups — C3×#81497 #11872573

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5643C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C32×#485C211yesmaximal, characteristic, complemented
4C3×#5050C211yesmaximal, characteristic, complemented
5C3×#5003C211yesmaximal, characteristic
6C3×#4889C211yesmaximal, characteristic, complemented
7C3×#4875C211yesmaximal, characteristic, complemented
8C3×#4854C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4798C211yesmaximal, characteristic, complemented
11C3×#4798C211yesmaximal, characteristic, complemented
12C3×#4790C211yesmaximal, characteristic, complemented
13C3×#4789C211yesmaximal, characteristic, complemented
14C3×#4738C211yesmaximal, characteristic
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3121—31nomaximal
17#81497C311yesmaximal, characteristic, direct product factor
18C22×C3×Dic6C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C3×#947C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C3×#898—21no—
30C3×#897—21no—
31C3×#893C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#887C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#887C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#885—21no—
38C3×#883—21no—
39C3×#877—21no—
40C3×#877—21no—
41C3×C4×Dic6—21no—
42C3×C4×Dic6—21no—
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#542—31no—
62C3×#519—31no—
63#5643C2×C311yescharacteristic
64#5516C2×C311yescharacteristic, complemented
65C3×#485—21no—
66C3×#485D311yescharacteristic, complemented
67C3×#485C2×C311yescharacteristic, complemented
68C3×#482—31no—
69C3×#477—31no—
70C3×#475—31no—
71C3×#464—31no—
72C3×#464—31no—
73C3×#451—31no—
74C3×#448—31no—
75C3×#441—31no—
76C3×#440—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5050C2×C311yescharacteristic, complemented
81#5003C2×C311yescharacteristic
82#4889C2×C311yescharacteristic, complemented
83#4875C2×C311yescharacteristic, complemented
84#4854C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4798C2×C311yescharacteristic, complemented
87#4798C2×C311yescharacteristic, complemented
88#4790C2×C311yescharacteristic, complemented
89#4789C2×C311yescharacteristic, complemented
90#4738C2×C311yescharacteristic
91#4720C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C22×C3×Dic3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—22no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C42—21no—
113C3×#217D411yescharacteristic
114C3×#217D411yescharacteristic
115C3×#216—22no—
116C3×#216—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×#204—22no—
141#3121—31noSylow
142C22×C3×Q8—31no—
143C22×Dic6C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C3×C4⋊Q8—31no—
149C3×#126—61no—
150C3×#124—31no—
151C3×#124—61no—
152C3×#123—61no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C22×C311yescharacteristic
157C3×#121—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—61no—
164C3×C4×Q8—61no—
165C3×C4×D4—31no—
166C3×#117—21no—
167C3×#117—31no—
168C3×#117—61no—
169C3×#117—61no—
170C3×#117C2×D311yescharacteristic
171C3×#117C22×C311yescharacteristic
172#947C22×C311yescharacteristic
173Q8×Dic3C22×C311yescharacteristic
174C2×#216C22×C311yescharacteristic
175C2×#216C22×C311yescharacteristic
176#930C22×C311yescharacteristic
177#926C22×C311yescharacteristic
178C2×#204C22×C311yescharacteristic
179C2×#204C22×C311yescharacteristic
180#898—21no—
181#897—21no—
182#893C22×C311yescharacteristic
183#888C22×C311yescharacteristic
184#887C22×C311yescharacteristic
185#887C22×C311yescharacteristic
186#887C22×C311yescharacteristic
187#887C22×C311yescharacteristic
188#885—21no—
189#883—21no—
190#877—21no—
191#877—21no—
192C4×Dic6—21no—
193C4×Dic6—21no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic
197C3×#107C22×C311yescharacteristic
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic
201C3×#106C22×C311yescharacteristic
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#103C22×C311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—21no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C22×C311yescharacteristic
220C3×#97—31no—
221C3×C4×C8—31no—
222#830C22×C311yescharacteristic
223#816C22×C311yescharacteristic
224#816C22×C311yescharacteristic
225#815C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227Dic3⋊C8C22×C311yescharacteristic
228C8×Dic3C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#809C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C3×#67—81no—
248C2×C3×Dic3—24no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×C4×D3—81no—
259C3×Dic6—24no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—81no—
263C3×Dic6#4112yes—
264C3×Dic6#4112yes—
265C32×C8—21no—
266C32×C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—31no—
270#519—31no—
271#485C3×D311yescharacteristic, complemented
272#482—31no—
273#477—31no—
274#475—31no—
275#464—31no—
276#464—31no—
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—31no—
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×Q8C23×C311yescharacteristic
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C22×C3×C4—21no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C23×C311yescharacteristic
300C2×#67—21no—
301C22×Dic3—21no—
302C2×D12C23×C311yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6—21no—
305C2×Dic6—22no—
306C2×Dic6—22no—
307C2×Dic6—21no—
308C2×Dic6C23×C311yescharacteristic
309C2×Dic6C23×C311yescharacteristic
310C3×Q16—62no—
311C3×Q16—62no—
312C3×SD16—62no—
313C3×SD16—62no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C23×C311yescharacteristic
321C2×C3×C8C23×C311yescharacteristic
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—41no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C23×C311yescharacteristic
341C3×C4⋊C4C23×C311yescharacteristic
342C3×C4⋊C4C23×C311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—41no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—21no—
356C3×C42—21no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—41no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42—61no—
365#217C3×D411yescharacteristic
366#217C3×D411yescharacteristic
367#216—22no—
368#216—22no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373C4⋊Dic3—21no—
374C4⋊Dic3C3×D411yescharacteristic
375C4⋊Dic3C3×D411yescharacteristic
376C4⋊Dic3C23×C311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3C23×C311yescharacteristic
388C4×Dic3C23×C311yescharacteristic
389C2×C3⋊C8C23×C311yescharacteristic
390C2×C3⋊C8C23×C311yescharacteristic
391#204—22no—
392#204—22no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32C22×D411yescharacteristic
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C32×C4—21no—
401C32×C4—41no—
402C32×C4—41no—
403C32×C4—41no—
404C32×C4—41no—
405C32×C4C2×#4111yescharacteristic
406C32×C4C2×#4111yescharacteristic
407C3×Dic3—22no—
408C3×Dic3—22no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C22×Q8—31no—
415C2×Q16—31no—
416C2×Q16—31no—
417C2×SD16—31no—
418C2×SD16—31no—
419C4⋊Q8—31no—
420#126—61no—
421#124—31no—
422#124—61no—
423#123—61no—
424C22⋊Q8—61no—
425C22⋊Q8C2×C3×D311yescharacteristic
426#121—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—61no—
433C4×Q8—61no—
434C4×D4—31no—
435#117—31no—
436#117—61no—
437#117—61no—
438#117C2×C3×D311yescharacteristic
439#107—31no—
440#107C2×C3×D311yescharacteristic
441#106—31no—
442#106C2×C3×D311yescharacteristic
443C4⋊C8—31no—
444C4⋊C8—31no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103C2×C3×D311yescharacteristic
450#103C2×C3×D311yescharacteristic
451#102—31no—
452#102—31no—
453C22⋊C8—31no—
454C22⋊C8C2×C3×D311yescharacteristic
455#97—31no—
456C4×C8—31no—
457C23×C3—21no—
458C23×C3—61no—
459C23×C3D3×D411yescharacteristic
460C23×C3C2×C3×D411yescharacteristic
461C22×D3—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—32no—
467C3×Q8—32no—
468C3×Q8—41no—
469C3×Q8—41no—
470C3×Q8—64no—
471C3×Q8—61no—
472C3×Q8—61no—
473C3×Q8—241no—
474C3×D4—61no—
475C3×D4—61no—
476C3×D4—241no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—64no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—241no—
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C2×C3×D411yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C24×C311yescharacteristic
510#67—81no—
511C2×Dic3—24no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3C2×C3×D411yescharacteristic
516C2×Dic3C2×C3×D411yescharacteristic
517C2×Dic3C2×C3×D411yescharacteristic
518C2×Dic3C2×C3×D411yescharacteristic
519D12—21no—
520D12—21no—
521C4×D3—81no—
522Dic6—24no—
523Dic6—21no—
524Dic6—21no—
525Dic6—81no—
526Dic6C3×#4112yes—
527Dic6C3×#4112yes—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—21no—
532C3×C8—41no—
533C3×C8—41no—
534C3×C8—61no—
535C3×C8—61no—
536C3⋊C8—21no—
537C3⋊C8—21no—
538C2×C32—41no—
539C2×C32#52511yescharacteristic
540C2×C32#57711yescharacteristic
541C2×C32#57811yescharacteristic
542C3×D3—81no—
543C2×Q8—31no—
544C2×Q8—31no—
545C2×Q8—61no—
546C2×Q8—62no—
547C2×Q8—62no—
548C2×Q8—61no—
549C2×Q8C22×C3×D311yescharacteristic
550C2×D4—31no—
551C2×D4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4C22×C3×D311yescharacteristic
555Q16—62no—
556Q16—62no—
557SD16—62no—
558SD16—62no—
559C2×C8—31no—
560C2×C8—31no—
561C2×C8C22×C3×D311yescharacteristic
562C2×C8C22×C3×D311yescharacteristic
563C4⋊C4—21no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4C22×C3×D311yescharacteristic
574C4⋊C4C22×C3×D311yescharacteristic
575C4⋊C4C22×C3×D311yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—31no—
579C22⋊C4—31no—
580C22⋊C4—61no—
581C22⋊C4—61no—
582C22⋊C4—61no—
583C22⋊C4—61no—
584C42—21no—
585C42—31no—
586C42—31no—
587C42—61no—
588C42—61no—
589C42—61no—
590C42—61no—
591C42—61no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3C2×D3×D411yescharacteristic
606C22×C3C22×C3×D411yescharacteristic
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—61no—
626C3×C4—61no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4—81no—
633C3×C4—121no—
634C3×C4D3×#4111yescharacteristic
635C3×C4D3×#4111yescharacteristic
636C3×C4C2×C3×#4111yescharacteristic
637C3×C4C2×C3×#4111yescharacteristic
638Dic3—21no—
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642Dic3—22no—
643Dic3—22no—
644Dic3—41no—
645C32#312111yescharacteristic, complemented, Sylow
646C23—61no—
647C23C3×D3×D411yescharacteristic
648Q8—21no—
649Q8—21no—
650Q8—32no—
651Q8—32no—
652Q8—64no—
653Q8—61no—
654Q8—61no—
655Q8—241no—
656D4—61no—
657D4—61no—
658D4—241no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—64no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—241no—
674C2×C4C3×D3×D411yescharacteristic
675C2×C4C23×C3×D311yescharacteristic
676C8—21no—
677C8—21no—
678C8—61no—
679C8—61no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—41no—
684C2×C3—41no—
685C2×C3—81no—
686C2×C3—241no—
687C2×C3#565611yescharacteristic
688C2×C3#577011yescharacteristic
689C2×C3#577911yescharacteristic
690C2×C3C3×#52511yescharacteristic
691C2×C3C3×#57711yescharacteristic
692C2×C3C3×#57811yescharacteristic
693D3—81no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—121no—
698C22—121no—
699C22—121no—
700C22C2×C3×D3×D411yescharacteristic
701C4—21no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—41no—
706C4—61no—
707C4—61no—
708C4—61no—
709C4—61no—
710C4—62no—
711C4—62no—
712C4—121no—
713C4C3×D3×#4111yescharacteristic
714C4C3×D3×#4111yescharacteristic
715C3—21no—
716C3#8149711yescharacteristic, direct product factor
717C3C3×#312111yescharacteristic, complemented
718C2—41no—
719C2—241no—
720C2C3×#565611yescharacteristic
721C2C3×#577011yescharacteristic
722C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC3×#930C22
hypercenterC3×#485D3
hypocenterC3C3×#3121
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
3. C32×#485C2semidirect
4. C3×#5050C2semidirect
6. C3×#4889C2semidirect
7. C3×#4875C2semidirect
8. C3×#4854C2semidirect
9. C3×#4852C2semidirect
10. C3×#4798C2semidirect
11. C3×#4798C2semidirect
12. C3×#4790C2semidirect
13. C3×#4789C2semidirect
15. C3×#4720C2semidirect
17. #81497C3direct (N × H)
64. #5516C2×C3semidirect
66. C3×#485D3semidirect
67. C3×#485C2×C3semidirect
80. #5050C2×C3semidirect
82. #4889C2×C3semidirect
83. #4875C2×C3semidirect
84. #4854C2×C3semidirect
85. #4852C2×C3semidirect
86. #4798C2×C3semidirect
87. #4798C2×C3semidirect
88. #4790C2×C3semidirect
89. #4789C2×C3semidirect
91. #4720C2×C3semidirect
271. #485C3×D3semidirect
645. C32#3121semidirect
716. C3#81497direct (N × H)
717. C3C3×#3121semidirect

Maximal subgroups

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

subgroupindex
C3×#56432
C3×#55162
C32×#4852
C3×#50502
C3×#50032
C3×#48892
C3×#48752
C3×#48542
C3×#48522
C3×#47982
C3×#47902
C3×#47892
C3×#47382
C3×#47202
C3×#31213
#814973