Finite Group Databasebeta

← C3×#81634 #11895512

Subgroups — C3×#81634 #11895512

Order 1152.

720 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5685C211yesmaximal, characteristic, complemented
2C3×#5671C211yesmaximal, characteristic
3C32×#488C211yesmaximal, characteristic
4C3×#5063C211yesmaximal, characteristic, complemented
5C3×#5054C211yesmaximal, characteristic
6C3×#4796C211yesmaximal, characteristic, complemented
7C3×#4795C211yesmaximal, characteristic, complemented
8C3×#4792C211yesmaximal, characteristic, complemented
9C3×#4790C211yesmaximal, characteristic, complemented
10C3×#4768C211yesmaximal, characteristic
11C3×#4767C211yesmaximal, characteristic
12C3×#4759C211yesmaximal, characteristic
13C3×#4758C211yesmaximal, characteristic
14C3×C4×Dic12C211yesmaximal, characteristic, complemented
15C3×C8×Dic6C211yesmaximal, characteristic, complemented
16C3×#3364—31nomaximal
17#81634C311yesmaximal, characteristic, direct product factor
18C32×#125C2211yescharacteristic
19C32×#124C2211yescharacteristic
20C3×Q8×Dic3C2211yescharacteristic
21C3×#944C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C3×#936C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×Dic12C2211yescharacteristic
27C3×#890C2211yescharacteristic
28C3×#889—21no—
29C3×#889—21no—
30C3×#888—21no—
31C3×#888C2211yescharacteristic
32C3×#887—21no—
33C3×#887C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#879—21no—
36C3×#879—21no—
37C3×#878—21no—
38C3×#877—21no—
39C3×C4×Dic6C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#557—31no—
62C3×#556—31no—
63#5685C2×C311yescharacteristic, complemented
64#5671C2×C311yescharacteristic
65C3×#488—21no—
66C3×#488—31no—
67C3×#488D311yescharacteristic
68C3×#488C2×C311yescharacteristic
69C3×#487—31no—
70C3×#479—31no—
71C3×#479—31no—
72C3×#474—31no—
73C3×#464—31no—
74C3×#464—31no—
75C3×#462—31no—
76C3×C8×Q8—31no—
77C3×C4×Q16—31no—
78C3×C4×Q16—31no—
79C3×C4×SD16—31no—
80#5063C2×C311yescharacteristic, complemented
81#5054C2×C311yescharacteristic
82#4796C2×C311yescharacteristic, complemented
83#4795C2×C311yescharacteristic, complemented
84#4792C2×C311yescharacteristic, complemented
85#4790C2×C311yescharacteristic, complemented
86#4768C2×C311yescharacteristic
87#4767C2×C311yescharacteristic
88#4759C2×C311yescharacteristic
89#4758C2×C311yescharacteristic
90C4×Dic12C2×C311yescharacteristic, complemented
91C8×Dic6C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3×Dic3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6D411yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C32×C8C2311yescharacteristic
100C2×C32×C8C2311yescharacteristic
101C32×C4⋊C4—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C32×C22⋊C4—21no—
106C32×C22⋊C4—21no—
107C32×C42C2311yescharacteristic
108C3×#217—21no—
109C3×#217—21no—
110C3×#217—21no—
111C3×#216—22no—
112C3×#214—22no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3D411yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×Dic12—22no—
138#3364—31noSylow
139C2×C3×Q16—31no—
140C2×C3×Q16—31no—
141C2×C3×SD16—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—31no—
144C3×C4⋊Q8—61no—
145C3×#126—61no—
146C3×#126—61no—
147C3×#125—21no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
151C3×#125C2×D311yescharacteristic
152C3×#125C22×C311yescharacteristic
153C3×#124—21no—
154C3×#124—31no—
155C3×#124C2×D311yescharacteristic
156C3×#124C22×C311yescharacteristic
157C3×C22⋊Q8—61no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—61no—
165C3×C4×D4—31no—
166C3×#117—61no—
167Q8×Dic3C22×C311yescharacteristic
168#944C22×C311yescharacteristic
169C2×#216C22×C311yescharacteristic
170#936C22×C311yescharacteristic
171D4×Dic3C22×C311yescharacteristic
172C2×#214C22×C311yescharacteristic
173C2×Dic12C22×C311yescharacteristic
174#890C22×C311yescharacteristic
175#889—21no—
176#889—21no—
177#888—21no—
178#888C22×C311yescharacteristic
179#887—21no—
180#887C22×C311yescharacteristic
181#887C22×C311yescharacteristic
182#879—21no—
183#879—21no—
184#878—21no—
185#877—21no—
186C4×Dic6C22×C311yescharacteristic
187C4×Dic6C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C3×#107—31no—
190C3×#107—31no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×#103—21no—
196C3×#103—21no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C2×D311yescharacteristic
204C3×#103C22×C311yescharacteristic
205C3×#103C22×C311yescharacteristic
206C3×#102—21no—
207C3×#102—21no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic
210C3×#102C2×D311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×C4×C8—21no—
214C3×C4×C8—31no—
215C3×C4×C8—31no—
216C3×C4×C8C2×D311yescharacteristic
217C3×C4×C8C22×C311yescharacteristic
218#835C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#818C22×C311yescharacteristic
221#816C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225C8×Dic3C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#808C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C23×C32—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C32×D4—21no—
236C32×D4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—42no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×Dic6—21no—
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—42no—
257C3×Dic6#4112yes—
258C32×C8—21no—
259C32×C8—21no—
260C3×C3⋊C8—21no—
261C3×C3⋊C8—21no—
262#557—31no—
263#556—31no—
264#488—31no—
265#488C3×D311yescharacteristic
266#487—31no—
267#479—31no—
268#479—31no—
269#474—31no—
270#464—31no—
271#464—31no—
272#462—31no—
273C8×Q8—31no—
274C4×Q16—31no—
275C4×Q16—31no—
276C4×SD16—31no—
277C2×C3×Q8—21no—
278C2×C3×Q8—31no—
279C2×C3×Q8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C23×C311yescharacteristic
284C2×C3×D4—21no—
285C2×C3×D4C22×D311yescharacteristic
286C2×C3×D4C23×C311yescharacteristic
287C22×C3×C4—61no—
288C22×Dic3—21no—
289C2×Dic6—21no—
290C2×Dic6C3×D411yescharacteristic
291C2×Dic6C23×C311yescharacteristic
292C2×Dic6C23×C311yescharacteristic
293C3×Q16—62no—
294C3×Q16—62no—
295C3×SD16—62no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—31no—
299C2×C3×C8—31no—
300C2×C3×C8C22×D311yescharacteristic
301C2×C3×C8C22×D311yescharacteristic
302C2×C3×C8C23×C311yescharacteristic
303C2×C3×C8C23×C311yescharacteristic
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—41no—
316C3×C4⋊C4—41no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C4⋊C4C22×D311yescharacteristic
329C3×C4⋊C4C23×C311yescharacteristic
330C3×C4⋊C4C23×C311yescharacteristic
331C3×C22⋊C4—21no—
332C3×C22⋊C4—21no—
333C3×C22⋊C4—21no—
334C3×C22⋊C4—21no—
335C3×C22⋊C4—41no—
336C3×C22⋊C4—41no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C42—21no—
341C3×C42—31no—
342C3×C42—31no—
343C3×C42—61no—
344C3×C42—61no—
345C3×C42—61no—
346C3×C42—61no—
347C3×C42—61no—
348C3×C42C22×D311yescharacteristic
349C3×C42C23×C311yescharacteristic
350#217—21no—
351#217—21no—
352#217—21no—
353#216—22no—
354#214—22no—
355C4⋊Dic3—21no—
356C4⋊Dic3—21no—
357C4⋊Dic3C3×D411yescharacteristic
358C4⋊Dic3C23×C311yescharacteristic
359C4⋊Dic3C23×C311yescharacteristic
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—21no—
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4C3×D411yescharacteristic
369Dic3⋊C4C3×D411yescharacteristic
370C4×Dic3—21no—
371C4×Dic3—21no—
372C4×Dic3—21no—
373C4×Dic3—21no—
374C4×Dic3—21no—
375C4×Dic3C23×C311yescharacteristic
376C4×Dic3C23×C311yescharacteristic
377C2×C3⋊C8C23×C311yescharacteristic
378C2×C3⋊C8C23×C311yescharacteristic
379Dic12—22no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32C22×D411yescharacteristic
384C32×C4—21no—
385C32×C4—21no—
386C32×C4—41no—
387C32×C4—41no—
388C32×C4—41no—
389C32×C4C2×#4111yescharacteristic
390C32×C42−1+411yescharacteristic
391C3×Dic3—22no—
392C3×Dic3—21no—
393C3×Dic3—21no—
394C3×Dic3—21no—
395C3×Dic3—41no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C3×Dic3#13512yes—
399C2×Q16—31no—
400C2×Q16—31no—
401C2×SD16—31no—
402C4⋊Q8—31no—
403C4⋊Q8—31no—
404C4⋊Q8—61no—
405#126—61no—
406#126—61no—
407#125—31no—
408#125—61no—
409#125—61no—
410#125C2×C3×D311yescharacteristic
411#124—31no—
412#124C2×C3×D311yescharacteristic
413C22⋊Q8—61no—
414C4×Q8—31no—
415C4×Q8—31no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—61no—
421C4×D4—31no—
422#117—61no—
423#107—31no—
424#107—31no—
425#106—31no—
426C4⋊C8—31no—
427C4⋊C8—31no—
428C4⋊C8—31no—
429#103—31no—
430#103—31no—
431#103—31no—
432#103—31no—
433#103—31no—
434#103C2×C3×D311yescharacteristic
435#103C2×C3×D311yescharacteristic
436#102—31no—
437#102C2×C3×D311yescharacteristic
438#102C2×C3×D311yescharacteristic
439C4×C8—31no—
440C4×C8—31no—
441C4×C8C2×C3×D311yescharacteristic
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—41no—
445C3×Q8—21no—
446C3×Q8—21no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—32no—
450C3×Q8—41no—
451C3×Q8—41no—
452C3×Q8—62no—
453C3×Q8—61no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—122no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—41no—
462C3×D4—41no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—122no—
484C2×C3×C4D3×D411yescharacteristic
485C2×C3×C4D3×D411yescharacteristic
486C2×C3×C4C2×C3×D411yescharacteristic
487C2×C3×C4C2×C3×D411yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C24×C311yescharacteristic
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—42no—
495C2×Dic3C2×C3×D411yescharacteristic
496C2×Dic3C2×C3×D411yescharacteristic
497C2×Dic3C2×C3×D411yescharacteristic
498C2×Dic3C2×C3×D411yescharacteristic
499Dic6—21no—
500Dic6—22no—
501Dic6—21no—
502Dic6—21no—
503Dic6—42no—
504Dic6C3×#4112yes—
505C3×C8—21no—
506C3×C8—21no—
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—41no—
510C3×C8—41no—
511C3×C8—61no—
512C3×C8—61no—
513C3⋊C8—21no—
514C3⋊C8—21no—
515C2×C32—81no—
516C2×C32#54811yescharacteristic
517C2×C32C2×#13511yescharacteristic
518C2×C32#57811yescharacteristic
519C2×Q8—31no—
520C2×Q8—31no—
521C2×Q8—31no—
522C2×Q8—61no—
523C2×Q8C22×C3×D311yescharacteristic
524C2×D4C22×C3×D311yescharacteristic
525C22×C4—61no—
526Q16—62no—
527Q16—62no—
528SD16—62no—
529C2×C8—31no—
530C2×C8—31no—
531C2×C8C22×C3×D311yescharacteristic
532C2×C8C22×C3×D311yescharacteristic
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4C22×C3×D311yescharacteristic
551C4⋊C4C22×C3×D311yescharacteristic
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—61no—
555C22⋊C4—61no—
556C22⋊C4—61no—
557C42—31no—
558C42—31no—
559C42—61no—
560C42—61no—
561C42—61no—
562C42—61no—
563C42—61no—
564C42C22×C3×D311yescharacteristic
565C22×C3—21no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—81no—
573C22×C3—81no—
574C22×C3—81no—
575C22×C3C2×D3×D411yescharacteristic
576C22×C3C22×C3×D411yescharacteristic
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—32no—
584C3×C4—41no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—62no—
593C3×C4—61no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—81no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4D3×#4111yescharacteristic
603C3×C4#101011yescharacteristic
604C3×C4C2×C3×#4111yescharacteristic
605C3×C4C3×2−1+411yescharacteristic
606Dic3—21no—
607Dic3—21no—
608Dic3—21no—
609Dic3—22no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3C3×#13512yes—
614C32#336411yescharacteristic, complemented, Sylow
615C23—21no—
616Q8—21no—
617Q8—21no—
618Q8—32no—
619Q8—62no—
620Q8—61no—
621Q8—61no—
622Q8—61no—
623Q8—122no—
624D4—21no—
625D4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—122no—
638C2×C4C3×D3×D411yescharacteristic
639C2×C4C3×D3×D411yescharacteristic
640C2×C4C23×C3×D311yescharacteristic
641C8—21no—
642C8—21no—
643C8—61no—
644C8—61no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—81no—
649C2×C3—81no—
650C2×C3—161no—
651C2×C3#567711yescharacteristic
652C2×C3D3×#13511yescharacteristic
653C2×C3#577111yescharacteristic
654C2×C3C3×#54811yescharacteristic
655C2×C3C2×C3×#13511yescharacteristic
656C2×C3C3×#57811yescharacteristic
657C22—41no—
658C22—41no—
659C22—41no—
660C22C2×C3×D3×D411yescharacteristic
661C4—21no—
662C4—21no—
663C4—32no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—61no—
668C4—61no—
669C4—61no—
670C4—62no—
671C4—121no—
672C4—121no—
673C4—121no—
674C4C3×D3×#4111yescharacteristic
675C4C3×#101011yescharacteristic
676C3—21no—
677C3#8163411yescharacteristic, direct product factor
678C3C3×#336411yescharacteristic, complemented
679C2—81no—
680C2C3×#567711yescharacteristic
681C2C3×D3×#13511yescharacteristic
682C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#488C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#488D3
hypocenterC3C3×#3364
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#488

Complements

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

NH ≅ G/Ntype
1. C3×#5685C2semidirect
4. C3×#5063C2semidirect
6. C3×#4796C2semidirect
7. C3×#4795C2semidirect
8. C3×#4792C2semidirect
9. C3×#4790C2semidirect
14. C3×C4×Dic12C2semidirect
15. C3×C8×Dic6C2semidirect
17. #81634C3direct (N × H)
63. #5685C2×C3semidirect
80. #5063C2×C3semidirect
82. #4796C2×C3semidirect
83. #4795C2×C3semidirect
84. #4792C2×C3semidirect
85. #4790C2×C3semidirect
90. C4×Dic12C2×C3semidirect
91. C8×Dic6C2×C3semidirect
614. C32#3364semidirect
677. C3#81634direct (N × H)
678. C3C3×#3364semidirect

Maximal subgroups

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

subgroupindex
C3×#56852
C3×#56712
C32×#4882
C3×#50632
C3×#50542
C3×#47962
C3×#47952
C3×#47922
C3×#47902
C3×#47682
C3×#47672
C3×#47592
C3×#47582
C3×C4×Dic122
C3×C8×Dic62
C3×#33643
#816343