Finite Group Databasebeta

← C3×#78882 #11858001

Subgroups — C3×#78882 #11858001

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C2×C3×#907C211yesmaximal, characteristic, complemented
3C3×#5504C211yesmaximal, characteristic, complemented
4C32×#417C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5131C211yesmaximal, characteristic, complemented
7C2×C3×#809C211yesmaximal, characteristic, complemented
8C3×#4804C212yesmaximal, complemented
9C3×#4803C212yesmaximal, complemented
10C3×#4770C212yesmaximal, complemented
11C3×D3×#102C212yesmaximal, complemented
12C3×#2897—31nomaximal
13#78882C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C3×#1009—24no—
16C3×#1009C418yescomplemented
17C2×C3×#239C2212yes—
18C2×C3×D3×D4—22no—
19C2×C3×D3×D4C2212yes—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C22×C3×D12—21no—
23C22×C3×D12C2211yescharacteristic
24C2×C32×M16C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C3×C4×#67—22no—
27C3×#926C2211yescharacteristic, complemented
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29C3×#907—24no—
30C2×C3×ΓL(1,𝔽25)C2212yescomplemented
31C2×C3×D3×C8C2212yescomplemented
32C3×#893—21no—
33C3×#892C2212yescomplemented
34C3×D3×C4⋊C4C2212yescomplemented
35C3×#887—21no—
36C32×#103C2212yescomplemented
37C32×#102C2212yescomplemented
38C3×#835C2211yescharacteristic, complemented
39C3×#835C2211yescharacteristic, complemented
40C3×#832C2211yescharacteristic, complemented
41C3×#832C2211yescharacteristic, complemented
42C3×#821C2212yescomplemented
43C3×#821C2212yescomplemented
44C3×#809C2212yescomplemented
45C3×#809C2212yescomplemented
46C2×C3×H(5,𝔽2)—31no—
47C2×#1009C2×C311yescharacteristic
48C2×C3×#131—31no—
49C3×#520—31no—
50C2×#907C2×C311yescharacteristic, complemented
51#5504C2×C311yescharacteristic, complemented
52C3×#418—31no—
53C3×#418—32no—
54C3×#417—21no—
55C3×#417—32no—
56C3×#417D311yescharacteristic, complemented
57C3×#417C2×C311yescharacteristic, complemented
58C3×#416—31no—
59C3×#416—32no—
60C2×C3×#102—31no—
61C2×C3×#102—32no—
62#5233C2×C311yescharacteristic, complemented
63#5131C2×C311yescharacteristic, complemented
64C2×#809C2×C311yescharacteristic, complemented
65#4804C2×C312yescomplemented
66#4803C2×C312yescomplemented
67#4770C2×C312yescomplemented
68D3×#102C2×C312yescomplemented
69C23×C3×D3—21no—
70C23×C3×D3—22no—
71C32×#41—22no—
72C32×#41C2×C414yescomplemented
73C2×C32×Q8C2311yescharacteristic
74C2×C32×D4—21no—
75C2×C32×D4C2311yescharacteristic
76C22×C32×C4—21no—
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C2×C3×#67—22no—
80C2×C3×#67D412yes—
81C3×#239—24no—
82C3×#239C2×C418yescomplemented
83C3×D3×D4—216no—
84C3×D3×D4—24no—
85C3×D3×D4C2×C418yescomplemented
86C3×#235—28no—
87C3×#235C2×C414yes—
88C3×#235D414yes—
89C2×C3×D12—22no—
90C2×C3×D12—21no—
91C2×C3×D12—22no—
92C2×C3×D12—28no—
93C2×C3×D12C2×C414yescomplemented
94C2×C3×D12D411yescharacteristic
95C2×C3×D12C2312yes—
96C2×C3×C4×D3—22no—
97C2×C3×C4×D3—22no—
98C2×C3×C4×D3C2312yes—
99C2×C3×Dic6D411yescharacteristic
100C32×M16—22no—
101C2×C32×C8C2312yes—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2312yes—
104C3×#217—21no—
105C3×(C2×D3)⋊C4—22no—
106C3×C4⋊Dic3C2311yescharacteristic
107C3×C4⋊Dic3C2311yescharacteristic
108C3×Dic3⋊C4—22no—
109C3×C4×Dic3—21no—
110C3×C4×Dic3—22no—
111C2×C3×C3⋊C8—22no—
112C2×C3×C3⋊C8C2311yescharacteristic
113C2×C3×C3⋊C8C2311yescharacteristic
114C3×ΓL(1,𝔽25)—24no—
115C3×D3×C8—24no—
116#2897—31noSylow
117C3×H(5,𝔽2)—38no—
118C3×H(5,𝔽2)—64no—
119C2×C3×#41—21no—
120C2×C3×#41—31no—
121C2×C3×#41—32no—
122C2×C3×#41—61no—
123C2×C3×#41C2×D311yescharacteristic
124C2×C3×#41C22×C311yescharacteristic
125C22×C3×D4—32no—
126C22×C3×D4—31no—
127C22×C3×D4—61no—
128C22×C3×D4—62no—
129#1009—24no—
130#1009C3×C418yescomplemented
131C2×#239C22×C312yes—
132C2×D3×D4—22no—
133C2×D3×D4C22×C312yes—
134C2×#235—21no—
135C2×#235C22×C311yescharacteristic
136C22×D12—21no—
137C22×D12C22×C311yescharacteristic
138C3×#131—64no—
139C2×C3×M16—21no—
140C2×C3×M16—32no—
141C2×C3×M16C2×D311yescharacteristic, complemented
142C2×C3×M16C22×C311yescharacteristic, complemented
143C22×C3×C8—31no—
144C22×C3×C8—32no—
145C3×C4×Q8—61no—
146C3×C4×D4—61no—
147C3×C4×D4—62no—
148C3×#117—31no—
149C3×#117—32no—
150C2×C3×C4⋊C4—21no—
151C2×C3×C4⋊C4—32no—
152C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
153C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
154C4×#67—22no—
155#926C22×C311yescharacteristic, complemented
156C22×C3⋊C8C22×C311yescharacteristic, complemented
157#907—24no—
158C2×ΓL(1,𝔽25)C22×C312yescomplemented
159C2×D3×C8C22×C312yescomplemented
160#893—21no—
161#892C22×C312yescomplemented
162D3×C4⋊C4C22×C312yescomplemented
163#887—21no—
164C3×#103—22no—
165C3×#103—31no—
166C3×#103—31no—
167C3×#103C2×D312yescomplemented
168C3×#103C22×C312yescomplemented
169C3×#102—22no—
170C3×#102—31no—
171C3×#102—31no—
172C3×#102—32no—
173C3×#102—32no—
174C3×#102—32no—
175C3×#102—32no—
176C3×#102C2×D312yescomplemented
177C3×#102C22×C312yescomplemented
178#835C22×C311yescharacteristic, complemented
179#835C22×C311yescharacteristic, complemented
180#832C22×C311yescharacteristic, complemented
181#832C22×C311yescharacteristic, complemented
182#821C22×C312yescomplemented
183#821C22×C312yescomplemented
184#809C22×C312yescomplemented
185#809C22×C312yescomplemented
186C23×C32—21no—
187C23×C32C2×D411yescharacteristic
188C22×C3×D3—22no—
189C22×C3×D3—24no—
190C22×C3×D3—28no—
191C22×C3×D3—82no—
192C22×C3×D3—82no—
193C22×C3×D3—81no—
194C22×C3×D3—81no—
195C22×C3×D3C2×D412yes—
196C32×Q8—21no—
197C32×Q8C22×C412yes—
198C32×D4—24no—
199C32×D4—21no—
200C32×D4C22×C412yes—
201C2×C32×C4—21no—
202C2×C32×C4—24no—
203C2×C32×C4—22no—
204C2×C32×C4—81no—
205C2×C32×C4C22×C412yes—
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D412yes—
208C2×C32×C4C2411yescharacteristic
209C3×#67—28no—
210C3×#67C22⋊C418yes—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3C2×D412yes—
214C3×D12—28no—
215C3×D12—24no—
216C3×D12—22no—
217C3×D12C22⋊C414yes—
218C3×D12C22×C414yes—
219C3×C4×D3—28no—
220C3×C4×D3—82no—
221C3×C4×D3C22×C414yes—
222C3×C4×D3C2×D414yes—
223C3×Dic6C22⋊C414yes—
224C32×C8—22no—
225C3×C3⋊C8—21no—
226C3×C3⋊C8—21no—
227C2×H(5,𝔽2)—31no—
228C2×#131—31no—
229#520—31no—
230#418—31no—
231#418—32no—
232#417—32no—
233#417C3×D311yescharacteristic, complemented
234#416—31no—
235#416—32no—
236C2×#102—31no—
237C2×#102—32no—
238C24×C3—62no—
239C24×C3—61no—
240C23×D3—21no—
241C23×D3—22no—
242C3×#41—22no—
243C3×#41—22no—
244C3×#41—24no—
245C3×#41—34no—
246C3×#41—34no—
247C3×#41—38no—
248C3×#41—42no—
249C3×#41—68no—
250C3×#41—64no—
251C3×#41C4×D314yescomplemented
252C3×#41C2×C3×C414yescomplemented
253C2×C3×Q8—21no—
254C2×C3×Q8—31no—
255C2×C3×Q8C22×D311yescharacteristic
256C2×C3×Q8C23×C311yescharacteristic
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—32no—
261C2×C3×D4—38no—
262C2×C3×D4—34no—
263C2×C3×D4—31no—
264C2×C3×D4—32no—
265C2×C3×D4—41no—
266C2×C3×D4—68no—
267C2×C3×D4—62no—
268C2×C3×D4—64no—
269C2×C3×D4—62no—
270C2×C3×D4—616no—
271C2×C3×D4—61no—
272C2×C3×D4—62no—
273C2×C3×D4C22×D311yescharacteristic
274C2×C3×D4C23×C311yescharacteristic
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—32no—
281C22×C3×C4—41no—
282C22×C3×C4—41no—
283C22×C3×C4—62no—
284C22×C3×C4—62no—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C23×C311yescharacteristic
287C2×#67—22no—
288C2×#67C3×D412yes—
289#239—24no—
290#239C2×C3×C418yescomplemented
291D3×D4—216no—
292D3×D4—24no—
293D3×D4C2×C3×C418yescomplemented
294#235—28no—
295#235C2×C3×C414yes—
296#235C3×D414yes—
297C2×D12—22no—
298C2×D12—21no—
299C2×D12—22no—
300C2×D12—28no—
301C2×D12C2×C3×C414yescomplemented
302C2×D12C3×D411yescharacteristic
303C2×D12C23×C312yes—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3C23×C312yes—
307C2×Dic6C3×D411yescharacteristic
308C3×M16—22no—
309C3×M16—22no—
310C3×M16—42no—
311C3×M16—64no—
312C2×C3×C8—22no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8—64no—
316C2×C3×C8—62no—
317C2×C3×C8C22×D312yes—
318C2×C3×C8C23×C312yes—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—41no—
325C3×C4⋊C4—62no—
326C3×C4⋊C4C22×D312yes—
327C3×C4⋊C4C23×C312yes—
328C3×C22⋊C4—62no—
329C3×C22⋊C4—61no—
330C3×C42—62no—
331C3×C42—61no—
332#217—21no—
333(C2×D3)⋊C4—22no—
334C4⋊Dic3C23×C311yescharacteristic
335C4⋊Dic3C23×C311yescharacteristic
336Dic3⋊C4—22no—
337C4×Dic3—21no—
338C4×Dic3—22no—
339C2×C3⋊C8—22no—
340C2×C3⋊C8C23×C311yescharacteristic
341C2×C3⋊C8C23×C311yescharacteristic
342ΓL(1,𝔽25)—24no—
343D3×C8—24no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—22no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32C2×C22⋊C412yes—
350C22×C32C22×D411yescharacteristic
351C2×C3×D3—22no—
352C2×C3×D3—22no—
353C2×C3×D3—24no—
354C2×C3×D3—42no—
355C2×C3×D3—42no—
356C2×C3×D3—88no—
357C2×C3×D3—84no—
358C2×C3×D3C2×C22⋊C414yes—
359C32×C4—22no—
360C32×C4—42no—
361C32×C4C2×C22⋊C412yes—
362C32×C4C23×C411yescharacteristic
363C32×C4C22×D411yescharacteristic
364C3×Dic3—41no—
365C3×Dic3—41no—
366C3×Dic3C2×C22⋊C414yes—
367H(5,𝔽2)—38no—
368H(5,𝔽2)—64no—
369C2×#41—31no—
370C2×#41—32no—
371C2×#41—61no—
372C2×#41C2×C3×D311yescharacteristic
373C22×D4—32no—
374C22×D4—31no—
375C22×D4—61no—
376C22×D4—62no—
377#131—64no—
378C2×M16—32no—
379C2×M16C2×C3×D311yescharacteristic, complemented
380C22×C8—31no—
381C22×C8—32no—
382C4×Q8—61no—
383C4×D4—61no—
384C4×D4—62no—
385#117—31no—
386#117—32no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
389#103—31no—
390#103—31no—
391#103C2×C3×D312yescomplemented
392#102—31no—
393#102—31no—
394#102—32no—
395#102—32no—
396#102—32no—
397#102—32no—
398#102C2×C3×D312yescomplemented
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—32no—
403C23×C3—41no—
404C23×C3—68no—
405C23×C3—62no—
406C23×C3—64no—
407C23×C3—241no—
408C23×C3—241no—
409C23×C3—242no—
410C23×C3—242no—
411C23×C3D3×D411yescharacteristic
412C23×C3C2×C3×D411yescharacteristic
413C22×D3—22no—
414C22×D3—24no—
415C22×D3—28no—
416C22×D3—82no—
417C22×D3—82no—
418C22×D3—81no—
419C22×D3—81no—
420C22×D3C2×C3×D412yes—
421C3×Q8—21no—
422C3×Q8—21no—
423C3×Q8—22no—
424C3×Q8—34no—
425C3×Q8—41no—
426C3×Q8C2×C4×D312yes—
427C3×Q8C22×C3×C412yes—
428C3×D4—24no—
429C3×D4—24no—
430C3×D4—21no—
431C3×D4—21no—
432C3×D4—22no—
433C3×D4—38no—
434C3×D4—34no—
435C3×D4—34no—
436C3×D4—41no—
437C3×D4—44no—
438C3×D4—68no—
439C3×D4—68no—
440C3×D4—64no—
441C3×D4—62no—
442C3×D4C2×C4×D312yes—
443C3×D4C22×C3×C412yes—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—32no—
455C2×C3×C4—34no—
456C2×C3×C4—34no—
457C2×C3×C4—44no—
458C2×C3×C4—41no—
459C2×C3×C4—42no—
460C2×C3×C4—68no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—81no—
464C2×C3×C4—81no—
465C2×C3×C4—82no—
466C2×C3×C4—242no—
467C2×C3×C4C2×C4×D312yes—
468C2×C3×C4D3×D411yescharacteristic
469C2×C3×C4D3×D412yes—
470C2×C3×C4C22×C3×C412yes—
471C2×C3×C4C2×C3×D411yescharacteristic
472C2×C3×C4C2×C3×D412yes—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C24×C311yescharacteristic
475#67—28no—
476#67C3×C22⋊C418yes—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3C2×C3×D412yes—
480D12—28no—
481D12—24no—
482D12—22no—
483D12C3×C22⋊C414yes—
484D12C22×C3×C414yes—
485C4×D3—28no—
486C4×D3—82no—
487C4×D3C22×C3×C414yes—
488C4×D3C2×C3×D414yes—
489Dic6C3×C22⋊C414yes—
490C3×C8—22no—
491C3×C8—22no—
492C3×C8—42no—
493C3×C8—61no—
494C3×C8—61no—
495C3⋊C8—21no—
496C3⋊C8—21no—
497C2×C32—22no—
498C2×C32—42no—
499C2×C32C22×C22⋊C411yescharacteristic
500C2×C32#57611yescharacteristic
501C2×C32#57711yescharacteristic
502C3×D3—24no—
503C3×D3—44no—
504C24—62no—
505C24—61no—
506#41—22no—
507#41—34no—
508#41—34no—
509#41—38no—
510#41—68no—
511#41—64no—
512#41C3×C4×D314yescomplemented
513C2×Q8—31no—
514C2×Q8C22×C3×D311yescharacteristic
515C2×D4—21no—
516C2×D4—32no—
517C2×D4—38no—
518C2×D4—32no—
519C2×D4—34no—
520C2×D4—31no—
521C2×D4—68no—
522C2×D4—62no—
523C2×D4—64no—
524C2×D4—62no—
525C2×D4—616no—
526C2×D4—61no—
527C2×D4—62no—
528C2×D4C22×C3×D311yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—32no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4C22×C3×D311yescharacteristic
535M16—22no—
536M16—64no—
537C2×C8—31no—
538C2×C8—31no—
539C2×C8—64no—
540C2×C8—62no—
541C2×C8C22×C3×D312yes—
542C4⋊C4—21no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—62no—
546C4⋊C4C22×C3×D312yes—
547C22⋊C4—62no—
548C22⋊C4—61no—
549C42—62no—
550C42—61no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—21no—
559C22×C3—34no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—42no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—64no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3—122no—
573C22×C3—122no—
574C22×C3—244no—
575C22×C3—248no—
576C22×C3D3×C22⋊C412yes—
577C22×C3C2×C3×C22⋊C412yes—
578C22×C3C2×D3×D411yescharacteristic
579C22×C3C22×C3×D411yescharacteristic
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—24no—
583C2×D3—42no—
584C2×D3—42no—
585C2×D3—88no—
586C2×D3—84no—
587C2×D3C2×C3×C22⋊C414yes—
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—22no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—34no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—42no—
597C3×C4—82no—
598C3×C4—121no—
599C3×C4—121no—
600C3×C4D3×C22⋊C412yes—
601C3×C4C2×C3×C22⋊C412yes—
602C3×C4C22×C4×D311yescharacteristic
603C3×C4C2×D3×D411yescharacteristic
604C3×C4C23×C3×C411yescharacteristic
605C3×C4C22×C3×D411yescharacteristic
606Dic3—41no—
607Dic3—41no—
608Dic3C2×C3×C22⋊C414yes—
609C32#289711yescharacteristic, complemented, Sylow
610C23—21no—
611C23—32no—
612C23—68no—
613C23—62no—
614C23—64no—
615C23—241no—
616C23—241no—
617C23—242no—
618C23—242no—
619C23C3×D3×D411yescharacteristic
620Q8—21no—
621Q8—34no—
622Q8C2×C3×C4×D312yes—
623D4—24no—
624D4—21no—
625D4—38no—
626D4—34no—
627D4—34no—
628D4—68no—
629D4—68no—
630D4—64no—
631D4—62no—
632D4C2×C3×C4×D312yes—
633C2×C4—21no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—32no—
637C2×C4—34no—
638C2×C4—34no—
639C2×C4—68no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—81no—
643C2×C4—242no—
644C2×C4C2×C3×C4×D312yes—
645C2×C4C3×D3×D411yescharacteristic
646C2×C4C3×D3×D412yes—
647C2×C4C23×C3×D311yescharacteristic
648C8—22no—
649C8—61no—
650C8—61no—
651C2×C3—22no—
652C2×C3—22no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—42no—
657C2×C3—42no—
658C2×C3—42no—
659C2×C3—64no—
660C2×C3—82no—
661C2×C3—124no—
662C2×C3C2×D3×C22⋊C411yescharacteristic
663C2×C3#577411yescharacteristic
664C2×C3#577811yescharacteristic
665C2×C3C22×C3×C22⋊C411yescharacteristic
666C2×C3C3×#57611yescharacteristic
667C2×C3C3×#57711yescharacteristic
668D3—24no—
669D3—44no—
670C22—21no—
671C22—21no—
672C22—22no—
673C22—34no—
674C22—41no—
675C22—41no—
676C22—62no—
677C22—62no—
678C22—64no—
679C22—122no—
680C22—122no—
681C22—244no—
682C22—248no—
683C22C3×D3×C22⋊C412yes—
684C22C2×C3×D3×D411yescharacteristic
685C4—22no—
686C4—34no—
687C4—42no—
688C4—121no—
689C4—121no—
690C4C3×D3×C22⋊C412yes—
691C4C22×C3×C4×D311yescharacteristic
692C4C2×C3×D3×D411yescharacteristic
693C3—21no—
694C3#7888211yescharacteristic, direct product factor
695C3C3×#289711yescharacteristic, complemented
696C2—22no—
697C2—42no—
698C2—64no—
699C2—124no—
700C2C2×C3×D3×C22⋊C411yescharacteristic
701C2C3×#577411yescharacteristic
702C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#417C2
socleC22×C32C22×D4
prime radicalC2×C3×#1009C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#417D3
hypocenterC3C3×#2897
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
2. C2×C3×#907C2semidirect
3. C3×#5504C2semidirect
4. C32×#417C2semidirect
5. C3×#5233C2semidirect
6. C3×#5131C2semidirect
7. C2×C3×#809C2semidirect
8. C3×#4804C2semidirect
9. C3×#4803C2semidirect
10. C3×#4770C2semidirect
11. C3×D3×#102C2semidirect
13. #78882C3direct (N × H)
16. C3×#1009C4semidirect
24. C2×C32×M16C22semidirect
25. C2×C32×C4⋊C4C22semidirect
27. C3×#926C22semidirect
28. C22×C3×C3⋊C8C22semidirect
30. C2×C3×ΓL(1,𝔽25)C22semidirect
31. C2×C3×D3×C8C22semidirect
33. C3×#892C22semidirect
34. C3×D3×C4⋊C4C22semidirect
36. C32×#103C22semidirect
37. C32×#102C22semidirect
38. C3×#835C22semidirect
39. C3×#835C22semidirect
40. C3×#832C22semidirect
41. C3×#832C22semidirect
42. C3×#821C22semidirect
43. C3×#821C22semidirect
44. C3×#809C22semidirect
45. C3×#809C22semidirect
50. C2×#907C2×C3semidirect
51. #5504C2×C3semidirect
56. C3×#417D3semidirect
57. C3×#417C2×C3semidirect
62. #5233C2×C3semidirect
63. #5131C2×C3semidirect
64. C2×#809C2×C3semidirect
65. #4804C2×C3semidirect
66. #4803C2×C3semidirect
67. #4770C2×C3semidirect
68. D3×#102C2×C3semidirect
72. C32×#41C2×C4semidirect
82. C3×#239C2×C4semidirect
85. C3×D3×D4C2×C4semidirect
93. C2×C3×D12C2×C4semidirect
130. #1009C3×C4semidirect
141. C2×C3×M16C2×D3semidirect
142. C2×C3×M16C22×C3semidirect
152. C2×C3×C4⋊C4C2×D3semidirect
153. C2×C3×C4⋊C4C22×C3semidirect
155. #926C22×C3semidirect
156. C22×C3⋊C8C22×C3semidirect
158. C2×ΓL(1,𝔽25)C22×C3semidirect
159. C2×D3×C8C22×C3semidirect
161. #892C22×C3semidirect
162. D3×C4⋊C4C22×C3semidirect
167. C3×#103C2×D3semidirect
168. C3×#103C22×C3semidirect
176. C3×#102C2×D3semidirect
177. C3×#102C22×C3semidirect
178. #835C22×C3semidirect
179. #835C22×C3semidirect
180. #832C22×C3semidirect
181. #832C22×C3semidirect
182. #821C22×C3semidirect
183. #821C22×C3semidirect
184. #809C22×C3semidirect
185. #809C22×C3semidirect
233. #417C3×D3semidirect
251. C3×#41C4×D3semidirect
252. C3×#41C2×C3×C4semidirect
290. #239C2×C3×C4semidirect
293. D3×D4C2×C3×C4semidirect
301. C2×D12C2×C3×C4semidirect
379. C2×M16C2×C3×D3semidirect
388. C2×C4⋊C4C2×C3×D3semidirect
391. #103C2×C3×D3semidirect
398. #102C2×C3×D3semidirect
512. #41C3×C4×D3semidirect
609. C32#2897semidirect
694. C3#78882direct (N × H)
695. C3C3×#2897semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×C3×#9072
C3×#55042
C32×#4172
C3×#52332
C3×#51312
C2×C3×#8092
C3×#48042
C3×#48032
C3×#47702
C3×D3×#1022
C3×#28973
#788823