Finite Group Databasebeta

← C3×D3×#485 #11869473

Subgroups — C3×D3×#485 #11869473

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C22⋊Q8C211yesmaximal, characteristic
2C3×D3×#117C211yesmaximal, characteristic
3C32×#485C211yesmaximal, characteristic, complemented
4C3×#5045C211yesmaximal, characteristic, complemented
5C3×#4996C211yesmaximal, characteristic, complemented
6C3×#4888C211yesmaximal, characteristic, complemented
7C3×D3×#107C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×D3×#106C211yesmaximal, characteristic, complemented
10C3×#4815C211yesmaximal, characteristic, complemented
11C3×#4814C211yesmaximal, characteristic, complemented
12C3×D3×#103C211yesmaximal, characteristic, complemented
13C3×D3×#103C211yesmaximal, characteristic, complemented
14C3×D3×C22⋊C8C211yesmaximal, characteristic
15C3×#4723C211yesmaximal, characteristic, complemented
16C2×C3×#485—31nomaximal
17D3×#485C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#896—21no—
29C3×#892C2211yescharacteristic
30C3×#892C2211yescharacteristic
31C3×D3×C4⋊C4—21no—
32C3×D3×C4⋊C4C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×D3×C4⋊C4C2211yescharacteristic
35C3×D3×C22⋊C4—21no—
36C3×D3×C22⋊C4—21no—
37C3×#878—21no—
38C3×#877—21no—
39C3×#872—21no—
40C3×C42×D3—21no—
41C32×#107C2211yescharacteristic, complemented
42C32×#106C2211yescharacteristic, complemented
43C32×#103C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×C22⋊C8C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C2×C3×C22⋊Q8—31no—
62C2×C3×#117—31no—
63D3×C22⋊Q8C2×C311yescharacteristic
64D3×#117C2×C311yescharacteristic
65C3×#485—21no—
66C3×#485—31no—
67C3×#485—31no—
68C3×#485—31no—
69C3×#485—31no—
70C3×#485—31no—
71C3×#485—31no—
72C3×#485—31no—
73C3×#485D311yescharacteristic, direct product factor
74C3×#485C2×C311yescharacteristic, complemented
75C2×C3×#107—31no—
76C2×C3×#106—31no—
77C2×C3×#103—31no—
78C2×C3×#103—31no—
79C2×C3×C22⋊C8—31no—
80#5045C2×C311yescharacteristic, complemented
81#4996C2×C311yescharacteristic, complemented
82#4888C2×C311yescharacteristic, complemented
83D3×#107C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85D3×#106C2×C311yescharacteristic, complemented
86#4815C2×C311yescharacteristic, complemented
87#4814C2×C311yescharacteristic, complemented
88D3×#103C2×C311yescharacteristic, complemented
89D3×#103C2×C311yescharacteristic, complemented
90D3×C22⋊C8C2×C311yescharacteristic
91#4723C2×C311yescharacteristic, complemented
92C23×C3×D3D411yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3×Dic3D411yescharacteristic
96C3×D3×Q8—22no—
97C3×D3×Q8—22no—
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C42—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D3×C8—22no—
140C3×D3×C8—22no—
141C2×#485—31noSylow
142C22×C3×Q8—31no—
143C23×C3×C4—31no—
144C2×D3×Q8C22×C311yescharacteristic
145C22×C4×D3C22×C311yescharacteristic
146C22×C3×C8—31no—
147C22×C3×C8—31no—
148C3×C22⋊Q8—21no—
149C3×C22⋊Q8—31no—
150C3×C22⋊Q8—31no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—61no—
153C3×C22⋊Q8—61no—
154C3×C22⋊Q8C2×D311yescharacteristic
155C3×C22⋊Q8C22×C311yescharacteristic
156C3×#117—21no—
157C3×#117—31no—
158C3×#117—31no—
159C3×#117—31no—
160C3×#117—61no—
161C3×#117—61no—
162C3×#117C2×D311yescharacteristic
163C3×#117C22×C311yescharacteristic
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—61no—
168C2×C3×C22⋊C4—61no—
169C2×C3×C22⋊C4—61no—
170C2×C3×C42—61no—
171#946C22×C311yescharacteristic
172#926C22×C311yescharacteristic
173#924C22×C311yescharacteristic
174C2×D3×C8C22×C311yescharacteristic
175C2×D3×C8C22×C311yescharacteristic
176#897C22×C311yescharacteristic
177#896—21no—
178#892C22×C311yescharacteristic
179#892C22×C311yescharacteristic
180D3×C4⋊C4—21no—
181D3×C4⋊C4C22×C311yescharacteristic
182D3×C4⋊C4C22×C311yescharacteristic
183D3×C4⋊C4C22×C311yescharacteristic
184D3×C22⋊C4—21no—
185D3×C22⋊C4—21no—
186#878—21no—
187#877—21no—
188#872—21no—
189C42×D3—21no—
190C3×#107—21no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#107—31no—
194C3×#107C2×D311yescharacteristic, complemented
195C3×#107C22×C311yescharacteristic, complemented
196C3×#106—21no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic, complemented
201C3×#106C22×C311yescharacteristic, complemented
202C3×#103—21no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic, complemented
211C3×#103C2×D311yescharacteristic, complemented
212C3×#103C22×C311yescharacteristic, complemented
213C3×#103C22×C311yescharacteristic, complemented
214C3×C22⋊C8—21no—
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C22×C311yescharacteristic
220#835C22×C311yescharacteristic, complemented
221#835C22×C311yescharacteristic, complemented
222#830C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225#818C22×C311yescharacteristic, complemented
226#817C22×C311yescharacteristic, complemented
227#816C22×C311yescharacteristic, complemented
228#816C22×C311yescharacteristic, complemented
229#810C22×C311yescharacteristic, complemented
230#810C22×C311yescharacteristic, complemented
231#808C22×C311yescharacteristic, complemented
232#808C22×C311yescharacteristic, complemented
233#807C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—22no—
237C22×C3×D3—22no—
238C22×C3×D3—22no—
239C22×C3×D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3×Dic3—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×C4×D3—22no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—22no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×C4×D3#4112yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C2×C22⋊Q8—31no—
276C2×#117—31no—
277#485—31no—
278#485—31no—
279#485—31no—
280#485—31no—
281#485—31no—
282#485—31no—
283#485—31no—
284#485C3×D311yescharacteristic, direct product factor
285C2×#107—31no—
286C2×#106—31no—
287C2×#103—31no—
288C2×#103—31no—
289C2×C22⋊C8—31no—
290C24×C3—31no—
291C23×D3C3×D411yescharacteristic
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—62no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C23×C311yescharacteristic
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—62no—
306C22×C3×C4—62no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C23×C311yescharacteristic
313C22×Dic3C3×D411yescharacteristic
314D3×Q8—22no—
315D3×Q8—22no—
316C2×C4×D3—22no—
317C2×C4×D3—22no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3C3×D411yescharacteristic
323C2×C4×D3C3×D411yescharacteristic
324C2×C4×D3C23×C311yescharacteristic
325C2×C4×D3C23×C311yescharacteristic
326C2×Dic6—21no—
327C2×Dic6C23×C311yescharacteristic
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8—62no—
333C2×C3×C8—62no—
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C23×C311yescharacteristic
337C2×C3×C8C23×C311yescharacteristic
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—41no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C23×C311yescharacteristic
357C3×C4⋊C4C23×C311yescharacteristic
358C3×C4⋊C4C23×C311yescharacteristic
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—41no—
374C3×C42—61no—
375C3×C42—61no—
376C3×C42—61no—
377#217—21no—
378#217—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3C23×C311yescharacteristic
385C4⋊Dic3C23×C311yescharacteristic
386C4⋊Dic3C23×C311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C2×C3⋊C8C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397D3×C8—22no—
398D3×C8—22no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—44no—
407C2×C3×D3#12312yes—
408C2×C3×D3#13512yes—
409C2×C3×D3#13712yes—
410C32×C4—21no—
411C32×C4—41no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3#12312yes—
423C22×Q8—31no—
424C23×C4—31no—
425C22×C8—31no—
426C22×C8—31no—
427C22⋊Q8—31no—
428C22⋊Q8—31no—
429C22⋊Q8—31no—
430C22⋊Q8—61no—
431C22⋊Q8—61no—
432C22⋊Q8C2×C3×D311yescharacteristic
433#117—31no—
434#117—31no—
435#117—31no—
436#117—61no—
437#117—61no—
438#117C2×C3×D311yescharacteristic
439C2×C4⋊C4—31no—
440C2×C4⋊C4—31no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—61no—
443C2×C22⋊C4—61no—
444C2×C22⋊C4—61no—
445C2×C42—61no—
446#107—31no—
447#107—31no—
448#107—31no—
449#107C2×C3×D311yescharacteristic, complemented
450#106—31no—
451#106—31no—
452#106—31no—
453#106C2×C3×D311yescharacteristic, complemented
454#103—31no—
455#103—31no—
456#103—31no—
457#103—31no—
458#103—31no—
459#103—31no—
460#103C2×C3×D311yescharacteristic, complemented
461#103C2×C3×D311yescharacteristic, complemented
462C22⋊C8—31no—
463C22⋊C8—31no—
464C22⋊C8—31no—
465C22⋊C8C2×C3×D311yescharacteristic
466C23×C3—21no—
467C23×C3—31no—
468C23×C3—31no—
469C23×C3—62no—
470C23×C3—62no—
471C23×C3—62no—
472C23×C3D3×D411yescharacteristic
473C23×C3C2×C3×D411yescharacteristic
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3C2×C3×D411yescharacteristic
478C22×D3C2×C3×D411yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—122no—
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—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—122no—
522C2×C3×C4—122no—
523C2×C3×C4—122no—
524C2×C3×C4—122no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C2×C3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C24×C311yescharacteristic
529C2×Dic3—22no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3C2×C3×D411yescharacteristic
535C2×Dic3C2×C3×D411yescharacteristic
536C4×D3—22no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—22no—
540C4×D3—42no—
541C4×D3—42no—
542C4×D3—42no—
543C4×D3—42no—
544C4×D3C3×#4112yes—
545C4×D3C3×#4112yes—
546Dic6—21no—
547Dic6—21no—
548Dic6—42no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C2×C32—41no—
560C2×C32C2×#12311yescharacteristic
561C2×C32C2×#13511yescharacteristic
562C2×C32C2×#13711yescharacteristic
563C3×D3—41no—
564C3×D3#48514yesdirect product factor
565C24—31no—
566C2×Q8—31no—
567C2×Q8—61no—
568C2×Q8—62no—
569C2×Q8—62no—
570C2×Q8C22×C3×D311yescharacteristic
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4C22×C3×D311yescharacteristic
583C2×C8—31no—
584C2×C8—31no—
585C2×C8—62no—
586C2×C8—62no—
587C2×C8C22×C3×D311yescharacteristic
588C2×C8C22×C3×D311yescharacteristic
589C4⋊C4—21no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4C22×C3×D311yescharacteristic
600C4⋊C4C22×C3×D311yescharacteristic
601C4⋊C4C22×C3×D311yescharacteristic
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C42—21no—
611C42—61no—
612C42—61no—
613C42—61no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—32no—
623C22×C3—32no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—124no—
631C22×C3C2×D3×D411yescharacteristic
632C22×C3C22×C3×D411yescharacteristic
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—44no—
637C2×D3C3×#12312yes—
638C2×D3C3×#13512yes—
639C2×D3C3×#13712yes—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—32no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—81no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4D3×#4111yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4C2×C3×#4111yescharacteristic
666C3×C4C2×C3×#4111yescharacteristic
667Dic3—21no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3C3×#12312yes—
673C32C2×#48511yescharacteristic, complemented, Sylow
674C23—31no—
675C23—31no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23C3×D3×D411yescharacteristic
680Q8—21no—
681Q8—21no—
682Q8—61no—
683Q8—61no—
684Q8—122no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—31no—
692C2×C4—32no—
693C2×C4—32no—
694C2×C4—31no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4C3×D3×D411yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C8—21no—
711C8—21no—
712C8—61no—
713C8—61no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—34no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—81no—
721C2×C3—121no—
722C2×C3D3×#12311yescharacteristic
723C2×C3D3×#13511yescharacteristic
724C2×C3D3×#13711yescharacteristic
725C2×C3C2×C3×#12311yescharacteristic
726C2×C3C2×C3×#13511yescharacteristic
727C2×C3C2×C3×#13711yescharacteristic
728D3—41no—
729D3C3×#48514yesdirect product factor
730C22—21no—
731C22—21no—
732C22—21no—
733C22—32no—
734C22—32no—
735C22—32no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—124no—
740C22C2×C3×D3×D411yescharacteristic
741C4—21no—
742C4—32no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—61no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4C3×D3×#4111yescharacteristic
753C4C3×D3×#4111yescharacteristic
754C3—21no—
755C3D3×#48511yescharacteristic, direct product factor
756C3C2×C3×#48511yescharacteristic, complemented
757C2—34no—
758C2—41no—
759C2—121no—
760C2C3×D3×#12311yescharacteristic
761C2C3×D3×#13511yescharacteristic
762C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
hypercenterC3×#485D3
hypocenterC3C2×C3×#485
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
3. C32×#485C2semidirect
4. C3×#5045C2semidirect
5. C3×#4996C2semidirect
6. C3×#4888C2semidirect
7. C3×D3×#107C2semidirect
8. C3×#4868C2semidirect
9. C3×D3×#106C2semidirect
10. C3×#4815C2semidirect
11. C3×#4814C2semidirect
12. C3×D3×#103C2semidirect
13. C3×D3×#103C2semidirect
15. C3×#4723C2semidirect
17. D3×#485C3direct (N × H)
41. C32×#107C22semidirect
42. C32×#106C22semidirect
43. C32×#103C22semidirect
44. C32×#103C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
51. C3×#818C22semidirect
52. C3×#817C22semidirect
53. C3×#816C22semidirect
54. C3×#816C22semidirect
55. C3×#810C22semidirect
56. C3×#810C22semidirect
57. C3×#808C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×#807C22semidirect
73. C3×#485D3direct (N × H)
74. C3×#485C2×C3semidirect
80. #5045C2×C3semidirect
81. #4996C2×C3semidirect
82. #4888C2×C3semidirect
83. D3×#107C2×C3semidirect
84. #4868C2×C3semidirect
85. D3×#106C2×C3semidirect
86. #4815C2×C3semidirect
87. #4814C2×C3semidirect
88. D3×#103C2×C3semidirect
89. D3×#103C2×C3semidirect
91. #4723C2×C3semidirect
194. C3×#107C2×D3semidirect
195. C3×#107C22×C3semidirect
200. C3×#106C2×D3semidirect
201. C3×#106C22×C3semidirect
210. C3×#103C2×D3semidirect
211. C3×#103C2×D3semidirect
212. C3×#103C22×C3semidirect
213. C3×#103C22×C3semidirect
220. #835C22×C3semidirect
221. #835C22×C3semidirect
225. #818C22×C3semidirect
226. #817C22×C3semidirect
227. #816C22×C3semidirect
228. #816C22×C3semidirect
229. #810C22×C3semidirect
230. #810C22×C3semidirect
231. #808C22×C3semidirect
232. #808C22×C3semidirect
233. #807C22×C3semidirect
234. #807C22×C3semidirect
284. #485C3×D3direct (N × H)
449. #107C2×C3×D3semidirect
453. #106C2×C3×D3semidirect
460. #103C2×C3×D3semidirect
461. #103C2×C3×D3semidirect
564. C3×D3#485direct (N × H)
673. C32C2×#485semidirect
729. D3C3×#485direct (N × H)
755. C3D3×#485direct (N × H)
756. C3C2×C3×#485semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C22⋊Q82
C3×D3×#1172
C32×#4852
C3×#50452
C3×#49962
C3×#48882
C3×D3×#1072
C3×#48682
C3×D3×#1062
C3×#48152
C3×#48142
C3×D3×#1032
C3×D3×C22⋊C82
C3×#47232
C2×C3×#4853
D3×#4853