Finite Group Databasebeta

← C3×#81515 #11869654

Subgroups — C3×#81515 #11869654

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5627C211yesmaximal, characteristic
2C3×D3×#117C211yesmaximal, characteristic, complemented
3C32×#485C211yesmaximal, characteristic, complemented
4C3×#5045C211yesmaximal, characteristic, complemented
5C3×#5003C211yesmaximal, characteristic, complemented
6C3×#4882C211yesmaximal, characteristic, complemented
7C3×#4880C211yesmaximal, characteristic, complemented
8C3×#4863C211yesmaximal, characteristic, complemented
9C3×#4860C211yesmaximal, characteristic, complemented
10C3×#4811C211yesmaximal, characteristic, complemented
11C3×#4805C211yesmaximal, characteristic, complemented
12C3×#4804C211yesmaximal, characteristic, complemented
13C3×#4804C211yesmaximal, characteristic, complemented
14C3×#4737C211yesmaximal, characteristic, complemented
15C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
16C3×#3091—31nomaximal
17#81515C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×#894—21no—
29C3×#893—21no—
30C3×#892C2211yescharacteristic
31C3×#892C2211yescharacteristic
32C3×#892C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×D3×C4⋊C4C2211yescharacteristic
35C3×#882—21no—
36C3×#67⋊C4—21no—
37C3×D3×C22⋊C4—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×#821C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#818C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#525—31no—
62C2×C3×#117—31no—
63#5627C2×C311yescharacteristic
64D3×#117C2×C311yescharacteristic, complemented
65C3×#485—21no—
66C3×#485—31no—
67C3×#485D311yescharacteristic, complemented
68C3×#485C2×C311yescharacteristic, complemented
69C3×#484—31no—
70C3×#483—31no—
71C3×#482—31no—
72C3×#482—31no—
73C3×#481—31no—
74C3×#480—31no—
75C3×#427—31no—
76C3×#427—31no—
77C3×#416—31no—
78C3×#416—31no—
79C2×C3×C22⋊C8—31no—
80#5045C2×C311yescharacteristic, complemented
81#5003C2×C311yescharacteristic, complemented
82#4882C2×C311yescharacteristic, complemented
83#4880C2×C311yescharacteristic, complemented
84#4863C2×C311yescharacteristic, complemented
85#4860C2×C311yescharacteristic, complemented
86#4811C2×C311yescharacteristic, complemented
87#4805C2×C311yescharacteristic, complemented
88#4804C2×C311yescharacteristic, complemented
89#4804C2×C311yescharacteristic, complemented
90#4737C2×C311yescharacteristic, complemented
91D3×C22⋊C8C2×C311yescharacteristic, complemented
92C23×C3×D3D411yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—21no—
96C22×C3×Dic3D411yescharacteristic
97C3×#239—22no—
98C3×#239—22no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C22⋊C4—21no—
119C32×C42—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×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—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—
141#3091—31noSylow
142C2×C3×#41—31no—
143C23×C3×C4—31no—
144C2×#239C22×C311yescharacteristic
145C22×C4×D3C22×C311yescharacteristic
146C22×C3×C8—31no—
147C22×C3×C8—31no—
148C3×#123—61no—
149C3×C22⋊Q8—21no—
150C3×C22⋊Q8—31no—
151C3×C22⋊Q8C2×D311yescharacteristic
152C3×C22⋊Q8C22×C311yescharacteristic
153C3×#121—31no—
154C3×#121—31no—
155C3×#120—61no—
156C3×C4×D4—61no—
157C3×C4×D4—61no—
158C3×#117—21no—
159C3×#117—31no—
160C3×#117—31no—
161C3×#117—31no—
162C3×#117—31no—
163C3×#117—61no—
164C3×#117—61no—
165C3×#117C2×D311yescharacteristic
166C3×#117C22×C311yescharacteristic
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—61no—
170C2×C3×C42—61no—
171#946C22×C311yescharacteristic
172#930C22×C311yescharacteristic
173#926C22×C311yescharacteristic
174C2×D3×C8C22×C311yescharacteristic
175C2×D3×C8C22×C311yescharacteristic
176#895C22×C311yescharacteristic
177#894—21no—
178#893—21no—
179#892C22×C311yescharacteristic
180#892C22×C311yescharacteristic
181#892C22×C311yescharacteristic
182D3×C4⋊C4C22×C311yescharacteristic
183D3×C4⋊C4C22×C311yescharacteristic
184#882—21no—
185#67⋊C4—21no—
186D3×C22⋊C4—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×#103C2×D311yescharacteristic, complemented
207C3×#103C2×D311yescharacteristic, complemented
208C3×#103C22×C311yescharacteristic, complemented
209C3×#103C22×C311yescharacteristic, complemented
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
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#821C22×C311yescharacteristic, complemented
224#821C22×C311yescharacteristic, complemented
225(C2×D3)⋊C8C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227#818C22×C311yescharacteristic, complemented
228#817C22×C311yescharacteristic, complemented
229#809C22×C311yescharacteristic, complemented
230#809C22×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—21no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—42no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—42no—
262C3×D12—42no—
263C3×C4×D3—22no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—22no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×C4×D3#4112yes—
271C3×C4×D3#4112yes—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—31no—
277C2×#117—31no—
278#485—31no—
279#485C3×D311yescharacteristic, complemented
280#484—31no—
281#483—31no—
282#482—31no—
283#482—31no—
284#481—31no—
285#480—31no—
286#427—31no—
287#427—31no—
288#416—31no—
289#416—31no—
290C2×C22⋊C8—31no—
291C24×C3—31no—
292C23×D3C3×D411yescharacteristic
293C3×#41—62no—
294C3×#41—62no—
295C2×C3×Q8—21no—
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C23×C311yescharacteristic
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—62no—
309C22×C3×C4—62no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C23×C311yescharacteristic
315C2×#67—21no—
316C22×Dic3C3×D411yescharacteristic
317#239—22no—
318#239—22no—
319C2×D12—21no—
320C2×D12—21no—
321C2×D12C23×C311yescharacteristic
322C2×C4×D3—22no—
323C2×C4×D3—22no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3C3×D411yescharacteristic
328C2×C4×D3C3×D411yescharacteristic
329C2×C4×D3C23×C311yescharacteristic
330C2×C4×D3C23×C311yescharacteristic
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—62no—
336C2×C3×C8—62no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C23×C311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—41no—
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×C22⋊C4—61no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—41no—
375C3×C42—61no—
376C3×C42—61no—
377C3×C42—61no—
378C3×C42—61no—
379#217—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386C4⋊Dic3C23×C311yescharacteristic
387C4⋊Dic3C23×C311yescharacteristic
388C4⋊Dic3C23×C311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396C2×C3⋊C8C23×C311yescharacteristic
397C2×C3⋊C8C23×C311yescharacteristic
398D3×C8—22no—
399D3×C8—22no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—44no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3#12312yes—
413C2×C3×D3#13512yes—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3×Dic3—21no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3#12312yes—
426C2×#41—31no—
427C23×C4—31no—
428C22×C8—31no—
429C22×C8—31no—
430#123—61no—
431C22⋊Q8—31no—
432C22⋊Q8C2×C3×D311yescharacteristic
433#121—31no—
434#121—31no—
435#120—61no—
436C4×D4—61no—
437C4×D4—61no—
438#117—31no—
439#117—31no—
440#117—31no—
441#117—31no—
442#117—61no—
443#117—61no—
444#117C2×C3×D311yescharacteristic
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C22⋊C4—61no—
448C2×C42—61no—
449#107—31no—
450#107—31no—
451#107—31no—
452#107C2×C3×D311yescharacteristic, complemented
453#106—31no—
454#106—31no—
455#106—31no—
456#106C2×C3×D311yescharacteristic, complemented
457#103—31no—
458#103—31no—
459#103C2×C3×D311yescharacteristic, complemented
460#103C2×C3×D311yescharacteristic, complemented
461#102—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465C22⋊C8—31no—
466C22⋊C8—31no—
467C22⋊C8—31no—
468C22⋊C8C2×C3×D311yescharacteristic
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—62no—
473C23×C3—62no—
474C23×C3—61no—
475C23×C3—121no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×C3×D411yescharacteristic
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—21no—
481C22×D3—41no—
482C22×D3C2×C3×D411yescharacteristic
483C22×D3C2×C3×D411yescharacteristic
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—122no—
493C3×D4—122no—
494C3×D4—122no—
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—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—62no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—122no—
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4C2×C3×D411yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C24×C311yescharacteristic
534#67—42no—
535C2×Dic3—22no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3C2×C3×D411yescharacteristic
540C2×Dic3C2×C3×D411yescharacteristic
541D12—21no—
542D12—21no—
543D12—42no—
544D12—42no—
545C4×D3—22no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—22no—
549C4×D3—42no—
550C4×D3—42no—
551C4×D3—42no—
552C4×D3C3×#4112yes—
553C4×D3C3×#4112yes—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—41no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C2×C32—41no—
565C2×C32C2×#12311yescharacteristic
566C2×C32C2×#13511yescharacteristic
567C2×C32#57511yescharacteristic
568C3×D3—22no—
569C3×D3—22no—
570C3×D3—81no—
571C24—31no—
572#41—62no—
573#41—62no—
574C2×Q8C22×C3×D311yescharacteristic
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4C22×C3×D311yescharacteristic
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—62no—
593C2×C8—62no—
594C2×C8C22×C3×D311yescharacteristic
595C2×C8C22×C3×D311yescharacteristic
596C4⋊C4—21no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4C22×C3×D311yescharacteristic
604C4⋊C4C22×C3×D311yescharacteristic
605C4⋊C4C22×C3×D311yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C42—21no—
616C42—61no—
617C42—61no—
618C42—61no—
619C42—61no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—32no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—124no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×C3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—44no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3C3×#12312yes—
651C2×D3C3×#13512yes—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—32no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—81no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4D3×#4111yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4C2×C3×#4111yescharacteristic
677C3×C4C2×C3×#4111yescharacteristic
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3C3×#12312yes—
683C32#309111yescharacteristic, complemented, Sylow
684C23—31no—
685C23—31no—
686C23—62no—
687C23—62no—
688C23—61no—
689C23—121no—
690C23C3×D3×D411yescharacteristic
691Q8—21no—
692Q8—21no—
693D4—61no—
694D4—61no—
695D4—122no—
696D4—122no—
697D4—122no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—31no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4C3×D3×D411yescharacteristic
720C2×C4C23×C3×D311yescharacteristic
721C8—21no—
722C8—21no—
723C8—61no—
724C8—61no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—41no—
729C2×C3—41no—
730C2×C3—62no—
731C2×C3—62no—
732C2×C3—81no—
733C2×C3—241no—
734C2×C3D3×#12311yescharacteristic
735C2×C3D3×#13511yescharacteristic
736C2×C3#577711yescharacteristic
737C2×C3C2×C3×#12311yescharacteristic
738C2×C3C2×C3×#13511yescharacteristic
739C2×C3C3×#57511yescharacteristic
740D3—22no—
741D3—22no—
742D3—81no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—32no—
747C22—32no—
748C22—61no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—124no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22C2×C3×D3×D411yescharacteristic
757C4—21no—
758C4—32no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—61no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4C3×D3×#4111yescharacteristic
768C4C3×D3×#4111yescharacteristic
769C3—21no—
770C3#8151511yescharacteristic, direct product factor
771C3C3×#309111yescharacteristic, complemented
772C2—41no—
773C2—62no—
774C2—62no—
775C2—241no—
776C2C3×D3×#12311yescharacteristic
777C2C3×D3×#13511yescharacteristic
778C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC3×#5627C2
hypercenterC3×#485D3
hypocenterC3C3×#3091
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×D3×#117C2semidirect
3. C32×#485C2semidirect
4. C3×#5045C2semidirect
5. C3×#5003C2semidirect
6. C3×#4882C2semidirect
7. C3×#4880C2semidirect
8. C3×#4863C2semidirect
9. C3×#4860C2semidirect
10. C3×#4811C2semidirect
11. C3×#4805C2semidirect
12. C3×#4804C2semidirect
13. C3×#4804C2semidirect
14. C3×#4737C2semidirect
15. C3×D3×C22⋊C8C2semidirect
17. #81515C3direct (N × H)
41. C32×#107C22semidirect
42. C32×#106C22semidirect
43. C32×#103C22semidirect
44. C32×#103C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
49. C3×#821C22semidirect
50. C3×#821C22semidirect
53. C3×#818C22semidirect
54. C3×#817C22semidirect
55. C3×#809C22semidirect
56. C3×#809C22semidirect
57. C3×#808C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×#807C22semidirect
64. D3×#117C2×C3semidirect
67. C3×#485D3semidirect
68. C3×#485C2×C3semidirect
80. #5045C2×C3semidirect
81. #5003C2×C3semidirect
82. #4882C2×C3semidirect
83. #4880C2×C3semidirect
84. #4863C2×C3semidirect
85. #4860C2×C3semidirect
86. #4811C2×C3semidirect
87. #4805C2×C3semidirect
88. #4804C2×C3semidirect
89. #4804C2×C3semidirect
90. #4737C2×C3semidirect
91. D3×C22⋊C8C2×C3semidirect
194. C3×#107C2×D3semidirect
195. C3×#107C22×C3semidirect
200. C3×#106C2×D3semidirect
201. C3×#106C22×C3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C2×D3semidirect
208. C3×#103C22×C3semidirect
209. C3×#103C22×C3semidirect
220. #835C22×C3semidirect
221. #835C22×C3semidirect
223. #821C22×C3semidirect
224. #821C22×C3semidirect
227. #818C22×C3semidirect
228. #817C22×C3semidirect
229. #809C22×C3semidirect
230. #809C22×C3semidirect
231. #808C22×C3semidirect
232. #808C22×C3semidirect
233. #807C22×C3semidirect
234. #807C22×C3semidirect
279. #485C3×D3semidirect
452. #107C2×C3×D3semidirect
456. #106C2×C3×D3semidirect
459. #103C2×C3×D3semidirect
460. #103C2×C3×D3semidirect
683. C32#3091semidirect
770. C3#81515direct (N × H)
771. C3C3×#3091semidirect

Maximal subgroups

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

subgroupindex
C3×#56272
C3×D3×#1172
C32×#4852
C3×#50452
C3×#50032
C3×#48822
C3×#48802
C3×#48632
C3×#48602
C3×#48112
C3×#48052
C3×#48042
C3×#47372
C3×D3×C22⋊C82
C3×#30913
#815153