Finite Group Databasebeta

← C3×#79590 #11870412

Subgroups — C3×#79590 #11870412

Order 1152.

1051 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5548C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6C3×C4×#213C211yesmaximal, characteristic, complemented
7C3×C4×#213C211yesmaximal, characteristic, complemented
8C3×#4890C211yesmaximal, characteristic, complemented
9C3×#4882C211yesmaximal, characteristic, complemented
10C3×#4786C211yesmaximal, characteristic, complemented
11C3×#4774C211yesmaximal, characteristic, complemented
12C3×#4773C211yesmaximal, characteristic, complemented
13C3×#4759C211yesmaximal, characteristic, complemented
14C3×C4×D24C211yesmaximal, characteristic, complemented
15C3×#4685C211yesmaximal, characteristic, complemented
16C3×#3100—31nomaximal
17#79590C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235—21no—
20C22×C3×C4×D3—21no—
21C2×C32×D8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic, complemented
25C3×#938C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×C4×#67—21no—
30C3×C4×#67—21no—
31C2×C3×D24C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×D3×C4⋊C4C2211yescharacteristic
35C3×#888C2211yescharacteristic, complemented
36C3×#885—21no—
37C3×#884—21no—
38C3×#67⋊C4—21no—
39C3×D3×C22⋊C4—21no—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic, complemented
42C3×C42×D3C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic, complemented
46C32×C4×C8C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#818C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4×C3⋊C8C2211yescharacteristic, complemented
61C3×#532—31no—
62C2×C3×C4×D4—31no—
63#5548C2×C311yescharacteristic, complemented
64C4×D3×D4C2×C311yescharacteristic, complemented
65C3×#480—31no—
66C3×#480—31no—
67C3×#474—31no—
68C3×#474—31no—
69C3×#459—31no—
70C3×#459—31no—
71C3×#447—31no—
72C3×#447—31no—
73C3×C4×D8—21no—
74C3×C4×D8—31no—
75C3×C4×D8—31no—
76C3×C4×D8—31no—
77C3×C4×D8D311yescharacteristic, complemented
78C3×C4×D8C2×C311yescharacteristic, complemented
79C3×#431—31no—
80#5156C2×C311yescharacteristic, complemented
81#5150C2×C311yescharacteristic, complemented
82C4×#213C2×C311yescharacteristic, complemented
83C4×#213C2×C311yescharacteristic, complemented
84#4890C2×C311yescharacteristic, complemented
85#4882C2×C311yescharacteristic, complemented
86#4786C2×C311yescharacteristic, complemented
87#4774C2×C311yescharacteristic, complemented
88#4773C2×C311yescharacteristic, complemented
89#4759C2×C311yescharacteristic, complemented
90C4×D24C2×C311yescharacteristic, complemented
91#4685C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×D4—22no—
103C3×D3×D4—22no—
104C3×#235—44no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—44no—
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C32×D8—22no—
118C2×C32×C8C2311yescharacteristic
119C2×C32×C8C2311yescharacteristic
120C32×C4⋊C4C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C22⋊C4—21no—
124C32×C42C2311yescharacteristic
125C3×#217—21no—
126C3×#217—21no—
127C3×#213—22no—
128C3×#213—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143#3100—31noSylow
144C2×C3×#41—61no—
145C22×C3×D4—31no—
146C23×C3×C4—61no—
147C2×D3×D4C22×C311yescharacteristic
148C2×#235—21no—
149C22×C4×D3—21no—
150C2×C3×D8—21no—
151C2×C3×D8—31no—
152C2×C3×D8—31no—
153C2×C3×D8—31no—
154C2×C3×D8C2×D311yescharacteristic
155C2×C3×D8C22×C311yescharacteristic
156C3×C4⋊Q8—31no—
157C3×#127—31no—
158C3×#124—61no—
159C3×#121—31no—
160C3×#121—31no—
161C3×#121—61no—
162C3×C4×D4—21no—
163C3×C4×D4—21no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—61no—
169C3×C4×D4—61no—
170C3×C4×D4—61no—
171C3×C4×D4C2×D311yescharacteristic
172C3×C4×D4C2×D311yescharacteristic, complemented
173C3×C4×D4C22×C311yescharacteristic
174C3×C4×D4C22×C311yescharacteristic, complemented
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—61no—
177C2×C3×C42—31no—
178#940C22×C311yescharacteristic, complemented
179#938C22×C311yescharacteristic
180D4×Dic3C22×C311yescharacteristic
181C2×#213C22×C311yescharacteristic
182C2×#213C22×C311yescharacteristic
183C4×#67—21no—
184C4×#67—21no—
185C2×D24C22×C311yescharacteristic
186#895C22×C311yescharacteristic
187#893C22×C311yescharacteristic
188D3×C4⋊C4C22×C311yescharacteristic
189#888C22×C311yescharacteristic, complemented
190#885—21no—
191#884—21no—
192#67⋊C4—21no—
193D3×C22⋊C4—21no—
194C4×D12C22×C311yescharacteristic
195C4×D12C22×C311yescharacteristic, complemented
196C42×D3C22×C311yescharacteristic
197C3×#107—21no—
198C3×#107—31no—
199C3×#107—31no—
200C3×#107—31no—
201C3×#107C2×D311yescharacteristic, complemented
202C3×#107C22×C311yescharacteristic, complemented
203C3×C4⋊C8—31no—
204C3×C4⋊C8—31no—
205C3×#102—21no—
206C3×#102—21no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102C2×D311yescharacteristic
214C3×#102C2×D311yescharacteristic, complemented
215C3×#102C22×C311yescharacteristic
216C3×#102C22×C311yescharacteristic, complemented
217C3×C22⋊C8—31no—
218C3×C22⋊C8—31no—
219C3×C4×C8—21no—
220C3×C4×C8—31no—
221C3×C4×C8C2×D311yescharacteristic, complemented
222C3×C4×C8C22×C311yescharacteristic, complemented
223#832C22×C311yescharacteristic
224#832C22×C311yescharacteristic, complemented
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic, complemented
227(C2×D3)⋊C8C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#818C22×C311yescharacteristic, complemented
230Dic3⋊C8C22×C311yescharacteristic, complemented
231Dic3⋊C8C22×C311yescharacteristic, complemented
232#809C22×C311yescharacteristic
233#809C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235#807C22×C311yescharacteristic, complemented
236C4×C3⋊C8C22×C311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C22×C3×D3—24no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4#4112yescomplemented
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—42no—
252C2×C32×C4—42no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—24no—
257C3×#67—42no—
258C3×#67—42no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—42no—
270C3×D12#4112yescomplemented
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—41no—
274C3×C4×D3—42no—
275C3×C4×D3—42no—
276C3×C4×D3—42no—
277C3×C4×D3—42no—
278C3×C4×D3D814yescomplemented
279C3×Dic6—42no—
280C32×C8—21no—
281C32×C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—31no—
285C2×C4×D4—31no—
286#480—31no—
287#480—31no—
288#474—31no—
289#474—31no—
290#459—31no—
291#459—31no—
292#447—31no—
293#447—31no—
294C4×D8—31no—
295C4×D8—31no—
296C4×D8—31no—
297C4×D8C3×D311yescharacteristic, complemented
298#431—31no—
299C24×C3—61no—
300C23×D3—21no—
301C3×#41—124no—
302C2×C3×Q8—61no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—62no—
312C2×C3×D4—62no—
313C2×C3×D4—61no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C23×C311yescharacteristic
317C2×C3×D4C23×C311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—41no—
326C22×C3×C4—41no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C22×C3×C4—124no—
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—21no—
337C22×Dic3—21no—
338D3×D4—22no—
339D3×D4—22no—
340#235—44no—
341C2×D12—21no—
342C2×D12C23×C311yescharacteristic
343C2×D12C23×C311yescharacteristic
344C2×C4×D3—21no—
345C2×C4×D3—21no—
346C2×C4×D3—21no—
347C2×C4×D3—21no—
348C2×C4×D3—44no—
349C2×C4×D3C3×D411yescharacteristic
350C2×C4×D3C3×D411yescharacteristic
351C2×C4×D3C23×C311yescharacteristic
352C2×Dic6—21no—
353C3×D8—24no—
354C3×D8—22no—
355C3×D8—22no—
356C3×D8—62no—
357C3×D8—62no—
358C3×D8—62no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8C22×D311yescharacteristic
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C23×C311yescharacteristic
366C2×C3×C8C23×C311yescharacteristic
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C23×C311yescharacteristic
376C3×C4⋊C4C23×C311yescharacteristic
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C22⋊C4—41no—
382C3×C22⋊C4—41no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C42—21no—
390C3×C42—31no—
391C3×C42—31no—
392C3×C42—31no—
393C3×C42C22×D311yescharacteristic
394C3×C42C23×C311yescharacteristic
395#217—21no—
396#217—21no—
397#213—22no—
398#213—22no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—21no—
403C4⋊Dic3C23×C311yescharacteristic
404C4⋊Dic3C23×C311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—21no—
407C4×Dic3C3×D411yescharacteristic
408C4×Dic3C3×D411yescharacteristic
409C4×Dic3C23×C311yescharacteristic
410C2×C3⋊C8C23×C311yescharacteristic
411C2×C3⋊C8C23×C311yescharacteristic
412D24—22no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—48no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3C2×D812yes—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4C2×D812yes—
434C32×C4C2×#4111yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3C2×D812yes—
441C2×#41—61no—
442C22×D4—31no—
443C23×C4—61no—
444C2×D8—31no—
445C2×D8—31no—
446C2×D8—31no—
447C2×D8C2×C3×D311yescharacteristic
448C4⋊Q8—31no—
449#127—31no—
450#124—61no—
451#121—31no—
452#121—31no—
453#121—61no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—61no—
459C4×D4—61no—
460C4×D4—61no—
461C4×D4C2×C3×D311yescharacteristic
462C4×D4C2×C3×D311yescharacteristic, complemented
463C2×C4⋊C4—31no—
464C2×C22⋊C4—61no—
465C2×C42—31no—
466#107—31no—
467#107—31no—
468#107—31no—
469#107C2×C3×D311yescharacteristic, complemented
470C4⋊C8—31no—
471C4⋊C8—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102C2×C3×D311yescharacteristic
479#102C2×C3×D311yescharacteristic, complemented
480C22⋊C8—31no—
481C22⋊C8—31no—
482C4×C8—31no—
483C4×C8C2×C3×D311yescharacteristic, complemented
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—64no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—122no—
495C23×C3—122no—
496C22×D3—24no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3C2×C3×D411yescharacteristic
502C3×Q8—122no—
503C3×D4—22no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—22no—
511C3×D4—32no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—64no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—122no—
519C3×D4—122no—
520C3×D4—122no—
521C3×D4—122no—
522C3×D4#23512yescomplemented
523C3×D4C3×#4112yescomplemented
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—34no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—42no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4—42no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—82no—
546C2×C3×C4—82no—
547C2×C3×C4—121no—
548C2×C3×C4—122no—
549C2×C3×C4—122no—
550C2×C3×C4—122no—
551C2×C3×C4—122no—
552C2×C3×C4—122no—
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4C2×C3×D411yescharacteristic
556C2×C3×C4C2×C3×D411yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C24×C311yescharacteristic
559#67—24no—
560#67—42no—
561#67—42no—
562#67—42no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—42no—
566C2×Dic3C2×C3×D411yescharacteristic
567C2×Dic3C2×C3×D411yescharacteristic
568C2×Dic3C2×C3×D411yescharacteristic
569D12—21no—
570D12—21no—
571D12—21no—
572D12—42no—
573D12C3×#4112yescomplemented
574C4×D3—21no—
575C4×D3—21no—
576C4×D3—41no—
577C4×D3—42no—
578C4×D3—42no—
579C4×D3—42no—
580C4×D3—42no—
581C4×D3C3×D814yescomplemented
582Dic6—42no—
583C3×C8—22no—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—41no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C2×C32—42no—
594C2×C32—81no—
595C2×C32#52511yescharacteristic
596C2×C32C22×D811yescharacteristic
597C2×C32#57511yescharacteristic
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—81no—
601C24—61no—
602#41—124no—
603C2×Q8—61no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—62no—
611C2×D4—62no—
612C2×D4—61no—
613C2×D4C22×C3×D311yescharacteristic
614C2×D4C22×C3×D311yescharacteristic
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—124no—
626D8—22no—
627D8—62no—
628D8—62no—
629D8—62no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8C22×C3×D311yescharacteristic
633C2×C8C22×C3×D311yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4C22×C3×D311yescharacteristic
639C4⋊C4C22×C3×D311yescharacteristic
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C42—31no—
649C42—31no—
650C42—31no—
651C42C22×C3×D311yescharacteristic
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—62no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—128no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C22×C3×D411yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—22no—
686C2×D3—48no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3C2×C3×D812yes—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—22no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—32no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—81no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4D3×D812yes—
711C3×C4C2×C3×D812yes—
712C3×C4C2×#23511yescharacteristic
713C3×C4D3×#4111yescharacteristic
714C3×C4C2×C3×#4111yescharacteristic
715C3×C4C2×C3×#4111yescharacteristic
716Dic3—21no—
717Dic3—21no—
718Dic3—41no—
719Dic3—41no—
720Dic3C2×C3×D812yes—
721C32#310011yescharacteristic, complemented, Sylow
722C23—21no—
723C23—21no—
724C23—31no—
725C23—64no—
726C23—61no—
727C23—61no—
728C23—122no—
729C23—122no—
730Q8—122no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—32no—
735D4—64no—
736D4—61no—
737D4—61no—
738D4—61no—
739D4—122no—
740D4—122no—
741D4—122no—
742D4—122no—
743D4C3×#23512yescomplemented
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—31no—
747C2×C4—34no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—121no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4C3×D3×D411yescharacteristic
763C2×C4C3×D3×D411yescharacteristic
764C2×C4C23×C3×D311yescharacteristic
765C8—21no—
766C8—21no—
767C8—61no—
768C8—61no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—42no—
773C2×C3—42no—
774C2×C3—62no—
775C2×C3—82no—
776C2×C3—82no—
777C2×C3—81no—
778C2×C3—81no—
779C2×C3—122no—
780C2×C3—241no—
781C2×C3#554711yescharacteristic
782C2×C3C2×D3×D811yescharacteristic
783C2×C3#576811yescharacteristic
784C2×C3C3×#52511yescharacteristic
785C2×C3C22×C3×D811yescharacteristic
786C2×C3C3×#57511yescharacteristic
787D3—22no—
788D3—42no—
789D3—81no—
790C22—22no—
791C22—32no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—61no—
798C22—61no—
799C22—62no—
800C22—128no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22C2×C3×D3×D411yescharacteristic
807C4—21no—
808C4—32no—
809C4—41no—
810C4—41no—
811C4—61no—
812C4—61no—
813C4—121no—
814C4—121no—
815C4C3×D3×D812yes—
816C4C2×C3×#23511yescharacteristic
817C4C3×D3×#4111yescharacteristic
818C3—21no—
819C3#7959011yescharacteristic, direct product factor
820C3C3×#310011yescharacteristic, complemented
821C2—42no—
822C2—62no—
823C2—81no—
824C2—122no—
825C2—241no—
826C2C3×#554711yescharacteristic
827C2C2×C3×D3×D811yescharacteristic
828C2C3×#576811yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
hypercenterC3×C4×D8D3
hypocenterC3C3×#3100
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5548C2semidirect
2. C3×C4×D3×D4C2semidirect
3. C32×C4×D8C2semidirect
4. C3×#5156C2semidirect
5. C3×#5150C2semidirect
6. C3×C4×#213C2semidirect
7. C3×C4×#213C2semidirect
8. C3×#4890C2semidirect
9. C3×#4882C2semidirect
10. C3×#4786C2semidirect
11. C3×#4774C2semidirect
12. C3×#4773C2semidirect
13. C3×#4759C2semidirect
14. C3×C4×D24C2semidirect
15. C3×#4685C2semidirect
17. #79590C3direct (N × H)
23. C32×C4×D4C22semidirect
24. C3×#940C22semidirect
35. C3×#888C22semidirect
41. C3×C4×D12C22semidirect
43. C32×#107C22semidirect
45. C32×#102C22semidirect
46. C32×C4×C8C22semidirect
48. C3×#832C22semidirect
50. C3×#821C22semidirect
53. C3×#818C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#807C22semidirect
59. C3×#807C22semidirect
60. C3×C4×C3⋊C8C22semidirect
63. #5548C2×C3semidirect
64. C4×D3×D4C2×C3semidirect
77. C3×C4×D8D3semidirect
78. C3×C4×D8C2×C3semidirect
80. #5156C2×C3semidirect
81. #5150C2×C3semidirect
82. C4×#213C2×C3semidirect
83. C4×#213C2×C3semidirect
84. #4890C2×C3semidirect
85. #4882C2×C3semidirect
86. #4786C2×C3semidirect
87. #4774C2×C3semidirect
88. #4773C2×C3semidirect
89. #4759C2×C3semidirect
90. C4×D24C2×C3semidirect
91. #4685C2×C3semidirect
172. C3×C4×D4C2×D3semidirect
174. C3×C4×D4C22×C3semidirect
178. #940C22×C3semidirect
189. #888C22×C3semidirect
195. C4×D12C22×C3semidirect
201. C3×#107C2×D3semidirect
202. C3×#107C22×C3semidirect
214. C3×#102C2×D3semidirect
216. C3×#102C22×C3semidirect
221. C3×C4×C8C2×D3semidirect
222. C3×C4×C8C22×C3semidirect
224. #832C22×C3semidirect
226. #821C22×C3semidirect
229. #818C22×C3semidirect
230. Dic3⋊C8C22×C3semidirect
231. Dic3⋊C8C22×C3semidirect
233. #809C22×C3semidirect
234. #807C22×C3semidirect
235. #807C22×C3semidirect
236. C4×C3⋊C8C22×C3semidirect
248. C32×D4#41semidirect
270. C3×D12#41semidirect
278. C3×C4×D3D8semidirect
297. C4×D8C3×D3semidirect
462. C4×D4C2×C3×D3semidirect
469. #107C2×C3×D3semidirect
479. #102C2×C3×D3semidirect
483. C4×C8C2×C3×D3semidirect
522. C3×D4#235semidirect
523. C3×D4C3×#41semidirect
573. D12C3×#41semidirect
581. C4×D3C3×D8semidirect
721. C32#3100semidirect
743. D4C3×#235semidirect
819. C3#79590direct (N × H)
820. C3C3×#3100semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
C3×C4×D3×D42
C32×C4×D82
C3×#51562
C3×#51502
C3×C4×#2132
C3×#48902
C3×#48822
C3×#47862
C3×#47742
C3×#47732
C3×#47592
C3×C4×D242
C3×#46852
C3×#31003
#795903