Finite Group Databasebeta

← C3×#80557 #11885791

Subgroups — C3×#80557 #11885791

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2C2×C3×D3×D8C211yesmaximal, characteristic, complemented
3C3×#5676C211yesmaximal, characteristic, complemented
4C3×#5554C211yesmaximal, characteristic, complemented
5C32×#463C211yesmaximal, characteristic, complemented
6C3×#5169C211yesmaximal, characteristic, complemented
7C3×#5158C211yesmaximal, characteristic, complemented
8C3×#5059C211yesmaximal, characteristic, complemented
9C3×C4×#213C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4834C211yesmaximal, characteristic, complemented
12C3×#4813C211yesmaximal, characteristic, complemented
13C3×#4810C211yesmaximal, characteristic, complemented
14C3×#4776C211yesmaximal, characteristic, complemented
15C3×#4775C211yesmaximal, characteristic, complemented
16C3×#3280—31nomaximal
17#80557C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C2×C32×D8C2211yescharacteristic
24C32×#124C2211yescharacteristic, complemented
25C32×C4×D4C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#938C2211yescharacteristic, complemented
30C2×C3×#214C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#930—21no—
34C2×C3×(C2×D3)⋊C4—21no—
35C3×#916—24no—
36C3×D3×D8—24no—
37C2×C3×D24C2211yescharacteristic
38C2×C3×#204C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic, complemented
41C3×#897C2211yescharacteristic
42C3×#895C2211yescharacteristic, complemented
43C3×#886—21no—
44C3×#884—21no—
45C3×#883—21no—
46C3×#882—21no—
47C3×#882—21no—
48C3×D3×C22⋊C4—21no—
49C3×#875C2211yescharacteristic, complemented
50C3×C4×D12C2211yescharacteristic
51C3×C4×D12C2211yescharacteristic, complemented
52C32×C4⋊C8C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61C3×#807C2211yescharacteristic, complemented
62C3×C4×C3⋊C8C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64C22×C3×D8—31no—
65C3×#546—31no—
66C3×#546—31no—
67C2×#916C2×C311yescharacteristic, complemented
68C2×D3×D8C2×C311yescharacteristic, complemented
69#5676C2×C311yescharacteristic, complemented
70#5554C2×C311yescharacteristic, complemented
71C3×#495—31no—
72C3×#467—31no—
73C3×#466—31no—
74C3×#463—21no—
75C3×#463—31no—
76C3×#463D311yescharacteristic, complemented
77C3×#463C2×C311yescharacteristic, complemented
78C3×#450—31no—
79C3×#450—31no—
80C3×#449—31no—
81C3×#449—31no—
82C3×C4×D8—31no—
83C3×C8×D4—31no—
84#5169C2×C311yescharacteristic, complemented
85#5158C2×C311yescharacteristic, complemented
86#5059C2×C311yescharacteristic, complemented
87C4×#213C2×C311yescharacteristic, complemented
88#4844C2×C311yescharacteristic, complemented
89#4834C2×C311yescharacteristic, complemented
90#4813C2×C311yescharacteristic, complemented
91#4810C2×C311yescharacteristic, complemented
92#4776C2×C311yescharacteristic, complemented
93#4775C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×#239—22no—
106C3×#239—41no—
107C3×#237—22no—
108C3×#237—41no—
109C3×D3×D4—22no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C3×D3×D4—41no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12D411yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123C32×SD16—22no—
124C32×D8—22no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128C32×C22⋊C4—21no—
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C32×C42C2311yescharacteristic
132C3×#217—21no—
133C3×#216—22no—
134C3×#215—41no—
135C3×#214—41no—
136C3×#213—22no—
137C3×#213D414yescomplemented
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4D411yescharacteristic
145C3×(C2×D3)⋊C4D411yescharacteristic
146C3×C4⋊Dic3—21no—
147C3×C4⋊Dic3D411yescharacteristic
148C3×C4⋊Dic3C2311yescharacteristic
149C3×Dic3⋊C4—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×D24—22no—
153C3×#204—22no—
154C3×D3×C8—22no—
155C3×D3×C8—22no—
156#3280—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C2×#239C22×C311yescharacteristic, complemented
162C2×#237C22×C311yescharacteristic, complemented
163C2×D3×D4C22×C311yescharacteristic
164C2×D3×D4C22×C311yescharacteristic
165C3×#135—64no—
166C2×C3×Q16—31no—
167C2×C3×SD16—21no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×SD16C22×C311yescharacteristic, complemented
173C2×C3×D8—21no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C2×C3×D8—64no—
178C2×C3×D8C2×D311yescharacteristic
179C2×C3×D8C22×C311yescharacteristic
180C22×C3×C8—31no—
181C22×C3×C8—31no—
182C3×#124—21no—
183C3×#124—31no—
184C3×#124C2×D311yescharacteristic, complemented
185C3×#124C22×C311yescharacteristic, complemented
186C3×#123—61no—
187C3×#123—61no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—31no—
190C3×#121—31no—
191C3×#121—31no—
192C3×#121—61no—
193C3×#121—61no—
194C3×#120—61no—
195C3×#120—61no—
196C3×C4×D4—21no—
197C3×C4×D4—31no—
198C3×C4×D4—31no—
199C3×C4×D4C2×D311yescharacteristic, complemented
200C3×C4×D4C22×C311yescharacteristic, complemented
201C2×C3×C22⋊C4—61no—
202C2×C3×C22⋊C4—61no—
203#946C22×C311yescharacteristic
204C2×#216C22×C311yescharacteristic, complemented
205C2×#215C22×C311yescharacteristic, complemented
206#938C22×C311yescharacteristic, complemented
207C2×#214C22×C311yescharacteristic, complemented
208C2×#213C22×C311yescharacteristic
209C2×#213C22×C311yescharacteristic
210#930—21no—
211C2×(C2×D3)⋊C4—21no—
212#916—24no—
213D3×D8—24no—
214C2×D24C22×C311yescharacteristic
215C2×#204C22×C311yescharacteristic, complemented
216C2×D3×C8C22×C311yescharacteristic
217C2×D3×C8C22×C311yescharacteristic, complemented
218#897C22×C311yescharacteristic
219#895C22×C311yescharacteristic, complemented
220#886—21no—
221#884—21no—
222#883—21no—
223#882—21no—
224#882—21no—
225D3×C22⋊C4—21no—
226#875C22×C311yescharacteristic, complemented
227C4×D12C22×C311yescharacteristic
228C4×D12C22×C311yescharacteristic, complemented
229C3×#107—31no—
230C3×C4⋊C8—21no—
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×C4⋊C8C22×C311yescharacteristic, complemented
233C3×#103—21no—
234C3×#103—31no—
235C3×#103C2×D311yescharacteristic, complemented
236C3×#103C22×C311yescharacteristic, complemented
237C3×#102—21no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102C2×D311yescharacteristic, complemented
242C3×#102C22×C311yescharacteristic, complemented
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×C4×C8—31no—
246#832C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic, complemented
248(C2×D3)⋊C8C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250#816C22×C311yescharacteristic, complemented
251#809C22×C311yescharacteristic, complemented
252#807C22×C311yescharacteristic, complemented
253C4×C3⋊C8C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C23×C32—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3—81no—
264C22×C3×D3C2×D411yescharacteristic
265C22×C3×D3C2×D411yescharacteristic
266C32×Q8—21no—
267C32×Q8—21no—
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4C2×D412yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—81no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—42no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—22no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—42no—
292C3×D12—81no—
293C3×D12C2×D412yes—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298C3×C4×D3—42no—
299C3×C4×D3—81no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302C32×C8—21no—
303C32×C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#135—31no—
307C22×D8—31no—
308#546—31no—
309#546—31no—
310#495—31no—
311#467—31no—
312#466—31no—
313#463—31no—
314#463C3×D311yescharacteristic, complemented
315#450—31no—
316#450—31no—
317#449—31no—
318#449—31no—
319C4×D8—31no—
320C8×D4—31no—
321C24×C3—61no—
322C24×C3—61no—
323C23×D3—21no—
324C23×D3—21no—
325C3×#41—62no—
326C3×#41—62no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C23×C311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—121no—
347C2×C3×D4—121no—
348C2×C3×D4C22×D311yescharacteristic
349C2×C3×D4C22×D311yescharacteristic
350C2×C3×D4C23×C311yescharacteristic
351C2×C3×D4C23×C311yescharacteristic
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—41no—
357C22×C3×C4—61no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C22×Dic3—21no—
365#239—22no—
366#239—41no—
367#237—22no—
368#237—41no—
369D3×D4—22no—
370D3×D4—22no—
371D3×D4—41no—
372D3×D4—41no—
373C2×D12—21no—
374C2×D12—21no—
375C2×D12C3×D411yescharacteristic
376C2×D12C23×C311yescharacteristic
377C2×D12C23×C311yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3—21no—
380C2×C4×D3C23×C311yescharacteristic
381C2×C4×D3C23×C311yescharacteristic
382C2×Dic6C23×C311yescharacteristic
383C3×Q16—62no—
384C3×SD16—22no—
385C3×SD16—22no—
386C3×SD16—42no—
387C3×SD16—62no—
388C3×SD16—121no—
389C3×SD16—121no—
390C3×D8—22no—
391C3×D8—22no—
392C3×D8—34no—
393C3×D8—42no—
394C3×D8—62no—
395C3×D8—62no—
396C2×C3×C8—21no—
397C2×C3×C8—21no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8—62no—
401C2×C3×C8—62no—
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C23×C311yescharacteristic
405C2×C3×C8C23×C311yescharacteristic
406C3×C4⋊C4—21no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4C22×D311yescharacteristic
412C3×C4⋊C4C23×C311yescharacteristic
413C3×C22⋊C4—21no—
414C3×C22⋊C4—21no—
415C3×C22⋊C4—21no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—41no—
422C3×C22⋊C4—41no—
423C3×C22⋊C4—41no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C42—21no—
432C3×C42C22×D311yescharacteristic
433C3×C42C23×C311yescharacteristic
434#217—21no—
435#216—22no—
436#215—41no—
437#214—41no—
438#213—22no—
439#213C3×D414yescomplemented
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4C3×D411yescharacteristic
447(C2×D3)⋊C4C3×D411yescharacteristic
448C4⋊Dic3—21no—
449C4⋊Dic3C3×D411yescharacteristic
450C4⋊Dic3C23×C311yescharacteristic
451Dic3⋊C4—21no—
452C2×C3⋊C8C23×C311yescharacteristic
453C2×C3⋊C8C23×C311yescharacteristic
454D24—22no—
455#204—22no—
456D3×C8—22no—
457D3×C8—22no—
458C22×C32—22no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32C22×D411yescharacteristic
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—22no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—84no—
477C2×C3×D3—84no—
478C2×C3×D3#13512yescomplemented
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4—41no—
483C32×C4C22×D411yescharacteristic
484C32×C4H(5,𝔽2)11yescharacteristic
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C2×#41—31no—
490C2×#41—31no—
491C22×D4—31no—
492C22×D4—31no—
493#135—64no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16C2×C3×D311yescharacteristic, complemented
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—31no—
502C2×D8—64no—
503C2×D8C2×C3×D311yescharacteristic
504C22×C8—31no—
505C22×C8—31no—
506#124—31no—
507#124C2×C3×D311yescharacteristic, complemented
508#123—61no—
509#123—61no—
510C22⋊Q8—31no—
511C22⋊Q8—31no—
512#121—31no—
513#121—31no—
514#121—61no—
515#121—61no—
516#120—61no—
517#120—61no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4C2×C3×D311yescharacteristic, complemented
521C2×C22⋊C4—61no—
522C2×C22⋊C4—61no—
523#107—31no—
524C4⋊C8C2×C3×D311yescharacteristic, complemented
525#103—31no—
526#103C2×C3×D311yescharacteristic, complemented
527#102—31no—
528#102—31no—
529#102—31no—
530#102C2×C3×D311yescharacteristic, complemented
531C22⋊C8—31no—
532C22⋊C8—31no—
533C4×C8—31no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—31no—
539C23×C3—31no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—122no—
545C23×C3—122no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C23×C3—241no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—81no—
557C22×D3—81no—
558C22×D3C2×C3×D411yescharacteristic
559C22×D3C2×C3×D411yescharacteristic
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8—41no—
565C3×Q8—41no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—22no—
575C3×D4—32no—
576C3×D4—41no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—62no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—122no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—241no—
588C3×D4—241no—
589C3×D4D3×D412yes—
590C3×D4C2×C3×D412yes—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—81no—
609C2×C3×C4—81no—
610C2×C3×C4—82no—
611C2×C3×C4—122no—
612C2×C3×C4—122no—
613C2×C3×C4—241no—
614C2×C3×C4D3×D411yescharacteristic
615C2×C3×C4D3×D411yescharacteristic
616C2×C3×C4C2×C3×D411yescharacteristic
617C2×C3×C4C2×C3×D411yescharacteristic
618C2×C3×C4C23×D311yescharacteristic
619C2×C3×C4C24×C311yescharacteristic
620#67—42no—
621#67—42no—
622#67—42no—
623#67—81no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—42no—
627C2×Dic3C2×C3×D411yescharacteristic
628C2×Dic3C2×C3×D411yescharacteristic
629D12—22no—
630D12—21no—
631D12—21no—
632D12—21no—
633D12—42no—
634D12—81no—
635D12C2×C3×D412yes—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—42no—
641C4×D3—81no—
642Dic6—21no—
643Dic6—21no—
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—21no—
647C3×C8—21no—
648C3×C8—32no—
649C3×C8—41no—
650C3×C8—41no—
651C3×C8—61no—
652C3⋊C8—21no—
653C3⋊C8C2×C3×D412yes—
654C2×C32—42no—
655C2×C32—81no—
656C2×C32D4211yescharacteristic
657C2×C32C2×#13511yescharacteristic
658C2×C32#57611yescharacteristic
659C3×D3—22no—
660C3×D3—41no—
661C3×D3—42no—
662C3×D3—81no—
663C24—61no—
664C24—61no—
665#41—62no—
666#41—62no—
667#41—121no—
668#41—121no—
669C2×Q8—31no—
670C2×Q8C22×C3×D311yescharacteristic
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—121no—
683C2×D4—121no—
684C2×D4C22×C3×D311yescharacteristic
685C2×D4C22×C3×D311yescharacteristic
686C22×C4—21no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692Q16—62no—
693SD16—22no—
694SD16—62no—
695SD16—121no—
696SD16—121no—
697D8—22no—
698D8—34no—
699D8—62no—
700D8—62no—
701C2×C8—31no—
702C2×C8—31no—
703C2×C8—62no—
704C2×C8—62no—
705C2×C8C22×C3×D311yescharacteristic
706C2×C8C22×C3×D311yescharacteristic
707C4⋊C4—31no—
708C4⋊C4—31no—
709C4⋊C4—61no—
710C4⋊C4—61no—
711C4⋊C4C22×C3×D311yescharacteristic
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—31no—
716C22⋊C4—31no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C42C22×C3×D311yescharacteristic
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—32no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—62no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—244no—
757C22×C3—244no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C22×C3×D411yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—22no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—84no—
772C2×D3—84no—
773C2×D3C3×#13512yescomplemented
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—61no—
787C3×C4—61no—
788C3×C4—81no—
789C3×C4—81no—
790C3×C4—121no—
791C3×C4—121no—
792C3×C4C2×D3×D411yescharacteristic
793C3×C4#100911yescharacteristic
794C3×C4C22×C3×D411yescharacteristic
795C3×C4C3×H(5,𝔽2)11yescharacteristic
796Dic3—21no—
797Dic3—21no—
798Dic3—41no—
799Dic3—41no—
800C32#328011yescharacteristic, complemented, Sylow
801C23—21no—
802C23—21no—
803C23—31no—
804C23—31no—
805C23—61no—
806C23—61no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—241no—
812C23—241no—
813Q8—21no—
814Q8—21no—
815Q8—61no—
816Q8—61no—
817D4—21no—
818D4—21no—
819D4—21no—
820D4—32no—
821D4—62no—
822D4—61no—
823D4—61no—
824D4—61no—
825D4—122no—
826D4—122no—
827D4—122no—
828D4—122no—
829D4—241no—
830D4—241no—
831D4C3×D3×D412yes—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—81no—
843C2×C4—122no—
844C2×C4—122no—
845C2×C4—241no—
846C2×C4C3×D3×D411yescharacteristic
847C2×C4C3×D3×D411yescharacteristic
848C2×C4C23×C3×D311yescharacteristic
849C8—21no—
850C8—21no—
851C8—32no—
852C8—61no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—42no—
858C2×C3—62no—
859C2×C3—82no—
860C2×C3—81no—
861C2×C3—81no—
862C2×C3—121no—
863C2×C3—122no—
864C2×C3—161no—
865C2×C3—241no—
866C2×C3#560911yescharacteristic
867C2×C3D3×#13511yescharacteristic
868C2×C3#577411yescharacteristic
869C2×C3C3×D4211yescharacteristic
870C2×C3C2×C3×#13511yescharacteristic
871C2×C3C3×#57611yescharacteristic
872D3—22no—
873D3—41no—
874D3—42no—
875D3—81no—
876C22—22no—
877C22—32no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—61no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—62no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—244no—
895C22—244no—
896C22C2×C3×D3×D411yescharacteristic
897C4—21no—
898C4—21no—
899C4—41no—
900C4—41no—
901C4—61no—
902C4—61no—
903C4—121no—
904C4—121no—
905C4C2×C3×D3×D411yescharacteristic
906C4C3×#100911yescharacteristic
907C3—21no—
908C3#8055711yescharacteristic, direct product factor
909C3C3×#328011yescharacteristic, complemented
910C2—42no—
911C2—62no—
912C2—81no—
913C2—121no—
914C2—122no—
915C2—241no—
916C2C3×#560911yescharacteristic
917C2C3×D3×#13511yescharacteristic
918C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
hypercenterC3×#463D3
hypocenterC3C3×#3280
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. C2×C3×D3×D8C2semidirect
3. C3×#5676C2semidirect
4. C3×#5554C2semidirect
5. C32×#463C2semidirect
6. C3×#5169C2semidirect
7. C3×#5158C2semidirect
8. C3×#5059C2semidirect
9. C3×C4×#213C2semidirect
10. C3×#4844C2semidirect
11. C3×#4834C2semidirect
12. C3×#4813C2semidirect
13. C3×#4810C2semidirect
14. C3×#4776C2semidirect
15. C3×#4775C2semidirect
17. #80557C3direct (N × H)
18. C2×C3×#239C22semidirect
19. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
24. C32×#124C22semidirect
25. C32×C4×D4C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#938C22semidirect
30. C2×C3×#214C22semidirect
38. C2×C3×#204C22semidirect
40. C2×C3×D3×C8C22semidirect
42. C3×#895C22semidirect
49. C3×#875C22semidirect
51. C3×C4×D12C22semidirect
52. C32×C4⋊C8C22semidirect
53. C32×#103C22semidirect
54. C32×#102C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#816C22semidirect
60. C3×#809C22semidirect
61. C3×#807C22semidirect
62. C3×C4×C3⋊C8C22semidirect
67. C2×#916C2×C3semidirect
68. C2×D3×D8C2×C3semidirect
69. #5676C2×C3semidirect
70. #5554C2×C3semidirect
76. C3×#463D3semidirect
77. C3×#463C2×C3semidirect
84. #5169C2×C3semidirect
85. #5158C2×C3semidirect
86. #5059C2×C3semidirect
87. C4×#213C2×C3semidirect
88. #4844C2×C3semidirect
89. #4834C2×C3semidirect
90. #4813C2×C3semidirect
91. #4810C2×C3semidirect
92. #4776C2×C3semidirect
93. #4775C2×C3semidirect
137. C3×#213D4semidirect
161. C2×#239C22×C3semidirect
162. C2×#237C22×C3semidirect
171. C2×C3×SD16C2×D3semidirect
172. C2×C3×SD16C22×C3semidirect
184. C3×#124C2×D3semidirect
185. C3×#124C22×C3semidirect
199. C3×C4×D4C2×D3semidirect
200. C3×C4×D4C22×C3semidirect
204. C2×#216C22×C3semidirect
205. C2×#215C22×C3semidirect
206. #938C22×C3semidirect
207. C2×#214C22×C3semidirect
215. C2×#204C22×C3semidirect
217. C2×D3×C8C22×C3semidirect
219. #895C22×C3semidirect
226. #875C22×C3semidirect
228. C4×D12C22×C3semidirect
231. C3×C4⋊C8C2×D3semidirect
232. C3×C4⋊C8C22×C3semidirect
235. C3×#103C2×D3semidirect
236. C3×#103C22×C3semidirect
241. C3×#102C2×D3semidirect
242. C3×#102C22×C3semidirect
246. #832C22×C3semidirect
247. #821C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. #816C22×C3semidirect
251. #809C22×C3semidirect
252. #807C22×C3semidirect
253. C4×C3⋊C8C22×C3semidirect
314. #463C3×D3semidirect
439. #213C3×D4semidirect
478. C2×C3×D3#135semidirect
498. C2×SD16C2×C3×D3semidirect
507. #124C2×C3×D3semidirect
520. C4×D4C2×C3×D3semidirect
524. C4⋊C8C2×C3×D3semidirect
526. #103C2×C3×D3semidirect
530. #102C2×C3×D3semidirect
773. C2×D3C3×#135semidirect
800. C32#3280semidirect
908. C3#80557direct (N × H)
909. C3C3×#3280semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
C2×C3×D3×D82
C3×#56762
C3×#55542
C32×#4632
C3×#51692
C3×#51582
C3×#50592
C3×C4×#2132
C3×#48442
C3×#48342
C3×#48132
C3×#48102
C3×#47762
C3×#47752
C3×#32803
#805573