Finite Group Databasebeta

← C3×#83505 #11885794

Subgroups — C3×#83505 #11885794

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#546C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic, complemented
4C3×#5550C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6C3×#5218C211yesmaximal, characteristic, complemented
7C3×#5059C211yesmaximal, characteristic, complemented
8C3×#5057C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#5046C211yesmaximal, characteristic, complemented
11C3×#5038C211yesmaximal, characteristic, complemented
12C3×#5037C211yesmaximal, characteristic, complemented
13C3×#5016C211yesmaximal, characteristic, complemented
14C3×C4×#213C211yesmaximal, characteristic, complemented
15C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
16C3×#3280—31nomaximal
17#83505C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic, complemented
19C22×C32×D4C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C32×#124C2211yescharacteristic, complemented
23C32×#123—21no—
24C32×C22⋊Q8C2211yescharacteristic
25C32×#121—21no—
26C32×#121C2211yescharacteristic, complemented
27C32×#120—21no—
28C32×C4×D4C2211yescharacteristic
29C32×C4×D4C2211yescharacteristic, complemented
30C2×C32×C22⋊C4—21no—
31C3×#950—24no—
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic, complemented
34C2×C3×#215C2211yescharacteristic, complemented
35C3×#937—21no—
36C2×C3×#214C2211yescharacteristic, complemented
37C2×C3×#214C2211yescharacteristic, complemented
38C2×C3×#213—24no—
39C2×C3×#213C2211yescharacteristic
40C2×C3×#213C2211yescharacteristic
41C2×C3×#213C2211yescharacteristic
42C2×C3×#213C2211yescharacteristic
43C3×#930C2211yescharacteristic, complemented
44C3×#924C2211yescharacteristic
45C22×C3×C3⋊C8C2211yescharacteristic
46C22×C3×C3⋊C8C2211yescharacteristic, complemented
47C3×#894—21no—
48C3×#884—21no—
49C3×D3×C22⋊C4—21no—
50C3×#875C2211yescharacteristic, complemented
51C3×C4×D12C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×#830C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
62C3×C4×C3⋊C8C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64C22×C3×D8—31no—
65C3×#546—21no—
66C3×#546—31no—
67C3×#546D311yescharacteristic, complemented
68C3×#546C2×C311yescharacteristic, complemented
69C2×#950C2×C311yescharacteristic, complemented
70C22×#213C2×C311yescharacteristic, complemented
71#5550C2×C311yescharacteristic, complemented
72C3×#495—31no—
73C3×#467—31no—
74C3×#466—31no—
75C3×#463—31no—
76C3×#463—31no—
77C3×#450—31no—
78C3×#450—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×C4×D8—31no—
82C3×C8×D4—31no—
83#5238C2×C311yescharacteristic, complemented
84#5218C2×C311yescharacteristic, complemented
85#5059C2×C311yescharacteristic, complemented
86#5057C2×C311yescharacteristic, complemented
87#5051C2×C311yescharacteristic, complemented
88#5046C2×C311yescharacteristic, complemented
89#5038C2×C311yescharacteristic, complemented
90#5037C2×C311yescharacteristic, complemented
91#5016C2×C311yescharacteristic, complemented
92C4×#213C2×C311yescharacteristic, complemented
93D4×C3⋊C8C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C23×C3×D3—21no—
96C32×#41—22no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4—21no—
103C2×C32×D4—41no—
104C2×C32×D4D411yescharacteristic
105C2×C32×D4C2311yescharacteristic
106C2×C32×D4C2311yescharacteristic
107C22×C32×C4—21no—
108C22×C32×C4—21no—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C3×#235—22no—
114C3×#235—41no—
115C2×C3×D12—22no—
116C2×C3×D12—21no—
117C2×C3×D12—41no—
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×Dic6C2311yescharacteristic
123C32×C4⋊C4—21no—
124C32×C4⋊C4D411yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127C32×C22⋊C4—21no—
128C32×C22⋊C4—21no—
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C32×C22⋊C4D411yescharacteristic
132C32×C22⋊C4D411yescharacteristic
133C32×C42C2311yescharacteristic
134C3×#217—21no—
135C3×#216—22no—
136C3×#215—22no—
137C3×#215—41no—
138C3×#214—22no—
139C3×#214—41no—
140C3×#213—22no—
141C3×#213—22no—
142C3×#213—22no—
143C3×#213D414yescomplemented
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4—21no—
146C3×(C2×D3)⋊C4—21no—
147C3×(C2×D3)⋊C4—21no—
148C3×C4⋊Dic3C2311yescharacteristic
149C3×Dic3⋊C4—21no—
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8—22no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156#3280—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C22×C311yescharacteristic, complemented
161C22×C3×D4—21no—
162C22×C3×D4—31no—
163C22×C3×D4C2×D311yescharacteristic
164C22×C3×D4C22×C311yescharacteristic
165C2×#235C22×C311yescharacteristic, complemented
166C22×D12C22×C311yescharacteristic
167C3×#135—64no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C2×C3×D8—64no—
178C22×C3×C8—31no—
179C22×C3×C8—31no—
180C3×#124—21no—
181C3×#124—31no—
182C3×#124C2×D311yescharacteristic, complemented
183C3×#124C22×C311yescharacteristic, complemented
184C3×#123—22no—
185C3×#123—21no—
186C3×#123—21no—
187C3×#123—61no—
188C3×C22⋊Q8—21no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8C2×D311yescharacteristic
191C3×C22⋊Q8C22×C311yescharacteristic
192C3×#121—22no—
193C3×#121—21no—
194C3×#121—21no—
195C3×#121—21no—
196C3×#121—31no—
197C3×#121—61no—
198C3×#121C2×D311yescharacteristic, complemented
199C3×#121C22×C311yescharacteristic, complemented
200C3×#120—22no—
201C3×#120—21no—
202C3×#120—21no—
203C3×#120—61no—
204C3×C4×D4—21no—
205C3×C4×D4—21no—
206C3×C4×D4—31no—
207C3×C4×D4C2×D311yescharacteristic
208C3×C4×D4C2×D311yescharacteristic, complemented
209C3×C4×D4C22×C311yescharacteristic
210C3×C4×D4C22×C311yescharacteristic, complemented
211C2×C3×C22⋊C4—22no—
212C2×C3×C22⋊C4—21no—
213C2×C3×C22⋊C4—21no—
214C2×C3×C22⋊C4—61no—
215#950—24no—
216C2×#216C22×C311yescharacteristic, complemented
217C2×#215C22×C311yescharacteristic, complemented
218C2×#215C22×C311yescharacteristic, complemented
219#937—21no—
220C2×#214C22×C311yescharacteristic, complemented
221C2×#214C22×C311yescharacteristic, complemented
222C2×#213—24no—
223C2×#213C22×C311yescharacteristic
224C2×#213C22×C311yescharacteristic
225C2×#213C22×C311yescharacteristic
226C2×#213C22×C311yescharacteristic
227#930C22×C311yescharacteristic, complemented
228#924C22×C311yescharacteristic
229C22×C3⋊C8C22×C311yescharacteristic
230C22×C3⋊C8C22×C311yescharacteristic, complemented
231#894—21no—
232#884—21no—
233D3×C22⋊C4—21no—
234#875C22×C311yescharacteristic, complemented
235C4×D12C22×C311yescharacteristic, complemented
236C3×#107—31no—
237C3×C4⋊C8—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×#102—31no—
243C3×#102—31no—
244C3×C22⋊C8—31no—
245C3×C22⋊C8—31no—
246C3×C4×C8—31no—
247#835C22×C311yescharacteristic, complemented
248#832C22×C311yescharacteristic, complemented
249#832C22×C311yescharacteristic, complemented
250#830C22×C311yescharacteristic
251#830C22×C311yescharacteristic, complemented
252#810C22×C311yescharacteristic, complemented
253#809C22×C311yescharacteristic, complemented
254#809C22×C311yescharacteristic, complemented
255#807C22×C311yescharacteristic, complemented
256C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
257C4×C3⋊C8C22×C311yescharacteristic, complemented
258C23×C32—21no—
259C23×C32—21no—
260C23×C32—42no—
261C23×C32—42no—
262C23×C32—81no—
263C23×C32C2×D411yescharacteristic
264C23×C32C2×D411yescharacteristic
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—42no—
268C22×C3×D3—42no—
269C22×C3×D3—81no—
270C32×Q8—21no—
271C32×Q8—21no—
272C32×D4—21no—
273C32×D4—22no—
274C32×D4—21no—
275C32×D4—21no—
276C32×D4—42no—
277C32×D4—42no—
278C32×D4—81no—
279C32×D4C2×D412yes—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—42no—
287C2×C32×C4—81no—
288C2×C32×C4C2×D411yescharacteristic
289C2×C32×C4C2×D411yescharacteristic
290C2×C32×C4C2×D411yescharacteristic
291C2×C32×C4C2×D411yescharacteristic
292C2×C32×C4C2411yescharacteristic
293C3×#67—42no—
294C3×#67—81no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—42no—
301C3×D12C2×D412yes—
302C3×C4×D3—42no—
303C3×C4×D3—81no—
304C3×Dic6—21no—
305C3×Dic6—21no—
306C3×C3⋊C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yes—
310C2×#135—31no—
311C22×D8—31no—
312#546—31no—
313#546C3×D311yescharacteristic, complemented
314#495—31no—
315#467—31no—
316#466—31no—
317#463—31no—
318#463—31no—
319#450—31no—
320#450—31no—
321#449—31no—
322#449—31no—
323C4×D8—31no—
324C8×D4—31no—
325C24×C3—22no—
326C24×C3—21no—
327C24×C3—21no—
328C24×C3—61no—
329C23×D3—21no—
330C3×#41—22no—
331C3×#41—22no—
332C3×#41—42no—
333C3×#41—41no—
334C3×#41—41no—
335C3×#41—42no—
336C3×#41—62no—
337C3×#41—121no—
338C2×C3×Q8—21no—
339C2×C3×Q8—31no—
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×Q8C23×C311yescharacteristic
342C2×C3×D4—22no—
343C2×C3×D4—22no—
344C2×C3×D4—22no—
345C2×C3×D4—22no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—22no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—21no—
352C2×C3×D4—21no—
353C2×C3×D4—21no—
354C2×C3×D4—21no—
355C2×C3×D4—21no—
356C2×C3×D4—31no—
357C2×C3×D4—31no—
358C2×C3×D4—42no—
359C2×C3×D4—41no—
360C2×C3×D4—41no—
361C2×C3×D4—42no—
362C2×C3×D4—62no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C2×C3×D4—61no—
366C2×C3×D4—121no—
367C2×C3×D4#6711yescharacteristic
368C2×C3×D4C3×D411yescharacteristic
369C2×C3×D4C22×D311yescharacteristic
370C2×C3×D4C22×D311yescharacteristic
371C2×C3×D4C23×C311yescharacteristic
372C2×C3×D4C23×C311yescharacteristic
373C22×C3×C4—22no—
374C22×C3×C4—22no—
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4—61no—
382C22×C3×C4—61no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C23×C311yescharacteristic
386C22×C3×C4C23×C311yescharacteristic
387C2×#67—21no—
388C2×#67—21no—
389#235—22no—
390#235—41no—
391C2×D12—22no—
392C2×D12—21no—
393C2×D12—41no—
394C2×D12C23×C311yescharacteristic
395C2×D12C23×C311yescharacteristic
396C2×C4×D3—21no—
397C2×C4×D3—21no—
398C2×Dic6C23×C311yescharacteristic
399C3×Q16—62no—
400C3×SD16—62no—
401C3×SD16—62no—
402C3×SD16—121no—
403C3×SD16—121no—
404C3×D8—34no—
405C3×D8—62no—
406C3×D8—62no—
407C3×D8—62no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8—31no—
411C2×C3×C8—31no—
412C2×C3×C8—62no—
413C2×C3×C8—62no—
414C3×C4⋊C4—22no—
415C3×C4⋊C4—21no—
416C3×C4⋊C4—21no—
417C3×C4⋊C4—21no—
418C3×C4⋊C4—21no—
419C3×C4⋊C4—31no—
420C3×C4⋊C4—61no—
421C3×C4⋊C4#6711yescharacteristic
422C3×C4⋊C4C3×D411yescharacteristic
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C4⋊C4C23×C311yescharacteristic
425C3×C22⋊C4—22no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—22no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—22no—
430C3×C22⋊C4—21no—
431C3×C22⋊C4—21no—
432C3×C22⋊C4—21no—
433C3×C22⋊C4—21no—
434C3×C22⋊C4—21no—
435C3×C22⋊C4—21no—
436C3×C22⋊C4—21no—
437C3×C22⋊C4—21no—
438C3×C22⋊C4—21no—
439C3×C22⋊C4—21no—
440C3×C22⋊C4—21no—
441C3×C22⋊C4—21no—
442C3×C22⋊C4—61no—
443C3×C22⋊C4—61no—
444C3×C22⋊C4—61no—
445C3×C22⋊C4—61no—
446C3×C22⋊C4—61no—
447C3×C22⋊C4#6711yescharacteristic
448C3×C22⋊C4#6711yescharacteristic
449C3×C22⋊C4C3×D411yescharacteristic
450C3×C22⋊C4C3×D411yescharacteristic
451C3×C42—21no—
452C3×C42C22×D311yescharacteristic
453C3×C42C23×C311yescharacteristic
454#217—21no—
455#216—22no—
456#215—22no—
457#215—41no—
458#214—22no—
459#214—41no—
460#213—22no—
461#213—22no—
462#213—22no—
463#213C3×D414yescomplemented
464(C2×D3)⋊C4—21no—
465(C2×D3)⋊C4—21no—
466(C2×D3)⋊C4—21no—
467(C2×D3)⋊C4—21no—
468C4⋊Dic3C23×C311yescharacteristic
469Dic3⋊C4—21no—
470C2×C3⋊C8—22no—
471C2×C3⋊C8—22no—
472C2×C3⋊C8C23×C311yescharacteristic
473C2×C3⋊C8C23×C311yescharacteristic
474C2×C3⋊C8C23×C311yescharacteristic
475C2×C3⋊C8C23×C311yescharacteristic
476C22×C32—22no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—84no—
488C22×C32#13512yescomplemented
489C22×C32C22×D411yescharacteristic
490C2×C3×D3—22no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—84no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—21no—
500C32×C4—21no—
501C32×C4—41no—
502C32×C4—41no—
503C32×C4C22×D411yescharacteristic
504C32×C4H(5,𝔽2)11yescharacteristic
505C3×Dic3—41no—
506C3×Dic3—41no—
507C2×#41—31no—
508C2×#41C2×C3×D311yescharacteristic, complemented
509C22×D4—31no—
510C22×D4C2×C3×D311yescharacteristic
511#135—64no—
512C2×Q16—31no—
513C2×SD16—31no—
514C2×SD16—31no—
515C2×SD16—31no—
516C2×SD16—31no—
517C2×D8—31no—
518C2×D8—31no—
519C2×D8—31no—
520C2×D8—31no—
521C2×D8—64no—
522C22×C8—31no—
523C22×C8—31no—
524#124—31no—
525#124C2×C3×D311yescharacteristic, complemented
526#123—21no—
527#123—61no—
528C22⋊Q8—31no—
529C22⋊Q8C2×C3×D311yescharacteristic
530#121—21no—
531#121—31no—
532#121—61no—
533#121C2×C3×D311yescharacteristic, complemented
534#120—21no—
535#120—61no—
536C4×D4—31no—
537C4×D4C2×C3×D311yescharacteristic
538C4×D4C2×C3×D311yescharacteristic, complemented
539C2×C22⋊C4—21no—
540C2×C22⋊C4—61no—
541#107—31no—
542C4⋊C8—31no—
543#103—31no—
544#103—31no—
545#102—31no—
546#102—31no—
547#102—31no—
548#102—31no—
549C22⋊C8—31no—
550C22⋊C8—31no—
551C4×C8—31no—
552C23×C3—22no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—22no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—42no—
561C23×C3—42no—
562C23×C3—44no—
563C23×C3—44no—
564C23×C3—42no—
565C23×C3—42no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—81no—
569C23×C3—81no—
570C23×C3—82no—
571C23×C3—122no—
572C23×C3—122no—
573C23×C3—241no—
574C23×C3C2×#6711yescharacteristic
575C23×C3C2×#6711yescharacteristic
576C23×C3C2×C3×D411yescharacteristic
577C23×C3C2×C3×D411yescharacteristic
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—42no—
581C22×D3—42no—
582C22×D3—81no—
583C3×Q8—21no—
584C3×Q8—21no—
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—41no—
588C3×Q8—41no—
589C3×Q8—61no—
590C3×Q8—61no—
591C3×D4—22no—
592C3×D4—22no—
593C3×D4—22no—
594C3×D4—21no—
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—22no—
601C3×D4—32no—
602C3×D4—41no—
603C3×D4—41no—
604C3×D4—42no—
605C3×D4—42no—
606C3×D4—42no—
607C3×D4—42no—
608C3×D4—42no—
609C3×D4—44no—
610C3×D4—44no—
611C3×D4—61no—
612C3×D4—61no—
613C3×D4—61no—
614C3×D4—81no—
615C3×D4—81no—
616C3×D4—82no—
617C3×D4—122no—
618C3×D4—122no—
619C3×D4—241no—
620C3×D4D3×D412yes—
621C3×D4C2×C3×D412yes—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—42no—
646C2×C3×C4—42no—
647C2×C3×C4—44no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—81no—
651C2×C3×C4—81no—
652C2×C3×C4—82no—
653C2×C3×C4—122no—
654C2×C3×C4—241no—
655C2×C3×C4C2×#6711yescharacteristic
656C2×C3×C4C2×#6711yescharacteristic
657C2×C3×C4C2×#6711yescharacteristic
658C2×C3×C4C2×#6711yescharacteristic
659C2×C3×C4C2×C3×D411yescharacteristic
660C2×C3×C4C2×C3×D411yescharacteristic
661C2×C3×C4C2×C3×D411yescharacteristic
662C2×C3×C4C2×C3×D411yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C24×C311yescharacteristic
665#67—42no—
666#67—81no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669D12—21no—
670D12—21no—
671D12—21no—
672D12—42no—
673D12C2×C3×D412yes—
674C4×D3—42no—
675C4×D3—81no—
676Dic6—21no—
677Dic6—21no—
678C3×C8—32no—
679C3×C8—61no—
680C3×C8—61no—
681C3×C8—61no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8—21no—
685C3⋊C8C2×C3×D412yes—
686C2×C32—22no—
687C2×C32—42no—
688C2×C32—41no—
689C2×C32—81no—
690C2×C32D4211yescharacteristic
691C2×C32C2×#13511yescharacteristic
692C2×C32#57611yescharacteristic
693C3×D3—42no—
694C3×D3—81no—
695C24—21no—
696C24—61no—
697#41—22no—
698#41—41no—
699#41—62no—
700#41—121no—
701C2×Q8—31no—
702C2×Q8C22×C3×D311yescharacteristic
703C2×D4—22no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—31no—
708C2×D4—31no—
709C2×D4—41no—
710C2×D4—62no—
711C2×D4—61no—
712C2×D4—61no—
713C2×D4—61no—
714C2×D4—121no—
715C2×D4C3×#6711yescharacteristic
716C2×D4C22×C3×D311yescharacteristic
717C2×D4C22×C3×D311yescharacteristic
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4C22×C3×D311yescharacteristic
723C22×C4C22×C3×D311yescharacteristic
724Q16—62no—
725SD16—62no—
726SD16—62no—
727SD16—121no—
728SD16—121no—
729D8—34no—
730D8—62no—
731D8—62no—
732D8—62no—
733C2×C8—31no—
734C2×C8—31no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—62no—
738C2×C8—62no—
739C4⋊C4—21no—
740C4⋊C4—31no—
741C4⋊C4—61no—
742C4⋊C4C3×#6711yescharacteristic
743C4⋊C4C22×C3×D311yescharacteristic
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—61no—
750C22⋊C4—61no—
751C22⋊C4—61no—
752C22⋊C4—61no—
753C22⋊C4—61no—
754C22⋊C4C3×#6711yescharacteristic
755C22⋊C4C3×#6711yescharacteristic
756C42C22×C3×D311yescharacteristic
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—24no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—22no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—21no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—62no—
793C22×C3—84no—
794C22×C3—84no—
795C22×C3—88no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—121no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3—244no—
802C22×C3#95012yescomplemented
803C22×C3C3×#13512yescomplemented
804C22×C3C22×#6711yescharacteristic
805C22×C3C22×C3×D411yescharacteristic
806C2×D3—22no—
807C2×D3—41no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—84no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—42no—
828C3×C4—42no—
829C3×C4—41no—
830C3×C4—41no—
831C3×C4—41no—
832C3×C4—41no—
833C3×C4—121no—
834C3×C4—121no—
835C3×C4C2×D3×D411yescharacteristic
836C3×C4#100411yescharacteristic
837C3×C4C22×C3×D411yescharacteristic
838C3×C4C3×H(5,𝔽2)11yescharacteristic
839Dic3—41no—
840Dic3—41no—
841C32#328011yescharacteristic, complemented, Sylow
842C23—21no—
843C23—21no—
844C23—42no—
845C23—42no—
846C23—61no—
847C23—61no—
848C23—81no—
849C23—122no—
850C23—122no—
851C23—241no—
852C23C2×C3×#6711yescharacteristic
853C23C2×C3×#6711yescharacteristic
854Q8—21no—
855Q8—21no—
856Q8—61no—
857Q8—61no—
858D4—22no—
859D4—21no—
860D4—21no—
861D4—21no—
862D4—32no—
863D4—42no—
864D4—42no—
865D4—61no—
866D4—61no—
867D4—61no—
868D4—81no—
869D4—122no—
870D4—122no—
871D4—241no—
872D4C3×D3×D412yes—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—42no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—81no—
883C2×C4—122no—
884C2×C4—241no—
885C2×C4C2×C3×#6711yescharacteristic
886C2×C4C2×C3×#6711yescharacteristic
887C2×C4C2×C3×#6711yescharacteristic
888C2×C4C2×C3×#6711yescharacteristic
889C2×C4C23×C3×D311yescharacteristic
890C8—32no—
891C8—61no—
892C8—61no—
893C8—61no—
894C2×C3—22no—
895C2×C3—22no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—42no—
900C2×C3—44no—
901C2×C3—41no—
902C2×C3—42no—
903C2×C3—41no—
904C2×C3—42no—
905C2×C3—81no—
906C2×C3—82no—
907C2×C3—81no—
908C2×C3—81no—
909C2×C3—122no—
910C2×C3—241no—
911C2×C3D4×#6711yescharacteristic
912C2×C3C2×#95011yescharacteristic
913C2×C3#583511yescharacteristic
914C2×C3C3×D4211yescharacteristic
915C2×C3C2×C3×#13511yescharacteristic
916C2×C3C3×#57611yescharacteristic
917D3—42no—
918D3—81no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—22no—
923C22—21no—
924C22—21no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—62no—
931C22—84no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22—244no—
938C22C3×#95012yescomplemented
939C22C22×C3×#6711yescharacteristic
940C4—21no—
941C4—21no—
942C4—21no—
943C4—21no—
944C4—41no—
945C4—41no—
946C4—121no—
947C4—121no—
948C4C2×C3×D3×D411yescharacteristic
949C4C3×#100411yescharacteristic
950C3—21no—
951C3#8350511yescharacteristic, direct product factor
952C3C3×#328011yescharacteristic, complemented
953C2—22no—
954C2—41no—
955C2—42no—
956C2—81no—
957C2—122no—
958C2—241no—
959C2C3×D4×#6711yescharacteristic
960C2C2×C3×#95011yescharacteristic
961C2C3×#583511yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#546C2
socleC22×C32C22×D4
hypercenterC3×#546D3
hypocenterC3C3×#3280
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#546

Complements

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

NH ≅ G/Ntype
1. C32×#546C2semidirect
2. C2×C3×#950C2semidirect
3. C22×C3×#213C2semidirect
4. C3×#5550C2semidirect
5. C3×#5238C2semidirect
6. C3×#5218C2semidirect
7. C3×#5059C2semidirect
8. C3×#5057C2semidirect
9. C3×#5051C2semidirect
10. C3×#5046C2semidirect
11. C3×#5038C2semidirect
12. C3×#5037C2semidirect
13. C3×#5016C2semidirect
14. C3×C4×#213C2semidirect
15. C3×D4×C3⋊C8C2semidirect
17. #83505C3direct (N × H)
18. C2×C32×#41C22semidirect
20. C2×C3×#235C22semidirect
22. C32×#124C22semidirect
26. C32×#121C22semidirect
29. C32×C4×D4C22semidirect
32. C2×C3×#216C22semidirect
33. C2×C3×#215C22semidirect
34. C2×C3×#215C22semidirect
36. C2×C3×#214C22semidirect
37. C2×C3×#214C22semidirect
43. C3×#930C22semidirect
46. C22×C3×C3⋊C8C22semidirect
50. C3×#875C22semidirect
51. C3×C4×D12C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#832C22semidirect
56. C3×#830C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. C3×#809C22semidirect
60. C3×#807C22semidirect
61. C3×C4⋊(C3⋊C8)C22semidirect
62. C3×C4×C3⋊C8C22semidirect
67. C3×#546D3semidirect
68. C3×#546C2×C3semidirect
69. C2×#950C2×C3semidirect
70. C22×#213C2×C3semidirect
71. #5550C2×C3semidirect
83. #5238C2×C3semidirect
84. #5218C2×C3semidirect
85. #5059C2×C3semidirect
86. #5057C2×C3semidirect
87. #5051C2×C3semidirect
88. #5046C2×C3semidirect
89. #5038C2×C3semidirect
90. #5037C2×C3semidirect
91. #5016C2×C3semidirect
92. C4×#213C2×C3semidirect
93. D4×C3⋊C8C2×C3semidirect
143. C3×#213D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C22×C3semidirect
165. C2×#235C22×C3semidirect
182. C3×#124C2×D3semidirect
183. C3×#124C22×C3semidirect
198. C3×#121C2×D3semidirect
199. C3×#121C22×C3semidirect
208. C3×C4×D4C2×D3semidirect
210. C3×C4×D4C22×C3semidirect
216. C2×#216C22×C3semidirect
217. C2×#215C22×C3semidirect
218. C2×#215C22×C3semidirect
220. C2×#214C22×C3semidirect
221. C2×#214C22×C3semidirect
227. #930C22×C3semidirect
230. C22×C3⋊C8C22×C3semidirect
234. #875C22×C3semidirect
235. C4×D12C22×C3semidirect
247. #835C22×C3semidirect
248. #832C22×C3semidirect
249. #832C22×C3semidirect
251. #830C22×C3semidirect
252. #810C22×C3semidirect
253. #809C22×C3semidirect
254. #809C22×C3semidirect
255. #807C22×C3semidirect
256. C4⋊(C3⋊C8)C22×C3semidirect
257. C4×C3⋊C8C22×C3semidirect
313. #546C3×D3semidirect
463. #213C3×D4semidirect
488. C22×C32#135semidirect
508. C2×#41C2×C3×D3semidirect
525. #124C2×C3×D3semidirect
533. #121C2×C3×D3semidirect
538. C4×D4C2×C3×D3semidirect
802. C22×C3#950semidirect
803. C22×C3C3×#135semidirect
841. C32#3280semidirect
938. C22C3×#950semidirect
951. C3#83505direct (N × H)
952. C3C3×#3280semidirect

Maximal subgroups

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

subgroupindex
C32×#5462
C2×C3×#9502
C22×C3×#2132
C3×#55502
C3×#52382
C3×#52182
C3×#50592
C3×#50572
C3×#50512
C3×#50462
C3×#50382
C3×#50372
C3×#50162
C3×C4×#2132
C3×D4×C3⋊C82
C3×#32803
#835053