Finite Group Databasebeta

← C3×#82585 #11810285

Subgroups — C3×#82585 #11810285

Order 1152.

1931 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#120C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic, complemented
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
5C3×#5247C211yesmaximal, characteristic, complemented
6C3×#5222C211yesmaximal, characteristic, complemented
7C3×#5222C211yesmaximal, characteristic, complemented
8C3×#5220C211yesmaximal, characteristic, complemented
9C3×#5220C211yesmaximal, characteristic, complemented
10C3×#4953C211yesmaximal, characteristic, complemented
11C3×#4949C211yesmaximal, characteristic, complemented
12C3×#4946C211yesmaximal, characteristic, complemented
13C3×#4944C211yesmaximal, characteristic, complemented
14C3×#4944C211yesmaximal, characteristic, complemented
15C3×#4942C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#82585C311yesmaximal, characteristic, direct product factor
18C25×C32C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic, complemented
25C32×#120—24no—
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C3×#217—24no—
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic, complemented
41C2×C3×#217C2211yescharacteristic, complemented
42C2×C3×#217C2211yescharacteristic, complemented
43C3×#935—24no—
44C3×D4×Dic3—24no—
45C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C3×C4×Dic3C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C2×C3×#123—31no—
58C2×C3×#120—21no—
59C2×C3×#120D311yescharacteristic
60C2×C3×#120C2×C311yescharacteristic
61C2×C3×C4×D4—31no—
62C22×C3×C22⋊C4—31no—
63C22×#217C2×C311yescharacteristic, complemented
64C2×#935C2×C311yescharacteristic, complemented
65C2×D4×Dic3C2×C311yescharacteristic, complemented
66C3×#399—31no—
67C3×#397—31no—
68C3×#394—31no—
69C3×#394—31no—
70C3×#388—31no—
71C3×#388—31no—
72C3×#386—31no—
73C3×#386—31no—
74C3×#385—31no—
75C3×#380—31no—
76C3×#379—31no—
77#5247C2×C311yescharacteristic, complemented
78#5222C2×C311yescharacteristic, complemented
79#5222C2×C311yescharacteristic, complemented
80#5220C2×C311yescharacteristic, complemented
81#5220C2×C311yescharacteristic, complemented
82#4953C2×C311yescharacteristic, complemented
83#4949C2×C311yescharacteristic, complemented
84#4946C2×C311yescharacteristic, complemented
85#4944C2×C311yescharacteristic, complemented
86#4944C2×C311yescharacteristic, complemented
87#4942C2×C311yescharacteristic, complemented
88C24×C32—22no—
89C24×C32—22no—
90C24×C32—22no—
91C24×C32—22no—
92C24×C32—22no—
93C24×C32—41no—
94C24×C32—41no—
95C24×C32C2311yescharacteristic
96C24×C32C2311yescharacteristic
97C24×C32C2311yescharacteristic
98C24×C32C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—22no—
102C2×C32×D4—22no—
103C2×C32×D4—22no—
104C2×C32×D4—22no—
105C2×C32×D4—41no—
106C2×C32×D4—41no—
107C2×C32×D4D414yes—
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C3×Dic3—22no—
112C22×C3×Dic3—22no—
113C22×C3×Dic3—22no—
114C22×C3×Dic3—22no—
115C22×C3×Dic3—22no—
116C22×C3×Dic3—22no—
117C22×C3×Dic3—41no—
118C22×C3×Dic3—41no—
119C22×C3×Dic3—41no—
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C32×C22⋊C4—22no—
129C32×C22⋊C4—22no—
130C32×C22⋊C4—22no—
131C3×#217—22no—
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217—22no—
137C3×#217—22no—
138C3×#217—22no—
139C3×#217—22no—
140C3×#217—41no—
141C3×#217—41no—
142C3×#217—41no—
143C3×#217D414yescomplemented
144C3×C4⋊Dic3—22no—
145C3×Dic3⋊C4—22no—
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—41no—
148C3×Dic3⋊C4—41no—
149C3×C4×Dic3—22no—
150#2418—31noSylow
151C25×C3—21no—
152C25×C3C2×D311yescharacteristic
153C25×C3C22×C311yescharacteristic
154C22×C3×D4—21no—
155C22×C3×D4—21no—
156C22×C3×D4—21no—
157C22×C3×D4C2×D311yescharacteristic
158C22×C3×D4C2×D311yescharacteristic
159C22×C3×D4C2×D311yescharacteristic
160C22×C3×D4C22×C311yescharacteristic
161C22×C3×D4C22×C311yescharacteristic
162C22×C3×D4C22×C311yescharacteristic
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C23×Dic3C22×C311yescharacteristic
167C23×Dic3C22×C311yescharacteristic
168C23×Dic3C22×C311yescharacteristic, complemented
169C3×#123—64no—
170C3×#120—28no—
171C3×#120—24no—
172C3×#120—24no—
173C3×C4×D4—64no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C22⋊C4—21no—
180C2×C3×C22⋊C4—21no—
181C2×C3×C22⋊C4—21no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—64no—
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C22⋊C4C2×D311yescharacteristic
199C2×C3×C22⋊C4C22×C311yescharacteristic
200C2×C3×C22⋊C4C22×C311yescharacteristic
201C2×C3×C22⋊C4C22×C311yescharacteristic
202C2×C3×C42—31no—
203C2×#217—24no—
204C2×#217C22×C311yescharacteristic
205C2×#217C22×C311yescharacteristic
206C2×#217C22×C311yescharacteristic
207C2×#217C22×C311yescharacteristic
208C2×#217C22×C311yescharacteristic
209C2×#217C22×C311yescharacteristic
210C2×#217C22×C311yescharacteristic
211C2×#217C22×C311yescharacteristic
212C2×#217C22×C311yescharacteristic
213C2×#217C22×C311yescharacteristic
214C2×#217C22×C311yescharacteristic, complemented
215C2×#217C22×C311yescharacteristic, complemented
216C2×#217C22×C311yescharacteristic, complemented
217#935—24no—
218D4×Dic3—24no—
219C2×C4⋊Dic3C22×C311yescharacteristic, complemented
220C2×Dic3⋊C4C22×C311yescharacteristic, complemented
221C2×Dic3⋊C4C22×C311yescharacteristic, complemented
222C2×Dic3⋊C4C22×C311yescharacteristic, complemented
223C2×Dic3⋊C4C22×C311yescharacteristic, complemented
224C2×C4×Dic3C22×C311yescharacteristic, complemented
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3×#95—31no—
230C3×#95—31no—
231C3⋊#95C22×C311yescharacteristic, complemented
232C3⋊#95C22×C311yescharacteristic, complemented
233C3⋊#95C22×C311yescharacteristic, complemented
234C3⋊#95C22×C311yescharacteristic, complemented
235C3⋊#95C22×C311yescharacteristic, complemented
236C3⋊#95C22×C311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—28no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—21no—
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—21no—
260C23×C32—44no—
261C23×C32—44no—
262C23×C32—44no—
263C23×C32—44no—
264C23×C32—44no—
265C23×C32—44no—
266C23×C32C2×D412yes—
267C23×C32C2×D412yes—
268C23×C32C2×D412yes—
269C23×C32#4112yes—
270C23×C32#4112yes—
271C23×C32#4112yes—
272C23×C32C2411yescharacteristic
273C32×D4—28no—
274C32×D4—44no—
275C32×D4—44no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4C2×D412yes—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—44no—
308C2×C3×Dic3—44no—
309C2×C3×Dic3—44no—
310C2×C3×Dic3C2×D412yes—
311C2×C3×Dic3C2×D412yes—
312C2×#123—31no—
313C2×#120C3×D311yescharacteristic
314C2×C4×D4—31no—
315C22×C22⋊C4—31no—
316#399—31no—
317#397—31no—
318#394—31no—
319#394—31no—
320#388—31no—
321#388—31no—
322#386—31no—
323#386—31no—
324#385—31no—
325#380—31no—
326#379—31no—
327C24×C3—22no—
328C24×C3—22no—
329C24×C3—22no—
330C24×C3—22no—
331C24×C3—22no—
332C24×C3—22no—
333C24×C3—24no—
334C24×C3—22no—
335C24×C3—22no—
336C24×C3—22no—
337C24×C3—22no—
338C24×C3—21no—
339C24×C3—21no—
340C24×C3—21no—
341C24×C3—21no—
342C24×C3—42no—
343C24×C3—42no—
344C24×C3—42no—
345C24×C3—42no—
346C24×C3—41no—
347C24×C3—41no—
348C24×C3—41no—
349C24×C3—41no—
350C24×C3—42no—
351C24×C3—42no—
352C24×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C24×C3C22×D311yescharacteristic
356C24×C3C23×C311yescharacteristic
357C24×C3C23×C311yescharacteristic
358C24×C3C23×C311yescharacteristic
359C24×C3C23×C311yescharacteristic
360C2×C3×D4—22no—
361C2×C3×D4—22no—
362C2×C3×D4—22no—
363C2×C3×D4—22no—
364C2×C3×D4—24no—
365C2×C3×D4—24no—
366C2×C3×D4—22no—
367C2×C3×D4—22no—
368C2×C3×D4—22no—
369C2×C3×D4—22no—
370C2×C3×D4—22no—
371C2×C3×D4—22no—
372C2×C3×D4—22no—
373C2×C3×D4—22no—
374C2×C3×D4—24no—
375C2×C3×D4—42no—
376C2×C3×D4—42no—
377C2×C3×D4—42no—
378C2×C3×D4—42no—
379C2×C3×D4—41no—
380C2×C3×D4—41no—
381C2×C3×D4—41no—
382C2×C3×D4—41no—
383C2×C3×D4—42no—
384C2×C3×D4—42no—
385C2×C3×D4#6714yes—
386C2×C3×D4C3×D414yes—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—62no—
399C22×C3×C4—62no—
400C22×C3×C4—62no—
401C22×C3×C4—62no—
402C22×C3×C4—62no—
403C22×C3×C4—62no—
404C22×C3×C4—121no—
405C22×C3×C4—121no—
406C22×C3×C4—121no—
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C22×C3×C4C23×C311yescharacteristic
411C22×C3×C4C23×C311yescharacteristic
412C22×C3×C4C23×C311yescharacteristic
413C22×Dic3—22no—
414C22×Dic3—22no—
415C22×Dic3—22no—
416C22×Dic3—22no—
417C22×Dic3—22no—
418C22×Dic3—22no—
419C22×Dic3—41no—
420C22×Dic3—41no—
421C22×Dic3—41no—
422C22×Dic3C23×C311yescharacteristic
423C22×Dic3C23×C311yescharacteristic
424C22×Dic3C23×C311yescharacteristic
425C22×Dic3C23×C311yescharacteristic
426C22×Dic3C23×C311yescharacteristic
427C22×Dic3C23×C311yescharacteristic
428C22×Dic3C23×C311yescharacteristic
429C22×Dic3C23×C311yescharacteristic
430C3×C4⋊C4—62no—
431C3×C4⋊C4—62no—
432C3×C4⋊C4—62no—
433C3×C4⋊C4—121no—
434C3×C4⋊C4—121no—
435C3×C22⋊C4—24no—
436C3×C22⋊C4—24no—
437C3×C22⋊C4—24no—
438C3×C22⋊C4—22no—
439C3×C22⋊C4—22no—
440C3×C22⋊C4—22no—
441C3×C22⋊C4—22no—
442C3×C22⋊C4—22no—
443C3×C22⋊C4—22no—
444C3×C22⋊C4—34no—
445C3×C22⋊C4—62no—
446C3×C22⋊C4—62no—
447C3×C22⋊C4—62no—
448C3×C22⋊C4—62no—
449C3×C22⋊C4—62no—
450C3×C22⋊C4—62no—
451C3×C22⋊C4—62no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—62no—
454C3×C22⋊C4—121no—
455C3×C22⋊C4—121no—
456C3×C22⋊C4—121no—
457C3×C42—62no—
458#217—22no—
459#217—22no—
460#217—22no—
461#217—22no—
462#217—22no—
463#217—22no—
464#217—22no—
465#217—22no—
466#217—22no—
467#217—41no—
468#217—41no—
469#217—41no—
470#217C3×D414yescomplemented
471C4⋊Dic3—22no—
472Dic3⋊C4—22no—
473Dic3⋊C4—22no—
474Dic3⋊C4—41no—
475Dic3⋊C4—41no—
476C4×Dic3—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—22no—
488C22×C32—22no—
489C22×C32—22no—
490C22×C32—22no—
491C22×C32—22no—
492C22×C32—416no—
493C22×C32—41no—
494C22×C32—41no—
495C22×C32—41no—
496C22×C32—41no—
497C22×C32—41no—
498C22×C32—41no—
499C22×C32—41no—
500C22×C32—41no—
501C22×C32—41no—
502C22×C32—41no—
503C22×C32—41no—
504C22×C32—41no—
505C22×C32#12314yescomplemented
506C22×C32C22×D411yescharacteristic
507C22×C32C22×D411yescharacteristic
508C22×C32C2×#4111yescharacteristic
509C22×C32C2×#4111yescharacteristic
510C22×C32C2×#4111yescharacteristic
511C22×C32H(5,𝔽2)11yescharacteristic
512C22×C32H(5,𝔽2)11yescharacteristic
513C32×C4—22no—
514C32×C4—41no—
515C32×C4—41no—
516C3×Dic3—22no—
517C3×Dic3—22no—
518C3×Dic3—41no—
519C3×Dic3—41no—
520C3×Dic3—41no—
521C3×Dic3—41no—
522C3×Dic3—41no—
523C3×Dic3—41no—
524C25C2×C3×D311yescharacteristic
525C22×D4C2×C3×D311yescharacteristic
526C22×D4C2×C3×D311yescharacteristic
527C22×D4C2×C3×D311yescharacteristic
528C23×C4—31no—
529C23×C4—31no—
530C23×C4—31no—
531#123—64no—
532#120—24no—
533C4×D4—64no—
534C2×C4⋊C4—31no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—64no—
553C2×C22⋊C4C2×C3×D311yescharacteristic
554C2×C22⋊C4C2×C3×D311yescharacteristic
555C2×C22⋊C4C2×C3×D311yescharacteristic
556C2×C42—31no—
557#95—31no—
558#95—31no—
559#95—31no—
560#95—31no—
561#95—31no—
562#95—31no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—28no—
576C23×C3—28no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—21no—
609C23×C3—21no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—41no—
621C23×C3—41no—
622C23×C3—41no—
623C23×C3—41no—
624C23×C3—41no—
625C23×C3—41no—
626C23×C3—41no—
627C23×C3—41no—
628C23×C3—41no—
629C23×C3—41no—
630C23×C3—41no—
631C23×C3—41no—
632C23×C3—41no—
633C23×C3—41no—
634C23×C3—41no—
635C23×C3—41no—
636C23×C3—41no—
637C23×C3—41no—
638C23×C3—48no—
639C23×C3—44no—
640C23×C3—44no—
641C23×C3—44no—
642C23×C3—44no—
643C23×C3—44no—
644C23×C3—44no—
645C23×C3—44no—
646C23×C3—44no—
647C23×C3—48no—
648C23×C3—48no—
649C23×C3—44no—
650C23×C3—44no—
651C23×C3—48no—
652C23×C3—48no—
653C23×C3—48no—
654C23×C3—48no—
655C23×C3—44no—
656C23×C3—44no—
657C23×C3D3×D412yes—
658C23×C3#23712yes—
659C23×C3#23712yes—
660C23×C3#23712yes—
661C23×C3C2×#6712yes—
662C23×C3C2×#6712yes—
663C23×C3C2×C3×D412yes—
664C23×C3C2×C3×D412yes—
665C23×C3C2×C3×D412yes—
666C23×C3C3×#4112yes—
667C23×C3C3×#4112yes—
668C23×C3C3×#4112yes—
669C23×C3C23×D311yescharacteristic
670C23×C3C24×C311yescharacteristic
671C3×D4—28no—
672C3×D4—28no—
673C3×D4—48no—
674C3×D4—44no—
675C3×D4—44no—
676C3×D4—44no—
677C3×D4—44no—
678C3×D4—48no—
679C3×D4—48no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—21no—
698C2×C3×C4—22no—
699C2×C3×C4—32no—
700C2×C3×C4—32no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
724C2×C3×C4—61no—
725C2×C3×C4—61no—
726C2×C3×C4—61no—
727C2×C3×C4—61no—
728C2×C3×C4—61no—
729C2×C3×C4—124no—
730C2×C3×C4—124no—
731C2×C3×C4—124no—
732C2×C3×C4C2×#6712yes—
733C2×C3×C4C2×C3×D412yes—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—21no—
737C2×Dic3—21no—
738C2×Dic3—21no—
739C2×Dic3—21no—
740C2×Dic3—21no—
741C2×Dic3—21no—
742C2×Dic3—21no—
743C2×Dic3—21no—
744C2×Dic3—21no—
745C2×Dic3—21no—
746C2×Dic3—21no—
747C2×Dic3—21no—
748C2×Dic3—21no—
749C2×Dic3—21no—
750C2×Dic3—21no—
751C2×Dic3—21no—
752C2×Dic3—21no—
753C2×Dic3—21no—
754C2×Dic3—21no—
755C2×Dic3—21no—
756C2×Dic3—44no—
757C2×Dic3—44no—
758C2×Dic3—44no—
759C2×Dic3C2×C3×D412yes—
760C2×Dic3C2×C3×D412yes—
761C2×C32—24no—
762C2×C32—42no—
763C2×C32—42no—
764C2×C32—42no—
765C2×C32C2×#12311yescharacteristic
766C2×C32#52511yescharacteristic
767C2×C32#53811yescharacteristic
768C2×C32D4211yescharacteristic
769C2×C32#54611yescharacteristic
770C2×C32#54611yescharacteristic
771C2×C32#55111yescharacteristic
772C24—22no—
773C24—22no—
774C24—22no—
775C24—22no—
776C24—22no—
777C24—41no—
778C24—41no—
779C24C22×C3×D311yescharacteristic
780C24C22×C3×D311yescharacteristic
781C24C22×C3×D311yescharacteristic
782C24C22×C3×D311yescharacteristic
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—41no—
790C2×D4—41no—
791C2×D4C3×#6714yes—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—62no—
801C22×C4—62no—
802C22×C4—62no—
803C22×C4—62no—
804C22×C4—62no—
805C22×C4—62no—
806C22×C4—121no—
807C22×C4—121no—
808C22×C4—121no—
809C22×C4C22×C3×D311yescharacteristic
810C22×C4C22×C3×D311yescharacteristic
811C22×C4C22×C3×D311yescharacteristic
812C4⋊C4—62no—
813C4⋊C4—62no—
814C4⋊C4—62no—
815C4⋊C4—121no—
816C4⋊C4—121no—
817C22⋊C4—22no—
818C22⋊C4—22no—
819C22⋊C4—22no—
820C22⋊C4—34no—
821C22⋊C4—62no—
822C22⋊C4—62no—
823C22⋊C4—62no—
824C22⋊C4—62no—
825C22⋊C4—62no—
826C22⋊C4—62no—
827C22⋊C4—62no—
828C22⋊C4—62no—
829C22⋊C4—62no—
830C22⋊C4—121no—
831C22⋊C4—121no—
832C22⋊C4—121no—
833C42—62no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—24no—
847C22×C3—24no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—22no—
851C22×C3—22no—
852C22×C3—22no—
853C22×C3—22no—
854C22×C3—22no—
855C22×C3—22no—
856C22×C3—22no—
857C22×C3—22no—
858C22×C3—22no—
859C22×C3—22no—
860C22×C3—22no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—24no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—21no—
871C22×C3—21no—
872C22×C3—21no—
873C22×C3—21no—
874C22×C3—42no—
875C22×C3—42no—
876C22×C3—42no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—42no—
886C22×C3—42no—
887C22×C3—416no—
888C22×C3—416no—
889C22×C3—42no—
890C22×C3—42no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—432no—
898C22×C3—41no—
899C22×C3—41no—
900C22×C3—41no—
901C22×C3—41no—
902C22×C3—41no—
903C22×C3—41no—
904C22×C3—41no—
905C22×C3—41no—
906C22×C3—41no—
907C22×C3—41no—
908C22×C3—41no—
909C22×C3—41no—
910C22×C3—41no—
911C22×C3—41no—
912C22×C3—41no—
913C22×C3—41no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—81no—
923C22×C3—81no—
924C22×C3—81no—
925C22×C3—81no—
926C22×C3#93514yescomplemented
927C22×C3C3×#12314yescomplemented
928C22×C3C2×D3×D411yescharacteristic
929C22×C3C2×#23711yescharacteristic
930C22×C3C2×#23711yescharacteristic
931C22×C3C2×#23711yescharacteristic
932C22×C3#100411yescharacteristic
933C22×C3#100411yescharacteristic
934C22×C3C22×#6711yescharacteristic
935C22×C3C22×C3×D411yescharacteristic
936C22×C3C22×C3×D411yescharacteristic
937C22×C3C2×C3×#4111yescharacteristic
938C22×C3C2×C3×#4111yescharacteristic
939C22×C3C2×C3×#4111yescharacteristic
940C22×C3C3×H(5,𝔽2)11yescharacteristic
941C22×C3C3×H(5,𝔽2)11yescharacteristic
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—42no—
945C3×C4—42no—
946C3×C4—42no—
947C3×C4—41no—
948C3×C4—41no—
949C3×C4—41no—
950C3×C4—41no—
951C3×C4—62no—
952C3×C4—62no—
953C3×C4—121no—
954C3×C4—121no—
955C3×C4—121no—
956C3×C4—121no—
957C3×C4—121no—
958C3×C4—121no—
959Dic3—22no—
960Dic3—22no—
961Dic3—41no—
962Dic3—41no—
963Dic3—41no—
964Dic3—41no—
965Dic3—41no—
966Dic3—41no—
967C32#241811yescharacteristic, complemented, Sylow
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—28no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—44no—
992C23—44no—
993C23—44no—
994C23—44no—
995C23—44no—
996C23—44no—
997C23C3×D3×D412yes—
998C23C3×#23712yes—
999C23C3×#23712yes—
1000C23C3×#23712yes—
1001C23C2×C3×#6712yes—
1002C23C2×C3×#6712yes—
1003C23C23×C3×D311yescharacteristic
1004D4—28no—
1005D4—44no—
1006D4—44no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—32no—
1016C2×C4—32no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—61no—
1031C2×C4—61no—
1032C2×C4—61no—
1033C2×C4—61no—
1034C2×C4—61no—
1035C2×C4—61no—
1036C2×C4—61no—
1037C2×C4—61no—
1038C2×C4—61no—
1039C2×C4—124no—
1040C2×C4—124no—
1041C2×C4—124no—
1042C2×C4C2×C3×#6712yes—
1043C2×C3—24no—
1044C2×C3—24no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—44no—
1053C2×C3—44no—
1054C2×C3—44no—
1055C2×C3—42no—
1056C2×C3—42no—
1057C2×C3—42no—
1058C2×C3—42no—
1059C2×C3—42no—
1060C2×C3—42no—
1061C2×C3—82no—
1062C2×C3#558611yescharacteristic
1063C2×C3#558711yescharacteristic
1064C2×C3#559111yescharacteristic
1065C2×C3#559311yescharacteristic
1066C2×C3C2×#93511yescharacteristic
1067C2×C3D4×#6711yescharacteristic
1068C2×C3#580611yescharacteristic
1069C2×C3C2×C3×#12311yescharacteristic
1070C2×C3C3×#52511yescharacteristic
1071C2×C3C3×#53811yescharacteristic
1072C2×C3C3×D4211yescharacteristic
1073C2×C3C3×#54611yescharacteristic
1074C2×C3C3×#54611yescharacteristic
1075C2×C3C3×#55111yescharacteristic
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—416no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22C3×#93514yescomplemented
1105C22C2×C3×D3×D411yescharacteristic
1106C22C2×C3×#23711yescharacteristic
1107C22C2×C3×#23711yescharacteristic
1108C22C2×C3×#23711yescharacteristic
1109C22C3×#100411yescharacteristic
1110C22C3×#100411yescharacteristic
1111C22C22×C3×#6711yescharacteristic
1112C4—22no—
1113C4—41no—
1114C4—41no—
1115C4—62no—
1116C4—62no—
1117C4—121no—
1118C4—121no—
1119C4—121no—
1120C4—121no—
1121C4—121no—
1122C4—121no—
1123C3—21no—
1124C3#8258511yescharacteristic, direct product factor
1125C3C3×#241811yescharacteristic, complemented
1126C2—24no—
1127C2—42no—
1128C2—42no—
1129C2—42no—
1130C2C3×#558611yescharacteristic
1131C2C3×#558711yescharacteristic
1132C2C3×#559111yescharacteristic
1133C2C3×#559311yescharacteristic
1134C2C2×C3×#93511yescharacteristic
1135C2C3×D4×#6711yescharacteristic
1136C2C3×#580611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
Fitting, prime radicalC2×C32×#120C2
socleC23×C32C24
hypercenterC2×C3×#120D3
hypocenterC3C3×#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
2. C22×C3×#217C2semidirect
3. C2×C3×#935C2semidirect
4. C2×C3×D4×Dic3C2semidirect
5. C3×#5247C2semidirect
6. C3×#5222C2semidirect
7. C3×#5222C2semidirect
8. C3×#5220C2semidirect
9. C3×#5220C2semidirect
10. C3×#4953C2semidirect
11. C3×#4949C2semidirect
12. C3×#4946C2semidirect
13. C3×#4944C2semidirect
14. C3×#4944C2semidirect
15. C3×#4942C2semidirect
17. #82585C3direct (N × H)
24. C23×C3×Dic3C22semidirect
40. C2×C3×#217C22semidirect
41. C2×C3×#217C22semidirect
42. C2×C3×#217C22semidirect
45. C2×C3×C4⋊Dic3C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. C2×C3×C4×Dic3C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
63. C22×#217C2×C3semidirect
64. C2×#935C2×C3semidirect
65. C2×D4×Dic3C2×C3semidirect
77. #5247C2×C3semidirect
78. #5222C2×C3semidirect
79. #5222C2×C3semidirect
80. #5220C2×C3semidirect
81. #5220C2×C3semidirect
82. #4953C2×C3semidirect
83. #4949C2×C3semidirect
84. #4946C2×C3semidirect
85. #4944C2×C3semidirect
86. #4944C2×C3semidirect
87. #4942C2×C3semidirect
143. C3×#217D4semidirect
168. C23×Dic3C22×C3semidirect
214. C2×#217C22×C3semidirect
215. C2×#217C22×C3semidirect
216. C2×#217C22×C3semidirect
219. C2×C4⋊Dic3C22×C3semidirect
220. C2×Dic3⋊C4C22×C3semidirect
221. C2×Dic3⋊C4C22×C3semidirect
222. C2×Dic3⋊C4C22×C3semidirect
223. C2×Dic3⋊C4C22×C3semidirect
224. C2×C4×Dic3C22×C3semidirect
231. C3⋊#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
236. C3⋊#95C22×C3semidirect
470. #217C3×D4semidirect
505. C22×C32#123semidirect
926. C22×C3#935semidirect
927. C22×C3C3×#123semidirect
967. C32#2418semidirect
1104. C22C3×#935semidirect
1124. C3#82585direct (N × H)
1125. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1202
C22×C3×#2172
C2×C3×#9352
C2×C3×D4×Dic32
C3×#52472
C3×#52222
C3×#52202
C3×#49532
C3×#49492
C3×#49462
C3×#49442
C3×#49422
C3×#24183
#825853