Finite Group Databasebeta

← C3×#75453 #11802155

Subgroups — C3×#75453 #11802155

Order 1152.

1471 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#883C211yesmaximal, characteristic
2C2×C3×#67⋊C4C211yesmaximal, characteristic
3C2×C3×C42×D3C211yesmaximal, characteristic, complemented
4C32×#388C211yesmaximal, characteristic, complemented
5C3×#4989C211yesmaximal, characteristic, complemented
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7C3×#4956C211yesmaximal, characteristic
8C3×#4944C211yesmaximal, characteristic, complemented
9C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
10C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
11C3×#4933C211yesmaximal, characteristic, complemented
12C3×#4666C211yesmaximal, characteristic, complemented
13C3×#4664C211yesmaximal, characteristic, complemented
14C3×#4653C211yesmaximal, characteristic, complemented
15C3×#4649C211yesmaximal, characteristic, complemented
16C3×C4×#123—31nomaximal
17#75453C311yesmaximal, characteristic, direct product factor
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C42C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#883C418yescomplemented
44C3×#67⋊C4—24no—
45C3×C42×D3—24no—
46C32×#95C2211yescharacteristic
47C32×#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C2×C3×#123—31no—
57C2×C3×C4×D4—31no—
58C22×C3×C42—31no—
59C2×#883C2×C311yescharacteristic
60C2×#67⋊C4C2×C311yescharacteristic
61C2×C42×D3C2×C311yescharacteristic, complemented
62C3×#388—21no—
63C3×#388—31no—
64C3×#388D311yescharacteristic, complemented
65C3×#388C2×C311yescharacteristic, complemented
66C3×#387—31no—
67C3×#387—31no—
68C3×#386—31no—
69C3×#385—31no—
70C3×#381—31no—
71C3×C4×C4⋊C4—31no—
72C3×C4×C4⋊C4—31no—
73C3×C4×C22⋊C4—31no—
74C3×C4×C22⋊C4—31no—
75C3×C4×C22⋊C4—31no—
76#4989C2×C311yescharacteristic, complemented
77Dic3×C4⋊C4C2×C311yescharacteristic, complemented
78#4956C2×C311yescharacteristic
79#4944C2×C311yescharacteristic, complemented
80Dic3×C22⋊C4C2×C311yescharacteristic, complemented
81Dic3×C22⋊C4C2×C311yescharacteristic, complemented
82#4933C2×C311yescharacteristic, complemented
83#4666C2×C311yescharacteristic, complemented
84#4664C2×C311yescharacteristic, complemented
85#4653C2×C311yescharacteristic, complemented
86#4649C2×C311yescharacteristic, complemented
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—22no—
96C2×C3×#67—22no—
97C2×C3×#67C2×C414yes—
98C22×C3×Dic3—22no—
99C22×C3×Dic3—22no—
100C22×C3×Dic3—22no—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3C2×C414yescomplemented
116C2×C3×C4×D3D414yes—
117C32×C4⋊C4—22no—
118C32×C22⋊C4—22no—
119C32×C22⋊C4—22no—
120C32×C22⋊C4C2×C414yescomplemented
121C32×C42—22no—
122C3×#217—22no—
123C3×#217C2×C414yescomplemented
124C3×(C2×D3)⋊C4—22no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4C2×C414yescomplemented
127C3×C4⋊Dic3C2×C414yescomplemented
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4C2×C414yescomplemented
131C3×C4×Dic3—22no—
132C3×C4×Dic3—22no—
133C3×C4×Dic3—22no—
134C3×C4×Dic3—22no—
135C3×C4×Dic3—22no—
136C3×C4×Dic3—22no—
137C4×#123—31noSylow
138C22×C3×D4—31no—
139C23×C3×C4—31no—
140C23×C3×C4—31no—
141C23×C3×C4—31no—
142C23×C3×C4—31no—
143C22×#67C22×C311yescharacteristic
144C23×Dic3C22×C311yescharacteristic
145C22×C4×D3C22×C311yescharacteristic
146C22×C4×D3C22×C311yescharacteristic
147C22×C4×D3C22×C311yescharacteristic
148C3×#123—38no—
149C3×C4×D4—64no—
150C2×C3×C4⋊C4—21no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C22×C311yescharacteristic
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—21no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4C2×D311yescharacteristic
166C2×C3×C22⋊C4C2×D311yescharacteristic
167C2×C3×C22⋊C4C2×D311yescharacteristic
168C2×C3×C22⋊C4C22×C311yescharacteristic
169C2×C3×C22⋊C4C22×C311yescharacteristic
170C2×C3×C22⋊C4C22×C311yescharacteristic
171C2×C3×C42—21no—
172C2×C3×C42—31no—
173C2×C3×C42—31no—
174C2×C3×C42—31no—
175C2×C3×C42—31no—
176C2×C3×C42—31no—
177C2×C3×C42—31no—
178C2×C3×C42—64no—
179C2×C3×C42C2×D311yescharacteristic
180C2×C3×C42C22×C311yescharacteristic
181C2×#217C22×C311yescharacteristic
182C2×#217C22×C311yescharacteristic
183C2×(C2×D3)⋊C4C22×C311yescharacteristic
184C2×(C2×D3)⋊C4C22×C311yescharacteristic
185C2×(C2×D3)⋊C4C22×C311yescharacteristic
186C2×C4⋊Dic3C22×C311yescharacteristic
187C2×Dic3⋊C4C22×C311yescharacteristic
188C2×Dic3⋊C4C22×C311yescharacteristic
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×C4×Dic3C22×C311yescharacteristic
191C2×C4×Dic3C22×C311yescharacteristic
192C2×C4×Dic3C22×C311yescharacteristic
193C2×C4×Dic3C22×C311yescharacteristic
194C2×C4×Dic3C22×C311yescharacteristic
195C2×C4×Dic3C22×C311yescharacteristic
196#883C3×C418yescomplemented
197#67⋊C4—24no—
198C42×D3—24no—
199C3×#95—21no—
200C3×#95—21no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95—31no—
206C3×#95—31no—
207C3×#95—31no—
208C3×#95—31no—
209C3×#95C2×D311yescharacteristic
210C3×#95C2×D311yescharacteristic
211C3×#95C22×C311yescharacteristic
212C3×#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C3⋊#95C22×C311yescharacteristic
215C3⋊#95C22×C311yescharacteristic
216C3⋊#95C22×C311yescharacteristic
217C3⋊#95C22×C311yescharacteristic
218C3⋊#95C22×C311yescharacteristic
219C3⋊#95C22×C311yescharacteristic
220C3⋊#95C22×C311yescharacteristic
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32C22×C412yes—
228C23×C32C2411yescharacteristic
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3C22×C412yes—
234C22×C3×D3C2×D412yes—
235C22×C3×D3#4112yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C22×C412yes—
251C2×C32×C4C22×C412yes—
252C2×C32×C4C2×D412yes—
253C2×C32×C4#4112yes—
254C3×#67—28no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—44no—
270C2×C3×Dic3C22×C412yes—
271C2×C3×Dic3C22×C412yes—
272C2×C3×Dic3C22×C412yes—
273C2×C3×Dic3C2×D412yes—
274C2×C3×Dic3#4112yes—
275C2×C3×Dic3#4112yes—
276C2×C3×Dic3#4112yes—
277C3×C4×D3—28no—
278C3×C4×D3—28no—
279C3×C4×D3—28no—
280C2×#123—31no—
281C2×C4×D4—31no—
282C22×C42—31no—
283#388—31no—
284#388C3×D311yescharacteristic, complemented
285#387—31no—
286#387—31no—
287#386—31no—
288#385—31no—
289#381—31no—
290C4×C4⋊C4—31no—
291C4×C4⋊C4—31no—
292C4×C22⋊C4—31no—
293C4×C22⋊C4—31no—
294C4×C22⋊C4—31no—
295C24×C3—21no—
296C24×C3—31no—
297C24×C3C22×D311yescharacteristic
298C24×C3C23×C311yescharacteristic
299C23×D3C23×C311yescharacteristic
300C2×C3×D4—34no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—34no—
315C22×C3×C4—34no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—62no—
319C22×C3×C4—62no—
320C22×C3×C4—62no—
321C22×C3×C4—62no—
322C22×C3×C4—62no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4—62no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C23×C311yescharacteristic
335C22×C3×C4C23×C311yescharacteristic
336C22×C3×C4C23×C311yescharacteristic
337C22×C3×C4C23×C311yescharacteristic
338C22×C3×C4C23×C311yescharacteristic
339C22×C3×C4C23×C311yescharacteristic
340C2×#67—22no—
341C2×#67—22no—
342C2×#67C2×C3×C414yes—
343C22×Dic3—22no—
344C22×Dic3—22no—
345C22×Dic3—22no—
346C22×Dic3C23×C311yescharacteristic
347C22×Dic3C23×C311yescharacteristic
348C22×Dic3C23×C311yescharacteristic
349C22×Dic3C23×C311yescharacteristic
350C22×Dic3C23×C311yescharacteristic
351C22×Dic3C23×C311yescharacteristic
352C22×Dic3C23×C311yescharacteristic
353C2×C4×D3—22no—
354C2×C4×D3—22no—
355C2×C4×D3—22no—
356C2×C4×D3—22no—
357C2×C4×D3—22no—
358C2×C4×D3—22no—
359C2×C4×D3—22no—
360C2×C4×D3C2×C3×C414yescomplemented
361C2×C4×D3C3×D414yes—
362C3×C4⋊C4—22no—
363C3×C4⋊C4—22no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—42no—
367C3×C4⋊C4—62no—
368C3×C4⋊C4—62no—
369C3×C22⋊C4—22no—
370C3×C22⋊C4—22no—
371C3×C22⋊C4—22no—
372C3×C22⋊C4—22no—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—34no—
375C3×C22⋊C4—34no—
376C3×C22⋊C4—42no—
377C3×C22⋊C4—42no—
378C3×C22⋊C4—62no—
379C3×C22⋊C4—62no—
380C3×C22⋊C4—62no—
381C3×C22⋊C4C4×D314yescomplemented
382C3×C22⋊C4C2×C3×C414yescomplemented
383C3×C42—22no—
384C3×C42—22no—
385C3×C42—42no—
386C3×C42—62no—
387C3×C42—62no—
388C3×C42—62no—
389C3×C42—62no—
390C3×C42—62no—
391C3×C42—62no—
392#217—22no—
393#217C2×C3×C414yescomplemented
394(C2×D3)⋊C4—22no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4C2×C3×C414yescomplemented
397C4⋊Dic3C2×C3×C414yescomplemented
398Dic3⋊C4—22no—
399Dic3⋊C4—22no—
400Dic3⋊C4C2×C3×C414yescomplemented
401C4×Dic3—22no—
402C4×Dic3—22no—
403C4×Dic3—22no—
404C4×Dic3—22no—
405C4×Dic3—22no—
406C4×Dic3—22no—
407C22×C32—22no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C23×C411yescharacteristic
415C22×C32C22×D411yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32C2×#4111yescharacteristic
418C22×C32C2×#4111yescharacteristic
419C22×C32C2×#4111yescharacteristic
420C22×C32C2×#4111yescharacteristic
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3C4×D414yes—
428C32×C4—22no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—41no—
433C32×C4—41no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3#12314yescomplemented
441C22×D4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446#123—38no—
447C4×D4—64no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4C2×C3×D311yescharacteristic
453C2×C22⋊C4—31no—
454C2×C22⋊C4—31no—
455C2×C22⋊C4—31no—
456C2×C22⋊C4—31no—
457C2×C22⋊C4—31no—
458C2×C22⋊C4C2×C3×D311yescharacteristic
459C2×C22⋊C4C2×C3×D311yescharacteristic
460C2×C22⋊C4C2×C3×D311yescharacteristic
461C2×C42—31no—
462C2×C42—31no—
463C2×C42—31no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—31no—
467C2×C42—64no—
468C2×C42C2×C3×D311yescharacteristic
469#95—31no—
470#95—31no—
471#95—31no—
472#95—31no—
473#95—31no—
474#95—31no—
475#95—31no—
476#95—31no—
477#95C2×C3×D311yescharacteristic
478#95C2×C3×D311yescharacteristic
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—22no—
493C23×C3—32no—
494C23×C3—32no—
495C23×C3—32no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3C2×C4×D312yes—
507C23×C3C22×C3×C412yes—
508C23×C3C23×D311yescharacteristic
509C23×C3C24×C311yescharacteristic
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3C22×C3×C412yes—
515C22×D3C2×C3×D412yes—
516C22×D3C3×#4112yes—
517C3×D4—68no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
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—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—32no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—68no—
572C2×C3×C4—68no—
573C2×C3×C4—68no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—124no—
589C2×C3×C4C2×C4×D312yes—
590C2×C3×C4C2×C4×D312yes—
591C2×C3×C4D3×D412yes—
592C2×C3×C4#23712yes—
593C2×C3×C4C22×C3×C412yes—
594C2×C3×C4C22×C3×C412yes—
595C2×C3×C4C2×C3×D412yes—
596C2×C3×C4C3×#4112yes—
597#67—28no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—44no—
613C2×Dic3C22×C3×C412yes—
614C2×Dic3C22×C3×C412yes—
615C2×Dic3C22×C3×C412yes—
616C2×Dic3C2×C3×D412yes—
617C2×Dic3C3×#4112yes—
618C2×Dic3C3×#4112yes—
619C2×Dic3C3×#4112yes—
620C4×D3—28no—
621C4×D3—28no—
622C4×D3—28no—
623C2×C32—42no—
624C2×C32C2×C4×D411yescharacteristic
625C2×C32C4×#4111yescharacteristic
626C2×C32C4×#4111yescharacteristic
627C2×C32C2×#12311yescharacteristic
628C2×C32#52511yescharacteristic
629C2×C32#52911yescharacteristic
630C2×C32#52911yescharacteristic
631C3×D3—24no—
632C24—31no—
633C24C22×C3×D311yescharacteristic
634C2×D4—34no—
635C2×D4—62no—
636C2×D4—62no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—34no—
643C22×C4—34no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4C22×C3×D311yescharacteristic
657C22×C4C22×C3×D311yescharacteristic
658C22×C4C22×C3×D311yescharacteristic
659C22×C4C22×C3×D311yescharacteristic
660C22×C4C22×C3×D311yescharacteristic
661C22×C4C22×C3×D311yescharacteristic
662C4⋊C4—22no—
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—62no—
666C4⋊C4—62no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—34no—
670C22⋊C4—34no—
671C22⋊C4—62no—
672C22⋊C4—62no—
673C22⋊C4—62no—
674C22⋊C4C3×C4×D314yescomplemented
675C42—22no—
676C42—62no—
677C42—62no—
678C42—62no—
679C42—62no—
680C42—62no—
681C42—62no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—34no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3C22×C4×D311yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C22×C3C2×#23711yescharacteristic
720C22×C3D3×#4111yescharacteristic
721C22×C3D3×#4111yescharacteristic
722C22×C3D3×#4111yescharacteristic
723C22×C3D3×#4111yescharacteristic
724C22×C3C23×C3×C411yescharacteristic
725C22×C3C22×C3×D411yescharacteristic
726C22×C3C2×C3×#4111yescharacteristic
727C22×C3C2×C3×#4111yescharacteristic
728C22×C3C2×C3×#4111yescharacteristic
729C22×C3C2×C3×#4111yescharacteristic
730C22×C3C2×C3×#4111yescharacteristic
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—22no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3C3×C4×D414yes—
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—22no—
741C3×C4—22no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—34no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—62no—
756C3×C4—62no—
757C3×C4—62no—
758C3×C4—62no—
759C3×C4—81no—
760C3×C4—81no—
761C3×C4—121no—
762C3×C4—121no—
763Dic3—22no—
764Dic3—22no—
765Dic3—22no—
766Dic3—22no—
767Dic3—41no—
768Dic3—41no—
769Dic3C3×#12314yescomplemented
770C32C4×#12311yescharacteristic, complemented, Sylow
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—32no—
778C23—32no—
779C23—32no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23C2×C3×C4×D312yes—
785C23C23×C3×D311yescharacteristic
786D4—68no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—68no—
809C2×C4—68no—
810C2×C4—68no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—124no—
826C2×C4C2×C3×C4×D312yes—
827C2×C4C2×C3×C4×D312yes—
828C2×C4C3×D3×D412yes—
829C2×C4C3×#23712yes—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—42no—
838C2×C3—42no—
839C2×C3—64no—
840C2×C3—82no—
841C2×C3#552211yescharacteristic
842C2×C3C4×#23711yescharacteristic
843C2×C3C4×D3×D411yescharacteristic
844C2×C3#560611yescharacteristic
845C2×C3D3×#12311yescharacteristic
846C2×C3#568011yescharacteristic
847C2×C3#570611yescharacteristic
848C2×C3C2×C3×C4×D411yescharacteristic
849C2×C3C3×C4×#4111yescharacteristic
850C2×C3C3×C4×#4111yescharacteristic
851C2×C3C2×C3×#12311yescharacteristic
852C2×C3C3×#52511yescharacteristic
853C2×C3C3×#52911yescharacteristic
854C2×C3C3×#52911yescharacteristic
855D3—24no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—34no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—62no—
868C22—62no—
869C22—62no—
870C22C22×C3×C4×D311yescharacteristic
871C22C2×C3×D3×D411yescharacteristic
872C22C2×C3×#23711yescharacteristic
873C22C3×D3×#4111yescharacteristic
874C22C3×D3×#4111yescharacteristic
875C22C3×D3×#4111yescharacteristic
876C22C3×D3×#4111yescharacteristic
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—34no—
882C4—41no—
883C4—41no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—121no—
889C4—121no—
890C3—21no—
891C3#7545311yescharacteristic, direct product factor
892C3C3×C4×#12311yescharacteristic, complemented
893C2—42no—
894C2—64no—
895C2C3×#552211yescharacteristic
896C2C3×C4×#23711yescharacteristic
897C2C3×C4×D3×D411yescharacteristic
898C2C3×#560611yescharacteristic
899C2C3×D3×#12311yescharacteristic
900C2C3×#568011yescharacteristic
901C2C3×#570611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#388C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC3×#388D3
hypocenterC3C3×C4×#123
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
3. C2×C3×C42×D3C2semidirect
4. C32×#388C2semidirect
5. C3×#4989C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
8. C3×#4944C2semidirect
9. C3×Dic3×C22⋊C4C2semidirect
10. C3×Dic3×C22⋊C4C2semidirect
11. C3×#4933C2semidirect
12. C3×#4666C2semidirect
13. C3×#4664C2semidirect
14. C3×#4653C2semidirect
15. C3×#4649C2semidirect
17. #75453C3direct (N × H)
43. C3×#883C4semidirect
61. C2×C42×D3C2×C3semidirect
64. C3×#388D3semidirect
65. C3×#388C2×C3semidirect
76. #4989C2×C3semidirect
77. Dic3×C4⋊C4C2×C3semidirect
79. #4944C2×C3semidirect
80. Dic3×C22⋊C4C2×C3semidirect
81. Dic3×C22⋊C4C2×C3semidirect
82. #4933C2×C3semidirect
83. #4666C2×C3semidirect
84. #4664C2×C3semidirect
85. #4653C2×C3semidirect
86. #4649C2×C3semidirect
115. C2×C3×C4×D3C2×C4semidirect
120. C32×C22⋊C4C2×C4semidirect
123. C3×#217C2×C4semidirect
126. C3×(C2×D3)⋊C4C2×C4semidirect
127. C3×C4⋊Dic3C2×C4semidirect
130. C3×Dic3⋊C4C2×C4semidirect
196. #883C3×C4semidirect
284. #388C3×D3semidirect
360. C2×C4×D3C2×C3×C4semidirect
381. C3×C22⋊C4C4×D3semidirect
382. C3×C22⋊C4C2×C3×C4semidirect
393. #217C2×C3×C4semidirect
396. (C2×D3)⋊C4C2×C3×C4semidirect
397. C4⋊Dic3C2×C3×C4semidirect
400. Dic3⋊C4C2×C3×C4semidirect
440. C3×Dic3#123semidirect
674. C22⋊C4C3×C4×D3semidirect
769. Dic3C3×#123semidirect
770. C32C4×#123semidirect
891. C3#75453direct (N × H)
892. C3C3×C4×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8832
C2×C3×#67⋊C42
C2×C3×C42×D32
C32×#3882
C3×#49892
C3×Dic3×C4⋊C42
C3×#49562
C3×#49442
C3×Dic3×C22⋊C42
C3×#49332
C3×#46662
C3×#46642
C3×#46532
C3×#46492
C3×C4×#1233
#754533