Finite Group Databasebeta

← C3×C4×#894 #11802152

Subgroups — C3×C4×#894 #11802152

Order 1152.

1473 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#894C211yesmaximal, characteristic
2C2×C3×C4×D12C211yesmaximal, characteristic
3C2×C3×C42×D3C211yesmaximal, characteristic, complemented
4C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#4990C211yesmaximal, characteristic, complemented
6C3×#4989C211yesmaximal, characteristic, complemented
7C3×#4980C211yesmaximal, characteristic, complemented
8C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
9C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×#4669C211yesmaximal, characteristic, complemented
13C3×#4665C211yesmaximal, characteristic
14C3×#4664C211yesmaximal, characteristic, complemented
15C3×#4655C211yesmaximal, characteristic, complemented
16C3×C4×#123—31nomaximal
17C4×#894C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×C32×C42C2211yescharacteristic
27C2×C32×C42C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#894C418yesdirect product factor
44C3×C4×D12—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×#894C2×C311yescharacteristic
60C2×C4×D12C2×C311yescharacteristic
61C2×C42×D3C2×C311yescharacteristic, complemented
62C3×#388—31no—
63C3×#388—31no—
64C3×#387—31no—
65C3×#387—31no—
66C3×#386—31no—
67C3×#385—31no—
68C3×#381—31no—
69C3×C4×C4⋊C4—21no—
70C3×C4×C4⋊C4—31no—
71C3×C4×C4⋊C4D311yescharacteristic, complemented
72C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
73C3×C4×C22⋊C4—31no—
74C3×C4×C22⋊C4—31no—
75C3×C4×C22⋊C4—31no—
76#4990C2×C311yescharacteristic, complemented
77#4989C2×C311yescharacteristic, complemented
78#4980C2×C311yescharacteristic, complemented
79C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
80C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
81C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
82C4×Dic3⋊C4C2×C311yescharacteristic, complemented
83#4669C2×C311yescharacteristic, complemented
84#4665C2×C311yescharacteristic
85#4664C2×C311yescharacteristic, complemented
86#4655C2×C311yescharacteristic, complemented
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×D12—22no—
103C2×C3×D12—22no—
104C2×C3×D12C2×C414yes—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
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×C4⋊C4C2×C414yescomplemented
119C32×C42—22no—
120C32×C42—22no—
121C32×C42—22no—
122C3×(C2×D3)⋊C4—22no—
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4—22no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4C2×C414yescomplemented
128C3×(C2×D3)⋊C4C2×C414yescomplemented
129C3×(C2×D3)⋊C4C2×C414yescomplemented
130C3×C4⋊Dic3—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4C2×C414yescomplemented
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×D12C22×C311yescharacteristic
144C22×C4×D3C22×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—21no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×C3×C4⋊C4C22×C311yescharacteristic
158C2×C3×C4⋊C4C22×C311yescharacteristic
159C2×C3×C22⋊C4—31no—
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⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C42—21no—
168C2×C3×C42—21no—
169C2×C3×C42—21no—
170C2×C3×C42—31no—
171C2×C3×C42—31no—
172C2×C3×C42—31no—
173C2×C3×C42—31no—
174C2×C3×C42—64no—
175C2×C3×C42C2×D311yescharacteristic
176C2×C3×C42C2×D311yescharacteristic
177C2×C3×C42C2×D311yescharacteristic
178C2×C3×C42C22×C311yescharacteristic
179C2×C3×C42C22×C311yescharacteristic
180C2×C3×C42C22×C311yescharacteristic
181C2×(C2×D3)⋊C4C22×C311yescharacteristic
182C2×(C2×D3)⋊C4C22×C311yescharacteristic
183C2×(C2×D3)⋊C4C22×C311yescharacteristic
184C2×(C2×D3)⋊C4C22×C311yescharacteristic
185C2×(C2×D3)⋊C4C22×C311yescharacteristic
186C2×(C2×D3)⋊C4C22×C311yescharacteristic
187C2×(C2×D3)⋊C4C22×C311yescharacteristic
188C2×(C2×D3)⋊C4C22×C311yescharacteristic
189C2×C4⋊Dic3C22×C311yescharacteristic
190C2×Dic3⋊C4C22×C311yescharacteristic
191C2×Dic3⋊C4C22×C311yescharacteristic
192C2×C4×Dic3C22×C311yescharacteristic
193C2×C4×Dic3C22×C311yescharacteristic
194C2×C4×Dic3C22×C311yescharacteristic
195C2×C4×Dic3C22×C311yescharacteristic
196#894C3×C418yesdirect product factor
197C4×D12—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×C32C2411yescharacteristic
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3C22×C412yes—
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×C4C22×C412yes—
253C2×C32×C4C2×D412yes—
254C2×C32×C4#4112yes—
255C2×C32×C4#4112yes—
256C2×C32×C4#4112yes—
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—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3C22×C412yes—
272C2×C3×Dic3C22×C412yes—
273C2×C3×Dic3C2×D412yes—
274C2×C3×Dic3#4112yes—
275C3×D12—28no—
276C3×C4×D3—28no—
277C3×C4×D3—28no—
278C3×C4×D3—28no—
279C3×C4×D3—44no—
280C2×#123—31no—
281C2×C4×D4—31no—
282C22×C42—31no—
283#388—31no—
284#388—31no—
285#387—31no—
286#387—31no—
287#386—31no—
288#385—31no—
289#381—31no—
290C4×C4⋊C4—31no—
291C4×C4⋊C4C3×D311yescharacteristic, complemented
292C4×C22⋊C4—31no—
293C4×C22⋊C4—31no—
294C4×C22⋊C4—31no—
295C24×C3—31no—
296C24×C3—31no—
297C23×D3C23×C311yescharacteristic
298C23×D3C23×C311yescharacteristic
299C2×C3×D4—34no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C22×C3×C4—21no—
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—34no—
314C22×C3×C4—34no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—62no—
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×C4C22×D311yescharacteristic
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
340C22×C3×C4C23×C311yescharacteristic
341C22×Dic3C23×C311yescharacteristic
342C22×Dic3C23×C311yescharacteristic
343C22×Dic3C23×C311yescharacteristic
344C22×Dic3C23×C311yescharacteristic
345C22×Dic3C23×C311yescharacteristic
346C22×Dic3C23×C311yescharacteristic
347C2×D12—22no—
348C2×D12—22no—
349C2×D12C2×C3×C414yes—
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
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—24no—
363C3×C4⋊C4—22no—
364C3×C4⋊C4—22no—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4—62no—
368C3×C4⋊C4—62no—
369C3×C4⋊C4C4×D314yescomplemented
370C3×C4⋊C4C2×C3×C414yescomplemented
371C3×C22⋊C4—34no—
372C3×C22⋊C4—34no—
373C3×C22⋊C4—34no—
374C3×C22⋊C4—62no—
375C3×C22⋊C4—62no—
376C3×C22⋊C4—62no—
377C3×C22⋊C4—62no—
378C3×C22⋊C4—62no—
379C3×C42—24no—
380C3×C42—22no—
381C3×C42—22no—
382C3×C42—22no—
383C3×C42—22no—
384C3×C42—22no—
385C3×C42—22no—
386C3×C42—42no—
387C3×C42—42no—
388C3×C42—62no—
389C3×C42—62no—
390C3×C42—62no—
391C3×C42—62no—
392(C2×D3)⋊C4—22no—
393(C2×D3)⋊C4—22no—
394(C2×D3)⋊C4—22no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4C2×C3×C414yescomplemented
398(C2×D3)⋊C4C2×C3×C414yescomplemented
399(C2×D3)⋊C4C2×C3×C414yescomplemented
400C4⋊Dic3—22no—
401Dic3⋊C4—22no—
402Dic3⋊C4C2×C3×C414yescomplemented
403C4×Dic3—22no—
404C4×Dic3—22no—
405C4×Dic3—22no—
406C4×Dic3—22no—
407C22×C32C23×C411yescharacteristic
408C22×C32C22×D411yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C22×C32C2×#4111yescharacteristic
413C22×C32C2×#4111yescharacteristic
414C2×C3×D3—22no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3C4×D414yes—
428C32×C4—22no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4#12314yescomplemented
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—41no—
440C3×Dic3—41no—
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⋊C4C2×C3×D311yescharacteristic
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⋊C4—31no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—31no—
461C2×C42—31no—
462C2×C42—31no—
463C2×C42—31no—
464C2×C42—31no—
465C2×C42—64no—
466C2×C42C2×C3×D311yescharacteristic
467C2×C42C2×C3×D311yescharacteristic
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—32no—
481C23×C3—32no—
482C23×C3—32no—
483C23×C3—32no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3C23×D311yescharacteristic
495C23×C3C24×C311yescharacteristic
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3C22×C3×C412yes—
507C22×D3C22×C3×C412yes—
508C22×D3C2×C3×D412yes—
509C22×D3C3×#4112yes—
510C3×D4—68no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
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—22no—
530C2×C3×C4—22no—
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—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
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—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
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—68no—
565C2×C3×C4—68no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—68no—
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—124no—
582C2×C3×C4C2×C4×D312yes—
583C2×C3×C4C2×C4×D312yes—
584C2×C3×C4C2×C4×D312yes—
585C2×C3×C4#23512yes—
586C2×C3×C4#23512yes—
587C2×C3×C4D3×D412yes—
588C2×C3×C4#23912yes—
589C2×C3×C4C22×C3×C412yes—
590C2×C3×C4C22×C3×C412yes—
591C2×C3×C4C22×C3×C412yes—
592C2×C3×C4C2×C3×D412yes—
593C2×C3×C4C3×#4112yes—
594C2×C3×C4C3×#4112yes—
595C2×C3×C4C3×#4112yes—
596C2×Dic3—21no—
597C2×Dic3—21no—
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×Dic3C22×C3×C412yes—
611C2×Dic3C22×C3×C412yes—
612C2×Dic3C2×C3×D412yes—
613C2×Dic3C3×#4112yes—
614D12—28no—
615C4×D3—28no—
616C4×D3—28no—
617C4×D3—28no—
618C4×D3—44no—
619C2×C32C2×C4×D411yescharacteristic
620C2×C32C4×#4111yescharacteristic
621C2×C32C4×#4111yescharacteristic
622C2×C32C2×#12311yescharacteristic
623C2×C32#52511yescharacteristic
624C2×C32#52911yescharacteristic
625C2×C32#52911yescharacteristic
626C3×D3—24no—
627C3×D3—42no—
628C24—31no—
629C24—31no—
630C2×D4—34no—
631C2×D4—62no—
632C2×D4—62no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—34no—
638C22×C4—34no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—62no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4C22×C3×D311yescharacteristic
652C22×C4C22×C3×D311yescharacteristic
653C22×C4C22×C3×D311yescharacteristic
654C22×C4C22×C3×D311yescharacteristic
655C22×C4C22×C3×D311yescharacteristic
656C22×C4C22×C3×D311yescharacteristic
657C22×C4C22×C3×D311yescharacteristic
658C4⋊C4—22no—
659C4⋊C4—34no—
660C4⋊C4—62no—
661C4⋊C4—62no—
662C4⋊C4C3×C4×D314yescomplemented
663C22⋊C4—34no—
664C22⋊C4—34no—
665C22⋊C4—34no—
666C22⋊C4—62no—
667C22⋊C4—62no—
668C22⋊C4—62no—
669C22⋊C4—62no—
670C22⋊C4—62no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—62no—
675C42—62no—
676C42—62no—
677C42—62no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—34no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3C22×C4×D311yescharacteristic
700C22×C3C2×#23511yescharacteristic
701C22×C3C2×#23511yescharacteristic
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×#23911yescharacteristic
704C22×C3D3×#4111yescharacteristic
705C22×C3D3×#4111yescharacteristic
706C22×C3C23×C3×C411yescharacteristic
707C22×C3C22×C3×D411yescharacteristic
708C22×C3C2×C3×#4111yescharacteristic
709C22×C3C2×C3×#4111yescharacteristic
710C22×C3C2×C3×#4111yescharacteristic
711C22×C3C2×C3×#4111yescharacteristic
712C22×C3C2×C3×#4111yescharacteristic
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—22no—
721C2×D3—22no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3C3×C4×D414yes—
727C3×C4—24no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—22no—
735C3×C4—22no—
736C3×C4—24no—
737C3×C4—42no—
738C3×C4—42no—
739C3×C4—42no—
740C3×C4—42no—
741C3×C4—42no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—62no—
747C3×C4—62no—
748C3×C4—62no—
749C3×C4—62no—
750C3×C4—121no—
751C3×C4—121no—
752C3×C4#89414yesdirect product factor
753C3×C4C3×#12314yescomplemented
754Dic3—22no—
755Dic3—22no—
756Dic3—22no—
757Dic3—22no—
758Dic3—41no—
759Dic3—41no—
760C32C4×#12311yescharacteristic, complemented, Sylow
761C23—32no—
762C23—32no—
763C23—32no—
764C23—32no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—61no—
771C23—61no—
772C23—61no—
773C23—61no—
774C23—61no—
775C23C23×C3×D311yescharacteristic
776D4—68no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—32no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—32no—
795C2×C4—68no—
796C2×C4—68no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—68no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—124no—
813C2×C4C2×C3×C4×D312yes—
814C2×C4C2×C3×C4×D312yes—
815C2×C4C2×C3×C4×D312yes—
816C2×C4C3×#23512yes—
817C2×C4C3×#23512yes—
818C2×C4C3×D3×D412yes—
819C2×C4C3×#23912yes—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—64no—
828C2×C3—122no—
829C2×C3C4×#23511yescharacteristic
830C2×C3C2×#89411yescharacteristic
831C2×C3#552811yescharacteristic
832C2×C3C4×D3×D411yescharacteristic
833C2×C3#554711yescharacteristic
834C2×C3C4×#23911yescharacteristic
835C2×C3#558011yescharacteristic
836C2×C3C2×C3×C4×D411yescharacteristic
837C2×C3C3×C4×#4111yescharacteristic
838C2×C3C3×C4×#4111yescharacteristic
839C2×C3C2×C3×#12311yescharacteristic
840C2×C3C3×#52511yescharacteristic
841C2×C3C3×#52911yescharacteristic
842C2×C3C3×#52911yescharacteristic
843D3—24no—
844D3—42no—
845C22—34no—
846C22—62no—
847C22—62no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22C22×C3×C4×D311yescharacteristic
860C22C2×C3×#23511yescharacteristic
861C22C2×C3×#23511yescharacteristic
862C22C2×C3×D3×D411yescharacteristic
863C22C2×C3×#23911yescharacteristic
864C22C3×D3×#4111yescharacteristic
865C22C3×D3×#4111yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—41no—
871C4—41no—
872C4—62no—
873C4—62no—
874C4—62no—
875C4—62no—
876C4—121no—
877C4—121no—
878C4C3×#89414yesdirect product factor
879C3—21no—
880C3C4×#89411yescharacteristic, direct product factor
881C3C3×C4×#12311yescharacteristic, complemented
882C2—64no—
883C2—122no—
884C2C3×C4×#23511yescharacteristic
885C2C2×C3×#89411yescharacteristic
886C2C3×#552811yescharacteristic
887C2C3×C4×D3×D411yescharacteristic
888C2C3×#554711yescharacteristic
889C2C3×C4×#23911yescharacteristic
890C2C3×#558011yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC22×C3×D12C22
cosocleC23×C3C24×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×C4×#123
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×C42×D3C2semidirect
4. C32×C4×C4⋊C4C2semidirect
5. C3×#4990C2semidirect
6. C3×#4989C2semidirect
7. C3×#4980C2semidirect
8. C3×C4×(C2×D3)⋊C4C2semidirect
9. C3×C4×(C2×D3)⋊C4C2semidirect
10. C3×C4×(C2×D3)⋊C4C2semidirect
11. C3×C4×Dic3⋊C4C2semidirect
12. C3×#4669C2semidirect
14. C3×#4664C2semidirect
15. C3×#4655C2semidirect
17. C4×#894C3direct (N × H)
43. C3×#894C4direct (N × H)
61. C2×C42×D3C2×C3semidirect
71. C3×C4×C4⋊C4D3semidirect
72. C3×C4×C4⋊C4C2×C3semidirect
76. #4990C2×C3semidirect
77. #4989C2×C3semidirect
78. #4980C2×C3semidirect
79. C4×(C2×D3)⋊C4C2×C3semidirect
80. C4×(C2×D3)⋊C4C2×C3semidirect
81. C4×(C2×D3)⋊C4C2×C3semidirect
82. C4×Dic3⋊C4C2×C3semidirect
83. #4669C2×C3semidirect
85. #4664C2×C3semidirect
86. #4655C2×C3semidirect
115. C2×C3×C4×D3C2×C4semidirect
118. C32×C4⋊C4C2×C4semidirect
127. C3×(C2×D3)⋊C4C2×C4semidirect
128. C3×(C2×D3)⋊C4C2×C4semidirect
129. C3×(C2×D3)⋊C4C2×C4semidirect
132. C3×Dic3⋊C4C2×C4semidirect
196. #894C3×C4direct (N × H)
291. C4×C4⋊C4C3×D3semidirect
360. C2×C4×D3C2×C3×C4semidirect
369. C3×C4⋊C4C4×D3semidirect
370. C3×C4⋊C4C2×C3×C4semidirect
397. (C2×D3)⋊C4C2×C3×C4semidirect
398. (C2×D3)⋊C4C2×C3×C4semidirect
399. (C2×D3)⋊C4C2×C3×C4semidirect
402. Dic3⋊C4C2×C3×C4semidirect
434. C32×C4#123semidirect
662. C4⋊C4C3×C4×D3semidirect
752. C3×C4#894direct (N × H)
753. C3×C4C3×#123semidirect
760. C32C4×#123semidirect
878. C4C3×#894direct (N × H)
880. C3C4×#894direct (N × H)
881. 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×#8942
C2×C3×C4×D122
C2×C3×C42×D32
C32×C4×C4⋊C42
C3×#49902
C3×#49892
C3×#49802
C3×C4×(C2×D3)⋊C42
C3×C4×Dic3⋊C42
C3×#46692
C3×#46652
C3×#46642
C3×#46552
C3×C4×#1233
C4×#8943