Finite Group Databasebeta

← C3×#74596 #11806086

Subgroups — C3×#74596 #11806086

Order 1152.

1973 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#893C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C32×#385C211yesmaximal, characteristic, complemented
7C3×#4990C211yesmaximal, characteristic, complemented
8C3×#4989C211yesmaximal, characteristic, complemented
9C3×#4988C211yesmaximal, characteristic, complemented
10C3×#4958C211yesmaximal, characteristic, complemented
11C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
12C3×#4669C211yesmaximal, characteristic, complemented
13C3×#4666C211yesmaximal, characteristic, complemented
14C3×#4665C211yesmaximal, characteristic, complemented
15C3×#4665C211yesmaximal, characteristic, complemented
16C3×#2358—31nomaximal
17#74596C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C3×C4×#67—24no—
33C2×C3×(C2×D3)⋊C4—24no—
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C2×C3×C4×Dic3C2211yescharacteristic, complemented
48C2×C3×C4×Dic3C2211yescharacteristic, complemented
49C3×#893—24no—
50C3×#882C418yescomplemented
51C3×D3×C22⋊C4—24no—
52C32×#95C2211yescharacteristic, complemented
53C32×#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C3×C3⋊#95C2211yescharacteristic, complemented
58C2×C3×#120—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—31no—
61C22×C3×C22⋊C4—31no—
62C22×C3×C22⋊C4—31no—
63C2×C4×#67C2×C311yescharacteristic, complemented
64C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
65C2×#893C2×C311yescharacteristic, complemented
66C2×#882C2×C311yescharacteristic
67C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
68C3×#390—31no—
69C3×#388—31no—
70C3×#388—31no—
71C3×#386—31no—
72C3×#386—31no—
73C3×#386—31no—
74C3×#385—21no—
75C3×#385—31no—
76C3×#385D311yescharacteristic, complemented
77C3×#385C2×C311yescharacteristic, complemented
78C3×C4×C22⋊C4—31no—
79C3×C4×C22⋊C4—31no—
80#4990C2×C311yescharacteristic, complemented
81#4989C2×C311yescharacteristic, complemented
82#4988C2×C311yescharacteristic, complemented
83#4958C2×C311yescharacteristic, complemented
84Dic3×C22⋊C4C2×C311yescharacteristic, complemented
85#4669C2×C311yescharacteristic, complemented
86#4666C2×C311yescharacteristic, complemented
87#4665C2×C311yescharacteristic, complemented
88#4665C2×C311yescharacteristic, complemented
89C24×C32C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—41no—
95C23×C3×D3—41no—
96C23×C3×D3C2×C414yescomplemented
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C23×C3×D3C2311yescharacteristic
100C22×C32×C4—22no—
101C22×C32×C4—22no—
102C22×C32×C4—41no—
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67C2×C414yescomplemented
112C22×C3×Dic3—22no—
113C22×C3×Dic3—22no—
114C22×C3×Dic3—41no—
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C2×C3×D12—22no—
121C2×C3×D12—22no—
122C2×C3×D12—41no—
123C2×C3×D12—41no—
124C2×C3×D12C2×C414yescomplemented
125C2×C3×D12C2×C414yescomplemented
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3—22no—
128C2×C3×C4×D3—22no—
129C2×C3×C4×D3—22no—
130C2×C3×C4×D3—22no—
131C2×C3×C4×D3—22no—
132C2×C3×C4×D3—41no—
133C2×C3×C4×D3—41no—
134C2×C3×C4×D3—41no—
135C32×C4⋊C4—22no—
136C32×C4⋊C4—41no—
137C32×C22⋊C4—22no—
138C32×C22⋊C4C2×C414yescomplemented
139C3×#217D414yescomplemented
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×(C2×D3)⋊C4—41no—
148C3×(C2×D3)⋊C4C2×C414yescomplemented
149C3×(C2×D3)⋊C4C2×C414yescomplemented
150C3×(C2×D3)⋊C4D414yescomplemented
151C3×Dic3⋊C4—22no—
152C3×C4×Dic3—22no—
153C3×C4×Dic3—22no—
154C3×C4×Dic3—41no—
155#2358—31noSylow
156C25×C3—31no—
157C24×D3C22×C311yescharacteristic
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C23×C3×C4—21no—
162C23×C3×C4—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C23×C3×C4C2×D311yescharacteristic
167C23×C3×C4C22×C311yescharacteristic
168C22×#67C22×C311yescharacteristic
169C23×Dic3C22×C311yescharacteristic
170C22×D12C22×C311yescharacteristic
171C22×D12C22×C311yescharacteristic
172C22×C4×D3C22×C311yescharacteristic
173C22×C4×D3C22×C311yescharacteristic
174C22×C4×D3C22×C311yescharacteristic, complemented
175C3×#120—38no—
176C3×C4×D4—64no—
177C3×C4×D4—64no—
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4—21no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
182C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
183C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
184C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
185C2×C3×C22⋊C4—21no—
186C2×C3×C22⋊C4—21no—
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—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—64no—
200C2×C3×C22⋊C4—64no—
201C2×C3×C22⋊C4C2×D311yescharacteristic
202C2×C3×C22⋊C4C2×D311yescharacteristic
203C2×C3×C22⋊C4C22×C311yescharacteristic
204C2×C3×C22⋊C4C22×C311yescharacteristic
205C2×C3×C42—31no—
206C2×C3×C42—31no—
207C2×C3×C42—31no—
208C2×#217C22×C311yescharacteristic
209C4×#67—24no—
210C2×(C2×D3)⋊C4—24no—
211C2×(C2×D3)⋊C4C22×C311yescharacteristic
212C2×(C2×D3)⋊C4C22×C311yescharacteristic
213C2×(C2×D3)⋊C4C22×C311yescharacteristic
214C2×(C2×D3)⋊C4C22×C311yescharacteristic
215C2×(C2×D3)⋊C4C22×C311yescharacteristic
216C2×(C2×D3)⋊C4C22×C311yescharacteristic
217C2×(C2×D3)⋊C4C22×C311yescharacteristic
218C2×(C2×D3)⋊C4C22×C311yescharacteristic
219C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
220C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
221C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
222C2×Dic3⋊C4C22×C311yescharacteristic, complemented
223C2×C4×Dic3C22×C311yescharacteristic, complemented
224C2×C4×Dic3C22×C311yescharacteristic, complemented
225C2×C4×Dic3C22×C311yescharacteristic, complemented
226#893—24no—
227#882C3×C418yescomplemented
228D3×C22⋊C4—24no—
229C3×#95—21no—
230C3×#95—21no—
231C3×#95—31no—
232C3×#95—31no—
233C3×#95—31no—
234C3×#95—31no—
235C3×#95C2×D311yescharacteristic, complemented
236C3×#95C2×D311yescharacteristic, complemented
237C3×#95C22×C311yescharacteristic, complemented
238C3×#95C22×C311yescharacteristic, complemented
239C3⋊#95C22×C311yescharacteristic, complemented
240C3⋊#95C22×C311yescharacteristic, complemented
241C3⋊#95C22×C311yescharacteristic, complemented
242C3⋊#95C22×C311yescharacteristic, complemented
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32C22×C412yes—
248C23×C32C2×D412yes—
249C23×C32#4112yes—
250C23×C32C2411yescharacteristic
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—28no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—28no—
269C22×C3×D3—44no—
270C22×C3×D3—44no—
271C22×C3×D3—44no—
272C22×C3×D3—44no—
273C22×C3×D3—44no—
274C22×C3×D3C22×C412yes—
275C22×C3×D3C22×C412yes—
276C22×C3×D3C22×C412yes—
277C22×C3×D3C2×D412yes—
278C22×C3×D3#4112yes—
279C2×C32×C4—21no—
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—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—44no—
295C2×C32×C4C22×C412yes—
296C2×C32×C4C22×C412yes—
297C2×C32×C4C2×D412yes—
298C3×#67—28no—
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—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—44no—
311C2×C3×Dic3C22×C412yes—
312C2×C3×Dic3C2×D412yes—
313C2×C3×Dic3C2×D412yes—
314C2×C3×Dic3C2×D412yes—
315C3×D12—28no—
316C3×D12—44no—
317C3×C4×D3—44no—
318C3×C4×D3—44no—
319C3×C4×D3—44no—
320C2×#120—31no—
321C2×C4×D4—31no—
322C2×C4×D4—31no—
323C22×C22⋊C4—31no—
324C22×C22⋊C4—31no—
325#390—31no—
326#388—31no—
327#388—31no—
328#386—31no—
329#386—31no—
330#386—31no—
331#385—31no—
332#385C3×D311yescharacteristic, complemented
333C4×C22⋊C4—31no—
334C4×C22⋊C4—31no—
335C24×C3—21no—
336C24×C3—31no—
337C24×C3—31no—
338C24×C3—31no—
339C24×C3—34no—
340C24×C3—62no—
341C24×C3—62no—
342C24×C3—62no—
343C24×C3—62no—
344C24×C3—121no—
345C24×C3—121no—
346C24×C3C22×D311yescharacteristic
347C24×C3C23×C311yescharacteristic
348C23×D3—22no—
349C23×D3—22no—
350C23×D3—22no—
351C23×D3—22no—
352C23×D3—41no—
353C23×D3—41no—
354C23×D3C2×C3×C414yescomplemented
355C23×D3C23×C311yescharacteristic
356C23×D3C23×C311yescharacteristic
357C23×D3C23×C311yescharacteristic
358C2×C3×D4—34no—
359C2×C3×D4—34no—
360C2×C3×D4—34no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—62no—
365C2×C3×D4—121no—
366C2×C3×D4—121no—
367C22×C3×C4—22no—
368C22×C3×C4—22no—
369C22×C3×C4—22no—
370C22×C3×C4—22no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—42no—
383C22×C3×C4—42no—
384C22×C3×C4—41no—
385C22×C3×C4—41no—
386C22×C3×C4—42no—
387C22×C3×C4—62no—
388C22×C3×C4—62no—
389C22×C3×C4—62no—
390C22×C3×C4—62no—
391C22×C3×C4—62no—
392C22×C3×C4—62no—
393C22×C3×C4—62no—
394C22×C3×C4—62no—
395C22×C3×C4—121no—
396C22×C3×C4—121no—
397C22×C3×C4—121no—
398C22×C3×C4—121no—
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C23×C311yescharacteristic
406C22×C3×C4C23×C311yescharacteristic
407C22×C3×C4C23×C311yescharacteristic
408C22×C3×C4C23×C311yescharacteristic
409C22×C3×C4C23×C311yescharacteristic
410C22×C3×C4C23×C311yescharacteristic
411C2×#67—22no—
412C2×#67—22no—
413C2×#67C2×C3×C414yescomplemented
414C22×Dic3—22no—
415C22×Dic3—22no—
416C22×Dic3—41no—
417C22×Dic3C23×C311yescharacteristic
418C22×Dic3C23×C311yescharacteristic
419C22×Dic3C23×C311yescharacteristic
420C22×Dic3C23×C311yescharacteristic
421C22×Dic3C23×C311yescharacteristic
422C2×D12—22no—
423C2×D12—22no—
424C2×D12—41no—
425C2×D12—41no—
426C2×D12C2×C3×C414yescomplemented
427C2×D12C2×C3×C414yescomplemented
428C2×C4×D3—22no—
429C2×C4×D3—22no—
430C2×C4×D3—22no—
431C2×C4×D3—22no—
432C2×C4×D3—22no—
433C2×C4×D3—22no—
434C2×C4×D3—41no—
435C2×C4×D3—41no—
436C2×C4×D3—41no—
437C3×C4⋊C4—22no—
438C3×C4⋊C4—22no—
439C3×C4⋊C4—42no—
440C3×C4⋊C4—41no—
441C3×C4⋊C4—41no—
442C3×C4⋊C4—42no—
443C3×C4⋊C4—62no—
444C3×C22⋊C4—22no—
445C3×C22⋊C4—22no—
446C3×C22⋊C4—24no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—42no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—62no—
454C3×C22⋊C4—62no—
455C3×C22⋊C4—62no—
456C3×C22⋊C4—62no—
457C3×C22⋊C4—62no—
458C3×C22⋊C4—62no—
459C3×C22⋊C4—121no—
460C3×C22⋊C4C4×D314yescomplemented
461C3×C22⋊C4C2×C3×C414yescomplemented
462C3×C42—62no—
463C3×C42—62no—
464C3×C42—121no—
465#217C3×D414yescomplemented
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—22no—
470(C2×D3)⋊C4—22no—
471(C2×D3)⋊C4—22no—
472(C2×D3)⋊C4—22no—
473(C2×D3)⋊C4—41no—
474(C2×D3)⋊C4C2×C3×C414yescomplemented
475(C2×D3)⋊C4C2×C3×C414yescomplemented
476(C2×D3)⋊C4C3×D414yescomplemented
477Dic3⋊C4—22no—
478C4×Dic3—22no—
479C4×Dic3—22no—
480C4×Dic3—41no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32C4×D414yescomplemented
488C22×C32C23×C411yescharacteristic
489C22×C32C22×D411yescharacteristic
490C22×C32C22×D411yescharacteristic
491C22×C32C2×#4111yescharacteristic
492C22×C32C2×#4111yescharacteristic
493C22×C32H(5,𝔽2)11yescharacteristic
494C22×C32H(5,𝔽2)11yescharacteristic
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—416no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—41no—
513C2×C3×D3—41no—
514C2×C3×D3—41no—
515C2×C3×D3—41no—
516C2×C3×D3C4×D414yescomplemented
517C32×C4—22no—
518C32×C4—22no—
519C32×C4—22no—
520C32×C4—41no—
521C32×C4—41no—
522C32×C4—41no—
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—41no—
528C25—31no—
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—31no—
532C23×C4—31no—
533C23×C4—31no—
534C23×C4—31no—
535C23×C4—31no—
536C23×C4C2×C3×D311yescharacteristic
537#120—38no—
538C4×D4—64no—
539C4×D4—64no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
542C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
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—31no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—64no—
556C2×C22⋊C4—64no—
557C2×C22⋊C4C2×C3×D311yescharacteristic
558C2×C22⋊C4C2×C3×D311yescharacteristic
559C2×C42—31no—
560C2×C42—31no—
561C2×C42—31no—
562#95—31no—
563#95—31no—
564#95—31no—
565#95—31no—
566#95C2×C3×D311yescharacteristic, complemented
567#95C2×C3×D311yescharacteristic, complemented
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—32no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—68no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—68no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—124no—
608C23×C3—124no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3—124no—
612C23×C3C2×C4×D312yes—
613C23×C3D3×D412yes—
614C23×C3#23912yes—
615C23×C3C22×C3×C412yes—
616C23×C3C2×C3×D412yes—
617C23×C3C3×#4112yes—
618C23×C3C23×D311yescharacteristic
619C23×C3C24×C311yescharacteristic
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—28no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—21no—
634C22×D3—21no—
635C22×D3—21no—
636C22×D3—21no—
637C22×D3—28no—
638C22×D3—44no—
639C22×D3—44no—
640C22×D3—44no—
641C22×D3—44no—
642C22×D3—44no—
643C22×D3C22×C3×C412yes—
644C22×D3C22×C3×C412yes—
645C22×D3C22×C3×C412yes—
646C22×D3C2×C3×D412yes—
647C22×D3C3×#4112yes—
648C3×D4—68no—
649C3×D4—68no—
650C3×D4—124no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—22no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—32no—
686C2×C3×C4—32no—
687C2×C3×C4—32no—
688C2×C3×C4—32no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—44no—
704C2×C3×C4—44no—
705C2×C3×C4—48no—
706C2×C3×C4—61no—
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—124no—
718C2×C3×C4—124no—
719C2×C3×C4—124no—
720C2×C3×C4—124no—
721C2×C3×C4C2×C4×D312yes—
722C2×C3×C4C2×C4×D312yes—
723C2×C3×C4D3×D412yes—
724C2×C3×C4C22×C3×C412yes—
725C2×C3×C4C22×C3×C412yes—
726C2×C3×C4C2×C3×D412yes—
727#67—28no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—21no—
737C2×Dic3—21no—
738C2×Dic3—21no—
739C2×Dic3—44no—
740C2×Dic3C22×C3×C412yes—
741C2×Dic3C2×C3×D412yes—
742C2×Dic3C2×C3×D412yes—
743C2×Dic3C2×C3×D412yes—
744D12—28no—
745D12—44no—
746C4×D3—44no—
747C4×D3—44no—
748C4×D3—44no—
749C2×C32—24no—
750C2×C32C2×C4×D411yescharacteristic
751C2×C32C2×C4×D411yescharacteristic
752C2×C32#51811yescharacteristic
753C2×C32D4211yescharacteristic
754C2×C32#54611yescharacteristic
755C2×C32#54611yescharacteristic
756C2×C32#55111yescharacteristic
757C3×D3—24no—
758C3×D3—42no—
759C3×D3—42no—
760C24—31no—
761C24—31no—
762C24—31no—
763C24—34no—
764C24—62no—
765C24—62no—
766C24—62no—
767C24—62no—
768C24—121no—
769C24—121no—
770C24C22×C3×D311yescharacteristic
771C2×D4—34no—
772C2×D4—34no—
773C2×D4—34no—
774C2×D4—62no—
775C2×D4—62no—
776C2×D4—62no—
777C2×D4—62no—
778C2×D4—121no—
779C2×D4—121no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—31no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—31no—
786C22×C4—31no—
787C22×C4—41no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—62no—
791C22×C4—62no—
792C22×C4—62no—
793C22×C4—62no—
794C22×C4—62no—
795C22×C4—62no—
796C22×C4—121no—
797C22×C4—121no—
798C22×C4—121no—
799C22×C4—121no—
800C22×C4C22×C3×D311yescharacteristic
801C22×C4C22×C3×D311yescharacteristic
802C22×C4C22×C3×D311yescharacteristic
803C22×C4C22×C3×D311yescharacteristic
804C22×C4C22×C3×D311yescharacteristic
805C22×C4C22×C3×D311yescharacteristic
806C4⋊C4—22no—
807C4⋊C4—41no—
808C4⋊C4—62no—
809C22⋊C4—22no—
810C22⋊C4—34no—
811C22⋊C4—34no—
812C22⋊C4—34no—
813C22⋊C4—34no—
814C22⋊C4—62no—
815C22⋊C4—62no—
816C22⋊C4—62no—
817C22⋊C4—62no—
818C22⋊C4—62no—
819C22⋊C4—62no—
820C22⋊C4—62no—
821C22⋊C4—121no—
822C22⋊C4C3×C4×D314yescomplemented
823C42—62no—
824C42—62no—
825C42—121no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—24no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—34no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—1216no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3#89314yescomplemented
875C22×C3C3×C4×D414yescomplemented
876C22×C3C22×C4×D311yescharacteristic
877C22×C3C2×D3×D411yescharacteristic
878C22×C3C2×D3×D411yescharacteristic
879C22×C3#100411yescharacteristic
880C22×C3C2×#23911yescharacteristic
881C22×C3D3×#4111yescharacteristic
882C22×C3#100911yescharacteristic
883C22×C3C23×C3×C411yescharacteristic
884C22×C3C22×C3×D411yescharacteristic
885C22×C3C22×C3×D411yescharacteristic
886C22×C3C2×C3×#4111yescharacteristic
887C22×C3C2×C3×#4111yescharacteristic
888C22×C3C3×H(5,𝔽2)11yescharacteristic
889C22×C3C3×H(5,𝔽2)11yescharacteristic
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—22no—
895C2×D3—22no—
896C2×D3—22no—
897C2×D3—22no—
898C2×D3—22no—
899C2×D3—22no—
900C2×D3—22no—
901C2×D3—22no—
902C2×D3—416no—
903C2×D3—41no—
904C2×D3—41no—
905C2×D3—41no—
906C2×D3—41no—
907C2×D3—41no—
908C2×D3—41no—
909C2×D3—41no—
910C2×D3—41no—
911C2×D3C3×C4×D414yescomplemented
912C3×C4—22no—
913C3×C4—22no—
914C3×C4—22no—
915C3×C4—22no—
916C3×C4—22no—
917C3×C4—22no—
918C3×C4—42no—
919C3×C4—42no—
920C3×C4—42no—
921C3×C4—42no—
922C3×C4—41no—
923C3×C4—41no—
924C3×C4—41no—
925C3×C4—41no—
926C3×C4—41no—
927C3×C4—41no—
928C3×C4—62no—
929C3×C4—62no—
930C3×C4—62no—
931C3×C4—62no—
932C3×C4—81no—
933C3×C4—81no—
934C3×C4—121no—
935Dic3—22no—
936Dic3—22no—
937Dic3—22no—
938Dic3—22no—
939Dic3—41no—
940C32#235811yescharacteristic, complemented, Sylow
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—32no—
946C23—32no—
947C23—32no—
948C23—32no—
949C23—32no—
950C23—68no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—68no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23—61no—
962C23—61no—
963C23—61no—
964C23—61no—
965C23—61no—
966C23—61no—
967C23—61no—
968C23—124no—
969C23—124no—
970C23—124no—
971C23—124no—
972C23—124no—
973C23C2×C3×C4×D312yes—
974C23C3×D3×D412yes—
975C23C3×#23912yes—
976C23C23×C3×D311yescharacteristic
977D4—68no—
978D4—68no—
979D4—124no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—32no—
996C2×C4—32no—
997C2×C4—32no—
998C2×C4—32no—
999C2×C4—44no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—124no—
1012C2×C4—124no—
1013C2×C4—124no—
1014C2×C4—124no—
1015C2×C4C2×C3×C4×D312yes—
1016C2×C4C2×C3×C4×D312yes—
1017C2×C4C3×D3×D412yes—
1018C2×C3—24no—
1019C2×C3—24no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—44no—
1028C2×C3—64no—
1029C2×C3—122no—
1030C2×C3—122no—
1031C2×C3C2×#89311yescharacteristic
1032C2×C3C4×D3×D411yescharacteristic
1033C2×C3#554511yescharacteristic
1034C2×C3#559011yescharacteristic
1035C2×C3#563011yescharacteristic
1036C2×C3#563711yescharacteristic
1037C2×C3#565411yescharacteristic
1038C2×C3C2×C3×C4×D411yescharacteristic
1039C2×C3C2×C3×C4×D411yescharacteristic
1040C2×C3C3×#51811yescharacteristic
1041C2×C3C3×D4211yescharacteristic
1042C2×C3C3×#54611yescharacteristic
1043C2×C3C3×#54611yescharacteristic
1044C2×C3C3×#55111yescharacteristic
1045D3—24no—
1046D3—42no—
1047D3—42no—
1048C22—22no—
1049C22—22no—
1050C22—22no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—34no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—62no—
1061C22—62no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—1216no—
1068C22—121no—
1069C22—121no—
1070C22—121no—
1071C22—121no—
1072C22—121no—
1073C22—121no—
1074C22—121no—
1075C22—121no—
1076C22C3×#89314yescomplemented
1077C22C22×C3×C4×D311yescharacteristic
1078C22C2×C3×D3×D411yescharacteristic
1079C22C2×C3×D3×D411yescharacteristic
1080C22C3×#100411yescharacteristic
1081C22C2×C3×#23911yescharacteristic
1082C22C3×D3×#4111yescharacteristic
1083C22C3×#100911yescharacteristic
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—62no—
1091C4—62no—
1092C4—62no—
1093C4—62no—
1094C4—121no—
1095C3—21no—
1096C3#7459611yescharacteristic, direct product factor
1097C3C3×#235811yescharacteristic, complemented
1098C2—24no—
1099C2—64no—
1100C2—122no—
1101C2—122no—
1102C2C2×C3×#89311yescharacteristic
1103C2C3×C4×D3×D411yescharacteristic
1104C2C3×#554511yescharacteristic
1105C2C3×#559011yescharacteristic
1106C2C3×#563011yescharacteristic
1107C2C3×#563711yescharacteristic
1108C2C3×#565411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#385C2
socleC23×C32C24
prime radicalC2×C3×#882C2
cosocleC23×C3C24×C3
hypercenterC3×#385D3
hypocenterC3C3×#2358
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#67C2semidirect
2. C22×C3×(C2×D3)⋊C4C2semidirect
3. C2×C3×#893C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C32×#385C2semidirect
7. C3×#4990C2semidirect
8. C3×#4989C2semidirect
9. C3×#4988C2semidirect
10. C3×#4958C2semidirect
11. C3×Dic3×C22⋊C4C2semidirect
12. C3×#4669C2semidirect
13. C3×#4666C2semidirect
14. C3×#4665C2semidirect
15. C3×#4665C2semidirect
17. #74596C3direct (N × H)
26. C22×C3×C4×D3C22semidirect
27. C2×C32×C4⋊C4C22semidirect
28. C2×C32×C4⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×C4×Dic3C22semidirect
47. C2×C3×C4×Dic3C22semidirect
48. C2×C3×C4×Dic3C22semidirect
50. C3×#882C4semidirect
52. C32×#95C22semidirect
53. C32×#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
63. C2×C4×#67C2×C3semidirect
64. C22×(C2×D3)⋊C4C2×C3semidirect
65. C2×#893C2×C3semidirect
67. C2×D3×C22⋊C4C2×C3semidirect
76. C3×#385D3semidirect
77. C3×#385C2×C3semidirect
80. #4990C2×C3semidirect
81. #4989C2×C3semidirect
82. #4988C2×C3semidirect
83. #4958C2×C3semidirect
84. Dic3×C22⋊C4C2×C3semidirect
85. #4669C2×C3semidirect
86. #4666C2×C3semidirect
87. #4665C2×C3semidirect
88. #4665C2×C3semidirect
96. C23×C3×D3C2×C4semidirect
111. C2×C3×#67C2×C4semidirect
124. C2×C3×D12C2×C4semidirect
125. C2×C3×D12C2×C4semidirect
138. C32×C22⋊C4C2×C4semidirect
139. C3×#217D4semidirect
148. C3×(C2×D3)⋊C4C2×C4semidirect
149. C3×(C2×D3)⋊C4C2×C4semidirect
150. C3×(C2×D3)⋊C4D4semidirect
174. C22×C4×D3C22×C3semidirect
181. C2×C3×C4⋊C4C2×D3semidirect
182. C2×C3×C4⋊C4C2×D3semidirect
183. C2×C3×C4⋊C4C22×C3semidirect
184. C2×C3×C4⋊C4C22×C3semidirect
219. C2×(C2×D3)⋊C4C22×C3semidirect
220. C2×(C2×D3)⋊C4C22×C3semidirect
221. C2×(C2×D3)⋊C4C22×C3semidirect
222. C2×Dic3⋊C4C22×C3semidirect
223. C2×C4×Dic3C22×C3semidirect
224. C2×C4×Dic3C22×C3semidirect
225. C2×C4×Dic3C22×C3semidirect
227. #882C3×C4semidirect
235. C3×#95C2×D3semidirect
236. C3×#95C2×D3semidirect
237. C3×#95C22×C3semidirect
238. C3×#95C22×C3semidirect
239. C3⋊#95C22×C3semidirect
240. C3⋊#95C22×C3semidirect
241. C3⋊#95C22×C3semidirect
242. C3⋊#95C22×C3semidirect
332. #385C3×D3semidirect
354. C23×D3C2×C3×C4semidirect
413. C2×#67C2×C3×C4semidirect
426. C2×D12C2×C3×C4semidirect
427. C2×D12C2×C3×C4semidirect
460. C3×C22⋊C4C4×D3semidirect
461. C3×C22⋊C4C2×C3×C4semidirect
465. #217C3×D4semidirect
474. (C2×D3)⋊C4C2×C3×C4semidirect
475. (C2×D3)⋊C4C2×C3×C4semidirect
476. (C2×D3)⋊C4C3×D4semidirect
487. C22×C32C4×D4semidirect
516. C2×C3×D3C4×D4semidirect
541. C2×C4⋊C4C2×C3×D3semidirect
542. C2×C4⋊C4C2×C3×D3semidirect
566. #95C2×C3×D3semidirect
567. #95C2×C3×D3semidirect
822. C22⋊C4C3×C4×D3semidirect
874. C22×C3#893semidirect
875. C22×C3C3×C4×D4semidirect
911. C2×D3C3×C4×D4semidirect
940. C32#2358semidirect
1076. C22C3×#893semidirect
1096. C3#74596direct (N × H)
1097. C3C3×#2358semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C22×C3×(C2×D3)⋊C42
C2×C3×#8932
C2×C3×#8822
C2×C3×D3×C22⋊C42
C32×#3852
C3×#49902
C3×#49892
C3×#49882
C3×#49582
C3×Dic3×C22⋊C42
C3×#46692
C3×#46662
C3×#46652
C3×#23583
#745963