Finite Group Databasebeta

← C2×C3×#2418 #10653255

Subgroups — C2×C3×#2418 #10653255

Order 768.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×C3×#120C211yesmaximal, characteristic
3C22×C3×C4×D4C211yesmaximal, characteristic, complemented
4C23×C3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#2418C2116yesmaximal, direct product factor
6C2×C3×#399C211yesmaximal, characteristic, complemented
7C2×C3×#397C211yesmaximal, characteristic, complemented
8C2×C3×#394C211yesmaximal, characteristic, complemented
9C2×C3×#394C211yesmaximal, characteristic, complemented
10C2×C3×#388C211yesmaximal, characteristic, complemented
11C2×C3×#388C211yesmaximal, characteristic, complemented
12C2×C3×#386C211yesmaximal, characteristic, complemented
13C2×C3×#386C211yesmaximal, characteristic, complemented
14C2×C3×#385C211yesmaximal, characteristic, complemented
15C2×C3×#380C211yesmaximal, characteristic, complemented
16C2×C3×#379C211yesmaximal, characteristic, complemented
17C2×#2418C311yesmaximal, characteristic, direct product factor, Sylow
18C26×C3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×C3×D4C2211yescharacteristic
22C24×C3×C4C2211yescharacteristic
23C24×C3×C4C2211yescharacteristic
24C24×C3×C4C2211yescharacteristic, complemented
25C2×C3×#123—28no—
26C2×C3×#123C2218yescomplemented
27C2×C3×#120—28no—
28C2×C3×#120C2218yes—
29C2×C3×C4×D4—28no—
30C2×C3×C4×D4C2218yescomplemented
31C22×C3×C4⋊C4C2211yescharacteristic, complemented
32C22×C3×C4⋊C4C2211yescharacteristic, complemented
33C22×C3×C4⋊C4C2211yescharacteristic, complemented
34C22×C3×C4⋊C4C2211yescharacteristic, complemented
35C22×C3×C4⋊C4C2211yescharacteristic, complemented
36C22×C3×C22⋊C4—28no—
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C22⋊C4C2211yescharacteristic
45C22×C3×C22⋊C4C2211yescharacteristic
46C22×C3×C22⋊C4C2211yescharacteristic
47C22×C3×C22⋊C4C2211yescharacteristic
48C22×C3×C22⋊C4C2211yescharacteristic
49C22×C3×C22⋊C4C2211yescharacteristic
50C22×C3×C22⋊C4C2218yescomplemented
51C22×C3×C22⋊C4C2211yescharacteristic, complemented
52C22×C3×C22⋊C4C2211yescharacteristic, complemented
53C22×C3×C22⋊C4C2211yescharacteristic, complemented
54C22×C3×C42C2211yescharacteristic, complemented
55C3×#399C2218yescomplemented
56C3×#397C2218yescomplemented
57C3×#394C2218yescomplemented
58C3×#394C2218yescomplemented
59C3×#388C2218yescomplemented
60C3×#388C2218yescomplemented
61C3×#386C2218yescomplemented
62C3×#386C2218yescomplemented
63C3×#385C2218yescomplemented
64C3×#380C2218yescomplemented
65C3×#379C2218yescomplemented
66C2×C3×#95C2211yescharacteristic, complemented
67C2×C3×#95C2211yescharacteristic, complemented
68C2×C3×#95C2211yescharacteristic, complemented
69C2×C3×#95C2211yescharacteristic, complemented
70C2×C3×#95C2211yescharacteristic, complemented
71C2×C3×#95C2211yescharacteristic, complemented
72C22×#123C2×C311yescharacteristic, complemented
73C22×#120C2×C311yescharacteristic
74C22×C4×D4C2×C311yescharacteristic, complemented
75C23×C22⋊C4C2×C311yescharacteristic, complemented
76#2418C2×C3116yesdirect product factor
77C2×#399C2×C311yescharacteristic, complemented
78C2×#397C2×C311yescharacteristic, complemented
79C2×#394C2×C311yescharacteristic, complemented
80C2×#394C2×C311yescharacteristic, complemented
81C2×#388C2×C311yescharacteristic, complemented
82C2×#388C2×C311yescharacteristic, complemented
83C2×#386C2×C311yescharacteristic, complemented
84C2×#386C2×C311yescharacteristic, complemented
85C2×#385C2×C311yescharacteristic, complemented
86C2×#380C2×C311yescharacteristic, complemented
87C2×#379C2×C311yescharacteristic, complemented
88C25×C3—24no—
89C25×C3—24no—
90C25×C3—24no—
91C25×C3—24no—
92C25×C3—24no—
93C25×C3—42no—
94C25×C3—42no—
95C25×C3C2311yescharacteristic
96C25×C3C2311yescharacteristic
97C25×C3C2311yescharacteristic
98C25×C3C2314yes—
99C25×C3C2311yescharacteristic
100C22×C3×D4—24no—
101C22×C3×D4—24no—
102C22×C3×D4—24no—
103C22×C3×D4—24no—
104C22×C3×D4—24no—
105C22×C3×D4—24no—
106C22×C3×D4—42no—
107C22×C3×D4—42no—
108C22×C3×D4D418yes—
109C22×C3×D4C2314yes—
110C22×C3×D4C2314yes—
111C22×C3×D4C2314yes—
112C23×C3×C4—24no—
113C23×C3×C4—24no—
114C23×C3×C4—24no—
115C23×C3×C4—24no—
116C23×C3×C4—24no—
117C23×C3×C4—24no—
118C23×C3×C4—42no—
119C23×C3×C4—42no—
120C23×C3×C4—42no—
121C23×C3×C4C2311yescharacteristic
122C23×C3×C4C2311yescharacteristic
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2311yescharacteristic
125C23×C3×C4C2311yescharacteristic
126C23×C3×C4C2311yescharacteristic
127C23×C3×C4C2311yescharacteristic
128C23×C3×C4C2311yescharacteristic
129C23×C3×C4C2314yes—
130C23×C3×C4C2314yes—
131C23×C3×C4C2311yescharacteristic
132C23×C3×C4C2311yescharacteristic
133C23×C3×C4C2311yescharacteristic
134C23×C3×C4C2314yescomplemented
135C3×#123—232no—
136C3×#120—232no—
137C3×C4×D4—232no—
138C2×C3×C4⋊C4—24no—
139C2×C3×C4⋊C4—24no—
140C2×C3×C4⋊C4—24no—
141C2×C3×C4⋊C4—42no—
142C2×C3×C4⋊C4—42no—
143C2×C3×C4⋊C4C2314yescomplemented
144C2×C3×C4⋊C4C2314yescomplemented
145C2×C3×C4⋊C4C2314yescomplemented
146C2×C3×C4⋊C4C2314yescomplemented
147C2×C3×C4⋊C4C2314yescomplemented
148C2×C3×C22⋊C4—24no—
149C2×C3×C22⋊C4—24no—
150C2×C3×C22⋊C4—24no—
151C2×C3×C22⋊C4—24no—
152C2×C3×C22⋊C4—24no—
153C2×C3×C22⋊C4—24no—
154C2×C3×C22⋊C4—24no—
155C2×C3×C22⋊C4—24no—
156C2×C3×C22⋊C4—24no—
157C2×C3×C22⋊C4—24no—
158C2×C3×C22⋊C4—24no—
159C2×C3×C22⋊C4—24no—
160C2×C3×C22⋊C4—232no—
161C2×C3×C22⋊C4—42no—
162C2×C3×C22⋊C4—42no—
163C2×C3×C22⋊C4—42no—
164C2×C3×C22⋊C4D418yescomplemented
165C2×C3×C22⋊C4C2314yes—
166C2×C3×C22⋊C4C2314yes—
167C2×C3×C22⋊C4C2314yes—
168C2×C3×C22⋊C4C2314yes—
169C2×C3×C22⋊C4C2314yes—
170C2×C3×C22⋊C4C2314yes—
171C2×C3×C22⋊C4C2314yes—
172C2×C3×C22⋊C4C2314yes—
173C2×C3×C22⋊C4C2314yes—
174C2×C3×C22⋊C4C2314yes—
175C2×C3×C22⋊C4C2314yes—
176C2×C3×C22⋊C4C2314yes—
177C2×C3×C22⋊C4C2314yes—
178C2×C3×C22⋊C4C2314yescomplemented
179C2×C3×C22⋊C4C2314yescomplemented
180C2×C3×C22⋊C4C2314yescomplemented
181C2×C3×C42—24no—
182C2×C3×C42C2314yescomplemented
183C3×#95C2314yescomplemented
184C3×#95C2314yescomplemented
185C3×#95C2314yescomplemented
186C3×#95C2314yescomplemented
187C3×#95C2314yescomplemented
188C3×#95C2314yescomplemented
189C26C22×C311yescharacteristic
190C23×D4C22×C311yescharacteristic
191C23×D4C22×C311yescharacteristic
192C23×D4C22×C311yescharacteristic
193C24×C4C22×C311yescharacteristic
194C24×C4C22×C311yescharacteristic
195C24×C4C22×C311yescharacteristic, complemented
196C2×#123—28no—
197C2×#123C22×C318yescomplemented
198C2×#120—28no—
199C2×#120C22×C318yes—
200C2×C4×D4—28no—
201C2×C4×D4C22×C318yescomplemented
202C22×C4⋊C4C22×C311yescharacteristic, complemented
203C22×C4⋊C4C22×C311yescharacteristic, complemented
204C22×C4⋊C4C22×C311yescharacteristic, complemented
205C22×C4⋊C4C22×C311yescharacteristic, complemented
206C22×C4⋊C4C22×C311yescharacteristic, complemented
207C22×C22⋊C4—28no—
208C22×C22⋊C4C22×C311yescharacteristic
209C22×C22⋊C4C22×C311yescharacteristic
210C22×C22⋊C4C22×C311yescharacteristic
211C22×C22⋊C4C22×C311yescharacteristic
212C22×C22⋊C4C22×C311yescharacteristic
213C22×C22⋊C4C22×C311yescharacteristic
214C22×C22⋊C4C22×C311yescharacteristic
215C22×C22⋊C4C22×C311yescharacteristic
216C22×C22⋊C4C22×C311yescharacteristic
217C22×C22⋊C4C22×C311yescharacteristic
218C22×C22⋊C4C22×C311yescharacteristic
219C22×C22⋊C4C22×C311yescharacteristic
220C22×C22⋊C4C22×C311yescharacteristic
221C22×C22⋊C4C22×C318yescomplemented
222C22×C22⋊C4C22×C311yescharacteristic, complemented
223C22×C22⋊C4C22×C311yescharacteristic, complemented
224C22×C22⋊C4C22×C311yescharacteristic, complemented
225C22×C42C22×C311yescharacteristic, complemented
226#399C22×C318yescomplemented
227#397C22×C318yescomplemented
228#394C22×C318yescomplemented
229#394C22×C318yescomplemented
230#388C22×C318yescomplemented
231#388C22×C318yescomplemented
232#386C22×C318yescomplemented
233#386C22×C318yescomplemented
234#385C22×C318yescomplemented
235#380C22×C318yescomplemented
236#379C22×C318yescomplemented
237C2×#95C22×C311yescharacteristic, complemented
238C2×#95C22×C311yescharacteristic, complemented
239C2×#95C22×C311yescharacteristic, complemented
240C2×#95C22×C311yescharacteristic, complemented
241C2×#95C22×C311yescharacteristic, complemented
242C2×#95C22×C311yescharacteristic, complemented
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—232no—
248C24×C3—28no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—28no—
254C24×C3—28no—
255C24×C3—22no—
256C24×C3—22no—
257C24×C3—22no—
258C24×C3—22no—
259C24×C3—22no—
260C24×C3—22no—
261C24×C3—22no—
262C24×C3—22no—
263C24×C3—22no—
264C24×C3—22no—
265C24×C3—22no—
266C24×C3—22no—
267C24×C3—22no—
268C24×C3—22no—
269C24×C3—28no—
270C24×C3—28no—
271C24×C3—44no—
272C24×C3—44no—
273C24×C3—416no—
274C24×C3—416no—
275C24×C3—416no—
276C24×C3—416no—
277C24×C3—416no—
278C24×C3—416no—
279C24×C3C2×D414yes—
280C24×C3C2×D414yes—
281C24×C3C2×D414yes—
282C24×C3#4114yes—
283C24×C3#4114yes—
284C24×C3#4114yes—
285C24×C3C2412yes—
286C24×C3C2412yes—
287C24×C3C2412yes—
288C24×C3C2412yes—
289C24×C3C2411yescharacteristic
290C2×C3×D4—232no—
291C2×C3×D4—28no—
292C2×C3×D4—28no—
293C2×C3×D4—28no—
294C2×C3×D4—28no—
295C2×C3×D4—28no—
296C2×C3×D4—28no—
297C2×C3×D4—44no—
298C2×C3×D4—44no—
299C2×C3×D4—416no—
300C2×C3×D4—416no—
301C2×C3×D4C2×D4116yes—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—28no—
319C22×C3×C4—28no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—28no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—22no—
328C22×C3×C4—22no—
329C22×C3×C4—22no—
330C22×C3×C4—22no—
331C22×C3×C4—22no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—22no—
335C22×C3×C4—28no—
336C22×C3×C4—28no—
337C22×C3×C4—28no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4—44no—
341C22×C3×C4—416no—
342C22×C3×C4—416no—
343C22×C3×C4—416no—
344C22×C3×C4C2×D414yes—
345C22×C3×C4C2×D414yes—
346C22×C3×C4C2×D414yes—
347C22×C3×C4C2412yes—
348C22×C3×C4C2412yes—
349C22×C3×C4C2412yes—
350C22×C3×C4C2412yes—
351C22×C3×C4C2412yes—
352C22×C3×C4C2412yes—
353C22×C3×C4C2412yes—
354C22×C3×C4C2412yes—
355C22×C3×C4C2412yes—
356C22×C3×C4C2412yes—
357C22×C3×C4C2412yes—
358C3×C4⋊C4—28no—
359C3×C4⋊C4—28no—
360C3×C4⋊C4—28no—
361C3×C4⋊C4—44no—
362C3×C4⋊C4—44no—
363C3×C22⋊C4—28no—
364C3×C22⋊C4—28no—
365C3×C22⋊C4—28no—
366C3×C22⋊C4—28no—
367C3×C22⋊C4—28no—
368C3×C22⋊C4—28no—
369C3×C22⋊C4—28no—
370C3×C22⋊C4—28no—
371C3×C22⋊C4—28no—
372C3×C22⋊C4—28no—
373C3×C22⋊C4—28no—
374C3×C22⋊C4—28no—
375C3×C22⋊C4—44no—
376C3×C22⋊C4—44no—
377C3×C22⋊C4—44no—
378C3×C22⋊C4C2×D4116yescomplemented
379C3×C42—28no—
380C25—24no—
381C25—24no—
382C25—24no—
383C25—24no—
384C25—24no—
385C25—42no—
386C25—42no—
387C25C23×C311yescharacteristic
388C25C23×C311yescharacteristic
389C25C23×C311yescharacteristic
390C25C23×C314yes—
391C25C23×C311yescharacteristic
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—24no—
398C22×D4—42no—
399C22×D4—42no—
400C22×D4C3×D418yes—
401C22×D4C23×C314yes—
402C22×D4C23×C314yes—
403C22×D4C23×C314yes—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4C23×C311yescharacteristic
414C23×C4C23×C311yescharacteristic
415C23×C4C23×C311yescharacteristic
416C23×C4C23×C311yescharacteristic
417C23×C4C23×C311yescharacteristic
418C23×C4C23×C311yescharacteristic
419C23×C4C23×C311yescharacteristic
420C23×C4C23×C311yescharacteristic
421C23×C4C23×C314yes—
422C23×C4C23×C314yes—
423C23×C4C23×C311yescharacteristic
424C23×C4C23×C311yescharacteristic
425C23×C4C23×C311yescharacteristic
426C23×C4C23×C314yescomplemented
427#123—232no—
428#120—232no—
429C4×D4—232no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4C23×C314yescomplemented
436C2×C4⋊C4C23×C314yescomplemented
437C2×C4⋊C4C23×C314yescomplemented
438C2×C4⋊C4C23×C314yescomplemented
439C2×C4⋊C4C23×C314yescomplemented
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—232no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4C3×D418yescomplemented
457C2×C22⋊C4C23×C314yes—
458C2×C22⋊C4C23×C314yes—
459C2×C22⋊C4C23×C314yes—
460C2×C22⋊C4C23×C314yes—
461C2×C22⋊C4C23×C314yes—
462C2×C22⋊C4C23×C314yes—
463C2×C22⋊C4C23×C314yes—
464C2×C22⋊C4C23×C314yes—
465C2×C22⋊C4C23×C314yes—
466C2×C22⋊C4C23×C314yes—
467C2×C22⋊C4C23×C314yes—
468C2×C22⋊C4C23×C314yes—
469C2×C22⋊C4C23×C314yes—
470C2×C22⋊C4C23×C314yescomplemented
471C2×C22⋊C4C23×C314yescomplemented
472C2×C22⋊C4C23×C314yescomplemented
473C2×C42—24no—
474C2×C42C23×C314yescomplemented
475#95C23×C314yescomplemented
476#95C23×C314yescomplemented
477#95C23×C314yescomplemented
478#95C23×C314yescomplemented
479#95C23×C314yescomplemented
480#95C23×C314yescomplemented
481C23×C3—28no—
482C23×C3—28no—
483C23×C3—28no—
484C23×C3—28no—
485C23×C3—28no—
486C23×C3—28no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—232no—
492C23×C3—28no—
493C23×C3—28no—
494C23×C3—28no—
495C23×C3—28no—
496C23×C3—28no—
497C23×C3—28no—
498C23×C3—28no—
499C23×C3—28no—
500C23×C3—28no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—416no—
520C23×C3—416no—
521C23×C3—416no—
522C23×C3—416no—
523C23×C3—4128no—
524C23×C3—416no—
525C23×C3—44no—
526C23×C3—44no—
527C23×C3—416no—
528C23×C3—44no—
529C23×C3—44no—
530C23×C3—44no—
531C23×C3—44no—
532C23×C3—44no—
533C23×C3—44no—
534C23×C3—44no—
535C23×C3—44no—
536C23×C3—44no—
537C23×C3—44no—
538C23×C3#123116yescomplemented
539C23×C3C22×D414yes—
540C23×C3C22×D414yes—
541C23×C3C22×D414yes—
542C23×C3C22×D412yes—
543C23×C3C22×D412yes—
544C23×C3C2×#4114yes—
545C23×C3C2×#4114yes—
546C23×C3C2×#4114yes—
547C23×C3C2×#4112yes—
548C23×C3C2×#4112yes—
549C23×C3C2×#4112yes—
550C23×C3H(5,𝔽2)12yes—
551C23×C3H(5,𝔽2)12yes—
552C23×C3C2511yescharacteristic
553C3×D4—232no—
554C3×D4—416no—
555C3×D4—416no—
556C2×C3×C4—28no—
557C2×C3×C4—28no—
558C2×C3×C4—28no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—416no—
590C2×C3×C4—416no—
591C2×C3×C4—416no—
592C2×C3×C4—44no—
593C2×C3×C4—44no—
594C2×C3×C4—44no—
595C2×C3×C4—44no—
596C2×C3×C4—44no—
597C2×C3×C4—44no—
598C2×C3×C4—44no—
599C2×C3×C4—44no—
600C2×C3×C4C22×D414yes—
601C2×C3×C4C22×D414yes—
602C2×C3×C4C22×D414yes—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—232no—
608C24—28no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—28no—
617C24—28no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—28no—
630C24—28no—
631C24—44no—
632C24—44no—
633C24—416no—
634C24—416no—
635C24—416no—
636C24—416no—
637C24—416no—
638C24—416no—
639C24C2×C3×D414yes—
640C24C2×C3×D414yes—
641C24C2×C3×D414yes—
642C24C3×#4114yes—
643C24C3×#4114yes—
644C24C3×#4114yes—
645C24C24×C312yes—
646C24C24×C312yes—
647C24C24×C312yes—
648C24C24×C312yes—
649C24C24×C311yescharacteristic
650C2×D4—232no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—416no—
660C2×D4—416no—
661C2×D4C2×C3×D4116yes—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—28no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—416no—
702C22×C4—416no—
703C22×C4—416no—
704C22×C4C2×C3×D414yes—
705C22×C4C2×C3×D414yes—
706C22×C4C2×C3×D414yes—
707C22×C4C24×C312yes—
708C22×C4C24×C312yes—
709C22×C4C24×C312yes—
710C22×C4C24×C312yes—
711C22×C4C24×C312yes—
712C22×C4C24×C312yes—
713C22×C4C24×C312yes—
714C22×C4C24×C312yes—
715C22×C4C24×C312yes—
716C22×C4C24×C312yes—
717C22×C4C24×C312yes—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—44no—
722C4⋊C4—44no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C22⋊C4—44no—
738C22⋊C4C2×C3×D4116yescomplemented
739C42—28no—
740C22×C3—24no—
741C22×C3—232no—
742C22×C3—24no—
743C22×C3—24no—
744C22×C3—24no—
745C22×C3—24no—
746C22×C3—24no—
747C22×C3—24no—
748C22×C3—24no—
749C22×C3—24no—
750C22×C3—24no—
751C22×C3—24no—
752C22×C3—24no—
753C22×C3—24no—
754C22×C3—24no—
755C22×C3—24no—
756C22×C3—464no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—416no—
761C22×C3—416no—
762C22×C3—416no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3C2×#12314yes—
773C22×C3C2×#12318yescomplemented
774C22×C3#52514yes—
775C22×C3#53814yes—
776C22×C3D4214yes—
777C22×C3#54614yes—
778C22×C3#54614yes—
779C22×C3#55114yes—
780C22×C3C23×D411yescharacteristic
781C22×C3C23×D411yescharacteristic
782C22×C3C22×#4111yescharacteristic
783C22×C3C22×#4111yescharacteristic
784C22×C3C22×#4111yescharacteristic
785C22×C3C2×H(5,𝔽2)11yescharacteristic
786C22×C3C2×H(5,𝔽2)11yescharacteristic
787C3×C4—24no—
788C3×C4—24no—
789C3×C4—24no—
790C3×C4—42no—
791C3×C4—42no—
792C3×C4—42no—
793C3×C4—42no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—42no—
797C3×C4—42no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—28no—
803C23—28no—
804C23—28no—
805C23—28no—
806C23—28no—
807C23—28no—
808C23—232no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—28no—
828C23—28no—
829C23—28no—
830C23—28no—
831C23—28no—
832C23—28no—
833C23—28no—
834C23—28no—
835C23—28no—
836C23—416no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—4128no—
842C23—44no—
843C23—44no—
844C23—416no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—44no—
855C23C3×#123116yescomplemented
856C23C22×C3×D414yes—
857C23C22×C3×D414yes—
858C23C22×C3×D414yes—
859C23C22×C3×D412yes—
860C23C22×C3×D412yes—
861C23C2×C3×#4114yes—
862C23C2×C3×#4114yes—
863C23C2×C3×#4114yes—
864C23C2×C3×#4112yes—
865C23C2×C3×#4112yes—
866C23C2×C3×#4112yes—
867C23C3×H(5,𝔽2)12yes—
868C23C3×H(5,𝔽2)12yes—
869C23C25×C311yescharacteristic
870D4—232no—
871D4—416no—
872D4—416no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—28no—
880C2×C4—28no—
881C2×C4—28no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—416no—
907C2×C4—416no—
908C2×C4—416no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—44no—
913C2×C4—44no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4C22×C3×D414yes—
918C2×C4C22×C3×D414yes—
919C2×C4C22×C3×D414yes—
920C2×C3—28no—
921C2×C3—44no—
922C2×C3—44no—
923C2×C3—44no—
924C2×C3#241818yesdirect product factor
925C2×C3C22×#12311yescharacteristic
926C2×C3C2×#52511yescharacteristic
927C2×C3C2×#53811yescharacteristic
928C2×C3C2×D4211yescharacteristic
929C2×C3C2×#54611yescharacteristic
930C2×C3C2×#54611yescharacteristic
931C2×C3C2×#55111yescharacteristic
932C22—24no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—232no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—464no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—416no—
962C22—416no—
963C22—416no—
964C22C2×C3×#12314yes—
965C22C2×C3×#12318yescomplemented
966C22C3×#52514yes—
967C22C3×#53814yes—
968C22C3×D4214yes—
969C22C3×#54614yes—
970C22C3×#54614yes—
971C22C3×#55114yes—
972C22C23×C3×D411yescharacteristic
973C22C23×C3×D411yescharacteristic
974C22C22×C3×#4111yescharacteristic
975C22C22×C3×#4111yescharacteristic
976C22C22×C3×#4111yescharacteristic
977C22C2×C3×H(5,𝔽2)11yescharacteristic
978C22C2×C3×H(5,𝔽2)11yescharacteristic
979C4—24no—
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C3C2×#241811yescharacteristic, direct product factor, Sylow
991C2—28no—
992C2—44no—
993C2—44no—
994C2—44no—
995C2C3×#241818yesdirect product factor
996C2C22×C3×#12311yescharacteristic
997C2C2×C3×#52511yescharacteristic
998C2C2×C3×#53811yescharacteristic
999C2C2×C3×D4211yescharacteristic
1000C2C2×C3×#54611yescharacteristic
1001C2C2×C3×#54611yescharacteristic
1002C2C2×C3×#55111yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
prime radicalC22×C3×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
3. C22×C3×C4×D4C2semidirect
4. C23×C3×C22⋊C4C2semidirect
5. C3×#2418C2direct (N × H)
6. C2×C3×#399C2semidirect
7. C2×C3×#397C2semidirect
8. C2×C3×#394C2semidirect
9. C2×C3×#394C2semidirect
10. C2×C3×#388C2semidirect
11. C2×C3×#388C2semidirect
12. C2×C3×#386C2semidirect
13. C2×C3×#386C2semidirect
14. C2×C3×#385C2semidirect
15. C2×C3×#380C2semidirect
16. C2×C3×#379C2semidirect
17. C2×#2418C3direct (N × H)
24. C24×C3×C4C22semidirect
26. C2×C3×#123C22semidirect
30. C2×C3×C4×D4C22semidirect
31. C22×C3×C4⋊C4C22semidirect
32. C22×C3×C4⋊C4C22semidirect
33. C22×C3×C4⋊C4C22semidirect
34. C22×C3×C4⋊C4C22semidirect
35. C22×C3×C4⋊C4C22semidirect
50. C22×C3×C22⋊C4C22semidirect
51. C22×C3×C22⋊C4C22semidirect
52. C22×C3×C22⋊C4C22semidirect
53. C22×C3×C22⋊C4C22semidirect
54. C22×C3×C42C22semidirect
55. C3×#399C22semidirect
56. C3×#397C22semidirect
57. C3×#394C22semidirect
58. C3×#394C22semidirect
59. C3×#388C22semidirect
60. C3×#388C22semidirect
61. C3×#386C22semidirect
62. C3×#386C22semidirect
63. C3×#385C22semidirect
64. C3×#380C22semidirect
65. C3×#379C22semidirect
66. C2×C3×#95C22semidirect
67. C2×C3×#95C22semidirect
68. C2×C3×#95C22semidirect
69. C2×C3×#95C22semidirect
70. C2×C3×#95C22semidirect
71. C2×C3×#95C22semidirect
72. C22×#123C2×C3semidirect
74. C22×C4×D4C2×C3semidirect
75. C23×C22⋊C4C2×C3semidirect
76. #2418C2×C3direct (N × H)
77. C2×#399C2×C3semidirect
78. C2×#397C2×C3semidirect
79. C2×#394C2×C3semidirect
80. C2×#394C2×C3semidirect
81. C2×#388C2×C3semidirect
82. C2×#388C2×C3semidirect
83. C2×#386C2×C3semidirect
84. C2×#386C2×C3semidirect
85. C2×#385C2×C3semidirect
86. C2×#380C2×C3semidirect
87. C2×#379C2×C3semidirect
134. C23×C3×C4C23semidirect
143. C2×C3×C4⋊C4C23semidirect
144. C2×C3×C4⋊C4C23semidirect
145. C2×C3×C4⋊C4C23semidirect
146. C2×C3×C4⋊C4C23semidirect
147. C2×C3×C4⋊C4C23semidirect
164. C2×C3×C22⋊C4D4semidirect
178. C2×C3×C22⋊C4C23semidirect
179. C2×C3×C22⋊C4C23semidirect
180. C2×C3×C22⋊C4C23semidirect
182. C2×C3×C42C23semidirect
183. C3×#95C23semidirect
184. C3×#95C23semidirect
185. C3×#95C23semidirect
186. C3×#95C23semidirect
187. C3×#95C23semidirect
188. C3×#95C23semidirect
195. C24×C4C22×C3semidirect
197. C2×#123C22×C3semidirect
201. C2×C4×D4C22×C3semidirect
202. C22×C4⋊C4C22×C3semidirect
203. C22×C4⋊C4C22×C3semidirect
204. C22×C4⋊C4C22×C3semidirect
205. C22×C4⋊C4C22×C3semidirect
206. C22×C4⋊C4C22×C3semidirect
221. C22×C22⋊C4C22×C3semidirect
222. C22×C22⋊C4C22×C3semidirect
223. C22×C22⋊C4C22×C3semidirect
224. C22×C22⋊C4C22×C3semidirect
225. C22×C42C22×C3semidirect
226. #399C22×C3semidirect
227. #397C22×C3semidirect
228. #394C22×C3semidirect
229. #394C22×C3semidirect
230. #388C22×C3semidirect
231. #388C22×C3semidirect
232. #386C22×C3semidirect
233. #386C22×C3semidirect
234. #385C22×C3semidirect
235. #380C22×C3semidirect
236. #379C22×C3semidirect
237. C2×#95C22×C3semidirect
238. C2×#95C22×C3semidirect
239. C2×#95C22×C3semidirect
240. C2×#95C22×C3semidirect
241. C2×#95C22×C3semidirect
242. C2×#95C22×C3semidirect
378. C3×C22⋊C4C2×D4semidirect
426. C23×C4C23×C3semidirect
435. C2×C4⋊C4C23×C3semidirect
436. C2×C4⋊C4C23×C3semidirect
437. C2×C4⋊C4C23×C3semidirect
438. C2×C4⋊C4C23×C3semidirect
439. C2×C4⋊C4C23×C3semidirect
456. C2×C22⋊C4C3×D4semidirect
470. C2×C22⋊C4C23×C3semidirect
471. C2×C22⋊C4C23×C3semidirect
472. C2×C22⋊C4C23×C3semidirect
474. C2×C42C23×C3semidirect
475. #95C23×C3semidirect
476. #95C23×C3semidirect
477. #95C23×C3semidirect
478. #95C23×C3semidirect
479. #95C23×C3semidirect
480. #95C23×C3semidirect
538. C23×C3#123semidirect
738. C22⋊C4C2×C3×D4semidirect
773. C22×C3C2×#123semidirect
855. C23C3×#123semidirect
924. C2×C3#2418direct (N × H)
965. C22C2×C3×#123semidirect
990. C3C2×#2418direct (N × H)
995. C2C3×#2418direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×C3×#1202
C22×C3×C4×D42
C23×C3×C22⋊C42
C3×#24182
C2×C3×#3992
C2×C3×#3972
C2×C3×#3942
C2×C3×#3882
C2×C3×#3862
C2×C3×#3852
C2×C3×#3802
C2×C3×#3792
C2×#24183