Finite Group Databasebeta

← C3×#14182 #10632789

Subgroups — C3×#14182 #10632789

Order 768.

2162 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#394C211yesmaximal, characteristic
2C2×C3×#388C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic
4C2×C3×#386C211yesmaximal, characteristic
5C2×C3×#385C211yesmaximal, characteristic, complemented
6C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8C3×#1443C211yesmaximal, characteristic, complemented
9C3×#1440C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1437C211yesmaximal, characteristic, complemented
12C3×#1436C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×C4⋊#95C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#14182C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C42C2211yescharacteristic
34C22×C3×C42C2211yescharacteristic
35C22×C3×C42C2211yescharacteristic
36C3×#394C418yescomplemented
37C3×#388—24no—
38C3×#386—24no—
39C3×#386—24no—
40C3×#385—24no—
41C3×C4×C22⋊C4—24no—
42C3×C4×C22⋊C4—24no—
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×#394C2×C311yescharacteristic
60C2×#388C2×C311yescharacteristic, complemented
61C2×#386C2×C311yescharacteristic
62C2×#386C2×C311yescharacteristic
63C2×#385C2×C311yescharacteristic, complemented
64C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
65C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
66#1443C2×C311yescharacteristic, complemented
67#1440C2×C311yescharacteristic, complemented
68#1439C2×C311yescharacteristic, complemented
69#1437C2×C311yescharacteristic, complemented
70#1436C2×C311yescharacteristic, complemented
71#1436C2×C311yescharacteristic, complemented
72C4⋊#95C2×C311yescharacteristic, complemented
73C22⋊#95C2×C311yescharacteristic, complemented
74C25×C3C2311yescharacteristic
75C25×C3C2311yescharacteristic
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C22×C3×D4C2×C414yes—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—22no—
92C23×C3×C4—22no—
93C23×C3×C4—41no—
94C23×C3×C4—41no—
95C23×C3×C4—41no—
96C23×C3×C4—41no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4C2×C414yescomplemented
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—41no—
140C2×C3×C22⋊C4—41no—
141C2×C3×C22⋊C4—41no—
142C2×C3×C22⋊C4—41no—
143C2×C3×C22⋊C4C2×C414yescomplemented
144C2×C3×C22⋊C4C2×C414yescomplemented
145C2×C3×C22⋊C4C2×C414yescomplemented
146C2×C3×C22⋊C4C2×C414yescomplemented
147C2×C3×C22⋊C4D414yes—
148C2×C3×C22⋊C4D414yes—
149C2×C3×C42—22no—
150C2×C3×C42—22no—
151C2×C3×C42—22no—
152C2×C3×C42—22no—
153C2×C3×C42—22no—
154C2×C3×C42—22no—
155C2×C3×C42—41no—
156C2×C3×C42—41no—
157C2×C3×C42—41no—
158C3×#95—22no—
159C3×#95—22no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—22no—
165C3×#95—22no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—22no—
170C3×#95—41no—
171C3×#95—41no—
172C3×#95C2×C414yescomplemented
173C3×#95D414yescomplemented
174C23×D4C22×C311yescharacteristic
175C24×C4C22×C311yescharacteristic
176C24×C4C22×C311yescharacteristic
177C22×C4⋊C4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C22⋊C4C22×C311yescharacteristic
181C22×C22⋊C4C22×C311yescharacteristic
182C22×C22⋊C4C22×C311yescharacteristic
183C22×C22⋊C4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C22×C22⋊C4C22×C311yescharacteristic
186C22×C22⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C42C22×C311yescharacteristic
191C22×C42C22×C311yescharacteristic
192C22×C42C22×C311yescharacteristic
193#394C3×C418yescomplemented
194#388—24no—
195#386—24no—
196#386—24no—
197#385—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200C2×#95C22×C311yescharacteristic
201C2×#95C22×C311yescharacteristic
202C2×#95C22×C311yescharacteristic
203C2×#95C22×C311yescharacteristic
204C2×#95C22×C311yescharacteristic
205C2×#95C22×C311yescharacteristic
206C2×#95C22×C311yescharacteristic
207C2×#95C22×C311yescharacteristic
208C2×#95C22×C311yescharacteristic
209C2×#95C22×C311yescharacteristic
210C2×#95C22×C311yescharacteristic
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3C22×C412yes—
241C24×C3C22×C412yes—
242C24×C3C2×D412yes—
243C24×C3C2×D412yes—
244C24×C3#4112yes—
245C24×C3#4112yes—
246C24×C3C2411yescharacteristic
247C2×C3×D4—28no—
248C2×C3×D4—28no—
249C2×C3×D4—44no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—28no—
267C22×C3×C4—28no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
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—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—44no—
331C22×C3×C4—44no—
332C22×C3×C4—44no—
333C22×C3×C4—44no—
334C22×C3×C4—44no—
335C22×C3×C4—44no—
336C22×C3×C4—44no—
337C22×C3×C4—44no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4—44no—
341C22×C3×C4—44no—
342C22×C3×C4C22×C412yes—
343C22×C3×C4C22×C412yes—
344C22×C3×C4C22×C412yes—
345C22×C3×C4C22×C412yes—
346C22×C3×C4C22×C412yes—
347C22×C3×C4C2×D412yes—
348C22×C3×C4C2×D412yes—
349C22×C3×C4C2×D412yes—
350C22×C3×C4C2×D412yes—
351C22×C3×C4C2×D412yes—
352C22×C3×C4C2×D412yes—
353C22×C3×C4C2×D412yes—
354C22×C3×C4#4112yes—
355C22×C3×C4#4112yes—
356C22×C3×C4#4112yes—
357C22×C3×C4#4112yes—
358C22×C3×C4#4112yes—
359C3×C4⋊C4—44no—
360C3×C4⋊C4—44no—
361C3×C4⋊C4—44no—
362C3×C22⋊C4—28no—
363C3×C22⋊C4—28no—
364C3×C22⋊C4—28no—
365C3×C22⋊C4—28no—
366C3×C22⋊C4—28no—
367C3×C22⋊C4—28no—
368C3×C22⋊C4—44no—
369C3×C22⋊C4—44no—
370C3×C22⋊C4—44no—
371C3×C22⋊C4—44no—
372C3×C42—44no—
373C3×C42—44no—
374C3×C42—44no—
375C25C23×C311yescharacteristic
376C25C23×C311yescharacteristic
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—41no—
382C22×D4—41no—
383C22×D4C2×C3×C414yes—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—41no—
395C23×C4—41no—
396C23×C4—41no—
397C23×C4—41no—
398C23×C4C23×C311yescharacteristic
399C23×C4C23×C311yescharacteristic
400C23×C4C23×C311yescharacteristic
401C23×C4C23×C311yescharacteristic
402C23×C4C23×C311yescharacteristic
403C23×C4C23×C311yescharacteristic
404C23×C4C23×C311yescharacteristic
405C23×C4C23×C311yescharacteristic
406C23×C4C23×C311yescharacteristic
407C23×C4C23×C311yescharacteristic
408C23×C4C23×C311yescharacteristic
409C23×C4C23×C311yescharacteristic
410C23×C4C23×C311yescharacteristic
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4C2×C3×C414yescomplemented
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—41no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4C2×C3×C414yescomplemented
445C2×C22⋊C4C2×C3×C414yescomplemented
446C2×C22⋊C4C2×C3×C414yescomplemented
447C2×C22⋊C4C2×C3×C414yescomplemented
448C2×C22⋊C4C3×D414yes—
449C2×C22⋊C4C3×D414yes—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—41no—
457C2×C42—41no—
458C2×C42—41no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—41no—
472#95—41no—
473#95C2×C3×C414yescomplemented
474#95C3×D414yescomplemented
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
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—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3C4×D414yes—
544C23×C3C4×D414yes—
545C23×C3C23×C411yescharacteristic
546C23×C3C22×D411yescharacteristic
547C23×C3C22×D411yescharacteristic
548C23×C3C22×D411yescharacteristic
549C23×C3C2×#4111yescharacteristic
550C23×C3C2×#4111yescharacteristic
551C23×C3C2×#4111yescharacteristic
552C23×C3C2×#4111yescharacteristic
553C23×C3C2×#4111yescharacteristic
554C23×C3C2×#4111yescharacteristic
555C23×C3C2×#4111yescharacteristic
556C23×C3H(5,𝔽2)11yescharacteristic
557C23×C3H(5,𝔽2)11yescharacteristic
558C23×C3H(5,𝔽2)11yescharacteristic
559C23×C32−1+411yescharacteristic
560C3×D4—416no—
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—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—416no—
604C2×C3×C4—416no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4C4×D414yes—
652C2×C3×C4#12114yes—
653C2×C3×C4#12314yes—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24C22×C3×C412yes—
679C24C22×C3×C412yes—
680C24C2×C3×D412yes—
681C24C2×C3×D412yes—
682C24C3×#4112yes—
683C24C3×#4112yes—
684C24C24×C311yescharacteristic
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4C22×C3×C412yes—
781C22×C4C22×C3×C412yes—
782C22×C4C22×C3×C412yes—
783C22×C4C22×C3×C412yes—
784C22×C4C22×C3×C412yes—
785C22×C4C2×C3×D412yes—
786C22×C4C2×C3×D412yes—
787C22×C4C2×C3×D412yes—
788C22×C4C2×C3×D412yes—
789C22×C4C2×C3×D412yes—
790C22×C4C2×C3×D412yes—
791C22×C4C2×C3×D412yes—
792C22×C4C3×#4112yes—
793C22×C4C3×#4112yes—
794C22×C4C3×#4112yes—
795C22×C4C3×#4112yes—
796C22×C4C3×#4112yes—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C42—44no—
811C42—44no—
812C42—44no—
813C22×C3—24no—
814C22×C3—24no—
815C22×C3—24no—
816C22×C3—24no—
817C22×C3—24no—
818C22×C3—24no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3C2×C4×D411yescharacteristic
844C22×C3C2×C4×D411yescharacteristic
845C22×C3C2×C4×D411yescharacteristic
846C22×C3C4×#4111yescharacteristic
847C22×C3C4×#4111yescharacteristic
848C22×C3#51811yescharacteristic
849C22×C3#52011yescharacteristic
850C22×C3C2×#12111yescharacteristic
851C22×C3C2×#12311yescharacteristic
852C22×C3#52511yescharacteristic
853C22×C3#52511yescharacteristic
854C22×C3#52911yescharacteristic
855C22×C3#52911yescharacteristic
856C22×C3#52911yescharacteristic
857C22×C3#53211yescharacteristic
858C22×C3#53811yescharacteristic
859C22×C3#53811yescharacteristic
860C22×C3#54211yescharacteristic
861C22×C3#54211yescharacteristic
862C22×C3D4211yescharacteristic
863C22×C3D4211yescharacteristic
864C22×C3#54611yescharacteristic
865C22×C3#54611yescharacteristic
866C22×C3#54611yescharacteristic
867C22×C3#54611yescharacteristic
868C22×C3#54611yescharacteristic
869C22×C3#54711yescharacteristic
870C22×C3#54711yescharacteristic
871C22×C3#54811yescharacteristic
872C22×C3#55111yescharacteristic
873C22×C3#55111yescharacteristic
874C22×C3#55211yescharacteristic
875C22×C3#55311yescharacteristic
876C22×C3#55311yescharacteristic
877C22×C3#55311yescharacteristic
878C3×C4—24no—
879C3×C4—24no—
880C3×C4—24no—
881C3×C4—42no—
882C3×C4—42no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—42no—
887C3×C4—42no—
888C3×C4—42no—
889C3×C4—81no—
890C3×C4—81no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23C3×C4×D414yes—
960C23C3×C4×D414yes—
961C23C23×C3×C411yescharacteristic
962C23C22×C3×D411yescharacteristic
963C23C22×C3×D411yescharacteristic
964C23C22×C3×D411yescharacteristic
965C23C2×C3×#4111yescharacteristic
966C23C2×C3×#4111yescharacteristic
967C23C2×C3×#4111yescharacteristic
968C23C2×C3×#4111yescharacteristic
969C23C2×C3×#4111yescharacteristic
970C23C2×C3×#4111yescharacteristic
971C23C2×C3×#4111yescharacteristic
972C23C3×H(5,𝔽2)11yescharacteristic
973C23C3×H(5,𝔽2)11yescharacteristic
974C23C3×H(5,𝔽2)11yescharacteristic
975C23C3×2−1+411yescharacteristic
976D4—416no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—416no—
1020C2×C4—416no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4C3×C4×D414yes—
1068C2×C4C3×#12114yes—
1069C2×C4C3×#12314yes—
1070C2×C3—44no—
1071C2×C3—44no—
1072C2×C3C4×#12111yescharacteristic
1073C2×C3C4×#12311yescharacteristic
1074C2×C3#233711yescharacteristic
1075C2×C3#235811yescharacteristic
1076C2×C3#235911yescharacteristic
1077C2×C3#236111yescharacteristic
1078C2×C3#236411yescharacteristic
1079C2×C3#241811yescharacteristic
1080C2×C3#242211yescharacteristic
1081C2×C3#242411yescharacteristic
1082C2×C3#242711yescharacteristic
1083C2×C3#247011yescharacteristic
1084C2×C3#247711yescharacteristic
1085C2×C3#255911yescharacteristic
1086C2×C3#257611yescharacteristic
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22C2×C3×C4×D411yescharacteristic
1118C22C2×C3×C4×D411yescharacteristic
1119C22C2×C3×C4×D411yescharacteristic
1120C22C3×C4×#4111yescharacteristic
1121C22C3×C4×#4111yescharacteristic
1122C22C3×#51811yescharacteristic
1123C22C3×#52011yescharacteristic
1124C22C2×C3×#12111yescharacteristic
1125C22C2×C3×#12311yescharacteristic
1126C22C3×#52511yescharacteristic
1127C22C3×#52511yescharacteristic
1128C22C3×#52911yescharacteristic
1129C22C3×#52911yescharacteristic
1130C22C3×#52911yescharacteristic
1131C22C3×#53211yescharacteristic
1132C22C3×#53811yescharacteristic
1133C22C3×#53811yescharacteristic
1134C22C3×#54211yescharacteristic
1135C22C3×#54211yescharacteristic
1136C22C3×D4211yescharacteristic
1137C22C3×D4211yescharacteristic
1138C22C3×#54611yescharacteristic
1139C22C3×#54611yescharacteristic
1140C22C3×#54611yescharacteristic
1141C22C3×#54611yescharacteristic
1142C22C3×#54611yescharacteristic
1143C22C3×#54711yescharacteristic
1144C22C3×#54711yescharacteristic
1145C22C3×#54811yescharacteristic
1146C22C3×#55111yescharacteristic
1147C22C3×#55111yescharacteristic
1148C22C3×#55211yescharacteristic
1149C22C3×#55311yescharacteristic
1150C22C3×#55311yescharacteristic
1151C22C3×#55311yescharacteristic
1152C4—24no—
1153C4—24no—
1154C4—24no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—81no—
1164C4—81no—
1165C3#1418211yescharacteristic, direct product factor, Sylow
1166C2—44no—
1167C2—44no—
1168C2C3×C4×#12111yescharacteristic
1169C2C3×C4×#12311yescharacteristic
1170C2C3×#233711yescharacteristic
1171C2C3×#235811yescharacteristic
1172C2C3×#235911yescharacteristic
1173C2C3×#236111yescharacteristic
1174C2C3×#236411yescharacteristic
1175C2C3×#241811yescharacteristic
1176C2C3×#242211yescharacteristic
1177C2C3×#242411yescharacteristic
1178C2C3×#242711yescharacteristic
1179C2C3×#247011yescharacteristic
1180C2C3×#247711yescharacteristic
1181C2C3×#255911yescharacteristic
1182C2C3×#257611yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#388C2semidirect
5. C2×C3×#385C2semidirect
6. C2×C3×C4×C22⋊C4C2semidirect
7. C2×C3×C4×C22⋊C4C2semidirect
8. C3×#1443C2semidirect
9. C3×#1440C2semidirect
10. C3×#1439C2semidirect
11. C3×#1437C2semidirect
12. C3×#1436C2semidirect
13. C3×#1436C2semidirect
14. C3×C4⋊#95C2semidirect
15. C3×C22⋊#95C2semidirect
16. #14182C3direct (N × H)
36. C3×#394C4semidirect
60. C2×#388C2×C3semidirect
63. C2×#385C2×C3semidirect
64. C2×C4×C22⋊C4C2×C3semidirect
65. C2×C4×C22⋊C4C2×C3semidirect
66. #1443C2×C3semidirect
67. #1440C2×C3semidirect
68. #1439C2×C3semidirect
69. #1437C2×C3semidirect
70. #1436C2×C3semidirect
71. #1436C2×C3semidirect
72. C4⋊#95C2×C3semidirect
73. C22⋊#95C2×C3semidirect
118. C2×C3×C4⋊C4C2×C4semidirect
143. C2×C3×C22⋊C4C2×C4semidirect
144. C2×C3×C22⋊C4C2×C4semidirect
145. C2×C3×C22⋊C4C2×C4semidirect
146. C2×C3×C22⋊C4C2×C4semidirect
172. C3×#95C2×C4semidirect
173. C3×#95D4semidirect
193. #394C3×C4semidirect
419. C2×C4⋊C4C2×C3×C4semidirect
444. C2×C22⋊C4C2×C3×C4semidirect
445. C2×C22⋊C4C2×C3×C4semidirect
446. C2×C22⋊C4C2×C3×C4semidirect
447. C2×C22⋊C4C2×C3×C4semidirect
473. #95C2×C3×C4semidirect
474. #95C3×D4semidirect
1165. C3#14182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3942
C2×C3×#3882
C2×C3×#3862
C2×C3×#3852
C2×C3×C4×C22⋊C42
C3×#14432
C3×#14402
C3×#14392
C3×#14372
C3×#14362
C3×C4⋊#952
C3×C22⋊#952
#141823