Finite Group Databasebeta

← C3×#14028 #10632635

Subgroups — C3×#14028 #10632635

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#387C211yesmaximal, characteristic, complemented
2C2×C3×#385C211yesmaximal, characteristic
3C2×C3×#380C211yesmaximal, characteristic
4C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
5C22×C3×#95C211yesmaximal, characteristic
6C3×#1445C211yesmaximal, characteristic, complemented
7C3×#1443C211yesmaximal, characteristic, complemented
8C3×#1442C211yesmaximal, characteristic, complemented
9C3×#1441C211yesmaximal, characteristic, complemented
10C3×#1436C211yesmaximal, characteristic, complemented
11C3×#1436C211yesmaximal, characteristic, complemented
12C3×#1434C211yesmaximal, characteristic, complemented
13C3×C22⋊#95C211yesmaximal, characteristic
14C3×C22⋊#95C211yesmaximal, characteristic
15C3×C22⋊#95C211yesmaximal, characteristic
16#14028C311yesmaximal, characteristic, direct product factor, Sylow
17C24×C3×C4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C3×#387—24no—
31C3×#385—24no—
32C3×#380C418yescomplemented
33C3×C4×C22⋊C4—24no—
34C2×C3×#95—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
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×#387C2×C311yescharacteristic, complemented
58C2×#385C2×C311yescharacteristic
59C2×#380C2×C311yescharacteristic
60C2×C4×C22⋊C4C2×C311yescharacteristic
61C22×#95C2×C311yescharacteristic
62#1445C2×C311yescharacteristic, complemented
63#1443C2×C311yescharacteristic, complemented
64#1442C2×C311yescharacteristic, complemented
65#1441C2×C311yescharacteristic, complemented
66#1436C2×C311yescharacteristic, complemented
67#1436C2×C311yescharacteristic, complemented
68#1434C2×C311yescharacteristic, complemented
69C22⋊#95C2×C311yescharacteristic
70C22⋊#95C2×C311yescharacteristic
71C22⋊#95C2×C311yescharacteristic
72C25×C3C2311yescharacteristic
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—41no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4—41no—
92C23×C3×C4C2×C414yes—
93C23×C3×C4Q814yes—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
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
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—41no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4C2×C414yescomplemented
119C2×C3×C4⋊C4C2×C414yescomplemented
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⋊C4C2×C414yes—
130C2×C3×C22⋊C4C2×C414yes—
131C2×C3×C22⋊C4D414yes—
132C2×C3×C42—22no—
133C2×C3×C42—22no—
134C2×C3×C42—22no—
135C2×C3×C42—22no—
136C2×C3×C42—41no—
137C2×C3×C42—41no—
138C3×#95—22no—
139C3×#95—22no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—22no—
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95—22no—
151C3×#95—41no—
152C3×#95—41no—
153C3×#95—41no—
154C3×#95—41no—
155C3×#95—41no—
156C3×#95—41no—
157C3×#95C2×C414yescomplemented
158C3×#95C2×C414yescomplemented
159C3×#95D414yes—
160C24×C4C22×C311yescharacteristic
161C24×C4C22×C311yescharacteristic
162C24×C4C22×C311yescharacteristic
163C22×C4⋊C4C22×C311yescharacteristic
164C22×C4⋊C4C22×C311yescharacteristic
165C22×C4⋊C4C22×C311yescharacteristic
166C22×C4⋊C4C22×C311yescharacteristic
167C22×C22⋊C4C22×C311yescharacteristic
168C22×C22⋊C4C22×C311yescharacteristic
169C22×C22⋊C4C22×C311yescharacteristic
170C22×C22⋊C4C22×C311yescharacteristic
171C22×C42C22×C311yescharacteristic
172C22×C42C22×C311yescharacteristic
173#387—24no—
174#385—24no—
175#380C3×C418yescomplemented
176C4×C22⋊C4—24no—
177C2×#95—24no—
178C2×#95C22×C311yescharacteristic
179C2×#95C22×C311yescharacteristic
180C2×#95C22×C311yescharacteristic
181C2×#95C22×C311yescharacteristic
182C2×#95C22×C311yescharacteristic
183C2×#95C22×C311yescharacteristic
184C2×#95C22×C311yescharacteristic
185C2×#95C22×C311yescharacteristic
186C2×#95C22×C311yescharacteristic
187C2×#95C22×C311yescharacteristic
188C2×#95C22×C311yescharacteristic
189C2×#95C22×C311yescharacteristic
190C2×#95C22×C311yescharacteristic
191C2×#95C22×C311yescharacteristic
192C2×#95C22×C311yescharacteristic
193C2×#95C22×C311yescharacteristic
194C2×#95C22×C311yescharacteristic
195C2×#95C22×C311yescharacteristic
196C2×#95C22×C311yescharacteristic
197C2×#95C22×C311yescharacteristic
198C2×#95C22×C311yescharacteristic
199C2×#95C22×C311yescharacteristic
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3C22×C412yes—
209C24×C3C2×D412yes—
210C24×C3C2×Q812yes—
211C24×C3#4112yes—
212C24×C3#4112yes—
213C24×C3#4112yes—
214C24×C3#4112yes—
215C24×C3C2411yescharacteristic
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—28no—
225C22×C3×C4—28no—
226C22×C3×C4—28no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
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—21no—
267C22×C3×C4—21no—
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—28no—
288C22×C3×C4—28no—
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—44no—
304C22×C3×C4—44no—
305C22×C3×C4—44no—
306C22×C3×C4—44no—
307C22×C3×C4—44no—
308C22×C3×C4—44no—
309C22×C3×C4—44no—
310C22×C3×C4—44no—
311C22×C3×C4—44no—
312C22×C3×C4—44no—
313C22×C3×C4—44no—
314C22×C3×C4—44no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4—44no—
318C22×C3×C4—44no—
319C22×C3×C4C22×C412yes—
320C22×C3×C4C22×C412yes—
321C22×C3×C4C22×C412yes—
322C22×C3×C4C22×C412yes—
323C22×C3×C4C22×C412yes—
324C22×C3×C4C22×C412yes—
325C22×C3×C4C2×D412yes—
326C22×C3×C4C2×D412yes—
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×Q812yes—
331C22×C3×C4C2×Q812yes—
332C22×C3×C4#4112yes—
333C22×C3×C4#4112yes—
334C22×C3×C4#4112yes—
335C3×C4⋊C4—28no—
336C3×C4⋊C4—44no—
337C3×C4⋊C4—44no—
338C3×C4⋊C4—44no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—28no—
341C3×C22⋊C4—28no—
342C3×C22⋊C4—44no—
343C3×C42—44no—
344C3×C42—44no—
345C25C23×C311yescharacteristic
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—41no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4C2×C3×C414yes—
366C23×C4C3×Q814yes—
367C23×C4C23×C311yescharacteristic
368C23×C4C23×C311yescharacteristic
369C23×C4C23×C311yescharacteristic
370C23×C4C23×C311yescharacteristic
371C23×C4C23×C311yescharacteristic
372C23×C4C23×C311yescharacteristic
373C23×C4C23×C311yescharacteristic
374C23×C4C23×C311yescharacteristic
375C23×C4C23×C311yescharacteristic
376C23×C4C23×C311yescharacteristic
377C23×C4C23×C311yescharacteristic
378C23×C4C23×C311yescharacteristic
379C23×C4C23×C311yescharacteristic
380C23×C4C23×C311yescharacteristic
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4—41no—
391C2×C4⋊C4C2×C3×C414yescomplemented
392C2×C4⋊C4C2×C3×C414yescomplemented
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4C2×C3×C414yes—
403C2×C22⋊C4C2×C3×C414yes—
404C2×C22⋊C4C3×D414yes—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—41no—
410C2×C42—41no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—41no—
425#95—41no—
426#95—41no—
427#95—41no—
428#95—41no—
429#95—41no—
430#95C2×C3×C414yescomplemented
431#95C2×C3×C414yescomplemented
432#95C3×D414yes—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3#11714yes—
462C23×C3C4×D414yes—
463C23×C3C4×Q814yes—
464C23×C3C22⋊Q814yes—
465C23×C3#12314yes—
466C23×C3#12514yes—
467C23×C3#12614yes—
468C23×C3C23×C411yescharacteristic
469C23×C3C22×D411yescharacteristic
470C23×C3C22×D411yescharacteristic
471C23×C3C22×Q811yescharacteristic
472C23×C3C2×#4111yescharacteristic
473C23×C3C2×#4111yescharacteristic
474C23×C3C2×#4111yescharacteristic
475C23×C3C2×#4111yescharacteristic
476C23×C3C2×#4111yescharacteristic
477C23×C3C2×#4111yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C23×C3H(5,𝔽2)11yescharacteristic
480C23×C3H(5,𝔽2)11yescharacteristic
481C23×C3H(5,𝔽2)11yescharacteristic
482C23×C32−1+411yescharacteristic
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—416no—
526C2×C3×C4—416no—
527C2×C3×C4—416no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
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—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4C4×D414yes—
583C2×C3×C4C22⋊Q814yes—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24C22×C3×C412yes—
593C24C2×C3×D412yes—
594C24C2×C3×Q812yes—
595C24C3×#4112yes—
596C24C3×#4112yes—
597C24C3×#4112yes—
598C24C3×#4112yes—
599C24C24×C311yescharacteristic
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4C22×C3×C412yes—
704C22×C4C22×C3×C412yes—
705C22×C4C22×C3×C412yes—
706C22×C4C22×C3×C412yes—
707C22×C4C22×C3×C412yes—
708C22×C4C22×C3×C412yes—
709C22×C4C2×C3×D412yes—
710C22×C4C2×C3×D412yes—
711C22×C4C2×C3×D412yes—
712C22×C4C2×C3×D412yes—
713C22×C4C2×C3×D412yes—
714C22×C4C2×C3×Q812yes—
715C22×C4C2×C3×Q812yes—
716C22×C4C3×#4112yes—
717C22×C4C3×#4112yes—
718C22×C4C3×#4112yes—
719C4⋊C4—28no—
720C4⋊C4—44no—
721C4⋊C4—44no—
722C4⋊C4—44no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—44no—
727C42—44no—
728C42—44no—
729C22×C3—24no—
730C22×C3—24no—
731C22×C3—24no—
732C22×C3—24no—
733C22×C3—24no—
734C22×C3—24no—
735C22×C3—24no—
736C22×C3—24no—
737C22×C3—24no—
738C22×C3—24no—
739C22×C3—24no—
740C22×C3—24no—
741C22×C3—24no—
742C22×C3—24no—
743C22×C3#38718yescomplemented
744C22×C3C2×#11711yescharacteristic
745C22×C3C2×C4×D411yescharacteristic
746C22×C3C2×C4×D411yescharacteristic
747C22×C3C2×C4×Q811yescharacteristic
748C22×C3C4×#4111yescharacteristic
749C22×C3#51811yescharacteristic
750C22×C3#52011yescharacteristic
751C22×C3C2×C22⋊Q811yescharacteristic
752C22×C3C2×C22⋊Q811yescharacteristic
753C22×C3C2×#12311yescharacteristic
754C22×C3#52511yescharacteristic
755C22×C3C2×#12511yescharacteristic
756C22×C3C2×#12611yescharacteristic
757C22×C3#52911yescharacteristic
758C22×C3#53311yescharacteristic
759C22×C3#53811yescharacteristic
760C22×C3#53911yescharacteristic
761C22×C3#54311yescharacteristic
762C22×C3#54411yescharacteristic
763C22×C3D4211yescharacteristic
764C22×C3#54611yescharacteristic
765C22×C3#54611yescharacteristic
766C22×C3#54611yescharacteristic
767C22×C3#54611yescharacteristic
768C22×C3#54711yescharacteristic
769C22×C3#54811yescharacteristic
770C22×C3#55111yescharacteristic
771C22×C3#55111yescharacteristic
772C22×C3#55111yescharacteristic
773C22×C3#55111yescharacteristic
774C22×C3#55211yescharacteristic
775C22×C3#55211yescharacteristic
776C22×C3#55311yescharacteristic
777C22×C3#55311yescharacteristic
778C22×C3#55311yescharacteristic
779C3×C4—24no—
780C3×C4—24no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—42no—
784C3×C4—42no—
785C3×C4—42no—
786C3×C4—42no—
787C3×C4—42no—
788C3×C4—42no—
789C3×C4—42no—
790C3×C4—42no—
791C3×C4—81no—
792C3×C4—81no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23C3×#11714yes—
822C23C3×C4×D414yes—
823C23C3×C4×Q814yes—
824C23C3×C22⋊Q814yes—
825C23C3×#12314yes—
826C23C3×#12514yes—
827C23C3×#12614yes—
828C23C23×C3×C411yescharacteristic
829C23C22×C3×D411yescharacteristic
830C23C22×C3×D411yescharacteristic
831C23C22×C3×Q811yescharacteristic
832C23C2×C3×#4111yescharacteristic
833C23C2×C3×#4111yescharacteristic
834C23C2×C3×#4111yescharacteristic
835C23C2×C3×#4111yescharacteristic
836C23C2×C3×#4111yescharacteristic
837C23C2×C3×#4111yescharacteristic
838C23C2×C3×#4111yescharacteristic
839C23C3×H(5,𝔽2)11yescharacteristic
840C23C3×H(5,𝔽2)11yescharacteristic
841C23C3×H(5,𝔽2)11yescharacteristic
842C23C3×2−1+411yescharacteristic
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—416no—
886C2×C4—416no—
887C2×C4—416no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4C3×C4×D414yes—
943C2×C4C3×C22⋊Q814yes—
944C2×C3—28no—
945C2×C3C2×#38711yescharacteristic
946C2×C3C4×C22⋊Q811yescharacteristic
947C2×C3#232911yescharacteristic
948C2×C3#234211yescharacteristic
949C2×C3#234311yescharacteristic
950C2×C3#236111yescharacteristic
951C2×C3#236411yescharacteristic
952C2×C3#241811yescharacteristic
953C2×C3#241911yescharacteristic
954C2×C3#243711yescharacteristic
955C2×C3#243811yescharacteristic
956C2×C3#244211yescharacteristic
957C2×C3#248111yescharacteristic
958C2×C3#251011yescharacteristic
959C2×C3#256911yescharacteristic
960C22—24no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22C3×#38718yescomplemented
975C22C2×C3×#11711yescharacteristic
976C22C2×C3×C4×D411yescharacteristic
977C22C2×C3×C4×D411yescharacteristic
978C22C2×C3×C4×Q811yescharacteristic
979C22C3×C4×#4111yescharacteristic
980C22C3×#51811yescharacteristic
981C22C3×#52011yescharacteristic
982C22C2×C3×C22⋊Q811yescharacteristic
983C22C2×C3×C22⋊Q811yescharacteristic
984C22C2×C3×#12311yescharacteristic
985C22C3×#52511yescharacteristic
986C22C2×C3×#12511yescharacteristic
987C22C2×C3×#12611yescharacteristic
988C22C3×#52911yescharacteristic
989C22C3×#53311yescharacteristic
990C22C3×#53811yescharacteristic
991C22C3×#53911yescharacteristic
992C22C3×#54311yescharacteristic
993C22C3×#54411yescharacteristic
994C22C3×D4211yescharacteristic
995C22C3×#54611yescharacteristic
996C22C3×#54611yescharacteristic
997C22C3×#54611yescharacteristic
998C22C3×#54611yescharacteristic
999C22C3×#54711yescharacteristic
1000C22C3×#54811yescharacteristic
1001C22C3×#55111yescharacteristic
1002C22C3×#55111yescharacteristic
1003C22C3×#55111yescharacteristic
1004C22C3×#55111yescharacteristic
1005C22C3×#55211yescharacteristic
1006C22C3×#55211yescharacteristic
1007C22C3×#55311yescharacteristic
1008C22C3×#55311yescharacteristic
1009C22C3×#55311yescharacteristic
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—81no—
1023C4—81no—
1024C3#1402811yescharacteristic, direct product factor, Sylow
1025C2—28no—
1026C2C2×C3×#38711yescharacteristic
1027C2C3×C4×C22⋊Q811yescharacteristic
1028C2C3×#232911yescharacteristic
1029C2C3×#234211yescharacteristic
1030C2C3×#234311yescharacteristic
1031C2C3×#236111yescharacteristic
1032C2C3×#236411yescharacteristic
1033C2C3×#241811yescharacteristic
1034C2C3×#241911yescharacteristic
1035C2C3×#243711yescharacteristic
1036C2C3×#243811yescharacteristic
1037C2C3×#244211yescharacteristic
1038C2C3×#248111yescharacteristic
1039C2C3×#251011yescharacteristic
1040C2C3×#256911yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#387C2semidirect
6. C3×#1445C2semidirect
7. C3×#1443C2semidirect
8. C3×#1442C2semidirect
9. C3×#1441C2semidirect
10. C3×#1436C2semidirect
11. C3×#1436C2semidirect
12. C3×#1434C2semidirect
16. #14028C3direct (N × H)
32. C3×#380C4semidirect
57. C2×#387C2×C3semidirect
62. #1445C2×C3semidirect
63. #1443C2×C3semidirect
64. #1442C2×C3semidirect
65. #1441C2×C3semidirect
66. #1436C2×C3semidirect
67. #1436C2×C3semidirect
68. #1434C2×C3semidirect
118. C2×C3×C4⋊C4C2×C4semidirect
119. C2×C3×C4⋊C4C2×C4semidirect
157. C3×#95C2×C4semidirect
158. C3×#95C2×C4semidirect
175. #380C3×C4semidirect
391. C2×C4⋊C4C2×C3×C4semidirect
392. C2×C4⋊C4C2×C3×C4semidirect
430. #95C2×C3×C4semidirect
431. #95C2×C3×C4semidirect
743. C22×C3#387semidirect
974. C22C3×#387semidirect
1024. C3#14028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3872
C2×C3×#3852
C2×C3×#3802
C2×C3×C4×C22⋊C42
C22×C3×#952
C3×#14452
C3×#14432
C3×#14422
C3×#14412
C3×#14362
C3×#14342
C3×C22⋊#952
#140283