Finite Group Databasebeta

← C3×#14761 #10633368

Subgroups — C3×#14761 #10633368

Order 768.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic
2C2×C3×#394C211yesmaximal, characteristic
3C2×C3×#389C211yesmaximal, characteristic, complemented
4C2×C3×#388C211yesmaximal, characteristic, complemented
5C2×C3×#385C211yesmaximal, characteristic, complemented
6C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#1444C211yesmaximal, characteristic, complemented
8C3×#1442C211yesmaximal, characteristic, complemented
9C3×#1440C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1439C211yesmaximal, characteristic, complemented
12C3×#1439C211yesmaximal, characteristic, complemented
13C3×#1438C211yesmaximal, characteristic
14C3×#1437C211yesmaximal, characteristic, complemented
15C3×#1436C211yesmaximal, characteristic, complemented
16#14761C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C2×C3×#123—24no—
20C2×C3×#123—24no—
21C2×C3×#123—24no—
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C42C2211yescharacteristic
40C22×C3×C42C2211yescharacteristic
41C3×#394—24no—
42C3×#389—24no—
43C3×#388—24no—
44C3×#385—24no—
45C3×C4×C22⋊C4—24no—
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×C3×#95C2211yescharacteristic
60C22×#123C2×C311yescharacteristic
61C2×#394C2×C311yescharacteristic
62C2×#389C2×C311yescharacteristic, complemented
63C2×#388C2×C311yescharacteristic, complemented
64C2×#385C2×C311yescharacteristic, complemented
65C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
66#1444C2×C311yescharacteristic, complemented
67#1442C2×C311yescharacteristic, complemented
68#1440C2×C311yescharacteristic, complemented
69#1439C2×C311yescharacteristic, complemented
70#1439C2×C311yescharacteristic, complemented
71#1439C2×C311yescharacteristic, complemented
72#1438C2×C311yescharacteristic
73#1437C2×C311yescharacteristic, complemented
74#1436C2×C311yescharacteristic, complemented
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—41no—
83C22×C3×D4—41no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4D414yes—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
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
104C3×#123—232no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
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—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—41no—
120C2×C3×C4⋊C4—41no—
121C2×C3×C4⋊C4—41no—
122C2×C3×C4⋊C4D414yes—
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—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—22no—
145C2×C3×C22⋊C4—22no—
146C2×C3×C22⋊C4—22no—
147C2×C3×C22⋊C4—22no—
148C2×C3×C22⋊C4—22no—
149C2×C3×C22⋊C4—22no—
150C2×C3×C22⋊C4—22no—
151C2×C3×C22⋊C4—22no—
152C2×C3×C22⋊C4—41no—
153C2×C3×C22⋊C4—41no—
154C2×C3×C22⋊C4D414yes—
155C2×C3×C22⋊C4D414yes—
156C2×C3×C42—22no—
157C2×C3×C42—22no—
158C2×C3×C42—22no—
159C2×C3×C42—22no—
160C2×C3×C42—41no—
161C2×C3×C42—41no—
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—22no—
171C3×#95—22no—
172C3×#95—22no—
173C3×#95—22no—
174C3×#95—22no—
175C3×#95—41no—
176C23×D4C22×C311yescharacteristic
177C24×C4C22×C311yescharacteristic
178C2×#123—24no—
179C2×#123—24no—
180C2×#123—24no—
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184C22×C4⋊C4C22×C311yescharacteristic
185C22×C4⋊C4C22×C311yescharacteristic
186C22×C4⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C22⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C22⋊C4C22×C311yescharacteristic
195C22×C22⋊C4C22×C311yescharacteristic
196C22×C22⋊C4C22×C311yescharacteristic
197C22×C22⋊C4C22×C311yescharacteristic
198C22×C42C22×C311yescharacteristic
199C22×C42C22×C311yescharacteristic
200#394—24no—
201#389—24no—
202#388—24no—
203#385—24no—
204C4×C22⋊C4—24no—
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
216C2×#95C22×C311yescharacteristic
217C2×#95C22×C311yescharacteristic
218C2×#95C22×C311yescharacteristic
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×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3C2×D412yes—
246C24×C3C2×D412yes—
247C24×C3C2×D412yes—
248C24×C3#4112yes—
249C24×C3C2411yescharacteristic
250C2×C3×D4—28no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C2×C3×D4—44no—
255C2×C3×D4—44no—
256C2×C3×D4—44no—
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—28no—
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—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—28no—
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—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—44no—
336C22×C3×C4—44no—
337C22×C3×C4—44no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4C2×D412yes—
341C22×C3×C4C2×D412yes—
342C22×C3×C4C2×D412yes—
343C22×C3×C4C2×D412yes—
344C22×C3×C4C2×D412yes—
345C22×C3×C4C2×D412yes—
346C22×C3×C4C2×D412yes—
347C22×C3×C4C2×D412yes—
348C22×C3×C4C2×D412yes—
349C22×C3×C4#4112yes—
350C22×C3×C4#4112yes—
351C22×C3×C4#4112yes—
352C22×C3×C4#4112yes—
353C22×C3×C4#4112yes—
354C22×C3×C4#4112yes—
355C3×C4⋊C4—28no—
356C3×C4⋊C4—28no—
357C3×C4⋊C4—28no—
358C3×C4⋊C4—44no—
359C3×C4⋊C4—44no—
360C3×C4⋊C4—44no—
361C3×C22⋊C4—28no—
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—
374C25C23×C311yescharacteristic
375C25C23×C311yescharacteristic
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—41no—
382C22×D4—41no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—41no—
388C23×C4—41no—
389C23×C4C3×D414yes—
390C23×C4C23×C311yescharacteristic
391C23×C4C23×C311yescharacteristic
392C23×C4C23×C311yescharacteristic
393C23×C4C23×C311yescharacteristic
394C23×C4C23×C311yescharacteristic
395C23×C4C23×C311yescharacteristic
396C23×C4C23×C311yescharacteristic
397C23×C4C23×C311yescharacteristic
398C23×C4C23×C311yescharacteristic
399C23×C4C23×C311yescharacteristic
400C23×C4C23×C311yescharacteristic
401C23×C4C23×C311yescharacteristic
402C23×C4C23×C311yescharacteristic
403#123—232no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4C3×D414yes—
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—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—41no—
452C2×C22⋊C4—41no—
453C2×C22⋊C4C3×D414yes—
454C2×C22⋊C4C3×D414yes—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—41no—
460C2×C42—41no—
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—22no—
472#95—22no—
473#95—22no—
474#95—41no—
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—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
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×C3—41no—
544C23×C3#12114yes—
545C23×C3C22×D411yescharacteristic
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×C32−1+411yescharacteristic
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—416no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
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×C4#12014yes—
652C2×C3×C4#12314yescomplemented
653C24—21no—
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—
678C24—21no—
679C24C2×C3×D412yes—
680C24C2×C3×D412yes—
681C24C2×C3×D412yes—
682C24C3×#4112yes—
683C24C24×C311yescharacteristic
684C2×D4—28no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—28no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
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—28no—
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—21no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4C2×C3×D412yes—
775C22×C4C2×C3×D412yes—
776C22×C4C2×C3×D412yes—
777C22×C4C2×C3×D412yes—
778C22×C4C2×C3×D412yes—
779C22×C4C2×C3×D412yes—
780C22×C4C2×C3×D412yes—
781C22×C4C2×C3×D412yes—
782C22×C4C2×C3×D412yes—
783C22×C4C3×#4112yes—
784C22×C4C3×#4112yes—
785C22×C4C3×#4112yes—
786C22×C4C3×#4112yes—
787C22×C4C3×#4112yes—
788C22×C4C3×#4112yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C42—44no—
807C42—44no—
808C22×C3—24no—
809C22×C3—24no—
810C22×C3—24no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
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—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3C2×#12011yescharacteristic
839C22×C3C2×#12111yescharacteristic
840C22×C3C2×#12311yescharacteristic
841C22×C3#52511yescharacteristic
842C22×C3#52511yescharacteristic
843C22×C3#52511yescharacteristic
844C22×C3#52511yescharacteristic
845C22×C3#52911yescharacteristic
846C22×C3#52911yescharacteristic
847C22×C3#53211yescharacteristic
848C22×C3#53211yescharacteristic
849C22×C3#53211yescharacteristic
850C22×C3#53211yescharacteristic
851C22×C3#53411yescharacteristic
852C22×C3#53611yescharacteristic
853C22×C3#53911yescharacteristic
854C22×C3#53911yescharacteristic
855C22×C3#54211yescharacteristic
856C22×C3#54211yescharacteristic
857C22×C3D4211yescharacteristic
858C22×C3D4211yescharacteristic
859C22×C3#54611yescharacteristic
860C22×C3#54611yescharacteristic
861C22×C3#54711yescharacteristic
862C22×C3#54711yescharacteristic
863C22×C3#54711yescharacteristic
864C22×C3#54711yescharacteristic
865C22×C3#54811yescharacteristic
866C22×C3#54811yescharacteristic
867C22×C3#55111yescharacteristic
868C22×C3#55211yescharacteristic
869C22×C3#55211yescharacteristic
870C22×C3#55311yescharacteristic
871C22×C3#55311yescharacteristic
872C22×C3#55911yescharacteristic
873C3×C4—24no—
874C3×C4—24no—
875C3×C4—42no—
876C3×C4—42no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—42no—
881C3×C4—42no—
882C3×C4—42no—
883C3×C4—42no—
884C3×C4—81no—
885C3×C4—81no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
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—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
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—
955C23C3×#12114yes—
956C23C22×C3×D411yescharacteristic
957C23C22×C3×D411yescharacteristic
958C23C22×C3×D411yescharacteristic
959C23C22×C3×D411yescharacteristic
960C23C2×C3×#4111yescharacteristic
961C23C2×C3×#4111yescharacteristic
962C23C2×C3×#4111yescharacteristic
963C23C2×C3×#4111yescharacteristic
964C23C2×C3×#4111yescharacteristic
965C23C2×C3×#4111yescharacteristic
966C23C2×C3×#4111yescharacteristic
967C23C3×H(5,𝔽2)11yescharacteristic
968C23C3×H(5,𝔽2)11yescharacteristic
969C23C3×2−1+411yescharacteristic
970C23C3×2−1+411yescharacteristic
971D4—416no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
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—416no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
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×C4C3×#12014yes—
1063C2×C4C3×#12314yescomplemented
1064C2×C3—44no—
1065C2×C3—82no—
1066C2×C3#238811yescharacteristic
1067C2×C3#241011yescharacteristic
1068C2×C3#241311yescharacteristic
1069C2×C3#242211yescharacteristic
1070C2×C3#243211yescharacteristic
1071C2×C3#244311yescharacteristic
1072C2×C3#245511yescharacteristic
1073C2×C3#245811yescharacteristic
1074C2×C3#246111yescharacteristic
1075C2×C3#247011yescharacteristic
1076C2×C3#255311yescharacteristic
1077C2×C3#255811yescharacteristic
1078C2×C3#260211yescharacteristic
1079C2×C3#266311yescharacteristic
1080C2×C3#285411yescharacteristic
1081C22—24no—
1082C22—24no—
1083C22—24no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22C2×C3×#12011yescharacteristic
1112C22C2×C3×#12111yescharacteristic
1113C22C2×C3×#12311yescharacteristic
1114C22C3×#52511yescharacteristic
1115C22C3×#52511yescharacteristic
1116C22C3×#52511yescharacteristic
1117C22C3×#52511yescharacteristic
1118C22C3×#52911yescharacteristic
1119C22C3×#52911yescharacteristic
1120C22C3×#53211yescharacteristic
1121C22C3×#53211yescharacteristic
1122C22C3×#53211yescharacteristic
1123C22C3×#53211yescharacteristic
1124C22C3×#53411yescharacteristic
1125C22C3×#53611yescharacteristic
1126C22C3×#53911yescharacteristic
1127C22C3×#53911yescharacteristic
1128C22C3×#54211yescharacteristic
1129C22C3×#54211yescharacteristic
1130C22C3×D4211yescharacteristic
1131C22C3×D4211yescharacteristic
1132C22C3×#54611yescharacteristic
1133C22C3×#54611yescharacteristic
1134C22C3×#54711yescharacteristic
1135C22C3×#54711yescharacteristic
1136C22C3×#54711yescharacteristic
1137C22C3×#54711yescharacteristic
1138C22C3×#54811yescharacteristic
1139C22C3×#54811yescharacteristic
1140C22C3×#55111yescharacteristic
1141C22C3×#55211yescharacteristic
1142C22C3×#55211yescharacteristic
1143C22C3×#55311yescharacteristic
1144C22C3×#55311yescharacteristic
1145C22C3×#55911yescharacteristic
1146C4—24no—
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—81no—
1158C4—81no—
1159C3#1476111yescharacteristic, direct product factor, Sylow
1160C2—44no—
1161C2—82no—
1162C2C3×#238811yescharacteristic
1163C2C3×#241011yescharacteristic
1164C2C3×#241311yescharacteristic
1165C2C3×#242211yescharacteristic
1166C2C3×#243211yescharacteristic
1167C2C3×#244311yescharacteristic
1168C2C3×#245511yescharacteristic
1169C2C3×#245811yescharacteristic
1170C2C3×#246111yescharacteristic
1171C2C3×#247011yescharacteristic
1172C2C3×#255311yescharacteristic
1173C2C3×#255811yescharacteristic
1174C2C3×#260211yescharacteristic
1175C2C3×#266311yescharacteristic
1176C2C3×#285411yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×#389C2semidirect
4. C2×C3×#388C2semidirect
5. C2×C3×#385C2semidirect
6. C2×C3×C4×C22⋊C4C2semidirect
7. C3×#1444C2semidirect
8. C3×#1442C2semidirect
9. C3×#1440C2semidirect
10. C3×#1439C2semidirect
11. C3×#1439C2semidirect
12. C3×#1439C2semidirect
14. C3×#1437C2semidirect
15. C3×#1436C2semidirect
16. #14761C3direct (N × H)
62. C2×#389C2×C3semidirect
63. C2×#388C2×C3semidirect
64. C2×#385C2×C3semidirect
65. C2×C4×C22⋊C4C2×C3semidirect
66. #1444C2×C3semidirect
67. #1442C2×C3semidirect
68. #1440C2×C3semidirect
69. #1439C2×C3semidirect
70. #1439C2×C3semidirect
71. #1439C2×C3semidirect
73. #1437C2×C3semidirect
74. #1436C2×C3semidirect
652. C2×C3×C4#123semidirect
1063. C2×C4C3×#123semidirect
1159. C3#14761direct (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
C2×C3×#3942
C2×C3×#3892
C2×C3×#3882
C2×C3×#3852
C2×C3×C4×C22⋊C42
C3×#14442
C3×#14422
C3×#14402
C3×#14392
C3×#14382
C3×#14372
C3×#14362
#147613