Finite Group Databasebeta

← C3×#14741 #10633348

Subgroups — C3×#14741 #10633348

Order 768.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#397C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic
3C2×C3×#394C211yesmaximal, characteristic
4C2×C3×#388C211yesmaximal, characteristic, complemented
5C2×C3×#386C211yesmaximal, characteristic
6C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#1444C211yesmaximal, characteristic, complemented
8C3×#1443C211yesmaximal, characteristic, complemented
9C3×#1440C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1439C211yesmaximal, characteristic, complemented
12C3×#1437C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×C4⋊#95C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#14741C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×C4⋊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×C22⋊C4C2211yescharacteristic
34C22×C3×C42C2211yescharacteristic
35C22×C3×C42C2211yescharacteristic
36C3×#397—24no—
37C3×#394—24no—
38C3×#394—24no—
39C3×#388—24no—
40C3×#386—24no—
41C3×C4×C22⋊C4—24no—
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×C3×#95C2211yescharacteristic
58C2×#397C2×C311yescharacteristic, complemented
59C2×#394C2×C311yescharacteristic
60C2×#394C2×C311yescharacteristic
61C2×#388C2×C311yescharacteristic, complemented
62C2×#386C2×C311yescharacteristic
63C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
64#1444C2×C311yescharacteristic, complemented
65#1443C2×C311yescharacteristic, complemented
66#1440C2×C311yescharacteristic, complemented
67#1439C2×C311yescharacteristic, complemented
68#1439C2×C311yescharacteristic, complemented
69#1437C2×C311yescharacteristic, complemented
70#1436C2×C311yescharacteristic, complemented
71C4⋊#95C2×C311yescharacteristic, complemented
72C22⋊#95C2×C311yescharacteristic, complemented
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
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
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—41no—
110C2×C3×C4⋊C4—41no—
111C2×C3×C4⋊C4—41no—
112C2×C3×C4⋊C4—41no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
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—41no—
139C2×C3×C22⋊C4—41no—
140C2×C3×C22⋊C4—41no—
141C2×C3×C22⋊C4—41no—
142C2×C3×C22⋊C4—41no—
143C2×C3×C22⋊C4—41no—
144C2×C3×C22⋊C4D414yes—
145C2×C3×C22⋊C4D414yes—
146C2×C3×C22⋊C4D414yes—
147C2×C3×C42—22no—
148C2×C3×C42—22no—
149C2×C3×C42—22no—
150C2×C3×C42—22no—
151C2×C3×C42—41no—
152C2×C3×C42—41no—
153C3×#95—22no—
154C3×#95—22no—
155C3×#95—22no—
156C3×#95—22no—
157C3×#95—22no—
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—41no—
169C23×D4C22×C311yescharacteristic
170C24×C4C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172C22×C4⋊C4C22×C311yescharacteristic
173C22×C4⋊C4C22×C311yescharacteristic
174C22×C4⋊C4C22×C311yescharacteristic
175C22×C22⋊C4C22×C311yescharacteristic
176C22×C22⋊C4C22×C311yescharacteristic
177C22×C22⋊C4C22×C311yescharacteristic
178C22×C22⋊C4C22×C311yescharacteristic
179C22×C22⋊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×C42C22×C311yescharacteristic
187C22×C42C22×C311yescharacteristic
188#397—24no—
189#394—24no—
190#394—24no—
191#388—24no—
192#386—24no—
193C4×C22⋊C4—24no—
194C2×#95C22×C311yescharacteristic
195C2×#95C22×C311yescharacteristic
196C2×#95C22×C311yescharacteristic
197C2×#95C22×C311yescharacteristic
198C2×#95C22×C311yescharacteristic
199C2×#95C22×C311yescharacteristic
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
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
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×C3C2×D412yes—
237C24×C3C2×D412yes—
238C24×C3C2×D412yes—
239C24×C3#4112yes—
240C24×C3C2411yescharacteristic
241C2×C3×D4—28no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C2×C3×D4—44no—
247C2×C3×D4—44no—
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—28no—
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—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—44no—
328C22×C3×C4—44no—
329C22×C3×C4—44no—
330C22×C3×C4—44no—
331C22×C3×C4—44no—
332C22×C3×C4—44no—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D412yes—
336C22×C3×C4C2×D412yes—
337C22×C3×C4C2×D412yes—
338C22×C3×C4C2×D412yes—
339C22×C3×C4#4112yes—
340C22×C3×C4#4112yes—
341C22×C3×C4#4112yes—
342C22×C3×C4#4112yes—
343C22×C3×C4#4112yes—
344C22×C3×C4#4112yes—
345C22×C3×C4#4112yes—
346C3×C4⋊C4—44no—
347C3×C4⋊C4—44no—
348C3×C4⋊C4—44no—
349C3×C4⋊C4—44no—
350C3×C22⋊C4—28no—
351C3×C22⋊C4—28no—
352C3×C22⋊C4—28no—
353C3×C22⋊C4—44no—
354C3×C22⋊C4—44no—
355C3×C22⋊C4—44no—
356C3×C22⋊C4—44no—
357C3×C22⋊C4—44no—
358C3×C22⋊C4—44no—
359C3×C22⋊C4—44no—
360C3×C22⋊C4—44no—
361C3×C42—44no—
362C3×C42—44no—
363C25C23×C311yescharacteristic
364C25C23×C311yescharacteristic
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—41no—
371C22×D4—41no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C23×C311yescharacteristic
380C23×C4C23×C311yescharacteristic
381C23×C4C23×C311yescharacteristic
382C23×C4C23×C311yescharacteristic
383C23×C4C23×C311yescharacteristic
384C23×C4C23×C311yescharacteristic
385C23×C4C23×C311yescharacteristic
386C23×C4C23×C311yescharacteristic
387C23×C4C23×C311yescharacteristic
388C23×C4C23×C311yescharacteristic
389C23×C4C23×C311yescharacteristic
390C23×C4C23×C311yescharacteristic
391C23×C4C23×C311yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—41no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
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—41no—
429C2×C22⋊C4—41no—
430C2×C22⋊C4—41no—
431C2×C22⋊C4—41no—
432C2×C22⋊C4—41no—
433C2×C22⋊C4—41no—
434C2×C22⋊C4C3×D414yes—
435C2×C22⋊C4C3×D414yes—
436C2×C22⋊C4C3×D414yes—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—41no—
442C2×C42—41no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—41no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
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—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
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#12114yes—
529C23×C3C22×D411yescharacteristic
530C23×C3C22×D411yescharacteristic
531C23×C3C22×D411yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3C2×#4111yescharacteristic
534C23×C3C2×#4111yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3C2×#4111yescharacteristic
539C23×C3C2×#4111yescharacteristic
540C23×C3H(5,𝔽2)11yescharacteristic
541C23×C3H(5,𝔽2)11yescharacteristic
542C23×C3H(5,𝔽2)11yescharacteristic
543C23×C32−1+411yescharacteristic
544C3×D4—416no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
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—416no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
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#12314yes—
636C2×C3×C4#12314yes—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24C2×C3×D412yes—
664C24C2×C3×D412yes—
665C24C2×C3×D412yes—
666C24C3×#4112yes—
667C24C24×C311yescharacteristic
668C2×D4—28no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
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—28no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
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—21no—
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—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C2×C3×D412yes—
761C22×C4C2×C3×D412yes—
762C22×C4C2×C3×D412yes—
763C22×C4C2×C3×D412yes—
764C22×C4C2×C3×D412yes—
765C22×C4C2×C3×D412yes—
766C22×C4C3×#4112yes—
767C22×C4C3×#4112yes—
768C22×C4C3×#4112yes—
769C22×C4C3×#4112yes—
770C22×C4C3×#4112yes—
771C22×C4C3×#4112yes—
772C22×C4C3×#4112yes—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C42—44no—
789C42—44no—
790C22×C3—24no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—81no—
813C22×C3—81no—
814C22×C3—81no—
815C22×C3—81no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3C2×#12111yescharacteristic
821C22×C3C2×#12311yescharacteristic
822C22×C3C2×#12311yescharacteristic
823C22×C3#52511yescharacteristic
824C22×C3#52511yescharacteristic
825C22×C3#52911yescharacteristic
826C22×C3#52911yescharacteristic
827C22×C3#52911yescharacteristic
828C22×C3#52911yescharacteristic
829C22×C3#52911yescharacteristic
830C22×C3#53211yescharacteristic
831C22×C3#53211yescharacteristic
832C22×C3#53211yescharacteristic
833C22×C3#53811yescharacteristic
834C22×C3#53811yescharacteristic
835C22×C3#53811yescharacteristic
836C22×C3#53911yescharacteristic
837C22×C3#54211yescharacteristic
838C22×C3#54211yescharacteristic
839C22×C3D4211yescharacteristic
840C22×C3D4211yescharacteristic
841C22×C3#54611yescharacteristic
842C22×C3#54611yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54611yescharacteristic
846C22×C3#54711yescharacteristic
847C22×C3#54711yescharacteristic
848C22×C3#54711yescharacteristic
849C22×C3#55111yescharacteristic
850C22×C3#55311yescharacteristic
851C22×C3#55311yescharacteristic
852C22×C3#55311yescharacteristic
853C22×C3#55511yescharacteristic
854C22×C3#55611yescharacteristic
855C3×C4—24no—
856C3×C4—24no—
857C3×C4—42no—
858C3×C4—42no—
859C3×C4—42no—
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—81no—
865C3×C4—81no—
866C3×C4—81no—
867C3×C4—81no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
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—
937C23C3×#12114yes—
938C23C22×C3×D411yescharacteristic
939C23C22×C3×D411yescharacteristic
940C23C22×C3×D411yescharacteristic
941C23C2×C3×#4111yescharacteristic
942C23C2×C3×#4111yescharacteristic
943C23C2×C3×#4111yescharacteristic
944C23C2×C3×#4111yescharacteristic
945C23C2×C3×#4111yescharacteristic
946C23C2×C3×#4111yescharacteristic
947C23C2×C3×#4111yescharacteristic
948C23C2×C3×#4111yescharacteristic
949C23C3×H(5,𝔽2)11yescharacteristic
950C23C3×H(5,𝔽2)11yescharacteristic
951C23C3×H(5,𝔽2)11yescharacteristic
952C23C3×2−1+411yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
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—416no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
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×C4C3×#12314yes—
1045C2×C4C3×#12314yes—
1046C2×C3—44no—
1047C2×C3—82no—
1048C2×C3#239511yescharacteristic
1049C2×C3#241811yescharacteristic
1050C2×C3#242211yescharacteristic
1051C2×C3#242211yescharacteristic
1052C2×C3#242411yescharacteristic
1053C2×C3#242511yescharacteristic
1054C2×C3#244411yescharacteristic
1055C2×C3#246611yescharacteristic
1056C2×C3#247411yescharacteristic
1057C2×C3#251811yescharacteristic
1058C2×C3#252111yescharacteristic
1059C2×C3#255511yescharacteristic
1060C2×C3#255911yescharacteristic
1061C2×C3#265311yescharacteristic
1062C2×C3#285411yescharacteristic
1063C22—24no—
1064C22—24no—
1065C22—24no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22C2×C3×#12111yescharacteristic
1094C22C2×C3×#12311yescharacteristic
1095C22C2×C3×#12311yescharacteristic
1096C22C3×#52511yescharacteristic
1097C22C3×#52511yescharacteristic
1098C22C3×#52911yescharacteristic
1099C22C3×#52911yescharacteristic
1100C22C3×#52911yescharacteristic
1101C22C3×#52911yescharacteristic
1102C22C3×#52911yescharacteristic
1103C22C3×#53211yescharacteristic
1104C22C3×#53211yescharacteristic
1105C22C3×#53211yescharacteristic
1106C22C3×#53811yescharacteristic
1107C22C3×#53811yescharacteristic
1108C22C3×#53811yescharacteristic
1109C22C3×#53911yescharacteristic
1110C22C3×#54211yescharacteristic
1111C22C3×#54211yescharacteristic
1112C22C3×D4211yescharacteristic
1113C22C3×D4211yescharacteristic
1114C22C3×#54611yescharacteristic
1115C22C3×#54611yescharacteristic
1116C22C3×#54611yescharacteristic
1117C22C3×#54611yescharacteristic
1118C22C3×#54611yescharacteristic
1119C22C3×#54711yescharacteristic
1120C22C3×#54711yescharacteristic
1121C22C3×#54711yescharacteristic
1122C22C3×#55111yescharacteristic
1123C22C3×#55311yescharacteristic
1124C22C3×#55311yescharacteristic
1125C22C3×#55311yescharacteristic
1126C22C3×#55511yescharacteristic
1127C22C3×#55611yescharacteristic
1128C4—24no—
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C3#1474111yescharacteristic, direct product factor, Sylow
1142C2—44no—
1143C2—82no—
1144C2C3×#239511yescharacteristic
1145C2C3×#241811yescharacteristic
1146C2C3×#242211yescharacteristic
1147C2C3×#242211yescharacteristic
1148C2C3×#242411yescharacteristic
1149C2C3×#242511yescharacteristic
1150C2C3×#244411yescharacteristic
1151C2C3×#246611yescharacteristic
1152C2C3×#247411yescharacteristic
1153C2C3×#251811yescharacteristic
1154C2C3×#252111yescharacteristic
1155C2C3×#255511yescharacteristic
1156C2C3×#255911yescharacteristic
1157C2C3×#265311yescharacteristic
1158C2C3×#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
1. C2×C3×#397C2semidirect
4. C2×C3×#388C2semidirect
6. C2×C3×C4×C22⋊C4C2semidirect
7. C3×#1444C2semidirect
8. C3×#1443C2semidirect
9. C3×#1440C2semidirect
10. C3×#1439C2semidirect
11. C3×#1439C2semidirect
12. C3×#1437C2semidirect
13. C3×#1436C2semidirect
14. C3×C4⋊#95C2semidirect
15. C3×C22⋊#95C2semidirect
16. #14741C3direct (N × H)
58. C2×#397C2×C3semidirect
61. C2×#388C2×C3semidirect
63. C2×C4×C22⋊C4C2×C3semidirect
64. #1444C2×C3semidirect
65. #1443C2×C3semidirect
66. #1440C2×C3semidirect
67. #1439C2×C3semidirect
68. #1439C2×C3semidirect
69. #1437C2×C3semidirect
70. #1436C2×C3semidirect
71. C4⋊#95C2×C3semidirect
72. C22⋊#95C2×C3semidirect
1141. C3#14741direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×C3×#3942
C2×C3×#3882
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14442
C3×#14432
C3×#14402
C3×#14392
C3×#14372
C3×#14362
C3×C4⋊#952
C3×C22⋊#952
#147413