Finite Group Databasebeta

← C3×#15126 #10633733

Subgroups — C3×#15126 #10633733

Order 768.

2506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C2×C3×#394C212yesmaximal, complemented
3C2×C3×#390C211yesmaximal, characteristic, complemented
4C2×C3×#390C211yesmaximal, characteristic, complemented
5C2×C3×#389C211yesmaximal, characteristic, complemented
6C2×C3×#380C211yesmaximal, characteristic, complemented
7C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8C3×#1440C212yesmaximal, complemented
9C3×#1439C212yesmaximal, complemented
10C3×#1438C212yesmaximal, complemented
11C3×C4⋊#95C211yesmaximal, characteristic, complemented
12#15126C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2212yes—
15C24×C3×C4C2211yescharacteristic
16C2×C3×#121—24no—
17C2×C3×#121—24no—
18C2×C3×#121—24no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C22⋊C4C2212yes—
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C42C2211yescharacteristic
32C22×C3×C42C2211yescharacteristic
33C3×#394—28no—
34C3×#390—24no—
35C3×#390—24no—
36C3×#389—24no—
37C3×#380—24no—
38C3×C4×C22⋊C4—24no—
39C2×C3×#95C2212yes—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2212yes—
43C2×C3×#95C2212yes—
44C2×C3×#95C2212yes—
45C22×#121C2×C311yescharacteristic
46C2×#394C2×C312yescomplemented
47C2×#390C2×C311yescharacteristic, complemented
48C2×#390C2×C311yescharacteristic, complemented
49C2×#389C2×C311yescharacteristic, complemented
50C2×#380C2×C311yescharacteristic, complemented
51C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
52#1440C2×C312yescomplemented
53#1439C2×C312yescomplemented
54#1438C2×C312yescomplemented
55C4⋊#95C2×C311yescharacteristic, complemented
56C25×C3C2312yes—
57C25×C3C2311yescharacteristic
58C22×C3×D4—24no—
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—24no—
62C22×C3×D4—22no—
63C22×C3×D4—24no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—42no—
70C22×C3×D4—42no—
71C22×C3×D4D414yes—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4D414yes—
79C23×C3×C4C2312yes—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2312yes—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2312yes—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C3×#121—232no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—24no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—24no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—42no—
99C2×C3×C4⋊C4D414yes—
100C2×C3×C4⋊C4D414yescomplemented
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—24no—
113C2×C3×C22⋊C4—24no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4—24no—
116C2×C3×C22⋊C4—24no—
117C2×C3×C22⋊C4—24no—
118C2×C3×C22⋊C4—24no—
119C2×C3×C22⋊C4—42no—
120C2×C3×C22⋊C4—42no—
121C2×C3×C22⋊C4—42no—
122C2×C3×C22⋊C4—42no—
123C2×C3×C22⋊C4—42no—
124C2×C3×C22⋊C4D414yescomplemented
125C2×C3×C42—22no—
126C2×C3×C42—22no—
127C2×C3×C42—22no—
128C2×C3×C42—22no—
129C2×C3×C42—22no—
130C2×C3×C42—22no—
131C3×#95—22no—
132C3×#95—22no—
133C3×#95—24no—
134C3×#95—24no—
135C3×#95—24no—
136C3×#95—42no—
137C23×D4C22×C311yescharacteristic
138C23×D4C22×C312yes—
139C24×C4C22×C311yescharacteristic
140C2×#121—24no—
141C2×#121—24no—
142C2×#121—24no—
143C22×C4⋊C4C22×C311yescharacteristic
144C22×C4⋊C4C22×C312yes—
145C22×C4⋊C4C22×C311yescharacteristic
146C22×C4⋊C4C22×C311yescharacteristic
147C22×C22⋊C4C22×C312yes—
148C22×C22⋊C4C22×C311yescharacteristic
149C22×C22⋊C4C22×C312yes—
150C22×C22⋊C4C22×C312yes—
151C22×C22⋊C4C22×C312yes—
152C22×C22⋊C4C22×C312yes—
153C22×C22⋊C4C22×C312yes—
154C22×C22⋊C4C22×C311yescharacteristic
155C22×C42C22×C311yescharacteristic
156C22×C42C22×C311yescharacteristic
157#394—28no—
158#390—24no—
159#390—24no—
160#389—24no—
161#380—24no—
162C4×C22⋊C4—24no—
163C2×#95C22×C312yes—
164C2×#95C22×C312yes—
165C2×#95C22×C311yescharacteristic
166C2×#95C22×C312yes—
167C2×#95C22×C311yescharacteristic
168C2×#95C22×C312yes—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—22no—
192C24×C3—22no—
193C24×C3—22no—
194C24×C3—22no—
195C24×C3C2×D414yes—
196C24×C3C2×D412yes—
197C24×C3C2×D412yes—
198C24×C3#4112yes—
199C24×C3C2411yescharacteristic
200C2×C3×D4—216no—
201C2×C3×D4—28no—
202C2×C3×D4—28no—
203C2×C3×D4—28no—
204C2×C3×D4—48no—
205C2×C3×D4—48no—
206C2×C3×D4—48no—
207C2×C3×D4—48no—
208C2×C3×D4—48no—
209C2×C3×D4—48no—
210C2×C3×D4—44no—
211C2×C3×D4—44no—
212C2×C3×D4—44no—
213C2×C3×D4—44no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
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—22no—
239C22×C3×C4—22no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—22no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—22no—
252C22×C3×C4—21no—
253C22×C3×C4—22no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—28no—
257C22×C3×C4—28no—
258C22×C3×C4—28no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—44no—
267C22×C3×C4—44no—
268C22×C3×C4—44no—
269C22×C3×C4—44no—
270C22×C3×C4C2×D412yes—
271C22×C3×C4C2×D412yes—
272C22×C3×C4C2×D414yes—
273C22×C3×C4C2×D414yes—
274C22×C3×C4C2×D412yes—
275C22×C3×C4C2×D412yes—
276C22×C3×C4C2×D412yes—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4#4112yes—
280C22×C3×C4#4112yes—
281C22×C3×C4#4112yes—
282C22×C3×C4#4112yes—
283C22×C3×C4#4112yes—
284C3×C4⋊C4—28no—
285C3×C4⋊C4—28no—
286C3×C4⋊C4—48no—
287C3×C4⋊C4—44no—
288C3×C22⋊C4—28no—
289C3×C22⋊C4—216no—
290C3×C22⋊C4—28no—
291C3×C22⋊C4—48no—
292C3×C22⋊C4—48no—
293C3×C22⋊C4—48no—
294C3×C22⋊C4—48no—
295C3×C22⋊C4—48no—
296C3×C42—44no—
297C3×C42—44no—
298C25C23×C312yes—
299C25C23×C311yescharacteristic
300C22×D4—24no—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—42no—
313C22×D4C3×D414yes—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4C3×D414yes—
321C23×C4C23×C312yes—
322C23×C4C23×C312yes—
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C311yescharacteristic
326C23×C4C23×C312yes—
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C311yescharacteristic
330#121—232no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4C3×D414yes—
342C2×C4⋊C4C3×D414yescomplemented
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4C3×D414yescomplemented
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373#95—22no—
374#95—22no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—42no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—24no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—42no—
448C23×C3#12114yes—
449C23×C3C22×D411yescharacteristic
450C23×C3C22×D411yescharacteristic
451C23×C3C22×D411yescharacteristic
452C23×C3C22×D411yescharacteristic
453C23×C3C22×D411yescharacteristic
454C23×C3C2×#4111yescharacteristic
455C23×C3C2×#4111yescharacteristic
456C23×C3C2×#4111yescharacteristic
457C23×C3C2×#4111yescharacteristic
458C23×C3C2×#4111yescharacteristic
459C23×C3C2×#4111yescharacteristic
460C23×C3H(5,𝔽2)11yescharacteristic
461C23×C3H(5,𝔽2)11yescharacteristic
462C23×C3H(5,𝔽2)11yescharacteristic
463C23×C32−1+411yescharacteristic
464C3×D4—432no—
465C3×D4—416no—
466C2×C3×C4—22no—
467C2×C3×C4—24no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—24no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—24no—
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—42no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—42no—
503C2×C3×C4—42no—
504C2×C3×C4—42no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—42no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—42no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—416no—
516C2×C3×C4—42no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—42no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4#12014yes—
524C2×C3×C4#12114yes—
525C2×C3×C4#12114yes—
526C2×C3×C4#12114yes—
527C2×C3×C4#12314yes—
528C2×C3×C4#12314yes—
529C2×C3×C4#12414yes—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24C2×C3×D414yes—
557C24C2×C3×D412yes—
558C24C2×C3×D412yes—
559C24C3×#4112yes—
560C24C24×C311yescharacteristic
561C2×D4—216no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4C2×C3×D412yes—
632C22×C4C2×C3×D412yes—
633C22×C4C2×C3×D414yes—
634C22×C4C2×C3×D414yes—
635C22×C4C2×C3×D412yes—
636C22×C4C2×C3×D412yes—
637C22×C4C2×C3×D412yes—
638C22×C4C2×C3×D412yes—
639C22×C4C2×C3×D412yes—
640C22×C4C3×#4112yes—
641C22×C4C3×#4112yes—
642C22×C4C3×#4112yes—
643C22×C4C3×#4112yes—
644C22×C4C3×#4112yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—48no—
648C4⋊C4—44no—
649C22⋊C4—216no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C42—44no—
658C42—44no—
659C22×C3—24no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—44no—
675C22×C3—44no—
676C22×C3—44no—
677C22×C3—44no—
678C22×C3—44no—
679C22×C3—44no—
680C22×C3—44no—
681C22×C3—82no—
682C22×C3—82no—
683C22×C3—82no—
684C22×C3—82no—
685C22×C3—82no—
686C22×C3—82no—
687C22×C3—82no—
688C22×C3—82no—
689C22×C3C2×#12011yescharacteristic
690C22×C3C2×#12111yescharacteristic
691C22×C3C2×#12111yescharacteristic
692C22×C3C2×#12111yescharacteristic
693C22×C3C2×#12111yescharacteristic
694C22×C3C2×#12311yescharacteristic
695C22×C3C2×#12311yescharacteristic
696C22×C3#52511yescharacteristic
697C22×C3C2×#12411yescharacteristic
698C22×C3#52911yescharacteristic
699C22×C3#52911yescharacteristic
700C22×C3#53211yescharacteristic
701C22×C3#53211yescharacteristic
702C22×C3#53511yescharacteristic
703C22×C3#53711yescharacteristic
704C22×C3#54011yescharacteristic
705C22×C3#54011yescharacteristic
706C22×C3#54211yescharacteristic
707C22×C3#54211yescharacteristic
708C22×C3D4211yescharacteristic
709C22×C3D4211yescharacteristic
710C22×C3D4211yescharacteristic
711C22×C3#54611yescharacteristic
712C22×C3#54611yescharacteristic
713C22×C3#54611yescharacteristic
714C22×C3#54611yescharacteristic
715C22×C3#54711yescharacteristic
716C22×C3#54711yescharacteristic
717C22×C3#54811yescharacteristic
718C22×C3#54811yescharacteristic
719C22×C3#55011yescharacteristic
720C22×C3#55011yescharacteristic
721C22×C3#55311yescharacteristic
722C22×C3#55311yescharacteristic
723C22×C3#55511yescharacteristic
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—44no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—44no—
731C3×C4—82no—
732C3×C4#39418yescomplemented
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23C3×#12114yes—
803C23C22×C3×D411yescharacteristic
804C23C22×C3×D411yescharacteristic
805C23C22×C3×D411yescharacteristic
806C23C22×C3×D411yescharacteristic
807C23C22×C3×D411yescharacteristic
808C23C2×C3×#4111yescharacteristic
809C23C2×C3×#4111yescharacteristic
810C23C2×C3×#4111yescharacteristic
811C23C2×C3×#4111yescharacteristic
812C23C2×C3×#4111yescharacteristic
813C23C2×C3×#4111yescharacteristic
814C23C3×H(5,𝔽2)11yescharacteristic
815C23C3×H(5,𝔽2)11yescharacteristic
816C23C3×H(5,𝔽2)11yescharacteristic
817C23C3×2−1+411yescharacteristic
818D4—432no—
819D4—416no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—416no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4C3×#12014yes—
878C2×C4C3×#12114yes—
879C2×C4C3×#12114yes—
880C2×C4C3×#12114yes—
881C2×C4C3×#12314yes—
882C2×C4C3×#12314yes—
883C2×C4C3×#12414yes—
884C2×C3—44no—
885C2×C3—84no—
886C2×C3C2×#39411yescharacteristic
887C2×C3#240711yescharacteristic
888C2×C3#240811yescharacteristic
889C2×C3#241411yescharacteristic
890C2×C3#241611yescharacteristic
891C2×C3#242011yescharacteristic
892C2×C3#242211yescharacteristic
893C2×C3#242611yescharacteristic
894C2×C3#242711yescharacteristic
895C2×C3#242811yescharacteristic
896C2×C3#242811yescharacteristic
897C2×C3#249011yescharacteristic
898C2×C3#249111yescharacteristic
899C2×C3#262411yescharacteristic
900C2×C3#285411yescharacteristic
901C22—24no—
902C22—24no—
903C22—24no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—82no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22C2×C3×#12011yescharacteristic
932C22C2×C3×#12111yescharacteristic
933C22C2×C3×#12111yescharacteristic
934C22C2×C3×#12111yescharacteristic
935C22C2×C3×#12111yescharacteristic
936C22C2×C3×#12311yescharacteristic
937C22C2×C3×#12311yescharacteristic
938C22C3×#52511yescharacteristic
939C22C2×C3×#12411yescharacteristic
940C22C3×#52911yescharacteristic
941C22C3×#52911yescharacteristic
942C22C3×#53211yescharacteristic
943C22C3×#53211yescharacteristic
944C22C3×#53511yescharacteristic
945C22C3×#53711yescharacteristic
946C22C3×#54011yescharacteristic
947C22C3×#54011yescharacteristic
948C22C3×#54211yescharacteristic
949C22C3×#54211yescharacteristic
950C22C3×D4211yescharacteristic
951C22C3×D4211yescharacteristic
952C22C3×D4211yescharacteristic
953C22C3×#54611yescharacteristic
954C22C3×#54611yescharacteristic
955C22C3×#54611yescharacteristic
956C22C3×#54611yescharacteristic
957C22C3×#54711yescharacteristic
958C22C3×#54711yescharacteristic
959C22C3×#54811yescharacteristic
960C22C3×#54811yescharacteristic
961C22C3×#55011yescharacteristic
962C22C3×#55011yescharacteristic
963C22C3×#55311yescharacteristic
964C22C3×#55311yescharacteristic
965C22C3×#55511yescharacteristic
966C4—42no—
967C4—42no—
968C4—44no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—44no—
973C4—82no—
974C4C3×#39418yescomplemented
975C3#1512611yescharacteristic, direct product factor, Sylow
976C2—44no—
977C2—84no—
978C2C2×C3×#39411yescharacteristic
979C2C3×#240711yescharacteristic
980C2C3×#240811yescharacteristic
981C2C3×#241411yescharacteristic
982C2C3×#241611yescharacteristic
983C2C3×#242011yescharacteristic
984C2C3×#242211yescharacteristic
985C2C3×#242611yescharacteristic
986C2C3×#242711yescharacteristic
987C2C3×#242811yescharacteristic
988C2C3×#242811yescharacteristic
989C2C3×#249011yescharacteristic
990C2C3×#249111yescharacteristic
991C2C3×#262411yescharacteristic
992C2C3×#285411yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC22×C3×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#394C2semidirect
3. C2×C3×#390C2semidirect
4. C2×C3×#390C2semidirect
5. C2×C3×#389C2semidirect
6. C2×C3×#380C2semidirect
7. C2×C3×C4×C22⋊C4C2semidirect
8. C3×#1440C2semidirect
9. C3×#1439C2semidirect
10. C3×#1438C2semidirect
11. C3×C4⋊#95C2semidirect
12. #15126C3direct (N × H)
46. C2×#394C2×C3semidirect
47. C2×#390C2×C3semidirect
48. C2×#390C2×C3semidirect
49. C2×#389C2×C3semidirect
50. C2×#380C2×C3semidirect
51. C2×C4×C22⋊C4C2×C3semidirect
52. #1440C2×C3semidirect
53. #1439C2×C3semidirect
54. #1438C2×C3semidirect
55. C4⋊#95C2×C3semidirect
100. C2×C3×C4⋊C4D4semidirect
124. C2×C3×C22⋊C4D4semidirect
342. C2×C4⋊C4C3×D4semidirect
366. C2×C22⋊C4C3×D4semidirect
732. C3×C4#394semidirect
974. C4C3×#394semidirect
975. C3#15126direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C2×C3×#3942
C2×C3×#3902
C2×C3×#3892
C2×C3×#3802
C2×C3×C4×C22⋊C42
C3×#14402
C3×#14392
C3×#14382
C3×C4⋊#952
#151263