Finite Group Databasebeta

← #10732196

Subgroups — #10732196

Order 768.

2770 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic, complemented
2C22×#878C211yesmaximal, characteristic, complemented
3C22×#67⋊C4C211yesmaximal, characteristic
4C2×#4942C211yesmaximal, characteristic, complemented
5C2×#4667C211yesmaximal, characteristic, complemented
6C2×#4646C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71568C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic
10#71550C211yesmaximal, characteristic
11#71547C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14#69420C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#15177—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#896—24no—
41C2×#896—24no—
42C2×#896—24no—
43C2×#67⋊C4—24no—
44C2×#67⋊C4—24no—
45C2×#67⋊C4—24no—
46C2×#878—24no—
47C2×#878—24no—
48C2×#878—24no—
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
60C2×C3⋊#95C2211yescharacteristic
61#4942—24no—
62#4667—24no—
63#4646—24no—
64C22×C22⋊Q8—31no—
65C22×C22⋊Q8—31no—
66C22×C4×D4—31no—
67C2×#391—31no—
68C2×#380—31no—
69C2×#380—31no—
70#1444—31no—
71#1444—31no—
72#1439—31no—
73#1439—31no—
74#1439—31no—
75#1439D311yescharacteristic, complemented
76#1438—31no—
77#1438—31no—
78C4⋊#95—31no—
79C25×C3C2311yescharacteristic
80C24×D3C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67Q814yescomplemented
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—22no—
97C23×Dic3—22no—
98C23×Dic3—22no—
99C23×Dic3—22no—
100C23×Dic3D414yes—
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3D414yes—
115C22×Dic6—22no—
116C22×Dic6—22no—
117C22×Dic6—22no—
118C22×Dic6—22no—
119C22×Dic6—22no—
120C22×Dic6—22no—
121C22×Dic6D414yescomplemented
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊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—41no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—41no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4D414yescomplemented
175C2×Dic3⋊C4D414yescomplemented
176C2×C4×Dic3—22no—
177C2×C4×Dic3—22no—
178C2×C4×Dic3D414yes—
179#896—232no—
180#67⋊C4—232no—
181#878—232no—
182C3×#95—22no—
183C3×#95—22no—
184C3×#95—41no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—41no—
194C23×Q8—31no—
195C23×D4—31no—
196C24×C4—31no—
197C24×C4—31no—
198C2×C22⋊Q8—64no—
199C2×C22⋊Q8—64no—
200C2×C22⋊Q8—64no—
201C2×C22⋊Q8—64no—
202C2×C22⋊Q8—64no—
203C2×C22⋊Q8—64no—
204C2×C4×D4—64no—
205C2×C4×D4—64no—
206C2×C4×D4—64no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—31no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—31no—
212C22×C4⋊C4—31no—
213C22×C4⋊C4—31no—
214C22×C4⋊C4C2×D311yescharacteristic
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4C2×D311yescharacteristic
223C22×C22⋊C4C2×D311yescharacteristic
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C42—31no—
226#391—64no—
227#380—64no—
228#380—64no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95—31no—
238C2×#95C2×D311yescharacteristic
239C2×#95C2×D311yescharacteristic
240C2×#95C2×D311yescharacteristic
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3C2×D412yes—
254C24×C3C2×Q812yes—
255C24×C3#4112yes—
256C24×C3C2411yescharacteristic
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3C2×D412yes—
270C23×D3C2×Q812yes—
271C23×D3#4112yes—
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×C4C2×D412yes—
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2×D412yes—
314C2×#67—28no—
315C2×#67—28no—
316C2×#67—28no—
317C2×#67—28no—
318C2×#67—28no—
319C2×#67—28no—
320C2×#67—28no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—28no—
350C22×Dic3—28no—
351C22×Dic3—28no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—44no—
360C22×Dic3—44no—
361C22×Dic3—44no—
362C22×Dic3—44no—
363C22×Dic3C2×D412yes—
364C22×Dic3C2×D412yes—
365C22×Dic3C2×D412yes—
366C22×Dic3C2×D412yes—
367C22×Dic3C2×D412yes—
368C22×Dic3C2×D412yes—
369C22×Dic3C2×D412yes—
370C22×Dic3C2×D412yes—
371C22×Dic3C2×D412yes—
372C22×Dic3C2×D412yes—
373C22×Dic3C2×D412yes—
374C22×Dic3C2×Q812yes—
375C22×Dic3#4112yes—
376C22×Dic3#4112yes—
377C2×C4×D3—28no—
378C2×C4×D3—28no—
379C2×C4×D3—28no—
380C2×C4×D3—44no—
381C2×C4×D3—44no—
382C2×C4×D3—44no—
383C2×C4×D3—44no—
384C2×Dic6—28no—
385C2×Dic6—28no—
386C2×Dic6—28no—
387C2×Dic6—44no—
388C2×Dic6—44no—
389C2×Dic6—44no—
390C2×Dic6—44no—
391C3×C4⋊C4—28no—
392C3×C22⋊C4—28no—
393C3×C22⋊C4—28no—
394C3×C22⋊C4—44no—
395#217—28no—
396#217—44no—
397(C2×D3)⋊C4—28no—
398(C2×D3)⋊C4—28no—
399(C2×D3)⋊C4—28no—
400(C2×D3)⋊C4—44no—
401(C2×D3)⋊C4—44no—
402C4⋊Dic3—28no—
403Dic3⋊C4—28no—
404Dic3⋊C4—28no—
405Dic3⋊C4—28no—
406Dic3⋊C4—28no—
407Dic3⋊C4—28no—
408Dic3⋊C4—44no—
409C4×Dic3—28no—
410C25—31no—
411C25C22×D311yescharacteristic
412C22×Q8—34no—
413C22×Q8—62no—
414C22×Q8—62no—
415C22×Q8—62no—
416C22×Q8—62no—
417C22×Q8—62no—
418C22×Q8—62no—
419C22×D4—34no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—34no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—31no—
432C23×C4—31no—
433C23×C4—34no—
434C23×C4—31no—
435C23×C4—62no—
436C23×C4—62no—
437C23×C4—62no—
438C23×C4—62no—
439C23×C4—62no—
440C23×C4—62no—
441C23×C4—62no—
442C23×C4—62no—
443C23×C4—62no—
444C23×C4—62no—
445C23×C4—62no—
446C23×C4—62no—
447C23×C4C22×D311yescharacteristic
448C23×C4C22×D311yescharacteristic
449C23×C4C22×D311yescharacteristic
450C23×C4C22×D311yescharacteristic
451C23×C4C22×D311yescharacteristic
452C23×C4C22×D311yescharacteristic
453C22⋊Q8—632no—
454C22⋊Q8—632no—
455C4×D4—632no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—34no—
460C2×C4⋊C4—34no—
461C2×C4⋊C4—62no—
462C2×C4⋊C4—62no—
463C2×C4⋊C4—62no—
464C2×C4⋊C4—62no—
465C2×C4⋊C4—62no—
466C2×C4⋊C4—62no—
467C2×C4⋊C4—62no—
468C2×C4⋊C4—62no—
469C2×C4⋊C4—62no—
470C2×C4⋊C4—62no—
471C2×C4⋊C4—62no—
472C2×C4⋊C4—62no—
473C2×C4⋊C4—62no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—62no—
478C2×C4⋊C4—62no—
479C2×C4⋊C4—62no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—41no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—121no—
508C2×C22⋊C4—121no—
509C2×C22⋊C4—121no—
510C2×C42—34no—
511C2×C42—62no—
512C2×C42—62no—
513#95—22no—
514#95—22no—
515#95—41no—
516#95—62no—
517#95—62no—
518#95—62no—
519#95—62no—
520#95—62no—
521#95—62no—
522#95—62no—
523#95—62no—
524#95—121no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3C22⋊Q814yescomplemented
560C23×C3C22×D411yescharacteristic
561C23×C3C22×D411yescharacteristic
562C23×C3C22×D411yescharacteristic
563C23×C3C22×D411yescharacteristic
564C23×C3C22×D411yescharacteristic
565C23×C3C22×D411yescharacteristic
566C23×C3C22×Q811yescharacteristic
567C23×C3C2×#4111yescharacteristic
568C23×C3C2×#4111yescharacteristic
569C23×C3C2×#4111yescharacteristic
570C23×C3C2×#4111yescharacteristic
571C23×C3H(5,𝔽2)11yescharacteristic
572C23×C32−1+411yescharacteristic
573C23×C32−1+411yescharacteristic
574C23×C32−1+411yescharacteristic
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3C22⋊Q814yescomplemented
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
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—41no—
652#67—232no—
653C2×Dic3—22no—
654C2×Dic3—22no—
655C2×Dic3—22no—
656C2×Dic3—22no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—41no—
678C2×Dic3—41no—
679C2×Dic3—41no—
680C2×Dic3—41no—
681C2×Dic3—41no—
682C2×Dic3—41no—
683C2×Dic3—41no—
684C2×Dic3—41no—
685C2×Dic3—41no—
686C2×Dic3—41no—
687C2×Dic3—416no—
688C2×Dic3—41no—
689C2×Dic3—41no—
690C2×Dic3—41no—
691C2×Dic3—41no—
692C2×Dic3—41no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3#12014yes—
696C2×Dic3#12014yes—
697C2×Dic3#12014yes—
698C2×Dic3#12114yes—
699C2×Dic3#12114yes—
700C2×Dic3#12114yes—
701C2×Dic3C22⋊Q814yescomplemented
702C2×Dic3#12714yes—
703C4×D3—416no—
704Dic6—416no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—32no—
718C24—32no—
719C24—32no—
720C24—61no—
721C24—61no—
722C24—61no—
723C24—61no—
724C24—61no—
725C24—61no—
726C24—61no—
727C24—61no—
728C24—61no—
729C24—61no—
730C24—61no—
731C24—61no—
732C24#23512yes—
733C24D3×D412yes—
734C24D3×Q812yes—
735C24C23×D311yescharacteristic
736C2×Q8—68no—
737C2×Q8—68no—
738C2×Q8—68no—
739C2×Q8—124no—
740C2×Q8—124no—
741C2×Q8—124no—
742C2×Q8—124no—
743C2×D4—68no—
744C2×D4—68no—
745C2×D4—68no—
746C2×D4—68no—
747C2×D4—68no—
748C2×D4—68no—
749C2×D4—68no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—32no—
788C22×C4—32no—
789C22×C4—32no—
790C22×C4—32no—
791C22×C4—32no—
792C22×C4—32no—
793C22×C4—32no—
794C22×C4—32no—
795C22×C4—32no—
796C22×C4—32no—
797C22×C4—32no—
798C22×C4—32no—
799C22×C4—32no—
800C22×C4—32no—
801C22×C4—68no—
802C22×C4—68no—
803C22×C4—68no—
804C22×C4—68no—
805C22×C4—68no—
806C22×C4—68no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—61no—
814C22×C4—61no—
815C22×C4—61no—
816C22×C4—61no—
817C22×C4—61no—
818C22×C4—61no—
819C22×C4—61no—
820C22×C4—61no—
821C22×C4—61no—
822C22×C4—61no—
823C22×C4—61no—
824C22×C4—61no—
825C22×C4—61no—
826C22×C4—61no—
827C22×C4—61no—
828C22×C4—61no—
829C22×C4—61no—
830C22×C4—61no—
831C22×C4—61no—
832C22×C4—61no—
833C22×C4—61no—
834C22×C4—61no—
835C22×C4—61no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—124no—
843C22×C4—124no—
844C22×C4—124no—
845C22×C4—124no—
846C22×C4—124no—
847C22×C4—124no—
848C22×C4—124no—
849C22×C4—124no—
850C22×C4D3×D412yes—
851C22×C4D3×D412yes—
852C22×C4D3×D412yes—
853C22×C4D3×D412yes—
854C22×C4D3×D412yes—
855C4⋊C4—28no—
856C4⋊C4—68no—
857C4⋊C4—68no—
858C4⋊C4—68no—
859C4⋊C4—68no—
860C4⋊C4—68no—
861C4⋊C4—68no—
862C4⋊C4—124no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—44no—
866C22⋊C4—68no—
867C22⋊C4—68no—
868C22⋊C4—68no—
869C22⋊C4—68no—
870C22⋊C4—124no—
871C22⋊C4—124no—
872C22⋊C4—124no—
873C42—68no—
874C22×C3—24no—
875C22×C3—24no—
876C22×C3—24no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—42no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—42no—
889C22×C3C2×#12011yescharacteristic
890C22×C3C2×#12011yescharacteristic
891C22×C3C2×#12011yescharacteristic
892C22×C3C2×#12111yescharacteristic
893C22×C3C2×#12111yescharacteristic
894C22×C3C2×#12111yescharacteristic
895C22×C3C2×C22⋊Q811yescharacteristic
896C22×C3C2×C22⋊Q811yescharacteristic
897C22×C3C2×C22⋊Q811yescharacteristic
898C22×C3#52511yescharacteristic
899C22×C3#52511yescharacteristic
900C22×C3#52511yescharacteristic
901C22×C3C2×#12711yescharacteristic
902C22×C3#53611yescharacteristic
903C22×C3#53611yescharacteristic
904C22×C3#53611yescharacteristic
905C22×C3#53711yescharacteristic
906C22×C3#53711yescharacteristic
907C22×C3#53711yescharacteristic
908C22×C3#54611yescharacteristic
909C22×C3#54611yescharacteristic
910C22×C3#54711yescharacteristic
911C22×C3#54711yescharacteristic
912C22×C3#54811yescharacteristic
913C22×C3#54811yescharacteristic
914C22×C3#54811yescharacteristic
915C22×C3#54811yescharacteristic
916C22×C3D4×Q811yescharacteristic
917C22×C3D4×Q811yescharacteristic
918C22×C3D4×Q811yescharacteristic
919C22×C3#55011yescharacteristic
920C22×C3#55211yescharacteristic
921C22×C3#55211yescharacteristic
922C22×C3#55411yescharacteristic
923C22×C3#55611yescharacteristic
924C2×D3—24no—
925C2×D3—24no—
926C2×D3—24no—
927C2×D3—42no—
928C2×D3—42no—
929C2×D3—42no—
930C2×D3—42no—
931C2×D3—42no—
932C2×D3—42no—
933C2×D3—42no—
934C2×D3—42no—
935C2×D3—42no—
936C2×D3—42no—
937C2×D3—42no—
938C2×D3—42no—
939C3×C4—42no—
940C3×C4—42no—
941C3×C4—42no—
942C3×C4—42no—
943C3×C4—42no—
944C3×C4—81no—
945Dic3—24no—
946Dic3—42no—
947Dic3—42no—
948Dic3—42no—
949Dic3—42no—
950Dic3—81no—
951Dic3#39218yes—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—34no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—62no—
994C23—62no—
995C23—62no—
996C23—62no—
997C23—62no—
998C23—62no—
999C23—62no—
1000C23—62no—
1001C23—62no—
1002C23—62no—
1003C23—62no—
1004C23—62no—
1005C23—121no—
1006C23—121no—
1007C23—121no—
1008C23—121no—
1009C23—121no—
1010C23—121no—
1011C23—121no—
1012C23—121no—
1013C23—121no—
1014C23—121no—
1015C23—121no—
1016C23—121no—
1017C23—121no—
1018C23—121no—
1019C23—121no—
1020C23—121no—
1021C23#89614yescomplemented
1022C23C2×#23511yescharacteristic
1023C23C2×D3×D411yescharacteristic
1024C23C2×D3×D411yescharacteristic
1025C23C2×D3×D411yescharacteristic
1026C23C2×D3×D411yescharacteristic
1027C23C2×D3×D411yescharacteristic
1028C23C2×D3×D411yescharacteristic
1029C23#100411yescharacteristic
1030C23C2×D3×Q811yescharacteristic
1031C23D3×#4111yescharacteristic
1032C23D3×#4111yescharacteristic
1033C23D3×#4111yescharacteristic
1034C23#101011yescharacteristic
1035C23#101011yescharacteristic
1036C23#101011yescharacteristic
1037Q8—1216no—
1038D4—632no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—34no—
1055C2×C4—34no—
1056C2×C4—34no—
1057C2×C4—34no—
1058C2×C4—34no—
1059C2×C4—34no—
1060C2×C4—34no—
1061C2×C4—34no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—62no—
1090C2×C4—62no—
1091C2×C4—62no—
1092C2×C4—62no—
1093C2×C4—62no—
1094C2×C4—62no—
1095C2×C4—62no—
1096C2×C4—62no—
1097C2×C4—62no—
1098C2×C4—62no—
1099C2×C4—62no—
1100C2×C4—62no—
1101C2×C4—62no—
1102C2×C4—62no—
1103C2×C4—62no—
1104C2×C4—62no—
1105C2×C4—62no—
1106C2×C4—62no—
1107C2×C4—1216no—
1108C2×C4—1216no—
1109C2×C4—121no—
1110C2×C4—121no—
1111C2×C4—121no—
1112C2×C4—121no—
1113C2×C4—121no—
1114C2×C4—121no—
1115C2×C4—121no—
1116C2×C4—121no—
1117C2×C4—121no—
1118C2×C4—121no—
1119C2×C4—121no—
1120C2×C4—121no—
1121C2×C4—121no—
1122C2×C4—121no—
1123C2×C4—121no—
1124C2×C4—121no—
1125C2×C4—121no—
1126C2×C4—121no—
1127C2×C4—121no—
1128C2×C4—121no—
1129C2×C4—121no—
1130C2×C4—121no—
1131C2×C4—121no—
1132C2×C3—44no—
1133C2×C3C2×#39211yescharacteristic
1134C2×C3#240711yescharacteristic
1135C2×C3#240711yescharacteristic
1136C2×C3#240911yescharacteristic
1137C2×C3#240911yescharacteristic
1138C2×C3#241511yescharacteristic
1139C2×C3#241511yescharacteristic
1140C2×C3#241711yescharacteristic
1141C2×C3#241711yescharacteristic
1142C2×C3#253611yescharacteristic
1143C2×C3#253811yescharacteristic
1144C2×C3#254011yescharacteristic
1145C2×C3#254211yescharacteristic
1146C2×C3#261611yescharacteristic
1147C2×C3#284811yescharacteristic
1148D3—44no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—64no—
1165C22—64no—
1166C22—64no—
1167C22—122no—
1168C22—122no—
1169C22—122no—
1170C22—122no—
1171C22—122no—
1172C22—122no—
1173C22—122no—
1174C22—122no—
1175C22—122no—
1176C22—122no—
1177C22—122no—
1178C22—122no—
1179C22#549011yescharacteristic
1180C22C2×#89611yescharacteristic
1181C22#553111yescharacteristic
1182C22#554711yescharacteristic
1183C22#554711yescharacteristic
1184C22#555211yescharacteristic
1185C22#555211yescharacteristic
1186C22D3×#12011yescharacteristic
1187C22D3×#12011yescharacteristic
1188C22D3×#12011yescharacteristic
1189C22#559711yescharacteristic
1190C22#559711yescharacteristic
1191C22#559911yescharacteristic
1192C22D3×#12111yescharacteristic
1193C22D3×#12111yescharacteristic
1194C22D3×#12111yescharacteristic
1195C22#560811yescharacteristic
1196C22#561011yescharacteristic
1197C22D3×C22⋊Q811yescharacteristic
1198C22D3×C22⋊Q811yescharacteristic
1199C22#563211yescharacteristic
1200C22#563211yescharacteristic
1201C22#563211yescharacteristic
1202C22#563611yescharacteristic
1203C22#564811yescharacteristic
1204C22#564811yescharacteristic
1205C22#565511yescharacteristic
1206C22#565511yescharacteristic
1207C22#565611yescharacteristic
1208C22#567511yescharacteristic
1209C22#567711yescharacteristic
1210C22#567711yescharacteristic
1211C22#570211yescharacteristic
1212C22#570811yescharacteristic
1213C22D3×#12711yescharacteristic
1214C4—38no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—42no—
1219C4—42no—
1220C4—64no—
1221C4—81no—
1222C4—122no—
1223C4—122no—
1224C4—122no—
1225C4—122no—
1226C4—241no—
1227C3#1517711yescharacteristic, complemented, Sylow
1228C2—44no—
1229C2—124no—
1230C2#7388911yescharacteristic
1231C2#7440511yescharacteristic
1232C2#7465511yescharacteristic
1233C2#7468811yescharacteristic
1234C2#7549611yescharacteristic
1235C2#7559211yescharacteristic
1236C2#7634711yescharacteristic
1237C2D3×#39211yescharacteristic
1238C2#7678011yescharacteristic
1239C2#7689411yescharacteristic
1240C2#7697011yescharacteristic
1241C2#7728511yescharacteristic
1242C2#7731411yescharacteristic
1243C2#7746211yescharacteristic
1244C2#7803711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#15177
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
2. C22×#878C2semidirect
4. C2×#4942C2semidirect
5. C2×#4667C2semidirect
6. C2×#4646C2semidirect
7. C3×#1439C2semidirect
8. #71568C2semidirect
11. #71547C2semidirect
12. #69428C2semidirect
13. #69427C2semidirect
14. #69420C2semidirect
15. Dic3⋊#95C2semidirect
75. #1439D3semidirect
93. C22×#67Q8semidirect
121. C22×Dic6D4semidirect
174. C2×Dic3⋊C4D4semidirect
175. C2×Dic3⋊C4D4semidirect
559. C23×C3C22⋊Q8semidirect
609. C22×D3C22⋊Q8semidirect
701. C2×Dic3C22⋊Q8semidirect
1021. C23#896semidirect
1227. C3#15177semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C22×#8782
C22×#67⋊C42
C2×#49422
C2×#46672
C2×#46462
C3×#14392
#715682
#715502
#715472
#694282
#694272
#694202
Dic3⋊#952
#151773