Finite Group Databasebeta

← #10732507

Subgroups — #10732507

Order 768.

2878 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C22×#885C211yesmaximal, characteristic, complemented
3C22×#878C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic, complemented
5C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#4646C211yesmaximal, characteristic, complemented
7C3×#1438C211yesmaximal, characteristic, complemented
8#72131C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71546C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69427C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#15215—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C2×#939—24no—
32C2×#939—24no—
33C2×#939—24no—
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C2×#885—24no—
46C2×#885—24no—
47C2×#885—24no—
48C2×#878—24no—
49C2×#878—24no—
50C2×#878—24no—
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#4957—24no—
62Dic3×C22⋊C4—24no—
63#4646—24no—
64C22×#124—31no—
65C22×C22⋊Q8—31no—
66C22×#121—31no—
67C2×#391—31no—
68C2×#390—31no—
69C2×C4×C22⋊C4—31no—
70#1439—31no—
71#1439—31no—
72#1439—31no—
73#1439—31no—
74#1438—31no—
75#1438—31no—
76#1438—31no—
77#1438D311yescharacteristic, complemented
78C4⋊#95—31no—
79C25×C3C2311yescharacteristic
80C25×C3C2311yescharacteristic
81C24×D3C2311yescharacteristic
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—41no—
88C22×C3×D4—41no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—22no—
103C22×#67—22no—
104C22×#67—22no—
105C22×#67—41no—
106C22×#67—41no—
107C22×#67D414yes—
108C23×Dic3—22no—
109C23×Dic3—22no—
110C23×Dic3—22no—
111C23×Dic3—22no—
112C23×Dic3—22no—
113C23×Dic3—22no—
114C23×Dic3D414yes—
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C22×Dic6—22no—
123C22×Dic6—22no—
124C22×Dic6—22no—
125C22×Dic6—22no—
126C22×Dic6—22no—
127C22×Dic6—22no—
128C22×Dic6D414yescomplemented
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—41no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—22no—
147C2×#217—22no—
148C2×#217—22no—
149C2×#217—22no—
150C2×#217—22no—
151C2×#217—22no—
152C2×#217—22no—
153C2×#217—22no—
154C2×#217—22no—
155C2×#217—41no—
156#939—232no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—22no—
168C2×(C2×D3)⋊C4—22no—
169C2×(C2×D3)⋊C4—22no—
170C2×(C2×D3)⋊C4—41no—
171C2×(C2×D3)⋊C4—41no—
172C2×C4⋊Dic3—22no—
173C2×C4⋊Dic3—22no—
174C2×C4⋊Dic3—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—22no—
178C2×Dic3⋊C4—22no—
179C2×Dic3⋊C4—22no—
180C2×Dic3⋊C4—22no—
181C2×Dic3⋊C4—22no—
182C2×Dic3⋊C4D414yes—
183C2×Dic3⋊C4D414yescomplemented
184C2×C4×Dic3—22no—
185C2×C4×Dic3—22no—
186C2×C4×Dic3—22no—
187C2×C4×Dic3—22no—
188C2×C4×Dic3—22no—
189C2×C4×Dic3D414yescomplemented
190#885—232no—
191#878—232no—
192C3×#95—22no—
193C3×#95—41no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198C3⋊#95—22no—
199C3⋊#95—41no—
200C3⋊#95—41no—
201C3⋊#95—41no—
202C23×Q8—31no—
203C23×D4—31no—
204C23×D4—31no—
205C23×D4C2×D311yescharacteristic
206C24×C4—31no—
207C2×#124—64no—
208C2×#124—64no—
209C2×#124—64no—
210C2×C22⋊Q8—64no—
211C2×C22⋊Q8—64no—
212C2×C22⋊Q8—64no—
213C2×#121—64no—
214C2×#121—64no—
215C2×#121—64no—
216C22×C4⋊C4—31no—
217C22×C4⋊C4—31no—
218C22×C4⋊C4—31no—
219C22×C4⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4—31no—
226C22×C22⋊C4—31no—
227C22×C22⋊C4—31no—
228C22×C22⋊C4—31no—
229C22×C22⋊C4—31no—
230C22×C22⋊C4C2×D311yescharacteristic
231C22×C22⋊C4C2×D311yescharacteristic
232C22×C22⋊C4C2×D311yescharacteristic
233C22×C22⋊C4C2×D311yescharacteristic
234C22×C42—31no—
235C22×C42—31no—
236#391—64no—
237#390—64no—
238C4×C22⋊C4—64no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95—31no—
243C2×#95—31no—
244C2×#95—31no—
245C2×#95—31no—
246C2×#95—31no—
247C2×#95C2×D311yescharacteristic
248C2×#95C2×D311yescharacteristic
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3—21no—
267C24×C3—21no—
268C24×C3—21no—
269C24×C3—21no—
270C24×C3—21no—
271C24×C3—21no—
272C24×C3—21no—
273C24×C3—21no—
274C24×C3—21no—
275C24×C3C2×D412yes—
276C24×C3C2×D412yes—
277C24×C3#4112yes—
278C24×C3#4112yes—
279C24×C3C2411yescharacteristic
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C23×D3—21no—
287C23×D3—21no—
288C23×D3—21no—
289C23×D3—21no—
290C23×D3—21no—
291C23×D3—21no—
292C23×D3—21no—
293C23×D3—21no—
294C23×D3C2×D412yes—
295C2×C3×D4—28no—
296C2×C3×D4—44no—
297C2×C3×D4—44no—
298C2×C3×D4—44no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—44no—
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—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D412yes—
336C22×C3×C4#4112yes—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—28no—
340C2×#67—28no—
341C2×#67—44no—
342C2×#67—44no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C2×#67—44no—
348C2×#67—44no—
349C2×#67—44no—
350C2×#67—44no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3—21no—
386C22×Dic3—21no—
387C22×Dic3—28no—
388C22×Dic3—28no—
389C22×Dic3—28no—
390C22×Dic3—44no—
391C22×Dic3—44no—
392C22×Dic3—44no—
393C22×Dic3—44no—
394C22×Dic3C2×D412yes—
395C22×Dic3C2×D412yes—
396C22×Dic3C2×D412yes—
397C22×Dic3C2×D412yes—
398C22×Dic3C2×D412yes—
399C22×Dic3C2×D412yes—
400C22×Dic3C2×D412yes—
401C22×Dic3C2×D412yes—
402C22×Dic3C2×D412yes—
403C22×Dic3C2×D412yes—
404C22×Dic3C2×D412yes—
405C22×Dic3#4112yes—
406C22×Dic3#4112yes—
407C2×Dic6—28no—
408C2×Dic6—28no—
409C2×Dic6—28no—
410C2×Dic6—44no—
411C2×Dic6—44no—
412C2×Dic6—44no—
413C2×Dic6—44no—
414C3×C22⋊C4—28no—
415C3×C22⋊C4—28no—
416C3×C22⋊C4—28no—
417C3×C22⋊C4—44no—
418#217—28no—
419#217—28no—
420#217—28no—
421#217—28no—
422#217—44no—
423(C2×D3)⋊C4—28no—
424(C2×D3)⋊C4—28no—
425(C2×D3)⋊C4—28no—
426(C2×D3)⋊C4—44no—
427(C2×D3)⋊C4—44no—
428C4⋊Dic3—28no—
429Dic3⋊C4—28no—
430Dic3⋊C4—28no—
431Dic3⋊C4—28no—
432C4×Dic3—28no—
433C4×Dic3—44no—
434C25—31no—
435C25C22×D311yescharacteristic
436C25C22×D311yescharacteristic
437C22×Q8—34no—
438C22×Q8—62no—
439C22×Q8—62no—
440C22×Q8—62no—
441C22×Q8—62no—
442C22×Q8—62no—
443C22×Q8—62no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—34no—
450C22×D4—41no—
451C22×D4—41no—
452C22×D4—62no—
453C22×D4—62no—
454C22×D4—62no—
455C22×D4—62no—
456C22×D4—62no—
457C22×D4—62no—
458C22×D4—62no—
459C22×D4—62no—
460C22×D4—62no—
461C22×D4—62no—
462C22×D4—62no—
463C22×D4—121no—
464C22×D4—121no—
465C23×C4—31no—
466C23×C4—34no—
467C23×C4—31no—
468C23×C4—31no—
469C23×C4—31no—
470C23×C4—31no—
471C23×C4—31no—
472C23×C4—31no—
473C23×C4—62no—
474C23×C4—62no—
475C23×C4—62no—
476C23×C4—62no—
477C23×C4—62no—
478C23×C4—62no—
479C23×C4C22×D311yescharacteristic
480C23×C4C22×D311yescharacteristic
481C23×C4C22×D311yescharacteristic
482C23×C4C22×D311yescharacteristic
483C23×C4C22×D311yescharacteristic
484#124—632no—
485C22⋊Q8—632no—
486#121—632no—
487C2×C4⋊C4—34no—
488C2×C4⋊C4—34no—
489C2×C4⋊C4—62no—
490C2×C4⋊C4—62no—
491C2×C4⋊C4—62no—
492C2×C4⋊C4—62no—
493C2×C4⋊C4—62no—
494C2×C4⋊C4—62no—
495C2×C4⋊C4—62no—
496C2×C4⋊C4—62no—
497C2×C4⋊C4—62no—
498C2×C4⋊C4—62no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—62no—
513C2×C22⋊C4—62no—
514C2×C22⋊C4—62no—
515C2×C22⋊C4—62no—
516C2×C22⋊C4—62no—
517C2×C22⋊C4—62no—
518C2×C22⋊C4—62no—
519C2×C22⋊C4—62no—
520C2×C22⋊C4—62no—
521C2×C22⋊C4—62no—
522C2×C22⋊C4—62no—
523C2×C22⋊C4—62no—
524C2×C22⋊C4—62no—
525C2×C22⋊C4—62no—
526C2×C22⋊C4—62no—
527C2×C22⋊C4—62no—
528C2×C22⋊C4—62no—
529C2×C22⋊C4—62no—
530C2×C22⋊C4—62no—
531C2×C22⋊C4—62no—
532C2×C22⋊C4—62no—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—62no—
535C2×C22⋊C4—62no—
536C2×C22⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—121no—
539C2×C22⋊C4—121no—
540C2×C22⋊C4—121no—
541C2×C42—34no—
542C2×C42—62no—
543C2×C42—62no—
544C2×C42—62no—
545C2×C42—62no—
546C2×C42—62no—
547#95—22no—
548#95—41no—
549#95—62no—
550#95—62no—
551#95—62no—
552#95—62no—
553#95—62no—
554#95—121no—
555#95—121no—
556#95—121no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—41no—
614C23×C3—41no—
615C23×C3—41no—
616C23×C3—41no—
617C23×C3—41no—
618C23×C3—41no—
619C23×C3—41no—
620C23×C3—41no—
621C23×C3—41no—
622C23×C3—41no—
623C23×C3—41no—
624C23×C3—41no—
625C23×C3—41no—
626C23×C3#12414yescomplemented
627C23×C3C22×D411yescharacteristic
628C23×C3C22×D411yescharacteristic
629C23×C3C22×D411yescharacteristic
630C23×C3C22×D411yescharacteristic
631C23×C3C22×D411yescharacteristic
632C23×C3C22×D411yescharacteristic
633C23×C3C2×#4111yescharacteristic
634C23×C3C2×#4111yescharacteristic
635C23×C3C2×#4111yescharacteristic
636C23×C3C2×#4111yescharacteristic
637C23×C3C2×#4111yescharacteristic
638C23×C3H(5,𝔽2)11yescharacteristic
639C23×C3H(5,𝔽2)11yescharacteristic
640C23×C32−1+411yescharacteristic
641C23×C32−1+411yescharacteristic
642C22×D3—22no—
643C22×D3—22no—
644C22×D3—22no—
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3—41no—
659C22×D3—41no—
660C22×D3—41no—
661C22×D3—41no—
662C22×D3—41no—
663C22×D3—41no—
664C22×D3—41no—
665C22×D3—41no—
666C22×D3—41no—
667C22×D3—41no—
668C22×D3—41no—
669C22×D3—41no—
670C22×D3—41no—
671C22×D3—41no—
672C22×D3—41no—
673C22×D3—41no—
674C22×D3—41no—
675C22×D3—41no—
676C22×D3—41no—
677C3×D4—416no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
690C2×C3×C4—22no—
691C2×C3×C4—22no—
692C2×C3×C4—22no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—41no—
712C2×C3×C4—41no—
713#67—416no—
714#67—416no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—22no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—22no—
726C2×Dic3—22no—
727C2×Dic3—22no—
728C2×Dic3—22no—
729C2×Dic3—22no—
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3—41no—
740C2×Dic3—41no—
741C2×Dic3—41no—
742C2×Dic3—41no—
743C2×Dic3—41no—
744C2×Dic3—41no—
745C2×Dic3—41no—
746C2×Dic3—41no—
747C2×Dic3—41no—
748C2×Dic3—41no—
749C2×Dic3—41no—
750C2×Dic3—41no—
751C2×Dic3—41no—
752C2×Dic3—41no—
753C2×Dic3—41no—
754C2×Dic3—41no—
755C2×Dic3—41no—
756C2×Dic3—41no—
757C2×Dic3—416no—
758C2×Dic3#12014yes—
759C2×Dic3#12014yes—
760C2×Dic3#12014yes—
761C2×Dic3#12114yes—
762C2×Dic3#12114yes—
763C2×Dic3#12114yes—
764C2×Dic3#12714yes—
765Dic6—416no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—32no—
793C24—61no—
794C24—61no—
795C24—61no—
796C24—61no—
797C24—61no—
798C24—61no—
799C24—61no—
800C24—61no—
801C24—61no—
802C24—61no—
803C24—61no—
804C24—61no—
805C24—61no—
806C24—61no—
807C24#23512yes—
808C24D3×D412yes—
809C24D3×D412yes—
810C24#23712yes—
811C24C23×D311yescharacteristic
812C2×Q8—68no—
813C2×Q8—68no—
814C2×Q8—68no—
815C2×Q8—124no—
816C2×Q8—124no—
817C2×Q8—124no—
818C2×Q8—124no—
819C2×D4—28no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—68no—
827C2×D4—68no—
828C2×D4—68no—
829C2×D4—68no—
830C2×D4—124no—
831C2×D4—124no—
832C2×D4—124no—
833C2×D4—124no—
834C2×D4—124no—
835C2×D4—124no—
836C2×D4—124no—
837C2×D4—124no—
838C2×D4—124no—
839C2×D4—124no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—32no—
871C22×C4—32no—
872C22×C4—32no—
873C22×C4—32no—
874C22×C4—32no—
875C22×C4—32no—
876C22×C4—32no—
877C22×C4—32no—
878C22×C4—32no—
879C22×C4—32no—
880C22×C4—32no—
881C22×C4—32no—
882C22×C4—32no—
883C22×C4—68no—
884C22×C4—68no—
885C22×C4—68no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—61no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4—61no—
900C22×C4—61no—
901C22×C4—61no—
902C22×C4—61no—
903C22×C4—61no—
904C22×C4—61no—
905C22×C4—61no—
906C22×C4—61no—
907C22×C4—61no—
908C22×C4—61no—
909C22×C4—61no—
910C22×C4—61no—
911C22×C4—61no—
912C22×C4—61no—
913C22×C4—61no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4—61no—
917C22×C4—61no—
918C22×C4—61no—
919C22×C4—61no—
920C22×C4—61no—
921C22×C4—61no—
922C22×C4—124no—
923C22×C4—124no—
924C22×C4—124no—
925C22×C4—124no—
926C22×C4D3×D412yes—
927C22×C4D3×D412yes—
928C22×C4D3×D412yes—
929C22×C4D3×D412yes—
930C22×C4#23712yes—
931C4⋊C4—68no—
932C4⋊C4—68no—
933C4⋊C4—68no—
934C4⋊C4—68no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—44no—
939C22⋊C4—68no—
940C22⋊C4—68no—
941C22⋊C4—68no—
942C22⋊C4—68no—
943C22⋊C4—68no—
944C22⋊C4—68no—
945C22⋊C4—68no—
946C22⋊C4—124no—
947C22⋊C4—124no—
948C22⋊C4—124no—
949C42—68no—
950C42—124no—
951C22×C3—24no—
952C22×C3—24no—
953C22×C3—24no—
954C22×C3—42no—
955C22×C3—42no—
956C22×C3—42no—
957C22×C3—42no—
958C22×C3—42no—
959C22×C3—42no—
960C22×C3—42no—
961C22×C3—42no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—42no—
965C22×C3—42no—
966C22×C3—42no—
967C22×C3—42no—
968C22×C3—42no—
969C22×C3—42no—
970C22×C3—42no—
971C22×C3—42no—
972C22×C3—42no—
973C22×C3—81no—
974C22×C3—81no—
975C22×C3—81no—
976C22×C3—81no—
977C22×C3—81no—
978C22×C3—81no—
979C22×C3—81no—
980C22×C3—81no—
981C22×C3C2×#12011yescharacteristic
982C22×C3C2×#12011yescharacteristic
983C22×C3C2×#12011yescharacteristic
984C22×C3C2×#12111yescharacteristic
985C22×C3C2×#12111yescharacteristic
986C22×C3C2×#12111yescharacteristic
987C22×C3#52511yescharacteristic
988C22×C3#52511yescharacteristic
989C22×C3C2×#12411yescharacteristic
990C22×C3#52911yescharacteristic
991C22×C3#52911yescharacteristic
992C22×C3C2×#12711yescharacteristic
993C22×C3#53211yescharacteristic
994C22×C3#53511yescharacteristic
995C22×C3#53611yescharacteristic
996C22×C3#53711yescharacteristic
997C22×C3#53711yescharacteristic
998C22×C3#54211yescharacteristic
999C22×C3#54211yescharacteristic
1000C22×C3#54611yescharacteristic
1001C22×C3#54611yescharacteristic
1002C22×C3#54611yescharacteristic
1003C22×C3#54611yescharacteristic
1004C22×C3#54611yescharacteristic
1005C22×C3#54611yescharacteristic
1006C22×C3#54711yescharacteristic
1007C22×C3#54711yescharacteristic
1008C22×C3#54811yescharacteristic
1009C22×C3#54811yescharacteristic
1010C22×C3#54811yescharacteristic
1011C22×C3#54811yescharacteristic
1012C22×C3#54811yescharacteristic
1013C22×C3#54811yescharacteristic
1014C22×C3#55011yescharacteristic
1015C22×C3#55011yescharacteristic
1016C2×D3—42no—
1017C2×D3—42no—
1018C2×D3—42no—
1019C2×D3—42no—
1020C2×D3—42no—
1021C2×D3—42no—
1022C2×D3—42no—
1023C2×D3—81no—
1024C2×D3—81no—
1025C2×D3—81no—
1026C2×D3—81no—
1027C2×D3—81no—
1028C2×D3—81no—
1029C2×D3—81no—
1030C2×D3—81no—
1031C3×C4—42no—
1032C3×C4—42no—
1033C3×C4—42no—
1034C3×C4—42no—
1035C3×C4—42no—
1036Dic3—42no—
1037Dic3—42no—
1038Dic3—42no—
1039Dic3—42no—
1040Dic3—42no—
1041Dic3—42no—
1042Dic3#39218yes—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—62no—
1113C23—62no—
1114C23—62no—
1115C23—62no—
1116C23—62no—
1117C23—62no—
1118C23—62no—
1119C23—121no—
1120C23—121no—
1121C23—121no—
1122C23—121no—
1123C23—121no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23—121no—
1128C23—121no—
1129C23—121no—
1130C23—121no—
1131C23—121no—
1132C23—121no—
1133C23—121no—
1134C23—121no—
1135C23—121no—
1136C23—121no—
1137C23—121no—
1138C23—121no—
1139C23—121no—
1140C23—121no—
1141C23—121no—
1142C23—121no—
1143C23—121no—
1144C23—121no—
1145C23—121no—
1146C23—121no—
1147C23#88514yescomplemented
1148C23C2×#23511yescharacteristic
1149C23C2×D3×D411yescharacteristic
1150C23C2×D3×D411yescharacteristic
1151C23C2×D3×D411yescharacteristic
1152C23C2×D3×D411yescharacteristic
1153C23C2×D3×D411yescharacteristic
1154C23C2×D3×D411yescharacteristic
1155C23C2×#23711yescharacteristic
1156C23C2×#23711yescharacteristic
1157C23#100411yescharacteristic
1158C23#100411yescharacteristic
1159C23D3×#4111yescharacteristic
1160C23D3×#4111yescharacteristic
1161C23#101011yescharacteristic
1162C23#101011yescharacteristic
1163Q8—1216no—
1164D4—416no—
1165D4—1216no—
1166D4—1216no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—34no—
1183C2×C4—34no—
1184C2×C4—34no—
1185C2×C4—34no—
1186C2×C4—34no—
1187C2×C4—34no—
1188C2×C4—34no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—62no—
1210C2×C4—62no—
1211C2×C4—62no—
1212C2×C4—62no—
1213C2×C4—62no—
1214C2×C4—62no—
1215C2×C4—62no—
1216C2×C4—62no—
1217C2×C4—62no—
1218C2×C4—62no—
1219C2×C4—62no—
1220C2×C4—62no—
1221C2×C4—62no—
1222C2×C4—62no—
1223C2×C4—62no—
1224C2×C4—62no—
1225C2×C4—62no—
1226C2×C4—62no—
1227C2×C4—1216no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4—121no—
1232C2×C4—121no—
1233C2×C4—121no—
1234C2×C4—121no—
1235C2×C4—121no—
1236C2×C4—121no—
1237C2×C4—121no—
1238C2×C4—121no—
1239C2×C4—121no—
1240C2×C4—121no—
1241C2×C4—121no—
1242C2×C4—121no—
1243C2×C4—121no—
1244C2×C4—121no—
1245C2×C4—121no—
1246C2×C4—121no—
1247C2×C4—121no—
1248C2×C4—121no—
1249C2×C4—121no—
1250C2×C4—121no—
1251C2×C4—121no—
1252C2×C3—44no—
1253C2×C3—82no—
1254C2×C3C2×#39211yescharacteristic
1255C2×C3#240711yescharacteristic
1256C2×C3#240711yescharacteristic
1257C2×C3#242611yescharacteristic
1258C2×C3#242611yescharacteristic
1259C2×C3#242711yescharacteristic
1260C2×C3#242711yescharacteristic
1261C2×C3#243111yescharacteristic
1262C2×C3#243211yescharacteristic
1263C2×C3#243511yescharacteristic
1264C2×C3#243611yescharacteristic
1265C2×C3#254011yescharacteristic
1266C2×C3#254011yescharacteristic
1267C2×C3#262011yescharacteristic
1268C2×C3#285011yescharacteristic
1269D3—82no—
1270C22—24no—
1271C22—24no—
1272C22—24no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—122no—
1301C22—122no—
1302C22—122no—
1303C22—122no—
1304C22—122no—
1305C22—122no—
1306C22—122no—
1307C22—241no—
1308C22—241no—
1309C22—241no—
1310C22—241no—
1311C22—241no—
1312C22—241no—
1313C22—241no—
1314C22—241no—
1315C22#549011yescharacteristic
1316C22#549011yescharacteristic
1317C22C2×#88511yescharacteristic
1318C22#553811yescharacteristic
1319C22#554711yescharacteristic
1320C22#555211yescharacteristic
1321C22#555211yescharacteristic
1322C22#558611yescharacteristic
1323C22D3×#12011yescharacteristic
1324C22D3×#12011yescharacteristic
1325C22D3×#12011yescharacteristic
1326C22#559111yescharacteristic
1327C22#559111yescharacteristic
1328C22#559111yescharacteristic
1329C22#559211yescharacteristic
1330C22#559611yescharacteristic
1331C22#559711yescharacteristic
1332C22#559811yescharacteristic
1333C22#559811yescharacteristic
1334C22#559811yescharacteristic
1335C22#559911yescharacteristic
1336C22D3×#12111yescharacteristic
1337C22D3×#12111yescharacteristic
1338C22D3×#12111yescharacteristic
1339C22#560811yescharacteristic
1340C22#561011yescharacteristic
1341C22#561111yescharacteristic
1342C22#564811yescharacteristic
1343C22#564911yescharacteristic
1344C22#565511yescharacteristic
1345C22#566211yescharacteristic
1346C22#566911yescharacteristic
1347C22#567711yescharacteristic
1348C22D3×#12711yescharacteristic
1349C22#571811yescharacteristic
1350C4—38no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—122no—
1357C4—122no—
1358C4—122no—
1359C4—122no—
1360C4—122no—
1361C4—122no—
1362C3#1521511yescharacteristic, complemented, Sylow
1363C2—44no—
1364C2—82no—
1365C2—242no—
1366C2#7382711yescharacteristic
1367C2#7468811yescharacteristic
1368C2#7469711yescharacteristic
1369C2#7470111yescharacteristic
1370C2#7486911yescharacteristic
1371C2#7631211yescharacteristic
1372C2#7634711yescharacteristic
1373C2#7666811yescharacteristic
1374C2#7667211yescharacteristic
1375C2#7668711yescharacteristic
1376C2D3×#39211yescharacteristic
1377C2#7690111yescharacteristic
1378C2#7690211yescharacteristic
1379C2#7690411yescharacteristic
1380C2#7697211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC22×#939C2
hypercenter#1438D3
hypocenterC3#15215
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C22×#885C2semidirect
3. C22×#878C2semidirect
4. C2×#4957C2semidirect
5. C2×Dic3×C22⋊C4C2semidirect
6. C2×#4646C2semidirect
7. C3×#1438C2semidirect
8. #72131C2semidirect
9. #71550C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
12. #71546C2semidirect
13. #69428C2semidirect
14. #69427C2semidirect
15. Dic3⋊#95C2semidirect
77. #1438D3semidirect
128. C22×Dic6D4semidirect
183. C2×Dic3⋊C4D4semidirect
189. C2×C4×Dic3D4semidirect
626. C23×C3#124semidirect
1147. C23#885semidirect
1362. C3#15215semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C22×#8852
C22×#8782
C2×#49572
C2×Dic3×C22⋊C42
C2×#46462
C3×#14382
#721312
#715502
#715472
#715462
#694282
#694272
Dic3⋊#952
#152153