Finite Group Databasebeta

← #10718643

Subgroups — #10718643

Order 768.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C22×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×#5220C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C2×#5220C211yesmaximal, characteristic, complemented
6C2×#5220C211yesmaximal, characteristic, complemented
7C22×C3⋊#95C211yesmaximal, characteristic, complemented
8#72131C211yesmaximal, characteristic, complemented
9#72127C211yesmaximal, characteristic, complemented
10#71565C211yesmaximal, characteristic, complemented
11#71564C211yesmaximal, characteristic, complemented
12#71548C211yesmaximal, characteristic, complemented
13#71546C211yesmaximal, characteristic, complemented
14#71545C211yesmaximal, characteristic, complemented
15#71544C211yesmaximal, characteristic, complemented
16#14023—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C24×Dic3C2211yescharacteristic
23C24×Dic3C2211yescharacteristic
24C2×C3×#121—24no—
25C2×C3×#121—24no—
26C2×C3×#121C418yescomplemented
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C2×D4×Dic3—24no—
40C2×D4×Dic3—24no—
41C2×D4×Dic3—24no—
42C22×C4⋊Dic3C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44#5220—24no—
45#5220—24no—
46#5220—24no—
47#5220—24no—
48C2×C3⋊#95—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
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63C22×#121D311yescharacteristic
64C22×C4×D4—31no—
65C2×#386—31no—
66C2×#386—31no—
67C2×#386—31no—
68C2×#386—31no—
69C22×#95—31no—
70#1441—31no—
71#1440—31no—
72#1439—31no—
73#1438—31no—
74#1437—31no—
75#1436—31no—
76C22⋊#95—31no—
77C22⋊#95—31no—
78C25×C3C2311yescharacteristic
79C25×C3C2311yescharacteristic
80C25×C3C2311yescharacteristic
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—22no—
88C22×C3×D4—22no—
89C22×C3×D4—22no—
90C22×C3×D4—22no—
91C22×C3×D4—22no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—22no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4C2×C414yes—
98C22×C3×D4C2×C414yescomplemented
99C22×C3×D4C2×C414yescomplemented
100C22×C3×D4D414yes—
101C22×C3×D4D414yes—
102C23×C3×C4—22no—
103C23×C3×C4—22no—
104C23×C3×C4—22no—
105C23×C3×C4—22no—
106C23×C3×C4—41no—
107C23×C3×C4—41no—
108C23×C3×C4C2×C414yescomplemented
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×Dic3—22no—
114C23×Dic3—22no—
115C23×Dic3—22no—
116C23×Dic3—22no—
117C23×Dic3—22no—
118C23×Dic3—22no—
119C23×Dic3—22no—
120C23×Dic3—22no—
121C23×Dic3—22no—
122C23×Dic3—22no—
123C23×Dic3—22no—
124C23×Dic3—22no—
125C23×Dic3—22no—
126C23×Dic3—22no—
127C23×Dic3—41no—
128C23×Dic3—41no—
129C23×Dic3—41no—
130C23×Dic3—41no—
131C23×Dic3—41no—
132C23×Dic3—41no—
133C23×Dic3D414yescomplemented
134C23×Dic3C2311yescharacteristic
135C23×Dic3C2311yescharacteristic
136C23×Dic3C2311yescharacteristic
137C23×Dic3C2311yescharacteristic
138C23×Dic3C2311yescharacteristic
139C23×Dic3C2311yescharacteristic
140C23×Dic3C2311yescharacteristic
141C23×Dic3C2311yescharacteristic
142C3×#121—232no—
143C2×C3×C4⋊C4—22no—
144C2×C3×C4⋊C4—22no—
145C2×C3×C4⋊C4C2×C414yescomplemented
146C2×C3×C22⋊C4—22no—
147C2×C3×C22⋊C4—22no—
148C2×C3×C22⋊C4—22no—
149C2×C3×C22⋊C4—22no—
150C2×C3×C22⋊C4C2×C414yescomplemented
151C2×C3×C22⋊C4C2×C414yescomplemented
152C2×#217—22no—
153C2×#217—22no—
154C2×#217—22no—
155C2×#217—22no—
156C2×#217—22no—
157C2×#217—22no—
158C2×#217—22no—
159C2×#217—22no—
160C2×#217—22no—
161C2×#217—22no—
162C2×#217—22no—
163C2×#217—22no—
164C2×#217—22no—
165C2×#217—22no—
166C2×#217—22no—
167C2×#217—22no—
168C2×#217—22no—
169C2×#217—22no—
170C2×#217—22no—
171C2×#217—22no—
172C2×#217—41no—
173C2×#217—41no—
174C2×#217—41no—
175C2×#217—41no—
176C2×#217—41no—
177C2×#217—41no—
178C2×#217D414yescomplemented
179D4×Dic3—232no—
180C2×C4⋊Dic3—22no—
181C2×C4⋊Dic3—22no—
182C2×C4⋊Dic3—22no—
183C2×C4×Dic3—22no—
184C2×C4×Dic3—22no—
185C2×C4×Dic3—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—22no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—41no—
198C3⋊#95—41no—
199C3⋊#95D414yescomplemented
200C23×D4C2×D311yescharacteristic
201C23×D4C2×D311yescharacteristic
202C23×D4C2×D311yescharacteristic
203C24×C4—31no—
204C24×C4—31no—
205C24×C4—31no—
206C24×C4C2×D311yescharacteristic
207C2×#121—24no—
208C2×#121—24no—
209C2×#121Dic318yescomplemented
210C2×C4×D4—64no—
211C2×C4×D4—64no—
212C2×C4×D4—64no—
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⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D311yescharacteristic
226C22×C42—31no—
227#386—64no—
228#386—64no—
229#386—64no—
230#386—64no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95—31no—
243C2×#95—31no—
244C2×#95—31no—
245C2×#95—64no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
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×C3—21no—
276C24×C3—21no—
277C24×C3—21no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3C22×C412yes—
281C24×C3C22×C412yes—
282C24×C3C22×C412yes—
283C24×C3C2×D412yes—
284C24×C3C2×D412yes—
285C24×C3C2×D412yes—
286C24×C3C2×D412yes—
287C24×C3C2×D412yes—
288C24×C3C2×D412yes—
289C24×C3#4112yes—
290C24×C3#4112yes—
291C24×C3C2411yescharacteristic
292C2×C3×D4—28no—
293C2×C3×D4—28no—
294C2×C3×D4—28no—
295C2×C3×D4—28no—
296C2×C3×D4—28no—
297C2×C3×D4—28no—
298C2×C3×D4—28no—
299C2×C3×D4—28no—
300C2×C3×D4—28no—
301C2×C3×D4—28no—
302C2×C3×D4—28no—
303C2×C3×D4—44no—
304C2×C3×D4—44no—
305C2×C3×D4—44no—
306C2×C3×D4—44no—
307C2×C3×D4—44no—
308C2×C3×D4—44no—
309C2×C3×D4—44no—
310C2×C3×D4—44no—
311C2×C3×D4—44no—
312C2×C3×D4C22⋊C4116yescomplemented
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—28no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—28no—
335C22×C3×C4—44no—
336C22×C3×C4—44no—
337C22×C3×C4—44no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4C22×C412yes—
341C22×C3×C4C22×C412yes—
342C22×C3×C4C22×C412yes—
343C22×C3×C4C22×C412yes—
344C22×C3×C4C2×D412yes—
345C22×C3×C4C2×D412yes—
346C22×C3×C4C2×D412yes—
347C22×C3×C4#4112yes—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—28no—
353C22×Dic3—28no—
354C22×Dic3—28no—
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—28no—
386C22×Dic3—21no—
387C22×Dic3—21no—
388C22×Dic3—21no—
389C22×Dic3—21no—
390C22×Dic3—21no—
391C22×Dic3—21no—
392C22×Dic3—21no—
393C22×Dic3—21no—
394C22×Dic3—21no—
395C22×Dic3—21no—
396C22×Dic3—21no—
397C22×Dic3—21no—
398C22×Dic3—21no—
399C22×Dic3—21no—
400C22×Dic3—44no—
401C22×Dic3—44no—
402C22×Dic3—44no—
403C22×Dic3—44no—
404C22×Dic3—44no—
405C22×Dic3—44no—
406C22×Dic3—44no—
407C22×Dic3—44no—
408C22×Dic3—44no—
409C22×Dic3—44no—
410C22×Dic3—44no—
411C22×Dic3—44no—
412C22×Dic3—44no—
413C22×Dic3—44no—
414C22×Dic3—44no—
415C22×Dic3—44no—
416C22×Dic3—44no—
417C22×Dic3C2×D412yes—
418C22×Dic3C2×D412yes—
419C22×Dic3C2×D412yes—
420C22×Dic3C2×D412yes—
421C22×Dic3C2×D412yes—
422C22×Dic3C2×D412yes—
423C22×Dic3#4112yes—
424C22×Dic3#4112yes—
425C3×C4⋊C4—28no—
426C3×C22⋊C4—28no—
427C3×C22⋊C4—28no—
428#217—28no—
429#217—28no—
430#217—44no—
431#217—44no—
432#217—44no—
433#217—44no—
434#217—44no—
435#217—44no—
436#217—44no—
437C4⋊Dic3—28no—
438C4×Dic3—28no—
439C25C22×D311yescharacteristic
440C25C22×D311yescharacteristic
441C25C22×D311yescharacteristic
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—41no—
457C22×D4—41no—
458C22×D4C2×Dic314yes—
459C22×D4C2×Dic314yescomplemented
460C22×D4C2×Dic314yescomplemented
461C22×D4#6714yes—
462C22×D4#6714yes—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—31no—
468C23×C4—31no—
469C23×C4—31no—
470C23×C4—31no—
471C23×C4—31no—
472C23×C4—31no—
473C23×C4—34no—
474C23×C4—31no—
475C23×C4—31no—
476C23×C4—41no—
477C23×C4—41no—
478C23×C4—62no—
479C23×C4—62no—
480C23×C4—62no—
481C23×C4—62no—
482C23×C4—62no—
483C23×C4—62no—
484C23×C4—62no—
485C23×C4—62no—
486C23×C4—62no—
487C23×C4—62no—
488C23×C4—62no—
489C23×C4—62no—
490C23×C4—62no—
491C23×C4—62no—
492C23×C4—121no—
493C23×C4—121no—
494C23×C4—121no—
495C23×C4—121no—
496C23×C4—121no—
497C23×C4—121no—
498C23×C4C2×Dic314yescomplemented
499C23×C4C22×D311yescharacteristic
500C23×C4C22×D311yescharacteristic
501C23×C4C22×D311yescharacteristic
502C23×C4C22×D311yescharacteristic
503#121—232no—
504C4×D4—632no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—62no—
508C2×C4⋊C4—62no—
509C2×C4⋊C4—62no—
510C2×C4⋊C4C2×Dic314yescomplemented
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—34no—
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—121no—
537C2×C22⋊C4—121no—
538C2×C22⋊C4—121no—
539C2×C22⋊C4—121no—
540C2×C22⋊C4—121no—
541C2×C22⋊C4—121no—
542C2×C22⋊C4C2×Dic314yescomplemented
543C2×C22⋊C4C2×Dic314yescomplemented
544C2×C42—62no—
545C2×C42—62no—
546C2×C42—62no—
547#95—34no—
548#95—62no—
549#95—62no—
550#95—62no—
551#95—62no—
552#95—62no—
553#95—62no—
554#95—62no—
555#95—62no—
556#95—62no—
557#95—62no—
558#95—62no—
559#95—121no—
560#95—121no—
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—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
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—41no—
627C23×C3—41no—
628C23×C3—41no—
629C23×C3—41no—
630C23×C3—41no—
631C23×C3—41no—
632C23×C3—41no—
633C23×C3—41no—
634C23×C3—41no—
635C23×C3—41no—
636C23×C3—41no—
637C23×C3—41no—
638C23×C3—41no—
639C23×C3—41no—
640C23×C3—41no—
641C23×C3—41no—
642C23×C3—41no—
643C23×C3—41no—
644C23×C3—41no—
645C23×C3—41no—
646C23×C3—41no—
647C23×C3—41no—
648C23×C3—41no—
649C23×C3—41no—
650C23×C3—41no—
651C23×C3—41no—
652C23×C3—41no—
653C23×C3—41no—
654C23×C3—41no—
655C23×C3—41no—
656C23×C3—41no—
657C23×C3—41no—
658C23×C3C2×C22⋊C414yes—
659C23×C3C2×C22⋊C414yes—
660C23×C3C4×D414yes—
661C23×C3C4×D414yes—
662C23×C3#12014yes—
663C23×C3#12114yes—
664C23×C3#12114yes—
665C23×C3#12314yes—
666C23×C3C23×C411yescharacteristic
667C23×C3C22×D411yescharacteristic
668C23×C3C22×D411yescharacteristic
669C23×C3C22×D411yescharacteristic
670C23×C3C22×D411yescharacteristic
671C23×C3C22×D411yescharacteristic
672C23×C3C2×#4111yescharacteristic
673C23×C3C2×#4111yescharacteristic
674C23×C3C2×#4111yescharacteristic
675C23×C3C2×#4111yescharacteristic
676C23×C3C2×#4111yescharacteristic
677C23×C3H(5,𝔽2)11yescharacteristic
678C23×C3H(5,𝔽2)11yescharacteristic
679C23×C3H(5,𝔽2)11yescharacteristic
680C23×C32−1+411yescharacteristic
681C3×D4—232no—
682C3×D4—416no—
683C3×D4—416no—
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—22no—
694C2×C3×C4—22no—
695C2×C3×C4—22no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—22no—
699C2×C3×C4—22no—
700C2×C3×C4—22no—
701C2×C3×C4—22no—
702C2×C3×C4—416no—
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×C4C2×C22⋊C414yes—
712C2×C3×C4C4×D414yescomplemented
713C2×Dic3—22no—
714C2×Dic3—22no—
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—22no—
734C2×Dic3—416no—
735C2×Dic3—416no—
736C2×Dic3—416no—
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—41no—
758C2×Dic3—41no—
759C2×Dic3—41no—
760C2×Dic3—41no—
761C2×Dic3—41no—
762C2×Dic3—41no—
763C2×Dic3—41no—
764C2×Dic3—41no—
765C2×Dic3—41no—
766C2×Dic3—41no—
767C2×Dic3—41no—
768C2×Dic3—41no—
769C2×Dic3—41no—
770C2×Dic3—41no—
771C2×Dic3#12114yescomplemented
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—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24D3×D412yes—
807C24D3×D412yes—
808C24#23712yes—
809C24#23712yes—
810C24C22×Dic312yes—
811C24C22×Dic312yes—
812C24C22×Dic312yes—
813C24C2×#6712yes—
814C24C2×#6712yes—
815C24C2×#6712yes—
816C24C2×#6712yes—
817C24C23×D311yescharacteristic
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—28no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4#217116yescomplemented
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—28no—
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—28no—
861C22×C4—32no—
862C22×C4—32no—
863C22×C4—32no—
864C22×C4—32no—
865C22×C4—32no—
866C22×C4—32no—
867C22×C4—32no—
868C22×C4—32no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—68no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—68no—
880C22×C4—68no—
881C22×C4—68no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
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—61no—
923C22×C4—61no—
924C22×C4—61no—
925C22×C4—61no—
926C22×C4—124no—
927C22×C4—124no—
928C22×C4—124no—
929C22×C4—124no—
930C22×C4—124no—
931C22×C4—124no—
932C22×C4—124no—
933C22×C4—124no—
934C22×C4—124no—
935C22×C4—124no—
936C22×C4—124no—
937C22×C4—124no—
938C22×C4—124no—
939C22×C4—124no—
940C22×C4—124no—
941C22×C4—124no—
942C22×C4—124no—
943C22×C4D3×D412yes—
944C22×C4#23712yes—
945C22×C4C22×Dic312yes—
946C22×C4C22×Dic312yes—
947C22×C4C22×Dic312yes—
948C22×C4C22×Dic312yes—
949C22×C4C2×#6712yes—
950C22×C4C2×#6712yes—
951C4⋊C4—28no—
952C4⋊C4—68no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—68no—
956C22⋊C4—68no—
957C22⋊C4—124no—
958C22⋊C4—124no—
959C22⋊C4—124no—
960C22⋊C4—124no—
961C22⋊C4—124no—
962C22⋊C4—124no—
963C22⋊C4—124no—
964C42—68no—
965C22×C3—24no—
966C22×C3—24no—
967C22×C3—24no—
968C22×C3—24no—
969C22×C3—24no—
970C22×C3—24no—
971C22×C3—24no—
972C22×C3—24no—
973C22×C3—24no—
974C22×C3—24no—
975C22×C3—24no—
976C22×C3—24no—
977C22×C3—24no—
978C22×C3—24no—
979C22×C3—24no—
980C22×C3—24no—
981C22×C3—24no—
982C22×C3—42no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—42no—
987C22×C3—42no—
988C22×C3—42no—
989C22×C3—42no—
990C22×C3—42no—
991C22×C3—42no—
992C22×C3—42no—
993C22×C3—42no—
994C22×C3—42no—
995C22×C3—42no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—81no—
1002C22×C3—81no—
1003C22×C3—81no—
1004C22×C3—81no—
1005C22×C3—81no—
1006C22×C3—81no—
1007C22×C3—81no—
1008C22×C3—81no—
1009C22×C3#38618yescomplemented
1010C22×C3C22×C22⋊C411yescharacteristic
1011C22×C3C2×C4×D411yescharacteristic
1012C22×C3C2×C4×D411yescharacteristic
1013C22×C3C2×C4×D411yescharacteristic
1014C22×C3C4×#4111yescharacteristic
1015C22×C3#51811yescharacteristic
1016C22×C3#52011yescharacteristic
1017C22×C3C2×#12011yescharacteristic
1018C22×C3C2×#12111yescharacteristic
1019C22×C3C2×#12111yescharacteristic
1020C22×C3C2×#12111yescharacteristic
1021C22×C3C2×#12311yescharacteristic
1022C22×C3#52511yescharacteristic
1023C22×C3#52911yescharacteristic
1024C22×C3#53211yescharacteristic
1025C22×C3#53411yescharacteristic
1026C22×C3#53711yescharacteristic
1027C22×C3#53811yescharacteristic
1028C22×C3#53911yescharacteristic
1029C22×C3D4211yescharacteristic
1030C22×C3D4211yescharacteristic
1031C22×C3D4211yescharacteristic
1032C22×C3#54611yescharacteristic
1033C22×C3#54611yescharacteristic
1034C22×C3#54611yescharacteristic
1035C22×C3#54611yescharacteristic
1036C22×C3#54611yescharacteristic
1037C22×C3#54611yescharacteristic
1038C22×C3#54711yescharacteristic
1039C22×C3#54711yescharacteristic
1040C22×C3#54711yescharacteristic
1041C22×C3#54811yescharacteristic
1042C22×C3#55311yescharacteristic
1043C22×C3#55311yescharacteristic
1044C22×C3#55311yescharacteristic
1045C3×C4—24no—
1046C3×C4—24no—
1047C3×C4—42no—
1048C3×C4—42no—
1049Dic3—24no—
1050Dic3—42no—
1051Dic3—42no—
1052Dic3—42no—
1053Dic3—42no—
1054Dic3—42no—
1055Dic3—81no—
1056Dic3—81no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23D4×Dic314yes—
1155C23D4×Dic314yes—
1156C23#93514yes—
1157C23#93714yes—
1158C23#93914yes—
1159C23#93914yes—
1160C23C2×#21714yes—
1161C23C2×#21714yes—
1162C23C2×D3×D411yescharacteristic
1163C23C2×D3×D411yescharacteristic
1164C23C2×D3×D411yescharacteristic
1165C23C2×#23711yescharacteristic
1166C23C2×#23711yescharacteristic
1167C23C2×#23711yescharacteristic
1168C23#100411yescharacteristic
1169C23#100411yescharacteristic
1170C23D3×#4111yescharacteristic
1171C23D3×#4111yescharacteristic
1172C23#100911yescharacteristic
1173C23#101011yescharacteristic
1174C23C23×Dic311yescharacteristic
1175C23C22×#6711yescharacteristic
1176C23C22×#6711yescharacteristic
1177D4—232no—
1178D4—416no—
1179D4—416no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—34no—
1199C2×C4—416no—
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—62no—
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—62no—
1228C2×C4—62no—
1229C2×C4—1216no—
1230C2×C4—1216no—
1231C2×C4—1216no—
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×C4—121no—
1253C2×C4—121no—
1254C2×C4—121no—
1255C2×C4—121no—
1256C2×C4—121no—
1257C2×C4—121no—
1258C2×C4—121no—
1259C2×C4—121no—
1260C2×C4—121no—
1261C2×C4—121no—
1262C2×C4—121no—
1263C2×C4—121no—
1264C2×C4—121no—
1265C2×C4—121no—
1266C2×C4D4×Dic314yescomplemented
1267C2×C4C2×#21714yes—
1268C2×C3—28no—
1269C2×C3—44no—
1270C2×C3—82no—
1271C2×C3C2×#38611yescharacteristic
1272C2×C3C4×#12111yescharacteristic
1273C2×C3#232511yescharacteristic
1274C2×C3D4×C22⋊C411yescharacteristic
1275C2×C3#233911yescharacteristic
1276C2×C3#236111yescharacteristic
1277C2×C3#236411yescharacteristic
1278C2×C3#241011yescharacteristic
1279C2×C3#241611yescharacteristic
1280C2×C3#242411yescharacteristic
1281C2×C3#242511yescharacteristic
1282C2×C3#243011yescharacteristic
1283C2×C3#244311yescharacteristic
1284C2×C3#244411yescharacteristic
1285C2×C3#254311yescharacteristic
1286C22—24no—
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22#522018yescomplemented
1331C22#559611yescharacteristic
1332C22#559711yescharacteristic
1333C22#559811yescharacteristic
1334C22#560011yescharacteristic
1335C22#560111yescharacteristic
1336C22#560111yescharacteristic
1337C22#560211yescharacteristic
1338C22D3×#12111yescharacteristic
1339C22#560511yescharacteristic
1340C22#560611yescharacteristic
1341C22#560911yescharacteristic
1342C22#561011yescharacteristic
1343C22#561011yescharacteristic
1344C22#561111yescharacteristic
1345C22#561711yescharacteristic
1346C22#561811yescharacteristic
1347C22C2×D4×Dic311yescharacteristic
1348C22C2×D4×Dic311yescharacteristic
1349C22C2×D4×Dic311yescharacteristic
1350C22C2×#93511yescharacteristic
1351C22#579811yescharacteristic
1352C22C2×#93711yescharacteristic
1353C22D4×#6711yescharacteristic
1354C22D4×#6711yescharacteristic
1355C22C2×#93911yescharacteristic
1356C22C2×#93911yescharacteristic
1357C22#580611yescharacteristic
1358C22#580611yescharacteristic
1359C22#582411yescharacteristic
1360C22#582411yescharacteristic
1361C22Dic3×#4111yescharacteristic
1362C22#582711yescharacteristic
1363C22#582911yescharacteristic
1364C22#582911yescharacteristic
1365C22C22×#21711yescharacteristic
1366C4—24no—
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—64no—
1371C4—122no—
1372C4—122no—
1373C4—122no—
1374C4—122no—
1375C4—122no—
1376C4—241no—
1377C4—241no—
1378C3#1402311yescharacteristic, complemented, Sylow
1379C2—28no—
1380C2—44no—
1381C2—82no—
1382C2Dic3×#12111yescharacteristic
1383C2#8263411yescharacteristic
1384C2#8263611yescharacteristic
1385C2#8263811yescharacteristic
1386C2#8264211yescharacteristic
1387C2#8264511yescharacteristic
1388C2#8265111yescharacteristic
1389C2#8265511yescharacteristic
1390C2#8265611yescharacteristic
1391C2#8267011yescharacteristic
1392C2#8270211yescharacteristic
1393C2#8270611yescharacteristic
1394C2C2×#522011yescharacteristic
1395C2D4×#21711yescharacteristic
1396C2#8408811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
Fitting, prime radicalC22×C3×#121C2
socle, cosocleC24×C3C24
hypercenterC22×#121D3
hypocenterC3#14023
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic3C2semidirect
3. C2×#5220C2semidirect
4. C2×#5220C2semidirect
5. C2×#5220C2semidirect
6. C2×#5220C2semidirect
7. C22×C3⋊#95C2semidirect
8. #72131C2semidirect
9. #72127C2semidirect
10. #71565C2semidirect
11. #71564C2semidirect
12. #71548C2semidirect
13. #71546C2semidirect
14. #71545C2semidirect
15. #71544C2semidirect
26. C2×C3×#121C4semidirect
98. C22×C3×D4C2×C4semidirect
99. C22×C3×D4C2×C4semidirect
108. C23×C3×C4C2×C4semidirect
133. C23×Dic3D4semidirect
145. C2×C3×C4⋊C4C2×C4semidirect
150. C2×C3×C22⋊C4C2×C4semidirect
151. C2×C3×C22⋊C4C2×C4semidirect
178. C2×#217D4semidirect
199. C3⋊#95D4semidirect
209. C2×#121Dic3semidirect
312. C2×C3×D4C22⋊C4semidirect
459. C22×D4C2×Dic3semidirect
460. C22×D4C2×Dic3semidirect
498. C23×C4C2×Dic3semidirect
510. C2×C4⋊C4C2×Dic3semidirect
542. C2×C22⋊C4C2×Dic3semidirect
543. C2×C22⋊C4C2×Dic3semidirect
712. C2×C3×C4C4×D4semidirect
771. C2×Dic3#121semidirect
838. C2×D4#217semidirect
1009. C22×C3#386semidirect
1266. C2×C4D4×Dic3semidirect
1330. C22#5220semidirect
1378. C3#14023semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×D4×Dic32
C2×#52202
C22×C3⋊#952
#721312
#721272
#715652
#715642
#715482
#715462
#715452
#715442
#140233