Finite Group Databasebeta

← #10726610

Subgroups — #10726610

Order 768.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#935C211yesmaximal, characteristic, complemented
2C22×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#392C211yesmaximal, characteristic
4C2×#5222C211yesmaximal, characteristic, complemented
5C2×#5220C211yesmaximal, characteristic, complemented
6C2×#4946C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic, complemented
8#72131C211yesmaximal, characteristic, complemented
9#71549C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71546C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#71544C211yesmaximal, characteristic, complemented
14#69420C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14721—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C2×#935—24no—
36C2×#935—24no—
37C2×#935—24no—
38C2×D4×Dic3—24no—
39C2×D4×Dic3—24no—
40C2×D4×Dic3—24no—
41C22×C4⋊Dic3C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×C4×Dic3C2211yescharacteristic
46C3×#392—24no—
47C2×C3×#95C2211yescharacteristic
48#5222—24no—
49#5220—24no—
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#4946—24no—
62C22×#123—31no—
63C22×C4×D4—31no—
64C2×#394—31no—
65C2×#392D311yescharacteristic
66C2×#386—31no—
67C2×#385—31no—
68#1444—31no—
69#1440—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1438—31no—
74#1437—31no—
75#1436—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C25×C3C2311yescharacteristic
79C25×C3C2311yescharacteristic
80C22×C3×D4—22no—
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—22no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C22×C3×D4—41no—
100C22×C3×D4D414yes—
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×Dic3—22no—
106C23×Dic3—22no—
107C23×Dic3—22no—
108C23×Dic3—22no—
109C23×Dic3—22no—
110C23×Dic3—22no—
111C23×Dic3—22no—
112C23×Dic3—22no—
113C23×Dic3—22no—
114C23×Dic3—41no—
115C23×Dic3—41no—
116C23×Dic3—41no—
117C23×Dic3—41no—
118C23×Dic3D414yescomplemented
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—41no—
135C2×C3×C22⋊C4—41no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
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—22no—
156C2×#217—22no—
157C2×#217—22no—
158C2×#217—22no—
159C2×#217—22no—
160C2×#217—41no—
161C2×#217—41no—
162C2×#217—41no—
163C2×#217—41no—
164C2×#217D414yescomplemented
165C2×#217D414yescomplemented
166#935—232no—
167D4×Dic3—232no—
168C2×C4⋊Dic3—22no—
169C2×C4⋊Dic3—22no—
170C2×C4⋊Dic3—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—22no—
178C2×Dic3⋊C4—41no—
179C2×Dic3⋊C4D414yescomplemented
180C2×C4×Dic3—22no—
181C2×C4×Dic3—22no—
182C2×C4×Dic3—22no—
183C3×#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—41no—
193C3⋊#95—41no—
194C3⋊#95—41no—
195C23×D4C2×D311yescharacteristic
196C23×D4C2×D311yescharacteristic
197C23×D4C2×D311yescharacteristic
198C24×C4—31no—
199C24×C4—31no—
200C2×#123—64no—
201C2×#123—64no—
202C2×#123—64no—
203C2×C4×D4—64no—
204C2×C4×D4—64no—
205C2×C4×D4—64no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4C2×D311yescharacteristic
221C22×C22⋊C4C2×D311yescharacteristic
222C22×C22⋊C4C2×D311yescharacteristic
223C22×C42—31no—
224#394—64no—
225#392—24no—
226#386—64no—
227#385—64no—
228C2×#95—31no—
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×#95—31no—
239C2×#95C2×D311yescharacteristic
240C24×C3—21no—
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×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×C3C2×D412yes—
279C24×C3C2×D412yes—
280C24×C3C2×D412yes—
281C24×C3C2×D412yes—
282C24×C3C2×D412yes—
283C24×C3#4112yes—
284C24×C3#4112yes—
285C24×C3C2411yescharacteristic
286C2×C3×D4—28no—
287C2×C3×D4—28no—
288C2×C3×D4—28no—
289C2×C3×D4—28no—
290C2×C3×D4—28no—
291C2×C3×D4—28no—
292C2×C3×D4—28no—
293C2×C3×D4—28no—
294C2×C3×D4—28no—
295C2×C3×D4—44no—
296C2×C3×D4—44no—
297C2×C3×D4—44no—
298C2×C3×D4—44no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—44no—
302C2×C3×D4—44no—
303C2×C3×D4—44no—
304C2×C3×D4—44no—
305C2×C3×D4—44no—
306C2×C3×D4—44no—
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×C4C2×D412yes—
331C22×C3×C4C2×D412yes—
332C22×C3×C4#4112yes—
333C22×C3×C4#4112yes—
334C22×C3×C4#4112yes—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—28no—
340C22×Dic3—28no—
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—21no—
350C22×Dic3—21no—
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—28no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3—44no—
386C22×Dic3—44no—
387C22×Dic3—44no—
388C22×Dic3—44no—
389C22×Dic3—44no—
390C22×Dic3—44no—
391C22×Dic3—44no—
392C22×Dic3—44no—
393C22×Dic3—44no—
394C22×Dic3—44no—
395C22×Dic3—44no—
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×Dic3#4112yes—
405C3×C22⋊C4—44no—
406C3×C22⋊C4—44no—
407C3×C22⋊C4—44no—
408#217—28no—
409#217—28no—
410#217—28no—
411#217—28no—
412#217—28no—
413#217—28no—
414#217—44no—
415#217—44no—
416#217—44no—
417#217—44no—
418C4⋊Dic3—28no—
419Dic3⋊C4—28no—
420Dic3⋊C4—28no—
421Dic3⋊C4—44no—
422C4×Dic3—28no—
423C25C22×D311yescharacteristic
424C25C22×D311yescharacteristic
425C25C22×D311yescharacteristic
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—41no—
443C22×D4—41no—
444C22×D4—41no—
445C22×D4—41no—
446C22×D4#6714yes—
447C23×C4—31no—
448C23×C4—31no—
449C23×C4—31no—
450C23×C4—31no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4—34no—
455C23×C4—31no—
456C23×C4—62no—
457C23×C4—62no—
458C23×C4—62no—
459C23×C4—62no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4—62no—
464C23×C4—62no—
465C23×C4—121no—
466C23×C4—121no—
467C23×C4—121no—
468C23×C4—121no—
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C23×C4C22×D311yescharacteristic
473#123—632no—
474C4×D4—632no—
475C2×C4⋊C4—34no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—62no—
478C2×C4⋊C4—62no—
479C2×C4⋊C4—62no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4—62no—
485C2×C4⋊C4—62no—
486C2×C4⋊C4—121no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—34no—
495C2×C22⋊C4—34no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—41no—
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—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
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—121no—
523C2×C22⋊C4—121no—
524C2×C22⋊C4—121no—
525C2×C22⋊C4—121no—
526C2×C42—62no—
527C2×C42—62no—
528C2×C42—62no—
529#95—22no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—62no—
537#95—62no—
538#95—121no—
539#95—121no—
540#95—121no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
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—22no—
583C23×C3—22no—
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—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#12014yes—
645C23×C3#12314yescomplemented
646C23×C3C22×D411yescharacteristic
647C23×C3C22×D411yescharacteristic
648C23×C3C22×D411yescharacteristic
649C23×C3C22×D411yescharacteristic
650C23×C3C22×D411yescharacteristic
651C23×C3C2×#4111yescharacteristic
652C23×C3C2×#4111yescharacteristic
653C23×C3C2×#4111yescharacteristic
654C23×C3C2×#4111yescharacteristic
655C23×C3C2×#4111yescharacteristic
656C23×C3C2×#4111yescharacteristic
657C23×C3H(5,𝔽2)11yescharacteristic
658C23×C3H(5,𝔽2)11yescharacteristic
659C23×C3H(5,𝔽2)11yescharacteristic
660C23×C32−1+411yescharacteristic
661C3×D4—232no—
662C3×D4—416no—
663C3×D4—416no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4#12314yescomplemented
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—416no—
717C2×Dic3—416no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
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#12014yes—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
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—
788C24D3×D412yes—
789C24D3×D412yes—
790C24D3×D412yes—
791C24#23712yes—
792C24#23712yes—
793C24C2×#6712yes—
794C24C2×#6712yes—
795C24C23×D311yescharacteristic
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—32no—
841C22×C4—32no—
842C22×C4—32no—
843C22×C4—32no—
844C22×C4—32no—
845C22×C4—32no—
846C22×C4—32no—
847C22×C4—32no—
848C22×C4—32no—
849C22×C4—68no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—68no—
855C22×C4—68no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
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—124no—
900C22×C4—124no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4—124no—
907C22×C4—124no—
908C22×C4—124no—
909C22×C4—124no—
910C22×C4D3×D412yes—
911C22×C4#23712yes—
912C22×C4#23712yes—
913C22×C4#23712yes—
914C22×C4C2×#6712yes—
915C4⋊C4—68no—
916C4⋊C4—68no—
917C4⋊C4—68no—
918C4⋊C4—124no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—68no—
923C22⋊C4—68no—
924C22⋊C4—68no—
925C22⋊C4—68no—
926C22⋊C4—68no—
927C22⋊C4—68no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C22⋊C4—124no—
931C22⋊C4—124no—
932C42—68no—
933C22×C3—24no—
934C22×C3—24no—
935C22×C3—24no—
936C22×C3—24no—
937C22×C3—24no—
938C22×C3—24no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—42no—
944C22×C3—42no—
945C22×C3—42no—
946C22×C3—42no—
947C22×C3—42no—
948C22×C3—42no—
949C22×C3—42no—
950C22×C3—42no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—42no—
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—81no—
971C22×C3—81no—
972C22×C3—81no—
973C22×C3—81no—
974C22×C3—81no—
975C22×C3—81no—
976C22×C3—81no—
977C22×C3—81no—
978C22×C3C2×#12011yescharacteristic
979C22×C3C2×#12011yescharacteristic
980C22×C3C2×#12311yescharacteristic
981C22×C3C2×#12311yescharacteristic
982C22×C3#52511yescharacteristic
983C22×C3#52511yescharacteristic
984C22×C3#52511yescharacteristic
985C22×C3#52511yescharacteristic
986C22×C3#52511yescharacteristic
987C22×C3#52511yescharacteristic
988C22×C3#53211yescharacteristic
989C22×C3#53211yescharacteristic
990C22×C3#53211yescharacteristic
991C22×C3#53411yescharacteristic
992C22×C3#53711yescharacteristic
993C22×C3#53811yescharacteristic
994C22×C3#53911yescharacteristic
995C22×C3#54011yescharacteristic
996C22×C3#54211yescharacteristic
997C22×C3D4211yescharacteristic
998C22×C3D4211yescharacteristic
999C22×C3D4211yescharacteristic
1000C22×C3D4211yescharacteristic
1001C22×C3#54611yescharacteristic
1002C22×C3#54611yescharacteristic
1003C22×C3#54611yescharacteristic
1004C22×C3#54711yescharacteristic
1005C22×C3#54711yescharacteristic
1006C22×C3#54711yescharacteristic
1007C22×C3#54811yescharacteristic
1008C22×C3#55011yescharacteristic
1009C22×C3#55111yescharacteristic
1010C22×C3#55311yescharacteristic
1011C22×C3#55311yescharacteristic
1012C22×C3#55911yescharacteristic
1013C3×C4—24no—
1014C3×C4—42no—
1015C3×C4—42no—
1016C3×C4—81no—
1017Dic3—24no—
1018Dic3—42no—
1019Dic3—42no—
1020Dic3—42no—
1021Dic3—42no—
1022Dic3—42no—
1023Dic3—42no—
1024Dic3—81no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
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—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#93514yescomplemented
1129C23#93714yes—
1130C23C2×D3×D411yescharacteristic
1131C23C2×D3×D411yescharacteristic
1132C23C2×D3×D411yescharacteristic
1133C23C2×D3×D411yescharacteristic
1134C23C2×#23711yescharacteristic
1135C23C2×#23711yescharacteristic
1136C23C2×#23711yescharacteristic
1137C23C2×#23711yescharacteristic
1138C23C2×#23711yescharacteristic
1139C23#100411yescharacteristic
1140C23#100411yescharacteristic
1141C23#100411yescharacteristic
1142C23D3×#4111yescharacteristic
1143C23#101011yescharacteristic
1144C23C22×#6711yescharacteristic
1145D4—232no—
1146D4—416no—
1147D4—416no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—34no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—62no—
1191C2×C4—62no—
1192C2×C4—62no—
1193C2×C4—62no—
1194C2×C4—62no—
1195C2×C4—62no—
1196C2×C4—62no—
1197C2×C4—62no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—1216no—
1201C2×C4—1216no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C4—121no—
1227C2×C4—121no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4—121no—
1232C2×C4—121no—
1233C2×C4#93514yescomplemented
1234C2×C3—44no—
1235C2×C3—44no—
1236C2×C3—82no—
1237C2×C3#238811yescharacteristic
1238C2×C3#240311yescharacteristic
1239C2×C3#240711yescharacteristic
1240C2×C3#241811yescharacteristic
1241C2×C3#242211yescharacteristic
1242C2×C3#243011yescharacteristic
1243C2×C3#244311yescharacteristic
1244C2×C3#244511yescharacteristic
1245C2×C3#245511yescharacteristic
1246C2×C3#245611yescharacteristic
1247C2×C3#246111yescharacteristic
1248C2×C3#246411yescharacteristic
1249C2×C3#260211yescharacteristic
1250C2×C3#263011yescharacteristic
1251C2×C3#284911yescharacteristic
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
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—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22#558611yescharacteristic
1298C22#558611yescharacteristic
1299C22#558611yescharacteristic
1300C22#558611yescharacteristic
1301C22#558611yescharacteristic
1302C22#558711yescharacteristic
1303C22D3×#12011yescharacteristic
1304C22#558911yescharacteristic
1305C22#559011yescharacteristic
1306C22#559011yescharacteristic
1307C22#559111yescharacteristic
1308C22#559311yescharacteristic
1309C22#559611yescharacteristic
1310C22#559611yescharacteristic
1311C22#559711yescharacteristic
1312C22#559811yescharacteristic
1313C22#560111yescharacteristic
1314C22#560211yescharacteristic
1315C22#560311yescharacteristic
1316C22#560611yescharacteristic
1317C22#561011yescharacteristic
1318C22#561111yescharacteristic
1319C22#561111yescharacteristic
1320C22#561411yescharacteristic
1321C22#571311yescharacteristic
1322C22#571611yescharacteristic
1323C22#571811yescharacteristic
1324C22#571911yescharacteristic
1325C22C2×#93511yescharacteristic
1326C22C2×#93511yescharacteristic
1327C22C2×#93711yescharacteristic
1328C22D4×#6711yescharacteristic
1329C22D4×#6711yescharacteristic
1330C22#580611yescharacteristic
1331C22#582411yescharacteristic
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—64no—
1336C4—81no—
1337C4—122no—
1338C4—122no—
1339C4—122no—
1340C4—122no—
1341C4—122no—
1342C4—122no—
1343C4—241no—
1344C3#1472111yescharacteristic, complemented, Sylow
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2#7666511yescharacteristic
1349C2#7666811yescharacteristic
1350C2#7667411yescharacteristic
1351C2#7667611yescharacteristic
1352C2#7668011yescharacteristic
1353C2#7668211yescharacteristic
1354C2#7669411yescharacteristic
1355C2#7669911yescharacteristic
1356C2#8258511yescharacteristic
1357C2#8260211yescharacteristic
1358C2#8260411yescharacteristic
1359C2#8264411yescharacteristic
1360C2#8265111yescharacteristic
1361C2#8265511yescharacteristic
1362C2#8317611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC2×C3×#392C2
hypercenterC2×#392D3
hypocenterC3#14721
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#935C2semidirect
2. C22×D4×Dic3C2semidirect
4. C2×#5222C2semidirect
5. C2×#5220C2semidirect
6. C2×#4946C2semidirect
7. #72131C2semidirect
8. #72131C2semidirect
9. #71549C2semidirect
10. #71547C2semidirect
11. #71546C2semidirect
12. #71545C2semidirect
13. #71544C2semidirect
14. #69420C2semidirect
15. #69406C2semidirect
118. C23×Dic3D4semidirect
164. C2×#217D4semidirect
165. C2×#217D4semidirect
179. C2×Dic3⋊C4D4semidirect
645. C23×C3#123semidirect
691. C2×C3×C4#123semidirect
1128. C23#935semidirect
1233. C2×C4#935semidirect
1344. C3#14721semidirect

Maximal subgroups

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

subgroupindex
C22×#9352
C22×D4×Dic32
C2×C3×#3922
C2×#52222
C2×#52202
C2×#49462
#721312
#715492
#715472
#715462
#715452
#715442
#694202
#694062
#147213