Finite Group Databasebeta

← #10729232

Subgroups — #10729232

Order 768.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#879C211yesmaximal, characteristic, complemented
2C2×#5221C211yesmaximal, characteristic
3C2×#4945C211yesmaximal, characteristic, complemented
4C2×#4951C211yesmaximal, characteristic, complemented
5C3×#1438C211yesmaximal, characteristic
6#72131C211yesmaximal, characteristic
7#71549C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71545C211yesmaximal, characteristic, complemented
12#69420C211yesmaximal, characteristic, complemented
13#69411C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14930—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×#879—24no—
39C2×#879—24no—
40C2×#879—24no—
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43#5221—24no—
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4951—24no—
57#4945—24no—
58C22×#126—31no—
59C2×#390—31no—
60C2×#388—31no—
61C2×#388—31no—
62#1444—31no—
63#1441—31no—
64#1440—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69#1438D311yescharacteristic
70#1437—31no—
71#1436—31no—
72C4×#95—31no—
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—41no—
104C2×C3×C22⋊C4—41no—
105C2×C3×C22⋊C4—41no—
106C2×C3×C22⋊C4—41no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—41no—
127C2×#217—41no—
128C2×#217—41no—
129C2×#217—41no—
130C2×#217D414yes—
131C2×C4⋊Dic3—22no—
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—41no—
136C2×C4⋊Dic3D414yescomplemented
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—41no—
145C2×Dic3⋊C4—41no—
146C2×C4×Dic3—22no—
147C2×C4×Dic3—22no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—41no—
153C2×C4×Dic3—41no—
154C2×C4×Dic3D414yescomplemented
155#879—232no—
156C3×#95—22no—
157C3×#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—41no—
168C3⋊#95—41no—
169C3⋊#95—41no—
170C23×D4C2×D311yescharacteristic
171C2×#126—64no—
172C2×#126—64no—
173C2×#126—64no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4C2×D311yescharacteristic
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C22⋊C4C2×D311yescharacteristic
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C42—31no—
192C22×C42—31no—
193C22×C42—31no—
194#390—64no—
195#388—64no—
196#388—64no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3C2×D412yes—
240C24×C3#4112yes—
241C24×C3C2411yescharacteristic
242C2×C3×D4—28no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C2×C3×D4—44no—
247C2×C3×D4—44no—
248C2×C3×D4—44no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
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×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4#4112yes—
281C22×C3×C4#4112yes—
282C22×C3×C4#4112yes—
283C22×C3×C4#4112yes—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
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×Dic3C2×D412yes—
332C22×Dic3C2×D412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3#4112yes—
338C22×Dic3#4112yes—
339C22×Dic3#4112yes—
340C3×C22⋊C4—28no—
341C3×C22⋊C4—28no—
342C3×C22⋊C4—44no—
343C3×C22⋊C4—44no—
344#217—28no—
345#217—28no—
346#217—28no—
347#217—44no—
348#217—44no—
349#217—44no—
350#217—44no—
351#217—44no—
352C4⋊Dic3—28no—
353C4⋊Dic3—44no—
354Dic3⋊C4—28no—
355Dic3⋊C4—28no—
356Dic3⋊C4—44no—
357C4×Dic3—28no—
358C4×Dic3—44no—
359C4×Dic3—44no—
360C25C22×D311yescharacteristic
361C25C22×D311yescharacteristic
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—41no—
368C22×D4—41no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382#126—632no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—121no—
396C2×C4⋊C4—121no—
397C2×C4⋊C4—121no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—121no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C42—34no—
435C2×C42—62no—
436C2×C42—62no—
437C2×C42—62no—
438C2×C42—62no—
439C2×C42—62no—
440C2×C42—62no—
441C2×C42—121no—
442C2×C42—121no—
443#95—22no—
444#95—22no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—121no—
455#95—121no—
456#95—121no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3C22×D411yescharacteristic
528C23×C3C22×D411yescharacteristic
529C23×C3C22×D411yescharacteristic
530C23×C3C2×#4111yescharacteristic
531C23×C3C2×#4111yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3C2×#4111yescharacteristic
534C23×C3C2×#4111yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3H(5,𝔽2)11yescharacteristic
539C23×C3H(5,𝔽2)11yescharacteristic
540C23×C3H(5,𝔽2)11yescharacteristic
541C23×C32−1+411yescharacteristic
542C3×D4—416no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4#12614yescomplemented
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3#12014yes—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24D3×D412yes—
663C24#23712yes—
664C24C23×D311yescharacteristic
665C2×D4—28no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—32no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4#23512yes—
758C22×C4D3×D412yes—
759C22×C4D3×D412yes—
760C22×C4#23712yes—
761C22×C4#23712yes—
762C22×C4#23712yes—
763C4⋊C4—68no—
764C4⋊C4—68no—
765C4⋊C4—68no—
766C4⋊C4—124no—
767C4⋊C4—124no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—68no—
773C22⋊C4—68no—
774C22⋊C4—68no—
775C22⋊C4—124no—
776C22⋊C4—124no—
777C22⋊C4—124no—
778C22⋊C4—124no—
779C22⋊C4—124no—
780C42—68no—
781C42—124no—
782C42—124no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3—81no—
805C22×C3—81no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3—81no—
811C22×C3—81no—
812C22×C3—81no—
813C22×C3C2×#12011yescharacteristic
814C22×C3#52511yescharacteristic
815C22×C3#52511yescharacteristic
816C22×C3#52511yescharacteristic
817C22×C3C2×#12611yescharacteristic
818C22×C3#52911yescharacteristic
819C22×C3#52911yescharacteristic
820C22×C3#52911yescharacteristic
821C22×C3#53211yescharacteristic
822C22×C3#53211yescharacteristic
823C22×C3#53211yescharacteristic
824C22×C3#53211yescharacteristic
825C22×C3#53211yescharacteristic
826C22×C3#53511yescharacteristic
827C22×C3#53711yescharacteristic
828C22×C3#53811yescharacteristic
829C22×C3#53811yescharacteristic
830C22×C3#54211yescharacteristic
831C22×C3#54211yescharacteristic
832C22×C3#54611yescharacteristic
833C22×C3#54611yescharacteristic
834C22×C3#54611yescharacteristic
835C22×C3#54611yescharacteristic
836C22×C3#54711yescharacteristic
837C22×C3#54711yescharacteristic
838C22×C3#55011yescharacteristic
839C22×C3#55011yescharacteristic
840C22×C3#55111yescharacteristic
841C22×C3#55111yescharacteristic
842C22×C3#55111yescharacteristic
843C22×C3#55211yescharacteristic
844C22×C3#55311yescharacteristic
845C22×C3#55311yescharacteristic
846C22×C3#55311yescharacteristic
847C22×C3#55611yescharacteristic
848C3×C4—24no—
849C3×C4—42no—
850C3×C4—42no—
851C3×C4—42no—
852C3×C4—81no—
853Dic3—24no—
854Dic3—42no—
855Dic3—42no—
856Dic3—42no—
857Dic3—42no—
858Dic3—42no—
859Dic3—42no—
860Dic3—81no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23C2×#23511yescharacteristic
932C23C2×D3×D411yescharacteristic
933C23C2×D3×D411yescharacteristic
934C23C2×D3×D411yescharacteristic
935C23C2×#23711yescharacteristic
936C23C2×#23711yescharacteristic
937C23C2×#23711yescharacteristic
938C23C2×#23711yescharacteristic
939C23#100411yescharacteristic
940C23#100411yescharacteristic
941C23#100411yescharacteristic
942C23D3×#4111yescharacteristic
943C23D3×#4111yescharacteristic
944C23D3×#4111yescharacteristic
945C23#101011yescharacteristic
946D4—416no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—34no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4#87914yescomplemented
1038C2×C3—82no—
1039C2×C3—82no—
1040C2×C3#238811yescharacteristic
1041C2×C3#243011yescharacteristic
1042C2×C3#243111yescharacteristic
1043C2×C3#246711yescharacteristic
1044C2×C3#246811yescharacteristic
1045C2×C3#247911yescharacteristic
1046C2×C3#248011yescharacteristic
1047C2×C3#251211yescharacteristic
1048C2×C3#252111yescharacteristic
1049C2×C3#255411yescharacteristic
1050C2×C3#255911yescharacteristic
1051C2×C3#260111yescharacteristic
1052C2×C3#260311yescharacteristic
1053C2×C3#266211yescharacteristic
1054C2×C3#286011yescharacteristic
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22C2×#87911yescharacteristic
1086C22#549011yescharacteristic
1087C22#549511yescharacteristic
1088C22#554811yescharacteristic
1089C22#555111yescharacteristic
1090C22#555711yescharacteristic
1091C22#555811yescharacteristic
1092C22#558611yescharacteristic
1093C22#558611yescharacteristic
1094C22#558711yescharacteristic
1095C22D3×#12011yescharacteristic
1096C22#559111yescharacteristic
1097C22#559211yescharacteristic
1098C22#559311yescharacteristic
1099C22#559311yescharacteristic
1100C22#559611yescharacteristic
1101C22#559611yescharacteristic
1102C22#559611yescharacteristic
1103C22#559911yescharacteristic
1104C22#560011yescharacteristic
1105C22#560111yescharacteristic
1106C22#560311yescharacteristic
1107C22#560311yescharacteristic
1108C22#560611yescharacteristic
1109C22#560811yescharacteristic
1110C22#561011yescharacteristic
1111C22#561211yescharacteristic
1112C22#565011yescharacteristic
1113C22#565511yescharacteristic
1114C22#565911yescharacteristic
1115C22#566111yescharacteristic
1116C22#567111yescharacteristic
1117C22#568011yescharacteristic
1118C22#571611yescharacteristic
1119C22#571811yescharacteristic
1120C4—24no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—64no—
1125C4—81no—
1126C4—122no—
1127C4—122no—
1128C4—122no—
1129C4—122no—
1130C4—122no—
1131C4—122no—
1132C4—241no—
1133C3#1493011yescharacteristic, complemented, Sylow
1134C2—82no—
1135C2—82no—
1136C2#7383111yescharacteristic
1137C2#7473411yescharacteristic
1138C2#7476111yescharacteristic
1139C2#7477811yescharacteristic
1140C2#7489611yescharacteristic
1141C2#7633911yescharacteristic
1142C2#7642511yescharacteristic
1143C2#7666511yescharacteristic
1144C2#7667211yescharacteristic
1145C2#7668411yescharacteristic
1146C2#7670911yescharacteristic
1147C2#7692311yescharacteristic
1148C2#7694011yescharacteristic
1149C2#7694811yescharacteristic
1150C2#7696411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC23×C3×D4C22
hypercenter#1438D3
hypocenterC3#14930
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#879C2semidirect
3. C2×#4945C2semidirect
4. C2×#4951C2semidirect
7. #71549C2semidirect
8. #71547C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #71545C2semidirect
12. #69420C2semidirect
13. #69411C2semidirect
14. #69407C2semidirect
15. Dic3×#95C2semidirect
136. C2×C4⋊Dic3D4semidirect
154. C2×C4×Dic3D4semidirect
577. C2×C3×C4#126semidirect
1037. C2×C4#879semidirect
1133. C3#14930semidirect

Maximal subgroups

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

subgroupindex
C22×#8792
C2×#52212
C2×#49452
C2×#49512
C3×#14382
#721312
#715492
#715472
#715452
#694202
#694112
#694072
Dic3×#952
#149303