Finite Group Databasebeta

← #10729224

Subgroups — #10729224

Order 768.

1506 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#889C211yesmaximal, characteristic
2C2×C3×#389C211yesmaximal, characteristic
3C2×#4976C211yesmaximal, characteristic
4C2×#4978C211yesmaximal, characteristic
5#71568C211yesmaximal, characteristic
6#71568C211yesmaximal, characteristic
7#71568C211yesmaximal, characteristic
8#71565C211yesmaximal, characteristic
9#71564C211yesmaximal, characteristic
10#71536C211yesmaximal, characteristic
11C4×C3⋊#95C211yesmaximal, characteristic
12#69420C211yesmaximal, characteristic
13#69414C211yesmaximal, characteristic
14#69414C211yesmaximal, characteristic
15#69409C211yesmaximal, characteristic
16#14929—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C2×#889—24no—
33C2×#889—24no—
34C2×#889—24no—
35C3×#389—24no—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
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#4978—24no—
57#4976—24no—
58C22×#125—31no—
59C2×#389—31no—
60C2×#389D311yescharacteristic
61C2×#387—31no—
62#1444—31no—
63#1444—31no—
64#1444—31no—
65#1444—31no—
66#1442—31no—
67#1442—31no—
68#1441—31no—
69#1441—31no—
70#1436—31no—
71#1436—31no—
72C4×#95—31no—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—41no—
99C2×C3×C4⋊C4D414yes—
100C2×C3×C42—22no—
101C2×C3×C42—22no—
102C2×C3×C42—41no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—22no—
106C2×Dic3⋊C4—22no—
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—22no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—41no—
126C2×Dic3⋊C4D414yes—
127C2×C4×Dic3—22no—
128C2×C4×Dic3—22no—
129C2×C4×Dic3—22no—
130C2×C4×Dic3—22no—
131C2×C4×Dic3—41no—
132C2×C4×Dic3D414yes—
133#889—232no—
134C3×#95—22no—
135C3×#95—22no—
136C3⋊#95—22no—
137C3⋊#95—22no—
138C3⋊#95—22no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—22no—
144C3⋊#95—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95Q814yes—
153C3⋊#95Q814yes—
154C2×#125—64no—
155C2×#125—64no—
156C2×#125—64no—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4—31no—
160C22×C4⋊C4—31no—
161C22×C4⋊C4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4C2×D311yescharacteristic
166C22×C4⋊C4C2×D311yescharacteristic
167C22×C4⋊C4C2×D311yescharacteristic
168C22×C4⋊C4C2×D311yescharacteristic
169C22×C42—31no—
170C22×C42—31no—
171C22×C42C2×D311yescharacteristic
172#389—24no—
173#389—64no—
174#387—64no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95C2×D311yescharacteristic
194C2×#95C2×D311yescharacteristic
195C24×C3C2411yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×D412yes—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×Q812yes—
241C22×C3×C4C2×Q812yes—
242C22×C3×C4#4112yes—
243C22×C3×C4#4112yes—
244C22×C3×C4#4112yes—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3C2×D412yes—
291C22×Dic3C2×D412yes—
292C22×Dic3C2×D412yes—
293C22×Dic3C2×D412yes—
294C22×Dic3C2×Q812yes—
295C22×Dic3C2×Q812yes—
296C22×Dic3C2×Q812yes—
297C22×Dic3C2×Q812yes—
298C22×Dic3#4112yes—
299C22×Dic3#4112yes—
300C22×Dic3#4112yes—
301C3×C4⋊C4—28no—
302C3×C4⋊C4—28no—
303C3×C4⋊C4—44no—
304C3×C4⋊C4—44no—
305C3×C42—44no—
306C4⋊Dic3—28no—
307Dic3⋊C4—28no—
308Dic3⋊C4—28no—
309Dic3⋊C4—28no—
310Dic3⋊C4—28no—
311Dic3⋊C4—28no—
312Dic3⋊C4—28no—
313Dic3⋊C4—44no—
314C4×Dic3—28no—
315C4×Dic3—44no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4C22×D311yescharacteristic
325C23×C4C22×D311yescharacteristic
326C23×C4C22×D311yescharacteristic
327C23×C4C22×D311yescharacteristic
328C23×C4C22×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331#125—632no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—34no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—62no—
346C2×C4⋊C4—62no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—62no—
349C2×C4⋊C4—62no—
350C2×C4⋊C4—62no—
351C2×C4⋊C4—62no—
352C2×C4⋊C4—62no—
353C2×C4⋊C4—62no—
354C2×C4⋊C4—62no—
355C2×C4⋊C4—62no—
356C2×C4⋊C4—62no—
357C2×C4⋊C4—62no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—62no—
363C2×C4⋊C4—62no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—121no—
367C2×C4⋊C4#6714yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—34no—
371C2×C42—41no—
372C2×C42—62no—
373C2×C42—62no—
374C2×C42—62no—
375C2×C42—62no—
376C2×C42—121no—
377#95—22no—
378#95—22no—
379#95—34no—
380#95—34no—
381#95—62no—
382#95—62no—
383#95—62no—
384#95—62no—
385#95—62no—
386#95—62no—
387#95—62no—
388#95—62no—
389#95—62no—
390#95—62no—
391#95—62no—
392#95—62no—
393#95—62no—
394#95—62no—
395#95—121no—
396#95—121no—
397C23×C3C22×D411yescharacteristic
398C23×C3C22×D411yescharacteristic
399C23×C3C22×D411yescharacteristic
400C23×C3C22×Q811yescharacteristic
401C23×C3C22×Q811yescharacteristic
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3C2×#4111yescharacteristic
406C23×C3C2×#4111yescharacteristic
407C23×C3C2×#4111yescharacteristic
408C23×C3H(5,𝔽2)11yescharacteristic
409C23×C32−1+411yescharacteristic
410C23×C32−1+411yescharacteristic
411C23×C32−1+411yescharacteristic
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4#12014yes—
460C2×C3×C4#12514yescomplemented
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3#12514yescomplemented
516C2×Dic3C4⋊Q814yes—
517C24C23×D311yescharacteristic
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—32no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4#23512yes—
614C22×C4#23512yes—
615C22×C4D3×D412yes—
616C22×C4D3×D412yes—
617C22×C4#23712yes—
618C22×C4D3×Q812yes—
619C22×C4D3×Q812yes—
620C22×C4C2×#6712yes—
621C22×C4C2×#6712yes—
622C22×C4C2×#6712yes—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—68no—
628C4⋊C4—68no—
629C4⋊C4—68no—
630C4⋊C4—68no—
631C4⋊C4—68no—
632C4⋊C4—68no—
633C4⋊C4—68no—
634C4⋊C4—124no—
635C42—44no—
636C42—68no—
637C42—124no—
638C22×C3C2×#12011yescharacteristic
639C22×C3#52511yescharacteristic
640C22×C3#52511yescharacteristic
641C22×C3#52511yescharacteristic
642C22×C3C2×#12511yescharacteristic
643C22×C3C2×#12511yescharacteristic
644C22×C3C2×C4⋊Q811yescharacteristic
645C22×C3#53211yescharacteristic
646C22×C3#53211yescharacteristic
647C22×C3#53211yescharacteristic
648C22×C3#53211yescharacteristic
649C22×C3#53311yescharacteristic
650C22×C3#53311yescharacteristic
651C22×C3#53611yescharacteristic
652C22×C3#53711yescharacteristic
653C22×C3#53911yescharacteristic
654C22×C3#53911yescharacteristic
655C22×C3#54111yescharacteristic
656C22×C3#54111yescharacteristic
657C22×C3#54611yescharacteristic
658C22×C3#54611yescharacteristic
659C22×C3#54711yescharacteristic
660C22×C3#54711yescharacteristic
661C22×C3D4×Q811yescharacteristic
662C22×C3D4×Q811yescharacteristic
663C22×C3D4×Q811yescharacteristic
664C22×C3D4×Q811yescharacteristic
665C22×C3#55211yescharacteristic
666C22×C3#55211yescharacteristic
667C22×C3#55211yescharacteristic
668C22×C3#55211yescharacteristic
669C22×C3#55411yescharacteristic
670C22×C3#55411yescharacteristic
671C22×C3#55711yescharacteristic
672C22×C3#55711yescharacteristic
673C3×C4—24no—
674C3×C4—24no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—81no—
680Dic3—24no—
681Dic3—24no—
682Dic3—42no—
683Dic3—42no—
684Dic3—42no—
685Dic3—42no—
686Dic3—42no—
687Dic3—81no—
688C23C2×#23511yescharacteristic
689C23C2×#23511yescharacteristic
690C23C2×D3×D411yescharacteristic
691C23C2×D3×D411yescharacteristic
692C23C2×#23711yescharacteristic
693C23#100411yescharacteristic
694C23C2×D3×Q811yescharacteristic
695C23C2×D3×Q811yescharacteristic
696C23#100711yescharacteristic
697C23#100711yescharacteristic
698C23D3×#4111yescharacteristic
699C23D3×#4111yescharacteristic
700C23D3×#4111yescharacteristic
701C23#101011yescharacteristic
702C23C22×#6711yescharacteristic
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—34no—
728C2×C4—34no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—121no—
802C2×C4—121no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4#88914yescomplemented
807C2×C4#93714yes—
808C2×C3#238811yescharacteristic
809C2×C3#243011yescharacteristic
810C2×C3#243411yescharacteristic
811C2×C3#246211yescharacteristic
812C2×C3#246211yescharacteristic
813C2×C3#247311yescharacteristic
814C2×C3#247311yescharacteristic
815C2×C3#250611yescharacteristic
816C2×C3#250611yescharacteristic
817C2×C3#255611yescharacteristic
818C2×C3#255611yescharacteristic
819C2×C3#258411yescharacteristic
820C2×C3#261111yescharacteristic
821C2×C3#266411yescharacteristic
822C2×C3#285911yescharacteristic
823C22C2×#88911yescharacteristic
824C22#551111yescharacteristic
825C22#551311yescharacteristic
826C22#551511yescharacteristic
827C22#554711yescharacteristic
828C22#554711yescharacteristic
829C22#554811yescharacteristic
830C22#554811yescharacteristic
831C22#556711yescharacteristic
832C22#557811yescharacteristic
833C22#558111yescharacteristic
834C22#558311yescharacteristic
835C22#559611yescharacteristic
836C22#559711yescharacteristic
837C22#561011yescharacteristic
838C22#561111yescharacteristic
839C22#562211yescharacteristic
840C22#563611yescharacteristic
841C22#563811yescharacteristic
842C22#563911yescharacteristic
843C22#568511yescharacteristic
844C22D3×#12511yescharacteristic
845C22#569311yescharacteristic
846C22#569611yescharacteristic
847C22D3×C4⋊Q811yescharacteristic
848C22#572411yescharacteristic
849C22#572711yescharacteristic
850C22#572711yescharacteristic
851C22#579111yescharacteristic
852C22C2×#93711yescharacteristic
853C22#580611yescharacteristic
854C22Q8×#6711yescharacteristic
855C22Q8×#6711yescharacteristic
856C22#582411yescharacteristic
857C22#583211yescharacteristic
858C4—24no—
859C4—24no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—64no—
865C4—64no—
866C4—81no—
867C4—122no—
868C4—122no—
869C4—122no—
870C4—122no—
871C4—122no—
872C4—241no—
873C3#1492911yescharacteristic, complemented, Sylow
874C2#7601711yescharacteristic
875C2#7602311yescharacteristic
876C2#7602911yescharacteristic
877C2#7606711yescharacteristic
878C2#7608011yescharacteristic
879C2#7610011yescharacteristic
880C2#7610811yescharacteristic
881C2#7619011yescharacteristic
882C2#8217411yescharacteristic
883C2#8240011yescharacteristic
884C2#8247211yescharacteristic
885C2#8265111yescharacteristic
886C2#8278211yescharacteristic
887C2#8303411yescharacteristic
888C2#8323211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC2×C3×#389C2
hypercenterC2×#389D3
hypocenterC3#14929
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
460. C2×C3×C4#125semidirect
515. C2×Dic3#125semidirect
806. C2×C4#889semidirect
873. C3#14929semidirect

Maximal subgroups

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

subgroupindex
C22×#8892
C2×C3×#3892
C2×#49762
C2×#49782
#715682
#715652
#715642
#715362
C4×C3⋊#952
#694202
#694142
#694092
#149293