Finite Group Databasebeta

← #10751746

Subgroups — #10751746

Order 768.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic
2C2×#4979C211yesmaximal, characteristic, complemented
3C2×#4946C211yesmaximal, characteristic
4C2×#4657C211yesmaximal, characteristic, complemented
5C3×#1439C211yesmaximal, characteristic
6#71568C211yesmaximal, characteristic, complemented
7#71547C211yesmaximal, characteristic
8#71547C211yesmaximal, characteristic
9#71546C211yesmaximal, characteristic
10#71544C211yesmaximal, characteristic
11#69424C211yesmaximal, characteristic, complemented
12#69421C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69410C211yesmaximal, characteristic, complemented
16#16606—31nomaximal, Sylow
17C24×Dic3C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×#878—24no—
35C2×#878—24no—
36C2×#878—24no—
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
55#4979—24no—
56#4946—24no—
57#4657—24no—
58C22×C22⋊Q8—31no—
59C2×#398—31no—
60C2×#395—31no—
61C2×#385—31no—
62#1446—31no—
63#1445—31no—
64#1444—31no—
65#1444—31no—
66#1441—31no—
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439D311yescharacteristic
72C22⋊#95—31no—
73C25×C3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3—22no—
81C23×Dic3—22no—
82C23×Dic3—41no—
83C23×Dic3—41no—
84C23×Dic3—41no—
85C23×Dic3—41no—
86C23×Dic3D414yes—
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C22×Dic6—22no—
96C22×Dic6—22no—
97C22×Dic6—41no—
98C22×Dic6—41no—
99C22×Dic6—41no—
100C22×Dic6—41no—
101C22×Dic6D414yes—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—41no—
104C2×C3×C4⋊C4—41no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—41no—
110C2×C3×C22⋊C4—41no—
111C2×C3×C22⋊C4—41no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4Q814yescomplemented
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—41no—
121C2×#217—41no—
122C2×#217Q814yescomplemented
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—22no—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—41no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—22no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—41no—
142C2×Dic3⋊C4—41no—
143C2×Dic3⋊C4—41no—
144C2×Dic3⋊C4—41no—
145C2×Dic3⋊C4—41no—
146C2×Dic3⋊C4D414yes—
147#878—232no—
148C3×#95—22no—
149C3×#95—41no—
150C3×#95—41no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C23×Q8—31no—
167C24×C4—31no—
168C2×C22⋊Q8—64no—
169C2×C22⋊Q8—64no—
170C2×C22⋊Q8—64no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4C2×D311yescharacteristic
184C22×C22⋊C4C2×D311yescharacteristic
185C22×C22⋊C4C2×D311yescharacteristic
186#398—64no—
187#395—64no—
188#385—64no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
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×C3C2×D412yes—
220C24×C3C2×Q812yes—
221C24×C3C2×Q812yes—
222C24×C3C2411yescharacteristic
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×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
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×C4C2×D412yes—
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×Q812yes—
264C22×C3×C4C2×Q812yes—
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×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—28no—
312C22×Dic3—44no—
313C22×Dic3—44no—
314C22×Dic3—44no—
315C22×Dic3—44no—
316C22×Dic3—44no—
317C22×Dic3—44no—
318C22×Dic3C2×D412yes—
319C22×Dic3C2×D412yes—
320C22×Dic3C2×D412yes—
321C22×Dic3C2×D412yes—
322C22×Dic3C2×D412yes—
323C22×Dic3C2×D412yes—
324C22×Dic3C2×Q812yes—
325C22×Dic3C2×Q812yes—
326C22×Dic3#4112yes—
327C22×Dic3#4112yes—
328C2×Dic6—28no—
329C2×Dic6—44no—
330C2×Dic6—44no—
331C2×Dic6—44no—
332C2×Dic6—44no—
333C2×Dic6—44no—
334C2×Dic6—44no—
335C3×C4⋊C4—44no—
336C3×C22⋊C4—28no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—44no—
339#217—28no—
340#217—28no—
341#217—44no—
342C4⋊Dic3—28no—
343C4⋊Dic3—44no—
344Dic3⋊C4—28no—
345Dic3⋊C4—28no—
346Dic3⋊C4—44no—
347Dic3⋊C4—44no—
348Dic3⋊C4—44no—
349Dic3⋊C4—44no—
350C25C22×D311yescharacteristic
351C22×Q8—34no—
352C22×Q8—62no—
353C22×Q8—62no—
354C22×Q8—121no—
355C22×Q8—121no—
356C22×Q8—121no—
357C22×Q8—121no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—34no—
367C23×C4—62no—
368C23×C4—62no—
369C23×C4—121no—
370C23×C4—121no—
371C23×C4—121no—
372C23×C4—121no—
373C23×C4C22×D311yescharacteristic
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C22⋊Q8—632no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—41no—
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—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—121no—
402C2×C4⋊C4—121no—
403C2×C4⋊C4—121no—
404C2×C4⋊C4—121no—
405C2×C4⋊C4—121no—
406C2×C4⋊C4—121no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—41no—
414C2×C22⋊C4—41no—
415C2×C22⋊C4—41no—
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—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4Dic614yescomplemented
425#95—22no—
426#95—41no—
427#95—41no—
428#95—62no—
429#95—62no—
430#95—62no—
431#95—62no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—121no—
438#95—121no—
439#95—121no—
440#95—121no—
441#95—121no—
442#95—121no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3C4⋊Q814yes—
478C23×C3C22×D411yescharacteristic
479C23×C3C22×D411yescharacteristic
480C23×C3C22×D411yescharacteristic
481C23×C3C22×Q811yescharacteristic
482C23×C3C22×Q811yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3H(5,𝔽2)11yescharacteristic
486C23×C3H(5,𝔽2)11yescharacteristic
487C23×C3H(5,𝔽2)11yescharacteristic
488C23×C3H(5,𝔽2)11yescharacteristic
489C23×C3H(5,𝔽2)11yescharacteristic
490C23×C32−1+411yescharacteristic
491C23×C32−1+411yescharacteristic
492C23×C32−1+411yescharacteristic
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—416no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3#12014yes—
592Dic6—416no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24C2×Dic612yes—
606C24D3×D412yes—
607C24D3×Q812yes—
608C24C23×D311yescharacteristic
609C2×Q8—68no—
610C2×Q8—124no—
611C2×Q8—124no—
612C2×Q8—124no—
613C2×Q8—124no—
614C2×Q8—124no—
615C2×Q8—124no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—32no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—32no—
663C22×C4—32no—
664C22×C4—68no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—124no—
712C22×C4—124no—
713C22×C4—124no—
714C22×C4—124no—
715C22×C4—124no—
716C22×C4—124no—
717C22×C4C2×Dic612yes—
718C22×C4C2×Dic612yes—
719C22×C4D3×D412yes—
720C22×C4D3×D412yes—
721C4⋊C4—44no—
722C4⋊C4—68no—
723C4⋊C4—68no—
724C4⋊C4—68no—
725C4⋊C4—124no—
726C4⋊C4—124no—
727C4⋊C4—124no—
728C4⋊C4—124no—
729C4⋊C4—124no—
730C22⋊C4—28no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—68no—
734C22⋊C4—68no—
735C22⋊C4—124no—
736C22×C3—24no—
737C22×C3—24no—
738C22×C3—24no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3C2×#12011yescharacteristic
752C22×C3#52511yescharacteristic
753C22×C3C2×C4⋊Q811yescharacteristic
754C22×C3#53411yescharacteristic
755C22×C3#53411yescharacteristic
756C22×C3#53411yescharacteristic
757C22×C3#53411yescharacteristic
758C22×C3#53511yescharacteristic
759C22×C3#53511yescharacteristic
760C22×C3#53611yescharacteristic
761C22×C3#53711yescharacteristic
762C22×C3#53911yescharacteristic
763C22×C3#53911yescharacteristic
764C22×C3#54211yescharacteristic
765C22×C3#54211yescharacteristic
766C22×C3#54311yescharacteristic
767C22×C3#54311yescharacteristic
768C22×C3#54411yescharacteristic
769C22×C3#54411yescharacteristic
770C22×C3#54611yescharacteristic
771C22×C3#54711yescharacteristic
772C22×C3#54811yescharacteristic
773C22×C3D4×Q811yescharacteristic
774C22×C3D4×Q811yescharacteristic
775C22×C3D4×Q811yescharacteristic
776C22×C3D4×Q811yescharacteristic
777C22×C3#55011yescharacteristic
778C22×C3#55411yescharacteristic
779C22×C3#55411yescharacteristic
780C22×C3#55411yescharacteristic
781C22×C3#55411yescharacteristic
782C22×C3#56211yescharacteristic
783C22×C3#56211yescharacteristic
784C22×C3#56311yescharacteristic
785C22×C3#56311yescharacteristic
786C3×C4—42no—
787C3×C4—42no—
788C3×C4—42no—
789C3×C4—42no—
790C3×C4—81no—
791C3×C4—81no—
792Dic3—24no—
793Dic3—42no—
794Dic3—42no—
795Dic3—42no—
796Dic3—42no—
797Dic3—42no—
798Dic3—42no—
799Dic3—42no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23#88814yes—
835C23C22×Dic611yescharacteristic
836C23C2×D3×D411yescharacteristic
837C23C2×D3×D411yescharacteristic
838C23C2×D3×D411yescharacteristic
839C23#100411yescharacteristic
840C23#100411yescharacteristic
841C23#100411yescharacteristic
842C23#100411yescharacteristic
843C23C2×D3×Q811yescharacteristic
844C23D3×#4111yescharacteristic
845C23D3×#4111yescharacteristic
846C23#100911yescharacteristic
847C23#101011yescharacteristic
848C23#101011yescharacteristic
849C23#101011yescharacteristic
850Q8—1216no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—34no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—1216no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4—121no—
946C2×C4—121no—
947C2×C4—121no—
948C2×C4—121no—
949C2×C4—121no—
950C2×C3—44no—
951C2×C3#240711yescharacteristic
952C2×C3#243411yescharacteristic
953C2×C3#258311yescharacteristic
954C2×C3#261311yescharacteristic
955C2×C3#263811yescharacteristic
956C2×C3#265911yescharacteristic
957C2×C3#269211yescharacteristic
958C2×C3#269211yescharacteristic
959C2×C3#272011yescharacteristic
960C2×C3#272011yescharacteristic
961C2×C3#272911yescharacteristic
962C2×C3#272911yescharacteristic
963C2×C3#273211yescharacteristic
964C2×C3#273211yescharacteristic
965C2×C3#281411yescharacteristic
966C22—24no—
967C22—24no—
968C22—24no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22#548311yescharacteristic
982C22C2×#88811yescharacteristic
983C22#551911yescharacteristic
984C22D4×Dic611yescharacteristic
985C22D4×Dic611yescharacteristic
986C22#553911yescharacteristic
987C22#553911yescharacteristic
988C22D3×#12011yescharacteristic
989C22#558911yescharacteristic
990C22#558911yescharacteristic
991C22#559711yescharacteristic
992C22#559911yescharacteristic
993C22#560511yescharacteristic
994C22#560511yescharacteristic
995C22#560711yescharacteristic
996C22#561011yescharacteristic
997C22#562111yescharacteristic
998C22#562111yescharacteristic
999C22#562311yescharacteristic
1000C22#563211yescharacteristic
1001C22#563211yescharacteristic
1002C22#563411yescharacteristic
1003C22#563611yescharacteristic
1004C22#563611yescharacteristic
1005C22#564811yescharacteristic
1006C22#565111yescharacteristic
1007C22#565511yescharacteristic
1008C22#565611yescharacteristic
1009C22#566011yescharacteristic
1010C22#566911yescharacteristic
1011C22#567211yescharacteristic
1012C22#567711yescharacteristic
1013C22#570711yescharacteristic
1014C22#571011yescharacteristic
1015C22#571511yescharacteristic
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—64no—
1021C4—81no—
1022C4—81no—
1023C4—122no—
1024C4—122no—
1025C4—122no—
1026C4—122no—
1027C4—122no—
1028C4—122no—
1029C4—122no—
1030C3#1660611yescharacteristic, complemented, Sylow
1031C2—44no—
1032C2#7395711yescharacteristic
1033C2#7441211yescharacteristic
1034C2#7448911yescharacteristic
1035C2#7483011yescharacteristic
1036C2#7569711yescharacteristic
1037C2#7570711yescharacteristic
1038C2#7638211yescharacteristic
1039C2#7676011yescharacteristic
1040C2#7683311yescharacteristic
1041C2#7689411yescharacteristic
1042C2#7708411yescharacteristic
1043C2#7737211yescharacteristic
1044C2#7743611yescharacteristic
1045C2#7754611yescharacteristic
1046C2#7806811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC25×C3C23
hypercenter#1439D3
hypocenterC3#16606
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#4979C2semidirect
4. C2×#4657C2semidirect
6. #71568C2semidirect
11. #69424C2semidirect
12. #69421C2semidirect
13. #69420C2semidirect
14. #69411C2semidirect
15. #69410C2semidirect
113. C2×C3×C22⋊C4Q8semidirect
122. C2×#217Q8semidirect
424. C2×C22⋊C4Dic6semidirect
1030. C3#16606semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C2×#49792
C2×#49462
C2×#46572
C3×#14392
#715682
#715472
#715462
#715442
#694242
#694212
#694202
#694112
#694102
#166063