Finite Group Databasebeta

← #10732219

Subgroups — #10732219

Order 768.

1946 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#897C211yesmaximal, characteristic
2C2×#4987C211yesmaximal, characteristic
3C2×#4973C211yesmaximal, characteristic, complemented
4C2×#4972C211yesmaximal, characteristic, complemented
5C2×#4929C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
7C3×C4⋊#95C211yesmaximal, characteristic, complemented
8#69429C212yesmaximal
9#69428C212yesmaximal
10#69412C212yesmaximal, complemented
11#69410C212yesmaximal, complemented
12#15179—31nomaximal, Sylow
13C23×C4×D3C2211yescharacteristic
14C23×Dic6C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×C4⋊Dic3C2212yes—
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×C4×Dic3C2211yescharacteristic
26C2×#897—24no—
27C2×#897—24no—
28C2×#897—24no—
29C2×C3×#95C2212yes—
30C2×C3×#95C2212yes—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4987—24no—
40#4973—24no—
41#4972—24no—
42C4×(C2×D3)⋊C4—24no—
43#4929—24no—
44C22×C22⋊Q8—31no—
45C2×#391—31no—
46C2×#391—31no—
47C2×#389—31no—
48C2×#380—31no—
49C2×C4×C22⋊C4—31no—
50#1442—32no—
51#1441—32no—
52#1440—32no—
53#1439—32no—
54C4⋊#95D311yescharacteristic, complemented
55C24×D3C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×Dic3C2312yes—
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2312yes—
64C23×Dic3C2311yescharacteristic
65C23×Dic3C2311yescharacteristic
66C22×C4×D3—22no—
67C22×C4×D3—22no—
68C22×C4×D3—22no—
69C22×C4×D3—22no—
70C22×C4×D3—22no—
71C22×C4×D3—22no—
72C22×C4×D3D414yes—
73C22×Dic6—22no—
74C22×Dic6—22no—
75C22×Dic6—22no—
76C22×Dic6—22no—
77C22×Dic6—22no—
78C22×Dic6—22no—
79C22×Dic6D414yes—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4D414yes—
86C2×C3×C42—22no—
87C2×C3×C42—22no—
88C2×C3×C42—22no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—42no—
100C2×(C2×D3)⋊C4Q814yescomplemented
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—24no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—24no—
105C2×C4⋊Dic3—24no—
106C2×C4⋊Dic3D414yes—
107C2×Dic3⋊C4—24no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—42no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3—22no—
112C2×C4×Dic3—22no—
113#897—232no—
114C3×#95—24no—
115C3×#95—42no—
116C3⋊#95—24no—
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—22no—
120C3⋊#95—22no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C23×Q8—31no—
125C24×C4—31no—
126C2×C22⋊Q8—64no—
127C2×C22⋊Q8—64no—
128C2×C22⋊Q8—64no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—32no—
131C22×C4⋊C4—32no—
132C22×C4⋊C4C2×D311yescharacteristic
133C22×C4⋊C4C2×D311yescharacteristic
134C22×C22⋊C4—31no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—31no—
137C22×C22⋊C4—32no—
138C22×C42—31no—
139C22×C42C2×D311yescharacteristic
140#391—64no—
141#391—64no—
142#389—64no—
143#380—64no—
144C4×C22⋊C4—64no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95—31no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95C2×D312yes—
154C2×#95C2×D312yes—
155C24×C3C2411yescharacteristic
156C23×D3—21no—
157C23×D3—21no—
158C23×D3—21no—
159C23×D3—21no—
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—21no—
163C23×D3—21no—
164C23×D3—21no—
165C23×D3—21no—
166C23×D3—21no—
167C23×D3—21no—
168C23×D3C2×D412yes—
169C23×D3C2×Q812yes—
170C23×D3#4112yes—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4C2×D414yes—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×Q812yes—
202C22×C3×C4#4112yes—
203C22×C3×C4#4112yes—
204C22×C3×C4#4112yes—
205C22×C3×C4#4112yes—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—22no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—22no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C2×D414yes—
237C22×Dic3C2×D412yes—
238C22×Dic3C2×D414yes—
239C22×Dic3C2×Q812yes—
240C22×Dic3#4112yes—
241C2×C4×D3—28no—
242C2×C4×D3—28no—
243C2×C4×D3—28no—
244C2×C4×D3—44no—
245C2×C4×D3—44no—
246C2×C4×D3—44no—
247C2×C4×D3—44no—
248C2×Dic6—28no—
249C2×Dic6—28no—
250C2×Dic6—28no—
251C2×Dic6—44no—
252C2×Dic6—44no—
253C2×Dic6—44no—
254C2×Dic6—44no—
255C3×C4⋊C4—28no—
256C3×C4⋊C4—44no—
257C3×C42—44no—
258(C2×D3)⋊C4—216no—
259(C2×D3)⋊C4—28no—
260(C2×D3)⋊C4—28no—
261(C2×D3)⋊C4—48no—
262C4⋊Dic3—216no—
263C4⋊Dic3—28no—
264Dic3⋊C4—48no—
265C4×Dic3—44no—
266C25—31no—
267C22×Q8—34no—
268C22×Q8—62no—
269C22×Q8—62no—
270C22×Q8—62no—
271C22×Q8—62no—
272C22×Q8—62no—
273C22×Q8—62no—
274C23×C4—32no—
275C23×C4—31no—
276C23×C4—32no—
277C23×C4—31no—
278C23×C4—31no—
279C23×C4—34no—
280C23×C4—62no—
281C23×C4—62no—
282C23×C4—62no—
283C23×C4—62no—
284C23×C4—62no—
285C23×C4—62no—
286C23×C4C22×D312yes—
287C23×C4C22×D312yes—
288C23×C4C22×D311yescharacteristic
289C23×C4C22×D311yescharacteristic
290C23×C4C22×D311yescharacteristic
291C22⋊Q8—632no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—34no—
298C2×C4⋊C4—64no—
299C2×C4⋊C4—64no—
300C2×C4⋊C4—64no—
301C2×C4⋊C4—62no—
302C2×C4⋊C4—62no—
303C2×C4⋊C4—64no—
304C2×C4⋊C4—64no—
305C2×C4⋊C4—122no—
306C2×C4⋊C4D1214yes—
307C2×C22⋊C4—34no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—62no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—62no—
313C2×C22⋊C4—62no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—122no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—62no—
323C2×C42—62no—
324C2×C42—62no—
325#95—24no—
326#95—42no—
327#95—62no—
328#95—62no—
329#95—64no—
330#95—64no—
331#95—64no—
332#95—64no—
333#95—64no—
334#95—64no—
335C23×C3C22×D411yescharacteristic
336C23×C3C22×D411yescharacteristic
337C23×C3C22×D411yescharacteristic
338C23×C3C22×D411yescharacteristic
339C23×C3C22×Q811yescharacteristic
340C23×C3C2×#4111yescharacteristic
341C23×C3C2×#4111yescharacteristic
342C23×C3C2×#4111yescharacteristic
343C23×C3C2×#4111yescharacteristic
344C23×C3C2×#4111yescharacteristic
345C23×C3C2×#4111yescharacteristic
346C23×C3H(5,𝔽2)11yescharacteristic
347C23×C32−1+411yescharacteristic
348C23×C32−1+411yescharacteristic
349C23×C32−1+411yescharacteristic
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—41no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—41no—
374C22×D3—41no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—41no—
378C22×D3—41no—
379C22×D3—41no—
380C22×D3—41no—
381C22×D3—41no—
382C22×D3—41no—
383C22×D3—41no—
384C22×D3C22⋊Q814yes—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4#12014yes—
414C2×C3×C4#12114yes—
415C2×C3×C4#12114yes—
416C2×C3×C4#12114yes—
417C2×C3×C4#12314yes—
418C2×C3×C4#12314yes—
419C2×C3×C4#12414yes—
420C2×Dic3—22no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—24no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—24no—
431C2×Dic3—24no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—42no—
442C2×Dic3—41no—
443C2×Dic3—42no—
444C2×Dic3—41no—
445C2×Dic3—42no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—42no—
454C2×Dic3—41no—
455C4×D3—416no—
456Dic6—416no—
457C24—32no—
458C24—32no—
459C24—32no—
460C24—61no—
461C24—61no—
462C24—61no—
463C24—61no—
464C24—61no—
465C24—61no—
466C24—61no—
467C24—61no—
468C24—61no—
469C24—61no—
470C24—61no—
471C24—61no—
472C24C23×D311yescharacteristic
473C2×Q8—68no—
474C2×Q8—68no—
475C2×Q8—68no—
476C2×Q8—124no—
477C2×Q8—124no—
478C2×Q8—124no—
479C2×Q8—124no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—34no—
506C22×C4—34no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—61no—
511C22×C4—62no—
512C22×C4—61no—
513C22×C4—62no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—62no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—61no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—68no—
541C22×C4—68no—
542C22×C4—68no—
543C22×C4—124no—
544C22×C4—124no—
545C22×C4—124no—
546C22×C4—124no—
547C22×C4C2×D1214yes—
548C22×C4C2×D1212yes—
549C22×C4#23512yes—
550C22×C4#23512yes—
551C22×C4D3×D412yes—
552C22×C4D3×D412yes—
553C22×C4D3×D412yes—
554C22×C4#23712yes—
555C22×C4D3×Q812yes—
556C22×C4#23912yes—
557C4⋊C4—28no—
558C4⋊C4—44no—
559C4⋊C4—616no—
560C4⋊C4—68no—
561C4⋊C4—128no—
562C22⋊C4—68no—
563C22⋊C4—616no—
564C22⋊C4—68no—
565C22⋊C4—128no—
566C42—44no—
567C42—124no—
568C22×C3C2×#12011yescharacteristic
569C22×C3C2×#12111yescharacteristic
570C22×C3C2×#12111yescharacteristic
571C22×C3C2×#12111yescharacteristic
572C22×C3C2×C22⋊Q811yescharacteristic
573C22×C3C2×#12311yescharacteristic
574C22×C3C2×#12311yescharacteristic
575C22×C3#52511yescharacteristic
576C22×C3C2×#12411yescharacteristic
577C22×C3#52911yescharacteristic
578C22×C3#52911yescharacteristic
579C22×C3#53311yescharacteristic
580C22×C3#53311yescharacteristic
581C22×C3#53611yescharacteristic
582C22×C3#53711yescharacteristic
583C22×C3#54111yescharacteristic
584C22×C3#54111yescharacteristic
585C22×C3#54211yescharacteristic
586C22×C3#54211yescharacteristic
587C22×C3#54611yescharacteristic
588C22×C3#54611yescharacteristic
589C22×C3#54711yescharacteristic
590C22×C3#54711yescharacteristic
591C22×C3#54811yescharacteristic
592C22×C3#54811yescharacteristic
593C22×C3#54811yescharacteristic
594C22×C3#54811yescharacteristic
595C22×C3D4×Q811yescharacteristic
596C22×C3D4×Q811yescharacteristic
597C22×C3D4×Q811yescharacteristic
598C22×C3#55011yescharacteristic
599C22×C3#55211yescharacteristic
600C22×C3#55211yescharacteristic
601C22×C3#55411yescharacteristic
602C22×C3#55611yescharacteristic
603C2×D3—24no—
604C2×D3—24no—
605C2×D3—24no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—42no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—42no—
618C3×C4—44no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—82no—
622C3×C4#39418yes—
623Dic3—44no—
624Dic3—42no—
625Dic3—42no—
626Dic3—42no—
627Dic3—44no—
628C23—34no—
629C23—62no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23—62no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23—121no—
662C23—121no—
663C23C22×D1211yescharacteristic
664C23C2×#23511yescharacteristic
665C23C2×#23511yescharacteristic
666C23C2×D3×D411yescharacteristic
667C23C2×D3×D411yescharacteristic
668C23C2×D3×D411yescharacteristic
669C23C2×#23711yescharacteristic
670C23#100411yescharacteristic
671C23C2×D3×Q811yescharacteristic
672C23C2×#23911yescharacteristic
673C23#100711yescharacteristic
674C23D3×#4111yescharacteristic
675C23D3×#4111yescharacteristic
676C23#101011yescharacteristic
677C23#101011yescharacteristic
678Q8—1216no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—64no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—64no—
713C2×C4—62no—
714C2×C4—64no—
715C2×C4—64no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—64no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—121no—
723C2×C4—122no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—122no—
732C2×C4—121no—
733C2×C4—122no—
734C2×C4—121no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—122no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—1216no—
743C2×C4#87514yes—
744C2×C4#88214yes—
745C2×C4#88414yes—
746C2×C4#88414yes—
747C2×C4#89414yes—
748C2×C4#89414yes—
749C2×C4#89514yes—
750C2×C3C2×#39411yescharacteristic
751C2×C3#240711yescharacteristic
752C2×C3#240911yescharacteristic
753C2×C3#241511yescharacteristic
754C2×C3#241711yescharacteristic
755C2×C3#242111yescharacteristic
756C2×C3#242311yescharacteristic
757C2×C3#242611yescharacteristic
758C2×C3#242711yescharacteristic
759C2×C3#242911yescharacteristic
760C2×C3#242911yescharacteristic
761C2×C3#248911yescharacteristic
762C2×C3#249211yescharacteristic
763C2×C3#262511yescharacteristic
764C2×C3#285511yescharacteristic
765D3—44no—
766C22—64no—
767C22—64no—
768C22—64no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22—122no—
778C22—122no—
779C22—122no—
780C22—122no—
781C22C2×#87511yescharacteristic
782C22C2×#88211yescharacteristic
783C22C2×#88411yescharacteristic
784C22C2×#88411yescharacteristic
785C22C2×#89411yescharacteristic
786C22C2×#89411yescharacteristic
787C22C2×#89511yescharacteristic
788C22#551111yescharacteristic
789C22#551311yescharacteristic
790C22#552911yescharacteristic
791C22#553311yescharacteristic
792C22#555411yescharacteristic
793C22#555511yescharacteristic
794C22#555711yescharacteristic
795C22#556111yescharacteristic
796C22Q8×D1211yescharacteristic
797C22#557611yescharacteristic
798C22#557811yescharacteristic
799C22#558311yescharacteristic
800C22#559811yescharacteristic
801C22#560611yescharacteristic
802C22#560811yescharacteristic
803C22#561211yescharacteristic
804C22D3×C22⋊Q811yescharacteristic
805C22#562811yescharacteristic
806C22#563111yescharacteristic
807C22#563211yescharacteristic
808C22#567711yescharacteristic
809C22#567711yescharacteristic
810C22#569111yescharacteristic
811C22#569811yescharacteristic
812C22#571811yescharacteristic
813C22#572711yescharacteristic
814C22#572811yescharacteristic
815C22#573311yescharacteristic
816C4—42no—
817C4—44no—
818C4—42no—
819C4—82no—
820C4—122no—
821C4—122no—
822C4—124no—
823C4—122no—
824C4—124no—
825C4#467218yes—
826C3#1517911yescharacteristic, complemented, Sylow
827C2—124no—
828C2C2×#467211yescharacteristic
829C2#7378611yescharacteristic
830C2#7378911yescharacteristic
831C2#7388811yescharacteristic
832C2#7402011yescharacteristic
833C2#7423211yescharacteristic
834C2#7436311yescharacteristic
835C2#7610211yescharacteristic
836C2#7621911yescharacteristic
837C2#7622111yescharacteristic
838C2#7628711yescharacteristic
839C2#7643511yescharacteristic
840C2#7644311yescharacteristic
841C2#7661911yescharacteristic
842C2#7662511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C4⋊#95C2
prime radicalC24×D3C23
hypercenterC4⋊#95D3
hypocenterC3#15179
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#4973C2semidirect
4. C2×#4972C2semidirect
5. C2×#4929C2semidirect
7. C3×C4⋊#95C2semidirect
10. #69412C2semidirect
11. #69410C2semidirect
54. C4⋊#95D3semidirect
100. C2×(C2×D3)⋊C4Q8semidirect
826. C3#15179semidirect

Maximal subgroups

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

subgroupindex
C22×#8972
C2×#49872
C2×#49732
C2×#49722
C2×#49292
C2×C4×(C2×D3)⋊C42
C3×C4⋊#952
#694292
#694282
#694122
#694102
#151793