Finite Group Databasebeta

← #10703001

Subgroups — #10703001

Order 768.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#821C211yesmaximal, characteristic
2C22×#821C211yesmaximal, characteristic
3C2×#4939C211yesmaximal, characteristic
4C2×C3×#336C211yesmaximal, characteristic, complemented
5C2×#4551C211yesmaximal, characteristic, complemented
6C2×#4551C211yesmaximal, characteristic, complemented
7#71535C211yesmaximal, characteristic, complemented
8#11189—31nomaximal, Sylow
9C23×D12C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×C3×C42C2211yescharacteristic
13C22×(C2×D3)⋊C4—21no—
14C22×(C2×D3)⋊C4—21no—
15C22×C4⋊Dic3C2211yescharacteristic
16C22×C4⋊Dic3C2211yescharacteristic
17C22×C4⋊Dic3C2211yescharacteristic
18C2×C3⋊#95—21no—
19C2×C3⋊#95—21no—
20C2×#821—22no—
21C2×#821—22no—
22C2×#821—22no—
23C2×#821—22no—
24C2×#821—22no—
25C2×#821C414yescomplemented
26#4939—22no—
27#4939—22no—
28C3×#336—22no—
29#4551—22no—
30#4551—22no—
31C22×#102—31no—
32C22×#102—31no—
33C2×#390—31no—
34C2×#340—31no—
35C2×#340—31no—
36C2×#336D311yescharacteristic, complemented
37C4⋊#95—31no—
38C24×D3—21no—
39C23×C3×C4D411yescharacteristic
40C23×C3×C4D411yescharacteristic
41C23×C3×C4C2311yescharacteristic
42C23×Dic3—21no—
43C23×Dic3—21no—
44C23×Dic3—21no—
45C22×D12—21no—
46C22×D12—21no—
47C22×D12—21no—
48C22×D12—21no—
49C22×D12—21no—
50C22×D12—21no—
51C22×D12—21no—
52C22×D12—21no—
53C22×D12—21no—
54C22×D12—21no—
55C22×D12—21no—
56C22×D12C2×C412yes—
57C22×D12D412yes—
58C22×D12D412yes—
59C22×C3×C8—21no—
60C22×C3×C8—21no—
61C22×C3×C8—21no—
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C22×C3×C8—21no—
66C22×C3×C8—21no—
67C22×C3×C8—21no—
68C22×C3×C8—21no—
69C22×C3×C8—21no—
70C22×C3×C8—21no—
71C22×C3×C8C2×C412yes—
72C22×C3×C8D412yes—
73C2×C3×C42—21no—
74C2×C3×C42—21no—
75C2×C3×C42—21no—
76C2×C3×C42—21no—
77C2×C3×C42—21no—
78C2×C3×C42—21no—
79C2×(C2×D3)⋊C4—24no—
80C2×(C2×D3)⋊C4—24no—
81C2×(C2×D3)⋊C4—42no—
82C2×(C2×D3)⋊C4—42no—
83C2×(C2×D3)⋊C4—42no—
84C2×(C2×D3)⋊C4—42no—
85C2×C4⋊Dic3—21no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3—21no—
89C2×C4⋊Dic3—21no—
90C2×C4⋊Dic3—21no—
91C2×C4⋊Dic3—21no—
92C2×C4⋊Dic3—21no—
93C2×C4⋊Dic3—21no—
94C2×C4⋊Dic3—21no—
95C2×C4⋊Dic3—21no—
96C2×C4⋊Dic3—21no—
97C2×C4⋊Dic3—21no—
98C2×C4⋊Dic3—21no—
99C2×C4⋊Dic3—21no—
100C2×C4⋊Dic3C2×C412yes—
101C2×C4⋊Dic3D412yes—
102C2×C4⋊Dic3D412yes—
103C3⋊#95—42no—
104C3⋊#95—42no—
105#821—28no—
106#821—28no—
107C23×D4—31no—
108C23×C8C2×D311yescharacteristic
109C23×C8C2×D311yescharacteristic
110C22×C4⋊C4—31no—
111C22×C4⋊C4—31no—
112C22×C4⋊C4—31no—
113C22×C22⋊C4—61no—
114C22×C22⋊C4—61no—
115C22×C42C2×D311yescharacteristic
116C2×#102—34no—
117C2×#102—62no—
118C2×#102—62no—
119C2×#102—62no—
120C2×#102—62no—
121C2×#102—62no—
122#390—62no—
123#390—62no—
124C2×#95—61no—
125C2×#95—61no—
126#340—62no—
127#340—62no—
128#336—22no—
129C24×C3C2×D411yescharacteristic
130C23×D3—22no—
131C23×D3—22no—
132C23×D3—22no—
133C23×D3—41no—
134C23×D3—41no—
135C23×D3—41no—
136C23×D3—41no—
137C23×D3—41no—
138C23×D3—41no—
139C23×D3—41no—
140C23×D3—41no—
141C23×D3—41no—
142C23×D3—41no—
143C23×D3—41no—
144C23×D3—41no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4D812yes—
158C22×C3×C4SD1612yes—
159C22×C3×C4C22×C411yescharacteristic
160C22×C3×C4C2×D411yescharacteristic
161C22×C3×C4C2×D411yescharacteristic
162C22×C3×C4C2×D411yescharacteristic
163C22×C3×C4C2×D411yescharacteristic
164C22×C3×C4C2×D411yescharacteristic
165C22×C3×C4#4111yescharacteristic
166C22×C3×C4#4111yescharacteristic
167C22×C3×C4#4111yescharacteristic
168C22×C3×C4#4111yescharacteristic
169C22×C3×C4#4111yescharacteristic
170C22×C3×C4#4111yescharacteristic
171C22×C3×C4#4111yescharacteristic
172C22×C3×C4#4111yescharacteristic
173C22×Dic3—22no—
174C22×Dic3—22no—
175C22×Dic3—22no—
176C22×Dic3—41no—
177C22×Dic3—41no—
178C22×Dic3—41no—
179C22×Dic3—41no—
180C22×Dic3—41no—
181C22×Dic3—41no—
182C22×Dic3—41no—
183C22×Dic3—41no—
184C22×Dic3—41no—
185C22×Dic3—41no—
186C22×Dic3—41no—
187C22×Dic3—41no—
188C22×Dic3—41no—
189C22×Dic3—41no—
190C22×Dic3—41no—
191C22×Dic3—41no—
192C22×Dic3—41no—
193C22×Dic3—41no—
194C2×D12—22no—
195C2×D12—22no—
196C2×D12—22no—
197C2×D12—22no—
198C2×D12—22no—
199C2×D12—22no—
200C2×D12—22no—
201C2×D12—22no—
202C2×D12—22no—
203C2×D12—22no—
204C2×D12—22no—
205C2×D12—22no—
206C2×D12—22no—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—41no—
210C2×D12—41no—
211C2×D12—41no—
212C2×D12—41no—
213C2×D12—41no—
214C2×D12—41no—
215C2×D12—41no—
216C2×D12—41no—
217C2×D12—41no—
218C2×D12—41no—
219C2×D12—41no—
220C2×D12—41no—
221C2×D12C22⋊C414yes—
222C2×C3×C8—22no—
223C2×C3×C8—22no—
224C2×C3×C8—22no—
225C2×C3×C8—22no—
226C2×C3×C8—22no—
227C2×C3×C8—22no—
228C2×C3×C8—41no—
229C2×C3×C8—41no—
230C2×C3×C8—41no—
231C2×C3×C8—41no—
232C2×C3×C8—41no—
233C2×C3×C8—41no—
234C2×C3×C8—41no—
235C2×C3×C8—41no—
236C3×C42—41no—
237C3×C42—41no—
238C3×C42—41no—
239C3×C42—41no—
240(C2×D3)⋊C4—48no—
241(C2×D3)⋊C4—48no—
242C4⋊Dic3—22no—
243C4⋊Dic3—22no—
244C4⋊Dic3—22no—
245C4⋊Dic3—22no—
246C4⋊Dic3—22no—
247C4⋊Dic3—22no—
248C4⋊Dic3—41no—
249C4⋊Dic3—41no—
250C4⋊Dic3—41no—
251C4⋊Dic3—41no—
252C4⋊Dic3—41no—
253C4⋊Dic3—41no—
254C25—61no—
255C22×D4—32no—
256C22×D4—32no—
257C22×D4—32no—
258C22×D4—61no—
259C22×D4—61no—
260C22×D4—61no—
261C22×D4—61no—
262C22×D4—61no—
263C22×D4—61no—
264C22×D4—61no—
265C22×D4—61no—
266C22×D4—61no—
267C22×D4—61no—
268C22×D4—61no—
269C23×C4—61no—
270C23×C4—61no—
271C23×C4—61no—
272C23×C4D1211yescharacteristic
273C23×C4D1211yescharacteristic
274C23×C4C22×D311yescharacteristic
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8C4×D312yes—
288C22×C8#6712yes—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—61no—
293C2×C4⋊C4—61no—
294C2×C4⋊C4—61no—
295C2×C4⋊C4—61no—
296C2×C4⋊C4—61no—
297C2×C4⋊C4—61no—
298C2×C4⋊C4—61no—
299C2×C4⋊C4—61no—
300C2×C4⋊C4—61no—
301C2×C4⋊C4—61no—
302C2×C4⋊C4—61no—
303C2×C4⋊C4—61no—
304C2×C4⋊C4—61no—
305C2×C4⋊C4—61no—
306C2×C4⋊C4—61no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—122no—
310C2×C22⋊C4—122no—
311C2×C22⋊C4—122no—
312C2×C22⋊C4—122no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319#102—68no—
320#102—68no—
321#95—122no—
322#95—122no—
323C23×C3C4×D411yescharacteristic
324C23×C3#12011yescharacteristic
325C23×C3#12111yescharacteristic
326C23×C3#12111yescharacteristic
327C23×C3#12111yescharacteristic
328C23×C3#12311yescharacteristic
329C23×C3#12411yescharacteristic
330C23×C3C2×D811yescharacteristic
331C23×C3C2×SD1611yescharacteristic
332C23×C3#13511yescharacteristic
333C23×C3#13511yescharacteristic
334C23×C3AGL(1,ℤ/8)11yescharacteristic
335C23×C3AGL(1,ℤ/8)11yescharacteristic
336C23×C3AGL(1,ℤ/8)11yescharacteristic
337C23×C3#13711yescharacteristic
338C22×D3—24no—
339C22×D3—42no—
340C22×D3—42no—
341C22×D3—42no—
342C22×D3—42no—
343C22×D3—42no—
344C22×D3—42no—
345C22×D3—42no—
346C22×D3—42no—
347C22×D3—42no—
348C22×D3—42no—
349C22×D3—42no—
350C22×D3—42no—
351C22×D3—42no—
352C22×D3—42no—
353C22×D3—42no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—81no—
358C22×D3—81no—
359C22×D3—81no—
360C22×D3—81no—
361C22×D3—81no—
362C22×D3—81no—
363C22×D3—81no—
364C22×D3—81no—
365C22×D3—81no—
366C22×D3—81no—
367C22×D3—81no—
368C22×D3—81no—
369C22×D3—81no—
370C22×D3—81no—
371C22×D3—81no—
372C22×D3—81no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4C2×C22⋊C411yescharacteristic
388C2×C3×C4#11711yescharacteristic
389C2×C3×C4#11711yescharacteristic
390C2×C3×C4C4×D411yescharacteristic
391C2×C3×C4C4×D411yescharacteristic
392C2×C3×C4C4×D411yescharacteristic
393C2×C3×C4#12011yescharacteristic
394C2×C3×C4#12111yescharacteristic
395C2×C3×C4#12111yescharacteristic
396C2×C3×C4#12111yescharacteristic
397C2×C3×C4#12111yescharacteristic
398C2×C3×C4#12111yescharacteristic
399C2×C3×C4#12311yescharacteristic
400C2×C3×C4#12311yescharacteristic
401C2×C3×C4#12311yescharacteristic
402C2×C3×C4#12311yescharacteristic
403C2×C3×C4#12311yescharacteristic
404C2×C3×C4#12311yescharacteristic
405C2×C3×C4#12311yescharacteristic
406C2×C3×C4#12311yescharacteristic
407C2×C3×C4#12311yescharacteristic
408C2×C3×C4#12411yescharacteristic
409C2×C3×C4#12411yescharacteristic
410C2×C3×C4#12411yescharacteristic
411C2×C3×C4#12611yescharacteristic
412C2×C3×C4#12611yescharacteristic
413C2×C3×C4#12611yescharacteristic
414C2×C3×C4#12611yescharacteristic
415C2×Dic3—42no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—81no—
425C2×Dic3—81no—
426C2×Dic3—81no—
427C2×Dic3—81no—
428C2×Dic3—81no—
429C2×Dic3—81no—
430C2×Dic3—81no—
431C2×Dic3—81no—
432C2×Dic3—81no—
433C2×Dic3—81no—
434C2×Dic3—81no—
435C2×Dic3—81no—
436D12—24no—
437D12—24no—
438D12—42no—
439D12—42no—
440D12—42no—
441D12—42no—
442D12—42no—
443D12—42no—
444C3×C8—42no—
445C3×C8—42no—
446C24—62no—
447C24—62no—
448C24—62no—
449C24—121no—
450C24—121no—
451C24—121no—
452C24—121no—
453C24—121no—
454C24—121no—
455C24—121no—
456C24—121no—
457C24—121no—
458C24—121no—
459C24—121no—
460C24—121no—
461C24C2×D1211yescharacteristic
462C2×D4—34no—
463C2×D4—62no—
464C2×D4—62no—
465C2×D4—62no—
466C2×D4—62no—
467C2×D4—62no—
468C2×D4—62no—
469C2×D4—62no—
470C2×D4—62no—
471C2×D4—62no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4—62no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—121no—
479C2×D4—121no—
480C2×D4—121no—
481C2×D4—121no—
482C2×D4—121no—
483C2×D4—121no—
484C2×D4—121no—
485C2×D4—121no—
486C2×D4—121no—
487C2×D4—121no—
488C2×D4—121no—
489C2×D4—121no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—121no—
506C22×C4—121no—
507C22×C4—121no—
508C22×C4—121no—
509C22×C4—121no—
510C22×C4—121no—
511C22×C4—121no—
512C22×C4—121no—
513C22×C4—121no—
514C22×C4—121no—
515C22×C4—121no—
516C22×C4—121no—
517C22×C4—121no—
518C22×C4—121no—
519C22×C4—121no—
520C22×C4—121no—
521C22×C4—121no—
522C22×C4—121no—
523C22×C4#20412yes—
524C22×C4D2412yes—
525C22×C4C2×C4×D311yescharacteristic
526C22×C4#23511yescharacteristic
527C22×C4#23511yescharacteristic
528C22×C4#23511yescharacteristic
529C22×C4#23511yescharacteristic
530C22×C4D3×D411yescharacteristic
531C22×C4D3×D411yescharacteristic
532C22×C4D3×D411yescharacteristic
533C22×C4D3×D411yescharacteristic
534C22×C4#23711yescharacteristic
535C22×C4#23711yescharacteristic
536C22×C4#23911yescharacteristic
537C22×C4#23911yescharacteristic
538C22×C4C2×#6711yescharacteristic
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C4⋊C4—62no—
554C4⋊C4—62no—
555C4⋊C4—62no—
556C4⋊C4—62no—
557C4⋊C4—62no—
558C4⋊C4—62no—
559C4⋊C4—121no—
560C4⋊C4—121no—
561C4⋊C4—121no—
562C4⋊C4—121no—
563C4⋊C4—121no—
564C4⋊C4—121no—
565C22⋊C4—128no—
566C22⋊C4—128no—
567C42—41no—
568C42—41no—
569C42—41no—
570C42—41no—
571C22×C3#38611yescharacteristic
572C22×C3#38811yescharacteristic
573C22×C3#38811yescharacteristic
574C22×C3#39411yescharacteristic
575C22×C3#39411yescharacteristic
576C22×C3#39411yescharacteristic
577C22×C3#39711yescharacteristic
578C22×C3C4×D811yescharacteristic
579C22×C3C4×SD1611yescharacteristic
580C22×C3#44011yescharacteristic
581C22×C3#44211yescharacteristic
582C22×C3#44711yescharacteristic
583C22×C3#44911yescharacteristic
584C22×C3#45011yescharacteristic
585C22×C3#45211yescharacteristic
586C22×C3#45911yescharacteristic
587C22×C3#45911yescharacteristic
588C22×C3#46011yescharacteristic
589C22×C3#46111yescharacteristic
590C22×C3#46311yescharacteristic
591C22×C3#46311yescharacteristic
592C22×C3#46311yescharacteristic
593C22×C3#46411yescharacteristic
594C22×C3#46511yescharacteristic
595C22×C3#46611yescharacteristic
596C22×C3#46811yescharacteristic
597C22×C3#46911yescharacteristic
598C22×C3#48011yescharacteristic
599C22×C3#48111yescharacteristic
600C22×C3#48211yescharacteristic
601C22×C3#48211yescharacteristic
602C22×C3#48611yescharacteristic
603C22×C3#48811yescharacteristic
604C22×C3#48911yescharacteristic
605C22×C3#49011yescharacteristic
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—82no—
610C2×D3—82no—
611C2×D3—82no—
612C2×D3—82no—
613C2×D3—82no—
614C2×D3—82no—
615C2×D3—82no—
616C2×D3—82no—
617C2×D3—82no—
618C2×D3—82no—
619C2×D3—82no—
620C2×D3—82no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4#38111yescharacteristic
624C3×C4#38611yescharacteristic
625C3×C4#38811yescharacteristic
626C3×C4#38811yescharacteristic
627C3×C4#39411yescharacteristic
628C3×C4#39711yescharacteristic
629C3×C4#39711yescharacteristic
630C3×C4#39711yescharacteristic
631Dic3—82no—
632Dic3—82no—
633Dic3—82no—
634C23—64no—
635C23—122no—
636C23—122no—
637C23—122no—
638C23—122no—
639C23—122no—
640C23—122no—
641C23—122no—
642C23—122no—
643C23—122no—
644C23—122no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—241no—
654C23—241no—
655C23—241no—
656C23—241no—
657C23—241no—
658C23—241no—
659C23—241no—
660C23—241no—
661C23—241no—
662C23—241no—
663C23—241no—
664C23—241no—
665C23—241no—
666C23—241no—
667C23—241no—
668C23—241no—
669C23C4×D1211yescharacteristic
670C23#87511yescharacteristic
671C23#88211yescharacteristic
672C23#88611yescharacteristic
673C23#89511yescharacteristic
674C23#89511yescharacteristic
675C23C2×#20411yescharacteristic
676C23C2×D2411yescharacteristic
677C23#90411yescharacteristic
678C23#90411yescharacteristic
679C23#90811yescharacteristic
680C23#90811yescharacteristic
681C23#90811yescharacteristic
682C23#90911yescharacteristic
683C23#93011yescharacteristic
684D4—64no—
685D4—64no—
686D4—122no—
687D4—122no—
688D4—122no—
689D4—122no—
690D4—122no—
691D4—122no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—241no—
718C2×C4—241no—
719C2×C4—241no—
720C2×C4—241no—
721C2×C4—241no—
722C2×C4—241no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4—241no—
726C2×C4—241no—
727C2×C4#87211yescharacteristic
728C2×C4#87611yescharacteristic
729C2×C4D3×C22⋊C411yescharacteristic
730C2×C4#67⋊C411yescharacteristic
731C2×C4#88311yescharacteristic
732C2×C4#88311yescharacteristic
733C2×C4#88311yescharacteristic
734C2×C4#88411yescharacteristic
735C2×C4#88411yescharacteristic
736C2×C4#88411yescharacteristic
737C2×C4#88511yescharacteristic
738C2×C4#88511yescharacteristic
739C2×C4#89211yescharacteristic
740C2×C4#89311yescharacteristic
741C2×C4#89411yescharacteristic
742C2×C4#89411yescharacteristic
743C2×C4#89411yescharacteristic
744C2×C4#89411yescharacteristic
745C2×C4#89411yescharacteristic
746C2×C4#89811yescharacteristic
747C2×C4#89811yescharacteristic
748C2×C4#89811yescharacteristic
749C2×C4C4×#6711yescharacteristic
750C2×C4#92911yescharacteristic
751C2×C4#93711yescharacteristic
752C2×C4#93811yescharacteristic
753C2×C4#93911yescharacteristic
754C2×C4#94711yescharacteristic
755C8—42no—
756C8—42no—
757C2×C3#144011yescharacteristic
758C2×C3#187711yescharacteristic
759C2×C3#187911yescharacteristic
760C2×C3#192511yescharacteristic
761C2×C3#192611yescharacteristic
762C2×C3#193411yescharacteristic
763C2×C3#193611yescharacteristic
764C2×C3#203311yescharacteristic
765C2×C3#203411yescharacteristic
766C2×C3#204111yescharacteristic
767C2×C3#204211yescharacteristic
768C2×C3#205411yescharacteristic
769C2×C3#205511yescharacteristic
770C2×C3#207111yescharacteristic
771C2×C3#207311yescharacteristic
772D3—84no—
773C22—124no—
774C22—124no—
775C22—124no—
776C22—242no—
777C22—242no—
778C22—242no—
779C22—242no—
780C22—242no—
781C22—242no—
782C22—242no—
783C22—242no—
784C22—242no—
785C22—242no—
786C22—242no—
787C22—242no—
788C22#466511yescharacteristic
789C22#467011yescharacteristic
790C22#467211yescharacteristic
791C22#467411yescharacteristic
792C22C4×#20411yescharacteristic
793C22C4×D2411yescharacteristic
794C22#469411yescharacteristic
795C22#469711yescharacteristic
796C22#471011yescharacteristic
797C22#471111yescharacteristic
798C22#471311yescharacteristic
799C22#471411yescharacteristic
800C22#473111yescharacteristic
801C22#473211yescharacteristic
802C22#473311yescharacteristic
803C22#473411yescharacteristic
804C22#473511yescharacteristic
805C22#473611yescharacteristic
806C22#473711yescharacteristic
807C22#473711yescharacteristic
808C22#484111yescharacteristic
809C22#484311yescharacteristic
810C22#484311yescharacteristic
811C22#484411yescharacteristic
812C22#484411yescharacteristic
813C22#484411yescharacteristic
814C22#484511yescharacteristic
815C22#484811yescharacteristic
816C22#494011yescharacteristic
817C22#496111yescharacteristic
818C22#499111yescharacteristic
819C22#511411yescharacteristic
820C22#511511yescharacteristic
821C22#513411yescharacteristic
822C22#513511yescharacteristic
823C4—42no—
824C4—42no—
825C4—242no—
826C4—242no—
827C4—242no—
828C4#466411yescharacteristic
829C4#466911yescharacteristic
830C4#467511yescharacteristic
831C4#467511yescharacteristic
832C4#495611yescharacteristic
833C4#495911yescharacteristic
834C4#499011yescharacteristic
835C4#499211yescharacteristic
836C3#1118911yescharacteristic, complemented, Sylow
837C2—244no—
838C2#6862511yescharacteristic
839C2#6862611yescharacteristic
840C2#6862911yescharacteristic
841C2#6863011yescharacteristic
842C2#6863511yescharacteristic
843C2#6863711yescharacteristic
844C2#6867211yescharacteristic
845C2#6867311yescharacteristic
846C2#6942911yescharacteristic
847C2#6976811yescharacteristic
848C2#6981811yescharacteristic
849C2#6993411yescharacteristic
850C2#6993511yescharacteristic
851C2#7048111yescharacteristic
852C2#7048211yescharacteristic
subgroupG/H
centerC24C2×D12
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#336C2
socleC24×C3C2×D4
prime radicalC23×D12C22
cosocleC23×C3×C4C23
hypercenterC2×#336D3
hypocenterC3#11189
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. C2×C3×#336C2semidirect
5. C2×#4551C2semidirect
6. C2×#4551C2semidirect
7. #71535C2semidirect
25. C2×#821C4semidirect
36. C2×#336D3semidirect
836. C3#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#8212
C2×#49392
C2×C3×#3362
C2×#45512
#715352
#111893