Finite Group Databasebeta

← #10702247

Subgroups — #10702247

Order 768.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 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×#4928C211yesmaximal, characteristic, complemented
5C2×C3×#336C211yesmaximal, characteristic, complemented
6C2×#4551C211yesmaximal, characteristic, complemented
7C2×#4551C211yesmaximal, characteristic, complemented
8#11066—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
18C22×Dic3⋊C4—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—
28#4928—22no—
29#4928—22no—
30C3×#336—22no—
31#4551—22no—
32#4551—22no—
33C22×#102—31no—
34C22×#102—31no—
35C2×#390—31no—
36C2×#389—31no—
37C2×#340—31no—
38C2×#340—31no—
39C2×#336D311yescharacteristic, complemented
40C24×D3—21no—
41C23×C3×C4D411yescharacteristic
42C23×C3×C4D411yescharacteristic
43C23×C3×C4C2311yescharacteristic
44C23×Dic3—21no—
45C23×Dic3—21no—
46C23×Dic3—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×D12—21no—
57C22×D12—21no—
58C22×D12C2×C412yes—
59C22×D12D412yes—
60C22×D12Q812yes—
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×C8—21no—
72C22×C3×C8—21no—
73C22×C3×C8C2×C412yes—
74C22×C3×C8D412yes—
75C2×C3×C42—21no—
76C2×C3×C42—21no—
77C2×C3×C42—21no—
78C2×C3×C42—21no—
79C2×C3×C42—21no—
80C2×C3×C42—21no—
81C2×(C2×D3)⋊C4—24no—
82C2×(C2×D3)⋊C4—24no—
83C2×(C2×D3)⋊C4—42no—
84C2×(C2×D3)⋊C4—42no—
85C2×(C2×D3)⋊C4—42no—
86C2×(C2×D3)⋊C4—42no—
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—
103C2×C4⋊Dic3D412yes—
104C2×C4⋊Dic3D412yes—
105C2×Dic3⋊C4—24no—
106C2×Dic3⋊C4—42no—
107C2×Dic3⋊C4—42no—
108C3⋊#95—24no—
109#821—28no—
110#821—28no—
111C23×D4—31no—
112C23×C8C2×D311yescharacteristic
113C23×C8C2×D311yescharacteristic
114C22×C4⋊C4—31no—
115C22×C4⋊C4—31no—
116C22×C4⋊C4—31no—
117C22×C4⋊C4—61no—
118C22×C22⋊C4—61no—
119C22×C22⋊C4—61no—
120C22×C42C2×D311yescharacteristic
121C2×#102—34no—
122C2×#102—62no—
123C2×#102—62no—
124C2×#102—62no—
125C2×#102—62no—
126C2×#102—62no—
127#390—62no—
128#390—62no—
129#389—62no—
130#389—62no—
131C2×#95—61no—
132#340—62no—
133#340—62no—
134#336—22no—
135C24×C3C2×D411yescharacteristic
136C23×D3—22no—
137C23×D3—22no—
138C23×D3—22no—
139C23×D3—41no—
140C23×D3—41no—
141C23×D3—41no—
142C23×D3—41no—
143C23×D3—41no—
144C23×D3—41no—
145C23×D3—41no—
146C23×D3—41no—
147C23×D3—41no—
148C23×D3—41no—
149C23×D3—41no—
150C23×D3—41no—
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×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4D812yes—
164C22×C3×C4SD1612yes—
165C22×C3×C4C22×C411yescharacteristic
166C22×C3×C4C2×D411yescharacteristic
167C22×C3×C4C2×D411yescharacteristic
168C22×C3×C4C2×D411yescharacteristic
169C22×C3×C4C2×D411yescharacteristic
170C22×C3×C4C2×D411yescharacteristic
171C22×C3×C4C2×D411yescharacteristic
172C22×C3×C4C2×Q811yescharacteristic
173C22×C3×C4#4111yescharacteristic
174C22×C3×C4#4111yescharacteristic
175C22×C3×C4#4111yescharacteristic
176C22×C3×C4#4111yescharacteristic
177C22×C3×C4#4111yescharacteristic
178C22×C3×C4#4111yescharacteristic
179C22×Dic3—22no—
180C22×Dic3—22no—
181C22×Dic3—22no—
182C22×Dic3—22no—
183C22×Dic3—22no—
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—
194C22×Dic3—41no—
195C22×Dic3—41no—
196C22×Dic3—41no—
197C22×Dic3—41no—
198C22×Dic3—41no—
199C22×Dic3—41no—
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—22no—
210C2×D12—22no—
211C2×D12—22no—
212C2×D12—22no—
213C2×D12—22no—
214C2×D12—22no—
215C2×D12—41no—
216C2×D12—41no—
217C2×D12—41no—
218C2×D12—41no—
219C2×D12—41no—
220C2×D12—41no—
221C2×D12—41no—
222C2×D12—41no—
223C2×D12—41no—
224C2×D12—41no—
225C2×D12—41no—
226C2×D12—41no—
227C2×D12C4⋊C414yescomplemented
228C2×C3×C8—22no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C2×C3×C8—22no—
234C2×C3×C8—41no—
235C2×C3×C8—41no—
236C2×C3×C8—41no—
237C2×C3×C8—41no—
238C2×C3×C8—41no—
239C2×C3×C8—41no—
240C2×C3×C8—41no—
241C2×C3×C8—41no—
242C3×C42—41no—
243C3×C42—41no—
244C3×C42—41no—
245C3×C42—41no—
246(C2×D3)⋊C4—48no—
247(C2×D3)⋊C4—48no—
248C4⋊Dic3—22no—
249C4⋊Dic3—22no—
250C4⋊Dic3—22no—
251C4⋊Dic3—22no—
252C4⋊Dic3—22no—
253C4⋊Dic3—22no—
254C4⋊Dic3—22no—
255C4⋊Dic3—41no—
256C4⋊Dic3—41no—
257C4⋊Dic3—41no—
258C4⋊Dic3—41no—
259C4⋊Dic3C22⋊C414yescomplemented
260Dic3⋊C4—48no—
261C25—61no—
262C22×D4—32no—
263C22×D4—32no—
264C22×D4—32no—
265C22×D4—61no—
266C22×D4—61no—
267C22×D4—61no—
268C22×D4—61no—
269C22×D4—61no—
270C22×D4—61no—
271C22×D4—61no—
272C22×D4—61no—
273C22×D4—61no—
274C22×D4—61no—
275C22×D4—61no—
276C23×C4—61no—
277C23×C4—61no—
278C23×C4—61no—
279C23×C4D1211yescharacteristic
280C23×C4D1211yescharacteristic
281C23×C4C22×D311yescharacteristic
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8C4×D312yes—
295C22×C8#6712yes—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—32no—
299C2×C4⋊C4—32no—
300C2×C4⋊C4—32no—
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×C4⋊C4—61no—
308C2×C4⋊C4—61no—
309C2×C4⋊C4—61no—
310C2×C4⋊C4—61no—
311C2×C4⋊C4—61no—
312C2×C4⋊C4—64no—
313C2×C4⋊C4—61no—
314C2×C4⋊C4—61no—
315C2×C4⋊C4—122no—
316C2×C4⋊C4—122no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C22⋊C4—122no—
322C2×C22⋊C4—122no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329#102—68no—
330#102—68no—
331#95—64no—
332C23×C3C4×D411yescharacteristic
333C23×C3#12011yescharacteristic
334C23×C3#12011yescharacteristic
335C23×C3#12111yescharacteristic
336C23×C3#12111yescharacteristic
337C23×C3C22⋊Q811yescharacteristic
338C23×C3#12411yescharacteristic
339C23×C3C2×D811yescharacteristic
340C23×C3C2×SD1611yescharacteristic
341C23×C3#13511yescharacteristic
342C23×C3#13511yescharacteristic
343C23×C3AGL(1,ℤ/8)11yescharacteristic
344C23×C3AGL(1,ℤ/8)11yescharacteristic
345C23×C3AGL(1,ℤ/8)11yescharacteristic
346C23×C3#13711yescharacteristic
347C22×D3—24no—
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—42no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—81no—
367C22×D3—81no—
368C22×D3—81no—
369C22×D3—81no—
370C22×D3—81no—
371C22×D3—81no—
372C22×D3—81no—
373C22×D3—81no—
374C22×D3—81no—
375C22×D3—81no—
376C22×D3—81no—
377C22×D3—81no—
378C22×D3—81no—
379C22×D3—81no—
380C22×D3—81no—
381C22×D3—81no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4C2×C22⋊C411yescharacteristic
397C2×C3×C4C2×C4⋊C411yescharacteristic
398C2×C3×C4#11711yescharacteristic
399C2×C3×C4C4×D411yescharacteristic
400C2×C3×C4C4×D411yescharacteristic
401C2×C3×C4C4×D411yescharacteristic
402C2×C3×C4#12011yescharacteristic
403C2×C3×C4#12111yescharacteristic
404C2×C3×C4#12111yescharacteristic
405C2×C3×C4#12111yescharacteristic
406C2×C3×C4#12111yescharacteristic
407C2×C3×C4#12111yescharacteristic
408C2×C3×C4#12111yescharacteristic
409C2×C3×C4C22⋊Q811yescharacteristic
410C2×C3×C4C22⋊Q811yescharacteristic
411C2×C3×C4C22⋊Q811yescharacteristic
412C2×C3×C4C22⋊Q811yescharacteristic
413C2×C3×C4C22⋊Q811yescharacteristic
414C2×C3×C4#12311yescharacteristic
415C2×C3×C4#12311yescharacteristic
416C2×C3×C4#12311yescharacteristic
417C2×C3×C4#12311yescharacteristic
418C2×C3×C4#12311yescharacteristic
419C2×C3×C4#12411yescharacteristic
420C2×C3×C4#12411yescharacteristic
421C2×C3×C4#12611yescharacteristic
422C2×C3×C4#12611yescharacteristic
423C2×C3×C4#12711yescharacteristic
424C2×Dic3—24no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—81no—
438C2×Dic3—81no—
439C2×Dic3—81no—
440C2×Dic3—81no—
441C2×Dic3—81no—
442C2×Dic3—81no—
443C2×Dic3—81no—
444C2×Dic3—81no—
445D12—24no—
446D12—24no—
447D12—42no—
448D12—42no—
449D12—42no—
450D12—42no—
451D12—42no—
452D12—42no—
453C3×C8—42no—
454C3×C8—42no—
455C24—62no—
456C24—62no—
457C24—62no—
458C24—121no—
459C24—121no—
460C24—121no—
461C24—121no—
462C24—121no—
463C24—121no—
464C24—121no—
465C24—121no—
466C24—121no—
467C24—121no—
468C24—121no—
469C24—121no—
470C24C2×D1211yescharacteristic
471C2×D4—34no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4—62no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—62no—
486C2×D4—62no—
487C2×D4—121no—
488C2×D4—121no—
489C2×D4—121no—
490C2×D4—121no—
491C2×D4—121no—
492C2×D4—121no—
493C2×D4—121no—
494C2×D4—121no—
495C2×D4—121no—
496C2×D4—121no—
497C2×D4—121no—
498C2×D4—121no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—121no—
517C22×C4—121no—
518C22×C4—121no—
519C22×C4—121no—
520C22×C4—121no—
521C22×C4—121no—
522C22×C4—121no—
523C22×C4—121no—
524C22×C4—121no—
525C22×C4—121no—
526C22×C4—121no—
527C22×C4—121no—
528C22×C4—121no—
529C22×C4—121no—
530C22×C4—121no—
531C22×C4—121no—
532C22×C4#20412yes—
533C22×C4D2412yes—
534C22×C4C2×C4×D311yescharacteristic
535C22×C4#23511yescharacteristic
536C22×C4#23511yescharacteristic
537C22×C4#23511yescharacteristic
538C22×C4#23511yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4D3×D411yescharacteristic
541C22×C4D3×D411yescharacteristic
542C22×C4D3×D411yescharacteristic
543C22×C4D3×D411yescharacteristic
544C22×C4#23711yescharacteristic
545C22×C4D3×Q811yescharacteristic
546C22×C4#23911yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C4⋊C4—34no—
563C4⋊C4—62no—
564C4⋊C4—62no—
565C4⋊C4—62no—
566C4⋊C4—62no—
567C4⋊C4—62no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—128no—
571C4⋊C4—121no—
572C4⋊C4—121no—
573C4⋊C4—121no—
574C4⋊C4—121no—
575C22⋊C4—128no—
576C22⋊C4—128no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C22×C3#38511yescharacteristic
582C22×C3#38611yescharacteristic
583C22×C3#38811yescharacteristic
584C22×C3#39211yescharacteristic
585C22×C3#39311yescharacteristic
586C22×C3#39411yescharacteristic
587C22×C3#39611yescharacteristic
588C22×C3C4×D811yescharacteristic
589C22×C3C4×SD1611yescharacteristic
590C22×C3#44011yescharacteristic
591C22×C3#44211yescharacteristic
592C22×C3#44711yescharacteristic
593C22×C3#44711yescharacteristic
594C22×C3#44811yescharacteristic
595C22×C3#44911yescharacteristic
596C22×C3#44911yescharacteristic
597C22×C3#44911yescharacteristic
598C22×C3#45011yescharacteristic
599C22×C3#45211yescharacteristic
600C22×C3#45911yescharacteristic
601C22×C3#46011yescharacteristic
602C22×C3#46311yescharacteristic
603C22×C3#46411yescharacteristic
604C22×C3#46511yescharacteristic
605C22×C3#46611yescharacteristic
606C22×C3#46811yescharacteristic
607C22×C3#46911yescharacteristic
608C22×C3#47411yescharacteristic
609C22×C3#47611yescharacteristic
610C22×C3#47811yescharacteristic
611C22×C3#47811yescharacteristic
612C22×C3#48611yescharacteristic
613C22×C3#48811yescharacteristic
614C22×C3#48911yescharacteristic
615C22×C3#49011yescharacteristic
616C2×D3—44no—
617C2×D3—44no—
618C2×D3—44no—
619C2×D3—82no—
620C2×D3—82no—
621C2×D3—82no—
622C2×D3—82no—
623C2×D3—82no—
624C2×D3—82no—
625C2×D3—82no—
626C2×D3—82no—
627C2×D3—82no—
628C2×D3—82no—
629C2×D3—82no—
630C2×D3—82no—
631C3×C4—42no—
632C3×C4—42no—
633C3×C4#38011yescharacteristic
634C3×C4#38511yescharacteristic
635C3×C4#38811yescharacteristic
636C3×C4#39011yescharacteristic
637C3×C4#39411yescharacteristic
638C3×C4#39611yescharacteristic
639C3×C4#39711yescharacteristic
640C3×C4#39911yescharacteristic
641Dic3—44no—
642Dic3—82no—
643Dic3—82no—
644C23—64no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—122no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23—122no—
661C23—122no—
662C23—122no—
663C23—241no—
664C23—241no—
665C23—241no—
666C23—241no—
667C23—241no—
668C23—241no—
669C23—241no—
670C23—241no—
671C23—241no—
672C23—241no—
673C23—241no—
674C23—241no—
675C23—241no—
676C23—241no—
677C23—241no—
678C23—241no—
679C23C4×D1211yescharacteristic
680C23#87511yescharacteristic
681C23#88211yescharacteristic
682C23#88211yescharacteristic
683C23#89511yescharacteristic
684C23#89711yescharacteristic
685C23C2×#20411yescharacteristic
686C23C2×D2411yescharacteristic
687C23#90411yescharacteristic
688C23#90411yescharacteristic
689C23#90811yescharacteristic
690C23#90811yescharacteristic
691C23#90811yescharacteristic
692C23#90911yescharacteristic
693C23#93011yescharacteristic
694D4—64no—
695D4—64no—
696D4—122no—
697D4—122no—
698D4—122no—
699D4—122no—
700D4—122no—
701D4—122no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—64no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—241no—
730C2×C4—241no—
731C2×C4—241no—
732C2×C4—241no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4#87211yescharacteristic
738C2×C4#87611yescharacteristic
739C2×C4D3×C22⋊C411yescharacteristic
740C2×C4#67⋊C411yescharacteristic
741C2×C4#88311yescharacteristic
742C2×C4#88411yescharacteristic
743C2×C4#88411yescharacteristic
744C2×C4#88411yescharacteristic
745C2×C4#88411yescharacteristic
746C2×C4#88411yescharacteristic
747C2×C4#88511yescharacteristic
748C2×C4#88511yescharacteristic
749C2×C4D3×C4⋊C411yescharacteristic
750C2×C4#89311yescharacteristic
751C2×C4#89411yescharacteristic
752C2×C4#89411yescharacteristic
753C2×C4#89411yescharacteristic
754C2×C4#89611yescharacteristic
755C2×C4#89611yescharacteristic
756C2×C4#89611yescharacteristic
757C2×C4#89611yescharacteristic
758C2×C4#89811yescharacteristic
759C2×C4C4×#6711yescharacteristic
760C2×C4#92911yescharacteristic
761C2×C4#93711yescharacteristic
762C2×C4#93911yescharacteristic
763C2×C4#94011yescharacteristic
764C2×C4#94611yescharacteristic
765C8—42no—
766C8—42no—
767C2×C3#143911yescharacteristic
768C2×C3#186211yescharacteristic
769C2×C3#186411yescharacteristic
770C2×C3#187911yescharacteristic
771C2×C3#188011yescharacteristic
772C2×C3#193411yescharacteristic
773C2×C3#193611yescharacteristic
774C2×C3#199911yescharacteristic
775C2×C3#200011yescharacteristic
776C2×C3#202311yescharacteristic
777C2×C3#202511yescharacteristic
778C2×C3#204111yescharacteristic
779C2×C3#204211yescharacteristic
780C2×C3#206511yescharacteristic
781C2×C3#206711yescharacteristic
782D3—84no—
783C22—124no—
784C22—124no—
785C22—124no—
786C22—242no—
787C22—242no—
788C22—242no—
789C22—242no—
790C22—242no—
791C22—242no—
792C22—242no—
793C22—242no—
794C22—242no—
795C22—242no—
796C22—242no—
797C22—242no—
798C22#466511yescharacteristic
799C22#466811yescharacteristic
800C22#467211yescharacteristic
801C22#467311yescharacteristic
802C22C4×#20411yescharacteristic
803C22C4×D2411yescharacteristic
804C22#469411yescharacteristic
805C22#469711yescharacteristic
806C22#471011yescharacteristic
807C22#471111yescharacteristic
808C22#471311yescharacteristic
809C22#471411yescharacteristic
810C22#473111yescharacteristic
811C22#473211yescharacteristic
812C22#473211yescharacteristic
813C22#473311yescharacteristic
814C22#473411yescharacteristic
815C22#473411yescharacteristic
816C22#473411yescharacteristic
817C22#473811yescharacteristic
818C22#484211yescharacteristic
819C22#484311yescharacteristic
820C22#484411yescharacteristic
821C22#484511yescharacteristic
822C22#484611yescharacteristic
823C22#484711yescharacteristic
824C22#484711yescharacteristic
825C22#484811yescharacteristic
826C22#494011yescharacteristic
827C22#496011yescharacteristic
828C22#499411yescharacteristic
829C22#511411yescharacteristic
830C22#511511yescharacteristic
831C22#513411yescharacteristic
832C22#513511yescharacteristic
833C4—42no—
834C4—42no—
835C4—124no—
836C4—242no—
837C4—242no—
838C4#466711yescharacteristic
839C4#466911yescharacteristic
840C4#467511yescharacteristic
841C4#467611yescharacteristic
842C4#495711yescharacteristic
843C4#495911yescharacteristic
844C4#498911yescharacteristic
845C4#499311yescharacteristic
846C3#1106611yescharacteristic, complemented, Sylow
847C2—244no—
848C2#6862911yescharacteristic
849C2#6863011yescharacteristic
850C2#6867011yescharacteristic
851C2#6867111yescharacteristic
852C2#6867311yescharacteristic
853C2#6867811yescharacteristic
854C2#6867911yescharacteristic
855C2#6868611yescharacteristic
856C2#6942811yescharacteristic
857C2#6976811yescharacteristic
858C2#6981811yescharacteristic
859C2#6996111yescharacteristic
860C2#6996211yescharacteristic
861C2#7048311yescharacteristic
862C2#7048411yescharacteristic
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#11066
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×#4928C2semidirect
5. C2×C3×#336C2semidirect
6. C2×#4551C2semidirect
7. C2×#4551C2semidirect
25. C2×#821C4semidirect
39. C2×#336D3semidirect
227. C2×D12C4⋊C4semidirect
259. C4⋊Dic3C22⋊C4semidirect
846. C3#11066semidirect

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×#49282
C2×C3×#3362
C2×#45512
#110663