Finite Group Databasebeta

← #10702997

Subgroups — #10702997

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
2C2×#4988C211yesmaximal, characteristic
3C22×#809C211yesmaximal, characteristic
4C2×C3×#340C211yesmaximal, characteristic, complemented
5C2×#4550C211yesmaximal, characteristic, complemented
6#71563C211yesmaximal, characteristic, complemented
7C2×#4529C211yesmaximal, characteristic, complemented
8#11189—31nomaximal, Sylow
9C23×D12C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×(C2×D3)⋊C4—21no—
14C22×(C2×D3)⋊C4—21no—
15C22×C4⋊Dic3C2211yescharacteristic
16C22×C4×Dic3C2211yescharacteristic
17C23×C3⋊C8C2211yescharacteristic
18C2×C3⋊#95—21no—
19C2×C3⋊#95—21no—
20C2×#821—22no—
21C2×#821—22no—
22C2×#821C414yescomplemented
23#4988—22no—
24#4988—22no—
25C2×#809—22no—
26C2×#809—22no—
27C2×#809—22no—
28C3×#340—22no—
29#4550—22no—
30#4529—22no—
31C22×#102—31no—
32C22×#102—31no—
33C2×#390—31no—
34C2×#340—31no—
35C2×#340D311yescharacteristic, complemented
36C2×#336—31no—
37C4⋊#95—31no—
38C24×D3—21no—
39C23×C3×C4—21no—
40C23×C3×C4—21no—
41C23×C3×C4C2311yescharacteristic
42C23×Dic3—21no—
43C23×Dic3D411yescharacteristic
44C23×Dic3D411yescharacteristic
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×C8C2×C412yes—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4D412yes—
77C2×C3×C4⋊C4D412yes—
78C2×(C2×D3)⋊C4—24no—
79C2×(C2×D3)⋊C4—24no—
80C2×(C2×D3)⋊C4—42no—
81C2×(C2×D3)⋊C4—42no—
82C2×(C2×D3)⋊C4—42no—
83C2×(C2×D3)⋊C4—42no—
84C2×C4⋊Dic3—21no—
85C2×C4⋊Dic3—21no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3—21no—
89C2×C4⋊Dic3C2×C412yes—
90C2×C4×Dic3—21no—
91C2×C4×Dic3—21no—
92C2×C4×Dic3—21no—
93C2×C4×Dic3—21no—
94C2×C4×Dic3—21no—
95C2×C4×Dic3—21no—
96C22×C3⋊C8—21no—
97C22×C3⋊C8—21no—
98C22×C3⋊C8—21no—
99C22×C3⋊C8—21no—
100C22×C3⋊C8—21no—
101C22×C3⋊C8—21no—
102C22×C3⋊C8D412yes—
103C3⋊#95—42no—
104C3⋊#95—42no—
105#821—28no—
106#809—28no—
107C23×D4—31no—
108C23×C8—31no—
109C23×C8C2×D311yescharacteristic
110C22×C4⋊C4—31no—
111C22×C4⋊C4C2×D311yescharacteristic
112C22×C4⋊C4C2×D311yescharacteristic
113C22×C22⋊C4—61no—
114C22×C22⋊C4—61no—
115C22×C42—31no—
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—22no—
127#340—62no—
128#336—62no—
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—22no—
146C22×C3×C4—22no—
147C22×C3×C4—41no—
148C22×C3×C4—41no—
149C22×C3×C4—41no—
150C22×C3×C4—41no—
151C22×C3×C4—41no—
152C22×C3×C4—41no—
153C22×C3×C4—41no—
154C22×C3×C4—41no—
155C22×C3×C4—41no—
156C22×C3×C4—41no—
157C22×C3×C4—41no—
158C22×C3×C4—41no—
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—21no—
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—22no—
186C22×Dic3—41no—
187C22×Dic3—41no—
188C22×Dic3—41no—
189C22×Dic3—41no—
190C22×Dic3—41no—
191C22×Dic3—41no—
192C22×Dic3D812yes—
193C22×Dic3SD1612yes—
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—41no—
226C2×C3×C8—41no—
227C2×C3×C8—41no—
228C2×C3×C8—41no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—41no—
237(C2×D3)⋊C4—48no—
238(C2×D3)⋊C4—48no—
239C4⋊Dic3—22no—
240C4⋊Dic3—22no—
241C4⋊Dic3—41no—
242C4⋊Dic3—41no—
243C4×Dic3—41no—
244C4×Dic3—41no—
245C4×Dic3—41no—
246C4×Dic3—41no—
247C2×C3⋊C8—22no—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8—41no—
251C2×C3⋊C8—41no—
252C2×C3⋊C8—41no—
253C2×C3⋊C8—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—21no—
270C23×C4—21no—
271C23×C4—31no—
272C23×C4—31no—
273C23×C4—61no—
274C23×C4C22×D311yescharacteristic
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—32no—
282C22×C8—61no—
283C22×C8—61no—
284C22×C8—61no—
285C22×C8—61no—
286C22×C8—61no—
287C22×C8—61no—
288C22×C8C4×D312yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—32no—
300C2×C4⋊C4—61no—
301C2×C4⋊C4—61no—
302C2×C4⋊C4—61no—
303C2×C4⋊C4—61no—
304C2×C4⋊C4—61no—
305C2×C4⋊C4D1212yes—
306C2×C4⋊C4#6712yes—
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—61no—
314C2×C42—61no—
315C2×C42—61no—
316C2×C42—61no—
317C2×C42—61no—
318C2×C42—61no—
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—42no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—81no—
380C2×C3×C4—81no—
381C2×C3×C4—81no—
382C2×C3×C4—81no—
383C2×C3×C4—81no—
384C2×C3×C4—81no—
385C2×C3×C4—81no—
386C2×C3×C4—81no—
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—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
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—
461C24D3×D411yescharacteristic
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—22no—
491C22×C4—22no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—62no—
519C22×C4—121no—
520C22×C4—121no—
521C22×C4—121no—
522C22×C4—121no—
523C22×C4—121no—
524C22×C4—121no—
525C22×C4C2×C4×D311yescharacteristic
526C22×C4C2×D1211yescharacteristic
527C22×C4#23511yescharacteristic
528C22×C4#23511yescharacteristic
529C22×C4#23511yescharacteristic
530C22×C4#23511yescharacteristic
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—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—62no—
547C2×C8—62no—
548C2×C8—62no—
549C2×C8—121no—
550C2×C8—121no—
551C2×C8—121no—
552C2×C8—121no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—62no—
562C4⋊C4—62no—
563C4⋊C4—121no—
564C4⋊C4—121no—
565C22⋊C4—128no—
566C22⋊C4—128no—
567C42—121no—
568C42—121no—
569C42—121no—
570C42—121no—
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—82no—
622C3×C4—82no—
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—42no—
632Dic3—42no—
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—
669C23#88211yescharacteristic
670C23#88411yescharacteristic
671C23#88411yescharacteristic
672C23#88511yescharacteristic
673C23#89311yescharacteristic
674C23#89411yescharacteristic
675C23D3×D811yescharacteristic
676C23#91111yescharacteristic
677C23D3×SD1611yescharacteristic
678C23#91411yescharacteristic
679C23#91411yescharacteristic
680C23#91611yescharacteristic
681C23#91811yescharacteristic
682C23#91911yescharacteristic
683C23#93911yescharacteristic
684D4—64no—
685D4—64no—
686D4—122no—
687D4—122no—
688D4—122no—
689D4—122no—
690D4—122no—
691D4—122no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4—241no—
726C2×C4—241no—
727C2×C4#87211yescharacteristic
728C2×C4C4×D1211yescharacteristic
729C2×C4#87511yescharacteristic
730C2×C4#87611yescharacteristic
731C2×C4D3×C22⋊C411yescharacteristic
732C2×C4#67⋊C411yescharacteristic
733C2×C4#88311yescharacteristic
734C2×C4#88311yescharacteristic
735C2×C4#88311yescharacteristic
736C2×C4#88411yescharacteristic
737C2×C4#88511yescharacteristic
738C2×C4#88611yescharacteristic
739C2×C4#89211yescharacteristic
740C2×C4#89411yescharacteristic
741C2×C4#89411yescharacteristic
742C2×C4#89411yescharacteristic
743C2×C4#89411yescharacteristic
744C2×C4#89511yescharacteristic
745C2×C4#89511yescharacteristic
746C2×C4#89811yescharacteristic
747C2×C4#89811yescharacteristic
748C2×C4#89811yescharacteristic
749C2×C4C4×#6711yescharacteristic
750C2×C4#92911yescharacteristic
751C2×C4#93011yescharacteristic
752C2×C4#93711yescharacteristic
753C2×C4#93811yescharacteristic
754C2×C4#94711yescharacteristic
755C8—42no—
756C8—122no—
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#466911yescharacteristic
790C22#467211yescharacteristic
791C22#467511yescharacteristic
792C22#476011yescharacteristic
793C22#476411yescharacteristic
794C22#477311yescharacteristic
795C22#477511yescharacteristic
796C22#477611yescharacteristic
797C22#478211yescharacteristic
798C22#478611yescharacteristic
799C22#478711yescharacteristic
800C22#479411yescharacteristic
801C22#480011yescharacteristic
802C22#480711yescharacteristic
803C22#480811yescharacteristic
804C22#481011yescharacteristic
805C22#481211yescharacteristic
806C22#481811yescharacteristic
807C22#481911yescharacteristic
808C22#485211yescharacteristic
809C22#486311yescharacteristic
810C22#486611yescharacteristic
811C22#486911yescharacteristic
812C22#487211yescharacteristic
813C22#488211yescharacteristic
814C22#488511yescharacteristic
815C22#488911yescharacteristic
816C22#495911yescharacteristic
817C22#496111yescharacteristic
818C22#499011yescharacteristic
819C22#515011yescharacteristic
820C22#516311yescharacteristic
821C22#516511yescharacteristic
822C22#518511yescharacteristic
823C4—82no—
824C4—82no—
825C4—122no—
826C4—122no—
827C4—242no—
828C4#466411yescharacteristic
829C4#467011yescharacteristic
830C4#467411yescharacteristic
831C4#467511yescharacteristic
832C4#494011yescharacteristic
833C4#495611yescharacteristic
834C4#499111yescharacteristic
835C4#499211yescharacteristic
836C3#1118911yescharacteristic, complemented, Sylow
837C2—244no—
838C2#6882211yescharacteristic
839C2#6882311yescharacteristic
840C2#6885211yescharacteristic
841C2#6885611yescharacteristic
842C2#6889611yescharacteristic
843C2#6889711yescharacteristic
844C2#6890211yescharacteristic
845C2#6890311yescharacteristic
846C2#6942911yescharacteristic
847C2#7017711yescharacteristic
848C2#7021211yescharacteristic
849C2#7024511yescharacteristic
850C2#7028011yescharacteristic
851C2#7056911yescharacteristic
852C2#7062311yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#340C2
socleC24×C3C2×D4
prime radicalC23×D12C22
cosocleC23×C3×C4C23
hypercenterC2×#340D3
hypocenterC3#11189
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×C3×#340C2semidirect
5. C2×#4550C2semidirect
6. #71563C2semidirect
7. C2×#4529C2semidirect
22. C2×#821C4semidirect
35. C2×#340D3semidirect
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×#49882
C22×#8092
C2×C3×#3402
C2×#45502
#715632
C2×#45292
#111893