Finite Group Databasebeta

← #10702244

Subgroups — #10702244

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×C3×#102C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic
3C22×#832C211yesmaximal, characteristic
4C2×#4984C211yesmaximal, characteristic, complemented
5C2×#4551C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7C2×#4529C211yesmaximal, characteristic, complemented
8#11066—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×#217—21no—
13C22×#217—21no—
14C22×C4⋊Dic3—21no—
15C22×C4⋊Dic3C2211yescharacteristic
16C22×C4⋊Dic3C2211yescharacteristic
17C22×C4×Dic3C2211yescharacteristic
18C23×C3⋊C8C2211yescharacteristic
19C2×C3×#102—22no—
20C2×C3×#102—22no—
21C2×C3×#102C414yescomplemented
22#5221—22no—
23#5221—22no—
24C2×#832—22no—
25C2×#832—22no—
26C2×#832—22no—
27C2×C3⋊#95—21no—
28#4984—22no—
29#4984—22no—
30#4551—22no—
31#4550—22no—
32#4529—22no—
33C22×#102—31no—
34C22×#102D311yescharacteristic
35C2×#390—31no—
36C2×#389—31no—
37C2×#340—31no—
38C2×#340—31no—
39C2×#336—31no—
40C25×C3—21no—
41C22×C3×D4—21no—
42C22×C3×D4—21no—
43C22×C3×D4—21no—
44C22×C3×D4—21no—
45C22×C3×D4—21no—
46C22×C3×D4—21no—
47C22×C3×D4—21no—
48C22×C3×D4—21no—
49C22×C3×D4—21no—
50C22×C3×D4—21no—
51C22×C3×D4—21no—
52C22×C3×D4C2×C412yes—
53C22×C3×D4D412yes—
54C22×C3×D4Q812yes—
55C23×C3×C4—21no—
56C23×C3×C4C2311yescharacteristic
57C23×Dic3—21no—
58C23×Dic3—21no—
59C23×Dic3D411yescharacteristic
60C23×Dic3D411yescharacteristic
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×C8C2×C412yes—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4C2×C412yes—
72C2×C3×C4⋊C4D412yes—
73C2×C3×C4⋊C4D412yes—
74C2×#217—24no—
75C2×#217—24no—
76C2×#217—42no—
77C2×#217—42no—
78C2×#217—42no—
79C2×#217—42no—
80C2×C4⋊Dic3—21no—
81C2×C4⋊Dic3—21no—
82C2×C4⋊Dic3—21no—
83C2×C4⋊Dic3—21no—
84C2×C4⋊Dic3—21no—
85C2×C4⋊Dic3—21no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3—24no—
89C2×C4⋊Dic3—21no—
90C2×C4⋊Dic3—21no—
91C2×C4⋊Dic3—42no—
92C2×C4⋊Dic3—42no—
93C2×C4⋊Dic3D412yes—
94C2×C4⋊Dic3D412yes—
95C2×C4×Dic3—21no—
96C2×C4×Dic3—21no—
97C2×C4×Dic3—21no—
98C2×C4×Dic3—21no—
99C2×C4×Dic3—21no—
100C2×C4×Dic3—21no—
101C22×C3⋊C8—21no—
102C22×C3⋊C8—21no—
103C22×C3⋊C8—21no—
104C22×C3⋊C8—21no—
105C22×C3⋊C8—21no—
106C22×C3⋊C8—21no—
107C22×C3⋊C8D412yes—
108C3×#102—28no—
109#832—28no—
110C3⋊#95—24no—
111C23×D4C2×D311yescharacteristic
112C23×C8—31no—
113C23×C8C2×D311yescharacteristic
114C22×C4⋊C4—31no—
115C22×C4⋊C4—31no—
116C22×C4⋊C4—61no—
117C22×C4⋊C4C2×D311yescharacteristic
118C22×C22⋊C4—61no—
119C22×C22⋊C4—61no—
120C22×C42—31no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—62no—
124C2×#102—62no—
125C2×#102—62no—
126C2×#102Dic314yescomplemented
127#390—62no—
128#390—62no—
129#389—62no—
130#389—62no—
131C2×#95—61no—
132#340—62no—
133#340—62no—
134#336—62no—
135C24×C3—22no—
136C24×C3—22no—
137C24×C3—22no—
138C24×C3—41no—
139C24×C3—41no—
140C24×C3—41no—
141C24×C3—41no—
142C24×C3—41no—
143C24×C3—41no—
144C24×C3—41no—
145C24×C3—41no—
146C24×C3—41no—
147C24×C3—41no—
148C24×C3—41no—
149C24×C3—41no—
150C24×C3C2×D411yescharacteristic
151C2×C3×D4—22no—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—22no—
160C2×C3×D4—22no—
161C2×C3×D4—22no—
162C2×C3×D4—22no—
163C2×C3×D4—22no—
164C2×C3×D4—22no—
165C2×C3×D4—22no—
166C2×C3×D4—41no—
167C2×C3×D4—41no—
168C2×C3×D4—41no—
169C2×C3×D4—41no—
170C2×C3×D4—41no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4—41no—
175C2×C3×D4—41no—
176C2×C3×D4—41no—
177C2×C3×D4—41no—
178C2×C3×D4C4⋊C414yescomplemented
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—41no—
183C22×C3×C4—41no—
184C22×C3×C4—41no—
185C22×C3×C4—41no—
186C22×C3×C4C22×C411yescharacteristic
187C22×C3×C4C2×D411yescharacteristic
188C22×C3×C4C2×D411yescharacteristic
189C22×C3×C4C2×D411yescharacteristic
190C22×C3×C4C2×D411yescharacteristic
191C22×C3×C4C2×D411yescharacteristic
192C22×C3×C4C2×D411yescharacteristic
193C22×C3×C4C2×Q811yescharacteristic
194C22×C3×C4#4111yescharacteristic
195C22×C3×C4#4111yescharacteristic
196C22×C3×C4#4111yescharacteristic
197C22×C3×C4#4111yescharacteristic
198C22×C3×C4#4111yescharacteristic
199C22×C3×C4#4111yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—41no—
215C22×Dic3—41no—
216C22×Dic3—41no—
217C22×Dic3—41no—
218C22×Dic3—41no—
219C22×Dic3—41no—
220C22×Dic3—41no—
221C22×Dic3—41no—
222C22×Dic3—41no—
223C22×Dic3—41no—
224C22×Dic3—41no—
225C22×Dic3—41no—
226C22×Dic3D812yes—
227C22×Dic3SD1612yes—
228C2×C3×C8—22no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—41no—
232C2×C3×C8—41no—
233C2×C3×C8—41no—
234C2×C3×C8—41no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4C22⋊C414yescomplemented
239#217—48no—
240#217—48no—
241C4⋊Dic3—22no—
242C4⋊Dic3—22no—
243C4⋊Dic3—22no—
244C4⋊Dic3—22no—
245C4⋊Dic3—48no—
246C4⋊Dic3—41no—
247C4⋊Dic3—41no—
248C4⋊Dic3—41no—
249C4⋊Dic3—41no—
250C4×Dic3—41no—
251C4×Dic3—41no—
252C4×Dic3—41no—
253C4×Dic3—41no—
254C2×C3⋊C8—22no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—41no—
258C2×C3⋊C8—41no—
259C2×C3⋊C8—41no—
260C2×C3⋊C8—41no—
261C25—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4Dic612yes—
274C22×D4D1212yes—
275C22×D4C2×Dic312yes—
276C23×C4—21no—
277C23×C4—31no—
278C23×C4—31no—
279C23×C4—61no—
280C23×C4—61no—
281C23×C4C22×D311yescharacteristic
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—32no—
289C22×C8—61no—
290C22×C8—61no—
291C22×C8—61no—
292C22×C8—61no—
293C22×C8—61no—
294C22×C8—61no—
295C22×C8C2×Dic312yes—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
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—64no—
310C2×C4⋊C4—61no—
311C2×C4⋊C4—61no—
312C2×C4⋊C4—122no—
313C2×C4⋊C4—122no—
314C2×C4⋊C4C2×Dic312yes—
315C2×C4⋊C4#6712yes—
316C2×C4⋊C4#6712yes—
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—61no—
324C2×C42—61no—
325C2×C42—61no—
326C2×C42—61no—
327C2×C42—61no—
328C2×C42—61no—
329#102—28no—
330#102—68no—
331#95—64no—
332C23×C3—24no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—81no—
352C23×C3—81no—
353C23×C3—81no—
354C23×C3—81no—
355C23×C3—81no—
356C23×C3—81no—
357C23×C3—81no—
358C23×C3—81no—
359C23×C3—81no—
360C23×C3—81no—
361C23×C3—81no—
362C23×C3—81no—
363C23×C3—81no—
364C23×C3—81no—
365C23×C3—81no—
366C23×C3—81no—
367C23×C3C4×D411yescharacteristic
368C23×C3#12011yescharacteristic
369C23×C3#12011yescharacteristic
370C23×C3#12111yescharacteristic
371C23×C3#12111yescharacteristic
372C23×C3C22⋊Q811yescharacteristic
373C23×C3#12411yescharacteristic
374C23×C3C2×D811yescharacteristic
375C23×C3C2×SD1611yescharacteristic
376C23×C3#13511yescharacteristic
377C23×C3#13511yescharacteristic
378C23×C3AGL(1,ℤ/8)11yescharacteristic
379C23×C3AGL(1,ℤ/8)11yescharacteristic
380C23×C3AGL(1,ℤ/8)11yescharacteristic
381C23×C3#13711yescharacteristic
382C3×D4—24no—
383C3×D4—24no—
384C3×D4—42no—
385C3×D4—42no—
386C3×D4—42no—
387C3×D4—42no—
388C3×D4—42no—
389C3×D4—42no—
390C2×C3×C4—24no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4C2×C22⋊C411yescharacteristic
398C2×C3×C4C2×C4⋊C411yescharacteristic
399C2×C3×C4#11711yescharacteristic
400C2×C3×C4C4×D411yescharacteristic
401C2×C3×C4C4×D411yescharacteristic
402C2×C3×C4C4×D411yescharacteristic
403C2×C3×C4#12011yescharacteristic
404C2×C3×C4#12111yescharacteristic
405C2×C3×C4#12111yescharacteristic
406C2×C3×C4#12111yescharacteristic
407C2×C3×C4#12111yescharacteristic
408C2×C3×C4#12111yescharacteristic
409C2×C3×C4#12111yescharacteristic
410C2×C3×C4C22⋊Q811yescharacteristic
411C2×C3×C4C22⋊Q811yescharacteristic
412C2×C3×C4C22⋊Q811yescharacteristic
413C2×C3×C4C22⋊Q811yescharacteristic
414C2×C3×C4C22⋊Q811yescharacteristic
415C2×C3×C4#12311yescharacteristic
416C2×C3×C4#12311yescharacteristic
417C2×C3×C4#12311yescharacteristic
418C2×C3×C4#12311yescharacteristic
419C2×C3×C4#12311yescharacteristic
420C2×C3×C4#12411yescharacteristic
421C2×C3×C4#12411yescharacteristic
422C2×C3×C4#12611yescharacteristic
423C2×C3×C4#12611yescharacteristic
424C2×C3×C4#12711yescharacteristic
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—81no—
446C2×Dic3—81no—
447C2×Dic3—81no—
448C2×Dic3—81no—
449C2×Dic3—81no—
450C2×Dic3—81no—
451C2×Dic3—81no—
452C2×Dic3—81no—
453C3×C8—42no—
454C3⋊C8—42no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24—41no—
463C24—41no—
464C24—41no—
465C24—41no—
466C24—41no—
467C24—41no—
468C24—41no—
469C24—41no—
470C24D3×D411yescharacteristic
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4C4⋊Dic314yescomplemented
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
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—61no—
519C22×C4—61no—
520C22×C4—62no—
521C22×C4—62no—
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—121no—
533C22×C4—121no—
534C22×C4C2×Dic611yescharacteristic
535C22×C4C2×D1211yescharacteristic
536C22×C4#23511yescharacteristic
537C22×C4#23511yescharacteristic
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4D3×D411yescharacteristic
541C22×C4#23711yescharacteristic
542C22×C4#23711yescharacteristic
543C22×C4#23711yescharacteristic
544C22×C4#23711yescharacteristic
545C22×C4C22×Dic311yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—62no—
556C2×C8—62no—
557C2×C8—62no—
558C2×C8—121no—
559C2×C8—121no—
560C2×C8—121no—
561C2×C8—121no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—62no—
566C4⋊C4—62no—
567C4⋊C4—62no—
568C4⋊C4—62no—
569C4⋊C4—128no—
570C4⋊C4—121no—
571C4⋊C4—121no—
572C4⋊C4—121no—
573C4⋊C4—121no—
574C4⋊C4#21714yescomplemented
575C22⋊C4—128no—
576C22⋊C4—128no—
577C42—121no—
578C42—121no—
579C42—121no—
580C42—121no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—82no—
585C22×C3—82no—
586C22×C3—82no—
587C22×C3—82no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3—82no—
593C22×C3—82no—
594C22×C3—82no—
595C22×C3—82no—
596C22×C3#38511yescharacteristic
597C22×C3#38611yescharacteristic
598C22×C3#38811yescharacteristic
599C22×C3#39211yescharacteristic
600C22×C3#39311yescharacteristic
601C22×C3#39411yescharacteristic
602C22×C3#39611yescharacteristic
603C22×C3C4×D811yescharacteristic
604C22×C3C4×SD1611yescharacteristic
605C22×C3#44011yescharacteristic
606C22×C3#44211yescharacteristic
607C22×C3#44711yescharacteristic
608C22×C3#44711yescharacteristic
609C22×C3#44811yescharacteristic
610C22×C3#44911yescharacteristic
611C22×C3#44911yescharacteristic
612C22×C3#44911yescharacteristic
613C22×C3#45011yescharacteristic
614C22×C3#45211yescharacteristic
615C22×C3#45911yescharacteristic
616C22×C3#46011yescharacteristic
617C22×C3#46311yescharacteristic
618C22×C3#46411yescharacteristic
619C22×C3#46511yescharacteristic
620C22×C3#46611yescharacteristic
621C22×C3#46811yescharacteristic
622C22×C3#46911yescharacteristic
623C22×C3#47411yescharacteristic
624C22×C3#47611yescharacteristic
625C22×C3#47811yescharacteristic
626C22×C3#47811yescharacteristic
627C22×C3#48611yescharacteristic
628C22×C3#48811yescharacteristic
629C22×C3#48911yescharacteristic
630C22×C3#49011yescharacteristic
631C3×C4—44no—
632C3×C4#38011yescharacteristic
633C3×C4#38511yescharacteristic
634C3×C4#38811yescharacteristic
635C3×C4#39011yescharacteristic
636C3×C4#39411yescharacteristic
637C3×C4#39611yescharacteristic
638C3×C4#39711yescharacteristic
639C3×C4#39911yescharacteristic
640Dic3—42no—
641Dic3—42no—
642Dic3—82no—
643Dic3—82no—
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—81no—
664C23—81no—
665C23—81no—
666C23—81no—
667C23—81no—
668C23—81no—
669C23—81no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23—81no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23#87811yescharacteristic
680C23#88211yescharacteristic
681C23#88411yescharacteristic
682C23#88511yescharacteristic
683C23D3×D811yescharacteristic
684C23#91111yescharacteristic
685C23#91111yescharacteristic
686C23#91211yescharacteristic
687C23D3×SD1611yescharacteristic
688C23#91411yescharacteristic
689C23#91511yescharacteristic
690C23#91611yescharacteristic
691C23D4×Dic311yescharacteristic
692C23#93711yescharacteristic
693C23#93911yescharacteristic
694D4—24no—
695D4—24no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702C2×C4—24no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
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#87811yescharacteristic
738C2×C4#87811yescharacteristic
739C2×C4#87811yescharacteristic
740C2×C4#87911yescharacteristic
741C2×C4#87911yescharacteristic
742C2×C4#88211yescharacteristic
743C2×C4#88311yescharacteristic
744C2×C4#88311yescharacteristic
745C2×C4#88411yescharacteristic
746C2×C4#88511yescharacteristic
747C2×C4#88611yescharacteristic
748C2×C4#88611yescharacteristic
749C2×C4#92411yescharacteristic
750C2×C4#92411yescharacteristic
751C2×C4C2×C4⋊Dic311yescharacteristic
752C2×C4#92611yescharacteristic
753C2×C4#93011yescharacteristic
754C2×C4#93011yescharacteristic
755C2×C4D4×Dic311yescharacteristic
756C2×C4D4×Dic311yescharacteristic
757C2×C4D4×Dic311yescharacteristic
758C2×C4#93511yescharacteristic
759C2×C4#93611yescharacteristic
760C2×C4#93811yescharacteristic
761C2×C4#93811yescharacteristic
762C2×C4#93911yescharacteristic
763C2×C4#94011yescharacteristic
764C2×C4C2×#21711yescharacteristic
765C8—42no—
766C8—122no—
767C2×C3—84no—
768C2×C3#143911yescharacteristic
769C2×C3#186211yescharacteristic
770C2×C3#186411yescharacteristic
771C2×C3#187911yescharacteristic
772C2×C3#188011yescharacteristic
773C2×C3#193411yescharacteristic
774C2×C3#193611yescharacteristic
775C2×C3#199911yescharacteristic
776C2×C3#200011yescharacteristic
777C2×C3#202311yescharacteristic
778C2×C3#202511yescharacteristic
779C2×C3#204111yescharacteristic
780C2×C3#204211yescharacteristic
781C2×C3#206511yescharacteristic
782C2×C3#206711yescharacteristic
783C22—44no—
784C22—44no—
785C22—44no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22#475911yescharacteristic
799C22#476011yescharacteristic
800C22#476111yescharacteristic
801C22#476311yescharacteristic
802C22#476411yescharacteristic
803C22#476511yescharacteristic
804C22#476611yescharacteristic
805C22#476811yescharacteristic
806C22#477311yescharacteristic
807C22#477511yescharacteristic
808C22#477611yescharacteristic
809C22#477811yescharacteristic
810C22#478011yescharacteristic
811C22#478111yescharacteristic
812C22#478211yescharacteristic
813C22#478311yescharacteristic
814C22#494711yescharacteristic
815C22#494811yescharacteristic
816C22#495011yescharacteristic
817C22#495111yescharacteristic
818C22#496011yescharacteristic
819C22#496111yescharacteristic
820C22Dic3×D811yescharacteristic
821C22#515011yescharacteristic
822C22#515211yescharacteristic
823C22#515311yescharacteristic
824C22#515611yescharacteristic
825C22#515811yescharacteristic
826C22Dic3×SD1611yescharacteristic
827C22#516311yescharacteristic
828C22#516411yescharacteristic
829C22#516611yescharacteristic
830C22#517011yescharacteristic
831C22#517211yescharacteristic
832C22#522011yescharacteristic
833C4—44no—
834C4—122no—
835C4—122no—
836C4—242no—
837C4—242no—
838C4#494811yescharacteristic
839C4#494911yescharacteristic
840C4#495011yescharacteristic
841C4#495111yescharacteristic
842C4#495311yescharacteristic
843C4#496111yescharacteristic
844C4#521211yescharacteristic
845C4#522111yescharacteristic
846C3#1106611yescharacteristic, complemented, Sylow
847C2—84no—
848C2#7016311yescharacteristic
849C2#7016411yescharacteristic
850C2#7016811yescharacteristic
851C2#7017011yescharacteristic
852C2#7017711yescharacteristic
853C2#7017811yescharacteristic
854C2#7018511yescharacteristic
855C2#7018711yescharacteristic
856C2#7019311yescharacteristic
857C2#7019411yescharacteristic
858C2#7020411yescharacteristic
859C2#7020511yescharacteristic
860C2#7154611yescharacteristic
861C2#7203711yescharacteristic
862C2#7204811yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#102C2
socleC24×C3C2×D4
prime radicalC23×C3×D4C22
cosocleC23×C3×C4C23
hypercenterC22×#102D3
hypocenterC3#11066
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
4. C2×#4984C2semidirect
5. C2×#4551C2semidirect
6. C2×#4550C2semidirect
7. C2×#4529C2semidirect
21. C2×C3×#102C4semidirect
126. C2×#102Dic3semidirect
178. C2×C3×D4C4⋊C4semidirect
238. C3×C4⋊C4C22⋊C4semidirect
498. C2×D4C4⋊Dic3semidirect
574. C4⋊C4#217semidirect
846. C3#11066semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1022
C2×#52212
C22×#8322
C2×#49842
C2×#45512
C2×#45502
C2×#45292
#110663