Finite Group Databasebeta

← #10702246

Subgroups — #10702246

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
1C2×C3×#390C211yesmaximal, characteristic
2C22×#832C211yesmaximal, characteristic
3C22×#832C211yesmaximal, characteristic
4C2×#4928C211yesmaximal, characteristic, complemented
5C2×#4529C211yesmaximal, characteristic, complemented
6C2×#4529C211yesmaximal, characteristic, complemented
7C2×#4524C211yesmaximal, characteristic, complemented
8#11066—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C22×C3×C4⋊C4C2211yescharacteristic
11C22×C3×C22⋊C4—21no—
12C22×C3×C22⋊C4—21no—
13C22×C3×C42C2211yescharacteristic
14C22×C4⋊Dic3C2211yescharacteristic
15C22×C4⋊Dic3C2211yescharacteristic
16C22×Dic3⋊C4—21no—
17C23×C3⋊C8C2211yescharacteristic
18C23×C3⋊C8C2211yescharacteristic
19C3×#390—22no—
20C3×#390—22no—
21C2×#832—22no—
22C2×#832—22no—
23C2×#832—22no—
24C2×#832—22no—
25C2×#832—22no—
26C2×#832C414yescomplemented
27C2×C3⋊#95—21no—
28#4928—22no—
29#4928—22no—
30#4529—22no—
31#4529—22no—
32#4524—22no—
33C22×#102—31no—
34C22×#102—31no—
35C2×#390D311yescharacteristic
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×C4D411yescharacteristic
57C23×C3×C4D411yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×Dic3—21no—
60C23×Dic3—21no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4D412yes—
67C2×C3×C22⋊C4—24no—
68C2×C3×C22⋊C4—24no—
69C2×C3×C22⋊C4—42no—
70C2×C3×C22⋊C4—42no—
71C2×C3×C22⋊C4—42no—
72C2×C3×C22⋊C4—42no—
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×C4⋊Dic3—21no—
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⋊Dic3C2×C412yes—
88C2×C4⋊Dic3D412yes—
89C2×C4⋊Dic3D412yes—
90C2×C4⋊Dic3D412yes—
91C2×Dic3⋊C4—24no—
92C2×Dic3⋊C4—42no—
93C2×Dic3⋊C4—42no—
94C22×C3⋊C8—21no—
95C22×C3⋊C8—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⋊C8—21no—
103C22×C3⋊C8—21no—
104C22×C3⋊C8—21no—
105C22×C3⋊C8—21no—
106C22×C3⋊C8C2×C412yes—
107C22×C3⋊C8D412yes—
108#832—28no—
109#832—28no—
110C3⋊#95—24no—
111C23×D4C2×D311yescharacteristic
112C23×C8—31no—
113C23×C8—31no—
114C22×C4⋊C4—31no—
115C22×C4⋊C4—31no—
116C22×C4⋊C4—61no—
117C22×C4⋊C4C2×D311yescharacteristic
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C42C2×D311yescharacteristic
121C2×#102—34no—
122C2×#102—62no—
123C2×#102—62no—
124C2×#102—62no—
125C2×#102—62no—
126C2×#102—62no—
127#390—22no—
128#390—22no—
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—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—41no—
193C22×C3×C4—41no—
194C22×C3×C4—41no—
195C22×C3×C4—41no—
196C22×C3×C4—41no—
197C22×C3×C4—41no—
198C22×C3×C4D812yes—
199C22×C3×C4SD1612yes—
200C22×C3×C4C22×C411yescharacteristic
201C22×C3×C4C2×D411yescharacteristic
202C22×C3×C4C2×D411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×Q811yescharacteristic
208C22×C3×C4#4111yescharacteristic
209C22×C3×C4#4111yescharacteristic
210C22×C3×C4#4111yescharacteristic
211C22×C3×C4#4111yescharacteristic
212C22×C3×C4#4111yescharacteristic
213C22×C3×C4#4111yescharacteristic
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
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×Dic3—41no—
227C22×Dic3—41no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—41no—
232C3×C22⋊C4—48no—
233C3×C22⋊C4—48no—
234C3×C42—41no—
235C3×C42—41no—
236C3×C42—41no—
237C3×C42—41no—
238C4⋊Dic3—22no—
239C4⋊Dic3—22no—
240C4⋊Dic3—22no—
241C4⋊Dic3—22no—
242C4⋊Dic3—22no—
243C4⋊Dic3—41no—
244C4⋊Dic3—41no—
245C4⋊Dic3C22⋊C414yescomplemented
246Dic3⋊C4—48no—
247C2×C3⋊C8—22no—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8—22no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8—22no—
253C2×C3⋊C8—41no—
254C2×C3⋊C8—41no—
255C2×C3⋊C8—41no—
256C2×C3⋊C8—41no—
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×D4C4×D312yes—
275C22×D4#6712yes—
276C23×C4—21no—
277C23×C4—61no—
278C23×C4—61no—
279C23×C4#6711yescharacteristic
280C23×C4#6711yescharacteristic
281C23×C4C22×D311yescharacteristic
282C22×C8—32no—
283C22×C8—32no—
284C22×C8—61no—
285C22×C8—61no—
286C22×C8—61no—
287C22×C8—61no—
288C22×C8—61no—
289C22×C8—61no—
290C22×C8—61no—
291C22×C8—61no—
292C22×C8—61no—
293C22×C8—61no—
294C22×C8—61no—
295C22×C8—61no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—32no—
302C2×C4⋊C4—32no—
303C2×C4⋊C4—32no—
304C2×C4⋊C4—32no—
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—122no—
315C2×C4⋊C4—122no—
316C2×C4⋊C4#6712yes—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
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×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—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—81no—
408C2×C3×C4—81no—
409C2×C3×C4—81no—
410C2×C3×C4—81no—
411C2×C3×C4C2×C22⋊C411yescharacteristic
412C2×C3×C4C2×C4⋊C411yescharacteristic
413C2×C3×C4#11711yescharacteristic
414C2×C3×C4C4×D411yescharacteristic
415C2×C3×C4C4×D411yescharacteristic
416C2×C3×C4C4×D411yescharacteristic
417C2×C3×C4#12011yescharacteristic
418C2×C3×C4#12111yescharacteristic
419C2×C3×C4#12111yescharacteristic
420C2×C3×C4#12111yescharacteristic
421C2×C3×C4#12111yescharacteristic
422C2×C3×C4#12111yescharacteristic
423C2×C3×C4#12111yescharacteristic
424C2×C3×C4C22⋊Q811yescharacteristic
425C2×C3×C4C22⋊Q811yescharacteristic
426C2×C3×C4C22⋊Q811yescharacteristic
427C2×C3×C4C22⋊Q811yescharacteristic
428C2×C3×C4C22⋊Q811yescharacteristic
429C2×C3×C4#12311yescharacteristic
430C2×C3×C4#12311yescharacteristic
431C2×C3×C4#12311yescharacteristic
432C2×C3×C4#12311yescharacteristic
433C2×C3×C4#12311yescharacteristic
434C2×C3×C4#12411yescharacteristic
435C2×C3×C4#12411yescharacteristic
436C2×C3×C4#12611yescharacteristic
437C2×C3×C4#12611yescharacteristic
438C2×C3×C4#12711yescharacteristic
439C2×Dic3—24no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
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—
470C24C2×#6711yescharacteristic
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×D4Dic3⋊C414yescomplemented
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—22no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—62no—
519C22×C4—62no—
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#21312yes—
533C22×C4#21412yes—
534C22×C4C2×Dic611yescharacteristic
535C22×C4C2×C4×D311yescharacteristic
536C22×C4#23511yescharacteristic
537C22×C4#23511yescharacteristic
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4D3×D411yescharacteristic
541C22×C4D3×D411yescharacteristic
542C22×C4#23711yescharacteristic
543C22×C4#23711yescharacteristic
544C22×C4#23711yescharacteristic
545C22×C4#23711yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C2×C8—62no—
549C2×C8—62no—
550C2×C8—62no—
551C2×C8—62no—
552C2×C8—62no—
553C2×C8—62no—
554C2×C8—121no—
555C2×C8—121no—
556C2×C8—121no—
557C2×C8—121no—
558C2×C8—121no—
559C2×C8—121no—
560C2×C8—121no—
561C2×C8—121no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—34no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—62no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—128no—
573C4⋊C4—121no—
574C4⋊C4—121no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
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—42no—
632C3×C4—42no—
633C3×C4—82no—
634C3×C4#38011yescharacteristic
635C3×C4#38511yescharacteristic
636C3×C4#38811yescharacteristic
637C3×C4#39011yescharacteristic
638C3×C4#39411yescharacteristic
639C3×C4#39611yescharacteristic
640C3×C4#39711yescharacteristic
641C3×C4#39911yescharacteristic
642Dic3—44no—
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#92411yescharacteristic
680C23C4×#6711yescharacteristic
681C23C2×#21311yescharacteristic
682C23#93211yescharacteristic
683C23#93211yescharacteristic
684C23C2×#21411yescharacteristic
685C23#93611yescharacteristic
686C23#93711yescharacteristic
687C23#93811yescharacteristic
688C23#93911yescharacteristic
689C23#94911yescharacteristic
690C23#95011yescharacteristic
691C23#95011yescharacteristic
692C23#95111yescharacteristic
693C23#95311yescharacteristic
694D4—24no—
695D4—24no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
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—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—64no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4#87711yescharacteristic
738C2×C4#87811yescharacteristic
739C2×C4#87811yescharacteristic
740C2×C4#87811yescharacteristic
741C2×C4#87811yescharacteristic
742C2×C4#87911yescharacteristic
743C2×C4#87911yescharacteristic
744C2×C4D3×C22⋊C411yescharacteristic
745C2×C4#67⋊C411yescharacteristic
746C2×C4#67⋊C411yescharacteristic
747C2×C4#88311yescharacteristic
748C2×C4#88311yescharacteristic
749C2×C4#88411yescharacteristic
750C2×C4#88411yescharacteristic
751C2×C4#88511yescharacteristic
752C2×C4#88511yescharacteristic
753C2×C4C2×Dic3⋊C411yescharacteristic
754C2×C4#92411yescharacteristic
755C2×C4C4×#6711yescharacteristic
756C2×C4#92911yescharacteristic
757C2×C4#93511yescharacteristic
758C2×C4#93511yescharacteristic
759C2×C4#93711yescharacteristic
760C2×C4#93811yescharacteristic
761C2×C4#93911yescharacteristic
762C2×C4#93911yescharacteristic
763C2×C4#93911yescharacteristic
764C2×C4#94011yescharacteristic
765C8—122no—
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#494511yescharacteristic
799C22#494711yescharacteristic
800C22#494811yescharacteristic
801C22#495611yescharacteristic
802C22#500711yescharacteristic
803C22#500811yescharacteristic
804C22#500911yescharacteristic
805C22#500911yescharacteristic
806C22C4×#21311yescharacteristic
807C22#501411yescharacteristic
808C22C4×#21411yescharacteristic
809C22#501811yescharacteristic
810C22#503611yescharacteristic
811C22#503711yescharacteristic
812C22#503711yescharacteristic
813C22#503811yescharacteristic
814C22#503911yescharacteristic
815C22#504011yescharacteristic
816C22#504111yescharacteristic
817C22#504211yescharacteristic
818C22#505411yescharacteristic
819C22#505511yescharacteristic
820C22#505611yescharacteristic
821C22#505711yescharacteristic
822C22#507011yescharacteristic
823C22#507111yescharacteristic
824C22#507211yescharacteristic
825C22#507511yescharacteristic
826C22#521011yescharacteristic
827C22#521711yescharacteristic
828C22#521811yescharacteristic
829C22#522211yescharacteristic
830C22#522311yescharacteristic
831C22#523811yescharacteristic
832C22#523911yescharacteristic
833C4—42no—
834C4—42no—
835C4—82no—
836C4—124no—
837C4—242no—
838C4#494211yescharacteristic
839C4#494411yescharacteristic
840C4#494611yescharacteristic
841C4#494811yescharacteristic
842C4#494911yescharacteristic
843C4#495211yescharacteristic
844C4#495711yescharacteristic
845C4#495911yescharacteristic
846C3#1106611yescharacteristic, complemented, Sylow
847C2—84no—
848C2#6963811yescharacteristic
849C2#6963911yescharacteristic
850C2#6964411yescharacteristic
851C2#6964511yescharacteristic
852C2#6965211yescharacteristic
853C2#6965311yescharacteristic
854C2#6965711yescharacteristic
855C2#6966011yescharacteristic
856C2#7154711yescharacteristic
857C2#7160611yescharacteristic
858C2#7160711yescharacteristic
859C2#7168411yescharacteristic
860C2#7168511yescharacteristic
861C2#7172211yescharacteristic
862C2#7176211yescharacteristic
subgroupG/H
centerC24C2×#67
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#390C2
socleC24×C3C2×D4
prime radicalC23×C3×D4C22
cosocleC23×C3×C4C23
hypercenterC2×#390D3
hypocenterC3#11066
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#4928C2semidirect
5. C2×#4529C2semidirect
6. C2×#4529C2semidirect
7. C2×#4524C2semidirect
26. C2×#832C4semidirect
178. C2×C3×D4C4⋊C4semidirect
245. C4⋊Dic3C22⋊C4semidirect
498. C2×D4Dic3⋊C4semidirect
846. C3#11066semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3902
C22×#8322
C2×#49282
C2×#45292
C2×#45242
#110663