Finite Group Databasebeta

← #29712641

Subgroups — #29712641

Order 15616.

1844 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D61C211yesmaximal, characteristic
2C2×#16840077C211yesmaximal, characteristic, complemented
3C2×#16840074C211yesmaximal, characteristic, complemented
4#380×D61C211yesmaximal, characteristic, complemented
5#21447002C211yesmaximal, characteristic, complemented
6#21447001C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446135C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446008C211yesmaximal, characteristic, complemented
11#21446005C211yesmaximal, characteristic, complemented
12#21445748C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445728C211yesmaximal, characteristic, complemented
15C61×#2033C211yesmaximal, characteristic, complemented
16C22×D4×D61—21no—
17C22×D4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519752C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519750—21no—
22C2×#14519749—21no—
23C2×#14519748C2211yescharacteristic
24#121×D61—24no—
25#121×D61—24no—
26C2×C4⋊C4×D61C2211yescharacteristic
27C2×C4⋊C4×D61C2211yescharacteristic, complemented
28C2×C4⋊C4×D61C2211yescharacteristic, complemented
29C2×C22⋊C4×D61—21no—
30C2×C22⋊C4×D61—21no—
31#16840077—24no—
32#16840074—24no—
33C2×#14519711C2211yescharacteristic, complemented
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519710C2211yescharacteristic, complemented
36C2×#14519699C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×#14519697C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic, complemented
42C2×C22⋊#92418C2211yescharacteristic, complemented
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic, complemented
46C2×#14519689C2211yescharacteristic, complemented
47#16839622C2211yescharacteristic, complemented
48#16839621—21no—
49#16839620—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52#95×D61—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C2×#121×C61C2211yescharacteristic
57C2×#107×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic, complemented
60C2×C22⋊C8×C61C2211yescharacteristic, complemented
61C61×#380C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C24×D61—21no—
64C24×D61D411yescharacteristic
65C22×D244—21no—
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C22⋊D61—21no—
70C2×D4×D61—28no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61—22no—
74C2×D4×D61—22no—
75C2×D4×D61—41no—
76C2×D4×D61—41no—
77C2×D4×D61—44no—
78C2×D4×D61—44no—
79C23×Dic61D411yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—41no—
88C22×C4×D61—41no—
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C22×C4×D61C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519752—22no—
96#14519752D414yes—
97#14519751—22no—
98#14519751—22no—
99#14519750—28no—
100#14519749—28no—
101#14519748—22no—
102#14519748D414yes—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C4⋊C4×D61—41no—
114C4⋊C4×D61—41no—
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C22⋊C4×D61—28no—
122C22⋊C4×D61—44no—
123#14519711—22no—
124#14519710—22no—
125#14519710—22no—
126#14519699—22no—
127#14519699—41no—
128#14519698—22no—
129#14519698—41no—
130#14519697—22no—
131#14519697—41no—
132C22⋊#92418—41no—
133#14519689—22no—
134#14519689—22no—
135#14519689—22no—
136#14519689—22no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140C22×D4×C61—21no—
141C22×D4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145#121×C61—22no—
146#121×C61—22no—
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152#107×C61—22no—
153#102×C61—22no—
154#102×C61—41no—
155C22⋊C8×C61—41no—
156#95×C61—21no—
157C24×C61—21no—
158C24×C61C2×D411yescharacteristic
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—24no—
164C23×D61—21no—
165C23×D61—41no—
166C23×D61—41no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61D814yes—
174C23×D61C2×D411yescharacteristic
175C23×D61C2×D411yescharacteristic
176C2×D4×C61—24no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61C2×D412yes—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—42no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C22×Dic61—21no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—41no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213D4×D61—44no—
214D4×D61—44no—
215D4×D61—44no—
216D4×D61—44no—
217D4×D61—432no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—24no—
223C2×D244—21no—
224C2×D244—42no—
225C2×D244—42no—
226C2×D244C2×D412yes—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—24no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—44no—
241C2×C4×D61—44no—
242C2×C4×D61—44no—
243C2×C4×D61—44no—
244C2×C4×D61—41no—
245C2×C4×D61—41no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61C2×D412yes—
255C2×C4×D61C2×D412yes—
256C2×C4×D61#4112yes—
257C2×C4×D61#4112yes—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61C2×D412yes—
270C22⋊C4×C61—24no—
271C22⋊C4×C61—42no—
272C22⋊Dic61—24no—
273C22⋊Dic61—42no—
274#11758198—24no—
275#11758198—24no—
276#11758198—42no—
277#11758198—42no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C2×D412yes—
284#11758196—24no—
285#11758196—42no—
286#11758196—42no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61C2×D812yes—
307C23×C61C22×D411yescharacteristic
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—28no—
317C22×D61—28no—
318C22×D61—22no—
319C22×D61—44no—
320C22×D61—44no—
321C22×D61—44no—
322C22×D61—44no—
323C22×D61—44no—
324C22×D61—48no—
325C22×D61—48no—
326C22×D61—48no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—84no—
334C22×D61—84no—
335C22×D61—84no—
336C22×D61—84no—
337C22×D61#12012yes—
338C22×D61#12312yes—
339C22×D61C2×D812yes—
340C22×D61C2×D812yes—
341C22×D61AGL(1,ℤ/8)12yes—
342C22×D61#13712yes—
343D4×C61—22no—
344D4×C61—22no—
345D4×C61—48no—
346D4×C61—41no—
347D4×C61—41no—
348C2×C4×C61—22no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C2×#4111yescharacteristic
367C2×C4×C61C2×#4111yescharacteristic
368C2×C4×C61H(5,𝔽2)11yescharacteristic
369C2×C4×C61H(5,𝔽2)11yescharacteristic
370C22⋊D61—48no—
371C22⋊D61—48no—
372C22⋊D61—48no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—22no—
378C2×Dic61—44no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61#12012yes—
388C2×Dic61#12312yes—
389D244—22no—
390D244—22no—
391D244—48no—
392D244—41no—
393D244—41no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—44no—
403C4×D61—44no—
404C4×D61—48no—
405C4×D61—84no—
406C4×D61—84no—
407C8×C61—41no—
408C8×C61—41no—
409#92418—41no—
410#92418—41no—
411#24002—611nomaximal, Sylow
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—81no—
423C22×C61—81no—
424C22×C61—81no—
425C22×C61—81no—
426C22×C61C2×#12011yescharacteristic
427C22×C61C2×#12311yescharacteristic
428C22×C61#53411yescharacteristic
429C22×C61C22×D811yescharacteristic
430C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C61C2×#13711yescharacteristic
432C22×C61#57511yescharacteristic
433C2×D61—22no—
434C2×D61—22no—
435C2×D61—22no—
436C2×D61—22no—
437C2×D61—22no—
438C2×D61—22no—
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—416no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—816no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61#44714yes—
455C2×D61#48014yescomplemented
456C4×C61—41no—
457C4×C61—42no—
458C4×C61—81no—
459C4×C61—81no—
460C4×C61#54611yescharacteristic
461C4×C61#54611yescharacteristic
462C4×C61#54611yescharacteristic
463C4×C61#54611yescharacteristic
464Dic61—22no—
465Dic61—22no—
466Dic61—42no—
467Dic61—81no—
468Dic61—81no—
469C22×#121—611no—
470C2×#480—611no—
471C2×#480—611no—
472C2×#380—611no—
473#2033—611no—
474#2033—611no—
475#2033—611no—
476#2033D6111yescharacteristic, complemented
477#1874—611no—
478#1874—611no—
479#1852—611no—
480#1852—611no—
481#1786—611no—
482#1786—611no—
483#1779—611no—
484C2×C61—42no—
485C2×C61—82no—
486C2×C61#240511yescharacteristic
487C2×C61C2×#44711yescharacteristic
488C2×C61#300711yescharacteristic
489C2×C61C2×#48011yescharacteristic
490C2×C61#309411yescharacteristic
491C2×C61#318611yescharacteristic
492C2×C61#319311yescharacteristic
493D61—24no—
494D61—24no—
495D61—82no—
496C23×D4—611no—
497C23×D4—1221no—
498C24×C4—611no—
499C2×#121—611no—
500C2×#121—611no—
501C2×#121—611no—
502C2×#121—1221no—
503C2×#121—1224no—
504C2×#121—1224no—
505C2×#121—1221no—
506C2×#121C2×D6111yescharacteristic
507C22×C4⋊C4—611no—
508C22×C4⋊C4—611no—
509C22×C4⋊C4—611no—
510C22×C22⋊C4—1221no—
511C22×C22⋊C4—1221no—
512#480—1224no—
513#480—1224no—
514C2×#107—611no—
515C2×#107—611no—
516C2×#107—611no—
517C2×#107C2×D6111yescharacteristic, complemented
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102C2×D6111yescharacteristic, complemented
525C2×#102C2×D6111yescharacteristic, complemented
526C2×C22⋊C8—611no—
527C2×C22⋊C8—611no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531C2×C22⋊C8C2×D6111yescharacteristic, complemented
532#380—611no—
533#380—611no—
534#380—611no—
535#380—1221no—
536#380—1221no—
537#380C2×D6111yescharacteristic, complemented
538C2×#95—1221no—
539#340—611no—
540#340—611no—
541#340—611no—
542#340C2×D6111yescharacteristic, complemented
543C61#2400211yescharacteristic, complemented, Sylow
544C25—611no—
545C25—1221no—
546C22×D4—21no—
547C22×D4—611no—
548C22×D4—1221no—
549C22×D4—1222no—
550C22×D4—1222no—
551C22×D4—1221no—
552C22×D4—1222no—
553C22×D4—1228no—
554C22×D4—1221no—
555C22×D4—1221no—
556C22×D4—1222no—
557C22×D4—2441no—
558C22×D4—2441no—
559C22×D4—2444no—
560C22×D4—2444no—
561C22×D4C22×D6111yescharacteristic
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—611no—
567C23×C4—1222no—
568C23×C4—1222no—
569C23×C4—1222no—
570C23×C4—1222no—
571C23×C4—1221no—
572C23×C4—1221no—
573C23×C4—1221no—
574C23×C4—2441no—
575C23×C4—2441no—
576C23×C4C22×D6111yescharacteristic
577C22×C8—611no—
578C22×C8—611no—
579C22×C8C22×D6111yescharacteristic
580C22×C8C22×D6111yescharacteristic
581#121—22no—
582#121—22no—
583#121—614no—
584#121—614no—
585#121—1228no—
586#121—1222no—
587#121—1222no—
588#121—1222no—
589#121—1222no—
590#121—1228no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—1222no—
595C2×C4⋊C4—1222no—
596C2×C4⋊C4—1222no—
597C2×C4⋊C4—1221no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—2441no—
602C2×C4⋊C4—2441no—
603C2×C4⋊C4C22×D6111yescharacteristic
604C2×C4⋊C4C22×D6111yescharacteristic
605C2×C4⋊C4C22×D6111yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—1228no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—2444no—
616#107—22no—
617#107—1222no—
618#107—1222no—
619#107—1222no—
620#102—22no—
621#102—41no—
622#102—1222no—
623#102—1222no—
624#102—1222no—
625#102—2441no—
626#102—2441no—
627#102—2441no—
628C22⋊C8—41no—
629C22⋊C8—1222no—
630C22⋊C8—1222no—
631C22⋊C8—1222no—
632C22⋊C8—1222no—
633C22⋊C8—2441no—
634#95—21no—
635#95—1221no—
636#95—1221no—
637#95—1221no—
638C24—21no—
639C24—611no—
640C24—611no—
641C24—614no—
642C24—1222no—
643C24—1222no—
644C24—1222no—
645C24—1222no—
646C24—1224no—
647C24—1221no—
648C24—2441no—
649C24—2441no—
650C24—2442no—
651C24—2442no—
652C24—2442no—
653C24—2442no—
654C24—2442no—
655C24—2442no—
656C24D4×D6111yescharacteristic
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—612no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—2442no—
676C2×D4—2442no—
677C2×D4—2442no—
678C2×D4—2444no—
679C2×D4—2444no—
680C2×D4—2444no—
681C2×D4—2444no—
682C2×D4—2442no—
683C2×D4—24432no—
684C2×D4—2442no—
685C2×D4—2442no—
686C2×D4—2442no—
687C2×D4—2442no—
688C2×D4D4×D6112yes—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1224no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—2441no—
723C22×C4—2441no—
724C22×C4—2444no—
725C22×C4—2444no—
726C22×C4—2444no—
727C22×C4—2444no—
728C22×C4—2442no—
729C22×C4—2442no—
730C22×C4—2442no—
731C22×C4—2442no—
732C22×C4—2442no—
733C22×C4—2442no—
734C22×C4—2442no—
735C22×C4—2442no—
736C22×C4—2441no—
737C22×C4D4×D6111yescharacteristic
738C22×C4C23×D6111yescharacteristic
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—612no—
757C4⋊C4—1224no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—2442no—
764C4⋊C4—2442no—
765C4⋊C4D4×D6112yes—
766C22⋊C4—24no—
767C22⋊C4—42no—
768C22⋊C4—1224no—
769C22⋊C4—1224no—
770C22⋊C4—1224no—
771C22⋊C4—2442no—
772C22⋊C4—2442no—
773C22⋊C4—2442no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—612no—
788C23—612no—
789C23—612no—
790C23—612no—
791C23—612no—
792C23—612no—
793C23—1228no—
794C23—1228no—
795C23—1221no—
796C23—1221no—
797C23—1221no—
798C23—1221no—
799C23—1221no—
800C23—1221no—
801C23—1221no—
802C23—1221no—
803C23—1222no—
804C23—4884no—
805C23—4884no—
806C23—4884no—
807C23—4884no—
808C23—2444no—
809C23—2444no—
810C23—2444no—
811C23—2444no—
812C23—2444no—
813C23—2448no—
814C23—2448no—
815C23—2448no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23D8×D6112yes—
823C23C2×D4×D6111yescharacteristic
824D4—22no—
825D4—22no—
826D4—48no—
827D4—41no—
828D4—41no—
829D4—1222no—
830D4—1222no—
831D4—2448no—
832D4—2448no—
833D4—2448no—
834D4—2448no—
835D4—2441no—
836D4—2441no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—612no—
854C2×C4—612no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—4884no—
869C2×C4—4884no—
870C2×C4—2444no—
871C2×C4—2444no—
872C2×C4—2448no—
873C2×C4—2444no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4C2×D4×D6111yescharacteristic
883C2×C4C2×D4×D6111yescharacteristic
884C2×C4#41×D6111yescharacteristic
885C2×C4#41×D6111yescharacteristic
886C2×C4#1451982211yescharacteristic
887C2×C4#1451982311yescharacteristic
888C8—41no—
889C8—41no—
890C8—2441no—
891C8—2441no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—614no—
907C22—614no—
908C22—1222no—
909C22—1222no—
910C22—1222no—
911C22—1222no—
912C22—1222no—
913C22—1222no—
914C22—1222no—
915C22—1222no—
916C22—1222no—
917C22—1222no—
918C22—1222no—
919C22—1222no—
920C22—48816no—
921C22—4881no—
922C22—4881no—
923C22—4881no—
924C22—4881no—
925C22—24416no—
926C22—2442no—
927C22—2442no—
928C22—2442no—
929C22#120×D6111yescharacteristic
930C22#123×D6111yescharacteristic
931C22#1684032011yescharacteristic
932C22C2×D8×D6111yescharacteristic
933C22AGL(1,ℤ/8)×D6111yescharacteristic
934C22#137×D6111yescharacteristic
935C22#1684055911yescharacteristic
936C4—42no—
937C4—41no—
938C4—81no—
939C4—81no—
940C4—1222no—
941C4—1222no—
942C4—4881no—
943C4—4881no—
944C4—2442no—
945C4#1684040111yescharacteristic
946C4#1684040411yescharacteristic
947C4#1684040511yescharacteristic
948C4#1684040911yescharacteristic
949C2—42no—
950C2—82no—
951C2—1224no—
952C2—1224no—
953C2—4882no—
954C2#2144914111yescharacteristic
955C2#447×D6111yescharacteristic
956C2#2145507611yescharacteristic
957C2#480×D6111yescharacteristic
958C2#2145575811yescharacteristic
959C2#2145656611yescharacteristic
960C2#2145662011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2033C2
socleC23×C61C22×D4
prime radicalC2×#121×D61C2
hypercenter#2033D61
hypocenterC61#24002
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#16840077C2semidirect
3. C2×#16840074C2semidirect
4. #380×D61C2semidirect
5. #21447002C2semidirect
6. #21447001C2semidirect
7. #21446998C2semidirect
8. #21446135C2semidirect
9. #21446133C2semidirect
10. #21446008C2semidirect
11. #21446005C2semidirect
12. #21445748C2semidirect
13. #21445748C2semidirect
14. #21445728C2semidirect
15. C61×#2033C2semidirect
27. C2×C4⋊C4×D61C22semidirect
28. C2×C4⋊C4×D61C22semidirect
33. C2×#14519711C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519710C22semidirect
36. C2×#14519699C22semidirect
37. C2×#14519699C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519698C22semidirect
40. C2×#14519697C22semidirect
41. C2×#14519697C22semidirect
42. C2×C22⋊#92418C22semidirect
45. C2×#14519689C22semidirect
46. C2×#14519689C22semidirect
47. #16839622C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
57. C2×#107×C61C22semidirect
58. C2×#102×C61C22semidirect
59. C2×#102×C61C22semidirect
60. C2×C22⋊C8×C61C22semidirect
61. C61×#380C22semidirect
62. C61×#340C22semidirect
455. C2×D61#480semidirect
476. #2033D61semidirect
517. C2×#107C2×D61semidirect
524. C2×#102C2×D61semidirect
525. C2×#102C2×D61semidirect
531. C2×C22⋊C8C2×D61semidirect
537. #380C2×D61semidirect
542. #340C2×D61semidirect
543. C61#24002semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D612
C2×#168400772
C2×#168400742
#380×D612
#214470022
#214470012
#214469982
#214461352
#214461332
#214460082
#214460052
#214457482
#214457282
C61×#20332
#2400261