Finite Group Databasebeta

← #29714857

Subgroups — #29714857

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840485C211yesmaximal, characteristic, complemented
2C2×#16839977C211yesmaximal, characteristic
3C2×C4×#11758200C211yesmaximal, characteristic, complemented
4#21447065C211yesmaximal, characteristic, complemented
5#21447060C211yesmaximal, characteristic, complemented
6#21446901C211yesmaximal, characteristic, complemented
7#21446895C211yesmaximal, characteristic
8#21446756C211yesmaximal, characteristic, complemented
9#21446628C211yesmaximal, characteristic, complemented
10#21446177C211yesmaximal, characteristic, complemented
11#21446170C211yesmaximal, characteristic
12#21446086C211yesmaximal, characteristic, complemented
13#21446079C211yesmaximal, characteristic, complemented
14#21445831C211yesmaximal, characteristic, complemented
15C61×#2580C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19#16840485—24no—
20#16840485—24no—
21C2×#14519777C2211yescharacteristic
22C2×#14519772—21no—
23C2×#14519772—21no—
24C2×#14519765C2211yescharacteristic
25C2×#14519765C2211yescharacteristic
26C2×#14519753—21no—
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×Dic122C2211yescharacteristic
29C2×C4×D244C2211yescharacteristic
30C2×#14519735—21no—
31#16839977—24no—
32C4×#11758200—24no—
33C2×#14519708C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×C4×#92418C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#399—21no—
55C61×#393—21no—
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#389C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#385—21no—
61C61×#385—21no—
62C61×#382C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×Dic122C2311yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C4×D61—21no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—41no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519777—22no—
81#14519777—22no—
82#14519772—28no—
83#14519772—28no—
84#14519765—22no—
85#14519765—22no—
86#14519765—22no—
87#14519765D414yes—
88#14519753—28no—
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122—22no—
92C4×Dic122D414yes—
93C4×D244—22no—
94C4×D244—22no—
95#14519735—28no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108#14519708—22no—
109C4⋊#92418—22no—
110#14519700—22no—
111#14519700—22no—
112#14519700—22no—
113#14519700—41no—
114#14519700—41no—
115#14519700—41no—
116#14519698—22no—
117#14519697—22no—
118#14519697—22no—
119#14519697—41no—
120C4×#92418—22no—
121C22×Q8×C61D411yescharacteristic
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61—21no—
124C4×Q8×C61—22no—
125C4×Q8×C61—22no—
126C4×D4×C61—22no—
127C4×D4×C61—22no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61D411yescharacteristic
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C42×C61C2311yescharacteristic
142C2×C42×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61—21no—
149C23×D61—21no—
150C2×Q8×C61—22no—
151C2×Q8×C61—22no—
152C2×Q8×C61—41no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61#4112yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—42no—
163C22×C4×C61—81no—
164C22×C4×C61—81no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2411yescharacteristic
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244C2×D412yes—
181C2×C4×D61—24no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122C2×D412yes—
195C2×Dic122C2×D412yes—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61—22no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—81no—
206C4⋊C4×C61—81no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—81no—
211C22⋊C4×C61—81no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61C2×D412yes—
217C42×C61C2×D412yes—
218#11758200—28no—
219#11758200—44no—
220#11758199—44no—
221#11758198—24no—
222#11758198—24no—
223#11758198—24no—
224#11758198—24no—
225#11758198—24no—
226C4⋊Dic61—24no—
227C4⋊Dic61—24no—
228C4⋊Dic61—21no—
229C4⋊Dic61C2×D412yes—
230#11758196—24no—
231#11758196—24no—
232C4×Dic61—24no—
233C4×Dic61—24no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418#4112yes—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61C22×D411yescharacteristic
254C22×D61—22no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261Q8×C61—44no—
262D4×C61—22no—
263D4×C61—22no—
264D4×C61—41no—
265D4×C61—41no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—84no—
291C2×C4×C61#12012yes—
292C2×C4×C61#12012yes—
293C2×C4×C61#13512yes—
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C612−1+411yescharacteristic
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309D244—22no—
310D244—22no—
311D244—41no—
312D244—41no—
313C4×D61—48no—
314Dic122—22no—
315Dic122—22no—
316Dic122—22no—
317Dic122—22no—
318Dic122—41no—
319Dic122—41no—
320Dic122—41no—
321Dic122—41no—
322#92418—22no—
323#92418—41no—
324#92418—41no—
325#92418—41no—
326#24193—611nomaximal, Sylow
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61C2×#12011yescharacteristic
335C22×C61#54811yescharacteristic
336C22×C61#55011yescharacteristic
337C22×C61C2×#13511yescharacteristic
338C22×C61#57511yescharacteristic
339C22×C61#57711yescharacteristic
340C22×C61#57711yescharacteristic
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—81no—
345C2×D61—81no—
346C2×D61—81no—
347C2×D61—81no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61—81no—
355C4×C61—81no—
356C4×C61—81no—
357C4×C61#52511yescharacteristic
358C4×C61#53711yescharacteristic
359C4×C61#54611yescharacteristic
360C4×C61#54711yescharacteristic
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364C2×#556—611no—
365C2×#463—611no—
366C2×C4×SD16—611no—
367#2580D6111yescharacteristic, complemented
368#2043—611no—
369#2042—611no—
370#2013—611no—
371#2012—611no—
372#1984—611no—
373#1958—611no—
374#1880—611no—
375#1879—611no—
376#1865—611no—
377#1864—611no—
378#1805—611no—
379C2×C61—82no—
380C2×C61#240711yescharacteristic
381C2×C61#300211yescharacteristic
382C2×C61#301011yescharacteristic
383C2×C61#336011yescharacteristic
384C2×C61#337611yescharacteristic
385C2×C61#339411yescharacteristic
386C2×C61#340111yescharacteristic
387D61—82no—
388C22×SD16—611no—
389C22×SD16—611no—
390C22×D8—611no—
391#556—1224no—
392#556—1224no—
393C2×C4⋊Q8—611no—
394C2×#126—1221no—
395C2×#126—1221no—
396C2×#124—611no—
397C2×#124—611no—
398C2×C22⋊Q8—1221no—
399C2×C4×Q8—611no—
400C2×C4×Q8—611no—
401C2×C4×Q8C2×D6111yescharacteristic
402C2×C4×D4—611no—
403C2×C4×D4C2×D6111yescharacteristic
404C2×#117—1221no—
405#463—1224no—
406C4×SD16—1224no—
407C2×#106—611no—
408C2×C4⋊C8—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×C4×C8—611no—
420#399—21no—
421#393—21no—
422#390C2×D6111yescharacteristic
423#390C2×D6111yescharacteristic
424#389C2×D6111yescharacteristic
425#389C2×D6111yescharacteristic
426#385—21no—
427#385—21no—
428#382C2×D6111yescharacteristic
429#340—611no—
430#340—611no—
431#336—611no—
432#336—611no—
433#336—611no—
434#336—611no—
435C61#2419311yescharacteristic, complemented, Sylow
436C22×Q8—611no—
437C22×Q8—611no—
438C22×Q8C22⋊D6111yescharacteristic
439C22×D4—611no—
440C22×D4C22×D6111yescharacteristic
441C23×C4—21no—
442C23×C4—1221no—
443C2×SD16—1222no—
444C2×SD16—1222no—
445C2×SD16—1222no—
446C2×SD16—1222no—
447C2×SD16—1222no—
448C2×SD16—2441no—
449C2×D8—1222no—
450C2×D8—1222no—
451C2×D8—2441no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C4⋊Q8—1222no—
457C4⋊Q8—1222no—
458#126—1228no—
459#126—1228no—
460#124—614no—
461#124—1222no—
462#124—1222no—
463#124—1222no—
464C22⋊Q8—1228no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—614no—
468C4×Q8—1222no—
469C4×Q8—1222no—
470C4×Q8—1222no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—1222no—
474C4×D4—1222no—
475#117—1228no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4C22⋊D6111yescharacteristic
484C2×C4⋊C4C22⋊D6111yescharacteristic
485C2×C4⋊C4C22⋊D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42C22×D6111yescharacteristic
502C2×C42C22×D6111yescharacteristic
503C2×C42C22×D6111yescharacteristic
504#106—1222no—
505C4⋊C8—1222no—
506#103—1222no—
507#103—1222no—
508#103—1222no—
509#103—2441no—
510#103—2441no—
511#103—2441no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—2441no—
516C4×C8—1222no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521C24—21no—
522C24—1221no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—41no—
526C2×Q8—612no—
527C2×Q8—612no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—612no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4#1175822612yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—1224no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4C2×C22⋊D6111yescharacteristic
563C22×C4C2×C22⋊D6111yescharacteristic
564C22×C4C2×C22⋊D6111yescharacteristic
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C2×C22⋊D6111yescharacteristic
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C23×D6111yescharacteristic
569SD16—1228no—
570SD16—2444no—
571D8—2444no—
572C2×C8—612no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—81no—
594C4⋊C4—81no—
595C4⋊C4—612no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1224no—
599C4⋊C4—1221no—
600C4⋊C4—1224no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—1224no—
607C22⋊C4—1224no—
608C22⋊C4—1224no—
609C22⋊C4—1224no—
610C22⋊C4—1224no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—1224no—
616C42—1224no—
617C42D4×D6112yes—
618C42D4×D6112yes—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—1222no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23C22×C22⋊D6111yescharacteristic
634Q8—44no—
635Q8—1222no—
636Q8—1222no—
637Q8—1222no—
638Q8—1222no—
639Q8—2441no—
640Q8—2441no—
641Q8—2441no—
642Q8—2441no—
643D4—22no—
644D4—22no—
645D4—41no—
646D4—41no—
647D4—1222no—
648D4—1222no—
649D4—2441no—
650D4—2441no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—84no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—2448no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4#1451974512yes—
687C2×C4#1451974512yes—
688C2×C4#1451979712yes—
689C2×C4C2×D4×D6111yescharacteristic
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4#41×D6111yescharacteristic
692C2×C4C2×#1175822611yescharacteristic
693C2×C4#1451982311yescharacteristic
694C2×C4#1451982511yescharacteristic
695C8—1222no—
696C8—2441no—
697C8—2441no—
698C8—2441no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—4881no—
707C22—4881no—
708C22—4881no—
709C22—4881no—
710C22—2442no—
711C22—2442no—
712C22—2442no—
713C22C2×#1451974511yescharacteristic
714C22#1684042311yescharacteristic
715C22#1684043111yescharacteristic
716C22C2×#1451979711yescharacteristic
717C22#1684056011yescharacteristic
718C22#1684057311yescharacteristic
719C22#1684057311yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4—2442no—
730C4—2442no—
731C4—2442no—
732C4#1684027511yescharacteristic
733C4#1684034211yescharacteristic
734C4#1684040311yescharacteristic
735C4#1684041411yescharacteristic
736C2—82no—
737C2—4882no—
738C2#2144916611yescharacteristic
739C2#2145503511yescharacteristic
740C2#2145510311yescharacteristic
741C2#2145846811yescharacteristic
742C2#2145864611yescharacteristic
743C2#2145881111yescharacteristic
744C2#2145887911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2580C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2580D61
hypocenterC61#24193
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2580

Complements

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

NH ≅ G/Ntype
1. C2×#16840485C2semidirect
3. C2×C4×#11758200C2semidirect
4. #21447065C2semidirect
5. #21447060C2semidirect
6. #21446901C2semidirect
8. #21446756C2semidirect
9. #21446628C2semidirect
10. #21446177C2semidirect
12. #21446086C2semidirect
13. #21446079C2semidirect
14. #21445831C2semidirect
15. C61×#2580C2semidirect
367. #2580D61semidirect
435. C61#24193semidirect

Maximal subgroups

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

subgroupindex
C2×#168404852
C2×#168399772
C2×C4×#117582002
#214470652
#214470602
#214469012
#214468952
#214467562
#214466282
#214461772
#214461702
#214460862
#214460792
#214458312
C61×#25802
#2419361