Finite Group Databasebeta

← #29680117

Subgroups — #29680117

Order 15616.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840242C211yesmaximal, characteristic
2C2×#16839823C211yesmaximal, characteristic, complemented
3#21445907C211yesmaximal, characteristic, complemented
4#21445903C211yesmaximal, characteristic, complemented
5#21445831C211yesmaximal, characteristic, complemented
6#21445826C211yesmaximal, characteristic, complemented
7#21445821C211yesmaximal, characteristic, complemented
8#21445816C211yesmaximal, characteristic, complemented
9#21445757C211yesmaximal, characteristic
10#21445757C211yesmaximal, characteristic
11#21445652C211yesmaximal, characteristic, complemented
12#21445647C211yesmaximal, characteristic, complemented
13C4×#14519700C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2314C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17#16840242—24no—
18#16840242C418yescomplemented
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519737—21no—
24C2×#14519737—21no—
25C2×#14519735—21no—
26C22×C4⋊Dic61C2211yescharacteristic
27C2×C4⋊C4×D61—21no—
28#16839823—24no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519688C2211yescharacteristic
42C2×C4×#92418C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C61×#388—21no—
53C61×#388—21no—
54C61×#387—21no—
55C61×#387—21no—
56C61×#384C2211yescharacteristic
57C61×#382C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222C2×C414yes—
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C4×Dic122—22no—
80C4×Dic122—22no—
81C4×Dic122C2×C414yes—
82C4×Dic122C2×C414yes—
83C4×D244—22no—
84C4×D244—22no—
85C4×D244C2×C414yes—
86C4×D244C2×C414yes—
87#14519737—28no—
88#14519737—28no—
89#14519735—28no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61C2×C414yes—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C4⋊C4×D61—28no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C4⋊#92418—22no—
103C4⋊#92418—22no—
104#14519700—22no—
105#14519700—22no—
106#14519700—22no—
107#14519700—22no—
108#14519697—22no—
109#14519697—22no—
110#14519697—22no—
111#14519697—22no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114#14519688—22no—
115C4×#92418—22no—
116C23×C4×C61C2311yescharacteristic
117#117×C61C2×C414yes—
118#117×C61D414yes—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61D411yescharacteristic
122C2×C4⋊C4×C61D411yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61—21no—
132C2×C42×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C2×C42×C61C2311yescharacteristic
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140#95×C61—21no—
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C22×C412yes—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—24no—
160C2×C22⋊D61—24no—
161C2×C22⋊D61—24no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—24no—
166C22×Dic61—81no—
167C22×Dic61—81no—
168#11758222—28no—
169#11758222—28no—
170#11758222—28no—
171#11758222—28no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244C22×C412yes—
176C2×D244#4112yes—
177C2×D244#4112yes—
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61—24no—
183C2×C4×D61—81no—
184C2×C4×D61—81no—
185C2×C4×D61—81no—
186C2×C4×D61—81no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122C22×C412yes—
191C2×Dic122#4112yes—
192C2×Dic122#4112yes—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—81no—
202C4⋊C4×C61—81no—
203C4⋊C4×C61C22⋊C414yes—
204C4⋊C4×C61C22⋊C414yes—
205C22⋊C4×C61—81no—
206C22⋊C4×C61—81no—
207C22⋊C4×C61C22⋊C414yes—
208C22⋊C4×C61C22⋊C414yes—
209C42×C61—81no—
210C42×C61—81no—
211C42×C61C22×C412yes—
212C42×C61C22×C412yes—
213C42×C61C2×D412yes—
214C42×C61C2×D412yes—
215#11758198—24no—
216#11758198—24no—
217C4⋊Dic61—24no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61C22×C412yes—
221C4⋊Dic61C22×C412yes—
222#11758196—24no—
223#11758196—24no—
224C4×Dic61—24no—
225C4×Dic61—24no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61C2×C22⋊C412yes—
245C23×C61C22×D411yescharacteristic
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61C2×C22⋊C412yes—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C2×C22⋊C412yes—
282C2×C4×C61C2×C22⋊C412yes—
283C2×C4×C61C2×C22⋊C412yes—
284C2×C4×C61C23×C411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C22⋊D61—216no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—84no—
301D244—22no—
302D244—22no—
303D244—22no—
304D244#11714yes—
305C4×D61—216no—
306C4×D61—84no—
307C4×D61—84no—
308Dic122—22no—
309Dic122—22no—
310Dic122—22no—
311Dic122#11714yes—
312#92418—41no—
313#92418—41no—
314#92418—41no—
315#92418—41no—
316#20746—611nomaximal, Sylow
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61C22×C22⋊C411yescharacteristic
325C22×C61#52511yescharacteristic
326C22×C61#52511yescharacteristic
327C22×C61#57611yescharacteristic
328C22×C61#57711yescharacteristic
329C22×C61#57711yescharacteristic
330C22×C61#57811yescharacteristic
331C2×D61—24no—
332C2×D61—42no—
333C2×D61—42no—
334C2×D61—42no—
335C2×D61—42no—
336C2×D61—42no—
337C2×D61—42no—
338C4×C61—22no—
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—22no—
342C4×C61—22no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61C2×#11711yescharacteristic
348C4×C61C2×#11711yescharacteristic
349C4×C61#52511yescharacteristic
350C4×C61#52511yescharacteristic
351Dic61—24no—
352Dic61—42no—
353Dic61—42no—
354C2×#520—611no—
355C2×#433—611no—
356#2314D6111yescharacteristic, complemented
357#1824—611no—
358#1823—611no—
359#1805—611no—
360#1804—611no—
361#1803—611no—
362#1802—611no—
363#1788—611no—
364#1788—611no—
365#1763—611no—
366#1762—611no—
367C4×#103—611no—
368C4×#102—611no—
369C2×C61—42no—
370C2×C61#228011yescharacteristic
371C2×C61#289711yescharacteristic
372C2×C61#289811yescharacteristic
373C2×C61#311911yescharacteristic
374C2×C61#312011yescharacteristic
375C2×C61#312411yescharacteristic
376C2×C61#312511yescharacteristic
377D61—44no—
378C22×#41—611no—
379#520—618no—
380#520—1224no—
381C2×C4×Q8—611no—
382C2×C4×Q8—611no—
383C2×C4×D4—611no—
384C2×C4×D4—611no—
385C2×C4×D4—1221no—
386C2×C4×D4—1221no—
387C2×#117—1221no—
388C2×#117C2×D6111yescharacteristic
389C22×C4⋊C4—611no—
390C22×C4⋊C4—1221no—
391#433—1224no—
392C2×C4⋊C8—611no—
393C2×C4⋊C8—611no—
394C2×#103—611no—
395C2×#103—611no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#102—611no—
399C2×#102—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×C22⋊C8—611no—
403C2×C22⋊C8—611no—
404C2×#97—611no—
405C2×C4×C8—611no—
406#388—21no—
407#388—21no—
408#387—21no—
409#387—21no—
410#384C2×D6111yescharacteristic
411#382C2×D6111yescharacteristic
412#380C2×D6111yescharacteristic
413#380C2×D6111yescharacteristic
414C4×C4⋊C4C2×D6111yescharacteristic
415C4×C4⋊C4C2×D6111yescharacteristic
416#340—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#340—611no—
421#340—611no—
422#340—611no—
423#340—611no—
424C61#2074611yescharacteristic, complemented, Sylow
425C2×#41—614no—
426C2×#41—1222no—
427C2×#41—1222no—
428C2×#41—1222no—
429C2×#41—1222no—
430C2×#41—1222no—
431C22×Q8—611no—
432C22×D4—611no—
433C22×D4—1221no—
434C23×C4—1221no—
435C23×C4—1221no—
436C23×C4—1221no—
437C23×C4—1221no—
438C23×C4C22×D6111yescharacteristic
439C22×C8—611no—
440C22×C8—611no—
441C22×C8—611no—
442C22×C8—611no—
443C4×Q8—614no—
444C4×Q8—614no—
445C4×Q8—1222no—
446C4×Q8—1222no—
447C4×D4—614no—
448C4×D4—614no—
449C4×D4—1228no—
450C4×D4—1228no—
451C4×D4—1222no—
452C4×D4—1222no—
453#117—1228no—
454#117C4×D6114yes—
455#117D24414yes—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—614no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—1222no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1228no—
466C2×C4⋊C4C22⋊D6111yescharacteristic
467C2×C4⋊C4C22⋊D6111yescharacteristic
468C2×C4⋊C4C22×D6111yescharacteristic
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C4⋊C4C22×D6111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4C22⋊D6111yescharacteristic
477C2×C22⋊C4C22⋊D6111yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—1221no—
481C2×C42—1221no—
482C2×C42C22×D6111yescharacteristic
483C2×C42C22×D6111yescharacteristic
484C4⋊C8—1222no—
485C4⋊C8—1222no—
486#103—1222no—
487#103—1222no—
488#103—1222no—
489#103—1222no—
490#102—1222no—
491#102—1222no—
492#102—1222no—
493#102—1222no—
494C22⋊C8—1222no—
495C22⋊C8—1222no—
496#97—1222no—
497C4×C8—1222no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504C24—1221no—
505C24C2×C22⋊D6111yescharacteristic
506#41—1228no—
507#41—1228no—
508#41—1228no—
509#41—1228no—
510C2×Q8—612no—
511C2×Q8—612no—
512C2×Q8—612no—
513C2×Q8—1221no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×D4—612no—
517C2×D4—612no—
518C2×D4—612no—
519C2×D4—1224no—
520C2×D4—1224no—
521C2×D4—1224no—
522C2×D4—1221no—
523C2×D4—1221no—
524C2×D4—1221no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—1224no—
534C22×C4—1224no—
535C22×C4—1221no—
536C22×C4—1224no—
537C22×C4—1224no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1224no—
541C22×C4—1224no—
542C22×C4—4881no—
543C22×C4—4881no—
544C22×C4—4881no—
545C22×C4—4881no—
546C22×C4—4881no—
547C22×C4—4881no—
548C22×C4C2×C4×D6112yes—
549C22×C4C2×D24412yes—
550C22×C4C2×C22⋊D6111yescharacteristic
551C22×C4C2×C22⋊D6111yescharacteristic
552C22×C4C2×C22⋊D6111yescharacteristic
553C22×C4C2×C22⋊D6111yescharacteristic
554C22×C4C2×C22⋊D6111yescharacteristic
555C22×C4C23×D6111yescharacteristic
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—612no—
579C4⋊C4—612no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1224no—
583C4⋊C4—1224no—
584C4⋊C4—1224no—
585C4⋊C4#1175819814yes—
586C4⋊C4#1175819814yes—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—1224no—
590C22⋊C4—1224no—
591C22⋊C4#1175819814yes—
592C22⋊C4#1175819814yes—
593C42—81no—
594C42—81no—
595C42—1224no—
596C42—1224no—
597C42C2×C4×D6112yes—
598C42C2×C4×D6112yes—
599C42C2×D24412yes—
600C42C2×D24412yes—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—1222no—
608C23—1222no—
609C23—1222no—
610C23—2441no—
611C23—2441no—
612C23—2441no—
613C23—2441no—
614C23C2×#1175819812yes—
615C23C22×C22⋊D6111yescharacteristic
616Q8—614no—
617Q8—1222no—
618Q8—1222no—
619Q8—1222no—
620D4—614no—
621D4—12216no—
622D4—1222no—
623D4—1222no—
624D4—1222no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—12216no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—4884no—
658C2×C4—4884no—
659C2×C4—4884no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4C2×#1175819812yes—
665C2×C4C2×#1175819812yes—
666C2×C4C2×#1175819812yes—
667C2×C4C2×#1175819812yes—
668C2×C4C2×#1175819812yes—
669C2×C4C22×C4×D6111yescharacteristic
670C2×C4C22×D24411yescharacteristic
671C2×C4#41×D6111yescharacteristic
672C2×C4#41×D6111yescharacteristic
673C2×C4#41×D6111yescharacteristic
674C2×C4#41×D6111yescharacteristic
675C8—2441no—
676C8—2441no—
677C8—2441no—
678C8—2441no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—1224no—
687C22—2442no—
688C22—2442no—
689C22—2442no—
690C22—2442no—
691C22—2442no—
692C22—2442no—
693C22C22×#1175819811yescharacteristic
694C22#1684026911yescharacteristic
695C22#1684026911yescharacteristic
696C22#1684056511yescharacteristic
697C22#1684057011yescharacteristic
698C22#1684057311yescharacteristic
699C22#1684057711yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—1224no—
710C4—2442no—
711C4—2442no—
712C4#117×D6111yescharacteristic
713C4#117×D6111yescharacteristic
714C4#1684027411yescharacteristic
715C4#1684027411yescharacteristic
716C2—42no—
717C2—2444no—
718C2#2144819811yescharacteristic
719C2#2145434211yescharacteristic
720C2#2145434911yescharacteristic
721C2#2145601211yescharacteristic
722C2#2145602711yescharacteristic
723C2#2145607511yescharacteristic
724C2#2145609011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2314C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#2314D61
hypocenterC61#20746
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#16839823C2semidirect
3. #21445907C2semidirect
4. #21445903C2semidirect
5. #21445831C2semidirect
6. #21445826C2semidirect
7. #21445821C2semidirect
8. #21445816C2semidirect
11. #21445652C2semidirect
12. #21445647C2semidirect
13. C4×#14519700C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2314C2semidirect
18. #16840242C4semidirect
356. #2314D61semidirect
424. C61#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#168402422
C2×#168398232
#214459072
#214459032
#214458312
#214458262
#214458212
#214458162
#214457572
#214456522
#214456472
C4×#145197002
C4×#145196972
C61×#23142
#2074661