Finite Group Databasebeta

← #29686714

Subgroups — #29686714

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840014C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C2×#16839714C211yesmaximal, characteristic, complemented
4C4×#14519752C211yesmaximal, characteristic, complemented
5C4×#14519748C211yesmaximal, characteristic, complemented
6#21446682C211yesmaximal, characteristic, complemented
7#21446546C211yesmaximal, characteristic, complemented
8#21446504C211yesmaximal, characteristic, complemented
9#21446500C211yesmaximal, characteristic, complemented
10#21446256C211yesmaximal, characteristic, complemented
11#21446254C211yesmaximal, characteristic, complemented
12#21445851C211yesmaximal, characteristic, complemented
13#21445717C211yesmaximal, characteristic, complemented
14#21445645C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519752C2211yescharacteristic
20C2×#14519748C2211yescharacteristic
21C2×C4×D244—21no—
22C2×C4×D244C2211yescharacteristic
23C2×C4×C22⋊D61—21no—
24C2×C42×D61C2211yescharacteristic
25#16840014C418yescomplemented
26#16839872—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34#16839714—24no—
35C2×#14519688C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839661C2211yescharacteristic
41#16839658C2211yescharacteristic
42#16839654—21no—
43#16839650—21no—
44#16839640—21no—
45#16839638—21no—
46#16839619C2211yescharacteristic
47#16839619C2211yescharacteristic
48C4×C4⋊Dic61C2211yescharacteristic
49C4×#11758198—21no—
50C4×C22⋊Dic61—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758199—22no—
70C2×#11758199—22no—
71C2×#11758199C2×C414yescomplemented
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—22no—
76C2×#11758189—22no—
77C2×#11758189C2×C414yescomplemented
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519752—22no—
81#14519752C2×C414yescomplemented
82#14519748—22no—
83#14519748C2×C414yescomplemented
84C4×D244—22no—
85C4×D244—22no—
86C4×D244—44no—
87C4×C22⋊D61—44no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C42×D61—22no—
107C42×D61—22no—
108#14519710—22no—
109#14519708—22no—
110#14519708C2×C414yescomplemented
111#14519699—22no—
112#14519699C2×C414yescomplemented
113#14519698—22no—
114#14519697—22no—
115#14519688D414yescomplemented
116C8×Dic61—22no—
117C8×Dic61—22no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#102×C61—22no—
136#102×C61C2×C414yescomplemented
137#97×C61—22no—
138#95×C61—21no—
139C24×C61—21no—
140C23×D61—21no—
141C23×D61C2×D411yescharacteristic
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C412yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—24no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—42no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—24no—
171C2×D244—21no—
172C2×D244—42no—
173C2×D244—42no—
174C2×D244C22×C412yes—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—41no—
184C2×C4×D61—41no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61C22×C412yes—
189C2×C4×D61#4112yes—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61C22×C412yes—
195C2×C8×C61#4112yes—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61C22×C412yes—
202C22⋊C4×C61—42no—
203C42×C61—42no—
204C42×C61C2×D412yes—
205C42×C61#4112yes—
206C22⋊Dic61—24no—
207C22⋊Dic61—42no—
208C22⋊Dic61—42no—
209#11758199—28no—
210#11758198—24no—
211#11758198—42no—
212#11758198—42no—
213#11758198—42no—
214#11758198—42no—
215#11758198—42no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—42no—
222C4⋊Dic61C22×C412yes—
223#11758196—42no—
224C4×Dic61—22no—
225C4×Dic61—22no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—42no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418C22×C412yes—
232C2×#92418C2×D412yes—
233C2×#92418C2×D412yes—
234C2×#92418#4112yes—
235#11758189—28no—
236#11758189—28no—
237C23×C61—22no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61C22×D411yescharacteristic
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—22no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61C4×D412yes—
259D4×C61—22no—
260D4×C61—22no—
261D4×C61—41no—
262D4×C61—41no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
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—84no—
277C2×C4×C61#12112yes—
278C2×C4×C61#12112yes—
279C2×C4×C61C23×C411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C22⋊D61—48no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—22no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61C4×D412yes—
302C2×Dic61AGL(1,ℤ/8)12yes—
303C2×Dic61AGL(1,ℤ/8)12yes—
304D244—22no—
305D244—22no—
306D244—48no—
307D244—41no—
308D244—41no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—44no—
314C4×D61—44no—
315C4×D61—84no—
316C8×C61—22no—
317C8×C61—22no—
318#92418—22no—
319#92418C4×D414yescomplemented
320#21538—611nomaximal, Sylow
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61C2×C4×D411yescharacteristic
329C22×C61C2×#12111yescharacteristic
330C22×C61#53211yescharacteristic
331C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C61#57511yescharacteristic
334C22×C61#57511yescharacteristic
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—81no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—81no—
353C4×C61—81no—
354C4×C61C2×C4×D411yescharacteristic
355C4×C61C4×#4111yescharacteristic
356C4×C61#52511yescharacteristic
357C4×C61#52911yescharacteristic
358Dic61—22no—
359Dic61—22no—
360Dic61—22no—
361Dic61—42no—
362Dic61—81no—
363Dic61—81no—
364C2×#469—611no—
365C2×#442—611no—
366C2×C4×M16—611no—
367C4×#121—611no—
368C4×#121—611no—
369#1970—611no—
370#1941—611no—
371#1934—611no—
372#1934—611no—
373#1895—611no—
374#1895—611no—
375#1809—611no—
376#1776—611no—
377#1762—611no—
378#1762D6111yescharacteristic, complemented
379C2×C61—82no—
380C2×C61C4×#12111yescharacteristic
381C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C61#305511yescharacteristic
384C2×C61#305511yescharacteristic
385C2×C61#318311yescharacteristic
386C2×C61#318411yescharacteristic
387D61—42no—
388D61—82no—
389C22×D8—611no—
390C22×M16—611no—
391C22×M16—611no—
392C2×#121—611no—
393C2×#121—611no—
394C2×C4×D4—611no—
395C2×C4×D4—1221no—
396C2×C4×D4—1221no—
397C2×C4×D4C2×D6111yescharacteristic
398C22×C42—611no—
399#469—618no—
400#442—1224no—
401C2×#107—611no—
402C2×#106—611no—
403C2×#106—611no—
404C2×#102—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×#102C2×D6111yescharacteristic
409C2×#102C2×D6111yescharacteristic
410C4×M16—1224no—
411C2×#97—611no—
412C2×#97C2×D6111yescharacteristic
413C2×C4×C8—611no—
414C2×C4×C8—611no—
415#390—611no—
416#390—611no—
417#389—611no—
418#389—611no—
419#388—1221no—
420#388—1221no—
421#386—1221no—
422#386—1221no—
423#380—611no—
424#380—611no—
425C4×C4⋊C4—611no—
426C4×C4⋊C4C2×D6111yescharacteristic
427C4×C22⋊C4—1221no—
428C4×C22⋊C4—1221no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340C2×D6111yescharacteristic
434#340C2×D6111yescharacteristic
435C61#2153811yescharacteristic, complemented, Sylow
436C22×D4—611no—
437C22×D4—1221no—
438C22×D4—1221no—
439C22×D4C22×D6111yescharacteristic
440C23×C4—21no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—1221no—
445C2×D8—614no—
446C2×D8—1222no—
447C2×D8—1222no—
448C2×M16—614no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8C22×D6111yescharacteristic
457C22×C8C22×D6111yescharacteristic
458#121—614no—
459#121—614no—
460#121—1222no—
461#121—1222no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—2444no—
467C4×D4—2444no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4C22×D6111yescharacteristic
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C42—21no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—1222no—
491C2×C42—1222no—
492C2×C42—1221no—
493C2×C42C22×D6111yescharacteristic
494#107—1222no—
495#106—614no—
496#106—1222no—
497#102—22no—
498#102—614no—
499#102—1222no—
500#102—1222no—
501#102—1222no—
502#102C4×D6114yescomplemented
503#97—22no—
504#97—614no—
505C4×C8—1222no—
506C4×C8—1222no—
507#95—21no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513C24—21no—
514C24—611no—
515C24—1221no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—612no—
522C2×D4—1224no—
523C2×D4—1224no—
524C2×D4—1221no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—2442no—
530C2×D4—2442no—
531C2×D4—2442no—
532C2×D4—2442no—
533C2×D4C2×C4×D6112yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—612no—
544C22×C4—612no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—2441no—
557C22×C4—2441no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4D4×D6111yescharacteristic
562C22×C4D4×D6111yescharacteristic
563C22×C4C23×D6111yescharacteristic
564D8—1228no—
565M16—1228no—
566M16—1228no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—612no—
572C2×C8—612no—
573C2×C8—612no—
574C2×C8—612no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8C2×C4×D6112yes—
578C2×C8#1175822212yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—612no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—2442no—
591C4⋊C4—2442no—
592C4⋊C4C2×C4×D6112yes—
593C22⋊C4—42no—
594C22⋊C4—1224no—
595C22⋊C4—1224no—
596C22⋊C4—2442no—
597C22⋊C4—2442no—
598C22⋊C4—2442no—
599C22⋊C4—2442no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C42—42no—
604C42—1221no—
605C42—1221no—
606C42—1222no—
607C42—1222no—
608C42—2442no—
609C42#1175822212yes—
610C42D4×D6112yes—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—612no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1222no—
626C23—2441no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23—2441no—
631C23—2441no—
632C23C2×D4×D6111yescharacteristic
633D4—22no—
634D4—22no—
635D4—41no—
636D4—41no—
637D4—1222no—
638D4—1222no—
639D4—2448no—
640D4—2448no—
641D4—2441no—
642D4—2441no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—84no—
657C2×C4—612no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—4884no—
672C2×C4—2444no—
673C2×C4—2444no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4#1451975012yes—
683C2×C4#1451975012yes—
684C2×C4C22×C4×D6111yescharacteristic
685C2×C4C2×D4×D6111yescharacteristic
686C2×C4#41×D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C2×C4C2×#1175822211yescharacteristic
689C2×C4C2×#1175822211yescharacteristic
690C8—22no—
691C8—22no—
692C8—614no—
693C8—1222no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—4881no—
705C22—4881no—
706C22—4881no—
707C22—4881no—
708C22—2442no—
709C22—2442no—
710C22—2442no—
711C22—2441no—
712C22—2441no—
713C22—2441no—
714C22—2441no—
715C22C4×D4×D6111yescharacteristic
716C22C2×#1451975011yescharacteristic
717C22#1684030911yescharacteristic
718C22AGL(1,ℤ/8)×D6111yescharacteristic
719C22AGL(1,ℤ/8)×D6111yescharacteristic
720C22#1684055811yescharacteristic
721C22#1684056111yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4—1222no—
728C4—1222no—
729C4—1222no—
730C4—4881no—
731C4—4881no—
732C4—2442no—
733C4C4×D4×D6111yescharacteristic
734C4C4×#1175822211yescharacteristic
735C4#1684027111yescharacteristic
736C4#1684029011yescharacteristic
737C2—82no—
738C2—4882no—
739C2—2442no—
740C2C4×#1451975011yescharacteristic
741C2#2145462411yescharacteristic
742C2#2145463011yescharacteristic
743C2#2145543611yescharacteristic
744C2#2145544111yescharacteristic
745C2#2145654411yescharacteristic
746C2#2145655411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#16840014C2
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#21538
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C2×#16839714C2semidirect
4. C4×#14519752C2semidirect
5. C4×#14519748C2semidirect
6. #21446682C2semidirect
7. #21446546C2semidirect
8. #21446504C2semidirect
9. #21446500C2semidirect
10. #21446256C2semidirect
11. #21446254C2semidirect
12. #21445851C2semidirect
13. #21445717C2semidirect
14. #21445645C2semidirect
15. C61×#1762C2semidirect
25. #16840014C4semidirect
71. C2×#11758199C2×C4semidirect
77. C2×#11758189C2×C4semidirect
81. #14519752C2×C4semidirect
83. #14519748C2×C4semidirect
110. #14519708C2×C4semidirect
112. #14519699C2×C4semidirect
115. #14519688D4semidirect
136. #102×C61C2×C4semidirect
319. #92418C4×D4semidirect
378. #1762D61semidirect
435. C61#21538semidirect
502. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400142
C2×#168398722
C2×#168397142
C4×#145197522
C4×#145197482
#214466822
#214465462
#214465042
#214465002
#214462562
#214462542
#214458512
#214457172
#214456452
C61×#17622
#2153861