Finite Group Databasebeta

← #29586178

Subgroups — #29586178

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519708C211yesmaximal, characteristic
2C2×#16839524C211yesmaximal, characteristic
3C2×#16839524C211yesmaximal, characteristic
4C2×#16839524C211yesmaximal, characteristic
5C2×#16839517C211yesmaximal, characteristic
6#21444049C211yesmaximal, characteristic
7C2×C4×C4⋊C4×C61C211yesmaximal, characteristic
8C23×#92418C2211yescharacteristic
9C23×#92418C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C2×#14519708—22no—
13C2×#14519708—22no—
14C2×#14519708C414yescomplemented
15C2×#14519684—21no—
16C2×#14519684—21no—
17#16839524—22no—
18#16839524—22no—
19#16839524C414yescomplemented
20#16839517C414yescomplemented
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C42×C61—21no—
24C22×C42×C61C2211yescharacteristic
25C4×C4⋊C4×C61—22no—
26C4×C4⋊C4×C61—22no—
27C2×#95×C61—21no—
28C23×Dic61—21no—
29C23×Dic61—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35C22×#92418—21no—
36C22×#92418—21no—
37C22×#92418—21no—
38C22×#92418—21no—
39C22×#92418—21no—
40C22×#92418C2×C412yes—
41C22×#92418C2×C412yes—
42C22×#92418C2×C412yes—
43C22×#92418C2×C412yes—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61C2×C412yes—
55C2×C4⋊Dic61C2×C412yes—
56#14519708—28no—
57#14519684—42no—
58#14519684—42no—
59C23×C4×C61—21no—
60C23×C4×C61—21no—
61C23×C4×C61D411yescharacteristic
62C23×C4×C61D411yescharacteristic
63C23×C4×C61C2311yescharacteristic
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61C2×C412yes—
71C2×C4⋊C4×C61C2×C412yes—
72C2×C4⋊C4×C61D412yes—
73C2×C4⋊C4×C61D412yes—
74C2×C4⋊C4×C61D412yes—
75C2×C4⋊C4×C61Q812yes—
76C2×C42×C61—21no—
77C2×C42×C61—21no—
78C2×C42×C61—21no—
79C2×C42×C61—21no—
80C2×C42×C61—24no—
81C2×C42×C61—42no—
82C2×C42×C61—42no—
83C2×C42×C61C2×C412yes—
84C2×C42×C61Q812yes—
85#95×C61—24no—
86C24×C61C2×D411yescharacteristic
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—21no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61—41no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61C4⋊C412yes—
112C22×C4×C61C4⋊C412yes—
113C22×C4×C61SD1612yes—
114C22×C4×C61SD1612yes—
115C22×C4×C61C22×C411yescharacteristic
116C22×C4×C61C22×C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×Q811yescharacteristic
122C22×C4×C61C2×Q811yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61#4111yescharacteristic
126C22×C4×C61#4111yescharacteristic
127C22×C4×C61#4111yescharacteristic
128C22×C4×C61#4111yescharacteristic
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—41no—
132C22×Dic61—41no—
133C22×Dic61—41no—
134C22×Dic61—41no—
135C22×Dic61—41no—
136C22×Dic61—41no—
137C22×Dic61—41no—
138C22×Dic61—41no—
139C22×Dic61—41no—
140C22×Dic61—41no—
141C22×Dic61—41no—
142C22×Dic61—41no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61C22⋊C414yes—
150C4⋊C4×C61C4⋊C414yes—
151C42×C61—22no—
152C42×C61—22no—
153C42×C61—22no—
154C42×C61—22no—
155C42×C61—48no—
156C4⋊Dic61—22no—
157C4⋊Dic61—22no—
158C4⋊Dic61—22no—
159C4⋊Dic61—22no—
160C4⋊Dic61—41no—
161C4⋊Dic61—41no—
162C4⋊Dic61—41no—
163C4⋊Dic61—41no—
164C2×#92418—22no—
165C2×#92418—22no—
166C2×#92418—22no—
167C2×#92418—22no—
168C2×#92418—22no—
169C2×#92418—22no—
170C2×#92418—22no—
171C2×#92418—22no—
172C2×#92418—22no—
173C2×#92418—41no—
174C2×#92418—41no—
175C2×#92418—41no—
176C2×#92418—41no—
177C2×#92418C4214yescomplemented
178C23×C61C2×C4⋊C411yescharacteristic
179C23×C61C4×D411yescharacteristic
180C23×C61C4×D411yescharacteristic
181C23×C61#12011yescharacteristic
182C23×C61#12111yescharacteristic
183C23×C61C22⋊Q811yescharacteristic
184C23×C61#12311yescharacteristic
185C23×C61C2×SD1611yescharacteristic
186C23×C61C2×SD1611yescharacteristic
187C23×C61#13511yescharacteristic
188C23×C61#13511yescharacteristic
189C23×C61AGL(1,ℤ/8)11yescharacteristic
190C23×C61AGL(1,ℤ/8)11yescharacteristic
191C23×C61#13711yescharacteristic
192C23×C61#13711yescharacteristic
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—24no—
201C2×C4×C61—24no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—41no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—41no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61#10614yescomplemented
221C2×C4×C61C2×C4211yescharacteristic
222C2×C4×C61C2×C22⋊C411yescharacteristic
223C2×C4×C61C2×C4⋊C411yescharacteristic
224C2×C4×C61#11711yescharacteristic
225C2×C4×C61#11711yescharacteristic
226C2×C4×C61#11711yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C4×Q811yescharacteristic
234C2×C4×C61C4×Q811yescharacteristic
235C2×C4×C61C4×Q811yescharacteristic
236C2×C4×C61C4×Q811yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61C22⋊Q811yescharacteristic
239C2×C4×C61C22⋊Q811yescharacteristic
240C2×C4×C61C22⋊Q811yescharacteristic
241C2×C4×C61#12311yescharacteristic
242C2×C4×C61#12311yescharacteristic
243C2×C4×C61#12411yescharacteristic
244C2×C4×C61#12511yescharacteristic
245C2×C4×C61#12511yescharacteristic
246C2×C4×C61#12611yescharacteristic
247C2×C4×C61#12611yescharacteristic
248C2×C4×C61C4⋊Q811yescharacteristic
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—81no—
256C2×Dic61—81no—
257C2×Dic61—81no—
258C2×Dic61—81no—
259C2×Dic61—81no—
260C2×Dic61—81no—
261C2×Dic61—81no—
262C2×Dic61—81no—
263#92418—24no—
264#92418—42no—
265#10908—611nomaximal, Sylow
266C22×C61C4×C4⋊C411yescharacteristic
267C22×C61#38511yescharacteristic
268C22×C61#38511yescharacteristic
269C22×C61#38611yescharacteristic
270C22×C61#38711yescharacteristic
271C22×C61#38811yescharacteristic
272C22×C61#38911yescharacteristic
273C22×C61C2×#10611yescharacteristic
274C22×C61#42711yescharacteristic
275C22×C61#42811yescharacteristic
276C22×C61#42811yescharacteristic
277C22×C61C4×SD1611yescharacteristic
278C22×C61C4×SD1611yescharacteristic
279C22×C61C4×SD1611yescharacteristic
280C22×C61C4×SD1611yescharacteristic
281C22×C61#44011yescharacteristic
282C22×C61#44011yescharacteristic
283C22×C61#44111yescharacteristic
284C22×C61#44211yescharacteristic
285C22×C61#44811yescharacteristic
286C22×C61#44911yescharacteristic
287C22×C61#45011yescharacteristic
288C22×C61#45211yescharacteristic
289C22×C61#46011yescharacteristic
290C22×C61#46111yescharacteristic
291C22×C61#46311yescharacteristic
292C22×C61#46411yescharacteristic
293C22×C61#47511yescharacteristic
294C22×C61#47611yescharacteristic
295C22×C61#47811yescharacteristic
296C22×C61#47911yescharacteristic
297C22×C61#48111yescharacteristic
298C22×C61#48211yescharacteristic
299C22×C61#48311yescharacteristic
300C22×C61#48511yescharacteristic
301C4×C61—24no—
302C4×C61—42no—
303C4×C61—44no—
304C4×C61—44no—
305C4×C61C4×C22⋊C411yescharacteristic
306C4×C61C4×C4⋊C411yescharacteristic
307C4×C61#38711yescharacteristic
308C4×C61#38711yescharacteristic
309C4×C61#38711yescharacteristic
310C4×C61#38811yescharacteristic
311C4×C61#38911yescharacteristic
312C4×C61#39111yescharacteristic
313Dic61—82no—
314Dic61—82no—
315C22×#106—611no—
316C2×C4×C4⋊C4D6111yescharacteristic
317C2×#340—611no—
318C2×#340—611no—
319C2×#340—611no—
320C2×#336—611no—
321C4⋊#95—611no—
322C2×C61#143611yescharacteristic
323C2×C61C4×#10611yescharacteristic
324C2×C61#177611yescharacteristic
325C2×C61#185311yescharacteristic
326C2×C61#185411yescharacteristic
327C2×C61#186411yescharacteristic
328C2×C61#186511yescharacteristic
329C2×C61#187711yescharacteristic
330C2×C61#188011yescharacteristic
331C2×C61#191911yescharacteristic
332C2×C61#192011yescharacteristic
333C2×C61#192611yescharacteristic
334C2×C61#192711yescharacteristic
335C2×C61#194811yescharacteristic
336C2×C61#194911yescharacteristic
337C23×C8—611no—
338C23×C8—611no—
339C22×C4⋊C4—611no—
340C22×C4⋊C4—611no—
341C22×C4⋊C4C2×D6111yescharacteristic
342C22×C4⋊C4C2×D6111yescharacteristic
343C22×C42—21no—
344C22×C42C2×D6111yescharacteristic
345C2×#106—614no—
346C2×#106—1222no—
347C2×#106—1222no—
348C4×C4⋊C4—22no—
349C4×C4⋊C4—22no—
350C2×#95—21no—
351C2×#95—1221no—
352C2×#95—1221no—
353#340—614no—
354#340—1222no—
355#340—1222no—
356#336—614no—
357C61#1090811yescharacteristic, complemented, Sylow
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—1221no—
361C23×C4—1221no—
362C23×C4C22⋊D6111yescharacteristic
363C23×C4C22⋊D6111yescharacteristic
364C23×C4C22×D6111yescharacteristic
365C22×C8—612no—
366C22×C8—612no—
367C22×C8—612no—
368C22×C8—612no—
369C22×C8—1221no—
370C22×C8—1221no—
371C22×C8—1221no—
372C22×C8—1221no—
373C22×C8—1221no—
374C22×C8—1221no—
375C22×C8—1221no—
376C22×C8—1221no—
377C22×C8—1221no—
378C22×C8—1221no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—612no—
386C2×C4⋊C4—612no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4Dic12212yes—
398C2×C4⋊C4C4×D6112yes—
399C2×C4⋊C4C4×D6112yes—
400C2×C4⋊C4D24412yes—
401C2×C4⋊C4C22⋊D6112yes—
402C2×C4⋊C4C22⋊D6112yes—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—24no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42Dic12212yes—
411C2×C42C4×D6112yes—
412#106—1228no—
413#95—24no—
414#95—2442no—
415#95—2442no—
416C24C2×C22⋊D6111yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4—2441no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4—2441no—
454C22×C4—2441no—
455C22×C4#1175819612yes—
456C22×C4#1175819612yes—
457C22×C4#1175820012yes—
458C22×C4#1175820112yes—
459C22×C4C2×Dic12211yescharacteristic
460C22×C4C2×Dic12211yescharacteristic
461C22×C4C2×C4×D6111yescharacteristic
462C22×C4C2×C4×D6111yescharacteristic
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4C2×D24411yescharacteristic
465C22×C4#1175822211yescharacteristic
466C22×C4#1175822211yescharacteristic
467C22×C4#1175822211yescharacteristic
468C22×C4#1175822211yescharacteristic
469C22×C4#1175822211yescharacteristic
470C22×C4#1175822211yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472C22×C4C2×C22⋊D6111yescharacteristic
473C2×C8—614no—
474C2×C8—1222no—
475C2×C8—1222no—
476C2×C8—1222no—
477C2×C8—1222no—
478C2×C8—1222no—
479C2×C8—1222no—
480C2×C8—1222no—
481C2×C8—1222no—
482C2×C8—1222no—
483C2×C8—2441no—
484C2×C8—2441no—
485C2×C8—2441no—
486C2×C8—2441no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—2441no—
498C4⋊C4—2441no—
499C4⋊C4—2441no—
500C4⋊C4—2441no—
501C4⋊C4#1175819614yes—
502C4⋊C4#1175819814yes—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—48no—
508C23C2×#1175819611yescharacteristic
509C23C4×C22⋊D6111yescharacteristic
510C23C4×C22⋊D6111yescharacteristic
511C23#1451974611yescharacteristic
512C23#1451975111yescharacteristic
513C23#1451975611yescharacteristic
514C23#1451976011yescharacteristic
515C23C2×#1175820111yescharacteristic
516C23C2×#1175820011yescharacteristic
517C23#1451979711yescharacteristic
518C23#1451979711yescharacteristic
519C23#1451980211yescharacteristic
520C23#1451980311yescharacteristic
521C23#1451980711yescharacteristic
522C23#1451980811yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—4881no—
551C2×C4—4881no—
552C2×C4—4881no—
553C2×C4—4881no—
554C2×C4—4881no—
555C2×C4—4881no—
556C2×C4—4881no—
557C2×C4—4881no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4#1451970814yescomplemented
565C2×C4C42×D6111yescharacteristic
566C2×C4C2×#1175819811yescharacteristic
567C2×C4C2×#1175819611yescharacteristic
568C2×C4#1451973411yescharacteristic
569C2×C4#1451973411yescharacteristic
570C2×C4#1451973411yescharacteristic
571C2×C4C4×C22⋊D6111yescharacteristic
572C2×C4C4×C22⋊D6111yescharacteristic
573C2×C4C4×C22⋊D6111yescharacteristic
574C2×C4C4×C22⋊D6111yescharacteristic
575C2×C4C4×D24411yescharacteristic
576C2×C4C4×D24411yescharacteristic
577C2×C4C4×Dic12211yescharacteristic
578C2×C4C4×Dic12211yescharacteristic
579C2×C4C4×Dic12211yescharacteristic
580C2×C4C4×Dic12211yescharacteristic
581C2×C4#1451975111yescharacteristic
582C2×C4#1451975611yescharacteristic
583C2×C4#1451975611yescharacteristic
584C2×C4#1451975611yescharacteristic
585C2×C4#1451976011yescharacteristic
586C2×C4#1451976011yescharacteristic
587C2×C4#1451976511yescharacteristic
588C2×C4#1451976911yescharacteristic
589C2×C4#1451976911yescharacteristic
590C2×C4#1451977111yescharacteristic
591C2×C4#1451977111yescharacteristic
592C2×C4#1451977711yescharacteristic
593C8—1224no—
594C8—2442no—
595C22C4×#1175819611yescharacteristic
596C22#1683963511yescharacteristic
597C22#1683963511yescharacteristic
598C22#1683964111yescharacteristic
599C22#1683964611yescharacteristic
600C22#1683965311yescharacteristic
601C22#1683966011yescharacteristic
602C22C2×#1451970811yescharacteristic
603C22#1683979811yescharacteristic
604C22#1683980211yescharacteristic
605C22#1683980511yescharacteristic
606C22C4×#1175820011yescharacteristic
607C22C4×#1175820011yescharacteristic
608C22C4×#1175820111yescharacteristic
609C22C4×#1175820111yescharacteristic
610C22#1683986011yescharacteristic
611C22#1683986211yescharacteristic
612C22#1683986711yescharacteristic
613C22#1683987211yescharacteristic
614C22#1683990111yescharacteristic
615C22#1683990711yescharacteristic
616C22#1683991311yescharacteristic
617C22#1683992411yescharacteristic
618C22#1683996211yescharacteristic
619C22#1683996711yescharacteristic
620C22#1683997711yescharacteristic
621C22#1683998411yescharacteristic
622C22#1684004711yescharacteristic
623C22#1684005211yescharacteristic
624C22#1684006211yescharacteristic
625C22#1684006911yescharacteristic
626C22#1684008011yescharacteristic
627C22#1684008611yescharacteristic
628C22#1684009211yescharacteristic
629C22#1684010311yescharacteristic
630C4—24no—
631C4—44no—
632C4—42no—
633C4—44no—
634C4—4882no—
635C4—4882no—
636C4C4×#1175819811yescharacteristic
637C4C4×#1175819611yescharacteristic
638C4#1683964611yescharacteristic
639C4#1683964611yescharacteristic
640C4#1683964611yescharacteristic
641C4#1683965311yescharacteristic
642C4#1683966011yescharacteristic
643C4#1683966811yescharacteristic
644C2#2144405211yescharacteristic
645C2C4×#1451970811yescharacteristic
646C2#2144571711yescharacteristic
647C2#2144601211yescharacteristic
648C2#2144601811yescharacteristic
649C2#2144608011yescharacteristic
650C2#2144608711yescharacteristic
651C2#2144615311yescharacteristic
652C2#2144617411yescharacteristic
653C2#2144639711yescharacteristic
654C2#2144640411yescharacteristic
655C2#2144644611yescharacteristic
656C2#2144645311yescharacteristic
657C2#2144658211yescharacteristic
658C2#2144658711yescharacteristic
subgroupG/H
centerC24C2×C22⋊D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C4×C4⋊C4×C61C2
socle, prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#10908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. C2×#14519708C4semidirect
19. #16839524C4semidirect
20. #16839517C4semidirect
177. C2×#92418C42semidirect
220. C2×C4×C61#106semidirect
357. C61#10908semidirect
564. C2×C4#14519708semidirect

Maximal subgroups

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

subgroupindex
C22×#145197082
C2×#168395242
C2×#168395172
#214440492
C2×C4×C4⋊C4×C612
#1090861