Finite Group Databasebeta

← #29586181

Subgroups — #29586181

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×#14519709C211yesmaximal, characteristic
2C2×C4×C4⋊Dic61C211yesmaximal, characteristic
3C2×#16839525C211yesmaximal, characteristic
4C2×#16839525C211yesmaximal, characteristic
5C2×#16839525C211yesmaximal, characteristic
6#21444049C211yesmaximal, characteristic
7C2×C61×#336C211yesmaximal, characteristic
8C22×C4⋊Dic61C2211yescharacteristic
9C22×C4⋊Dic61C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×C4×Dic61—21no—
13C2×#14519709—22no—
14C2×#14519709—22no—
15C2×#14519709C414yescomplemented
16C4×C4⋊Dic61—22no—
17C4×C4⋊Dic61—22no—
18C2×#14519684—21no—
19C2×#14519684—21no—
20C2×#14519684—21no—
21#16839525—22no—
22#16839525—22no—
23#16839525C414yescomplemented
24C23×C8×C61C2211yescharacteristic
25C23×C8×C61C2211yescharacteristic
26C22×C42×C61C2211yescharacteristic
27C61×#336C414yescomplemented
28C23×Dic61—21no—
29C23×Dic61—21no—
30C23×Dic61—21no—
31C23×Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61C2×C412yes—
49C2×C4⋊Dic61C2×C412yes—
50C2×C4⋊Dic61C2×C412yes—
51C2×C4⋊Dic61C2×C412yes—
52C2×C4⋊Dic61D412yes—
53C2×C4⋊Dic61D412yes—
54C2×C4⋊Dic61D412yes—
55C2×C4⋊Dic61Q812yes—
56C2×C4×Dic61—24no—
57C2×C4×Dic61—42no—
58C2×C4×Dic61—42no—
59#14519709—28no—
60#14519684—24no—
61#14519684—42no—
62#14519684—42no—
63C23×C4×C61D411yescharacteristic
64C23×C4×C61D411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61—21no—
67C22×C8×C61—21no—
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C22×C8×C61—21no—
73C22×C8×C61—21no—
74C22×C8×C61—21no—
75C22×C8×C61—21no—
76C22×C8×C61C2×C412yes—
77C22×C8×C61C2×C412yes—
78C22×C8×C61C2×C412yes—
79C22×C8×C61C2×C412yes—
80C2×C42×C61—21no—
81C2×C42×C61—21no—
82C2×C42×C61—21no—
83C2×C42×C61—21no—
84C2×C42×C61C2×C412yes—
85C2×C42×C61Q812yes—
86C24×C61C2×D411yescharacteristic
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61C4⋊C412yes—
98C22×C4×C61C4⋊C412yes—
99C22×C4×C61SD1612yes—
100C22×C4×C61SD1612yes—
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×Q811yescharacteristic
108C22×C4×C61C2×Q811yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×Dic61—22no—
116C22×Dic61—22no—
117C22×Dic61—22no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—22no—
123C22×Dic61—41no—
124C22×Dic61—41no—
125C22×Dic61—41no—
126C22×Dic61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129C22×Dic61—41no—
130C22×Dic61—41no—
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—
143C2×C8×C61—22no—
144C2×C8×C61—22no—
145C2×C8×C61—22no—
146C2×C8×C61—22no—
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61—22no—
150C2×C8×C61—22no—
151C2×C8×C61—22no—
152C2×C8×C61—41no—
153C2×C8×C61—41no—
154C2×C8×C61—41no—
155C2×C8×C61—41no—
156C2×C8×C61C4214yescomplemented
157C42×C61—22no—
158C42×C61—22no—
159C42×C61—22no—
160C42×C61—22no—
161C4⋊Dic61—22no—
162C4⋊Dic61—22no—
163C4⋊Dic61—22no—
164C4⋊Dic61—22no—
165C4⋊Dic61—22no—
166C4⋊Dic61—22no—
167C4⋊Dic61—22no—
168C4⋊Dic61—22no—
169C4⋊Dic61—22no—
170C4⋊Dic61—22no—
171C4⋊Dic61—41no—
172C4⋊Dic61—41no—
173C4⋊Dic61—41no—
174C4⋊Dic61—41no—
175C4⋊Dic61C22⋊C414yes—
176C4⋊Dic61C4⋊C414yes—
177C4×Dic61—48no—
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—22no—
201C2×C4×C61—22no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61#10614yescomplemented
207C2×C4×C61C2×C4211yescharacteristic
208C2×C4×C61C2×C22⋊C411yescharacteristic
209C2×C4×C61C2×C4⋊C411yescharacteristic
210C2×C4×C61#11711yescharacteristic
211C2×C4×C61#11711yescharacteristic
212C2×C4×C61#11711yescharacteristic
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C4×Q811yescharacteristic
220C2×C4×C61C4×Q811yescharacteristic
221C2×C4×C61C4×Q811yescharacteristic
222C2×C4×C61C4×Q811yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61C22⋊Q811yescharacteristic
225C2×C4×C61C22⋊Q811yescharacteristic
226C2×C4×C61C22⋊Q811yescharacteristic
227C2×C4×C61#12311yescharacteristic
228C2×C4×C61#12311yescharacteristic
229C2×C4×C61#12411yescharacteristic
230C2×C4×C61#12511yescharacteristic
231C2×C4×C61#12511yescharacteristic
232C2×C4×C61#12611yescharacteristic
233C2×C4×C61#12611yescharacteristic
234C2×C4×C61C4⋊Q811yescharacteristic
235C2×Dic61—24no—
236C2×Dic61—24no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
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—
263C8×C61—24no—
264C8×C61—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×C61C4×C22⋊C411yescharacteristic
304C4×C61C4×C4⋊C411yescharacteristic
305C4×C61#38711yescharacteristic
306C4×C61#38711yescharacteristic
307C4×C61#38711yescharacteristic
308C4×C61#38811yescharacteristic
309C4×C61#38911yescharacteristic
310C4×C61#39111yescharacteristic
311Dic61—44no—
312Dic61—44no—
313Dic61—82no—
314Dic61—82no—
315C22×#106—611no—
316C2×C4×C4⋊C4—611no—
317C2×#340—611no—
318C2×#340—611no—
319C2×#340—611no—
320C2×#336D6111yescharacteristic
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×C8C2×D6111yescharacteristic
338C23×C8C2×D6111yescharacteristic
339C22×C4⋊C4—611no—
340C22×C4⋊C4—611no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—611no—
343C22×C42—1221no—
344C22×C42C2×D6111yescharacteristic
345C2×#106—614no—
346C2×#106—1222no—
347C2×#106—1222no—
348C4×C4⋊C4—1222no—
349C4×C4⋊C4—1222no—
350C2×#95—1221no—
351C2×#95—1221no—
352C2×#95—1221no—
353#340—614no—
354#340—1222no—
355#340—1222no—
356#336Dic6114yescomplemented
357C61#1090811yescharacteristic, complemented, Sylow
358C23×C4—1221no—
359C23×C4—1221no—
360C23×C4—1221no—
361C23×C4—1221no—
362C23×C4D24411yescharacteristic
363C23×C4D24411yescharacteristic
364C23×C4C22×D6111yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8C4×D6112yes—
376C22×C8C4×D6112yes—
377C22×C8C2×Dic6112yes—
378C22×C8C2×Dic6112yes—
379C2×C4⋊C4—612no—
380C2×C4⋊C4—612no—
381C2×C4⋊C4—612no—
382C2×C4⋊C4—612no—
383C2×C4⋊C4—612no—
384C2×C4⋊C4—612no—
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⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—1224no—
408C2×C42—2442no—
409C2×C42—2442no—
410C2×C42Dic12212yes—
411C2×C42C2×Dic6112yes—
412#106—1228no—
413#95—1224no—
414#95—2442no—
415#95—2442no—
416C24C2×D24411yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—2441no—
436C22×C4—2441no—
437C22×C4—2441no—
438C22×C4—2441no—
439C22×C4—2441no—
440C22×C4—2441no—
441C22×C4—2441no—
442C22×C4—2441no—
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#1175819012yes—
456C22×C4#1175819012yes—
457C22×C4C4⋊Dic6112yes—
458C22×C4C4⋊Dic6112yes—
459C22×C4C2×Dic12211yescharacteristic
460C22×C4C2×C4×D6111yescharacteristic
461C22×C4C2×C4×D6111yescharacteristic
462C22×C4#1175822211yescharacteristic
463C22×C4#1175822211yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C22×C4D4×D6111yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4#1175822411yescharacteristic
468C22×C4#1175822411yescharacteristic
469C22×C4#1175822411yescharacteristic
470C22×C4Q8×D6111yescharacteristic
471C22×C4#1175822611yescharacteristic
472C22×C4C22×Dic6111yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8C4×Dic6114yescomplemented
487C4⋊C4—614no—
488C4⋊C4—614no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—2441no—
500C4⋊C4—2441no—
501C4⋊C4—2441no—
502C4⋊C4—2441no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—2448no—
508C23C2×C4⋊Dic6111yescharacteristic
509C23C4×D24411yescharacteristic
510C23C4×D24411yescharacteristic
511C23#1451974711yescharacteristic
512C23#1451975211yescharacteristic
513C23#1451975711yescharacteristic
514C23#1451976111yescharacteristic
515C23C2×#1175819011yescharacteristic
516C23C2×#1175819011yescharacteristic
517C23#1451979911yescharacteristic
518C23#1451979911yescharacteristic
519C23#1451980511yescharacteristic
520C23#1451980511yescharacteristic
521C23#1451981011yescharacteristic
522C23#1451981011yescharacteristic
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—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—1224no—
537C2×C4—1224no—
538C2×C4—4881no—
539C2×C4—4881no—
540C2×C4—4881no—
541C2×C4—4881no—
542C2×C4—4881no—
543C2×C4—4881no—
544C2×C4—4881no—
545C2×C4—4881no—
546C2×C4—2442no—
547C2×C4—2442no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4—2442no—
556C2×C4—2442no—
557C2×C4—2442no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4#1451970914yescomplemented
565C2×C4C2×C4×Dic6111yescharacteristic
566C2×C4C22⋊C4×D6111yescharacteristic
567C2×C4C4⋊C4×D6111yescharacteristic
568C2×C4#1451973311yescharacteristic
569C2×C4#1451973511yescharacteristic
570C2×C4#1451973611yescharacteristic
571C2×C4#1451973711yescharacteristic
572C2×C4#1451973711yescharacteristic
573C2×C4#1451973911yescharacteristic
574C2×C4D4×Dic6111yescharacteristic
575C2×C4D4×Dic6111yescharacteristic
576C2×C4D4×Dic6111yescharacteristic
577C2×C4#1451974211yescharacteristic
578C2×C4C4×Dic12211yescharacteristic
579C2×C4C4×Dic12211yescharacteristic
580C2×C4Q8×Dic6111yescharacteristic
581C2×C4#1451975011yescharacteristic
582C2×C4#1451975411yescharacteristic
583C2×C4#1451975411yescharacteristic
584C2×C4#1451975511yescharacteristic
585C2×C4#1451975911yescharacteristic
586C2×C4#1451976211yescharacteristic
587C2×C4#1451976311yescharacteristic
588C2×C4#1451976711yescharacteristic
589C2×C4#1451976811yescharacteristic
590C2×C4#1451977011yescharacteristic
591C2×C4#1451977211yescharacteristic
592C2×C4#1451977611yescharacteristic
593C8—24no—
594C8—42no—
595C22C4×C4⋊Dic6111yescharacteristic
596C22#1683963611yescharacteristic
597C22#1683963711yescharacteristic
598C22#1683964011yescharacteristic
599C22#1683964711yescharacteristic
600C22#1683965411yescharacteristic
601C22#1683966111yescharacteristic
602C22C2×#1451970911yescharacteristic
603C22#1683980011yescharacteristic
604C22#1683980411yescharacteristic
605C22#1683980411yescharacteristic
606C22C4×#1175819011yescharacteristic
607C22C4×#1175819011yescharacteristic
608C22C4×#1175819011yescharacteristic
609C22C4×#1175819011yescharacteristic
610C22#1683986411yescharacteristic
611C22#1683986411yescharacteristic
612C22#1683987011yescharacteristic
613C22#1683987511yescharacteristic
614C22#1683990311yescharacteristic
615C22#1683990911yescharacteristic
616C22#1683991511yescharacteristic
617C22#1683992611yescharacteristic
618C22#1683996311yescharacteristic
619C22#1683996811yescharacteristic
620C22#1683997811yescharacteristic
621C22#1683998511yescharacteristic
622C22#1684004811yescharacteristic
623C22#1684005311yescharacteristic
624C22#1684006311yescharacteristic
625C22#1684007011yescharacteristic
626C22#1684008111yescharacteristic
627C22#1684008711yescharacteristic
628C22#1684009311yescharacteristic
629C22#1684010411yescharacteristic
630C4—24no—
631C4—42no—
632C4—4882no—
633C4—4882no—
634C4—2444no—
635C4—2444no—
636C4C22⋊C4×Dic6111yescharacteristic
637C4C4⋊C4×Dic6111yescharacteristic
638C4#1683964511yescharacteristic
639C4#1683964811yescharacteristic
640C4#1683964911yescharacteristic
641C4#1683965511yescharacteristic
642C4#1683965911yescharacteristic
643C4#1683966611yescharacteristic
644C2#2144405311yescharacteristic
645C2C4×#1451970911yescharacteristic
646C2#2144571611yescharacteristic
647C2#2144601411yescharacteristic
648C2#2144602011yescharacteristic
649C2#2144608311yescharacteristic
650C2#2144609011yescharacteristic
651C2#2144615211yescharacteristic
652C2#2144617311yescharacteristic
653C2#2144639811yescharacteristic
654C2#2144640511yescharacteristic
655C2#2144644711yescharacteristic
656C2#2144645411yescharacteristic
657C2#2144658311yescharacteristic
658C2#2144658911yescharacteristic
subgroupG/H
centerC24C2×D244
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#336C2
socle, prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC2×#336D61
hypocenterC61#10908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
15. C2×#14519709C4semidirect
23. #16839525C4semidirect
27. C61×#336C4semidirect
156. C2×C8×C61C42semidirect
206. C2×C4×C61#106semidirect
356. #336Dic61semidirect
357. C61#10908semidirect
486. C2×C8C4×Dic61semidirect
564. C2×C4#14519709semidirect

Maximal subgroups

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

subgroupindex
C22×#145197092
C2×C4×C4⋊Dic612
C2×#168395252
#214440492
C2×C61×#3362
#1090861