Finite Group Databasebeta

← #29603388

Subgroups — #29603388

Order 15616.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839639C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C2×#16839637C211yesmaximal, characteristic, complemented
5C22×#14519684C211yesmaximal, characteristic, complemented
6#21444074C212yesmaximal, complemented
7#21444065C212yesmaximal, complemented
8#21444053C212yesmaximal, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C24×Dic61C2211yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C2×C4×C22⋊D61—24no—
17C2×C4×C22⋊D61—24no—
18C2×C4×C22⋊D61—24no—
19C22×C4⋊Dic61C2212yes—
20C22×#11758196C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×C4×Dic61C2211yescharacteristic
26#16839639—24no—
27#16839639C418yescomplemented
28#16839637—24no—
29C2×#14519684—24no—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C24×C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C2×#95×C61C2212yes—
42C24×D61C2311yescharacteristic
43C22×C22⋊D61—22no—
44C22×C22⋊D61—22no—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61C2×C414yes—
48C22×C22⋊D61D414yes—
49C22×C22⋊D61Q814yes—
50C23×Dic61—22no—
51C23×Dic61—22no—
52C23×Dic61—22no—
53C23×Dic61—24no—
54C23×Dic61—22no—
55C23×Dic61—22no—
56C23×Dic61—42no—
57C23×Dic61—42no—
58C23×Dic61—42no—
59C23×Dic61C2×C414yescomplemented
60C23×Dic61C2312yes—
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2312yes—
64C23×Dic61C2311yescharacteristic
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—24no—
69C22×C4×D61—42no—
70C4×C22⋊D61—232no—
71C2×C4⋊Dic61—24no—
72C2×C4⋊Dic61—24no—
73C2×C4⋊Dic61—42no—
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—22no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—22no—
79C2×C22⋊Dic61D414yes—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—42no—
86C2×#11758198—42no—
87C2×#11758198—42no—
88C2×#11758198C2×C418yescomplemented
89C2×C4×Dic61—22no—
90C2×C4×Dic61—22no—
91C2×C4×Dic61—22no—
92#14519684—24no—
93#14519684—24no—
94#14519684—24no—
95#14519684—24no—
96#14519684—42no—
97#14519684—42no—
98#14519684C2×C418yescomplemented
99C25×C61C2311yescharacteristic
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—24no—
103C23×C4×C61—42no—
104C23×C4×C61D414yes—
105C23×C4×C61C2312yes—
106C23×C4×C61C2312yes—
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61C2×C414yescomplemented
115#95×C61—24no—
116#95×C61—42no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61C22×C412yes—
122C24×C61C2×D412yes—
123C24×C61C2×D412yes—
124C24×C61C2×D412yes—
125C24×C61C2×Q812yes—
126C24×C61#4112yes—
127C24×C61#4112yes—
128C24×C61C2411yescharacteristic
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—22no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61C22×C412yes—
138C23×D61C2×D412yes—
139C23×D61C2×Q812yes—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—28no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—28no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—44no—
163C22×C4×C61—48no—
164C22×C4×C61—48no—
165C22×C4×C61C22×C414yes—
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61#4114yes—
169C2×C22⋊D61—28no—
170C2×C22⋊D61—28no—
171C2×C22⋊D61—28no—
172C2×C22⋊D61—28no—
173C2×C22⋊D61—28no—
174C2×C22⋊D61—28no—
175C2×C22⋊D61C4⋊C4116yescomplemented
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—28no—
181C22×Dic61—28no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—48no—
203C22×Dic61—48no—
204C22×Dic61—48no—
205C22×Dic61—44no—
206C22×Dic61—44no—
207C22×Dic61—44no—
208C22×Dic61—48no—
209C22×Dic61—44no—
210C22×Dic61C22×C414yes—
211C22×Dic61C22×C412yes—
212C22×Dic61C2×D412yes—
213C22×Dic61C2×D412yes—
214C22×Dic61C2×D412yes—
215C22×Dic61C2×Q812yes—
216C22×Dic61#4114yes—
217C2×C4×D61—28no—
218C2×C4×D61—48no—
219C2×C4×D61—48no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C22⋊C4×C61—28no—
223C22⋊C4×C61—44no—
224C22⋊Dic61—28no—
225#11758198—28no—
226#11758198—48no—
227#11758198—48no—
228C4⋊Dic61—48no—
229#11758196—28no—
230C4×Dic61—28no—
231C23×C61—24no—
232C23×C61—24no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—24no—
236C23×C61—22no—
237C23×C61—22no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61—24no—
246C23×C61—24no—
247C23×C61C2×C4⋊C414yes—
248C23×C61C4×D414yes—
249C23×C61C4×D414yes—
250C23×C61#12014yes—
251C23×C61C22⋊Q814yes—
252C23×C61C22⋊Q814yes—
253C23×C61#12314yes—
254C23×C61C23×C411yescharacteristic
255C23×C61C22×D411yescharacteristic
256C23×C61C22×D411yescharacteristic
257C23×C61C22×D411yescharacteristic
258C23×C61C22×Q811yescharacteristic
259C23×C61C2×#4111yescharacteristic
260C23×C61C2×#4111yescharacteristic
261C23×C61C2×#4112yes—
262C23×C61C2×#4112yes—
263C23×C61H(5,𝔽2)12yes—
264C23×C61H(5,𝔽2)12yes—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—24no—
268C22×D61—24no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—42no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61C2×C4⋊C414yes—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—416no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61#12314yes—
313C22⋊D61—232no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—24no—
326C2×Dic61—24no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—416no—
331C2×Dic61—416no—
332C2×Dic61—42no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—42no—
337C2×Dic61—41no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61C2×C4⋊C414yes—
347C4×D61—416no—
348#14016—611nomaximal, Sylow
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—28no—
352C22×C61—28no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—28no—
356C22×C61—28no—
357C22×C61—24no—
358C22×C61—24no—
359C22×C61#38518yes—
360C22×C61C22×C4⋊C411yescharacteristic
361C22×C61C2×C4×D411yescharacteristic
362C22×C61C2×C4×D411yescharacteristic
363C22×C61C4×#4112yes—
364C22×C61#51812yes—
365C22×C61C2×#12011yescharacteristic
366C22×C61C2×C22⋊Q811yescharacteristic
367C22×C61C2×C22⋊Q811yescharacteristic
368C22×C61C2×#12311yescharacteristic
369C22×C61C2×#12311yescharacteristic
370C22×C61#52511yescharacteristic
371C22×C61#52912yes—
372C22×C61#53411yescharacteristic
373C22×C61#53511yescharacteristic
374C22×C61#53812yes—
375C22×C61#54612yes—
376C22×C61#54612yes—
377C22×C61#54612yes—
378C22×C61#54612yes—
379C22×C61#55312yes—
380C22×C61#55312yes—
381C22×C61#55412yes—
382C22×C61#55412yes—
383C2×D61—28no—
384C2×D61—24no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—44no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—44no—
391C2×D61—44no—
392C2×D61—42no—
393C2×D61—42no—
394C4×C61—24no—
395C4×C61—44no—
396C4×C61—42no—
397C4×C61—82no—
398Dic61—24no—
399Dic61—44no—
400Dic61—42no—
401Dic61—44no—
402Dic61—42no—
403C22×C4×D4—611no—
404C2×#386—611no—
405C2×#386—611no—
406C2×#385—611no—
407C22×#95—611no—
408#1442—612no—
409#1439—612no—
410#1436—612no—
411C22⋊#95—612no—
412C22⋊#95—611no—
413C22⋊#95D6111yescharacteristic, complemented
414C2×C61—28no—
415C2×C61C2×#38511yescharacteristic
416C2×C61C4×#12311yescharacteristic
417C2×C61#232111yescharacteristic
418C2×C61#234912yes—
419C2×C61#236412yes—
420C2×C61#240411yescharacteristic
421C2×C61#240511yescharacteristic
422C2×C61#244412yes—
423C2×C61#245012yes—
424C2×C61#248711yescharacteristic
425C2×C61#257911yescharacteristic
426D61—44no—
427C23×D4—611no—
428C24×C4—611no—
429C24×C4—611no—
430C24×C4—611no—
431C24×C4C2×D6111yescharacteristic
432C2×C4×D4—1224no—
433C2×C4×D4—1224no—
434C2×C4×D4—1224no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—612no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4—612no—
439C22×C22⋊C4—611no—
440C22×C22⋊C4—612no—
441C22×C22⋊C4C2×D6111yescharacteristic
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C42—611no—
444#386—618no—
445#386—1224no—
446#385—1224no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—612no—
454C2×#95—1224no—
455C2×#95C2×D6112yes—
456C2×#95C2×D6112yes—
457C61#1401611yescharacteristic, complemented, Sylow
458C25—611no—
459C25C22×D6111yescharacteristic
460C22×D4—614no—
461C22×D4—614no—
462C22×D4—614no—
463C22×D4—1222no—
464C22×D4—1222no—
465C22×D4—1222no—
466C22×D4—1222no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—24no—
470C23×C4—42no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—612no—
475C23×C4—612no—
476C23×C4—614no—
477C23×C4—1222no—
478C23×C4—1222no—
479C23×C4—1224no—
480C23×C4—1222no—
481C23×C4—1222no—
482C23×C4—1222no—
483C23×C4—1222no—
484C23×C4—1222no—
485C23×C4—1222no—
486C23×C4—1224no—
487C23×C4—2442no—
488C23×C4—2442no—
489C23×C4—2442no—
490C23×C4—2442no—
491C23×C4D24414yes—
492C23×C4C22×D6112yes—
493C23×C4C22×D6112yes—
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496C4×D4—12232no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4—1224no—
502C2×C4⋊C4—2442no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—614no—
509C2×C22⋊C4—618no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1222no—
513C2×C22⋊C4—1222no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1224no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—2442no—
518C2×C22⋊C4—2442no—
519C2×C22⋊C4—2442no—
520C2×C22⋊C4C4×D6114yescomplemented
521C2×C42—1222no—
522C2×C42—1222no—
523C2×C42—1222no—
524#95—24no—
525#95—42no—
526#95—618no—
527#95—1224no—
528#95—1224no—
529#95—1224no—
530#95—1224no—
531#95—2442no—
532#95—2442no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—612no—
538C24—612no—
539C24—612no—
540C24—1221no—
541C24—1221no—
542C24—1222no—
543C24—1222no—
544C24—1221no—
545C24—1221no—
546C24—1222no—
547C24—1222no—
548C24C2×C4×D6112yes—
549C24C2×D24412yes—
550C24#1175822212yes—
551C24D4×D6112yes—
552C24D4×D6112yes—
553C24#1175822412yes—
554C24Q8×D6112yes—
555C24C23×D6111yescharacteristic
556C2×D4—6116no—
557C2×D4—1228no—
558C2×D4—1228no—
559C2×D4—1228no—
560C2×D4—1228no—
561C2×D4—1228no—
562C2×D4—1228no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—614no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—614no—
595C22×C4—1228no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1228no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1228no—
622C22×C4—2448no—
623C22×C4—2448no—
624C22×C4—2444no—
625C22×C4—2448no—
626C22×C4—2448no—
627C22×C4—2448no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2444no—
631C22×C4—2448no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4C2×C4×D6114yes—
635C22×C4C2×D24412yes—
636C22×C4C2×D24412yes—
637C22×C4#1175822414yes—
638C4⋊C4—1228no—
639C4⋊C4—2448no—
640C22⋊C4—28no—
641C22⋊C4—44no—
642C22⋊C4—1228no—
643C22⋊C4—1228no—
644C22⋊C4—2448no—
645C22⋊C4—2448no—
646C42—1228no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—614no—
664C23—1224no—
665C23—1224no—
666C23—1222no—
667C23—1222no—
668C23—1224no—
669C23—1224no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1224no—
675C23—1224no—
676C23—2442no—
677C23—2442no—
678C23—2441no—
679C23—2441no—
680C23—2442no—
681C23—2441no—
682C23—2441no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23C4⋊C4×D6114yes—
687C23#1451973714yes—
688C23C4×D24414yes—
689C23#1451974714yes—
690C23#1451975514yes—
691C23#1451975714yes—
692C23#1451975914yes—
693C23C22×C4×D6111yescharacteristic
694C23C2×D4×D6111yescharacteristic
695C23C2×D4×D6111yescharacteristic
696C23C22×D24411yescharacteristic
697C23C2×Q8×D6111yescharacteristic
698C23#41×D6112yes—
699C23C2×#1175822411yescharacteristic
700C23C2×#1175822412yes—
701C23C2×#1175822211yescharacteristic
702C23#1451982212yes—
703C23#1451982312yes—
704D4—12232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—416no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—614no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1224no—
742C2×C4—1224no—
743C2×C4—1224no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—24416no—
747C2×C4—24416no—
748C2×C4—24416no—
749C2×C4—2442no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2442no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4#1451976114yes—
764C22—28no—
765C22—24no—
766C22—28no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—1228no—
775C22—1224no—
776C22—2442no—
777C22—2444no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2444no—
782C22—2444no—
783C22—2442no—
784C22—2442no—
785C22#1683963618yes—
786C22C2×C4⋊C4×D6111yescharacteristic
787C22C2×#1451973711yescharacteristic
788C22C2×C4×D24411yescharacteristic
789C22C4×#1175822412yes—
790C22#1684023412yes—
791C22C2×#1451974711yescharacteristic
792C22C2×#1451975511yescharacteristic
793C22C2×#1451975711yescharacteristic
794C22C2×#1451975911yescharacteristic
795C22C2×#1451976111yescharacteristic
796C22#1684027411yescharacteristic
797C22#1684029212yes—
798C22#1684032411yescharacteristic
799C22#1684033111yescharacteristic
800C22#1684034512yes—
801C22#1684039912yes—
802C22#1684039912yes—
803C22#1684040412yes—
804C22#1684040412yes—
805C22#1684045512yes—
806C22#1684046412yes—
807C22#1684046612yes—
808C22#1684047012yes—
809C4—24no—
810C4—44no—
811C4—42no—
812C4—82no—
813C4—1224no—
814C4—2444no—
815C4—2442no—
816C4—2444no—
817C4—2442no—
818C2—28no—
819C2—2444no—
820C2C2×#1683963611yescharacteristic
821C2C4×#1451976111yescharacteristic
822C2#2144847911yescharacteristic
823C2#2144872512yes—
824C2#2144886712yes—
825C2#2144914011yescharacteristic
826C2#2144914711yescharacteristic
827C2#2144957112yes—
828C2#2144964512yes—
829C2#2145013711yescharacteristic
830C2#2145116811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#14016
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#16839637C2semidirect
5. C22×#14519684C2semidirect
6. #21444074C2semidirect
7. #21444065C2semidirect
8. #21444053C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
27. #16839639C4semidirect
59. C23×Dic61C2×C4semidirect
88. C2×#11758198C2×C4semidirect
98. #14519684C2×C4semidirect
114. C2×C22⋊C4×C61C2×C4semidirect
175. C2×C22⋊D61C4⋊C4semidirect
413. C22⋊#95D61semidirect
457. C61#14016semidirect
520. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168396392
C2×#168396372
C22×#145196842
#214440742
#214440652
#214440532
#214440412
#214440402
C61×C22⋊#952
#1401661