Finite Group Databasebeta

← #29602793

Subgroups — #29602793

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519761C211yesmaximal, characteristic
2C22×#14519737C211yesmaximal, characteristic
3C2×#16839641C211yesmaximal, characteristic
4C2×#16839623C211yesmaximal, characteristic, complemented
5C22×#14519684C211yesmaximal, characteristic, complemented
6#21444071C212yesmaximal, complemented
7#21444067C212yesmaximal, 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×#14519761—24no—
17C2×#14519761—24no—
18C2×#14519761C418yescomplemented
19C2×#14519737—24no—
20C2×#14519737—24no—
21C2×#14519737—24no—
22C22×C4⋊Dic61C2212yes—
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2212yes—
27C22×#11758198C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29#16839641—24no—
30#16839623—24no—
31C2×#14519684—24no—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C2×#14519684C2212yes—
39C24×C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61C2×C414yes—
50C22×C22⋊D61D414yes—
51C22×C22⋊D61D414yes—
52C23×Dic61—22no—
53C23×Dic61—22no—
54C23×Dic61—22no—
55C23×Dic61—22no—
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—24no—
61C23×Dic61—42no—
62C23×Dic61C2×C414yescomplemented
63C23×Dic61D414yes—
64C23×Dic61C2312yes—
65C23×Dic61C2312yes—
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—24no—
73C22×C4×D61—42no—
74#14519761—232no—
75#14519737—232no—
76C2×C4⋊Dic61—24no—
77C2×C4⋊Dic61—24no—
78C2×C4⋊Dic61C2×C418yescomplemented
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×#11758198—22no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—24no—
91C2×#11758198—24no—
92C2×#11758198—42no—
93C2×#11758198C2×C418yescomplemented
94C2×C4×Dic61—22no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—22no—
97#14519684—24no—
98#14519684—24no—
99#14519684—24no—
100#14519684—24no—
101#14519684—24no—
102#14519684—24no—
103#14519684—42no—
104C25×C61C2311yescharacteristic
105C23×C4×C61—22no—
106C23×C4×C61—24no—
107C23×C4×C61—22no—
108C23×C4×C61—22no—
109C23×C4×C61—42no—
110C23×C4×C61C2312yes—
111C23×C4×C61C2311yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2312yes—
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61C2×C414yescomplemented
119C2×C22⋊C4×C61D414yes—
120#95×C61—24no—
121#95×C61—42no—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61C22×C412yes—
127C24×C61C2×D412yes—
128C24×C61C2×D412yes—
129C24×C61C2×D412yes—
130C24×C61C2×D412yes—
131C24×C61#4112yes—
132C24×C61#4112yes—
133C24×C61C2411yescharacteristic
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—22no—
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61C22×C412yes—
143C23×D61C2×D412yes—
144C23×D61C2×D412yes—
145C22×C4×C61—28no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
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—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—48no—
167C22×C4×C61—48no—
168C22×C4×C61—44no—
169C22×C4×C61—44no—
170C22×C4×C61C22×C414yes—
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D412yes—
173C22×C4×C61#4114yes—
174C2×C22⋊D61—28no—
175C2×C22⋊D61—28no—
176C2×C22⋊D61—28no—
177C2×C22⋊D61—28no—
178C2×C22⋊D61—28no—
179C2×C22⋊D61—28no—
180C2×C22⋊D61C22⋊C4116yes—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—22no—
188C22×Dic61—28no—
189C22×Dic61—28no—
190C22×Dic61—28no—
191C22×Dic61—28no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—28no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—44no—
211C22×Dic61—48no—
212C22×Dic61—48no—
213C22×Dic61—44no—
214C22×Dic61—44no—
215C22×Dic61—44no—
216C22×Dic61—44no—
217C22×Dic61C22×C414yes—
218C22×Dic61C22×C412yes—
219C22×Dic61C2×D412yes—
220C22×Dic61C2×D412yes—
221C22×Dic61C2×D412yes—
222C22×Dic61C2×D412yes—
223C22×Dic61#4114yes—
224C2×C4×D61—28no—
225C2×C4×D61—48no—
226C2×C4×D61—48no—
227C2×C4×D61—44no—
228C2×C4×D61—44no—
229C22⋊C4×C61—28no—
230C22⋊C4×C61—28no—
231C22⋊Dic61—44no—
232#11758198—28no—
233#11758198—216no—
234#11758198—48no—
235C4⋊Dic61—216no—
236#11758196—28no—
237C4×Dic61—28no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—24no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—24no—
246C23×C61—24no—
247C23×C61—24no—
248C23×C61—24no—
249C23×C61—24no—
250C23×C61—24no—
251C23×C61—24no—
252C23×C61—24no—
253C23×C61—24no—
254C23×C61C2×C22⋊C414yes—
255C23×C61C4×D414yes—
256C23×C61C4×D414yes—
257C23×C61#12014yes—
258C23×C61#12114yes—
259C23×C61#12114yes—
260C23×C61#12314yes—
261C23×C61C23×C411yescharacteristic
262C23×C61C22×D411yescharacteristic
263C23×C61C22×D411yescharacteristic
264C23×C61C22×D411yescharacteristic
265C23×C61C22×D411yescharacteristic
266C23×C61C2×#4111yescharacteristic
267C23×C61C2×#4111yescharacteristic
268C23×C61C2×#4112yes—
269C23×C61C2×#4112yes—
270C23×C61H(5,𝔽2)12yes—
271C23×C612−1+412yes—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61—24no—
283C22×D61—24no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—42no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61C2×C22⋊C414yes—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—24no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—24no—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—24no—
305C2×C4×C61—416no—
306C2×C4×C61—42no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—42no—
311C2×C4×C61—41no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C22⋊D61—232no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—24no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—24no—
333C2×Dic61—24no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—416no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—416no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61C2×C22⋊C414yes—
353C2×Dic61#12314yescomplemented
354C4×D61—416no—
355#13968—611nomaximal, Sylow
356C22×C61—24no—
357C22×C61—28no—
358C22×C61—28no—
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—28no—
362C22×C61—28no—
363C22×C61—24no—
364C22×C61—24no—
365C22×C61—24no—
366C22×C61#38618yes—
367C22×C61C22×C22⋊C411yescharacteristic
368C22×C61C2×C4×D411yescharacteristic
369C22×C61C2×C4×D411yescharacteristic
370C22×C61C4×#4112yes—
371C22×C61#52012yes—
372C22×C61C2×#12011yescharacteristic
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×#12111yescharacteristic
375C22×C61C2×#12311yescharacteristic
376C22×C61C2×#12311yescharacteristic
377C22×C61#52511yescharacteristic
378C22×C61#52912yes—
379C22×C61#53411yescharacteristic
380C22×C61#53611yescharacteristic
381C22×C61#53912yes—
382C22×C61#54612yes—
383C22×C61#54612yes—
384C22×C61#54612yes—
385C22×C61#54712yes—
386C22×C61#54712yes—
387C22×C61#54712yes—
388C22×C61#55112yes—
389C22×C61#55212yes—
390C2×D61—28no—
391C2×D61—24no—
392C2×D61—42no—
393C2×D61—44no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—44no—
397C2×D61—44no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C4×C61—44no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—44no—
405Dic61—24no—
406Dic61—24no—
407Dic61—42no—
408Dic61—44no—
409Dic61—82no—
410C22×#123—611no—
411C22×C4×D4—611no—
412C2×#386—611no—
413C2×#381—611no—
414C22×#95—611no—
415#1441—612no—
416#1440—612no—
417#1436—612no—
418C22⋊#95—612no—
419C22⋊#95—611no—
420C22⋊#95D6111yescharacteristic, complemented
421C2×C61—28no—
422C2×C61C2×#38611yescharacteristic
423C2×C61C4×#12311yescharacteristic
424C2×C61#232211yescharacteristic
425C2×C61#233912yes—
426C2×C61#235912yes—
427C2×C61#240511yescharacteristic
428C2×C61#240611yescharacteristic
429C2×C61#241912yes—
430C2×C61#242512yes—
431C2×C61#248611yescharacteristic
432C2×C61#253411yescharacteristic
433D61—44no—
434C23×D4—611no—
435C24×C4—611no—
436C24×C4—611no—
437C24×C4—611no—
438C24×C4C2×D6111yescharacteristic
439C2×#123—618no—
440C2×#123—1224no—
441C2×#123—1224no—
442C2×C4×D4—1224no—
443C2×C4×D4—1224no—
444C2×C4×D4—1224no—
445C22×C4⋊C4—612no—
446C22×C4⋊C4—611no—
447C22×C22⋊C4—612no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—612no—
451C22×C22⋊C4C2×D6111yescharacteristic
452C22×C22⋊C4C2×D6111yescharacteristic
453C22×C42—611no—
454#386—1224no—
455#381—1224no—
456C2×#95—612no—
457C2×#95—612no—
458C2×#95—612no—
459C2×#95—612no—
460C2×#95—612no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—1224no—
464C2×#95C2×D6112yes—
465C2×#95C2×D6112yes—
466C61#1396811yescharacteristic, complemented, Sylow
467C25—611no—
468C25C22×D6111yescharacteristic
469C22×D4—614no—
470C22×D4—614no—
471C22×D4—614no—
472C22×D4—1222no—
473C22×D4—1222no—
474C22×D4—1222no—
475C22×D4—1222no—
476C23×C4—22no—
477C23×C4—24no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—42no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—614no—
484C23×C4—612no—
485C23×C4—611no—
486C23×C4—614no—
487C23×C4—612no—
488C23×C4—1222no—
489C23×C4—1224no—
490C23×C4—1222no—
491C23×C4—1224no—
492C23×C4—1222no—
493C23×C4—1222no—
494C23×C4—1222no—
495C23×C4—1222no—
496C23×C4—1222no—
497C23×C4—1222no—
498C23×C4—1222no—
499C23×C4—1222no—
500C23×C4—1222no—
501C23×C4—2442no—
502C23×C4—2442no—
503C23×C4C22×D6112yes—
504C23×C4C22×D6111yescharacteristic
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6112yes—
507#123—12232no—
508C4×D4—12232no—
509C2×C4⋊C4—618no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1224no—
513C2×C4⋊C4—1224no—
514C2×C4⋊C4—1222no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—618no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1222no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—1224no—
524C2×C22⋊C4—1222no—
525C2×C22⋊C4—1224no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1222no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4—2442no—
531C2×C22⋊C4C4×D6114yescomplemented
532C2×C22⋊C4D24414yes—
533C2×C42—1222no—
534C2×C42—1222no—
535C2×C42—1222no—
536#95—24no—
537#95—42no—
538#95—1224no—
539#95—1224no—
540#95—1224no—
541#95—1224no—
542#95—1224no—
543#95—1224no—
544#95—2442no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—612no—
550C24—612no—
551C24—612no—
552C24—1221no—
553C24—1221no—
554C24—1222no—
555C24—1222no—
556C24—1221no—
557C24—1221no—
558C24—1222no—
559C24—1222no—
560C24C2×C4×D6112yes—
561C24C2×D24412yes—
562C24#1175822212yes—
563C24D4×D6112yes—
564C24D4×D6112yes—
565C24D4×D6112yes—
566C24#1175822612yes—
567C24C23×D6111yescharacteristic
568C2×D4—6116no—
569C2×D4—1228no—
570C2×D4—1228no—
571C2×D4—1228no—
572C2×D4—1228no—
573C2×D4—1228no—
574C2×D4—1228no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—614no—
605C22×C4—614no—
606C22×C4—612no—
607C22×C4—1228no—
608C22×C4—1228no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1221no—
620C22×C4—1222no—
621C22×C4—1221no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1228no—
627C22×C4—1228no—
628C22×C4—1228no—
629C22×C4—1228no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—2448no—
638C22×C4—2444no—
639C22×C4—2448no—
640C22×C4—2444no—
641C22×C4—2444no—
642C22×C4—2448no—
643C22×C4—2448no—
644C22×C4—2444no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4C2×C4×D6114yes—
649C22×C4C2×D24412yes—
650C22×C4C2×D24412yes—
651C22×C4#1175822414yes—
652C4⋊C4—12216no—
653C4⋊C4—1228no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—12216no—
657C22⋊C4—1228no—
658C22⋊C4—2448no—
659C22⋊C4—2444no—
660C42—1228no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—614no—
678C23—1222no—
679C23—1222no—
680C23—1224no—
681C23—1224no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—1224no—
687C23—1224no—
688C23—1224no—
689C23—1224no—
690C23—2441no—
691C23—2441no—
692C23—2442no—
693C23—2441no—
694C23—2441no—
695C23—2442no—
696C23—2442no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23C22⋊C4×D6114yes—
701C23#1451973914yes—
702C23C4×D24414yes—
703C23#1451974714yes—
704C23#1451975014yes—
705C23#1451975214yes—
706C23#1451976214yes—
707C23C22×C4×D6111yescharacteristic
708C23C2×D4×D6111yescharacteristic
709C23C2×D4×D6111yescharacteristic
710C23C2×D4×D6111yescharacteristic
711C23C22×D24411yescharacteristic
712C23#41×D6112yes—
713C23C2×#1175822412yes—
714C23C2×#1175822211yescharacteristic
715C23C2×#1175822611yescharacteristic
716C23#1451982212yes—
717C23#1451982412yes—
718D4—12232no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—614no—
745C2×C4—614no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1224no—
755C2×C4—1224no—
756C2×C4—1224no—
757C2×C4—1224no—
758C2×C4—1224no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—24416no—
763C2×C4—24416no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4—24416no—
778C22—24no—
779C22—28no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—1224no—
789C22—1228no—
790C22—2442no—
791C22—2444no—
792C22—2444no—
793C22—2442no—
794C22—2442no—
795C22—2444no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22#1683964018yes—
800C22C2×C22⋊C4×D6111yescharacteristic
801C22C2×#1451973911yescharacteristic
802C22C2×C4×D24411yescharacteristic
803C22C4×#1175822412yes—
804C22#1684024112yes—
805C22C2×#1451974711yescharacteristic
806C22C2×#1451975011yescharacteristic
807C22C2×#1451975211yescharacteristic
808C22#123×D6111yescharacteristic
809C22C2×#1451976211yescharacteristic
810C22#1684026811yescharacteristic
811C22#1684029812yes—
812C22#1684032211yescharacteristic
813C22#1684033411yescharacteristic
814C22#1684036112yes—
815C22#1684039912yes—
816C22#1684040112yes—
817C22#1684040712yes—
818C22#1684041012yes—
819C22#1684041212yes—
820C22#1684041612yes—
821C22#1684043812yes—
822C22#1684044512yes—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—44no—
827C4—1224no—
828C4—1224no—
829C4—4882no—
830C4—2444no—
831C4—2442no—
832C2—28no—
833C2—2444no—
834C2C2×#1683964011yescharacteristic
835C2#2144833811yescharacteristic
836C2#2144848711yescharacteristic
837C2#2144864512yes—
838C2#2144881312yes—
839C2#2144914511yescharacteristic
840C2#2144915311yescharacteristic
841C2#2144930212yes—
842C2#2144936812yes—
843C2#2145012611yescharacteristic
844C2#2145071211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#13968
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#16839623C2semidirect
5. C22×#14519684C2semidirect
6. #21444071C2semidirect
7. #21444067C2semidirect
8. #21444053C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
18. C2×#14519761C4semidirect
62. C23×Dic61C2×C4semidirect
78. C2×C4⋊Dic61C2×C4semidirect
93. C2×#11758198C2×C4semidirect
118. C2×C22⋊C4×C61C2×C4semidirect
353. C2×Dic61#123semidirect
420. C22⋊#95D61semidirect
466. C61#13968semidirect
531. 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×#145197612
C22×#145197372
C2×#168396412
C2×#168396232
C22×#145196842
#214440712
#214440672
#214440532
#214440412
#214440402
C61×C22⋊#952
#1396861