Finite Group Databasebeta

← #29681645

Subgroups — #29681645

Order 15616.

2126 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840324C211yesmaximal, characteristic
2C2×#16840235C211yesmaximal, characteristic, complemented
3C22×#14519691C211yesmaximal, characteristic, complemented
4#21448394C211yesmaximal, characteristic, complemented
5#21448394C211yesmaximal, characteristic, complemented
6#21446231C214yesmaximal, complemented
7#21446226C214yesmaximal, complemented
8C2×#16839528C211yesmaximal, characteristic, complemented
9C2×C61×#342C211yesmaximal, characteristic, complemented
10C23×C22⋊D61C2211yescharacteristic
11C23×C22⋊D61C2211yescharacteristic
12#16840324—24no—
13#16840324C418yescomplemented
14C2×#14519761—21no—
15C2×#14519761C2212yes—
16C2×#14519751—22no—
17C2×#14519747—21no—
18C2×#14519747C2212yes—
19#16840235—22no—
20#16840235—22no—
21#16840235—22no—
22#16840235C2214yes—
23C2×C4×C22⋊D61—22no—
24C2×#14519737—22no—
25C2×#14519733—21no—
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊C4×D61—21no—
29C2×#14519691—24no—
30C2×#14519691C2214yes—
31#16839641—22no—
32#16839641—22no—
33#16839639—22no—
34#16839639—22no—
35#16839623C2212yescomplemented
36#16839623C2212yescomplemented
37#16839617C2212yescomplemented
38#16839617C2212yescomplemented
39#16839528C2214yescomplemented
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C22×C22⋊C4×C61C2211yescharacteristic
43C61×#342C2214yescomplemented
44C24×D61D411yescharacteristic
45C24×D61C2311yescharacteristic
46C22×D244—22no—
47C22×C22⋊D61—21no—
48C22×C22⋊D61—21no—
49C22×C22⋊D61—21no—
50C22×C22⋊D61—21no—
51C22×C22⋊D61—22no—
52C22×C22⋊D61—22no—
53C22×C22⋊D61—21no—
54C22×C22⋊D61—21no—
55C22×C22⋊D61—22no—
56C22×C22⋊D61—21no—
57C22×C22⋊D61—21no—
58C22×C22⋊D61—21no—
59C22×C22⋊D61—21no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—22no—
62C22×C22⋊D61C2×C414yes—
63C22×C22⋊D61C2×C414yescomplemented
64C22×C22⋊D61D414yes—
65C22×C22⋊D61D412yes—
66C22×C22⋊D61C2312yes—
67C23×Dic61—21no—
68C23×Dic61D411yescharacteristic
69C23×Dic61D412yescomplemented
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—22no—
72#14519761—24no—
73#14519761—28no—
74#14519761C2×C418yescomplemented
75#14519751—216no—
76#14519747—28no—
77#14519747—24no—
78#14519747C2×C418yescomplemented
79C4×C22⋊D61—28no—
80C4×C22⋊D61—28no—
81#14519737—28no—
82#14519737—28no—
83#14519733—24no—
84#14519733—24no—
85C2×C4⋊Dic61—22no—
86C2×#11758196—22no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61D412yescomplemented
95C2×C22⋊Dic61C2312yes—
96C2×C22⋊Dic61C2312yes—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—24no—
101C2×#11758198—24no—
102C22⋊C4×D61—24no—
103C22⋊C4×D61—24no—
104C2×C4×Dic61—22no—
105#14519691—28no—
106#14519684—24no—
107#14519684—24no—
108C25×C61C2311yescharacteristic
109C23×C4×C61—21no—
110C23×C4×C61—21no—
111C23×C4×C61D412yescomplemented
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61C2×C414yescomplemented
122C2×C22⋊C4×C61D412yescomplemented
123C2×C22⋊C4×C61C2312yes—
124C2×C22⋊C4×C61C2312yes—
125C2×C22⋊C4×C61C2312yes—
126C24×C61—82no—
127C24×C61C22×C412yes—
128C24×C61C2×D411yescharacteristic
129C24×C61C2×D411yescharacteristic
130C24×C61C2×D411yescharacteristic
131C24×C61C2×D411yescharacteristic
132C24×C61C2×D411yescharacteristic
133C24×C61C2×D411yescharacteristic
134C24×C61C2×D412yes—
135C24×C61#4112yes—
136C24×C61#4112yes—
137C24×C61C2411yescharacteristic
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—22no—
141C23×D61—21no—
142C23×D61—21no—
143C23×D61—21no—
144C23×D61—21no—
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—82no—
148C23×D61—82no—
149C23×D61C22⋊C414yescomplemented
150C23×D61C22×C412yescomplemented
151C23×D61C2×D412yes—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—24no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—42no—
158C22×C4×C61—82no—
159C22×C4×C61—82no—
160C22×C4×C61—82no—
161C22×C4×C61C2×D414yes—
162C2×C22⋊D61—24no—
163C2×C22⋊D61—24no—
164C2×C22⋊D61—24no—
165C2×C22⋊D61—24no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—24no—
169C2×C22⋊D61—24no—
170C2×C22⋊D61—24no—
171C2×C22⋊D61—24no—
172C2×C22⋊D61—24no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C2×C22⋊D61—24no—
180C2×C22⋊D61—24no—
181C2×C22⋊D61—24no—
182C2×C22⋊D61—24no—
183C2×C22⋊D61—41no—
184C2×C22⋊D61—41no—
185C2×C22⋊D61—41no—
186C2×C22⋊D61—41no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61C22⋊C418yescomplemented
194C2×C22⋊D61C22×C414yes—
195C2×C22⋊D61C2×D414yes—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—42no—
209C22×Dic61—82no—
210C22×Dic61—82no—
211C22×Dic61C22⋊C414yescomplemented
212C22×Dic61C22×C412yescomplemented
213C22×Dic61C2×D412yes—
214C22×Dic61C2×D414yes—
215C2×D244—28no—
216C2×D244—84no—
217C2×C4×D61—28no—
218C2×C4×D61—84no—
219C22⋊C4×C61—24no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61C22×C414yescomplemented
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—42no—
236#11758198—28no—
237#11758198—28no—
238#11758198—28no—
239#11758198—84no—
240#11758198—84no—
241C4⋊Dic61—28no—
242#11758196—28no—
243C4×Dic61—28no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61—82no—
252C23×C61—82no—
253C23×C61—82no—
254C23×C61—82no—
255C23×C61C2×C22⋊C412yes—
256C23×C61C2×C22⋊C412yes—
257C23×C61C4×D412yes—
258C23×C61C4×D412yes—
259C23×C61C4×D412yes—
260C23×C61C4×D412yes—
261C23×C61#12011yescharacteristic
262C23×C61#12011yescharacteristic
263C23×C61#12011yescharacteristic
264C23×C61#12011yescharacteristic
265C23×C61#12112yes—
266C23×C61#12112yes—
267C23×C61#12112yes—
268C23×C61#12112yes—
269C23×C61#12312yes—
270C23×C61#12312yes—
271C23×C61C23×C411yescharacteristic
272C23×C61C22×D411yescharacteristic
273C23×C61C22×D411yescharacteristic
274C23×C61C22×D411yescharacteristic
275C23×C61C22×D411yescharacteristic
276C23×C61C2×#4111yescharacteristic
277C23×C61C2×#4111yescharacteristic
278C22×D61—22no—
279C22×D61—24no—
280C22×D61—22no—
281C22×D61—24no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—44no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61—44no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—82no—
295C22×D61—84no—
296C22×D61—82no—
297C22×D61—84no—
298C22×D61—82no—
299C22×D61—82no—
300C22×D61—82no—
301C22×D61C2×C22⋊C414yes—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—44no—
305C2×C4×C61—44no—
306C2×C4×C61—44no—
307C2×C4×C61—44no—
308C2×C4×C61—42no—
309C2×C4×C61—82no—
310C2×C4×C61—84no—
311C2×C4×C61—84no—
312C22⋊D61—24no—
313C22⋊D61—24no—
314C22⋊D61—24no—
315C22⋊D61—24no—
316C22⋊D61—28no—
317C22⋊D61—28no—
318C22⋊D61—44no—
319C22⋊D61—44no—
320C22⋊D61—44no—
321C22⋊D61—44no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—24no—
325C2×Dic61—24no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—24no—
330C2×Dic61—44no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—44no—
336C2×Dic61—44no—
337C2×Dic61—42no—
338C2×Dic61—82no—
339C2×Dic61—84no—
340C2×Dic61C2×C22⋊C414yes—
341D244—88no—
342C4×D61—88no—
343#20960—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61#38612yes—
368C22×C61#38612yes—
369C22×C61#38612yes—
370C22×C61#38612yes—
371C22×C61C22×C22⋊C411yescharacteristic
372C22×C61C2×C4×D411yescharacteristic
373C22×C61C2×C4×D411yescharacteristic
374C22×C61C2×#12011yescharacteristic
375C22×C61C2×#12111yescharacteristic
376C22×C61C2×#12111yescharacteristic
377C22×C61C2×#12311yescharacteristic
378C2×D61—24no—
379C2×D61—48no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61—44no—
385C2×D61—42no—
386C2×D61—82no—
387C2×D61—84no—
388C2×D61—82no—
389C2×D61—82no—
390C2×D61—82no—
391C2×D61—82no—
392C4×C61—44no—
393C4×C61—44no—
394C4×C61—82no—
395Dic61—24no—
396Dic61—44no—
397Dic61—42no—
398Dic61—82no—
399C2×#534—611no—
400C2×#518—611no—
401C22×#99—611no—
402#2308—611no—
403#2308—611no—
404#1890—614no—
405#1889—614no—
406C2×#342—611no—
407C2×#342D6111yescharacteristic, complemented
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—22no—
414C2×C61—21no—
415C2×C61—22no—
416C2×C61—22no—
417C2×C61—22no—
418C2×C61C2×#38611yescharacteristic
419C2×C61#302612yes—
420D61—44no—
421D61—82no—
422C23×D4—611no—
423C23×D4—611no—
424#534—618no—
425#534—1224no—
426C2×#123—612no—
427C2×#123—1221no—
428C2×#121—1222no—
429C2×#120—612no—
430C2×#120—1221no—
431#518—614no—
432#518—1222no—
433#518—1222no—
434#518—1222no—
435C2×C4×D4—1222no—
436C2×C4×D4—1222no—
437C2×#117—1221no—
438C22×C22⋊C4—611no—
439C22×C22⋊C4—611no—
440C22×C22⋊C4—1221no—
441C22×C22⋊C4C2×D6111yescharacteristic
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4C2×D6111yescharacteristic
444C2×#99—614no—
445C2×#99—1224no—
446#386—1222no—
447#386—1222no—
448#386—1222no—
449#386—1222no—
450#381—612no—
451#381—612no—
452#379—612no—
453#379—612no—
454#342—614no—
455#342C2×D6114yescomplemented
456C61#2096011yescharacteristic, complemented, Sylow
457C25—611no—
458C25—611no—
459C25C22×D6111yescharacteristic
460C22×D4—614no—
461C22×D4—612no—
462C22×D4—614no—
463C22×D4—612no—
464C22×D4—614no—
465C22×D4—1222no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1222no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1222no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4—1222no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4—1222no—
478C22×D4—1221no—
479C22×D4—1221no—
480C22×D4—1222no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—612no—
486C23×C4—1222no—
487C23×C4—1221no—
488C23×C4D24412yescomplemented
489#123—618no—
490#123—1228no—
491#123—1224no—
492#121—12216no—
493#120—618no—
494#120—1224no—
495#120—1228no—
496C4×D4—1228no—
497C4×D4—1228no—
498C4×D4—1228no—
499C4×D4—1228no—
500#117—1224no—
501#117—1224no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1222no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—612no—
514C2×C22⋊C4—612no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1222no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1222no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1224no—
528C2×C22⋊C4—1224no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4C4×D6114yescomplemented
531C2×C22⋊C4D24412yescomplemented
532C2×C22⋊C4C22×D6112yes—
533C2×C22⋊C4C22×D6112yes—
534C2×C22⋊C4C22×D6112yes—
535C2×C42—1222no—
536#99—1228no—
537#95—1224no—
538#95—1224no—
539C24—82no—
540C24—614no—
541C24—612no—
542C24—612no—
543C24—1221no—
544C24—1222no—
545C24—1221no—
546C24—1221no—
547C24—1221no—
548C24—1221no—
549C24—1221no—
550C24—1221no—
551C24—1221no—
552C24—4882no—
553C24—4882no—
554C24C2×C4×D6112yes—
555C24C2×D24411yescharacteristic
556C24C2×D24411yescharacteristic
557C24#1175822212yes—
558C24D4×D6111yescharacteristic
559C24D4×D6111yescharacteristic
560C24D4×D6111yescharacteristic
561C24D4×D6111yescharacteristic
562C24D4×D6112yes—
563C24#1175822612yes—
564C24C23×D6111yescharacteristic
565C2×D4—614no—
566C2×D4—614no—
567C2×D4—618no—
568C2×D4—1228no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1224no—
574C2×D4—1224no—
575C2×D4—1224no—
576C2×D4—1224no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—1224no—
580C2×D4—1224no—
581C2×D4—1224no—
582C2×D4—1224no—
583C2×D4—1224no—
584C2×D4—1224no—
585C2×D4—1224no—
586C2×D4—1224no—
587C2×D4—1224no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—4884no—
591C2×D4—2441no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4—2442no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2442no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—42no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—612no—
611C22×C4—614no—
612C22×C4—612no—
613C22×C4—614no—
614C22×C4—1228no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—4884no—
628C22×C4—4882no—
629C22×C4—4882no—
630C22×C4—2442no—
631C22×C4C2×D24414yes—
632C4⋊C4—1228no—
633C4⋊C4—1228no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—24no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—42no—
643C22⋊C4—1228no—
644C22⋊C4—1228no—
645C22⋊C4—1228no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—4884no—
653C22⋊C4—4884no—
654C22⋊C4—2442no—
655C22⋊C4C2×C4×D6114yescomplemented
656C42—1228no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—82no—
665C23—82no—
666C23—82no—
667C23—82no—
668C23—614no—
669C23—1222no—
670C23—1224no—
671C23—1222no—
672C23—1224no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—4882no—
677C23—4882no—
678C23—4882no—
679C23—4882no—
680C23—4884no—
681C23—4884no—
682C23—4882no—
683C23—2444no—
684C23—2444no—
685C23—2444no—
686C23—2444no—
687C23—2444no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23C22⋊C4×D6112yes—
693C23C22⋊C4×D6112yes—
694C23#1451973912yes—
695C23#1451973912yes—
696C23C4×D24412yes—
697C23C4×D24412yes—
698C23#1451974711yescharacteristic
699C23#1451974711yescharacteristic
700C23#1451974711yescharacteristic
701C23#1451974711yescharacteristic
702C23#1451975012yes—
703C23#1451975012yes—
704C23#1451975212yes—
705C23#1451975212yes—
706C23#1451976212yes—
707C23#1451976212yes—
708C23C22×C4×D6111yescharacteristic
709C23C2×D4×D6111yescharacteristic
710C23C2×D4×D6111yescharacteristic
711C23C2×D4×D6111yescharacteristic
712C23C22×D24411yescharacteristic
713C23C2×#1175822211yescharacteristic
714C23C2×#1175822611yescharacteristic
715D4—1224no—
716D4—1224no—
717D4—1224no—
718D4—1224no—
719D4—1228no—
720D4—1228no—
721D4—4888no—
722D4—2444no—
723D4—2444no—
724D4—2444no—
725D4—2444no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—614no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1224no—
745C2×C4—4888no—
746C2×C4—4884no—
747C2×C4—4882no—
748C2×C4—2444no—
749C2×C4—2442no—
750C2×C4—2444no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2444no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—1224no—
780C22—4882no—
781C22—4882no—
782C22—4882no—
783C22—4884no—
784C22—4882no—
785C22—4882no—
786C22—2444no—
787C22—2444no—
788C22—2444no—
789C22—2444no—
790C22—2448no—
791C22—2442no—
792C22—2444no—
793C22#1683964012yes—
794C22#1683964012yes—
795C22#1683964012yes—
796C22#1683964012yes—
797C22C2×C22⋊C4×D6111yescharacteristic
798C22C2×#1451973911yescharacteristic
799C22C2×C4×D24411yescharacteristic
800C22C2×#1451974711yescharacteristic
801C22C2×#1451975011yescharacteristic
802C22C2×#1451975211yescharacteristic
803C22C2×#1451976211yescharacteristic
804C4—44no—
805C4—44no—
806C4—82no—
807C4—1224no—
808C4—4882no—
809C4—2442no—
810C4—2444no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—22no—
816C2—21no—
817C2—21no—
818C2—22no—
819C2—22no—
820C2—22no—
821C2—4882no—
822C2—2444no—
823C2C2×#1683964011yescharacteristic
824C2#2145521812yes—
subgroupG/H
centerC22C2×#14519747
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#342C2
socleC22×C61C2×#120
prime radicalC2×#16840324C2
cosocleC24×C61C24
hypercenterC2×#342D61
hypocenterC61#20960
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C2×#16840235C2semidirect
3. C22×#14519691C2semidirect
4. #21448394C2semidirect
5. #21448394C2semidirect
6. #21446231C2semidirect
7. #21446226C2semidirect
8. C2×#16839528C2semidirect
9. C2×C61×#342C2semidirect
13. #16840324C4semidirect
35. #16839623C22semidirect
36. #16839623C22semidirect
37. #16839617C22semidirect
38. #16839617C22semidirect
39. #16839528C22semidirect
43. C61×#342C22semidirect
63. C22×C22⋊D61C2×C4semidirect
69. C23×Dic61D4semidirect
74. #14519761C2×C4semidirect
78. #14519747C2×C4semidirect
94. C2×C22⋊Dic61D4semidirect
111. C23×C4×C61D4semidirect
121. C2×C22⋊C4×C61C2×C4semidirect
122. C2×C22⋊C4×C61D4semidirect
149. C23×D61C22⋊C4semidirect
150. C23×D61C22×C4semidirect
193. C2×C22⋊D61C22⋊C4semidirect
211. C22×Dic61C22⋊C4semidirect
212. C22×Dic61C22×C4semidirect
228. C22⋊C4×C61C22×C4semidirect
407. C2×#342D61semidirect
455. #342C2×D61semidirect
456. C61#20960semidirect
488. C23×C4D244semidirect
530. C2×C22⋊C4C4×D61semidirect
531. C2×C22⋊C4D244semidirect
655. C22⋊C4C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403242
C2×#168402352
C22×#145196912
#214483942
#214462312
#214462262
C2×#168395282
C2×C61×#3422
#2096061