Finite Group Databasebeta

← #29686007

Subgroups — #29686007

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519822C211yesmaximal, characteristic
2C2×#16839951C211yesmaximal, characteristic
3#21448488C212yesmaximal, complemented
4#21446233C211yesmaximal, characteristic, complemented
5#21446229C212yesmaximal, complemented
6#21446099C211yesmaximal, characteristic, complemented
7#21446098C212yesmaximal, complemented
8#21445766C211yesmaximal, characteristic
9C4×#14519691C212yesmaximal, complemented
10C4×#14519692C211yesmaximal, characteristic, complemented
11C61×#2322C211yesmaximal, characteristic, complemented
12C2×#14519822C2211yescharacteristic
13C2×#14519760C2212yes—
14#16840243—21no—
15#16840241—22no—
16#16840237C2211yescharacteristic
17#16840235—21no—
18#16840235C2212yes—
19#16840234—22no—
20C4×#11758222—21no—
21C4×#11758224—22no—
22C2×C4×C22⋊D61—21no—
23C2×C4×C22⋊D61C2212yes—
24C4×D4×D61—22no—
25#16839951C418yescomplemented
26C2×#14519692C2211yescharacteristic
27C2×#14519692C2211yescharacteristic
28C2×#14519691C2212yes—
29C2×#14519691C2212yes—
30#16839657—22no—
31#16839652—22no—
32#16839643—22no—
33#16839641C2212yes—
34#16839635C2212yescomplemented
35#16839633—22no—
36#16839625C2212yescomplemented
37C4×C22⋊Dic61C2212yescomplemented
38#16839529C2212yescomplemented
39#16839528C2212yescomplemented
40#16839528C2212yescomplemented
41C2×#123×C61C2211yescharacteristic
42C2×C4×D4×C61C2211yescharacteristic
43C22×C4⋊C4×C61C2211yescharacteristic, complemented
44C61×#389—21no—
45C61×#388—21no—
46C61×#387—21no—
47C61×#386C2211yescharacteristic
48C61×#385—21no—
49C61×#385C2211yescharacteristic, complemented
50C61×#381C2211yescharacteristic, complemented
51C4×C22⋊C4×C61C2211yescharacteristic, complemented
52#14519822—22no—
53#14519822—24no—
54#14519822C2×C414yes—
55C2×#11758222—21no—
56C2×#11758224—22no—
57C22×C22⋊D61—21no—
58C22×C22⋊D61C2312yes—
59C2×D4×D61—22no—
60C22×C4×D61—21no—
61C22×C4×D61D412yes—
62#14519760—24no—
63#14519760C2×C418yescomplemented
64C4×Dic122—21no—
65C4×Dic122—21no—
66#14519742—22no—
67C4×D244—21no—
68C4×D244—21no—
69D4×Dic61—22no—
70D4×Dic61—22no—
71#14519739—22no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—22no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78C4×C22⋊D61—22no—
79C4×C22⋊D61—22no—
80#14519737—22no—
81#14519737—22no—
82#14519737—22no—
83#14519737—22no—
84#14519736—21no—
85#14519735—22no—
86#14519734—22no—
87#14519733—22no—
88#14519733—22no—
89C2×#11758196—21no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196D412yes—
93C4⋊C4×D61—22no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61C2312yes—
96C2×C22⋊Dic61C2312yes—
97C2×C22⋊Dic61C2312yes—
98C2×#11758198—21no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198D412yes—
102C22⋊C4×D61—22no—
103C22⋊C4×D61—22no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61D412yes—
107C42×D61—22no—
108#14519692—22no—
109#14519692C2×C414yescomplemented
110#14519691—24no—
111#14519691C2×C418yescomplemented
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117C22×D4×C61C2311yescharacteristic
118C23×C4×C61D411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122#123×C61—22no—
123#123×C61C2×C414yescomplemented
124C4×D4×C61—22no—
125C4×D4×C61—22no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C42×C61—21no—
140C2×C42×C61D411yescharacteristic
141#95×C61—21no—
142#95×C61—21no—
143#95×C61—21no—
144#95×C61—21no—
145#95×C61—21no—
146C24×C61C2×D411yescharacteristic
147C24×C61C2411yescharacteristic
148C23×D61—21no—
149C23×D61C2×D412yes—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61C22×C412yes—
153C2×D4×C61#4112yes—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—21no—
158C22×C4×C61—22no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—22no—
164C22×C4×C61—81no—
165C22×C4×C61—81no—
166C22×C4×C61—81no—
167C22×C4×C61C22×C412yescomplemented
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C2×C22⋊D61—22no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—24no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—22no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61C22×C414yes—
183C2×C22⋊D61#4114yes—
184C22×Dic61—21no—
185C22×Dic61—22no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—22no—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×D412yes—
191C22×Dic61C2×D412yes—
192#11758224—28no—
193#11758224—28no—
194D4×D61—28no—
195D4×D61—28no—
196#11758222—24no—
197#11758222—24no—
198C2×D244—21no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—82no—
205C2×C4×D61—82no—
206C2×Dic122—21no—
207C4⋊C4×C61—24no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—41no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61—41no—
212C4⋊C4×C61—81no—
213C22⋊C4×C61—24no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—21no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—81no—
219C22⋊C4×C61C22×C412yescomplemented
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—81no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61C22×C414yescomplemented
230#11758198—22no—
231#11758198—22no—
232#11758198—28no—
233#11758198—22no—
234#11758198—22no—
235#11758198—82no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241#11758196—22no—
242#11758196—28no—
243#11758196—82no—
244C4×Dic61—22no—
245C4×Dic61—22no—
246C4×Dic61—22no—
247C4×Dic61—22no—
248C4×Dic61—22no—
249C4×Dic61—82no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61C4×D412yes—
257C23×C61C23×C411yescharacteristic
258C23×C61C22×D412yes—
259C23×C61C22×D411yescharacteristic
260C23×C61C2×#4112yes—
261C23×C61C2×#4111yescharacteristic
262C22×D61—22no—
263C22×D61—24no—
264C22×D61—22no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—81no—
268C22×D61—81no—
269C22×D61C4×D414yes—
270D4×C61—24no—
271D4×C61—24no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—24no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—42no—
280C2×C4×C61—41no—
281C2×C4×C61—42no—
282C2×C4×C61—41no—
283C2×C4×C61—42no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—42no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—81no—
300C2×C4×C61C4×D412yes—
301C2×C4×C61#12011yescharacteristic
302C2×C4×C61#12012yes—
303C2×C4×C61#12011yescharacteristic
304C22⋊D61—28no—
305C22⋊D61—24no—
306C22⋊D61—24no—
307C22⋊D61—24no—
308C22⋊D61—24no—
309C2×Dic61—24no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—24no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—81no—
323C2×Dic61—81no—
324C2×Dic61C4×D414yes—
325D244—24no—
326C4×D61—28no—
327C4×D61—44no—
328C4×D61—82no—
329C4×D61—82no—
330C4×D61—82no—
331Dic122—24no—
332#21481—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—21no—
335C22×C61—22no—
336C22×C61—21no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—42no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—81no—
345C22×C61C2×C4×D412yes—
346C22×C61C2×C4×D411yescharacteristic
347C22×C61C2×#12011yescharacteristic
348C22×C61#52511yescharacteristic
349C22×C61#52512yes—
350C2×D61—24no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—44no—
354C2×D61—82no—
355C2×D61—84no—
356C4×C61—21no—
357C4×C61—22no—
358C4×C61—21no—
359C4×C61—22no—
360C4×C61—42no—
361C4×C61—41no—
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—81no—
365C4×C61—81no—
366Dic61—24no—
367Dic61—44no—
368Dic61—42no—
369Dic61—42no—
370Dic61—82no—
371C4×H(5,𝔽2)—611no—
372C2×#458—611no—
373#2322—612no—
374#2322D6111yescharacteristic, complemented
375#1890—612no—
376#1890—611no—
377#1867—611no—
378#1867—612no—
379#1790—611no—
380C4×#99—612no—
381C4×#99—611no—
382C2×C61—22no—
383C2×C61—22no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—42no—
387C2×C61C4×#12011yescharacteristic
388C2×C61#302611yescharacteristic
389C2×C61#302811yescharacteristic
390D61—44no—
391C2×H(5,𝔽2)—611no—
392C2×#123—612no—
393C2×#123C2×D6111yescharacteristic
394#520—1222no—
395#520—1221no—
396#518—611no—
397#518—612no—
398#518—1222no—
399#518—1221no—
400C4×#41—1222no—
401C4×#41—1221no—
402C2×C4×D4—612no—
403C2×C4×D4—1222no—
404C2×C4×D4—1221no—
405C2×C4×D4C2×D6111yescharacteristic
406C22×C4⋊C4C2×D6111yescharacteristic, complemented
407#458—618no—
408C2×#99—611no—
409C2×#99—612no—
410C2×#99—611no—
411C2×#99—612no—
412#389—21no—
413#389—1222no—
414#388—21no—
415#388—1222no—
416#387—21no—
417#387—1222no—
418#386—612no—
419#386C2×D6111yescharacteristic
420#385—21no—
421#385—612no—
422#385—1222no—
423#385C2×D6111yescharacteristic, complemented
424#381—612no—
425#381C2×D6111yescharacteristic, complemented
426C4×C22⋊C4—612no—
427C4×C22⋊C4C2×D6111yescharacteristic, complemented
428#342—612no—
429#342—612no—
430#342—612no—
431C61#2148111yescharacteristic, complemented, Sylow
432H(5,𝔽2)—614no—
433H(5,𝔽2)—1224no—
434H(5,𝔽2)—1222no—
435C2×#41—1222no—
436C2×#41—1221no—
437C22×D4—612no—
438C22×D4—1222no—
439C22×D4—1221no—
440C22×D4C22×D6111yescharacteristic
441C23×C4—612no—
442C23×C4—1221no—
443C23×C4C22⋊D6111yescharacteristic
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447#123—22no—
448#123—618no—
449#123—1224no—
450#123C4×D6114yescomplemented
451C4×Q8—1221no—
452C4×Q8—1221no—
453C4×Q8—1222no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—1221no—
457C4×D4—1221no—
458C4×D4—1222no—
459C4×D4—1222no—
460C4×D4—1222no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4—1222no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473#117—1222no—
474#117—1222no—
475#117—1222no—
476#117—1222no—
477#117—1221no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—612no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4C22⋊D6111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—612no—
493C2×C22⋊C4—612no—
494C2×C22⋊C4—612no—
495C2×C22⋊C4—612no—
496C2×C22⋊C4—1222no—
497C2×C22⋊C4—1222no—
498C2×C22⋊C4—1222no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1222no—
502C2×C22⋊C4C22⋊D6111yescharacteristic
503C2×C22⋊C4C22×D6111yescharacteristic
504C2×C22⋊C4C22×D6111yescharacteristic
505C2×C22⋊C4C22×D6111yescharacteristic
506C2×C42—21no—
507C2×C42—612no—
508C2×C42—1222no—
509C2×C42—1221no—
510C2×C42—1222no—
511C2×C42C22⋊D6111yescharacteristic
512#99—614no—
513#99—618no—
514#99—1224no—
515#99—1222no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—1222no—
522#95—1222no—
523#95—1222no—
524#95—1222no—
525#95—1222no—
526C24—612no—
527C24—1221no—
528C24C2×C22⋊D6111yescharacteristic
529C24C23×D6111yescharacteristic
530#41—1224no—
531#41—1228no—
532#41—1228no—
533#41—1224no—
534C2×Q8—1221no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—614no—
538C2×D4—614no—
539C2×D4—1221no—
540C2×D4—1228no—
541C2×D4—1228no—
542C2×D4—1222no—
543C2×D4—1224no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1222no—
548C2×D4—1224no—
549C2×D4C2×C4×D6112yes—
550C2×D4#1175822212yes—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—4882no—
578C22×C4—4882no—
579C22×C4C2×C4×D6112yescomplemented
580C22×C4D4×D6112yes—
581C22×C4D4×D6112yes—
582C22×C4C2×C22⋊D6111yescharacteristic
583C22×C4C2×C22⋊D6111yescharacteristic
584C22×C4C2×C22⋊D6111yescharacteristic
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C2×C22⋊D6111yescharacteristic
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—42no—
592C4⋊C4—81no—
593C4⋊C4—1228no—
594C4⋊C4—1222no—
595C4⋊C4—1221no—
596C4⋊C4—1222no—
597C4⋊C4—1221no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C4⋊C4—4882no—
601C22⋊C4—22no—
602C22⋊C4—21no—
603C22⋊C4—24no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—81no—
607C22⋊C4—614no—
608C22⋊C4—1228no—
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—4882no—
620C22⋊C4C2×C4×D6112yescomplemented
621C42—21no—
622C42—21no—
623C42—81no—
624C42—1222no—
625C42—1222no—
626C42—1222no—
627C42—1222no—
628C42—1222no—
629C42—4882no—
630C23—21no—
631C23—21no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—614no—
637C23—1224no—
638C23—1222no—
639C23—1222no—
640C23—4881no—
641C23—4881no—
642C23—2442no—
643C23—2442no—
644C23C4×C22⋊D6112yes—
645C23C22×C4×D6111yescharacteristic
646C23C2×D4×D6112yes—
647C23C22×C22⋊D6111yescharacteristic
648C23#41×D6112yes—
649C23C2×#1175822211yescharacteristic
650Q8—1224no—
651D4—24no—
652D4—24no—
653D4—1224no—
654D4—1228no—
655D4—1224no—
656D4—1224no—
657D4—1224no—
658D4—1224no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—81no—
687C2×C4—614no—
688C2×C4—1228no—
689C2×C4—1224no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1224no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—4882no—
696C2×C4—4882no—
697C2×C4—4882no—
698C2×C4—4881no—
699C2×C4—4881no—
700C2×C4—2444no—
701C2×C4—2442no—
702C2×C4—2442no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4C4×C22⋊D6112yes—
709C2×C4#1451974511yescharacteristic
710C2×C4#1451974511yescharacteristic
711C2×C4#1451974512yes—
712C22—21no—
713C22—22no—
714C22—21no—
715C22—22no—
716C22—22no—
717C22—41no—
718C22—42no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—41no—
723C22—81no—
724C22—1224no—
725C22—4882no—
726C22—4884no—
727C22—2444no—
728C22—2442no—
729C22—2442no—
730C22C4×D4×D6112yes—
731C22C2×C4×C22⋊D6111yescharacteristic
732C22C2×#1451974511yescharacteristic
733C22#1684026911yescharacteristic
734C22#1684027112yes—
735C4—21no—
736C4—21no—
737C4—22no—
738C4—22no—
739C4—42no—
740C4—41no—
741C4—41no—
742C4—42no—
743C4—81no—
744C4—81no—
745C4—1224no—
746C4—4882no—
747C4—2444no—
748C4—2442no—
749C4—2442no—
750C2—21no—
751C2—21no—
752C2—22no—
753C2—22no—
754C2—42no—
755C2—2444no—
756C2C4×#1451974511yescharacteristic
757C2#2145521511yescharacteristic
758C2#2145522411yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2322C2
socleC22×C61C2×#120
prime radicalC2×#14519822C22
cosocleC24×C61C24
hypercenter#2322D61
hypocenterC61#21481
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2322

Complements

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

NH ≅ G/Ntype
3. #21448488C2semidirect
4. #21446233C2semidirect
5. #21446229C2semidirect
6. #21446099C2semidirect
7. #21446098C2semidirect
9. C4×#14519691C2semidirect
10. C4×#14519692C2semidirect
11. C61×#2322C2semidirect
25. #16839951C4semidirect
34. #16839635C22semidirect
36. #16839625C22semidirect
37. C4×C22⋊Dic61C22semidirect
38. #16839529C22semidirect
39. #16839528C22semidirect
40. #16839528C22semidirect
43. C22×C4⋊C4×C61C22semidirect
49. C61×#385C22semidirect
50. C61×#381C22semidirect
51. C4×C22⋊C4×C61C22semidirect
63. #14519760C2×C4semidirect
109. #14519692C2×C4semidirect
111. #14519691C2×C4semidirect
123. #123×C61C2×C4semidirect
167. C22×C4×C61C22×C4semidirect
219. C22⋊C4×C61C22×C4semidirect
229. C22⋊Dic61C22×C4semidirect
374. #2322D61semidirect
406. C22×C4⋊C4C2×D61semidirect
423. #385C2×D61semidirect
425. #381C2×D61semidirect
427. C4×C22⋊C4C2×D61semidirect
431. C61#21481semidirect
450. #123C4×D61semidirect
579. C22×C4C2×C4×D61semidirect
620. C22⋊C4C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
C4×#145198222
C2×#168399512
#214484882
#214462332
#214462292
#214460992
#214460982
#214457662
C4×#145196912
C4×#145196922
C61×#23222
#2148161