Finite Group Databasebeta

← #29686014

Subgroups — #29686014

Order 15616.

1630 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519822C211yesmaximal, characteristic, complemented
2C2×#16839948C211yesmaximal, characteristic
3#21448477C212yesmaximal, complemented
4#21446228C211yesmaximal, characteristic, complemented
5#21446224C212yesmaximal, complemented
6#21446099C211yesmaximal, characteristic, complemented
7#21446098C212yesmaximal, complemented
8#21445766C211yesmaximal, characteristic, complemented
9C4×#14519691C212yesmaximal, complemented
10C4×#14519692C211yesmaximal, characteristic, complemented
11C61×#2321C211yesmaximal, characteristic, complemented
12C2×#14519822C2211yescharacteristic
13C2×#14519746C2212yes—
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#16839948C418yescomplemented
26C2×#14519692C2211yescharacteristic
27C2×#14519692C2211yescharacteristic
28C2×#14519691C2212yes—
29C2×#14519691C2212yes—
30#16839662—22no—
31#16839656—22no—
32#16839650—22no—
33#16839641C2212yes—
34#16839638—22no—
35#16839635C2212yescomplemented
36#16839618C2212yescomplemented
37C4×C22⋊Dic61C2212yescomplemented
38#16839529C2212yescomplemented
39#16839528C2212yescomplemented
40#16839528C2212yescomplemented
41C2×#120×C61C2211yescharacteristic
42C2×C4×D4×C61C2211yescharacteristic
43C22×C22⋊C4×C61C2211yescharacteristic, complemented
44C61×#390—21no—
45C61×#388—21no—
46C61×#388—21no—
47C61×#386—21no—
48C61×#386C2211yescharacteristic
49C61×#385C2211yescharacteristic, complemented
50C61×#379C2211yescharacteristic, 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⋊D61—22no—
59C22×C22⋊D61C2312yes—
60C2×D4×D61—22no—
61C22×C4×D61—21no—
62C22×C4×D61D412yescomplemented
63#14519746—24no—
64#14519746C2×C418yescomplemented
65C4×Dic122—21no—
66C4×Dic122—21no—
67#14519742—22no—
68C4×D244—21no—
69C4×D244—21no—
70D4×Dic61—22no—
71D4×Dic61—22no—
72#14519739—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—
80C4×C22⋊D61—22no—
81#14519737—22no—
82#14519737—22no—
83#14519737—22no—
84#14519737—22no—
85#14519736—21no—
86#14519735—22no—
87#14519734—22no—
88#14519733—22no—
89#14519733—22no—
90C2×#11758196—21no—
91C2×#11758196—22no—
92C2×#11758196D412yescomplemented
93C4⋊C4×D61—22no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61C2312yes—
99C2×C22⋊Dic61C2312yes—
100C2×C22⋊Dic61C2312yes—
101C2×#11758198—21no—
102C2×#11758198—22no—
103C2×#11758198D412yescomplemented
104C22⋊C4×D61—22no—
105C22⋊C4×D61—22no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61D412yescomplemented
109C42×D61—22no—
110#14519692—22no—
111#14519692C2×C414yescomplemented
112#14519691—24no—
113#14519691C2×C418yescomplemented
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117C25×C61C2311yescharacteristic
118C22×D4×C61—21no—
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61D411yescharacteristic, complemented
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123#120×C61—22no—
124#120×C61C2×C414yescomplemented
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61D411yescharacteristic, complemented
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—22no—
133C2×C22⋊C4×C61—22no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61D411yescharacteristic, complemented
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61C2311yescharacteristic
141C2×C42×C61—21no—
142C2×C42×C61D411yescharacteristic, complemented
143#95×C61—21no—
144#95×C61—21no—
145#95×C61—21no—
146C24×C61—22no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—22no—
150C24×C61—81no—
151C24×C61—81no—
152C24×C61C22×C412yescomplemented
153C24×C61C2×D411yescharacteristic
154C24×C61C2411yescharacteristic
155C23×D61—21no—
156C23×D61C2×D412yes—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—24no—
160C2×D4×C61—81no—
161C2×D4×C61—81no—
162C2×D4×C61C22×C412yes—
163C2×D4×C61#4112yes—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—22no—
170C22×C4×C61—81no—
171C22×C4×C61—81no—
172C22×C4×C61—81no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D412yes—
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C2×C22⋊D61—22no—
181C2×C22⋊D61—24no—
182C2×C22⋊D61—24no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—22no—
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—28no—
188C2×C22⋊D61—82no—
189C2×C22⋊D61—82no—
190C2×C22⋊D61C22×C414yes—
191C2×C22⋊D61#4114yes—
192C22×Dic61—21no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61C2×D412yes—
198C22×Dic61C2×D412yes—
199C22×Dic61C2×D412yes—
200#11758224—28no—
201#11758224—28no—
202D4×D61—28no—
203D4×D61—28no—
204#11758222—24no—
205#11758222—24no—
206C2×D244—21no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—82no—
213C2×C4×D61—82no—
214C2×Dic122—21no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—81no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—24no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—41no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—41no—
225C22⋊C4×C61—81no—
226C22⋊C4×C61—81no—
227C22⋊C4×C61—81no—
228C22⋊C4×C61C22×C412yescomplemented
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—81no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—22no—
236C22⋊Dic61—28no—
237C22⋊Dic61—22no—
238C22⋊Dic61—22no—
239C22⋊Dic61—82no—
240C22⋊Dic61—82no—
241C22⋊Dic61C22×C414yescomplemented
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—82no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249#11758196—22no—
250#11758196—22no—
251#11758196—22no—
252#11758196—22no—
253#11758196—82no—
254C4×Dic61—22no—
255C4×Dic61—22no—
256C4×Dic61—22no—
257C4×Dic61—22no—
258C4×Dic61—22no—
259C4×Dic61—82no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—24no—
263C23×C61—22no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—42no—
269C23×C61—42no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—42no—
273C23×C61—42no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—42no—
279C23×C61—82no—
280C23×C61—84no—
281C23×C61—82no—
282C23×C61C4×D412yes—
283C23×C61C23×C411yescharacteristic
284C23×C61C22×D412yes—
285C23×C61C22×D411yescharacteristic
286C23×C61C2×#4112yes—
287C23×C61C2×#4111yescharacteristic
288C22×D61—22no—
289C22×D61—24no—
290C22×D61—22no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—81no—
294C22×D61—81no—
295C22×D61C4×D414yes—
296D4×C61—24no—
297D4×C61—24no—
298D4×C61—84no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—22no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—42no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61—41no—
308C2×C4×C61—42no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—81no—
322C2×C4×C61C4×D412yes—
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61#12012yes—
325C2×C4×C61#12011yescharacteristic
326C22⋊D61—28no—
327C22⋊D61—24no—
328C22⋊D61—24no—
329C22⋊D61—24no—
330C22⋊D61—24no—
331C22⋊D61—88no—
332C2×Dic61—24no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—24no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—81no—
346C2×Dic61—81no—
347C2×Dic61C4×D414yes—
348D244—24no—
349C4×D61—28no—
350C4×D61—44no—
351C4×D61—82no—
352C4×D61—82no—
353C4×D61—82no—
354Dic122—24no—
355#21482—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—21no—
358C22×C61—22no—
359C22×C61—21no—
360C22×C61—22no—
361C22×C61—41no—
362C22×C61—42no—
363C22×C61—41no—
364C22×C61—42no—
365C22×C61—44no—
366C22×C61—42no—
367C22×C61—44no—
368C22×C61—42no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—42no—
372C22×C61—81no—
373C22×C61—82no—
374C22×C61—82no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61C2×C4×D412yes—
380C22×C61C2×C4×D411yescharacteristic
381C22×C61C2×#12011yescharacteristic
382C22×C61#52511yescharacteristic
383C22×C61#52512yes—
384C2×D61—24no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—44no—
388C2×D61—82no—
389C2×D61—84no—
390C4×C61—21no—
391C4×C61—22no—
392C4×C61—21no—
393C4×C61—22no—
394C4×C61—42no—
395C4×C61—41no—
396C4×C61—41no—
397C4×C61—81no—
398C4×C61—81no—
399Dic61—24no—
400Dic61—44no—
401Dic61—42no—
402Dic61—42no—
403Dic61—82no—
404C4×H(5,𝔽2)—611no—
405C2×B(4,𝔽2)—611no—
406#2321—612no—
407#2321D6111yescharacteristic, complemented
408#1889—612no—
409#1889—611no—
410#1867—611no—
411#1867—612no—
412#1790—611no—
413C4×#99—612no—
414C4×#99—611no—
415C2×C61—22no—
416C2×C61—22no—
417C2×C61—21no—
418C2×C61—21no—
419C2×C61—42no—
420C2×C61—82no—
421C2×C61C4×#12011yescharacteristic
422C2×C61#302611yescharacteristic
423C2×C61#302711yescharacteristic
424D61—44no—
425C2×H(5,𝔽2)—611no—
426C2×#120—612no—
427C2×#120C2×D6111yescharacteristic
428#520—1222no—
429#520—1221no—
430#518—611no—
431#518—612no—
432#518—1222no—
433#518—1221no—
434C4×#41—1222no—
435C4×#41—1221no—
436C2×C4×D4—612no—
437C2×C4×D4—1222no—
438C2×C4×D4—1221no—
439C2×C4×D4C2×D6111yescharacteristic
440C22×C22⋊C4C2×D6111yescharacteristic, complemented
441B(4,𝔽2)—618no—
442C2×#99—611no—
443C2×#99—612no—
444C2×#99—611no—
445C2×#99—612no—
446#390—21no—
447#390—1222no—
448#388—21no—
449#388—21no—
450#388—1222no—
451#388—1222no—
452#386—21no—
453#386—612no—
454#386—1222no—
455#386C2×D6111yescharacteristic
456#385—612no—
457#385C2×D6111yescharacteristic, complemented
458#379—612no—
459#379C2×D6111yescharacteristic, complemented
460C4×C22⋊C4—612no—
461C4×C22⋊C4C2×D6111yescharacteristic, complemented
462#342—612no—
463#342—612no—
464#342—612no—
465C61#2148211yescharacteristic, complemented, Sylow
466C25C22×D6111yescharacteristic
467H(5,𝔽2)—614no—
468H(5,𝔽2)—1224no—
469H(5,𝔽2)—1222no—
470C2×#41—1222no—
471C2×#41—1221no—
472C22×D4—21no—
473C22×D4—612no—
474C22×D4—1222no—
475C22×D4—1221no—
476C22×D4—1222no—
477C22×D4C22×D6111yescharacteristic
478C23×C4—612no—
479C23×C4—1221no—
480C23×C4C22⋊D6111yescharacteristic, complemented
481C23×C4C22×D6111yescharacteristic
482C23×C4C22×D6111yescharacteristic
483#120—22no—
484#120—618no—
485#120—1224no—
486#120C4×D6114yescomplemented
487C4×Q8—1221no—
488C4×Q8—1221no—
489C4×Q8—1222no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—1221no—
493C4×D4—1221no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509#117—1222no—
510#117—1222no—
511#117—1222no—
512#117—1222no—
513#117—1221no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—612no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
520C2×C22⋊C4—21no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—612no—
529C2×C22⋊C4—612no—
530C2×C22⋊C4—612no—
531C2×C22⋊C4—612no—
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1222no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1222no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4C22⋊D6111yescharacteristic, complemented
541C2×C22⋊C4C22×D6111yescharacteristic
542C2×C22⋊C4C22×D6111yescharacteristic
543C2×C22⋊C4C22×D6111yescharacteristic
544C2×C42—21no—
545C2×C42—612no—
546C2×C42—1222no—
547C2×C42—1221no—
548C2×C42—1222no—
549C2×C42C22⋊D6111yescharacteristic, complemented
550#99—614no—
551#99—618no—
552#99—1224no—
553#99—1222no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—1222no—
558#95—1222no—
559#95—1222no—
560C24—22no—
561C24—21no—
562C24—22no—
563C24—21no—
564C24—81no—
565C24—81no—
566C24—612no—
567C24—1221no—
568C24C2×C4×D6112yescomplemented
569C24C2×C22⋊D6111yescharacteristic
570C24C23×D6111yescharacteristic
571#41—1224no—
572#41—1228no—
573#41—1228no—
574#41—1224no—
575C2×Q8—1221no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—24no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4—614no—
582C2×D4—614no—
583C2×D4—1221no—
584C2×D4—1228no—
585C2×D4—1228no—
586C2×D4—1222no—
587C2×D4—1224no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1224no—
593C2×D4—1228no—
594C2×D4—4882no—
595C2×D4—4882no—
596C2×D4C2×C4×D6112yes—
597C2×D4#1175822212yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—612no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—4882no—
621C22×C4—4882no—
622C22×C4D4×D6112yes—
623C22×C4D4×D6112yes—
624C22×C4C2×C22⋊D6111yescharacteristic
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C2×C22⋊D6111yescharacteristic
629C4⋊C4—22no—
630C4⋊C4—81no—
631C4⋊C4—1222no—
632C4⋊C4—1221no—
633C4⋊C4—1222no—
634C4⋊C4—1221no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—4882no—
638C22⋊C4—22no—
639C22⋊C4—21no—
640C22⋊C4—24no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—614no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1228no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—4882no—
662C22⋊C4—4882no—
663C22⋊C4—4882no—
664C22⋊C4C2×C4×D6112yescomplemented
665C42—21no—
666C42—21no—
667C42—81no—
668C42—1222no—
669C42—1222no—
670C42—1222no—
671C42—1222no—
672C42—1222no—
673C42—4882no—
674C23—21no—
675C23—21no—
676C23—24no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—41no—
691C23—41no—
692C23—42no—
693C23—82no—
694C23—84no—
695C23—82no—
696C23—614no—
697C23—1224no—
698C23—1222no—
699C23—1222no—
700C23—4881no—
701C23—4881no—
702C23—2442no—
703C23—2442no—
704C23C4×C22⋊D6112yes—
705C23C22×C4×D6111yescharacteristic
706C23C2×D4×D6112yes—
707C23C22×C22⋊D6111yescharacteristic
708C23#41×D6112yes—
709C23C2×#1175822211yescharacteristic
710Q8—1224no—
711D4—24no—
712D4—24no—
713D4—84no—
714D4—1224no—
715D4—1228no—
716D4—1224no—
717D4—1224no—
718D4—1224no—
719D4—1224no—
720D4—4888no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—81no—
744C2×C4—614no—
745C2×C4—1228no—
746C2×C4—1224no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1224no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—4882no—
753C2×C4—4882no—
754C2×C4—4882no—
755C2×C4—4881no—
756C2×C4—4881no—
757C2×C4—2444no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4C4×C22⋊D6112yes—
766C2×C4#1451974511yescharacteristic
767C2×C4#1451974511yescharacteristic
768C2×C4#1451974512yes—
769C22—21no—
770C22—22no—
771C22—21no—
772C22—22no—
773C22—22no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—42no—
781C22—44no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—82no—
789C22—82no—
790C22—81no—
791C22—81no—
792C22—1224no—
793C22—4882no—
794C22—4884no—
795C22—2444no—
796C22—2442no—
797C22—2442no—
798C22C4×D4×D6112yes—
799C22C2×C4×C22⋊D6111yescharacteristic
800C22C2×#1451974511yescharacteristic
801C22#1684026911yescharacteristic
802C22#1684027112yes—
803C4—21no—
804C4—21no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—41no—
809C4—41no—
810C4—81no—
811C4—81no—
812C4—1224no—
813C4—4882no—
814C4—2444no—
815C4—2442no—
816C4—2442no—
817C2—21no—
818C2—21no—
819C2—22no—
820C2—22no—
821C2—42no—
822C2—82no—
823C2—2444no—
824C2C4×#1451974511yescharacteristic
825C2#2145521511yescharacteristic
826C2#2145522011yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2321C2
socleC22×C61C2×#120
prime radicalC2×#16839948C2
cosocleC24×C61C24
hypercenter#2321D61
hypocenterC61#21482
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2321

Complements

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

NH ≅ G/Ntype
1. C4×#14519822C2semidirect
3. #21448477C2semidirect
4. #21446228C2semidirect
5. #21446224C2semidirect
6. #21446099C2semidirect
7. #21446098C2semidirect
8. #21445766C2semidirect
9. C4×#14519691C2semidirect
10. C4×#14519692C2semidirect
11. C61×#2321C2semidirect
25. #16839948C4semidirect
35. #16839635C22semidirect
36. #16839618C22semidirect
37. C4×C22⋊Dic61C22semidirect
38. #16839529C22semidirect
39. #16839528C22semidirect
40. #16839528C22semidirect
43. C22×C22⋊C4×C61C22semidirect
49. C61×#385C22semidirect
50. C61×#379C22semidirect
51. C4×C22⋊C4×C61C22semidirect
62. C22×C4×D61D4semidirect
64. #14519746C2×C4semidirect
92. C2×#11758196D4semidirect
103. C2×#11758198D4semidirect
108. C2×C4×Dic61D4semidirect
111. #14519692C2×C4semidirect
113. #14519691C2×C4semidirect
120. C23×C4×C61D4semidirect
124. #120×C61C2×C4semidirect
128. C2×C4⋊C4×C61D4semidirect
137. C2×C22⋊C4×C61D4semidirect
142. C2×C42×C61D4semidirect
152. C24×C61C22×C4semidirect
228. C22⋊C4×C61C22×C4semidirect
241. C22⋊Dic61C22×C4semidirect
407. #2321D61semidirect
440. C22×C22⋊C4C2×D61semidirect
457. #385C2×D61semidirect
459. #379C2×D61semidirect
461. C4×C22⋊C4C2×D61semidirect
465. C61#21482semidirect
480. C23×C4C22⋊D61semidirect
486. #120C4×D61semidirect
519. C2×C4⋊C4C22⋊D61semidirect
540. C2×C22⋊C4C22⋊D61semidirect
549. C2×C42C22⋊D61semidirect
568. C24C2×C4×D61semidirect
664. 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×#168399482
#214484772
#214462282
#214462242
#214460992
#214460982
#214457662
C4×#145196912
C4×#145196922
C61×#23212
#2148261