Finite Group Databasebeta

← #29886851

Subgroups — #29886851

Order 15616.

2910 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840339C211yesmaximal, characteristic, complemented
2C22×#14519760C211yesmaximal, characteristic, complemented
3#21454101C211yesmaximal, characteristic, complemented
4#21452373C214yesmaximal, complemented
5#21452369C214yesmaximal, complemented
6#21452089C214yesmaximal, complemented
7#21452081C214yesmaximal, complemented
8#21451556C211yesmaximal, characteristic, complemented
9#21451555C211yesmaximal, characteristic, complemented
10#21451298C212yesmaximal, complemented
11#21449454C212yesmaximal, complemented
12#21449137C212yesmaximal, complemented
13#21449135C212yesmaximal, complemented
14#21448421C211yesmaximal, characteristic, complemented
15C61×#2847C211yesmaximal, characteristic, complemented
16C22×#11758224C2212yes—
17C23×C22⋊D61C2211yescharacteristic
18#16840339—28no—
19C2×#14519773C2214yes—
20C2×#14519760—28no—
21C2×#14519760C2214yes—
22C2×#14519760C2214yes—
23C2×#14519755C2212yescomplemented
24C2×#14519754C2212yescomplemented
25C2×#14519751C2211yescharacteristic
26C2×#14519751C2212yescomplemented
27C2×#14519750C2212yescomplemented
28C2×#14519749C2212yes—
29C2×#14519749C2212yescomplemented
30C2×#14519747C2212yes—
31C2×#14519746C2212yes—
32C2×#14519745C2212yes—
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38#16839703C2214yescomplemented
39#16839689C2212yescomplemented
40#16839688C2212yescomplemented
41#16839679C2214yescomplemented
42#16839678C2214yescomplemented
43#16839677C2214yescomplemented
44#16839675C2214yescomplemented
45#16839674C2214yescomplemented
46#16839672C2212yescomplemented
47#16839671C2214yes—
48#16839671C2214yescomplemented
49#16839670C2214yes—
50#16839670C2212yescomplemented
51#16839670C2214yescomplemented
52#16839662C2214yes—
53#16839651C2214yescomplemented
54#16839650C2214yescomplemented
55#16839649C2214yescomplemented
56#16839643C2214yescomplemented
57#16839642C2212yes—
58#16839642C2214yescomplemented
59#16839641C2212yes—
60#16839641C2214yescomplemented
61#16839640C2214yescomplemented
62#16839639C2212yes—
63#16839639C2214yescomplemented
64#16839638C2214yescomplemented
65#16839623C2212yes—
66#16839622C2211yescharacteristic
67#16839622C2212yescomplemented
68C22⋊C4×Dic61C2212yes—
69C24×C4×C61C2211yescharacteristic
70C2×#121×C61C2211yescharacteristic
71C2×#121×C61C2212yescomplemented
72C2×#120×C61C2212yes—
73C61×#386C2212yes—
74C61×#386C2214yescomplemented
75C61×#380C2211yescharacteristic
76C61×#380C2212yescomplemented
77C24×D61C2311yescharacteristic
78C2×#11758224—28no—
79C2×#11758224—44no—
80C2×#11758224—44no—
81C22×Dic122C2312yes—
82C22×D244C2311yescharacteristic
83C22×D244C2314yes—
84C22×C22⋊D61—24no—
85C22×C22⋊D61—44no—
86C22×C22⋊D61C2312yes—
87C22×C22⋊D61C2314yes—
88C22×C22⋊D61C2314yes—
89C22×C22⋊D61C2312yes—
90C22×C22⋊D61C2312yes—
91C22×C22⋊D61C2314yes—
92C23×Dic61C2311yescharacteristic
93C23×Dic61C2311yescharacteristic
94C23×Dic61C2312yes—
95C23×Dic61C2311yescharacteristic
96C22×C4×D61C2312yes—
97#14519773—48no—
98#14519760—216no—
99#14519760—216no—
100#14519755—28no—
101#14519754—28no—
102#14519751—24no—
103#14519751—44no—
104#14519750—28no—
105#14519749—28no—
106#14519749—28no—
107#14519747—44no—
108#14519746—44no—
109#14519745—44no—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2312yes—
112C2×#11758196—24no—
113C2×#11758196D418yescomplemented
114C2×#11758196C2314yes—
115C2×#11758196C2312yes—
116C2×#11758196C2312yes—
117C2×#11758196C2312yes—
118C2×C22⋊Dic61—24no—
119C2×C22⋊Dic61C2314yes—
120C2×C22⋊Dic61C2312yes—
121C2×C22⋊Dic61C2312yes—
122C2×C22⋊Dic61C2314yes—
123C2×C22⋊Dic61C2314yes—
124C2×#11758198—24no—
125C2×#11758198—24no—
126C2×#11758198C2312yes—
127C2×#11758198C2312yes—
128C2×#11758198C2314yes—
129C2×#11758198C2312yes—
130C2×#11758198C2312yes—
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×C4×Dic61C2314yes—
136#14519684C2314yes—
137#14519684C2312yes—
138#14519684C2314yes—
139#14519684C2314yes—
140#14519684C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143C25×C61C2311yescharacteristic
144C22×D4×C61C2312yes—
145C22×D4×C61C2311yescharacteristic
146C22×D4×C61C2314yes—
147C23×C4×C61—24no—
148C23×C4×C61—44no—
149C23×C4×C61C2312yes—
150C23×C4×C61C2312yes—
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153#121×C61—24no—
154#121×C61—44no—
155#120×C61—44no—
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C4⋊C4×C61C2312yes—
158C2×C22⋊C4×C61C2312yes—
159C2×C22⋊C4×C61C2312yes—
160C2×C22⋊C4×C61C2314yes—
161C2×C22⋊C4×C61C2314yes—
162#95×C61C2312yes—
163#95×C61C2314yes—
164C24×C61—22no—
165C24×C61—24no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—42no—
169C24×C61C2412yes—
170C24×C61C2412yes—
171C24×C61C2411yescharacteristic
172C23×D61—22no—
173C23×D61—22no—
174C23×D61—22no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61C2412yes—
178C23×D61C2412yes—
179C2×D4×C61—24no—
180C2×D4×C61—24no—
181C2×D4×C61—24no—
182C2×D4×C61—28no—
183C2×D4×C61—22no—
184C2×D4×C61—44no—
185C2×D4×C61—42no—
186C2×D4×C61—44no—
187C22×C4×C61—22no—
188C22×C4×C61—24no—
189C22×C4×C61—24no—
190C22×C4×C61—24no—
191C22×C4×C61—24no—
192C22×C4×C61—42no—
193C22×C4×C61—42no—
194C22×C4×C61—42no—
195C22×C4×C61—42no—
196C22×C4×C61—416no—
197C22×C4×C61C2×D414yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2414yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—28no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—28no—
208C2×C22⋊D61—28no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—42no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61—44no—
216C2×C22⋊D61—44no—
217C2×C22⋊D61—44no—
218C2×C22⋊D61—44no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—416no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—24no—
225C22×Dic61—42no—
226C22×Dic61—42no—
227C22×Dic61—42no—
228C22×Dic61—42no—
229C22×Dic61C2×D414yes—
230C22×Dic61C2×D414yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2414yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236#11758224—432no—
237C2×D244—22no—
238C2×D244—44no—
239C2×D244—44no—
240C2×D244—42no—
241C2×D244—44no—
242C2×C4×D61—24no—
243C2×C4×D61—42no—
244C2×C4×D61—42no—
245C2×Dic122—24no—
246C2×Dic122—42no—
247C2×Dic122—42no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—42no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—44no—
253C22⋊C4×C61—44no—
254C22⋊Dic61—24no—
255C22⋊Dic61—28no—
256C22⋊Dic61—24no—
257C22⋊Dic61—44no—
258C22⋊Dic61—44no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—28no—
263#11758198—24no—
264#11758198—44no—
265#11758198—44no—
266#11758198—44no—
267#11758198—44no—
268C4⋊Dic61—22no—
269C4⋊Dic61—42no—
270#11758196—28no—
271#11758196—24no—
272#11758196C2×D418yes—
273#11758196C2×D418yes—
274C4×Dic61—44no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—28no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—24no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—24no—
289C23×C61—48no—
290C23×C61—48no—
291C23×C61—44no—
292C23×C61—44no—
293C23×C61C22×D412yes—
294C23×C61H(5,𝔽2)14yes—
295C23×C61H(5,𝔽2)12yes—
296C23×C61H(5,𝔽2)12yes—
297C23×C61C2511yescharacteristic
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—24no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—24no—
306C22×D61—24no—
307C22×D61—24no—
308C22×D61—44no—
309C22×D61—44no—
310C22×D61—44no—
311C22×D61—84no—
312C22×D61—84no—
313D4×C61—48no—
314D4×C61—82no—
315D4×C61—88no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—24no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—24no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—24no—
327C2×C4×C61—44no—
328C2×C4×C61—48no—
329C2×C4×C61—48no—
330C2×C4×C61—44no—
331C2×C4×C61C22×D412yes—
332C2×C4×C61C22×D412yes—
333C22⋊D61—416no—
334C22⋊D61—48no—
335C22⋊D61—48no—
336C22⋊D61—84no—
337C22⋊D61—88no—
338C22⋊D61—88no—
339C2×Dic61—28no—
340C2×Dic61—24no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—24no—
346C2×Dic61—22no—
347C2×Dic61—24no—
348C2×Dic61—22no—
349C2×Dic61—24no—
350C2×Dic61—24no—
351C2×Dic61—44no—
352C2×Dic61—48no—
353C2×Dic61—44no—
354C2×Dic61C22×D414yes—
355C2×Dic61C22×D414yes—
356D244—82no—
357D244—88no—
358C4×D61—48no—
359Dic122—48no—
360#36710—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—24no—
364C22×C61—24no—
365C22×C61—24no—
366C22×C61—24no—
367C22×C61—24no—
368C22×C61—416no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—44no—
377C22×C61—44no—
378C22×C61#53514yes—
379C22×C61C23×D411yescharacteristic
380C22×C61C2×H(5,𝔽2)11yescharacteristic
381C22×C61C2×H(5,𝔽2)12yes—
382C22×C61C2×H(5,𝔽2)11yescharacteristic
383C22×C61#58512yes—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—44no—
391C2×D61—44no—
392C2×D61—44no—
393C2×D61—44no—
394C2×D61—88no—
395C4×C61—22no—
396C4×C61—22no—
397C4×C61—42no—
398C4×C61—42no—
399C4×C61—44no—
400Dic61—24no—
401Dic61—24no—
402Dic61—42no—
403Dic61—42no—
404Dic61—44no—
405C2×#537—611no—
406C22×#123—611no—
407#2847—611no—
408#2847D6111yescharacteristic, complemented
409#2696—614no—
410#2696—614no—
411#2673—614no—
412#2673—614no—
413#2617—611no—
414#2617—611no—
415#2591—612no—
416#2433—612no—
417#2404—612no—
418#2404—612no—
419#2313—611no—
420C2×C61—24no—
421C2×C61—44no—
422C2×C61—82no—
423C2×C61C2×#53511yescharacteristic
424C2×C61#348411yescharacteristic
425C2×C61#348711yescharacteristic
426C2×C61#353412yes—
427C2×C61#353412yes—
428D61—82no—
429D61—82no—
430C22×#41—612no—
431C23×D4—611no—
432C24×C4C2×D6111yescharacteristic
433#537—1228no—
434C2×#127—614no—
435C2×#123—614no—
436C2×#123—614no—
437C2×#123—1228no—
438C2×C22⋊Q8—612no—
439C2×C22⋊Q8—612no—
440C2×#121—612no—
441C2×#121—612no—
442C2×#121—611no—
443C2×#121—612no—
444C2×#121—612no—
445C2×#121C2×D6111yescharacteristic
446C2×#121C2×D6112yescomplemented
447C2×#120—612no—
448C2×#120—612no—
449C2×#120—612no—
450C2×#120C2×D6112yes—
451C22×C4⋊C4—611no—
452C22×C4⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—611no—
456#400—614no—
457#397—612no—
458#397—612no—
459#394—614no—
460#394—614no—
461#394—614no—
462#393—614no—
463#393—614no—
464#392—612no—
465#392—614no—
466#392—614no—
467#392—614no—
468#392—614no—
469#392—612no—
470#390—614no—
471#388—614no—
472#388—614no—
473#387—614no—
474#387—614no—
475#386—612no—
476#386—614no—
477#386—612no—
478#386—614no—
479#386—612no—
480#386—614no—
481#386—614no—
482#386—614no—
483#386C2×D6112yes—
484#386C2×D6114yescomplemented
485#381—612no—
486#380—611no—
487#380—612no—
488#380C2×D6111yescharacteristic
489#380C2×D6112yescomplemented
490C4×C22⋊C4—612no—
491C61#3671011yescharacteristic, complemented, Sylow
492C25—611no—
493C25C22×D6111yescharacteristic
494C2×#41—1228no—
495C2×#41—2444no—
496C2×#41—2444no—
497C22×Q8—612no—
498C22×D4—612no—
499C22×D4—614no—
500C22×D4—614no—
501C22×D4—612no—
502C22×D4—612no—
503C22×D4—614no—
504C22×D4—611no—
505C22×D4—614no—
506C22×D4—1224no—
507C22×D4—2444no—
508C22×D4C22×D6112yes—
509C22×D4C22×D6114yes—
510C22×D4C22×D6111yescharacteristic
511C23×C4—24no—
512C23×C4—44no—
513C23×C4—611no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—612no—
517C23×C4—612no—
518C23×C4C22×D6112yes—
519C23×C4C22×D6112yes—
520C23×C4C22×D6111yescharacteristic
521C23×C4C22×D6111yescharacteristic
522#127—2448no—
523#123—12216no—
524#123—12216no—
525C22⋊Q8—1228no—
526C22⋊Q8—1228no—
527#121—24no—
528#121—44no—
529#121—1228no—
530#121—1228no—
531#121—1228no—
532#121—1224no—
533#121—2444no—
534#120—44no—
535#120—2444no—
536#120—2444no—
537#120—2444no—
538C2×C4⋊C4—618no—
539C2×C4⋊C4—612no—
540C2×C4⋊C4—612no—
541C2×C4⋊C4—614no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—612no—
544C2×C4⋊C4—612no—
545C2×C4⋊C4—1224no—
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6112yes—
548C2×C22⋊C4—614no—
549C2×C22⋊C4—612no—
550C2×C22⋊C4—612no—
551C2×C22⋊C4—614no—
552C2×C22⋊C4—612no—
553C2×C22⋊C4—612no—
554C2×C22⋊C4—612no—
555C2×C22⋊C4—612no—
556C2×C22⋊C4—614no—
557C2×C22⋊C4—614no—
558C2×C22⋊C4—614no—
559C2×C22⋊C4—614no—
560C2×C22⋊C4—614no—
561C2×C22⋊C4—614no—
562C2×C22⋊C4—1224no—
563C2×C22⋊C4—1224no—
564C2×C22⋊C4—1224no—
565C2×C22⋊C4C22×D6112yes—
566C2×C22⋊C4C22×D6112yes—
567C2×C22⋊C4C22×D6114yes—
568C2×C22⋊C4C22×D6114yes—
569C2×C42—614no—
570#95—614no—
571#95—614no—
572#95—612no—
573#95—614no—
574#95—614no—
575#95—614no—
576#95—614no—
577#95C22×D6112yes—
578#95C22×D6114yes—
579C24—22no—
580C24—24no—
581C24—22no—
582C24—22no—
583C24—42no—
584C24—612no—
585C24—612no—
586C24—1222no—
587C24—1222no—
588C24—1222no—
589C24—2442no—
590C24—2442no—
591C24C23×D6112yes—
592C24C23×D6112yes—
593C24C23×D6111yescharacteristic
594#41—24432no—
595C2×Q8—1224no—
596C2×Q8—2442no—
597C2×Q8—2442no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—28no—
602C2×D4—22no—
603C2×D4—44no—
604C2×D4—42no—
605C2×D4—44no—
606C2×D4—1224no—
607C2×D4—1224no—
608C2×D4—1228no—
609C2×D4—1228no—
610C2×D4—1224no—
611C2×D4—1224no—
612C2×D4—1228no—
613C2×D4—1224no—
614C2×D4—1222no—
615C2×D4—2444no—
616C2×D4—2442no—
617C2×D4—2444no—
618C2×D4—2444no—
619C2×D4—2444no—
620C2×D4—2444no—
621C2×D4—2444no—
622C2×D4—2444no—
623C2×D4—2444no—
624C2×D4—2444no—
625C2×D4—2444no—
626C2×D4—2442no—
627C2×D4—2442no—
628C2×D4—24416no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—416no—
639C22×C4—614no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—614no—
643C22×C4—614no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—1224no—
647C22×C4—1224no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656C22×C4—2442no—
657C22×C4D4×D6114yes—
658C22×C4C23×D6114yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C22×C4C23×D6111yescharacteristic
662C22×C4C23×D6111yescharacteristic
663C4⋊C4—22no—
664C4⋊C4—42no—
665C4⋊C4—618no—
666C4⋊C4—618no—
667C4⋊C4—1228no—
668C4⋊C4—1224no—
669C4⋊C4—1222no—
670C4⋊C4—2442no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—1228no—
676C22⋊C4—1224no—
677C22⋊C4—1228no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—2444no—
684C22⋊C4—2444no—
685C22⋊C4—2444no—
686C22⋊C4—2444no—
687C22⋊C4—2444no—
688C22⋊C4—2444no—
689C42—2444no—
690C23—22no—
691C23—22no—
692C23—28no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—48no—
705C23—48no—
706C23—44no—
707C23—44no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—1224no—
712C23—1222no—
713C23—1224no—
714C23—1222no—
715C23—1222no—
716C23—1224no—
717C23—1224no—
718C23—4884no—
719C23—4884no—
720C23—2444no—
721C23—2444no—
722C23—2444no—
723C23C2×D4×D6112yes—
724C23#1451982214yes—
725C23#1451982212yes—
726C23#1451982312yes—
727C23C24×D6111yescharacteristic
728Q8—2448no—
729D4—48no—
730D4—82no—
731D4—88no—
732D4—4882no—
733D4—4888no—
734D4—4884no—
735D4—4888no—
736D4—4888no—
737D4—24416no—
738D4—2448no—
739D4—2448no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—44no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—44no—
755C2×C4—614no—
756C2×C4—614no—
757C2×C4—1228no—
758C2×C4—1224no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1224no—
764C2×C4—1222no—
765C2×C4—1224no—
766C2×C4—1222no—
767C2×C4—1224no—
768C2×C4—1224no—
769C2×C4—2448no—
770C2×C4—2444no—
771C2×C4—2448no—
772C2×C4—2444no—
773C2×C4C2×D4×D6112yes—
774C2×C4C2×D4×D6112yes—
775C22—22no—
776C22—24no—
777C22—24no—
778C22—22no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—416no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—42no—
791C22—42no—
792C22—4888no—
793C22—2442no—
794C22—2442no—
795C22—2444no—
796C22—2444no—
797C22—2444no—
798C22—2444no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22#1684032814yes—
804C22C22×D4×D6111yescharacteristic
805C22C2×#1451982212yes—
806C22C2×#1451982211yescharacteristic
807C22C2×#1451982311yescharacteristic
808C22#1684059812yes—
809C4—22no—
810C4—22no—
811C4—44no—
812C4—42no—
813C4—42no—
814C4—1224no—
815C4—1224no—
816C4—2442no—
817C4—2444no—
818C4—2442no—
819C2—24no—
820C2—44no—
821C2—82no—
822C2—4882no—
823C2—4882no—
824C2C2×#1684032811yescharacteristic
825C2#2145944811yescharacteristic
826C2#2145947311yescharacteristic
827C2#2146000312yes—
828C2#2146000912yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2847C2
hypercenter#2847D61
hypocenterC61#36710
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#16840339C2semidirect
2. C22×#14519760C2semidirect
3. #21454101C2semidirect
4. #21452373C2semidirect
5. #21452369C2semidirect
6. #21452089C2semidirect
7. #21452081C2semidirect
8. #21451556C2semidirect
9. #21451555C2semidirect
10. #21451298C2semidirect
11. #21449454C2semidirect
12. #21449137C2semidirect
13. #21449135C2semidirect
14. #21448421C2semidirect
15. C61×#2847C2semidirect
23. C2×#14519755C22semidirect
24. C2×#14519754C22semidirect
26. C2×#14519751C22semidirect
27. C2×#14519750C22semidirect
29. C2×#14519749C22semidirect
38. #16839703C22semidirect
39. #16839689C22semidirect
40. #16839688C22semidirect
41. #16839679C22semidirect
42. #16839678C22semidirect
43. #16839677C22semidirect
44. #16839675C22semidirect
45. #16839674C22semidirect
46. #16839672C22semidirect
48. #16839671C22semidirect
50. #16839670C22semidirect
51. #16839670C22semidirect
53. #16839651C22semidirect
54. #16839650C22semidirect
55. #16839649C22semidirect
56. #16839643C22semidirect
58. #16839642C22semidirect
60. #16839641C22semidirect
61. #16839640C22semidirect
63. #16839639C22semidirect
64. #16839638C22semidirect
67. #16839622C22semidirect
71. C2×#121×C61C22semidirect
74. C61×#386C22semidirect
76. C61×#380C22semidirect
113. C2×#11758196D4semidirect
408. #2847D61semidirect
446. C2×#121C2×D61semidirect
484. #386C2×D61semidirect
489. #380C2×D61semidirect
491. C61#36710semidirect

Maximal subgroups

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

subgroupindex
C2×#168403392
C22×#145197602
#214541012
#214523732
#214523692
#214520892
#214520812
#214515562
#214515552
#214512982
#214494542
#214491372
#214491352
#214484212
C61×#28472
#3671061