Finite Group Databasebeta

← D61×#1897 #29681768

Subgroups — D61×#1897 #29681768

Order 15616.

1954 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
1#525×D61C211yesmaximal, characteristic
2C2×#117×D61C211yesmaximal, characteristic, complemented
3C2×#104×D61C212yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic, complemented
5#21446268C211yesmaximal, characteristic, complemented
6#21446267C211yesmaximal, characteristic, complemented
7#21446266C212yesmaximal, complemented
8#21446265C211yesmaximal, characteristic, complemented
9#21446264C212yesmaximal, complemented
10#339×D61C212yesmaximal, complemented
11C61×#1897C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×M16×D61C2212yes—
15#16840275C412yescomplemented
16#16840274C2211yescharacteristic
17#16840273C2211yescharacteristic
18#16840272C412yescomplemented
19#16840271—22no—
20#16840270—21no—
21#16840269C2211yescharacteristic
22#16840268—21no—
23#123×D61—21no—
24C22⋊Q8×D61C412yescomplemented
25#121×D61C412yescomplemented
26#120×D61—21no—
27C4×D4×D61—22no—
28C2×#14519736C2211yescharacteristic, complemented
29C2×#14519735—21no—
30C2×#14519734C2212yescomplemented
31C2×#14519733—21no—
32#117×D61—28no—
33#117×D61C2211yescharacteristic
34C2×C4⋊C4×D61—21no—
35C2×C22⋊C4×D61—21no—
36C2×C42×D61C2212yes—
37C2×#14519705C2212yescomplemented
38C2×#14519704C2212yescomplemented
39C2×#14519703C2212yescomplemented
40#104×D61—28no—
41#16839726C2211yescharacteristic, complemented
42#16839725C2212yescomplemented
43#16839724—22no—
44C22⋊C8×D61—22no—
45#16839523C2212yescomplemented
46#16839522C2212yescomplemented
47#16839521C2212yescomplemented
48C61×#525C2211yescharacteristic
49C2×#117×C61C2211yescharacteristic, complemented
50C2×#104×C61C2212yescomplemented
51C61×#407C2211yescharacteristic, complemented
52C61×#339C2212yescomplemented
53C24×D61D411yescharacteristic
54C2×#11758226C2×C411yescharacteristic
55C2×#11758222—21no—
56C2×#11758222C2311yescharacteristic
57C2×#11758224—21no—
58C2×#11758224C2×C411yescharacteristic
59#41×D61—24no—
60#41×D61—24no—
61C2×Q8×D61C2×C411yescharacteristic
62C2×D4×D61—22no—
63C2×D4×D61—21no—
64C2×D4×D61C2×C411yescharacteristic
65C23×Dic61D411yescharacteristic
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—22no—
69C22×C4×D61—21no—
70C22×C4×D61C2×C412yes—
71C22×C4×D61C2×C412yes—
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D412yes—
75C22×C4×D61D412yes—
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×#11758194C2312yes—
79C2×#11758189—22no—
80M16×D61—24no—
81M16×D61—24no—
82C2×C8×D61—22no—
83#14519762—22no—
84#14519761—21no—
85#14519760—21no—
86#14519759—22no—
87#14519758—21no—
88#14519757C2×C412yescomplemented
89#14519756C2×C412yescomplemented
90#14519755—22no—
91#14519754—22no—
92#14519753C2×C412yescomplemented
93#14519752C2×C412yescomplemented
94#14519751C2×C412yescomplemented
95#14519750—22no—
96#14519749—22no—
97#14519748C2×C412yescomplemented
98#14519747—22no—
99#14519747—21no—
100#14519746—21no—
101#14519745—22no—
102#14519745—21no—
103C4×D244—22no—
104D4×Dic61—22no—
105#14519739—22no—
106C4×C22⋊D61—22no—
107C4×C22⋊D61—22no—
108#14519737—22no—
109#14519737—22no—
110#14519736—24no—
111#14519736C2311yescharacteristic
112#14519735—28no—
113#14519735C2×C412yes—
114#14519734—21no—
115#14519734—24no—
116#14519734—24no—
117#14519733—28no—
118#14519733—21no—
119C2×C4⋊Dic61—21no—
120C2×#11758196—22no—
121C4⋊C4×D61—28no—
122C4⋊C4×D61—22no—
123C4⋊C4×D61C2×C412yes—
124C2×C22⋊Dic61—21no—
125C2×#11758198—22no—
126C22⋊C4×D61—28no—
127C22⋊C4×D61—22no—
128C22⋊C4×D61—21no—
129C22⋊C4×D61—22no—
130C2×C4×Dic61—22no—
131C2×C4×Dic61C2312yes—
132C42×D61—24no—
133C42×D61—21no—
134C42×D61D418yescomplemented
135#14519705—24no—
136#14519704—24no—
137#14519703—24no—
138C22⋊#92418—22no—
139#14519689—24no—
140C2×#41×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C2×M16×C61C2312yes—
143#123×C61—21no—
144C22⋊Q8×C61C2×C412yescomplemented
145#121×C61C2×C412yescomplemented
146#120×C61—21no—
147C4×D4×C61—22no—
148#117×C61—24no—
149#117×C61C2311yescharacteristic
150C2×C4⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C42×C61C2312yes—
153#104×C61—24no—
154C22⋊C8×C61—22no—
155C24×C61C2×D411yescharacteristic
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—21no—
159C23×D61—44no—
160C23×D61C22⋊C412yes—
161C23×D61C22⋊C412yes—
162C23×D61C2×D411yescharacteristic
163C23×D61C2×D411yescharacteristic
164#41×C61—22no—
165#41×C61—22no—
166C2×Q8×C61C22×C411yescharacteristic
167C2×D4×C61—22no—
168C2×D4×C61—21no—
169C2×D4×C61C22×C411yescharacteristic
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—21no—
174C22×C4×C61C22×C412yes—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D412yes—
177C22×C4×C61C2411yescharacteristic
178C2×C22⋊D61—22no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—21no—
187C22×Dic61C22⋊C412yes—
188C22×Dic61C22⋊C412yes—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191#11758226—24no—
192Q8×D61—24no—
193#11758224—24no—
194#11758224—42no—
195#11758224—42no—
196D4×D61—24no—
197D4×D61—48no—
198D4×D61—42no—
199D4×D61—42no—
200#11758222—22no—
201#11758222—22no—
202#11758222—44no—
203C2×D244—21no—
204C2×D244—22no—
205C2×D244C22×C411yescharacteristic
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—28no—
213C2×C4×D61—28no—
214C2×C4×D61—28no—
215C2×C4×D61—28no—
216C2×C4×D61—21no—
217C2×C4×D61—22no—
218C2×C4×D61—28no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—48no—
222C2×C4×D61—44no—
223C2×C4×D61C22⋊C412yes—
224C2×C4×D61C22⋊C412yes—
225C2×C4×D61C22⋊C412yes—
226C2×C4×D61C22⋊C412yes—
227C2×C4×D61C22×C412yes—
228C2×C4×D61C22×C411yescharacteristic
229C2×C4×D61C22×C411yescharacteristic
230C2×C4×D61C2×D412yes—
231C2×C4×D61C2×D414yes—
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61#4114yes—
235C2×Dic122—21no—
236C2×Dic122C22×C411yescharacteristic
237M16×C61—22no—
238M16×C61—22no—
239C2×C8×C61—22no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—22no—
242C4⋊C4×C61C22×C412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—22no—
247C42×C61—22no—
248C42×C61—21no—
249C42×C61C2×D414yescomplemented
250C22⋊Dic61—24no—
251C22⋊Dic61—22no—
252C22⋊Dic61—21no—
253C22⋊Dic61—22no—
254#11758198—28no—
255#11758198—22no—
256#11758198—22no—
257#11758198—22no—
258#11758198—22no—
259#11758198—22no—
260C4⋊Dic61—24no—
261C4⋊Dic61—22no—
262C4⋊Dic61C22×C412yes—
263#11758196—28no—
264#11758196—22no—
265#11758196—22no—
266#11758196—22no—
267C4×Dic61—22no—
268C4×Dic61—21no—
269C4×Dic61—22no—
270C4×Dic61—28no—
271C4×Dic61C2×D414yescomplemented
272#11758194—22no—
273#11758194—22no—
274C2×#92418—22no—
275#11758189—44no—
276C8×D61—44no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—42no—
281C23×C61C2×C22⋊C412yes—
282C23×C61C22×D411yescharacteristic
283C22×D61—24no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—24no—
287C22×D61—24no—
288C22×D61—24no—
289C22×D61—24no—
290C22×D61—21no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—48no—
295C22×D61—48no—
296C22×D61—42no—
297C22×D61—44no—
298C22×D61C2×C22⋊C412yes—
299C22×D61C2×C22⋊C411yescharacteristic
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61#12012yes—
302C22×D61#12312yes—
303Q8×C61—22no—
304D4×C61—22no—
305D4×C61—44no—
306D4×C61—41no—
307D4×C61—41no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—24no—
311C2×C4×C61—24no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—24no—
315C2×C4×C61—44no—
316C2×C4×C61—42no—
317C2×C4×C61C2×C22⋊C412yes—
318C2×C4×C61C23×C411yescharacteristic
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4112yes—
322C22⋊D61—44no—
323C22⋊D61—44no—
324C22⋊D61—41no—
325C22⋊D61—41no—
326C22⋊D61—42no—
327C22⋊D61—42no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—22no—
333C2×Dic61—21no—
334C2×Dic61—24no—
335C2×Dic61—44no—
336C2×Dic61—42no—
337C2×Dic61C2×C22⋊C412yes—
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61#12012yes—
341C2×Dic61#12312yes—
342D244—22no—
343D244—44no—
344D244—42no—
345C4×D61—24no—
346C4×D61—24no—
347C4×D61—24no—
348C4×D61—24no—
349C4×D61—24no—
350C4×D61—24no—
351C4×D61—416no—
352C4×D61—42no—
353C4×D61—44no—
354C4×D61—42no—
355C4×D61—42no—
356C4×D61C4×D414yes—
357C4×D61C4×D414yes—
358C4×D61#12114yes—
359C4×D61#12114yes—
360Dic122—22no—
361Dic122—42no—
362C8×C61—42no—
363#92418—42no—
364C2×#1897—611nomaximal, Sylow
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—41no—
373C22×C61C22×C22⋊C411yescharacteristic
374C22×C61C2×#12011yescharacteristic
375C22×C61C2×#12311yescharacteristic
376C2×D61—22no—
377C2×D61—24no—
378C2×D61—24no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—48no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—48no—
386C2×D61—42no—
387C2×D61—41no—
388C2×D61—84no—
389C2×D61#38612yes—
390C2×D61#38612yes—
391C2×D61#42114yes—
392C4×C61—22no—
393C4×C61—44no—
394C4×C61—42no—
395C4×C61—41no—
396C4×C61C2×C4×D412yes—
397C4×C61C2×#12112yes—
398Dic61—22no—
399Dic61—44no—
400Dic61—42no—
401Dic61—41no—
402Dic61#38612yes—
403Dic61#38612yes—
404C2×#525—611no—
405C22×#117—611no—
406C22×#104—612no—
407C2×#407—611no—
408#1897—612no—
409#1897—611no—
410#1897—612no—
411#1897—611no—
412#1897—611no—
413#1897D6111yescharacteristic, direct product factor
414C2×#339—612no—
415C2×C61—21no—
416C2×C61—21no—
417C2×C61—42no—
418C2×C61—81no—
419C2×C61C2×#38611yescharacteristic
420C2×C61C2×#42112yes—
421D61—22no—
422D61—42no—
423D61—81no—
424D61#189714yesdirect product factor
425C22×#41—611no—
426C24×C4—611no—
427C22×M16—612no—
428#525—611no—
429#525—611no—
430#525—612no—
431#525—612no—
432#525—611no—
433#525—1222no—
434#525—1221no—
435#525—1221no—
436#525C2×D6111yescharacteristic
437C2×#123—1221no—
438C2×C22⋊Q8—612no—
439C2×#121—612no—
440C2×#120—1221no—
441C2×C4×D4—1222no—
442C2×#117—611no—
443C2×#117—612no—
444C2×#117—611no—
445C2×#117—1228no—
446C2×#117—1221no—
447C2×#117—1221no—
448C2×#117C2×D6111yescharacteristic, complemented
449C22×C4⋊C4—1221no—
450C22×C22⋊C4—1221no—
451C22×C42—612no—
452C2×#104—612no—
453C2×#104—612no—
454C2×#104—612no—
455C2×#104—1228no—
456C2×#104C2×D6112yescomplemented
457#407—611no—
458#407—612no—
459#407—1222no—
460#407C2×D6111yescharacteristic, complemented
461C2×C22⋊C8—1222no—
462#339—612no—
463#339—612no—
464#339—612no—
465#339C2×D6112yescomplemented
466C61C2×#189711yescharacteristic, complemented, Sylow
467C25—611no—
468C2×#41—611no—
469C2×#41—611no—
470C2×#41—611no—
471C2×#41—1221no—
472C2×#41—1221no—
473C2×#41—1224no—
474C2×#41—1224no—
475C2×#41C22×D6111yescharacteristic
476C22×Q8—611no—
477C22×D4—611no—
478C22×D4—1222no—
479C22×D4—1221no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—612no—
483C23×C4—612no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—612no—
487C23×C4—612no—
488C23×C4—611no—
489C23×C4—1224no—
490C23×C4—1224no—
491C23×C4—1221no—
492C23×C4—1222no—
493C23×C4C22×D6111yescharacteristic
494C2×M16—612no—
495C2×M16—1222no—
496C2×M16—1224no—
497C2×M16—1224no—
498C2×M16C22×D6112yes—
499C22×C8—1222no—
500#123—21no—
501#123—1222no—
502#123—1221no—
503#123—1222no—
504#123—1221no—
505#123—1221no—
506C22⋊Q8—612no—
507C22⋊Q8—612no—
508C22⋊Q8—612no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511C22⋊Q8C4×D6112yescomplemented
512#121—612no—
513#121—612no—
514#121—612no—
515#121—1222no—
516#121—1222no—
517#121C4×D6112yescomplemented
518#120—21no—
519#120—1221no—
520#120—1222no—
521#120—1222no—
522#120—1221no—
523#120—1221no—
524C4×D4—22no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532#117—24no—
533#117—611no—
534#117—612no—
535#117—1224no—
536#117—1221no—
537#117—1224no—
538#117—1221no—
539#117—1228no—
540#117—1228no—
541#117—1224no—
542#117C22×D6111yescharacteristic
543C2×C4⋊C4—21no—
544C2×C4⋊C4—612no—
545C2×C4⋊C4—1222no—
546C2×C4⋊C4—1228no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4—1221no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1222no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—1228no—
554C2×C22⋊C4—1222no—
555C2×C22⋊C4—1221no—
556C2×C42—612no—
557C2×C42—618no—
558C2×C42—1221no—
559C2×C42—1224no—
560C2×C42—1222no—
561C2×C42C22×D6112yes—
562#104—24no—
563#104—1224no—
564#104—1224no—
565#104—1224no—
566C22⋊C8—22no—
567C22⋊C8—1224no—
568C22⋊C8—1222no—
569C24—611no—
570C24—612no—
571C24—611no—
572C24—612no—
573C24—1222no—
574C24—1222no—
575C24—1221no—
576C24—2444no—
577C24D4×D6111yescharacteristic
578#41—22no—
579#41—22no—
580#41—1224no—
581#41—1224no—
582#41—1222no—
583#41—1222no—
584#41—2444no—
585#41—2442no—
586#41—2442no—
587C2×Q8—611no—
588C2×Q8—1221no—
589C2×Q8—1224no—
590C2×Q8C2×C4×D6111yescharacteristic
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—611no—
594C2×D4—1222no—
595C2×D4—1221no—
596C2×D4—1224no—
597C2×D4—1221no—
598C2×D4—1222no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1222no—
602C2×D4—2442no—
603C2×D4—2442no—
604C2×D4—2448no—
605C2×D4C2×C4×D6111yescharacteristic
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—614no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—614no—
617C22×C4—611no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1228no—
629C22×C4—1228no—
630C22×C4—1228no—
631C22×C4—1228no—
632C22×C4—1221no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1228no—
636C22×C4—1222no—
637C22×C4—1221no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1221no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1221no—
645C22×C4—2444no—
646C22×C4—2448no—
647C22×C4C2×C4×D6112yes—
648C22×C4D4×D6112yes—
649C22×C4D4×D6111yescharacteristic
650C22×C4C23×D6111yescharacteristic
651M16—22no—
652M16—22no—
653M16—1222no—
654M16—1222no—
655M16—2444no—
656C2×C8—22no—
657C2×C8—1222no—
658C2×C8—2444no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—612no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1228no—
666C4⋊C4—1224no—
667C4⋊C4—1222no—
668C4⋊C4C2×C4×D6112yes—
669C22⋊C4—24no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—1228no—
678C22⋊C4—1222no—
679C22⋊C4—1224no—
680C22⋊C4—1221no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C42—22no—
684C42—21no—
685C42—614no—
686C42—1228no—
687C42—1222no—
688C42—1222no—
689C42—1221no—
690C42D4×D6114yescomplemented
691C23—21no—
692C23—21no—
693C23—21no—
694C23—42no—
695C23—611no—
696C23—611no—
697C23—612no—
698C23—612no—
699C23—612no—
700C23—1224no—
701C23—1224no—
702C23—1224no—
703C23—1224no—
704C23—1224no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23—2444no—
713C23—2448no—
714C23—2448no—
715C23C22⋊C4×D6112yes—
716C23C2×D4×D6111yescharacteristic
717Q8—22no—
718Q8—1222no—
719Q8—2442no—
720D4—22no—
721D4—44no—
722D4—41no—
723D4—41no—
724D4—1222no—
725D4—2442no—
726D4—2444no—
727D4—2442no—
728D4—2444no—
729D4—2442no—
730D4—2444no—
731D4—2441no—
732D4—2441no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—24no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—612no—
745C2×C4—612no—
746C2×C4—614no—
747C2×C4—614no—
748C2×C4—614no—
749C2×C4—614no—
750C2×C4—612no—
751C2×C4—1224no—
752C2×C4—1224no—
753C2×C4—1224no—
754C2×C4—1224no—
755C2×C4—1224no—
756C2×C4—1224no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1224no—
760C2×C4—1224no—
761C2×C4—1222no—
762C2×C4—1221no—
763C2×C4—1224no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2444no—
767C2×C4—24416no—
768C2×C4—2442no—
769C2×C4—2444no—
770C2×C4—2442no—
771C2×C4C22⋊C4×D6112yes—
772C2×C4C22×C4×D6111yescharacteristic
773C2×C4C2×D4×D6112yes—
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4#41×D6112yes—
776C8—42no—
777C8—2442no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—41no—
786C22—614no—
787C22—612no—
788C22—612no—
789C22—1224no—
790C22—1224no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—1222no—
795C22—4884no—
796C22—2442no—
797C22—2442no—
798C22—2448no—
799C22—2448no—
800C22—2442no—
801C22—2441no—
802C22C2×C22⋊C4×D6111yescharacteristic
803C22#120×D6111yescharacteristic
804C22#123×D6111yescharacteristic
805C4—22no—
806C4—44no—
807C4—42no—
808C4—41no—
809C4—612no—
810C4—612no—
811C4—1222no—
812C4—2444no—
813C4—2442no—
814C4—2441no—
815C4C4×D4×D6112yes—
816C4#121×D6112yes—
817C2—21no—
818C2—21no—
819C2—42no—
820C2—81no—
821C2—614no—
822C2—1222no—
823C2—4881no—
824C2—2442no—
825C2#386×D6111yescharacteristic
826C2#421×D6112yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1897C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1897D61
hypocenterC61C2×#1897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. C2×#117×D61C2semidirect
3. C2×#104×D61C2semidirect
4. #407×D61C2semidirect
5. #21446268C2semidirect
6. #21446267C2semidirect
7. #21446266C2semidirect
8. #21446265C2semidirect
9. #21446264C2semidirect
10. #339×D61C2semidirect
11. C61×#1897C2semidirect
15. #16840275C4semidirect
18. #16840272C4semidirect
24. C22⋊Q8×D61C4semidirect
25. #121×D61C4semidirect
28. C2×#14519736C22semidirect
30. C2×#14519734C22semidirect
37. C2×#14519705C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519703C22semidirect
41. #16839726C22semidirect
42. #16839725C22semidirect
45. #16839523C22semidirect
46. #16839522C22semidirect
47. #16839521C22semidirect
49. C2×#117×C61C22semidirect
50. C2×#104×C61C22semidirect
51. C61×#407C22semidirect
52. C61×#339C22semidirect
88. #14519757C2×C4semidirect
89. #14519756C2×C4semidirect
92. #14519753C2×C4semidirect
93. #14519752C2×C4semidirect
94. #14519751C2×C4semidirect
97. #14519748C2×C4semidirect
134. C42×D61D4semidirect
144. C22⋊Q8×C61C2×C4semidirect
145. #121×C61C2×C4semidirect
249. C42×C61C2×D4semidirect
271. C4×Dic61C2×D4semidirect
413. #1897D61direct (N × H)
424. D61#1897direct (N × H)
448. C2×#117C2×D61semidirect
456. C2×#104C2×D61semidirect
460. #407C2×D61semidirect
465. #339C2×D61semidirect
466. C61C2×#1897semidirect
511. C22⋊Q8C4×D61semidirect
517. #121C4×D61semidirect
690. C42D4×D61semidirect

Maximal subgroups

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

subgroupindex
#525×D612
C2×#117×D612
C2×#104×D612
#407×D612
#214462682
#214462672
#214462662
#214462652
#214462642
#339×D612
C61×#18972
C2×#189761