Finite Group Databasebeta

← #29646106

Subgroups — #29646106

Order 15616.

1034 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×#126×D61C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#21454447C211yesmaximal, characteristic, complemented
4#21444189C211yesmaximal, characteristic, complemented
5#21444188C211yesmaximal, characteristic, complemented
6#21444187C212yesmaximal, complemented
7#21444186C211yesmaximal, characteristic, complemented
8#21444185C212yesmaximal, complemented
9#21444147C212yesmaximal, complemented
10#21444144C212yesmaximal
11C61×#1473C211yesmaximal, characteristic, complemented
12C2×#14519772C411yescharacteristic
13C2×#14519772C411yescharacteristic
14C2×#14519772C2211yescharacteristic
15C2×#14519771C2211yescharacteristic
16C2×#14519770C411yescharacteristic
17C2×#14519770C411yescharacteristic
18C2×#14519770C2211yescharacteristic
19#126×D61—21no—
20#126×D61—21no—
21#126×D61—21no—
22#126×D61—21no—
23#126×D61—21no—
24#126×D61—21no—
25#126×D61—21no—
26#126×D61—21no—
27C2×C4⋊C4×D61C411yescharacteristic
28C2×C4⋊C4×D61C411yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61C411yescharacteristic
31C2×C22⋊C4×D61C411yescharacteristic
32C2×C22⋊C4×D61C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839819C2211yescharacteristic, complemented
35#16839818—21no—
36#16839817—21no—
37#16839816C2212yescomplemented
38#16839815C2211yescharacteristic, complemented
39#16839814—21no—
40#16839813—21no—
41#16839812C2212yescomplemented
42#16839784—21no—
43#16839784—21no—
44#16839724C2212yes—
45#16839724C2212yes—
46#16839714—21no—
47C4×#11758189—21no—
48#16839488C2212yescomplemented
49#16839487C2212yescomplemented
50#16839487C2212yescomplemented
51#16839486C2212yes—
52#16839485C2212yes—
53#16839485C2212yes—
54C2×#126×C61C2211yescharacteristic
55C61×#432C2211yescharacteristic, complemented
56C61×#431C2211yescharacteristic, complemented
57C61×#324C2212yescomplemented
58C61×#323C2212yes—
59C24×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758189—22no—
67C2×#11758189—22no—
68#14519772—21no—
69#14519772—21no—
70#14519772—21no—
71#14519772—21no—
72#14519772—21no—
73#14519772—21no—
74#14519772—21no—
75#14519772—21no—
76#14519772—21no—
77#14519772—21no—
78#14519772—21no—
79#14519772—21no—
80#14519771—21no—
81#14519771—21no—
82#14519771—21no—
83#14519771—21no—
84#14519770—21no—
85#14519770—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519770—21no—
94#14519770—21no—
95#14519770—21no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2311yescharacteristic
105C4⋊C4×D61—21no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C4⋊C4×D61—21no—
111C4⋊C4×D61—21no—
112C4⋊C4×D61—21no—
113C4⋊C4×D61—21no—
114C4⋊C4×D61—21no—
115C4⋊C4×D61—21no—
116C4⋊C4×D61—21no—
117C2×C22⋊Dic61C2×C411yescharacteristic
118C2×C22⋊Dic61C2×C411yescharacteristic
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2311yescharacteristic
126C22⋊C4×D61—21no—
127C22⋊C4×D61—21no—
128C22⋊C4×D61—21no—
129C22⋊C4×D61—21no—
130C22⋊C4×D61—21no—
131C22⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C22⋊C4×D61—21no—
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C22⋊C4×D61—21no—
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141C42×D61D411yescharacteristic
142C42×D61D411yescharacteristic
143C42×D61D411yescharacteristic
144C42×D61D411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C4⋊#92418—21no—
150C4⋊#92418—21no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418C2312yes—
154C22⋊#92418C2312yes—
155#14519689—22no—
156#14519689—22no—
157#14519688—21no—
158#14519687—22no—
159C4×#92418—21no—
160C8×Dic61—22no—
161#126×C61—21no—
162#126×C61—21no—
163#126×C61—21no—
164#126×C61—21no—
165C2×C4⋊C4×C61C2×C411yescharacteristic
166C2×C4⋊C4×C61C2×C411yescharacteristic
167C2×C4⋊C4×C61C2311yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2×C411yescharacteristic
170C2×C22⋊C4×C61C2311yescharacteristic
171C2×C42×C61C2311yescharacteristic
172C4⋊C8×C61—21no—
173C4⋊C8×C61—21no—
174C22⋊C8×C61C2312yes—
175C22⋊C8×C61C2312yes—
176#97×C61—21no—
177C4×C8×C61—21no—
178C24×C61C22×C411yescharacteristic
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—42no—
182C23×D61—42no—
183C23×D61—42no—
184C23×D61C22×C411yescharacteristic
185C23×D61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C22×C411yescharacteristic
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C2411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C22×C411yescharacteristic
194C22×Dic61C22×C411yescharacteristic
195C22×Dic61C22×C411yescharacteristic
196C22×Dic61C22×C411yescharacteristic
197C22×Dic61C22×C411yescharacteristic
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C8×C61—22no—
223C2×C8×C61—22no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C42×C61C2×D411yescharacteristic
237C42×C61C2×D411yescharacteristic
238C42×C61C2×D411yescharacteristic
239C42×C61C2×D411yescharacteristic
240C22⋊Dic61—21no—
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C2×#92418—22no—
289C2×#92418—22no—
290#11758189—44no—
291#11758189—44no—
292C23×C61—21no—
293C23×C61—22no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61C23×C411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—21no—
301C22×D61—22no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—88no—
311C22×D61C2×C22⋊C411yescharacteristic
312C22×D61C2×C22⋊C411yescharacteristic
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C2×C22⋊C411yescharacteristic
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×Dic61—22no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—22no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—42no—
358C4×D61—42no—
359C4×D61—42no—
360C4×D61—42no—
361C8×C61—42no—
362C8×C61—42no—
363#92418—42no—
364#92418—42no—
365#17398—611nomaximal, Sylow
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—82no—
372C22×C61C22×C22⋊C411yescharacteristic
373C22×C61#56812yes—
374C2×D61—28no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—84no—
383C2×D61—84no—
384C2×D61—82no—
385C2×D61#41012yes—
386C2×D61#41312yes—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61—41no—
396Dic61—21no—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—41no—
403Dic61—41no—
404Dic61—41no—
405C22×#126—611no—
406#2920—611no—
407#2920—611no—
408#1473—611no—
409#1473—611no—
410#1473—612no—
411#1473—612no—
412#1473—611no—
413#1473D6111yescharacteristic, complemented
414#1463—612no—
415#1462—612no—
416C2×C61—22no—
417C2×C61—81no—
418C2×C61#287911yescharacteristic
419C2×C61C2×#41011yescharacteristic
420C2×C61C2×#41311yescharacteristic
421D61—22no—
422D61—22no—
423D61—81no—
424C2×#126—611no—
425C2×#126—611no—
426C2×#126—611no—
427C2×#126—611no—
428C2×#126—611no—
429C2×#126—611no—
430C2×#126—611no—
431C2×#126—1221no—
432C2×#126—1221no—
433C2×#126—1221no—
434C2×#126—1221no—
435C2×#126—1221no—
436C2×#126—1221no—
437C2×#126—1221no—
438C2×#126—1221no—
439C2×#126C2×D6111yescharacteristic
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C22⋊C4—611no—
444C22×C22⋊C4—611no—
445C22×C22⋊C4—611no—
446C22×C42—611no—
447#432—611no—
448#432—612no—
449#432—1221no—
450#432—1221no—
451#432C2×D6111yescharacteristic, complemented
452#431—611no—
453#431—612no—
454#431—1221no—
455#431—1221no—
456#431C2×D6111yescharacteristic, complemented
457#423—1221no—
458#423—1221no—
459#407—612no—
460#407—612no—
461C4×M16—1221no—
462C4×M16—1221no—
463#324—612no—
464#324—612no—
465#324—612no—
466#324C2×D6112yescomplemented
467#323—612no—
468#323—612no—
469#323—612no—
470#323C2×D6112yes—
471C61#1739811yescharacteristic, complemented, Sylow
472C25—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C2×M16—1222no—
480C2×M16—1222no—
481#126—21no—
482#126—21no—
483#126—21no—
484#126—21no—
485#126—1221no—
486#126—1221no—
487#126—1221no—
488#126—1221no—
489#126—1221no—
490#126—1221no—
491#126—1221no—
492#126—1221no—
493#126—1221no—
494#126—1221no—
495#126—1221no—
496#126—1221no—
497#126—1221no—
498#126—1221no—
499#126—1221no—
500#126—1221no—
501#126—1221no—
502#126—1221no—
503#126—1221no—
504#126—1221no—
505#126—1221no—
506#126—1221no—
507#126—1221no—
508#126—1221no—
509#126—1221no—
510#126—1221no—
511#126—1221no—
512#126—1221no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4C4×D6111yescharacteristic
535C2×C4⋊C4C4×D6111yescharacteristic
536C2×C4⋊C4C22×D6111yescharacteristic
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4—611no—
544C2×C22⋊C4—611no—
545C2×C22⋊C4—611no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4C4×D6111yescharacteristic
559C2×C22⋊C4C4×D6111yescharacteristic
560C2×C22⋊C4C22×D6111yescharacteristic
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42C22×D6111yescharacteristic
573C4⋊C8—21no—
574C4⋊C8—21no—
575C4⋊C8—1222no—
576C4⋊C8—1222no—
577C4⋊C8—1221no—
578C4⋊C8—1221no—
579C22⋊C8—612no—
580C22⋊C8—612no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8C22×D6112yes—
584C22⋊C8C22×D6112yes—
585#97—21no—
586#97—1222no—
587#97—1221no—
588C4×C8—21no—
589C4×C8—1222no—
590C4×C8—1221no—
591C24—611no—
592C24—611no—
593C24—1221no—
594C24—1221no—
595C24—2442no—
596C24—2442no—
597C24—2442no—
598C24C2×C4×D6111yescharacteristic
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4C2×C4×D6111yescharacteristic
630C22×C4C2×C4×D6111yescharacteristic
631C22×C4C2×C4×D6111yescharacteristic
632C22×C4C2×C4×D6111yescharacteristic
633C22×C4C2×C4×D6111yescharacteristic
634C22×C4C23×D6111yescharacteristic
635M16—2444no—
636M16—2444no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—1222no—
640C2×C8—1222no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42D4×D6111yescharacteristic
702C42D4×D6111yescharacteristic
703C42D4×D6111yescharacteristic
704C42D4×D6111yescharacteristic
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—611no—
710C23—611no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—1221no—
716C23—4888no—
717C23—2441no—
718C23—2441no—
719C23—2442no—
720C23—2442no—
721C23—2442no—
722C23—2442no—
723C23—2442no—
724C23—2442no—
725C23C22×C4×D6111yescharacteristic
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1222no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4C22⋊C4×D6111yescharacteristic
769C2×C4C22⋊C4×D6111yescharacteristic
770C2×C4C22⋊C4×D6111yescharacteristic
771C2×C4C22⋊C4×D6111yescharacteristic
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4C2×D4×D6111yescharacteristic
774C8—42no—
775C8—42no—
776C8—2442no—
777C8—2442no—
778C22—21no—
779C22—21no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—82no—
784C22—612no—
785C22—612no—
786C22—1228no—
787C22—1221no—
788C22—1221no—
789C22—1221no—
790C22—1221no—
791C22—4882no—
792C22—4884no—
793C22—4884no—
794C22—2441no—
795C22—2441no—
796C22—2441no—
797C22C2×C22⋊C4×D6111yescharacteristic
798C22#1684052712yes—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—1221no—
809C4—1221no—
810C4—1221no—
811C4—1221no—
812C4—1221no—
813C4—1221no—
814C4—2441no—
815C4—2441no—
816C4—2441no—
817C2—22no—
818C2—81no—
819C2—1222no—
820C2—1222no—
821C2—4881no—
822C2#2145426111yescharacteristic
823C2#410×D6111yescharacteristic
824C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1473C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1473D61
hypocenterC61#17398
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. #21454447C2semidirect
4. #21444189C2semidirect
5. #21444188C2semidirect
6. #21444187C2semidirect
7. #21444186C2semidirect
8. #21444185C2semidirect
9. #21444147C2semidirect
11. C61×#1473C2semidirect
34. #16839819C22semidirect
37. #16839816C22semidirect
38. #16839815C22semidirect
41. #16839812C22semidirect
48. #16839488C22semidirect
49. #16839487C22semidirect
50. #16839487C22semidirect
55. C61×#432C22semidirect
56. C61×#431C22semidirect
57. C61×#324C22semidirect
413. #1473D61semidirect
451. #432C2×D61semidirect
456. #431C2×D61semidirect
466. #324C2×D61semidirect
471. C61#17398semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D612
#214544492
#214544472
#214441892
#214441882
#214441872
#214441862
#214441852
#214441472
#214441442
C61×#14732
#1739861