Finite Group Databasebeta

← #29646000

Subgroups — #29646000

Order 15616.

1446 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840271C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
4#21444181C212yesmaximal, complemented
5#21444177C212yesmaximal, complemented
6#21444166C212yesmaximal, complemented
7#21444164C212yesmaximal, complemented
8#21444137C211yesmaximal, characteristic, complemented
9#21444135C211yesmaximal, characteristic, complemented
10#21444135C211yesmaximal, characteristic, complemented
11C61×#1459C211yesmaximal, characteristic, complemented
12C22×#11758222C411yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C22×#11758189—21no—
15C22×C8×D61—21no—
16#16840271—21no—
17#16840271—21no—
18#16840271—21no—
19#16840271—21no—
20#16840271—21no—
21#16840271—21no—
22#16840271—21no—
23#16840271—21no—
24C2×#14519762C2211yescharacteristic
25C2×#14519759C2211yescharacteristic
26C2×#14519755C2211yescharacteristic
27C2×#14519754C411yescharacteristic
28C2×#14519750C2211yescharacteristic
29C2×#14519749C411yescharacteristic
30C2×#14519747C411yescharacteristic
31C2×#14519745C411yescharacteristic
32C2×C4×D244C411yescharacteristic
33C2×C4×C22⋊D61C411yescharacteristic
34C2×C4×C22⋊D61C2211yescharacteristic
35C2×#14519734C411yescharacteristic
36#16839724—21no—
37#16839724—21no—
38#16839724C2212yes—
39#16839724C2212yes—
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689—21no—
43C2×#14519689—21no—
44C22⋊C8×D61—21no—
45C22⋊C8×D61—21no—
46C22⋊C8×D61C2212yes—
47C22⋊C8×D61C2212yes—
48#16839488C2212yescomplemented
49#16839487C2212yescomplemented
50#16839487C2212yescomplemented
51#16839486C2212yescomplemented
52#16839485C2212yescomplemented
53#16839485C2212yescomplemented
54C2×C4×D4×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#324C2212yescomplemented
58C61×#323C2212yescomplemented
59C24×D61C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222—44no—
65C22×Dic122C2×C411yescharacteristic
66C22×D244C2×C411yescharacteristic
67C22×D244C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C23×Dic61C2×C411yescharacteristic
73C22×C4×D61—44no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—22no—
88C2×#11758189—22no—
89C2×#11758189—44no—
90C22×#92418—21no—
91C22×#92418—21no—
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94C2×C8×D61—44no—
95#14519762—21no—
96#14519762—21no—
97#14519762—21no—
98#14519762—21no—
99#14519759—21no—
100#14519759—21no—
101#14519759—21no—
102#14519759—21no—
103#14519755—21no—
104#14519755—21no—
105#14519755—21no—
106#14519755—21no—
107#14519754—21no—
108#14519754—21no—
109#14519754—21no—
110#14519754—21no—
111#14519750—21no—
112#14519750—21no—
113#14519750—21no—
114#14519750—21no—
115#14519749—21no—
116#14519749—21no—
117#14519749—21no—
118#14519749—21no—
119#14519747—21no—
120#14519747—21no—
121#14519747—21no—
122#14519747—21no—
123#14519745—21no—
124#14519745—21no—
125#14519745—21no—
126#14519745—21no—
127C4×D244—21no—
128C4×D244—21no—
129C4×D244—21no—
130C4×D244—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61—21no—
135C4×C22⋊D61—21no—
136C4×C22⋊D61—21no—
137C4×C22⋊D61—21no—
138C4×C22⋊D61—21no—
139#14519734—21no—
140#14519734—21no—
141#14519734—21no—
142#14519734—21no—
143C2×C4⋊Dic61C2×C411yescharacteristic
144C2×#11758196C2×C411yescharacteristic
145C2×#11758196C2×C411yescharacteristic
146C2×#11758196C2×C411yescharacteristic
147C2×#11758196C2311yescharacteristic
148C2×C22⋊Dic61C2×C411yescharacteristic
149C2×C22⋊Dic61C2×C411yescharacteristic
150C2×#11758198C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2311yescharacteristic
156C2×C4×Dic61C2×C411yescharacteristic
157C22⋊#92418—21no—
158C22⋊#92418—21no—
159C22⋊#92418C2312yes—
160C22⋊#92418C2312yes—
161#14519689—22no—
162#14519689—22no—
163#14519689—22no—
164#14519689—22no—
165C22×D4×C61C2×C411yescharacteristic
166C23×C4×C61C2×C411yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C22×C8×C61—21no—
169C22×C8×C61—21no—
170C4×D4×C61—21no—
171C4×D4×C61—21no—
172C4×D4×C61—21no—
173C4×D4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2311yescharacteristic
177C2×C42×C61C2×C411yescharacteristic
178C22⋊C8×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61C2312yes—
181C22⋊C8×C61C2312yes—
182C24×C61C22×C411yescharacteristic
183C24×C61C22×C411yescharacteristic
184C23×D61—22no—
185C23×D61—22no—
186C23×D61—42no—
187C23×D61—42no—
188C23×D61C22⋊C411yescharacteristic
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C22⋊C411yescharacteristic
192C23×D61C22×C411yescharacteristic
193C23×D61C22×C411yescharacteristic
194C23×D61C22×C411yescharacteristic
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—42no—
202C22×C4×C61—42no—
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—22no—
215C2×C22⋊D61—22no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—42no—
224C2×C22⋊D61—42no—
225C22×Dic61—42no—
226C22×Dic61C22⋊C411yescharacteristic
227C22×Dic61C22⋊C411yescharacteristic
228C22×Dic61C22⋊C411yescharacteristic
229C22×Dic61C22⋊C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C22×Dic61C22×C411yescharacteristic
232C22×Dic61C22×C411yescharacteristic
233C22×Dic61C22×C411yescharacteristic
234C22×Dic61C22×C411yescharacteristic
235#11758222—44no—
236#11758222—44no—
237#11758222—44no—
238#11758222—44no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—42no—
244C2×D244—42no—
245C2×C4×D61—24no—
246C2×C4×D61—24no—
247C2×C4×D61—24no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—42no—
258C2×C4×D61—42no—
259C2×C4×D61—42no—
260C2×C4×D61C22⋊C411yescharacteristic
261C2×C4×D61C22⋊C411yescharacteristic
262C2×C4×D61C22⋊C411yescharacteristic
263C2×C4×D61C22⋊C411yescharacteristic
264C2×C4×D61C22⋊C411yescharacteristic
265C2×C4×D61C22⋊C411yescharacteristic
266C2×C4×D61C22⋊C411yescharacteristic
267C2×C4×D61C22⋊C411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×Dic122—21no—
277C2×Dic122—21no—
278C2×Dic122—42no—
279C2×C8×C61—22no—
280C2×C8×C61—22no—
281C2×C8×C61—42no—
282C2×C8×C61—42no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C42×C61—21no—
290C42×C61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C2×#92418—22no—
320C2×#92418—22no—
321C2×#92418—42no—
322C2×#92418—42no—
323#11758189—44no—
324#11758189—44no—
325C8×D61—44no—
326C8×D61—44no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61C2×C22⋊C411yescharacteristic
335C23×C61C2×C22⋊C411yescharacteristic
336C23×C61#13112yes—
337C23×C61#13112yes—
338C23×C61C23×C411yescharacteristic
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—21no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—48no—
363C22×D61—48no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61C2×C22⋊C411yescharacteristic
367C22×D61C2×C22⋊C411yescharacteristic
368C22×D61C2×C22⋊C411yescharacteristic
369C22×D61C2×C22⋊C411yescharacteristic
370D4×C61—42no—
371D4×C61—42no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—42no—
394C22⋊D61—42no—
395C22⋊D61—42no—
396C22⋊D61—42no—
397C22⋊D61—42no—
398C22⋊D61—42no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416D244—42no—
417D244—42no—
418D244—42no—
419D244—42no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—22no—
427C4×D61—22no—
428C4×D61—22no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—42no—
436C4×D61—42no—
437C4×D61#9914yes—
438Dic122—42no—
439Dic122—42no—
440C8×C61—42no—
441C8×C61—42no—
442#92418—42no—
443#92418—42no—
444#17381—611nomaximal, Sylow
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—42no—
452C22×C61—42no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—81no—
457C22×C61—81no—
458C22×C61#40812yes—
459C22×C61#40812yes—
460C22×C61C22×C22⋊C411yescharacteristic
461C22×C61C2×#13111yescharacteristic
462C22×C61C2×#13111yescharacteristic
463C2×D61—28no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—21no—
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—21no—
473C2×D61—21no—
474C2×D61—42no—
475C2×D61—42no—
476C2×D61—44no—
477C2×D61—42no—
478C2×D61—42no—
479C2×D61—44no—
480C2×D61—44no—
481C2×D61—41no—
482C2×D61—41no—
483C2×D61—41no—
484C2×D61—81no—
485C2×D61—81no—
486C2×D61C2×#9912yes—
487C2×D61#41312yes—
488C4×C61—21no—
489C4×C61—21no—
490C4×C61—21no—
491C4×C61—41no—
492C4×C61—41no—
493C4×C61—41no—
494C4×C61C2×#9912yes—
495Dic61—21no—
496Dic61—21no—
497Dic61—21no—
498Dic61—41no—
499Dic61—41no—
500Dic61—41no—
501Dic61C2×#9912yes—
502C2×#525—611no—
503C2×#407—611no—
504C22×C22⋊C8—611no—
505#1472—612no—
506#1471—612no—
507#1468—612no—
508#1468—612no—
509#1459—611no—
510#1459—611no—
511#1459—611no—
512#1459D6111yescharacteristic, complemented
513C2×C61—22no—
514C2×C61—21no—
515C2×C61—21no—
516C2×C61—22no—
517C2×C61—81no—
518C2×C61C2×#40811yescharacteristic
519C2×C61C22×#9911yescharacteristic
520C2×C61C2×#41311yescharacteristic
521D61—22no—
522D61—22no—
523D61—41no—
524D61—41no—
525D61—81no—
526C22×#41—611no—
527C24×C4—611no—
528C22×M16—1221no—
529C23×C8—1221no—
530#525—1221no—
531#525—1221no—
532#525—1221no—
533#525—1221no—
534#525—1221no—
535#525—1221no—
536#525—1221no—
537#525—1221no—
538C2×#123—611no—
539C2×#123—611no—
540C2×C22⋊Q8—611no—
541C2×C22⋊Q8—611no—
542C2×#121—611no—
543C2×#121—611no—
544C2×#120—611no—
545C2×#120—611no—
546C2×C4×D4—611no—
547C2×C4×D4—611no—
548C2×C4×D4—611no—
549C2×C4×D4C2×D6111yescharacteristic
550C2×#117—611no—
551#407—612no—
552#407—612no—
553#407—1221no—
554#407—1221no—
555C2×C22⋊C8—611no—
556C2×C22⋊C8—611no—
557C2×C22⋊C8—612no—
558C2×C22⋊C8—612no—
559C2×C22⋊C8—1221no—
560C2×C22⋊C8—1221no—
561C2×C22⋊C8—1221no—
562C2×C22⋊C8—1221no—
563C2×C22⋊C8C2×D6111yescharacteristic
564C2×C22⋊C8C2×D6111yescharacteristic
565#324—612no—
566#324—612no—
567#324—612no—
568#324C2×D6112yescomplemented
569#323—612no—
570#323—612no—
571#323—612no—
572#323C2×D6112yescomplemented
573C61#1738111yescharacteristic, complemented, Sylow
574C25—611no—
575C2×#41—1221no—
576C2×#41—1221no—
577C2×#41—1221no—
578C2×#41—1221no—
579C2×#41—2444no—
580C22×Q8—611no—
581C22×D4—611no—
582C22×D4—611no—
583C22×D4—611no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4C4×D6111yescharacteristic
588C23×C4—611no—
589C23×C4—611no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—611no—
602C23×C4—2444no—
603C23×C4C4×D6111yescharacteristic
604C23×C4C22×D6111yescharacteristic
605C2×M16—1222no—
606C2×M16—1222no—
607C2×M16—2444no—
608C22×C8—21no—
609C22×C8—21no—
610C22×C8—1222no—
611C22×C8—1222no—
612C22×C8—1221no—
613C22×C8—1221no—
614C22×C8—2444no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620#123—1221no—
621#123—1221no—
622#123—1221no—
623C22⋊Q8—1221no—
624C22⋊Q8—1221no—
625C22⋊Q8—1221no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#120—1221no—
640#120—1221no—
641#120—1221no—
642#120—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647C4×D4—21no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663#117—1221no—
664#117—1221no—
665#117—1221no—
666#117—1221no—
667C2×C4⋊C4—611no—
668C2×C4⋊C4—611no—
669C2×C4⋊C4—611no—
670C2×C4⋊C4—611no—
671C2×C4⋊C4—611no—
672C2×C4⋊C4C22×D6111yescharacteristic
673C2×C22⋊C4—611no—
674C2×C22⋊C4—611no—
675C2×C22⋊C4—611no—
676C2×C22⋊C4—611no—
677C2×C22⋊C4—611no—
678C2×C22⋊C4—611no—
679C2×C22⋊C4—611no—
680C2×C22⋊C4—611no—
681C2×C22⋊C4C4×D6111yescharacteristic
682C2×C22⋊C4C22×D6111yescharacteristic
683C2×C42—611no—
684C2×C42C4×D6111yescharacteristic
685C22⋊C8—21no—
686C22⋊C8—21no—
687C22⋊C8—612no—
688C22⋊C8—612no—
689C22⋊C8—1222no—
690C22⋊C8—1222no—
691C22⋊C8—1222no—
692C22⋊C8—1222no—
693C22⋊C8—1221no—
694C22⋊C8—1221no—
695C22⋊C8C22×D6112yes—
696C22⋊C8C22×D6112yes—
697C24—611no—
698C24—611no—
699C24—611no—
700C24—611no—
701C24—611no—
702C24—611no—
703C24—611no—
704C24—1222no—
705C24—1222no—
706C24—2442no—
707C24—2442no—
708C24C2×C4×D6111yescharacteristic
709C24C2×C4×D6111yescharacteristic
710#41—2444no—
711#41—2444no—
712#41—2444no—
713#41—2444no—
714C2×Q8—1221no—
715C2×Q8—1221no—
716C2×Q8—2442no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1222no—
734C2×D4—1222no—
735C2×D4—2442no—
736C2×D4—2442no—
737C2×D4—2442no—
738C2×D4—2442no—
739C2×D4—2442no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—1224no—
770C22×C4—1224no—
771C22×C4—1224no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—2442no—
775C22×C4—2442no—
776C22×C4—2442no—
777C22×C4—2442no—
778C22×C4—2442no—
779C22×C4—2442no—
780C22×C4—2442no—
781C22×C4—2442no—
782C22×C4—2442no—
783C22×C4—2442no—
784C22×C4—2442no—
785C22×C4C2×C4×D6111yescharacteristic
786C22×C4C2×C4×D6111yescharacteristic
787C22×C4C2×C4×D6111yescharacteristic
788C22×C4C2×C4×D6111yescharacteristic
789C22×C4D4×D6111yescharacteristic
790C22×C4D4×D6111yescharacteristic
791C22×C4D4×D6111yescharacteristic
792C22×C4D4×D6111yescharacteristic
793C22×C4C23×D6111yescharacteristic
794M16—2444no—
795M16—2444no—
796C2×C8—22no—
797C2×C8—22no—
798C2×C8—42no—
799C2×C8—42no—
800C2×C8—1222no—
801C2×C8—1222no—
802C2×C8—2444no—
803C2×C8—2444no—
804C2×C8—2442no—
805C2×C8—2442no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1221no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C42—21no—
839C42—21no—
840C42—1221no—
841C42—1221no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—611no—
850C23—611no—
851C23—611no—
852C23—611no—
853C23—1222no—
854C23—1222no—
855C23—1222no—
856C23—1222no—
857C23—1222no—
858C23—1222no—
859C23—1222no—
860C23—1222no—
861C23—1222no—
862C23—1222no—
863C23—1221no—
864C23—1221no—
865C23—1221no—
866C23—1221no—
867C23—1221no—
868C23—1221no—
869C23—1221no—
870C23—2441no—
871C23—2441no—
872C23—2441no—
873C23—2441no—
874C23—2441no—
875C23—2441no—
876C23—2441no—
877C23—2441no—
878C23—2448no—
879C23—2448no—
880C23C22⋊C4×D6111yescharacteristic
881C23C22⋊C4×D6111yescharacteristic
882C23#1451978312yes—
883C23#1451978512yes—
884C23C22×C4×D6111yescharacteristic
885Q8—2442no—
886Q8—2442no—
887D4—42no—
888D4—42no—
889D4—2442no—
890D4—2442no—
891D4—2442no—
892D4—2442no—
893D4—2442no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4—2442no—
898D4—2442no—
899D4—2442no—
900D4—2442no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—611no—
917C2×C4—614no—
918C2×C4—611no—
919C2×C4—611no—
920C2×C4—611no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1222no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1222no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1221no—
934C2×C4—1221no—
935C2×C4—1221no—
936C2×C4—1221no—
937C2×C4—1221no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2442no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2442no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4C22⋊C4×D6111yescharacteristic
952C2×C4C22⋊C4×D6111yescharacteristic
953C2×C4C2×D4×D6111yescharacteristic
954C2×C4C2×D4×D6111yescharacteristic
955C8—42no—
956C8—42no—
957C8—2442no—
958C8—2442no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—42no—
966C22—42no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—81no—
971C22—81no—
972C22—612no—
973C22—612no—
974C22—1228no—
975C22—1221no—
976C22—1221no—
977C22—1221no—
978C22—1221no—
979C22—1221no—
980C22—1221no—
981C22—1221no—
982C22—1221no—
983C22—1221no—
984C22—1221no—
985C22—4881no—
986C22—4881no—
987C22—2442no—
988C22—2442no—
989C22—2442no—
990C22—2442no—
991C22—2444no—
992C22—2444no—
993C22—2444no—
994C22—2441no—
995C22—2441no—
996C22—2441no—
997C22#1683972712yes—
998C22#1683972712yes—
999C22C2×C22⋊C4×D6111yescharacteristic
1000C22C2×#1451978311yescharacteristic
1001C22C2×#1451978511yescharacteristic
1002C4—21no—
1003C4—21no—
1004C4—21no—
1005C4—41no—
1006C4—41no—
1007C4—41no—
1008C4—612no—
1009C4—1221no—
1010C4—1221no—
1011C4—1221no—
1012C4—2441no—
1013C4—2441no—
1014C4—2441no—
1015C4#99×D6112yes—
1016C2—21no—
1017C2—21no—
1018C2—22no—
1019C2—22no—
1020C2—81no—
1021C2—1222no—
1022C2—1222no—
1023C2—4881no—
1024C2—2441no—
1025C2—2441no—
1026C2C2×#1683972711yescharacteristic
1027C2C2×#99×D6111yescharacteristic
1028C2#413×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1459C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840271C2
cosocleC22×C4×C61C24
hypercenter#1459D61
hypocenterC61#17381
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. C2×C22⋊C8×D61C2semidirect
4. #21444181C2semidirect
5. #21444177C2semidirect
6. #21444166C2semidirect
7. #21444164C2semidirect
8. #21444137C2semidirect
9. #21444135C2semidirect
10. #21444135C2semidirect
11. C61×#1459C2semidirect
48. #16839488C22semidirect
49. #16839487C22semidirect
50. #16839487C22semidirect
51. #16839486C22semidirect
52. #16839485C22semidirect
53. #16839485C22semidirect
57. C61×#324C22semidirect
58. C61×#323C22semidirect
512. #1459D61semidirect
568. #324C2×D61semidirect
572. #323C2×D61semidirect
573. C61#17381semidirect

Maximal subgroups

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

subgroupindex
C2×#168402712
C2×#168397242
C2×C22⋊C8×D612
#214441812
#214441772
#214441662
#214441642
#214441372
#214441352
C61×#14592
#1738161