Finite Group Databasebeta

← #29646196

Subgroups — #29646196

Order 15616.

1424 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840404C211yesmaximal, characteristic
2#21454269C211yesmaximal, characteristic, complemented
3#21454265C211yesmaximal, characteristic, complemented
4#21444177C211yesmaximal, characteristic, complemented
5#21444177C211yesmaximal, characteristic, complemented
6#21444167C211yesmaximal, characteristic, complemented
7#21444166C211yesmaximal, characteristic, complemented
8#21444166C211yesmaximal, characteristic, complemented
9#21444156C211yesmaximal, characteristic, complemented
10#21444145C211yesmaximal, characteristic, complemented
11#21444144C211yesmaximal, characteristic, complemented
12#21444136C211yesmaximal, characteristic, complemented
13C2×#16839485C211yesmaximal, characteristic, complemented
14#323×D61C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C411yescharacteristic
18C2×#14519785—21no—
19C2×#14519783—21no—
20#16840404—21no—
21#16840404—21no—
22#16840404—21no—
23#16840404—21no—
24#16840404—21no—
25#16840404—21no—
26#16840404—21no—
27#16840404—21no—
28C2×#14519763C411yescharacteristic
29C2×#14519762C2211yescharacteristic
30C2×#14519755C411yescharacteristic
31C2×#14519752C411yescharacteristic
32C2×#14519750C2211yescharacteristic
33C2×#14519749C411yescharacteristic
34C2×#14519747C411yescharacteristic
35C2×#14519747C411yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519737C411yescharacteristic
38C22×#11758198C2211yescharacteristic
39C2×C22⋊C4×D61C2211yescharacteristic
40#16839730—21no—
41#16839728—21no—
42#16839727—21no—
43#16839727—21no—
44#16839727—21no—
45#16839727—21no—
46#16839726C2211yescharacteristic, complemented
47#16839724C2211yescharacteristic, complemented
48#16839724C2211yescharacteristic, complemented
49#16839724C2211yescharacteristic, complemented
50#16839724C2211yescharacteristic, complemented
51C2×C22⋊#92418C2211yescharacteristic, complemented
52C22⋊C8×D61C2211yescharacteristic, complemented
53C22⋊C8×D61C2211yescharacteristic, complemented
54C22⋊C8×D61C2211yescharacteristic, complemented
55C22⋊C8×D61C2211yescharacteristic, complemented
56#16839488C2211yescharacteristic, complemented
57#16839488C2211yescharacteristic, complemented
58#16839486C2211yescharacteristic, complemented
59#16839486C2211yescharacteristic, complemented
60#16839485C2211yescharacteristic
61#16839485C2211yescharacteristic
62#16839485C2211yescharacteristic
63#16839485C2211yescharacteristic
64#16839485C2211yescharacteristic, complemented
65#16839485C2211yescharacteristic, complemented
66#16839485C2211yescharacteristic, complemented
67#16839485C2211yescharacteristic, complemented
68C2×#123×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic, complemented
70C2×C22⋊C8×C61C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic, complemented
74C61×#323C2211yescharacteristic, complemented
75C24×D61C2×C411yescharacteristic
76C24×D61C2×C411yescharacteristic
77C2×#11758222—44no—
78C2×#11758222D411yescharacteristic
79C2×#11758222D411yescharacteristic
80C2×#11758222D411yescharacteristic
81C2×#11758222D411yescharacteristic
82C2×#11758222D411yescharacteristic
83C2×#11758222D411yescharacteristic
84C2×#11758222D411yescharacteristic
85C2×#11758222D411yescharacteristic
86C22×Dic122C2×C411yescharacteristic
87C22×D244C2×C411yescharacteristic
88C22×D244C2×C411yescharacteristic
89C22×D244C2×C411yescharacteristic
90C22×D244C2×C411yescharacteristic
91C22×C22⋊D61C2×C411yescharacteristic
92C22×C22⋊D61C2×C411yescharacteristic
93C22×C22⋊D61C2×C411yescharacteristic
94C22×C22⋊D61C2×C411yescharacteristic
95C2×D4×D61—21no—
96C2×D4×D61—21no—
97C2×D4×D61—21no—
98C2×D4×D61—21no—
99C2×D4×D61—44no—
100C23×Dic61C2×C411yescharacteristic
101C22×C4×D61C2×C411yescharacteristic
102C22×C4×D61C2×C411yescharacteristic
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105#14519785—44no—
106#14519783—44no—
107C2×#11758194—21no—
108C2×#11758189—21no—
109C2×#11758189—21no—
110C2×#11758189—21no—
111C2×#11758189—21no—
112C22×#92418—21no—
113C2×C8×D61—21no—
114C2×C8×D61—21no—
115C2×C8×D61—21no—
116C2×C8×D61—21no—
117#14519763—21no—
118#14519763—21no—
119#14519763—21no—
120#14519763—21no—
121#14519762—21no—
122#14519762—21no—
123#14519762—21no—
124#14519762—21no—
125#14519755—21no—
126#14519755—21no—
127#14519755—21no—
128#14519755—21no—
129#14519752—21no—
130#14519752—21no—
131#14519752—21no—
132#14519752—21no—
133#14519750—21no—
134#14519750—21no—
135#14519750—21no—
136#14519750—21no—
137#14519749—21no—
138#14519749—21no—
139#14519749—21no—
140#14519749—21no—
141#14519747—21no—
142#14519747—21no—
143#14519747—21no—
144#14519747—21no—
145#14519747—21no—
146#14519747—21no—
147#14519747—21no—
148#14519747—21no—
149#14519739—21no—
150#14519739—21no—
151#14519739—21no—
152#14519739—21no—
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519737—21no—
157C2×#11758196C2×C411yescharacteristic
158C2×#11758196C2×C411yescharacteristic
159C2×C22⋊Dic61C2×C411yescharacteristic
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198C2×C411yescharacteristic
165C2×#11758198C2×C411yescharacteristic
166C2×#11758198C2×C411yescharacteristic
167C2×#11758198C2×C411yescharacteristic
168C2×#11758198C2×C411yescharacteristic
169C2×#11758198C2×C411yescharacteristic
170C2×#11758198C2311yescharacteristic
171C2×#11758198C2311yescharacteristic
172C22⋊C4×D61—21no—
173C22⋊C4×D61—21no—
174C22⋊C4×D61—21no—
175C22⋊C4×D61—21no—
176C2×C4×Dic61C2×C411yescharacteristic
177C22⋊#92418—21no—
178C22⋊#92418—21no—
179C22⋊#92418C2311yescharacteristic
180C22⋊#92418C2311yescharacteristic
181C22⋊#92418C2311yescharacteristic
182C22⋊#92418C2311yescharacteristic
183#14519689—21no—
184#14519689—21no—
185#14519689—21no—
186#14519689—21no—
187#14519689—21no—
188#14519689—21no—
189#14519689—21no—
190#14519689—21no—
191C22×D4×C61C2×C411yescharacteristic
192C23×C4×C61C2311yescharacteristic
193C2×M16×C61—21no—
194C22×C8×C61—21no—
195#123×C61—21no—
196#123×C61—21no—
197#123×C61—21no—
198#123×C61—21no—
199C2×C4⋊C4×C61C2×C411yescharacteristic
200C2×C4⋊C4×C61C2311yescharacteristic
201C2×C22⋊C4×C61C2×C411yescharacteristic
202C2×C22⋊C4×C61C2×C411yescharacteristic
203C2×C22⋊C4×C61C2311yescharacteristic
204C22⋊C8×C61—21no—
205C22⋊C8×C61—21no—
206C22⋊C8×C61C2311yescharacteristic
207C22⋊C8×C61C2311yescharacteristic
208C22⋊C8×C61C2311yescharacteristic
209C22⋊C8×C61C2311yescharacteristic
210C24×C61C22×C411yescharacteristic
211C24×C61C22×C411yescharacteristic
212C23×D61—21no—
213C23×D61—21no—
214C23×D61—21no—
215C23×D61—21no—
216C23×D61—22no—
217C23×D61—22no—
218C23×D61—41no—
219C23×D61—41no—
220C23×D61—42no—
221C23×D61—42no—
222C23×D61—81no—
223C23×D61—81no—
224C23×D61C22×C411yescharacteristic
225C23×D61C22×C411yescharacteristic
226C23×D61C22×C411yescharacteristic
227C23×D61C22×C411yescharacteristic
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—42no—
231C22×C4×C61—42no—
232C22×C4×C61C22×C411yescharacteristic
233C22×C4×C61C22×C411yescharacteristic
234C22×C4×C61C22×C411yescharacteristic
235C22×C4×C61C22×C411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2411yescharacteristic
241C2×C22⋊D61—24no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C2×C22⋊D61—42no—
247C2×C22⋊D61—42no—
248C2×C22⋊D61—81no—
249C2×C22⋊D61C22⋊C411yescharacteristic
250C2×C22⋊D61C22⋊C411yescharacteristic
251C2×C22⋊D61C22⋊C411yescharacteristic
252C2×C22⋊D61C22⋊C411yescharacteristic
253C2×C22⋊D61C22⋊C411yescharacteristic
254C2×C22⋊D61C22⋊C411yescharacteristic
255C2×C22⋊D61C22⋊C411yescharacteristic
256C2×C22⋊D61C22⋊C411yescharacteristic
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—81no—
260C22×Dic61C22×C411yescharacteristic
261C22×Dic61C22×C411yescharacteristic
262C22×Dic61C22×C411yescharacteristic
263C22×Dic61C22×C411yescharacteristic
264D4×D61—44no—
265D4×D61—44no—
266D4×D61—44no—
267D4×D61—44no—
268#11758222—24no—
269#11758222—24no—
270#11758222—42no—
271#11758222—42no—
272#11758222—42no—
273#11758222—42no—
274#11758222—42no—
275#11758222—42no—
276C2×D244—21no—
277C2×D244—21no—
278C2×D244—21no—
279C2×D244—21no—
280C2×D244—22no—
281C2×D244—21no—
282C2×D244—21no—
283C2×D244—42no—
284C2×D244—41no—
285C2×D244—42no—
286C2×D244—81no—
287C2×D244C22⋊C411yescharacteristic
288C2×D244C22⋊C411yescharacteristic
289C2×D244C22⋊C411yescharacteristic
290C2×D244C22⋊C411yescharacteristic
291C2×C4×D61—21no—
292C2×C4×D61—21no—
293C2×C4×D61—21no—
294C2×C4×D61—21no—
295C2×C4×D61—42no—
296C2×C4×D61—42no—
297C2×C4×D61—42no—
298C2×C4×D61—81no—
299C2×C4×D61C2×D411yescharacteristic
300C2×C4×D61C2×D411yescharacteristic
301C2×C4×D61C2×D411yescharacteristic
302C2×C4×D61C2×D411yescharacteristic
303C2×C4×D61C2×D411yescharacteristic
304C2×C4×D61C2×D411yescharacteristic
305C2×C4×D61C2×D411yescharacteristic
306C2×C4×D61C2×D411yescharacteristic
307C2×Dic122—42no—
308C2×Dic122C22⋊C411yescharacteristic
309C2×Dic122C22⋊C411yescharacteristic
310C2×Dic122C22⋊C411yescharacteristic
311C2×Dic122C22⋊C411yescharacteristic
312M16×C61—42no—
313C2×C8×C61—21no—
314C2×C8×C61—21no—
315C2×C8×C61—21no—
316C2×C8×C61—21no—
317C2×C8×C61—42no—
318C4⋊C4×C61—21no—
319C4⋊C4×C61—21no—
320C4⋊C4×C61—21no—
321C4⋊C4×C61—21no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊Dic61—21no—
329C22⋊Dic61—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198—21no—
338#11758198—21no—
339#11758198—21no—
340#11758198—21no—
341#11758198—21no—
342#11758198—21no—
343#11758198—21no—
344#11758198—21no—
345#11758198—21no—
346#11758196—21no—
347#11758196—21no—
348#11758196—21no—
349#11758196—21no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352#11758194—42no—
353C2×#92418—21no—
354C2×#92418—21no—
355C2×#92418—21no—
356C2×#92418—21no—
357C2×#92418—42no—
358#11758189—42no—
359#11758189—42no—
360#11758189—42no—
361#11758189—42no—
362C8×D61—42no—
363C8×D61—42no—
364C8×D61—42no—
365C8×D61—42no—
366C23×C61—21no—
367C23×C61—21no—
368C23×C61—22no—
369C23×C61—21no—
370C23×C61—21no—
371C23×C61—21no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61C2×C22⋊C411yescharacteristic
376C23×C61C2×C22⋊C411yescharacteristic
377C23×C61C23×C411yescharacteristic
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61—22no—
385C22×D61—21no—
386C22×D61—21no—
387C22×D61—21no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—42no—
392C22×D61—42no—
393C22×D61—42no—
394C22×D61—42no—
395C22×D61—42no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—42no—
399C22×D61—42no—
400C22×D61—42no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—81no—
404C22×D61—81no—
405C22×D61—81no—
406C22×D61—81no—
407C22×D61—84no—
408C22×D61—84no—
409C22×D61—84no—
410C22×D61—84no—
411C22×D61C2×C22⋊C411yescharacteristic
412C22×D61C2×C22⋊C411yescharacteristic
413C22×D61C2×C22⋊C411yescharacteristic
414C22×D61C2×C22⋊C411yescharacteristic
415C22×D61#13112yescomplemented
416D4×C61—42no—
417D4×C61—42no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—21no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61C2×C22⋊C411yescharacteristic
432C2×C4×C61C2×C22⋊C411yescharacteristic
433C2×C4×C61C22×D411yescharacteristic
434C2×C4×C61C22×D411yescharacteristic
435C22⋊D61—22no—
436C22⋊D61—22no—
437C22⋊D61—22no—
438C22⋊D61—22no—
439C22⋊D61—22no—
440C22⋊D61—41no—
441C22⋊D61—41no—
442C22⋊D61—42no—
443C22⋊D61—42no—
444C22⋊D61—81no—
445C22⋊D61—81no—
446C22⋊D61#9914yes—
447C2×Dic61—22no—
448C2×Dic61—21no—
449C2×Dic61—21no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—81no—
454C2×Dic61—81no—
455C2×Dic61C2×C22⋊C411yescharacteristic
456C2×Dic61C2×C22⋊C411yescharacteristic
457C2×Dic61C2×C22⋊C411yescharacteristic
458C2×Dic61C2×C22⋊C411yescharacteristic
459D244—22no—
460D244—22no—
461D244—41no—
462D244—41no—
463D244—42no—
464D244—42no—
465D244—42no—
466D244—42no—
467D244—81no—
468D244—81no—
469C4×D61—22no—
470C4×D61—22no—
471C4×D61—22no—
472C4×D61—22no—
473C4×D61—41no—
474C4×D61—41no—
475C4×D61—41no—
476C4×D61—41no—
477C4×D61—42no—
478C4×D61—42no—
479C4×D61—81no—
480C4×D61—81no—
481Dic122—22no—
482Dic122—22no—
483Dic122—41no—
484Dic122—41no—
485C8×C61—41no—
486C8×C61—41no—
487C8×C61—41no—
488C8×C61—41no—
489#92418—41no—
490#92418—41no—
491#92418—41no—
492#92418—41no—
493#17411—611nomaximal, Sylow
494C22×C61—21no—
495C22×C61—21no—
496C22×C61—21no—
497C22×C61—21no—
498C22×C61—21no—
499C22×C61—21no—
500C22×C61—21no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—41no—
504C22×C61—41no—
505C22×C61—41no—
506C22×C61—81no—
507C22×C61—81no—
508C22×C61C2×#9912yes—
509C22×C61C22×C22⋊C411yescharacteristic
510C22×C61C2×#13111yescharacteristic
511C22×C61#56811yescharacteristic
512C2×D61—21no—
513C2×D61—21no—
514C2×D61—22no—
515C2×D61—21no—
516C2×D61—21no—
517C2×D61—21no—
518C2×D61—21no—
519C2×D61—21no—
520C2×D61—21no—
521C2×D61—21no—
522C2×D61—21no—
523C2×D61—21no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—41no—
528C2×D61—41no—
529C2×D61—42no—
530C2×D61—41no—
531C2×D61—41no—
532C2×D61—41no—
533C2×D61—84no—
534C2×D61—81no—
535C2×D61—81no—
536C2×D61—84no—
537C2×D61—84no—
538C2×D61—84no—
539C2×D61—81no—
540C2×D61—81no—
541C2×D61C2×#9912yes—
542C4×C61—21no—
543C4×C61—21no—
544C4×C61—21no—
545C4×C61—21no—
546C4×C61—41no—
547C4×C61—41no—
548C4×C61—41no—
549Dic61—21no—
550Dic61—21no—
551Dic61—21no—
552Dic61—41no—
553Dic61—41no—
554Dic61C2×#9912yes—
555C2×#546—611no—
556#2880—611no—
557#2880—611no—
558#1471—611no—
559#1471—611no—
560#1468—611no—
561#1468—611no—
562#1468—611no—
563#1468D6111yescharacteristic, complemented
564#1465—611no—
565#1462—611no—
566#1462—611no—
567#1459—611no—
568C2×#323—611no—
569C2×#323—611no—
570C2×C61—21no—
571C2×C61—21no—
572C2×C61—22no—
573C2×C61—41no—
574C2×C61—81no—
575C2×C61#288011yescharacteristic
576C2×C61C22×#9911yescharacteristic
577C2×C61#288811yescharacteristic
578D61—22no—
579D61—41no—
580D61—41no—
581D61—41no—
582D61—42no—
583D61—81no—
584C22×#41—611no—
585C23×D4—611no—
586C2×#131—1221no—
587C2×#131—1221no—
588#546—1221no—
589#546—1221no—
590#546—1221no—
591#546—1221no—
592#546—1221no—
593#546—1221no—
594#546—1221no—
595#546—1221no—
596C2×#124—611no—
597C2×#123—611no—
598C2×#123C2×D6111yescharacteristic
599C2×C22⋊Q8—611no—
600C2×#121—611no—
601C2×#121—611no—
602C2×#121—611no—
603C2×#120—611no—
604C2×#120—611no—
605C2×C4×D4—611no—
606C2×C4×D4—611no—
607C22×C22⋊C4—611no—
608C22×C22⋊C4—611no—
609#408—1221no—
610#408—1221no—
611#408—1221no—
612#408—1221no—
613#408—1221no—
614#408—1221no—
615#407—611no—
616#407—611no—
617#407—611no—
618#407—611no—
619#407—611no—
620#407C2×D6111yescharacteristic, complemented
621C2×C22⋊C8—611no—
622C2×C22⋊C8—611no—
623C2×C22⋊C8—611no—
624C2×C22⋊C8—611no—
625C2×C22⋊C8—611no—
626C2×C22⋊C8C2×D6111yescharacteristic, complemented
627#324—611no—
628#324—611no—
629#324C2×D6111yescharacteristic, complemented
630#324C2×D6111yescharacteristic, complemented
631#323—611no—
632#323—611no—
633#323—611no—
634#323—611no—
635#323—611no—
636#323—611no—
637#323—611no—
638#323—611no—
639#323—611no—
640#323—611no—
641#323C2×D6111yescharacteristic, complemented
642#323C2×D6111yescharacteristic, complemented
643C61#1741111yescharacteristic, complemented, Sylow
644C25—611no—
645C25—611no—
646C2×#41—611no—
647C2×#41—611no—
648C2×#41—611no—
649C2×#41—611no—
650C2×#41—611no—
651C2×#41—611no—
652C2×#41—611no—
653C2×#41—611no—
654C2×#41—2444no—
655C22×Q8—611no—
656C22×D4—611no—
657C22×D4—611no—
658C22×D4—611no—
659C22×D4—611no—
660C22×D4—611no—
661C22×D4—611no—
662C22×D4—611no—
663C22×D4—611no—
664C22×D4—1221no—
665C22×D4—1221no—
666C22×D4—1221no—
667C22×D4—1221no—
668C22×D4—2444no—
669C22×D4C4×D6111yescharacteristic
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—611no—
673C23×C4—611no—
674C23×C4—611no—
675C23×C4C22×D6111yescharacteristic
676#131—2444no—
677#131—2444no—
678C2×M16—21no—
679C2×M16—1221no—
680C2×M16—1221no—
681C2×M16—1221no—
682C2×M16—1221no—
683C2×M16—1221no—
684C22×C8—21no—
685C22×C8—1221no—
686C22×C8—1221no—
687C22×C8—1221no—
688C22×C8—1221no—
689C22×C8—1221no—
690#124—1221no—
691#124—1221no—
692#124—1221no—
693#124—1221no—
694#123—21no—
695#123—21no—
696#123—21no—
697#123—21no—
698#123—1221no—
699#123—1221no—
700#123—1221no—
701#123—1221no—
702C22⋊Q8—1221no—
703C22⋊Q8—1221no—
704C22⋊Q8—1221no—
705C22⋊Q8—1221no—
706#121—1221no—
707#121—1221no—
708#121—1221no—
709#121—1221no—
710#121—1221no—
711#121—1221no—
712#121—1221no—
713#121—1221no—
714#121—1221no—
715#121—1221no—
716#121—1221no—
717#121—1221no—
718#120—1221no—
719#120—1221no—
720#120—1221no—
721#120—1221no—
722#120—1221no—
723#120—1221no—
724#120—1221no—
725#120—1221no—
726C4×D4—1221no—
727C4×D4—1221no—
728C4×D4—1221no—
729C4×D4—1221no—
730C4×D4—1221no—
731C4×D4—1221no—
732C4×D4—1221no—
733C4×D4—1221no—
734C2×C4⋊C4—611no—
735C2×C4⋊C4—611no—
736C2×C4⋊C4C4×D6111yescharacteristic
737C2×C4⋊C4C22×D6111yescharacteristic
738C2×C22⋊C4—611no—
739C2×C22⋊C4—611no—
740C2×C22⋊C4—611no—
741C2×C22⋊C4—611no—
742C2×C22⋊C4—611no—
743C2×C22⋊C4—611no—
744C2×C22⋊C4—611no—
745C2×C22⋊C4—611no—
746C2×C22⋊C4—611no—
747C2×C22⋊C4—1221no—
748C2×C22⋊C4—1221no—
749C2×C22⋊C4—1221no—
750C2×C22⋊C4—1221no—
751C2×C22⋊C4—1221no—
752C2×C22⋊C4—1221no—
753C2×C22⋊C4—1221no—
754C2×C22⋊C4—1221no—
755C2×C22⋊C4C4×D6111yescharacteristic
756C2×C22⋊C4C4×D6111yescharacteristic
757C2×C22⋊C4C22×D6111yescharacteristic
758C2×C42—611no—
759C22⋊C8—21no—
760C22⋊C8—21no—
761C22⋊C8—611no—
762C22⋊C8—611no—
763C22⋊C8—611no—
764C22⋊C8—611no—
765C22⋊C8—1221no—
766C22⋊C8—1221no—
767C22⋊C8—1221no—
768C22⋊C8—1221no—
769C22⋊C8—1221no—
770C22⋊C8—1221no—
771C22⋊C8—1221no—
772C22⋊C8—1221no—
773C22⋊C8—1221no—
774C22⋊C8—1221no—
775C22⋊C8C22×D6111yescharacteristic
776C22⋊C8C22×D6111yescharacteristic
777C22⋊C8C22×D6111yescharacteristic
778C22⋊C8C22×D6111yescharacteristic
779C24—611no—
780C24—611no—
781C24—611no—
782C24—611no—
783C24—1222no—
784C24—1222no—
785C24—1221no—
786C24—1221no—
787C24—1221no—
788C24—1221no—
789C24—4881no—
790C24—4881no—
791C24—2441no—
792C24—2441no—
793C24—2442no—
794C24—2442no—
795C24C2×C4×D6111yescharacteristic
796C24C2×C4×D6111yescharacteristic
797#41—1224no—
798#41—1224no—
799#41—2442no—
800#41—2442no—
801#41—2442no—
802#41—2442no—
803#41—2442no—
804#41—2442no—
805C2×Q8—611no—
806C2×Q8—611no—
807C2×Q8—611no—
808C2×Q8—611no—
809C2×Q8—2442no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—42no—
813C2×D4—611no—
814C2×D4—611no—
815C2×D4—611no—
816C2×D4—611no—
817C2×D4—611no—
818C2×D4—611no—
819C2×D4—611no—
820C2×D4—611no—
821C2×D4—611no—
822C2×D4—611no—
823C2×D4—611no—
824C2×D4—611no—
825C2×D4—1221no—
826C2×D4—1221no—
827C2×D4—1221no—
828C2×D4—1221no—
829C2×D4—1221no—
830C2×D4—1221no—
831C2×D4—1222no—
832C2×D4—1221no—
833C2×D4—1221no—
834C2×D4—1224no—
835C2×D4—1221no—
836C2×D4—1221no—
837C2×D4—4881no—
838C2×D4—4881no—
839C2×D4—2441no—
840C2×D4—2442no—
841C2×D4—2442no—
842C2×D4—2442no—
843C2×D4—2444no—
844C2×D4—2444no—
845C2×D4—2444no—
846C2×D4—2444no—
847C2×D4—2442no—
848C22×C4—42no—
849C22×C4—611no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—611no—
856C22×C4—611no—
857C22×C4—611no—
858C22×C4—611no—
859C22×C4—611no—
860C22×C4—611no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—4881no—
868C22×C4—4881no—
869C22×C4—2442no—
870C22×C4—2442no—
871C22×C4—2442no—
872C22×C4C2×C4×D6111yescharacteristic
873C22×C4C2×C4×D6111yescharacteristic
874C22×C4C2×C4×D6111yescharacteristic
875C22×C4C2×C4×D6111yescharacteristic
876C22×C4D4×D6111yescharacteristic
877C22×C4D4×D6111yescharacteristic
878C22×C4D4×D6111yescharacteristic
879C22×C4D4×D6111yescharacteristic
880C22×C4C23×D6111yescharacteristic
881M16—42no—
882M16—2442no—
883M16—2442no—
884M16—2442no—
885M16—2442no—
886M16—2442no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—42no—
892C2×C8—1221no—
893C2×C8—1221no—
894C2×C8—1221no—
895C2×C8—1221no—
896C2×C8—2442no—
897C2×C8—2442no—
898C2×C8—2442no—
899C2×C8—2442no—
900C2×C8—2442no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—1221no—
906C4⋊C4—1221no—
907C4⋊C4—1221no—
908C4⋊C4—1221no—
909C22⋊C4—21no—
910C22⋊C4—21no—
911C22⋊C4—21no—
912C22⋊C4—21no—
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—1221no—
916C22⋊C4—1221no—
917C22⋊C4—1221no—
918C22⋊C4—1221no—
919C22⋊C4—1221no—
920C22⋊C4—1221no—
921C22⋊C4—1221no—
922C22⋊C4—1221no—
923C22⋊C4—1221no—
924C22⋊C4—1221no—
925C22⋊C4—1221no—
926C22⋊C4—1221no—
927C22⋊C4—1221no—
928C22⋊C4—1221no—
929C22⋊C4—1221no—
930C22⋊C4—1221no—
931C22⋊C4—1221no—
932C22⋊C4—1221no—
933C42—1221no—
934C42—1221no—
935C23—22no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—611no—
945C23—611no—
946C23—611no—
947C23—611no—
948C23—612no—
949C23—1222no—
950C23—1221no—
951C23—1221no—
952C23—1221no—
953C23—1221no—
954C23—1221no—
955C23—1221no—
956C23—1221no—
957C23—1221no—
958C23—1221no—
959C23—4881no—
960C23—4881no—
961C23—4881no—
962C23—4881no—
963C23—4884no—
964C23—4884no—
965C23—4884no—
966C23—4884no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2442no—
971C23—2442no—
972C23—2441no—
973C23—2441no—
974C23—2442no—
975C23—2441no—
976C23—2441no—
977C23—2442no—
978C23—2442no—
979C23—2442no—
980C23—2442no—
981C23—2442no—
982C23C22⋊C4×D6111yescharacteristic
983C23C22⋊C4×D6111yescharacteristic
984C23C22×C4×D6111yescharacteristic
985Q8—1222no—
986Q8—1222no—
987Q8—2441no—
988Q8—2441no—
989D4—42no—
990D4—42no—
991D4—614no—
992D4—1222no—
993D4—1222no—
994D4—1222no—
995D4—1222no—
996D4—1222no—
997D4—1222no—
998D4—1222no—
999D4—4881no—
1000D4—4881no—
1001D4—4881no—
1002D4—4881no—
1003D4—2441no—
1004D4—2441no—
1005D4—2442no—
1006D4—2442no—
1007D4—2442no—
1008D4—2442no—
1009D4—2442no—
1010D4—2441no—
1011D4—2441no—
1012D4—2442no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—611no—
1027C2×C4—611no—
1028C2×C4—611no—
1029C2×C4—611no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1221no—
1036C2×C4—1221no—
1037C2×C4—4881no—
1038C2×C4—4881no—
1039C2×C4—4881no—
1040C2×C4—4881no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2442no—
1046C2×C4—2442no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4C22⋊C4×D6111yescharacteristic
1051C2×C4C22⋊C4×D6111yescharacteristic
1052C2×C4C2×D4×D6111yescharacteristic
1053C2×C4C2×D4×D6111yescharacteristic
1054C8—41no—
1055C8—41no—
1056C8—41no—
1057C8—41no—
1058C8—2441no—
1059C8—2441no—
1060C8—2441no—
1061C8—2441no—
1062C22—21no—
1063C22—21no—
1064C22—21no—
1065C22—21no—
1066C22—21no—
1067C22—21no—
1068C22—21no—
1069C22—42no—
1070C22—42no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—81no—
1075C22—81no—
1076C22—612no—
1077C22—1221no—
1078C22—1221no—
1079C22—1221no—
1080C22—1221no—
1081C22—1222no—
1082C22—1221no—
1083C22—1221no—
1084C22—1221no—
1085C22—1221no—
1086C22—1221no—
1087C22—1221no—
1088C22—1221no—
1089C22—4881no—
1090C22—4881no—
1091C22—4884no—
1092C22—4881no—
1093C22—4881no—
1094C22—4884no—
1095C22—4884no—
1096C22—4884no—
1097C22—2442no—
1098C22—2442no—
1099C22—2442no—
1100C22—2442no—
1101C22—2441no—
1102C22—2441no—
1103C22—2441no—
1104C22—2441no—
1105C22—2441no—
1106C22#99×D6112yes—
1107C22C2×C22⋊C4×D6111yescharacteristic
1108C22#131×D6111yescharacteristic
1109C22#1684052711yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—21no—
1113C4—21no—
1114C4—41no—
1115C4—41no—
1116C4—41no—
1117C4—612no—
1118C4—1221no—
1119C4—1221no—
1120C4—1221no—
1121C4—2441no—
1122C4—2441no—
1123C2—21no—
1124C2—21no—
1125C2—22no—
1126C2—41no—
1127C2—81no—
1128C2—1222no—
1129C2—4881no—
1130C2—2441no—
1131C2—2441no—
1132C2—2441no—
1133C2—2442no—
1134C2#2145426711yescharacteristic
1135C2C2×#99×D6111yescharacteristic
1136C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1468C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840404C2
cosocleC22×C4×C61C24
hypercenter#1468D61
hypocenterC61#17411
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #21454269C2semidirect
3. #21454265C2semidirect
4. #21444177C2semidirect
5. #21444177C2semidirect
6. #21444167C2semidirect
7. #21444166C2semidirect
8. #21444166C2semidirect
9. #21444156C2semidirect
10. #21444145C2semidirect
11. #21444144C2semidirect
12. #21444136C2semidirect
13. C2×#16839485C2semidirect
14. #323×D61C2semidirect
15. C61×#1468C2semidirect
46. #16839726C22semidirect
47. #16839724C22semidirect
48. #16839724C22semidirect
49. #16839724C22semidirect
50. #16839724C22semidirect
51. C2×C22⋊#92418C22semidirect
52. C22⋊C8×D61C22semidirect
53. C22⋊C8×D61C22semidirect
54. C22⋊C8×D61C22semidirect
55. C22⋊C8×D61C22semidirect
56. #16839488C22semidirect
57. #16839488C22semidirect
58. #16839486C22semidirect
59. #16839486C22semidirect
64. #16839485C22semidirect
65. #16839485C22semidirect
66. #16839485C22semidirect
67. #16839485C22semidirect
69. C61×#407C22semidirect
70. C2×C22⋊C8×C61C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
73. C61×#323C22semidirect
74. C61×#323C22semidirect
415. C22×D61#131semidirect
563. #1468D61semidirect
620. #407C2×D61semidirect
626. C2×C22⋊C8C2×D61semidirect
629. #324C2×D61semidirect
630. #324C2×D61semidirect
641. #323C2×D61semidirect
642. #323C2×D61semidirect
643. C61#17411semidirect

Maximal subgroups

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

subgroupindex
C2×#168404042
#214542692
#214542652
#214441772
#214441672
#214441662
#214441562
#214441452
#214441442
#214441362
C2×#168394852
#323×D612
C61×#14682
#1741161