Finite Group Databasebeta

← #29689145

Subgroups — #29689145

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3#21448198C211yesmaximal, characteristic, complemented
4#21446268C211yesmaximal, characteristic, complemented
5#21446267C211yesmaximal, characteristic, complemented
6#21446265C211yesmaximal, characteristic, complemented
7#21446120C212yesmaximal, complemented
8#21446118C212yesmaximal, complemented
9#21445917C212yesmaximal, complemented
10#21445761C212yesmaximal, complemented
11C61×#1897C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×M16×D61C2212yescomplemented
15#16840275C411yescharacteristic, complemented
16#16840275C411yescharacteristic, complemented
17#16840274C2211yescharacteristic
18#16840273C2211yescharacteristic
19#16840272C411yescharacteristic, complemented
20#16840272C411yescharacteristic, complemented
21#16840271—21no—
22#16840271—21no—
23#16840270—21no—
24#16840269C2211yescharacteristic
25#16840268—21no—
26#123×D61—21no—
27C22⋊Q8×D61C411yescharacteristic, complemented
28C22⋊Q8×D61C411yescharacteristic, complemented
29#121×D61C411yescharacteristic, complemented
30#121×D61C411yescharacteristic, complemented
31#120×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34C2×#14519736C2211yescharacteristic, complemented
35#117×D61C2211yescharacteristic
36C2×#14519705C2212yescomplemented
37C2×#14519704C2212yescomplemented
38C2×#14519703C2212yescomplemented
39#16839726C2211yescharacteristic, complemented
40#16839725C2212yes—
41#16839724—21no—
42#16839724—21no—
43C22⋊C8×D61—21no—
44C22⋊C8×D61—21no—
45#16839623—21no—
46#16839619—21no—
47#16839619—21no—
48#16839617—21no—
49C4×#11758198C2212yes—
50C4×#11758198C2212yescomplemented
51#16839523C2212yescomplemented
52#16839522C2212yescomplemented
53#16839521C2212yescomplemented
54C61×#525C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic, complemented
56C2×#104×C61C2212yescomplemented
57C61×#407C2211yescharacteristic, complemented
58C61×#339C2212yescomplemented
59C24×D61D411yescharacteristic
60C2×#11758226C2×C411yescharacteristic
61C2×#11758222—21no—
62C2×#11758222C2311yescharacteristic
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic
65#41×D61—42no—
66#41×D61—42no—
67C2×Q8×D61C2×C411yescharacteristic
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61C2×C411yescharacteristic
72C23×Dic61D411yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—42no—
75C22×C4×D61—42no—
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×#11758194C2312yes—
89C2×#11758189—22no—
90M16×D61—42no—
91M16×D61—42no—
92C2×C8×D61—22no—
93#14519762—21no—
94#14519762—21no—
95#14519761—21no—
96#14519760—21no—
97#14519759—21no—
98#14519759—21no—
99#14519758—21no—
100#14519757C2×C411yescharacteristic
101#14519757C2×C411yescharacteristic
102#14519756C2×C411yescharacteristic
103#14519756C2×C411yescharacteristic
104#14519755—21no—
105#14519755—21no—
106#14519754—21no—
107#14519754—21no—
108#14519753C2×C411yescharacteristic
109#14519753C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111#14519752C2×C411yescharacteristic
112#14519751C2×C411yescharacteristic
113#14519751C2×C411yescharacteristic
114#14519750—21no—
115#14519750—21no—
116#14519749—21no—
117#14519749—21no—
118#14519748C2×C411yescharacteristic
119#14519748C2×C411yescharacteristic
120#14519747—21no—
121#14519747—21no—
122#14519747—21no—
123#14519746—21no—
124#14519745—21no—
125#14519745—21no—
126#14519745—21no—
127C4×D244—21no—
128C4×D244—21no—
129D4×Dic61—21no—
130D4×Dic61—21no—
131#14519739—21no—
132#14519739—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61—21no—
135C4×C22⋊D61—21no—
136C4×C22⋊D61—21no—
137#14519737—21no—
138#14519737—21no—
139#14519737—21no—
140#14519737—21no—
141#14519736—42no—
142#14519736C2311yescharacteristic
143#14519735C2×C411yescharacteristic
144#14519735C2×C411yescharacteristic
145#14519734—21no—
146#14519733—21no—
147C2×C4⋊Dic61—21no—
148C4⋊C4×D61—21no—
149C4⋊C4×D61—21no—
150C4⋊C4×D61C2×C411yescharacteristic
151C4⋊C4×D61C2×C411yescharacteristic
152C2×C22⋊Dic61—21no—
153C2×#11758198—22no—
154C2×#11758198—22no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C22⋊C4×D61—21no—
158C22⋊C4×D61—21no—
159C22⋊C4×D61—21no—
160C2×C4×Dic61C2312yes—
161C42×D61—21no—
162#14519705—42no—
163#14519704—42no—
164#14519703—42no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167#14519689—22no—
168#14519689—22no—
169#14519684—22no—
170#14519684—22no—
171C2×#41×C61C2311yescharacteristic
172C23×C4×C61C2311yescharacteristic
173C2×M16×C61C2312yes—
174#123×C61—21no—
175C22⋊Q8×C61C2×C411yescharacteristic
176C22⋊Q8×C61C2×C411yescharacteristic
177#121×C61C2×C411yescharacteristic
178#121×C61C2×C411yescharacteristic
179#120×C61—21no—
180C4×D4×C61—21no—
181C4×D4×C61—21no—
182#117×C61—42no—
183#117×C61C2311yescharacteristic
184C2×C4⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186C2×C42×C61C2312yes—
187#104×C61—42no—
188C22⋊C8×C61—21no—
189C22⋊C8×C61—21no—
190C24×C61C2×D411yescharacteristic
191C23×D61—21no—
192C23×D61—42no—
193C23×D61—42no—
194C23×D61—41no—
195C23×D61—41no—
196C23×D61C22⋊C411yescharacteristic
197C23×D61C22⋊C411yescharacteristic
198C23×D61C22⋊C411yescharacteristic
199C23×D61C22⋊C411yescharacteristic
200C23×D61C2×D411yescharacteristic
201C23×D61C2×D411yescharacteristic
202#41×C61—22no—
203#41×C61—22no—
204C2×Q8×C61C22×C411yescharacteristic
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61C22×C411yescharacteristic
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—21no—
212C22×C4×C61—22no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C22×Dic61—21no—
227C22×Dic61—22no—
228C22×Dic61—41no—
229C22×Dic61—41no—
230C22×Dic61C22⋊C411yescharacteristic
231C22×Dic61C22⋊C411yescharacteristic
232C22×Dic61C22⋊C411yescharacteristic
233C22×Dic61C22⋊C411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236#11758226—42no—
237Q8×D61—42no—
238#11758224—42no—
239#11758224—42no—
240#11758224—42no—
241D4×D61—42no—
242D4×D61—44no—
243D4×D61—44no—
244D4×D61—42no—
245D4×D61—42no—
246#11758222—22no—
247#11758222—22no—
248#11758222—44no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244C22×C411yescharacteristic
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—42no—
263C2×C4×D61—42no—
264C2×C4×D61—42no—
265C2×C4×D61—42no—
266C2×C4×D61—42no—
267C2×C4×D61—42no—
268C2×C4×D61—42no—
269C2×C4×D61—42no—
270C2×C4×D61—44no—
271C2×C4×D61—41no—
272C2×C4×D61—41no—
273C2×C4×D61—41no—
274C2×C4×D61—41no—
275C2×C4×D61C22⋊C411yescharacteristic
276C2×C4×D61C22⋊C411yescharacteristic
277C2×C4×D61C22⋊C411yescharacteristic
278C2×C4×D61C22⋊C411yescharacteristic
279C2×C4×D61C22⋊C411yescharacteristic
280C2×C4×D61C22⋊C411yescharacteristic
281C2×C4×D61C22⋊C411yescharacteristic
282C2×C4×D61C22⋊C411yescharacteristic
283C2×C4×D61C22×C411yescharacteristic
284C2×C4×D61C22×C411yescharacteristic
285C2×C4×D61C22×C411yescharacteristic
286C2×C4×D61C22×C411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×Dic122—21no—
292C2×Dic122C22×C411yescharacteristic
293M16×C61—22no—
294M16×C61—22no—
295C2×C8×C61—22no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298C4⋊C4×C61—42no—
299C4⋊C4×C61C22×C411yescharacteristic
300C4⋊C4×C61C22×C411yescharacteristic
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—42no—
307C42×C61—21no—
308C42×C61—22no—
309C42×C61—22no—
310C22⋊Dic61—21no—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—42no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—44no—
327#11758198—44no—
328C4⋊Dic61—21no—
329C4⋊Dic61—21no—
330C4⋊Dic61—42no—
331C4⋊Dic61C22×C411yescharacteristic
332C4⋊Dic61C22×C411yescharacteristic
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339C4×Dic61—21no—
340C4×Dic61—21no—
341C4×Dic61—21no—
342C4×Dic61—22no—
343C4×Dic61—22no—
344#11758194—22no—
345#11758194—22no—
346C2×#92418—22no—
347#11758189—44no—
348C8×D61—44no—
349C23×C61—21no—
350C23×C61—21no—
351C23×C61—21no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61C2×C22⋊C411yescharacteristic
355C23×C61C2×C22⋊C411yescharacteristic
356C23×C61C22×D411yescharacteristic
357C22×D61—21no—
358C22×D61—21no—
359C22×D61—21no—
360C22×D61—21no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—21no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—42no—
379C22×D61—42no—
380C22×D61—48no—
381C22×D61—48no—
382C22×D61—42no—
383C22×D61C2×C22⋊C411yescharacteristic
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C2×C22⋊C411yescharacteristic
387Q8×C61—22no—
388D4×C61—22no—
389D4×C61—42no—
390D4×C61—42no—
391D4×C61—41no—
392D4×C61—41no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—42no—
406C2×C4×C61C2×C22⋊C411yescharacteristic
407C2×C4×C61C2×C22⋊C411yescharacteristic
408C2×C4×C61C23×C411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61H(5,𝔽2)12yes—
411C2×C4×C61H(5,𝔽2)12yes—
412C22⋊D61—42no—
413C22⋊D61—42no—
414C22⋊D61—42no—
415C22⋊D61—42no—
416C22⋊D61—42no—
417C22⋊D61—41no—
418C22⋊D61—41no—
419C22⋊D61—42no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—42no—
432C2×Dic61—42no—
433C2×Dic61—42no—
434C2×Dic61—42no—
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438C2×Dic61C2×C22⋊C411yescharacteristic
439D244—22no—
440D244—42no—
441D244—42no—
442D244—42no—
443C4×D61—22no—
444C4×D61—22no—
445C4×D61—22no—
446C4×D61—22no—
447C4×D61—22no—
448C4×D61—22no—
449C4×D61—22no—
450C4×D61—22no—
451C4×D61—41no—
452C4×D61—41no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61—42no—
460C4×D61—42no—
461C4×D61—42no—
462C4×D61—42no—
463C4×D61—42no—
464Dic122—22no—
465Dic122—42no—
466C8×C61—42no—
467#92418—42no—
468#21774—611nomaximal, Sylow
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—42no—
478C22×C61—42no—
479C22×C61—41no—
480C22×C61—41no—
481C22×C61—41no—
482C22×C61C22×C22⋊C411yescharacteristic
483C22×C61#53411yescharacteristic
484C22×C61#53411yescharacteristic
485C2×D61—21no—
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—21no—
495C2×D61—44no—
496C2×D61—42no—
497C2×D61—42no—
498C2×D61—42no—
499C2×D61—42no—
500C2×D61—44no—
501C2×D61—44no—
502C2×D61—44no—
503C2×D61—41no—
504C2×D61—41no—
505C2×D61—41no—
506C2×D61—84no—
507C2×D61#42112yes—
508C2×D61#42112yes—
509C4×C61—21no—
510C4×C61—21no—
511C4×C61—41no—
512C4×C61—41no—
513C4×C61—41no—
514C4×C61—82no—
515C4×C61#51812yes—
516C4×C61#53412yes—
517Dic61—21no—
518Dic61—21no—
519Dic61—21no—
520Dic61—21no—
521Dic61—41no—
522Dic61—41no—
523Dic61—41no—
524Dic61—82no—
525C2×#525—611no—
526C2×#407—611no—
527#2280—611no—
528#1897—611no—
529#1897—611no—
530#1897—611no—
531#1897D6111yescharacteristic, complemented
532#1871—612no—
533#1871—612no—
534#1826—612no—
535#1789—612no—
536C2×C61—21no—
537C2×C61—21no—
538C2×C61—41no—
539C2×C61—41no—
540C2×C61—81no—
541C2×C61#230811yescharacteristic
542C2×C61C2×#42111yescharacteristic
543C2×C61C2×#42111yescharacteristic
544D61—22no—
545D61—22no—
546D61—41no—
547D61—41no—
548D61—81no—
549C22×#41—611no—
550C24×C4—611no—
551C22×M16—612no—
552#525—611no—
553#525—611no—
554#525—611no—
555#525—611no—
556#525—611no—
557#525—611no—
558#525—611no—
559#525—1221no—
560#525—1221no—
561#525—1221no—
562#525—1221no—
563#525C2×D6111yescharacteristic
564C2×#123—1221no—
565C2×C22⋊Q8—611no—
566C2×C22⋊Q8—611no—
567C2×#121—611no—
568C2×#121—611no—
569C2×#120—1221no—
570C2×C4×D4—1221no—
571C2×C4×D4—1221no—
572C2×#117—611no—
573C2×#117—611no—
574C2×#117C2×D6111yescharacteristic, complemented
575C2×#104—612no—
576C2×#104—612no—
577C2×#104—612no—
578C2×#104C2×D6112yescomplemented
579#407—611no—
580#407—612no—
581#407—1221no—
582#407—1221no—
583#407C2×D6111yescharacteristic, complemented
584C2×C22⋊C8—1221no—
585C2×C22⋊C8—1221no—
586#381—1221no—
587#380—1221no—
588#380—1221no—
589#379—1221no—
590C4×C22⋊C4—612no—
591C4×C22⋊C4—612no—
592#339—612no—
593#339—612no—
594#339—612no—
595#339C2×D6112yescomplemented
596C61#2177411yescharacteristic, complemented, Sylow
597C25—611no—
598C2×#41—611no—
599C2×#41—611no—
600C2×#41—611no—
601C2×#41—1221no—
602C2×#41—1221no—
603C2×#41—2442no—
604C2×#41—2442no—
605C2×#41C22×D6111yescharacteristic
606C22×Q8—611no—
607C22×D4—611no—
608C22×D4—1221no—
609C22×D4—1221no—
610C22×D4—1221no—
611C23×C4—611no—
612C23×C4—611no—
613C23×C4—611no—
614C23×C4—611no—
615C23×C4—611no—
616C23×C4—611no—
617C23×C4—611no—
618C23×C4—611no—
619C23×C4—611no—
620C23×C4—611no—
621C23×C4—611no—
622C23×C4—611no—
623C23×C4—611no—
624C23×C4—1221no—
625C23×C4—2442no—
626C23×C4—2442no—
627C23×C4C22×D6111yescharacteristic
628C2×M16—612no—
629C2×M16—1222no—
630C2×M16—2442no—
631C2×M16—2442no—
632C2×M16C22×D6112yes—
633C22×C8—1222no—
634#123—21no—
635#123—1221no—
636#123—1221no—
637#123—1221no—
638#123—1221no—
639#123—1221no—
640#123—1221no—
641#123—1221no—
642C22⋊Q8—611no—
643C22⋊Q8—611no—
644C22⋊Q8—611no—
645C22⋊Q8—611no—
646C22⋊Q8—611no—
647C22⋊Q8—611no—
648C22⋊Q8—1221no—
649C22⋊Q8—1221no—
650C22⋊Q8—1221no—
651C22⋊Q8—1221no—
652C22⋊Q8C4×D6111yescharacteristic
653C22⋊Q8C4×D6111yescharacteristic
654#121—611no—
655#121—611no—
656#121—611no—
657#121—611no—
658#121—611no—
659#121—611no—
660#121—1221no—
661#121—1221no—
662#121—1221no—
663#121—1221no—
664#121C4×D6111yescharacteristic
665#121C4×D6111yescharacteristic
666#120—21no—
667#120—1221no—
668#120—1221no—
669#120—1221no—
670#120—1221no—
671#120—1221no—
672#120—1221no—
673#120—1221no—
674C4×D4—21no—
675C4×D4—21no—
676C4×D4—1221no—
677C4×D4—1221no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4—1221no—
682C4×D4—1221no—
683C4×D4—1221no—
684C4×D4—1221no—
685C4×D4—1221no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4—1221no—
690#117—42no—
691#117—611no—
692#117—611no—
693#117—611no—
694#117—1221no—
695#117—1221no—
696#117—2442no—
697#117C22×D6111yescharacteristic
698C2×C4⋊C4—21no—
699C2×C4⋊C4—611no—
700C2×C4⋊C4—611no—
701C2×C4⋊C4—1221no—
702C2×C4⋊C4—1221no—
703C2×C4⋊C4—1221no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—1221no—
706C2×C22⋊C4—1221no—
707C2×C22⋊C4—1221no—
708C2×C22⋊C4—1221no—
709C2×C22⋊C4—1221no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1221no—
713C2×C42—612no—
714C2×C42—1221no—
715C2×C42C22×D6112yes—
716#104—42no—
717#104—2442no—
718#104—2442no—
719#104—2442no—
720C22⋊C8—21no—
721C22⋊C8—21no—
722C22⋊C8—1222no—
723C22⋊C8—1222no—
724C22⋊C8—1221no—
725C22⋊C8—1221no—
726#95—1222no—
727#95—1222no—
728C24—611no—
729C24—611no—
730C24—611no—
731C24—611no—
732C24—611no—
733C24—611no—
734C24—1221no—
735C24—2441no—
736C24—2441no—
737C24—2442no—
738C24—2442no—
739C24D4×D6111yescharacteristic
740#41—22no—
741#41—22no—
742#41—1222no—
743#41—1222no—
744#41—2444no—
745#41—2442no—
746#41—2442no—
747#41—2442no—
748#41—2442no—
749C2×Q8—611no—
750C2×Q8—1221no—
751C2×Q8—2442no—
752C2×Q8C2×C4×D6111yescharacteristic
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—611no—
757C2×D4—1221no—
758C2×D4—1221no—
759C2×D4—1221no—
760C2×D4—1221no—
761C2×D4—1221no—
762C2×D4—1221no—
763C2×D4—1221no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—2442no—
768C2×D4—2442no—
769C2×D4—2442no—
770C2×D4—2444no—
771C2×D4—2444no—
772C2×D4C2×C4×D6111yescharacteristic
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1222no—
805C22×C4—1222no—
806C22×C4—1222no—
807C22×C4—1222no—
808C22×C4—1221no—
809C22×C4—1222no—
810C22×C4—2442no—
811C22×C4—2442no—
812C22×C4—2442no—
813C22×C4—2442no—
814C22×C4—2442no—
815C22×C4—2442no—
816C22×C4—2442no—
817C22×C4—2442no—
818C22×C4—2441no—
819C22×C4—2441no—
820C22×C4—2441no—
821C22×C4—2441no—
822C22×C4—2444no—
823C22×C4—2441no—
824C22×C4—2441no—
825C22×C4C2×C4×D6111yescharacteristic
826C22×C4C2×C4×D6111yescharacteristic
827C22×C4D4×D6111yescharacteristic
828C22×C4D4×D6111yescharacteristic
829C22×C4D4×D6111yescharacteristic
830C22×C4C23×D6111yescharacteristic
831M16—22no—
832M16—22no—
833M16—1222no—
834M16—1222no—
835M16—2444no—
836C2×C8—22no—
837C2×C8—1222no—
838C2×C8—2444no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—42no—
842C4⋊C4—611no—
843C4⋊C4—611no—
844C4⋊C4—1221no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—1221no—
848C4⋊C4—1221no—
849C4⋊C4—1221no—
850C4⋊C4—1221no—
851C4⋊C4—1221no—
852C4⋊C4—2442no—
853C4⋊C4C2×C4×D6111yescharacteristic
854C4⋊C4C2×C4×D6111yescharacteristic
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—21no—
859C22⋊C4—21no—
860C22⋊C4—42no—
861C22⋊C4—1221no—
862C22⋊C4—1221no—
863C22⋊C4—1221no—
864C22⋊C4—1221no—
865C22⋊C4—1221no—
866C22⋊C4—1221no—
867C22⋊C4—1221no—
868C22⋊C4—1221no—
869C22⋊C4—1221no—
870C22⋊C4—1221no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—2444no—
877C22⋊C4—2444no—
878C22⋊C4—2442no—
879C42—21no—
880C42—22no—
881C42—22no—
882C42—1221no—
883C42—1221no—
884C42—1221no—
885C42—1222no—
886C42—1222no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—41no—
891C23—41no—
892C23—611no—
893C23—611no—
894C23—611no—
895C23—611no—
896C23—1222no—
897C23—1222no—
898C23—1222no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1221no—
903C23—1221no—
904C23—1221no—
905C23—1221no—
906C23—1221no—
907C23—2441no—
908C23—2441no—
909C23—2441no—
910C23—2441no—
911C23—2441no—
912C23—2441no—
913C23—2441no—
914C23—2441no—
915C23—2441no—
916C23—2441no—
917C23—2442no—
918C23—2442no—
919C23—2442no—
920C23—2448no—
921C23—2448no—
922C23C22⋊C4×D6111yescharacteristic
923C23C22⋊C4×D6111yescharacteristic
924C23C2×D4×D6111yescharacteristic
925Q8—22no—
926Q8—1222no—
927Q8—2442no—
928D4—22no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—1222no—
934D4—2442no—
935D4—2442no—
936D4—2442no—
937D4—2442no—
938D4—2442no—
939D4—2442no—
940D4—2442no—
941D4—2442no—
942D4—2442no—
943D4—2441no—
944D4—2441no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—611no—
959C2×C4—611no—
960C2×C4—611no—
961C2×C4—611no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1221no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2442no—
986C2×C4—2442no—
987C2×C4—2442no—
988C2×C4—2442no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2442no—
994C2×C4—2442no—
995C2×C4—2442no—
996C2×C4—2442no—
997C2×C4—2442no—
998C2×C4C22⋊C4×D6111yescharacteristic
999C2×C4C22⋊C4×D6111yescharacteristic
1000C2×C4C22×C4×D6111yescharacteristic
1001C2×C4C2×D4×D6111yescharacteristic
1002C2×C4#1451982212yes—
1003C2×C4#1451982312yes—
1004C8—42no—
1005C8—2442no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—42no—
1015C22—42no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—612no—
1020C22—612no—
1021C22—1221no—
1022C22—1221no—
1023C22—1221no—
1024C22—1221no—
1025C22—1221no—
1026C22—1221no—
1027C22—1221no—
1028C22—1221no—
1029C22—1221no—
1030C22—1221no—
1031C22—4884no—
1032C22—2442no—
1033C22—2442no—
1034C22—2442no—
1035C22—2442no—
1036C22—2444no—
1037C22—2444no—
1038C22—2444no—
1039C22—2444no—
1040C22—2441no—
1041C22—2441no—
1042C22—2441no—
1043C22C2×C22⋊C4×D6111yescharacteristic
1044C22#1684032211yescharacteristic
1045C22#1684032311yescharacteristic
1046C4—21no—
1047C4—21no—
1048C4—41no—
1049C4—41no—
1050C4—41no—
1051C4—82no—
1052C4—1221no—
1053C4—1221no—
1054C4—1221no—
1055C4—1221no—
1056C4—4882no—
1057C4—2441no—
1058C4—2441no—
1059C4—2441no—
1060C4#1684023412yes—
1061C4#1684032012yes—
1062C2—21no—
1063C2—21no—
1064C2—41no—
1065C2—41no—
1066C2—81no—
1067C2—1222no—
1068C2—1222no—
1069C2—4881no—
1070C2—2441no—
1071C2—2441no—
1072C2#2144839311yescharacteristic
1073C2#421×D6111yescharacteristic
1074C2#421×D6111yescharacteristic
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
hypocenterC61#21774
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. #407×D61C2semidirect
3. #21448198C2semidirect
4. #21446268C2semidirect
5. #21446267C2semidirect
6. #21446265C2semidirect
7. #21446120C2semidirect
8. #21446118C2semidirect
9. #21445917C2semidirect
10. #21445761C2semidirect
11. C61×#1897C2semidirect
14. C2×M16×D61C22semidirect
15. #16840275C4semidirect
16. #16840275C4semidirect
19. #16840272C4semidirect
20. #16840272C4semidirect
27. C22⋊Q8×D61C4semidirect
28. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
30. #121×D61C4semidirect
34. C2×#14519736C22semidirect
36. C2×#14519705C22semidirect
37. C2×#14519704C22semidirect
38. C2×#14519703C22semidirect
39. #16839726C22semidirect
50. C4×#11758198C22semidirect
51. #16839523C22semidirect
52. #16839522C22semidirect
53. #16839521C22semidirect
55. C2×#117×C61C22semidirect
56. C2×#104×C61C22semidirect
57. C61×#407C22semidirect
58. C61×#339C22semidirect
531. #1897D61semidirect
574. C2×#117C2×D61semidirect
578. C2×#104C2×D61semidirect
583. #407C2×D61semidirect
595. #339C2×D61semidirect
596. C61#21774semidirect

Maximal subgroups

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

subgroupindex
#525×D612
#407×D612
#214481982
#214462682
#214462672
#214462652
#214461202
#214461182
#214459172
#214457612
C61×#18972
#2177461