Finite Group Databasebeta

← #29689148

Subgroups — #29689148

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2C2×#16839725C211yesmaximal, characteristic, complemented
3#21448200C211yesmaximal, characteristic, complemented
4#21446266C212yesmaximal, complemented
5#21446264C212yesmaximal, complemented
6#21446122C211yesmaximal, characteristic, complemented
7#21446121C211yesmaximal, characteristic, complemented
8#21446119C211yesmaximal, characteristic, complemented
9#21445917C212yesmaximal, complemented
10#21445761C212yesmaximal, complemented
11C61×#1871C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C22×#11758194C2211yescharacteristic, complemented
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×#14519734C2212yescomplemented
35#117×D61C2211yescharacteristic
36C2×#14519705C2212yescomplemented
37C2×#14519704C2212yescomplemented
38C2×#14519703C2212yescomplemented
39#16839725—21no—
40#16839725—21no—
41#16839725C2212yes—
42#16839725C2212yescomplemented
43C2×#14519689—21no—
44C2×#14519689—21no—
45#16839624—21no—
46#16839621—21no—
47#16839620—21no—
48#16839617—21no—
49C4×#11758198C2212yes—
50C4×C22⋊Dic61C2211yescharacteristic, complemented
51#16839523C2212yescomplemented
52#16839522C2212yescomplemented
53#16839521C2212yescomplemented
54C22×M16×C61C2211yescharacteristic, complemented
55C61×#525C2211yescharacteristic
56C2×#104×C61C2212yescomplemented
57C4×C22⋊C4×C61C2211yescharacteristic, 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×#11758194—21no—
89C2×#11758194—42no—
90C2×#11758194C2312yes—
91C22×#92418—21no—
92#14519762—21no—
93#14519762—21no—
94#14519761—21no—
95#14519760—21no—
96#14519759—21no—
97#14519759—21no—
98#14519758—21no—
99#14519757C2×C411yescharacteristic
100#14519757C2×C411yescharacteristic
101#14519756C2×C411yescharacteristic
102#14519756C2×C411yescharacteristic
103#14519755—21no—
104#14519755—21no—
105#14519754—21no—
106#14519754—21no—
107#14519753C2×C411yescharacteristic
108#14519753C2×C411yescharacteristic
109#14519752C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111#14519751C2×C411yescharacteristic
112#14519751C2×C411yescharacteristic
113#14519750—21no—
114#14519750—21no—
115#14519749—21no—
116#14519749—21no—
117#14519748C2×C411yescharacteristic
118#14519748C2×C411yescharacteristic
119#14519747—21no—
120#14519747—21no—
121#14519747—21no—
122#14519746—21no—
123#14519745—21no—
124#14519745—21no—
125#14519745—21no—
126C4×D244—21no—
127C4×D244—21no—
128D4×Dic61—21no—
129D4×Dic61—21no—
130#14519739—21no—
131#14519739—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61—21no—
135C4×C22⋊D61—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519737—21no—
140#14519736C2311yescharacteristic
141#14519735C2×C411yescharacteristic
142#14519735C2×C411yescharacteristic
143#14519734—21no—
144#14519734—42no—
145#14519734—42no—
146#14519733—21no—
147C2×#11758196—22no—
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—
165#14519689—22no—
166#14519689—22no—
167#14519689—22no—
168#14519689—22no—
169#14519684—21no—
170#14519684—22no—
171C2×#41×C61C2311yescharacteristic
172C23×C4×C61C2311yescharacteristic
173C2×M16×C61—21no—
174C2×M16×C61—42no—
175C2×M16×C61C2312yes—
176C22×C8×C61—21no—
177#123×C61—21no—
178C22⋊Q8×C61C2×C411yescharacteristic
179C22⋊Q8×C61C2×C411yescharacteristic
180#121×C61C2×C411yescharacteristic
181#121×C61C2×C411yescharacteristic
182#120×C61—21no—
183C4×D4×C61—21no—
184C4×D4×C61—21no—
185#117×C61C2311yescharacteristic
186C2×C22⋊C4×C61—21no—
187C2×C42×C61C2312yes—
188#104×C61—42no—
189#95×C61—21no—
190C24×C61C2×D411yescharacteristic
191C23×D61—21no—
192C23×D61—42no—
193C23×D61—42no—
194C23×D61—42no—
195C23×D61C22⋊C411yescharacteristic
196C23×D61C22⋊C411yescharacteristic
197C23×D61C22⋊C411yescharacteristic
198C23×D61C22⋊C411yescharacteristic
199C23×D61C2×D411yescharacteristic
200C23×D61C2×D411yescharacteristic
201#41×C61—22no—
202#41×C61—22no—
203C2×Q8×C61C22×C411yescharacteristic
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61C22×C411yescharacteristic
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—21no—
211C22×C4×C61—22no—
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C22×Dic61—21no—
226C22×Dic61—22no—
227C22×Dic61—42no—
228C22×Dic61C22⋊C411yescharacteristic
229C22×Dic61C22⋊C411yescharacteristic
230C22×Dic61C22⋊C411yescharacteristic
231C22×Dic61C22⋊C411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234#11758226—42no—
235Q8×D61—42no—
236#11758224—42no—
237#11758224—44no—
238D4×D61—42no—
239D4×D61—44no—
240D4×D61—44no—
241D4×D61—44no—
242#11758222—22no—
243#11758222—22no—
244#11758222—42no—
245#11758222—42no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244C22×C411yescharacteristic
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—42no—
260C2×C4×D61—42no—
261C2×C4×D61—42no—
262C2×C4×D61—42no—
263C2×C4×D61—41no—
264C2×C4×D61—41no—
265C2×C4×D61—41no—
266C2×C4×D61—41no—
267C2×C4×D61—41no—
268C2×C4×D61—41no—
269C2×C4×D61—41no—
270C2×C4×D61—41no—
271C2×C4×D61—42no—
272C2×C4×D61—42no—
273C2×C4×D61—42no—
274C2×C4×D61—42no—
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—
295M16×C61—42no—
296C2×C8×C61—22no—
297C2×C8×C61—42no—
298C4⋊C4×C61—21no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61C22×C411yescharacteristic
301C4⋊C4×C61C22×C411yescharacteristic
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—42no—
308C42×C61—21no—
309C42×C61—22no—
310C42×C61—22no—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—42no—
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—21no—
327#11758198—44no—
328#11758198—44no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331C4⋊Dic61C22×C411yescharacteristic
332C4⋊Dic61C22×C411yescharacteristic
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—44no—
340C4×Dic61—21no—
341C4×Dic61—21no—
342C4×Dic61—21no—
343C4×Dic61—22no—
344C4×Dic61—22no—
345#11758194—22no—
346#11758194—22no—
347#11758194—42no—
348C2×#92418—22no—
349C2×#92418—42no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—21no—
353C23×C61—41no—
354C23×C61C2×C22⋊C411yescharacteristic
355C23×C61C2×C22⋊C411yescharacteristic
356C23×C61C22×D411yescharacteristic
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—21no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
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—42no—
377C22×D61—42no—
378C22×D61—416no—
379C22×D61—42no—
380C22×D61C2×C22⋊C411yescharacteristic
381C22×D61C2×C22⋊C411yescharacteristic
382C22×D61C2×C22⋊C411yescharacteristic
383C22×D61C2×C22⋊C411yescharacteristic
384Q8×C61—22no—
385D4×C61—22no—
386D4×C61—42no—
387D4×C61—42no—
388D4×C61—42no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—42no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61C2×C22⋊C411yescharacteristic
405C2×C4×C61C2×C22⋊C411yescharacteristic
406C2×C4×C61C23×C411yescharacteristic
407C2×C4×C61C22×D411yescharacteristic
408C2×C4×C61H(5,𝔽2)12yes—
409C2×C4×C61H(5,𝔽2)12yes—
410C22⋊D61—42no—
411C22⋊D61—42no—
412C22⋊D61—42no—
413C22⋊D61—42no—
414C22⋊D61—42no—
415C22⋊D61—42no—
416C22⋊D61—42no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—42no—
427C2×Dic61—42no—
428C2×Dic61—42no—
429C2×Dic61—42no—
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C2×C22⋊C411yescharacteristic
433C2×Dic61C2×C22⋊C411yescharacteristic
434D244—22no—
435D244—42no—
436D244—42no—
437D244—42no—
438C4×D61—22no—
439C4×D61—22no—
440C4×D61—22no—
441C4×D61—22no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—41no—
451C4×D61—41no—
452C4×D61—41no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—41no—
458C4×D61—42no—
459C4×D61—42no—
460C4×D61—42no—
461C4×D61—42no—
462C4×D61—41no—
463C4×D61—41no—
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—44no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61#42112yes—
481C22×C61C22×C22⋊C411yescharacteristic
482C22×C61#53412yes—
483C2×D61—21no—
484C2×D61—21no—
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—44no—
495C2×D61—44no—
496C2×D61—44no—
497C2×D61—44no—
498C2×D61—44no—
499C2×D61—44no—
500C2×D61—41no—
501C2×D61—41no—
502C2×D61—41no—
503C2×D61—84no—
504C2×D61#42112yes—
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—41no—
508C4×C61—41no—
509C4×C61—41no—
510C4×C61—82no—
511C4×C61#51812yes—
512C4×C61#53411yescharacteristic
513C4×C61#53411yescharacteristic
514Dic61—21no—
515Dic61—21no—
516Dic61—21no—
517Dic61—21no—
518Dic61—41no—
519Dic61—41no—
520Dic61—41no—
521Dic61—82no—
522C2×#525—611no—
523C2×#407—611no—
524#2280—611no—
525#1897—612no—
526#1897—612no—
527#1871—611no—
528#1871—611no—
529#1871—611no—
530#1871D6111yescharacteristic, complemented
531#1826—612no—
532#1789—612no—
533C2×C61—22no—
534C2×C61—22no—
535C2×C61—41no—
536C2×C61—81no—
537C2×C61#230811yescharacteristic
538C2×C61C2×#42111yescharacteristic
539C2×C61C2×#42111yescharacteristic
540D61—22no—
541D61—41no—
542D61—41no—
543D61—41no—
544D61—81no—
545C22×#41—611no—
546C24×C4—611no—
547C22×M16—611no—
548C22×M16C2×D6111yescharacteristic, complemented
549#525—611no—
550#525—611no—
551#525—611no—
552#525—611no—
553#525—611no—
554#525—611no—
555#525—611no—
556#525—1221no—
557#525—1221no—
558#525—1221no—
559#525—1221no—
560#525C2×D6111yescharacteristic
561C2×#123—1221no—
562C2×C22⋊Q8—611no—
563C2×C22⋊Q8—611no—
564C2×#121—611no—
565C2×#121—611no—
566C2×#120—1221no—
567C2×C4×D4—1221no—
568C2×C4×D4—1221no—
569C2×#117—612no—
570C2×#117—611no—
571C2×#104—612no—
572C2×#104—612no—
573C2×#104—612no—
574C2×#104C2×D6112yescomplemented
575#407—612no—
576#407—612no—
577#407—1221no—
578#407—1221no—
579C2×C22⋊C8—1221no—
580C2×C22⋊C8—1221no—
581#381—1221no—
582#380—1221no—
583#380—1221no—
584#379—1221no—
585C4×C22⋊C4—611no—
586C4×C22⋊C4—612no—
587C4×C22⋊C4C2×D6111yescharacteristic, complemented
588#339—612no—
589#339—612no—
590#339—612no—
591#339C2×D6112yescomplemented
592C61#2177411yescharacteristic, complemented, Sylow
593C25—611no—
594C2×#41—611no—
595C2×#41—611no—
596C2×#41—611no—
597C2×#41—1221no—
598C2×#41—1221no—
599C2×#41—2442no—
600C2×#41—2442no—
601C2×#41C22×D6111yescharacteristic
602C22×Q8—611no—
603C22×D4—611no—
604C22×D4—1221no—
605C22×D4—1221no—
606C22×D4—1221no—
607C23×C4—611no—
608C23×C4—611no—
609C23×C4—611no—
610C23×C4—611no—
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—1221no—
621C23×C4—2442no—
622C23×C4—2442no—
623C23×C4C22×D6111yescharacteristic
624C2×M16—21no—
625C2×M16—42no—
626C2×M16—612no—
627C2×M16—1221no—
628C2×M16—2442no—
629C2×M16C22×D6112yes—
630C22×C8—21no—
631C22×C8—1221no—
632#123—21no—
633#123—1221no—
634#123—1221no—
635#123—1221no—
636#123—1221no—
637#123—1221no—
638#123—1221no—
639#123—1221no—
640C22⋊Q8—611no—
641C22⋊Q8—611no—
642C22⋊Q8—611no—
643C22⋊Q8—611no—
644C22⋊Q8—611no—
645C22⋊Q8—611no—
646C22⋊Q8—1221no—
647C22⋊Q8—1221no—
648C22⋊Q8—1221no—
649C22⋊Q8—1221no—
650C22⋊Q8C4×D6111yescharacteristic
651C22⋊Q8C4×D6111yescharacteristic
652#121—611no—
653#121—611no—
654#121—611no—
655#121—611no—
656#121—611no—
657#121—611no—
658#121—1221no—
659#121—1221no—
660#121—1221no—
661#121—1221no—
662#121C4×D6111yescharacteristic
663#121C4×D6111yescharacteristic
664#120—21no—
665#120—1221no—
666#120—1221no—
667#120—1221no—
668#120—1221no—
669#120—1221no—
670#120—1221no—
671#120—1221no—
672C4×D4—21no—
673C4×D4—21no—
674C4×D4—1221no—
675C4×D4—1221no—
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—
688#117—611no—
689#117—611no—
690#117—611no—
691#117—1221no—
692#117—1221no—
693#117—2442no—
694#117—2442no—
695#117C22×D6111yescharacteristic
696C2×C4⋊C4—611no—
697C2×C4⋊C4—611no—
698C2×C4⋊C4—1221no—
699C2×C4⋊C4—1221no—
700C2×C4⋊C4—1222no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—1221no—
703C2×C22⋊C4—1221no—
704C2×C22⋊C4—1221no—
705C2×C22⋊C4—1221no—
706C2×C22⋊C4—1221no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1221no—
710C2×C42—612no—
711C2×C42—1221no—
712C2×C42C22×D6112yes—
713#104—42no—
714#104—2442no—
715#104—2442no—
716#104—2442no—
717C22⋊C8—1222no—
718C22⋊C8—1222no—
719C22⋊C8—1222no—
720C22⋊C8—1222no—
721#95—21no—
722#95—1222no—
723#95—1221no—
724C24—611no—
725C24—611no—
726C24—611no—
727C24—611no—
728C24—611no—
729C24—611no—
730C24—1221no—
731C24—2442no—
732C24—2442no—
733C24—2442no—
734C24D4×D6111yescharacteristic
735#41—22no—
736#41—22no—
737#41—1222no—
738#41—1222no—
739#41—2442no—
740#41—2442no—
741#41—2442no—
742#41—2444no—
743#41—2442no—
744C2×Q8—611no—
745C2×Q8—1221no—
746C2×Q8—2442no—
747C2×Q8C2×C4×D6111yescharacteristic
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—611no—
752C2×D4—1221no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—1221no—
756C2×D4—1221no—
757C2×D4—1221no—
758C2×D4—1221no—
759C2×D4—1221no—
760C2×D4—1221no—
761C2×D4—1221no—
762C2×D4—2442no—
763C2×D4—2444no—
764C2×D4—2444no—
765C2×D4—2444no—
766C2×D4C2×C4×D6111yescharacteristic
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
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—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1222no—
799C22×C4—1222no—
800C22×C4—1222no—
801C22×C4—1222no—
802C22×C4—1221no—
803C22×C4—1222no—
804C22×C4—2442no—
805C22×C4—2442no—
806C22×C4—2442no—
807C22×C4—2442no—
808C22×C4—2441no—
809C22×C4—2441no—
810C22×C4—2441no—
811C22×C4—2441no—
812C22×C4—2441no—
813C22×C4—2441no—
814C22×C4—2441no—
815C22×C4—2441no—
816C22×C4—2442no—
817C22×C4—2442no—
818C22×C4—2442no—
819C22×C4—2442no—
820C22×C4—2442no—
821C22×C4C2×C4×D6111yescharacteristic
822C22×C4C2×C4×D6111yescharacteristic
823C22×C4D4×D6111yescharacteristic
824C22×C4D4×D6111yescharacteristic
825C22×C4D4×D6111yescharacteristic
826C22×C4C23×D6111yescharacteristic
827M16—22no—
828M16—22no—
829M16—42no—
830M16—1222no—
831M16—1222no—
832M16—2442no—
833C2×C8—22no—
834C2×C8—42no—
835C2×C8—1222no—
836C2×C8—2442no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—611no—
840C4⋊C4—611no—
841C4⋊C4—1221no—
842C4⋊C4—1221no—
843C4⋊C4—1221no—
844C4⋊C4—1221no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—1221no—
848C4⋊C4—1221no—
849C4⋊C4—2444no—
850C4⋊C4C2×C4×D6111yescharacteristic
851C4⋊C4C2×C4×D6111yescharacteristic
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—42no—
858C22⋊C4—1221no—
859C22⋊C4—1221no—
860C22⋊C4—1221no—
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—2444no—
874C22⋊C4—2444no—
875C22⋊C4—2442no—
876C42—21no—
877C42—22no—
878C42—22no—
879C42—1221no—
880C42—1221no—
881C42—1221no—
882C42—1222no—
883C42—1222no—
884C23—22no—
885C23—22no—
886C23—21no—
887C23—41no—
888C23—611no—
889C23—611no—
890C23—611no—
891C23—611no—
892C23—1222no—
893C23—1222no—
894C23—1222no—
895C23—1222no—
896C23—1222no—
897C23—1222no—
898C23—1222no—
899C23—1221no—
900C23—2441no—
901C23—2441no—
902C23—2441no—
903C23—2441no—
904C23—2441no—
905C23—2441no—
906C23—2441no—
907C23—2441no—
908C23—2441no—
909C23—2441no—
910C23—2441no—
911C23—2442no—
912C23—2442no—
913C23—2442no—
914C23—24416no—
915C23C22⋊C4×D6111yescharacteristic
916C23C22⋊C4×D6111yescharacteristic
917C23C2×D4×D6111yescharacteristic
918Q8—22no—
919Q8—1222no—
920Q8—2442no—
921D4—22no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—1222no—
926D4—2442no—
927D4—2442no—
928D4—2442no—
929D4—2442no—
930D4—2442no—
931D4—2442no—
932D4—2442no—
933D4—2442no—
934D4—2442no—
935D4—2442no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—611no—
952C2×C4—611no—
953C2×C4—611no—
954C2×C4—611no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—1221no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2442no—
981C2×C4—2442no—
982C2×C4—2442no—
983C2×C4—2442no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2442no—
989C2×C4—2442no—
990C2×C4—2442no—
991C2×C4—2442no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4C22⋊C4×D6111yescharacteristic
995C2×C4C22⋊C4×D6111yescharacteristic
996C2×C4C22×C4×D6111yescharacteristic
997C2×C4C2×D4×D6111yescharacteristic
998C2×C4#1451982212yes—
999C2×C4#1451982312yes—
1000C8—42no—
1001C8—2442no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—44no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—612no—
1014C22—1221no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—1221no—
1024C22—1221no—
1025C22—4884no—
1026C22—2444no—
1027C22—2444no—
1028C22—2444no—
1029C22—2444no—
1030C22—2444no—
1031C22—2444no—
1032C22—2441no—
1033C22—2441no—
1034C22—2441no—
1035C22#1683977712yes—
1036C22C2×C22⋊C4×D6111yescharacteristic
1037C22#1684032012yes—
1038C4—21no—
1039C4—21no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—82no—
1044C4—1221no—
1045C4—1221no—
1046C4—1221no—
1047C4—1221no—
1048C4—4882no—
1049C4—2441no—
1050C4—2441no—
1051C4—2441no—
1052C4#1684023412yes—
1053C4#1684032211yescharacteristic
1054C4#1684032311yescharacteristic
1055C2—22no—
1056C2—22no—
1057C2—41no—
1058C2—81no—
1059C2—1222no—
1060C2—4881no—
1061C2—2441no—
1062C2—2441no—
1063C2—2441no—
1064C2#2144839311yescharacteristic
1065C2#421×D6111yescharacteristic
1066C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61#21774
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×#16839725C2semidirect
3. #21448200C2semidirect
4. #21446266C2semidirect
5. #21446264C2semidirect
6. #21446122C2semidirect
7. #21446121C2semidirect
8. #21446119C2semidirect
9. #21445917C2semidirect
10. #21445761C2semidirect
11. C61×#1871C2semidirect
14. C22×#11758194C22semidirect
15. #16840275C4semidirect
16. #16840275C4semidirect
19. #16840272C4semidirect
20. #16840272C4semidirect
27. C22⋊Q8×D61C4semidirect
28. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
30. #121×D61C4semidirect
34. C2×#14519734C22semidirect
36. C2×#14519705C22semidirect
37. C2×#14519704C22semidirect
38. C2×#14519703C22semidirect
42. #16839725C22semidirect
50. C4×C22⋊Dic61C22semidirect
51. #16839523C22semidirect
52. #16839522C22semidirect
53. #16839521C22semidirect
54. C22×M16×C61C22semidirect
56. C2×#104×C61C22semidirect
57. C4×C22⋊C4×C61C22semidirect
58. C61×#339C22semidirect
530. #1871D61semidirect
548. C22×M16C2×D61semidirect
574. C2×#104C2×D61semidirect
587. C4×C22⋊C4C2×D61semidirect
591. #339C2×D61semidirect
592. C61#21774semidirect

Maximal subgroups

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

subgroupindex
#525×D612
C2×#168397252
#214482002
#214462662
#214462642
#214461222
#214461212
#214461192
#214459172
#214457612
C61×#18712
#2177461