Finite Group Databasebeta

← #29697013

Subgroups — #29697013

Order 15616.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839822C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×D61C211yesmaximal, characteristic
3#21448200C211yesmaximal, characteristic
4#21446435C211yesmaximal, characteristic, complemented
5#21446434C211yesmaximal, characteristic, complemented
6#21446422C211yesmaximal, characteristic, complemented
7#21445998C211yesmaximal, characteristic, complemented
8#21445995C211yesmaximal, characteristic, complemented
9#21445889C211yesmaximal, characteristic, complemented
10#21445802C211yesmaximal, characteristic, complemented
11#21445728C211yesmaximal, characteristic
12#21445594C211yesmaximal, characteristic, complemented
13C8×#11758198C211yesmaximal, characteristic, complemented
14#21445586C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519734C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21#16839822—24no—
22C2×C4⋊#92418C2211yescharacteristic, complemented
23C2×#14519706C2211yescharacteristic, complemented
24C2×#14519706C2211yescharacteristic, complemented
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C22⋊C8×D61—24no—
34C2×#14519688C2211yescharacteristic, complemented
35C2×#14519687C2211yescharacteristic, complemented
36C2×C8×Dic61C2211yescharacteristic, complemented
37#16839624C411yescharacteristic
38#16839624C411yescharacteristic
39#16839621C411yescharacteristic
40#16839621C411yescharacteristic
41#16839620C411yescharacteristic
42#16839620C411yescharacteristic
43#16839617C411yescharacteristic
44#16839617C411yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C2×C4⋊C8×C61C2211yescharacteristic, complemented
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic, complemented
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic, complemented
60C61×#336C2211yescharacteristic, complemented
61C24×D61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—41no—
68C22×C4×D61—41no—
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C2×C8×D61—22no—
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—41no—
82C2×C8×D61—41no—
83#14519734—22no—
84#14519734—22no—
85#14519734—41no—
86#14519734—41no—
87C2×#11758196C2×C411yescharacteristic
88C2×#11758196C2×C411yescharacteristic
89C2×#11758196C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×C22⋊Dic61C2×C411yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C4⋊#92418—22no—
104#14519706—41no—
105#14519706—41no—
106C22⋊#92418—22no—
107C22⋊#92418—41no—
108#14519689—22no—
109#14519689—22no—
110#14519689—22no—
111#14519689—22no—
112#14519689—22no—
113#14519689D414yes—
114#14519688—41no—
115#14519687—22no—
116C8×Dic61—22no—
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C22⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C4⋊C8×C61—22no—
133C22⋊C8×C61—22no—
134C22⋊C8×C61—41no—
135C4×C8×C61—41no—
136#95×C61C2×C411yescharacteristic
137#95×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61—41no—
145C23×D61—41no—
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—41no—
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—44no—
182C2×C4×D61—44no—
183C2×C4×D61—44no—
184C2×C4×D61—44no—
185C2×C4×D61—41no—
186C2×C4×D61—41no—
187C2×C4×D61C2×D412yes—
188C2×C4×D61#4112yes—
189C2×C4×D61#4112yes—
190C2×C4×D61#4112yes—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61C2×D412yes—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—41no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61—21no—
209C22⋊Dic61—22no—
210C22⋊Dic61—41no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217#11758198—41no—
218#11758198—41no—
219#11758196—22no—
220#11758196—22no—
221#11758196—41no—
222#11758196—41no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418C2×D412yes—
239C8×D61—44no—
240C8×D61—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61#13112yes—
248C23×C61C23×C411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—28no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—44no—
261C22×D61—44no—
262C22×D61—44no—
263C22×D61—44no—
264C22×D61—44no—
265C22×D61—44no—
266C22×D61#11712yes—
267C22×D61C4×D412yes—
268C22×D61#13112yes—
269C22×D61#13112yes—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—44no—
312C2×Dic61#11712yes—
313C2×Dic61C4×D412yes—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—44no—
323C4×D61—44no—
324C8×C61—22no—
325C8×C61—41no—
326C8×C61—41no—
327C8×C61—41no—
328#92418—22no—
329#92418—41no—
330#92418—41no—
331#92418—41no—
332#22558—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×#11711yescharacteristic
341C22×C61C2×C4×D411yescharacteristic
342C22×C61#51811yescharacteristic
343C22×C61C2×#13111yescharacteristic
344C22×C61C2×#13111yescharacteristic
345C22×C61C2×#13111yescharacteristic
346C22×C61#56811yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—416no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61#43314yescomplemented
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61#54611yescharacteristic
368C4×C61#54611yescharacteristic
369C4×C61#55111yescharacteristic
370C4×C61#55111yescharacteristic
371Dic61—22no—
372Dic61—22no—
373Dic61—41no—
374Dic61—41no—
375Dic61—41no—
376Dic61—41no—
377C2×#433—611no—
378C22×C22⋊C8—611no—
379#2280—611no—
380#1924—611no—
381#1924—611no—
382#1923—611no—
383#1923D6111yescharacteristic, complemented
384#1850—611no—
385#1850—611no—
386#1818—611no—
387#1798—611no—
388#1779—611no—
389#1752—611no—
390C8×C22⋊C4—611no—
391#1750—611no—
392C2×C61—42no—
393C2×C61#234211yescharacteristic
394C2×C61C2×#43311yescharacteristic
395C2×C61#292411yescharacteristic
396C2×C61#292911yescharacteristic
397C2×C61#293311yescharacteristic
398C2×C61#297611yescharacteristic
399C2×C61#297711yescharacteristic
400D61—24no—
401D61—42no—
402C24×C4—611no—
403C23×C8—611no—
404C23×C8—611no—
405C2×#117—611no—
406C2×#117—611no—
407#433—1224no—
408C2×C4⋊C8—611no—
409C2×C4⋊C8—611no—
410C2×C4⋊C8—611no—
411C2×C4⋊C8C2×D6111yescharacteristic, complemented
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—1224no—
421C2×C22⋊C8C2×D6111yescharacteristic
422C2×C22⋊C8C2×D6111yescharacteristic
423C2×#97—611no—
424C2×#97—611no—
425C2×C4×C8—611no—
426C2×C4×C8C2×D6111yescharacteristic, complemented
427#381—611no—
428#381—611no—
429#380—611no—
430#380—611no—
431#380—611no—
432#380—611no—
433#379—611no—
434#379—611no—
435C4×C22⋊C4—611no—
436C4×C22⋊C4—611no—
437C4×C22⋊C4—611no—
438C4×C22⋊C4C2×D6111yescharacteristic
439#336—611no—
440#336—611no—
441#336—611no—
442#336—611no—
443#336—611no—
444#336—611no—
445#336C2×D6111yescharacteristic, complemented
446#336C2×D6111yescharacteristic, complemented
447C61#2255811yescharacteristic, complemented, Sylow
448C25—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—1222no—
455C23×C4—1222no—
456C23×C4—1222no—
457C23×C4—1222no—
458C23×C4—2441no—
459C23×C4—2441no—
460C23×C4C22×D6111yescharacteristic
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—1222no—
466C22×C8—1222no—
467C22×C8—1222no—
468C22×C8—1222no—
469C22×C8—2441no—
470C22×C8—2441no—
471C22×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475#117—1222no—
476#117—1222no—
477#117—2441no—
478#117—2441no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4C4×D6111yescharacteristic
494C2×C22⋊C4C4×D6111yescharacteristic
495C2×C42—611no—
496C2×C42—611no—
497C2×C42C22×D6111yescharacteristic
498C2×C42C22×D6111yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—1222no—
501C4⋊C8—2441no—
502C4⋊C8—2441no—
503C22⋊C8—22no—
504C22⋊C8—41no—
505C22⋊C8—614no—
506C22⋊C8—1222no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511C22⋊C8—1222no—
512C22⋊C8—2441no—
513#97—1222no—
514#97—2441no—
515C4×C8—41no—
516C4×C8—1222no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95—611no—
522#95—611no—
523#95C4×D6111yescharacteristic
524#95C4×D6111yescharacteristic
525C24—611no—
526C24—611no—
527C24—1222no—
528C24—1222no—
529C24—1222no—
530C24—1222no—
531C24—1222no—
532C24—2441no—
533C24—2441no—
534C24C2×C4×D6111yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—612no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—2441no—
566C22×C4—2441no—
567C22×C4—2444no—
568C22×C4—2444no—
569C22×C4—2444no—
570C22×C4—2444no—
571C22×C4—2441no—
572C22×C4C2×C4×D6111yescharacteristic
573C22×C4C2×C4×D6111yescharacteristic
574C22×C4C2×C4×D6111yescharacteristic
575C22×C4C2×C4×D6111yescharacteristic
576C22×C4C2×C4×D6111yescharacteristic
577C22×C4C23×D6111yescharacteristic
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—612no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—2444no—
602C2×C8—2444no—
603C2×C8D4×D6112yes—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—2441no—
607C4⋊C4—2441no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—2441no—
618C22⋊C4—2441no—
619C22⋊C4—2441no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—612no—
635C23—612no—
636C23—612no—
637C23—612no—
638C23—1228no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—2444no—
650C23—2444no—
651C23—2444no—
652C23—2444no—
653C23—2444no—
654C23—2444no—
655C23#1451978312yes—
656C23C22×C4×D6111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—2444no—
703C2×C4—2444no—
704C2×C4—2444no—
705C2×C4C2×D4×D6111yescharacteristic
706C2×C4#41×D6111yescharacteristic
707C2×C4#41×D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4#1451982211yescharacteristic
710C2×C4#1451982311yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—1222no—
716C8—2441no—
717C8—2441no—
718C8—2441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—614no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—1222no—
734C22—1222no—
735C22—1222no—
736C22—24416no—
737C22—2441no—
738C22—2441no—
739C22—2441no—
740C22—2441no—
741C22#117×D6111yescharacteristic
742C22C4×D4×D6111yescharacteristic
743C22#1684023411yescharacteristic
744C22#131×D6111yescharacteristic
745C22#131×D6111yescharacteristic
746C22C2×#1451978311yescharacteristic
747C22#1684052811yescharacteristic
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—1222no—
754C4—1222no—
755C4—2441no—
756C4—2441no—
757C4—2441no—
758C4—2441no—
759C4#1684040111yescharacteristic
760C4#1684040511yescharacteristic
761C4#1684043711yescharacteristic
762C4#1684044011yescharacteristic
763C2—42no—
764C2—1224no—
765C2—2442no—
766C2#2144866711yescharacteristic
767C2#433×D6111yescharacteristic
768C2#2145447211yescharacteristic
769C2#2145450811yescharacteristic
770C2#2145454811yescharacteristic
771C2#2145486611yescharacteristic
772C2#2145487211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1923C2
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1923D61
hypocenterC61#22558
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#16839822C2semidirect
4. #21446435C2semidirect
5. #21446434C2semidirect
6. #21446422C2semidirect
7. #21445998C2semidirect
8. #21445995C2semidirect
9. #21445889C2semidirect
10. #21445802C2semidirect
12. #21445594C2semidirect
13. C8×#11758198C2semidirect
14. #21445586C2semidirect
15. C61×#1923C2semidirect
22. C2×C4⋊#92418C22semidirect
23. C2×#14519706C22semidirect
24. C2×#14519706C22semidirect
34. C2×#14519688C22semidirect
35. C2×#14519687C22semidirect
36. C2×C8×Dic61C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
54. C2×C4⋊C8×C61C22semidirect
57. C2×C4×C8×C61C22semidirect
59. C61×#336C22semidirect
60. C61×#336C22semidirect
361. C2×D61#433semidirect
383. #1923D61semidirect
411. C2×C4⋊C8C2×D61semidirect
426. C2×C4×C8C2×D61semidirect
445. #336C2×D61semidirect
446. #336C2×D61semidirect
447. C61#22558semidirect

Maximal subgroups

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

subgroupindex
C2×#168398222
C2×C22⋊C8×D612
#214482002
#214464352
#214464342
#214464222
#214459982
#214459952
#214458892
#214458022
#214457282
#214455942
C8×#117581982
#214455862
C61×#19232
#2255861