Finite Group Databasebeta

← #29696999

Subgroups — #29696999

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×#16839823C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×D61C211yesmaximal, characteristic
3#21448198C211yesmaximal, characteristic
4#21446433C211yesmaximal, characteristic, complemented
5#21446430C211yesmaximal, characteristic, complemented
6#21446426C211yesmaximal, characteristic, complemented
7#21446423C211yesmaximal, characteristic, complemented
8#21445998C211yesmaximal, characteristic, complemented
9#21445998C211yesmaximal, characteristic, complemented
10#21445801C211yesmaximal, characteristic, complemented
11#21445728C211yesmaximal, characteristic
12#21445594C211yesmaximal, characteristic, complemented
13#21445589C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1818C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839823—24no—
21C2×C4⋊#92418C2211yescharacteristic, complemented
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×C4×#92418C2211yescharacteristic, complemented
37C2×C8×Dic61C2211yescharacteristic, complemented
38#16839623C411yescharacteristic
39#16839623C411yescharacteristic
40#16839619C411yescharacteristic
41#16839619C411yescharacteristic
42#16839619C411yescharacteristic
43#16839619C411yescharacteristic
44#16839617C411yescharacteristic
45#16839617C411yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×#11758198C2211yescharacteristic
48C4×#11758198C2211yescharacteristic
49C4×#11758198C2211yescharacteristic
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C2×#117×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic, complemented
58C61×#336C2211yescharacteristic, complemented
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#14519736—41no—
84#14519736—41no—
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C4⋊#92418—22no—
100C4⋊#92418—22no—
101#14519706—41no—
102#14519706—41no—
103C22⋊#92418—22no—
104C22⋊#92418D414yes—
105#14519689—22no—
106#14519689—22no—
107#14519689—22no—
108#14519689—22no—
109#14519689—41no—
110#14519689—41no—
111#14519688—22no—
112#14519687—41no—
113C4×#92418—22no—
114C8×Dic61—41no—
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
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
128#117×C61—22no—
129#117×C61—22no—
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C22⋊C8×C61—22no—
137C22⋊C8×C61—22no—
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×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61#4112yes—
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—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—22no—
183C2×C4×D61—44no—
184C2×C4×D61—44no—
185C2×C4×D61—44no—
186C2×C4×D61—44no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
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×C61—21no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—21no—
211C22⋊Dic61—41no—
212C22⋊Dic61—41no—
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217#11758198—22no—
218#11758198—22no—
219#11758198—41no—
220#11758198—41no—
221C4⋊Dic61—41no—
222C4⋊Dic61—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×#92418C2×D412yes—
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×C61C4×D412yes—
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×D61#13112yes—
268C22×D61#13112yes—
269C22×D61#13112yes—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
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—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61C4×D412yes—
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—21no—
312C2×Dic61—44no—
313C2×Dic61#11712yes—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—44no—
319C4×D61—44no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
324C8×C61—41no—
325C8×C61—41no—
326C8×C61—41no—
327C8×C61—41no—
328#92418—22no—
329#92418—22no—
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—22no—
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—41no—
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#1923—611no—
384#1850—611no—
385#1850—611no—
386#1818D6111yescharacteristic, complemented
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×#117C2×D6111yescharacteristic
407#433—1224no—
408C2×C4⋊C8—611no—
409C2×C4⋊C8—611no—
410C2×C4⋊C8—611no—
411C2×C4⋊C8—611no—
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×C8—611no—
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⋊C4—611no—
439#336—611no—
440#336—611no—
441#336—611no—
442#336—611no—
443#336C2×D6111yescharacteristic, complemented
444#336C2×D6111yescharacteristic, complemented
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—22no—
476#117—22no—
477#117—2441no—
478#117—2441no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4C4×D6111yescharacteristic
482C2×C4⋊C4C4×D6111yescharacteristic
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—1222no—
500C4⋊C8—1222no—
501C4⋊C8—2441no—
502C4⋊C8—2441no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—614no—
506C22⋊C8—1222no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511C22⋊C8—2441no—
512C22⋊C8—2441no—
513#97—1222no—
514#97—2441no—
515C4×C8—1222no—
516C4×C8—2441no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95—611no—
522#95—611no—
523#95—611no—
524#95—611no—
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—611no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1222no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—2441no—
564C22×C4—2441no—
565C22×C4—2444no—
566C22×C4—2444no—
567C22×C4—2444no—
568C22×C4—2444no—
569C22×C4—2441no—
570C22×C4C2×C4×D6111yescharacteristic
571C22×C4C2×C4×D6111yescharacteristic
572C22×C4C2×C4×D6111yescharacteristic
573C22×C4C2×C4×D6111yescharacteristic
574C22×C4C2×C4×D6111yescharacteristic
575C22×C4D4×D6112yes—
576C22×C4#1175822412yes—
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—21no—
590C2×C8—612no—
591C2×C8—612no—
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—1221no—
602C2×C8—2444no—
603C2×C8—2444no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—2441no—
607C4⋊C4—2441no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—2441no—
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#1451973712yes—
656C23C22×C4×D6111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
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—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—612no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—2444no—
698C2×C4—2444no—
699C2×C4—2444no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4#1451973712yes—
705C2×C4C2×D4×D6111yescharacteristic
706C2×C4#41×D6111yescharacteristic
707C2×C4#41×D6111yescharacteristic
708C2×C4C2×#1175822411yescharacteristic
709C2×C4#1451982311yescharacteristic
710C2×C4#1451982311yescharacteristic
711C8—41no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—1222no—
716C8—1222no—
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
742C22C2×#1451973711yescharacteristic
743C22#1684023611yescharacteristic
744C22#131×D6111yescharacteristic
745C22#131×D6111yescharacteristic
746C22#131×D6111yescharacteristic
747C22#1684052711yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—1222no—
754C4—2441no—
755C4—2441no—
756C4—2441no—
757C4—2441no—
758C4—2441no—
759C4#1684040411yescharacteristic
760C4#1684040411yescharacteristic
761C4#1684043511yescharacteristic
762C4#1684043511yescharacteristic
763C2—42no—
764C2—1224no—
765C2—2442no—
766C2#2144866111yescharacteristic
767C2#433×D6111yescharacteristic
768C2#2145447511yescharacteristic
769C2#2145451611yescharacteristic
770C2#2145454911yescharacteristic
771C2#2145486511yescharacteristic
772C2#2145487411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1818C2
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1818D61
hypocenterC61#22558
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
1. C2×#16839823C2semidirect
4. #21446433C2semidirect
5. #21446430C2semidirect
6. #21446426C2semidirect
7. #21446423C2semidirect
8. #21445998C2semidirect
9. #21445998C2semidirect
10. #21445801C2semidirect
12. #21445594C2semidirect
13. #21445589C2semidirect
14. #21445587C2semidirect
15. C61×#1818C2semidirect
21. C2×C4⋊#92418C22semidirect
22. C2×C4⋊#92418C22semidirect
23. C2×#14519706C22semidirect
24. C2×#14519706C22semidirect
34. C2×#14519688C22semidirect
35. C2×#14519687C22semidirect
36. C2×C4×#92418C22semidirect
37. C2×C8×Dic61C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
57. C61×#336C22semidirect
58. C61×#336C22semidirect
59. C61×#336C22semidirect
60. C61×#336C22semidirect
361. C2×D61#433semidirect
386. #1818D61semidirect
443. #336C2×D61semidirect
444. #336C2×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×#168398232
C2×C22⋊C8×D612
#214481982
#214464332
#214464302
#214464262
#214464232
#214459982
#214458012
#214457282
#214455942
#214455892
#214455872
C61×#18182
#2255861