Finite Group Databasebeta

← #29700479

Subgroups — #29700479

Order 15616.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839894C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4#21448862C211yesmaximal, characteristic, complemented
5#21448640C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446063C211yesmaximal, characteristic, complemented
12#21446015C211yesmaximal, characteristic, complemented
13C4×#14519699C211yesmaximal, characteristic, complemented
14#21445602C211yesmaximal, characteristic, complemented
15C61×#1970C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic, complemented
22C2×#14519739C2211yescharacteristic
23C2×#14519735C2211yescharacteristic
24C2×C22⋊C4×D61—21no—
25#16839894C418yescomplemented
26#16839871—24no—
27C2×#14519708C2211yescharacteristic, complemented
28#16839765—24no—
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic, complemented
34C2×#14519697C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519687C2211yescharacteristic, complemented
37#16839665C2211yescharacteristic
38#16839662—21no—
39#16839658C2211yescharacteristic, complemented
40#16839656—21no—
41#16839639—21no—
42#16839638—21no—
43#16839638—21no—
44#16839619C2211yescharacteristic
45#16839617—21no—
46C4×C4⋊Dic61C2211yescharacteristic, complemented
47C22⋊C4×Dic61—21no—
48C4×#11758198C2211yescharacteristic
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C22×D8×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic, complemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic, complemented
59C2×C4×C8×C61C2211yescharacteristic, complemented
60C61×#390C2211yescharacteristic
61C61×#390C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—41no—
70C2×D4×D61—41no—
71C2×D4×D61C2×C414yescomplemented
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61C2311yescharacteristic
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758199C2×C414yes—
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189—41no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519748—22no—
85#14519748C2×C414yescomplemented
86C4×D244—22no—
87C4×D244—41no—
88D4×Dic61—22no—
89D4×Dic61—41no—
90#14519739—22no—
91#14519739—41no—
92#14519735—22no—
93#14519735—41no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198D411yescharacteristic
107C2×#11758198D411yescharacteristic
108C22⋊C4×D61—44no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61C2311yescharacteristic
112#14519708—22no—
113#14519699C2×C414yescomplemented
114#14519699D414yescomplemented
115#14519698—22no—
116#14519698—41no—
117#14519698C2×C414yescomplemented
118#14519697—22no—
119#14519689C2×C414yescomplemented
120#14519687—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684D411yescharacteristic
125#14519684D411yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C22×D4×C61C2311yescharacteristic
128C2×D8×C61—41no—
129C2×D8×C61—41no—
130C2×D8×C61C2×C414yescomplemented
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#107×C61—41no—
141#102×C61—22no—
142#102×C61—22no—
143C4×C8×C61—41no—
144C24×C61—21no—
145C24×C61—21no—
146C23×D61—21no—
147C23×D61—24no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—81no—
153C23×D61—81no—
154C23×D61C2×D411yescharacteristic
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61C22×C412yes—
166C2×D4×C61C22×C412yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2411yescharacteristic
172C2×C22⋊D61—24no—
173C2×C22⋊D61—24no—
174C2×C22⋊D61—42no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—81no—
177C2×C22⋊D61—81no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—81no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187D4×D61—28no—
188D4×D61—44no—
189D4×D61—44no—
190D4×D61—44no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244C22×C412yes—
195C2×D244C2×D412yes—
196C2×D244#4112yes—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—81no—
206C2×C4×D61—81no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61#4112yes—
209D8×C61—44no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61C22×C412yes—
215C2×C8×C61C2×D412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—81no—
223C22⋊C4×C61—81no—
224C42×C61—21no—
225C42×C61—21no—
226C22⋊Dic61—24no—
227C22⋊Dic61—42no—
228C22⋊Dic61—42no—
229C22⋊Dic61—81no—
230#11758199—28no—
231#11758198—22no—
232#11758198—41no—
233#11758198—42no—
234#11758198—42no—
235#11758198—42no—
236#11758198—42no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61C22×C412yes—
242C4⋊Dic61C2×D412yes—
243#11758196—81no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—42no—
247C4×Dic61—81no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418C22×C412yes—
254#11758189—44no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—21no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—48no—
280C22×D61—48no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61C4×D412yes—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—41no—
298D4×C61—41no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61AGL(1,ℤ/8)12yes—
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C22⋊D61—48no—
318C22⋊D61—84no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—84no—
337C2×Dic61C4×D412yes—
338D244—22no—
339D244—22no—
340D244—22no—
341D244C4×D414yes—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—84no—
347C4×D61—84no—
348C8×C61—22no—
349C8×C61—22no—
350#92418—22no—
351#92418—41no—
352#22868—611nomaximal, Sylow
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61C2×C4×D411yescharacteristic
368C22×C61D4211yescharacteristic
369C22×C61#54611yescharacteristic
370C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C61#57511yescharacteristic
372C22×C61#57611yescharacteristic
373C22×C61#57611yescharacteristic
374C2×D61—22no—
375C2×D61—24no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—41no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—41no—
384C2×D61—42no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—42no—
388C2×D61—816no—
389C4×C61—22no—
390C4×C61—41no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61C2×C4×D411yescharacteristic
394C4×C61#51811yescharacteristic
395C4×C61#54611yescharacteristic
396C4×C61#55111yescharacteristic
397Dic61—22no—
398Dic61—42no—
399Dic61—41no—
400Dic61—42no—
401Dic61—41no—
402Dic61—81no—
403C2×#447—611no—
404C2×#442—611no—
405C2×#418—611no—
406#2363—611no—
407D4×C22⋊C4—611no—
408#1970D6111yescharacteristic, complemented
409#1936—611no—
410#1926—611no—
411#1895—611no—
412#1879—611no—
413#1879—611no—
414#1862—611no—
415#1854—611no—
416C4×#102—611no—
417#1753—611no—
418C2×C61—82no—
419C2×C61—82no—
420C2×C61#235811yescharacteristic
421C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
422C2×C61#294811yescharacteristic
423C2×C61#327311yescharacteristic
424C2×C61#327411yescharacteristic
425C2×C61#331811yescharacteristic
426C2×C61#331911yescharacteristic
427D61—42no—
428D61—44no—
429C23×D4—611no—
430C22×D8—611no—
431C22×D8C2×D6111yescharacteristic
432C22×M16—611no—
433C2×#121—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×#117—611no—
438C22×C22⋊C4—1221no—
439#447—618no—
440#442—1224no—
441C2×#107C2×D6111yescharacteristic, complemented
442C2×#106—611no—
443#418—1224no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102C2×D6111yescharacteristic
451C2×#102C2×D6111yescharacteristic, complemented
452C2×C22⋊C8—611no—
453C2×#97—611no—
454C2×C4×C8C2×D6111yescharacteristic, complemented
455#390—611no—
456#390—1221no—
457#390C2×D6111yescharacteristic
458#390C2×D6111yescharacteristic, complemented
459#389—611no—
460#388—1221no—
461#386—1221no—
462#386—1221no—
463#386—1221no—
464#380—611no—
465#379—1221no—
466C4×C4⋊C4—611no—
467C4×C22⋊C4—611no—
468C4×C22⋊C4—1221no—
469#340—611no—
470#340—611no—
471#340—611no—
472#340—611no—
473#336—611no—
474#336—611no—
475C61#2286811yescharacteristic, complemented, Sylow
476C25—1221no—
477C22×D4—614no—
478C22×D4—611no—
479C22×D4—1222no—
480C22×D4—1221no—
481C22×D4—1222no—
482C22×D4—1222no—
483C22×D4—1221no—
484C22×D4—2441no—
485C22×D4—2441no—
486C22×D4C22×D6111yescharacteristic
487C22×D4C22×D6111yescharacteristic
488C23×C4—611no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×D8—41no—
493C2×D8—41no—
494C2×D8—614no—
495C2×D8—1222no—
496C2×D8—1222no—
497C2×D8C4×D6114yescomplemented
498C2×M16—1222no—
499C2×M16—1222no—
500C2×M16—2441no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505#121—614no—
506#121—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—2441no—
511C4×D4—2441no—
512C4×D4—2441no—
513#117—1222no—
514#117—2441no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—2444no—
536C2×C42—611no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540#107—41no—
541#106—1222no—
542#102—22no—
543#102—22no—
544#102—614no—
545#102—614no—
546#102—614no—
547#102—1222no—
548#102—1222no—
549#102—2441no—
550C22⋊C8—614no—
551#97—1222no—
552C4×C8—41no—
553#95—611no—
554#95—611no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558C24—21no—
559C24—21no—
560C24—611no—
561C24—1224no—
562C24—1221no—
563C24—4881no—
564C24—4881no—
565C24—2442no—
566C24—2442no—
567C24—2442no—
568C24—2442no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—612no—
580C2×D4—612no—
581C2×D4—612no—
582C2×D4—1224no—
583C2×D4—1228no—
584C2×D4—1224no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—4881no—
589C2×D4—4881no—
590C2×D4—2444no—
591C2×D4—2444no—
592C2×D4—2444no—
593C2×D4—2442no—
594C2×D4—2442no—
595C2×D4C2×C4×D6112yes—
596C2×D4C2×C4×D6112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—611no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—4881no—
614C22×C4—2442no—
615C22×C4—2442no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4D4×D6111yescharacteristic
621C22×C4D4×D6111yescharacteristic
622C22×C4C23×D6111yescharacteristic
623D8—44no—
624D8—1228no—
625M16—2444no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—612no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8C2×C4×D6112yes—
637C2×C8D4×D6112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—612no—
643C4⋊C4—612no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—4881no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C22⋊C4—1224no—
654C22⋊C4—1222no—
655C22⋊C4—4881no—
656C22⋊C4—2441no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—21no—
664C42—21no—
665C42—1221no—
666C42—1221no—
667C42—4881no—
668C42—2442no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—612no—
684C23—1222no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1222no—
691C23—1222no—
692C23—1221no—
693C23—4884no—
694C23—4884no—
695C23—4884no—
696C23—4884no—
697C23—4884no—
698C23—2448no—
699C23—2448no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23C2×D4×D6111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—614no—
714D4—1222no—
715D4—1222no—
716D4—1222no—
717D4—4884no—
718D4—2448no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—612no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1222no—
745C2×C4—4884no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4#1451980112yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4#41×D6111yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982211yescharacteristic
762C8—22no—
763C8—22no—
764C8—1222no—
765C8—2441no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—1222no—
781C22—1222no—
782C22—1222no—
783C22—1224no—
784C22—48816no—
785C22—2441no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2441no—
790C22—2442no—
791C22—2441no—
792C22—2441no—
793C22—2442no—
794C22—2442no—
795C22C4×D4×D6111yescharacteristic
796C22#1684039711yescharacteristic
797C22#1684040111yescharacteristic
798C22C2×#1451980111yescharacteristic
799C22#1684055911yescharacteristic
800C22#1684056311yescharacteristic
801C22#1684056411yescharacteristic
802C4—22no—
803C4—41no—
804C4—81no—
805C4—81no—
806C4—1222no—
807C4—4881no—
808C4—2441no—
809C4—2442no—
810C4—2441no—
811C4—2442no—
812C4C4×D4×D6111yescharacteristic
813C4#1684023511yescharacteristic
814C4#1684040111yescharacteristic
815C4#1684044211yescharacteristic
816C2—82no—
817C2—82no—
818C2—2442no—
819C2—2444no—
820C2#2144880011yescharacteristic
821C2C4×#1451980111yescharacteristic
822C2#2145466611yescharacteristic
823C2#2145742811yescharacteristic
824C2#2145743811yescharacteristic
825C2#2145796611yescharacteristic
826C2#2145798111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1970C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenter#1970D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. C2×#16839765C2semidirect
4. #21448862C2semidirect
5. #21448640C2semidirect
6. #21446513C2semidirect
7. #21446443C2semidirect
8. #21446254C2semidirect
9. #21446170C2semidirect
10. #21446169C2semidirect
11. #21446063C2semidirect
12. #21446015C2semidirect
13. C4×#14519699C2semidirect
14. #21445602C2semidirect
15. C61×#1970C2semidirect
21. C2×D4×Dic61C22semidirect
25. #16839894C4semidirect
27. C2×#14519708C22semidirect
33. C2×#14519698C22semidirect
36. C2×#14519687C22semidirect
39. #16839658C22semidirect
46. C4×C4⋊Dic61C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839517C22semidirect
54. #16839516C22semidirect
56. C2×#107×C61C22semidirect
58. C2×#102×C61C22semidirect
59. C2×C4×C8×C61C22semidirect
61. C61×#390C22semidirect
71. C2×D4×D61C2×C4semidirect
85. #14519748C2×C4semidirect
113. #14519699C2×C4semidirect
114. #14519699D4semidirect
117. #14519698C2×C4semidirect
119. #14519689C2×C4semidirect
130. C2×D8×C61C2×C4semidirect
408. #1970D61semidirect
441. C2×#107C2×D61semidirect
451. C2×#102C2×D61semidirect
454. C2×C4×C8C2×D61semidirect
458. #390C2×D61semidirect
475. C61#22868semidirect
497. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398942
C2×#168398712
C2×#168397652
#214488622
#214486402
#214465132
#214464432
#214462542
#214461702
#214461692
#214460632
#214460152
C4×#145196992
#214456022
C61×#19702
#2286861