Finite Group Databasebeta

← #29700329

Subgroups — #29700329

Order 15616.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839894C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic, complemented
4#21448840C211yesmaximal, characteristic, complemented
5#21448640C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446077C211yesmaximal, characteristic, complemented
12#21446010C211yesmaximal, characteristic, complemented
13#21445645C211yesmaximal, characteristic, complemented
14#21445596C211yesmaximal, characteristic, complemented
15C61×#1972C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic, complemented
22C2×#14519739C2211yescharacteristic
23C2×#14519737—21no—
24C2×C4⋊C4×D61C2211yescharacteristic
25C2×C22⋊C4×D61—21no—
26#16839894C418yescomplemented
27#16839871—24no—
28C2×#14519708C2211yescharacteristic, complemented
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic, complemented
34C2×#14519697C2211yescharacteristic
35#102×D61—24no—
36C2×#14519689C2211yescharacteristic
37C2×#14519687C2211yescharacteristic, complemented
38#16839665C2211yescharacteristic
39#16839658C2211yescharacteristic, complemented
40#16839650—21no—
41#16839638—21no—
42#16839638—21no—
43#16839638—21no—
44#16839634—21no—
45#16839619C2211yescharacteristic
46#16839617—21no—
47C4×C4⋊Dic61C2211yescharacteristic, complemented
48C4×#11758198C2211yescharacteristic
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C22×D8×C61C2211yescharacteristic
56C2×#106×C61C2211yescharacteristic, complemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic, complemented
59C2×#97×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×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×#11758199—22no—
78C2×#11758199—22no—
79C2×#11758199C2×C414yescomplemented
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—41no—
85#14519748—22no—
86#14519748C2×C414yescomplemented
87C4×D244—22no—
88C4×D244—41no—
89D4×Dic61—22no—
90D4×Dic61—41no—
91#14519739—22no—
92#14519739—41no—
93#14519737—44no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—21no—
99C4⋊C4×D61—22no—
100C4⋊C4×D61—41no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198D411yescharacteristic
109C2×#11758198D411yescharacteristic
110C22⋊C4×D61—44no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519708—22no—
114#14519699C2×C414yescomplemented
115#14519699D414yescomplemented
116#14519698—22no—
117#14519698—41no—
118#14519698C2×C414yescomplemented
119#14519697—22no—
120#14519689C2×C414yescomplemented
121#14519687—22no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684D411yescharacteristic
126#14519684D411yescharacteristic
127C22×D4×C61C2311yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C2×D8×C61—41no—
130C2×D8×C61—41no—
131C2×D8×C61C2×C414yescomplemented
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61C2311yescharacteristic
141#106×C61—41no—
142#102×C61—22no—
143#102×C61—22no—
144#97×C61—41no—
145C24×C61—21no—
146C24×C61—21no—
147C23×D61—21no—
148C23×D61—24no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61—81no—
154C23×D61—81no—
155C23×D61C2×D411yescharacteristic
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×C61—21no—
166C2×D4×C61C22×C412yes—
167C2×D4×C61C22×C412yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C2×C22⋊D61—24no—
174C2×C22⋊D61—24no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—42no—
183C22×Dic61—42no—
184C22×Dic61—81no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188D4×D61—28no—
189D4×D61—44no—
190D4×D61—44no—
191D4×D61—44no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244C22×C412yes—
196C2×D244C2×D412yes—
197C2×D244#4112yes—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—81no—
209C2×C4×D61—81no—
210C2×C4×D61—81no—
211C2×C4×D61C22×C412yes—
212C2×C4×D61#4112yes—
213D8×C61—44no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61C22×C412yes—
219C2×C8×C61C2×D412yes—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—81no—
227C22⋊C4×C61—81no—
228C42×C61—21no—
229C42×C61—21no—
230C22⋊Dic61—24no—
231C22⋊Dic61—42no—
232C22⋊Dic61—42no—
233C22⋊Dic61—81no—
234#11758199—28no—
235#11758198—22no—
236#11758198—22no—
237#11758198—42no—
238#11758198—42no—
239#11758198—42no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61C22×C412yes—
245C4⋊Dic61C2×D412yes—
246#11758196—42no—
247#11758196—42no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—42no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418C22×C412yes—
257C8×D61—44no—
258C23×C61—22no—
259C23×C61—22no—
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×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61C22×D411yescharacteristic
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—48no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—48no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61—84no—
291C22×D61C4×D412yes—
292C22×D61AGL(1,ℤ/8)12yes—
293C22×D61AGL(1,ℤ/8)12yes—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—41no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61—41no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C23×C411yescharacteristic
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C22⋊D61—48no—
321C22⋊D61—48no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—84no—
340C2×Dic61C4×D412yes—
341D244—22no—
342D244—22no—
343D244—22no—
344D244C4×D414yescomplemented
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—84no—
350C4×D61—84no—
351C4×D61—84no—
352C8×C61—22no—
353C8×C61—22no—
354#92418—22no—
355#92418—41no—
356#22858—611nomaximal, Sylow
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61C2×C4×D411yescharacteristic
372C22×C61D4211yescharacteristic
373C22×C61#54611yescharacteristic
374C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C61#57611yescharacteristic
377C22×C61#57711yescharacteristic
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—24no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—816no—
392C2×D61#44214yescomplemented
393C4×C61—41no—
394C4×C61—41no—
395C4×C61—81no—
396C4×C61—81no—
397C4×C61C2×C4×D411yescharacteristic
398C4×C61#51811yescharacteristic
399C4×C61#54611yescharacteristic
400C4×C61#55111yescharacteristic
401Dic61—22no—
402Dic61—42no—
403Dic61—42no—
404Dic61—41no—
405Dic61—41no—
406Dic61—81no—
407C2×#447—611no—
408C2×#442—611no—
409C22×#102—611no—
410#2361—611no—
411D4×C22⋊C4—611no—
412#1972D6111yescharacteristic, complemented
413#1936—611no—
414#1926—611no—
415#1893—611no—
416#1879—611no—
417#1879—611no—
418#1864—611no—
419#1853—611no—
420#1762—611no—
421#1752—611no—
422C2×C61—82no—
423C2×C61—82no—
424C2×C61#235811yescharacteristic
425C2×C61C2×#44211yescharacteristic
426C2×C61#294611yescharacteristic
427C2×C61#326411yescharacteristic
428C2×C61#326511yescharacteristic
429C2×C61#330611yescharacteristic
430C2×C61#331811yescharacteristic
431D61—24no—
432D61—44no—
433C23×D4—611no—
434C22×D8—611no—
435C22×D8C2×D6111yescharacteristic
436C23×C8—611no—
437C2×#121—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×C4×D4—1221no—
442C22×C4⋊C4—611no—
443C22×C22⋊C4—1221no—
444#447—618no—
445#442—1224no—
446C2×#106—611no—
447C2×#106C2×D6111yescharacteristic, complemented
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—1224no—
455C2×#102C2×D6111yescharacteristic
456C2×#102C2×D6111yescharacteristic, complemented
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×#97C2×D6111yescharacteristic, complemented
460#390—611no—
461#390C2×D6111yescharacteristic
462#390C2×D6111yescharacteristic, complemented
463#389—611no—
464#388—1221no—
465#386—1221no—
466#386—1221no—
467#386—1221no—
468#385—1221no—
469#380—611no—
470#379—1221no—
471C4×C4⋊C4—611no—
472C4×C22⋊C4—611no—
473#340—611no—
474#340—611no—
475#340—611no—
476#340—611no—
477#336—611no—
478#336—611no—
479C61#2285811yescharacteristic, complemented, Sylow
480C25—1221no—
481C22×D4—614no—
482C22×D4—611no—
483C22×D4—1222no—
484C22×D4—1221no—
485C22×D4—1222no—
486C22×D4—1222no—
487C22×D4—1221no—
488C22×D4—2441no—
489C22×D4—2441no—
490C22×D4C22×D6111yescharacteristic
491C22×D4C22×D6111yescharacteristic
492C23×C4—611no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4—1221no—
497C2×D8—41no—
498C2×D8—41no—
499C2×D8—614no—
500C2×D8—1222no—
501C2×D8—1222no—
502C2×D8C4×D6114yescomplemented
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—1222no—
506C22×C8—1222no—
507C22×C8—2441no—
508C22×C8C22×D6111yescharacteristic
509C22×C8C22×D6111yescharacteristic
510#121—614no—
511#121—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—2441no—
516C4×D4—2441no—
517C4×D4—2441no—
518C4×D4—2444no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1222no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—2441no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—2444no—
542C2×C42—611no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545#106—41no—
546#106—1222no—
547#102—22no—
548#102—22no—
549#102—614no—
550#102—614no—
551#102—614no—
552#102—1222no—
553#102—1222no—
554#102—2441no—
555C22⋊C8—614no—
556#97—41no—
557#97—1222no—
558#95—611no—
559#95—611no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563C24—21no—
564C24—21no—
565C24—611no—
566C24—1224no—
567C24—1221no—
568C24—4881no—
569C24—4881no—
570C24—2442no—
571C24—2442no—
572C24—2442no—
573C24—2442no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—612no—
585C2×D4—612no—
586C2×D4—612no—
587C2×D4—1224no—
588C2×D4—1228no—
589C2×D4—1224no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—2444no—
594C2×D4—2444no—
595C2×D4—2444no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4C2×C4×D6112yes—
601C2×D4C2×C4×D6112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—611no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—4881no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4D4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4C23×D6111yescharacteristic
631D8—44no—
632D8—1228no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—612no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—2444no—
644C2×C8C2×C4×D6112yes—
645C2×C8D4×D6112yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—2442no—
657C4⋊C4—2442no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—1222no—
663C22⋊C4—1222no—
664C22⋊C4—1224no—
665C22⋊C4—4881no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C42—21no—
672C42—21no—
673C42—1221no—
674C42—1221no—
675C42—2442no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—612no—
691C23—612no—
692C23—612no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—4884no—
701C23—4884no—
702C23—4884no—
703C23—4884no—
704C23—4884no—
705C23—2448no—
706C23—2448no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23C2×D4×D6111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—614no—
721D4—1222no—
722D4—1222no—
723D4—1222no—
724D4—2448no—
725D4—2448no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—612no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1222no—
753C2×C4—4884no—
754C2×C4—4884no—
755C2×C4—4884no—
756C2×C4—4884no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6111yescharacteristic
767C2×C4#41×D6111yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982211yescharacteristic
770C8—22no—
771C8—22no—
772C8—1222no—
773C8—2441no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—614no—
789C22—1222no—
790C22—1222no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—1222no—
795C22—1224no—
796C22—48816no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22C4×D4×D6111yescharacteristic
804C22#1684039711yescharacteristic
805C22#1684040111yescharacteristic
806C22AGL(1,ℤ/8)×D6111yescharacteristic
807C22AGL(1,ℤ/8)×D6111yescharacteristic
808C22#1684056611yescharacteristic
809C22#1684057211yescharacteristic
810C4—41no—
811C4—41no—
812C4—81no—
813C4—81no—
814C4—1222no—
815C4—4881no—
816C4—2442no—
817C4—2441no—
818C4—2442no—
819C4—2441no—
820C4C4×D4×D6111yescharacteristic
821C4#1684023511yescharacteristic
822C4#1684040111yescharacteristic
823C4#1684044211yescharacteristic
824C2—82no—
825C2—82no—
826C2—1224no—
827C2—2444no—
828C2#2144880011yescharacteristic
829C2#442×D6111yescharacteristic
830C2#2145464811yescharacteristic
831C2#2145729811yescharacteristic
832C2#2145731311yescharacteristic
833C2#2145777511yescharacteristic
834C2#2145795511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1972C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenter#1972D61
hypocenterC61#22858
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. C2×#102×D61C2semidirect
4. #21448840C2semidirect
5. #21448640C2semidirect
6. #21446513C2semidirect
7. #21446443C2semidirect
8. #21446244C2semidirect
9. #21446170C2semidirect
10. #21446169C2semidirect
11. #21446077C2semidirect
12. #21446010C2semidirect
13. #21445645C2semidirect
14. #21445596C2semidirect
15. C61×#1972C2semidirect
21. C2×D4×Dic61C22semidirect
26. #16839894C4semidirect
28. C2×#14519708C22semidirect
33. C2×#14519698C22semidirect
37. C2×#14519687C22semidirect
39. #16839658C22semidirect
47. C4×C4⋊Dic61C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839517C22semidirect
54. #16839516C22semidirect
56. C2×#106×C61C22semidirect
58. C2×#102×C61C22semidirect
59. C2×#97×C61C22semidirect
61. C61×#390C22semidirect
71. C2×D4×D61C2×C4semidirect
79. C2×#11758199C2×C4semidirect
86. #14519748C2×C4semidirect
114. #14519699C2×C4semidirect
115. #14519699D4semidirect
118. #14519698C2×C4semidirect
120. #14519689C2×C4semidirect
131. C2×D8×C61C2×C4semidirect
344. D244C4×D4semidirect
392. C2×D61#442semidirect
412. #1972D61semidirect
447. C2×#106C2×D61semidirect
456. C2×#102C2×D61semidirect
459. C2×#97C2×D61semidirect
462. #390C2×D61semidirect
479. C61#22858semidirect
502. 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×#102×D612
#214488402
#214486402
#214465132
#214464432
#214462442
#214461702
#214461692
#214460772
#214460102
#214456452
#214455962
C61×#19722
#2285861