Finite Group Databasebeta

← #29700477

Subgroups — #29700477

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×#16839895C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3C2×#16839768C211yesmaximal, characteristic, complemented
4#21448861C211yesmaximal, characteristic, complemented
5#21448639C211yesmaximal, characteristic, complemented
6#21446682C211yesmaximal, characteristic, complemented
7#21446517C211yesmaximal, characteristic, complemented
8#21446444C211yesmaximal, characteristic, complemented
9#21446165C211yesmaximal, characteristic, complemented
10#21446164C211yesmaximal, characteristic, complemented
11#21446067C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C61×#1895C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic, complemented
20C2×#14519739C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23C2×C22⋊C4×D61—21no—
24#16839895C418yescomplemented
25#16839871—24no—
26C2×#14519710C2211yescharacteristic, complemented
27C2×#14519708C2211yescharacteristic, complemented
28#16839768—24no—
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519687C2211yescharacteristic, complemented
37C2×C8×Dic61C2211yescharacteristic, complemented
38#16839665—21no—
39#16839665C2211yescharacteristic, complemented
40#16839663C2211yescharacteristic
41#16839663C2211yescharacteristic
42#16839661C2211yescharacteristic, complemented
43#16839655—21no—
44#16839642—21no—
45#16839640—21no—
46#16839640—21no—
47#16839617—21no—
48C4⋊C4×Dic61C2211yescharacteristic, complemented
49C22⋊C4×Dic61—21no—
50C4×C22⋊Dic61C2211yescharacteristic
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C22×M16×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic, complemented
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—21no—
66C22×D244—22no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244C2×C414yescomplemented
70C22×D244C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—41no—
78C2×#11758199—41no—
79C2×#11758199C2×C414yes—
80C2×#11758199C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83D4×Dic61—22no—
84D4×Dic61—41no—
85#14519739—22no—
86#14519739—22no—
87#14519739—41no—
88#14519739—41no—
89#14519736—22no—
90#14519736—41no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61D411yescharacteristic
99C2×C22⋊Dic61D411yescharacteristic
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C22⋊C4×D61—44no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111#14519710—41no—
112#14519708—22no—
113#14519699—22no—
114#14519699—22no—
115#14519699—22no—
116#14519699D414yescomplemented
117#14519697C2×C414yescomplemented
118#14519697C2×C414yescomplemented
119C22⋊#92418C2×C414yescomplemented
120#14519687—22no—
121C8×Dic61—41no—
122#14519684—21no—
123#14519684—21no—
124#14519684D411yescharacteristic
125#14519684D411yescharacteristic
126C22×D4×C61—21no—
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C2×M16×C61—22no—
130C2×M16×C61—22no—
131C2×M16×C61—41no—
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134#121×C61—22no—
135#121×C61C2×C414yescomplemented
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141#102×C61—22no—
142#102×C61—41no—
143#95×C61—21no—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C23×D61—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—
155C2×D4×C61—24no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—81no—
162C2×D4×C61—81no—
163C2×D4×C61C22×C412yes—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C22×C412yes—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61#4112yes—
174C22×C4×C61C2411yescharacteristic
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—42no—
178C22×Dic61—42no—
179C22×Dic61—81no—
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—28no—
192C2×D244—24no—
193C2×D244—21no—
194C2×D244—44no—
195C2×D244—44no—
196C2×D244—44no—
197C2×D244—42no—
198C2×D244—42no—
199C2×D244C22×C412yes—
200C2×D244C22×C412yes—
201C2×D244C2×D412yes—
202C2×D244#4112yes—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209M16×C61—44no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61C2×D412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C22×C412yes—
222C22⋊C4×C61—24no—
223C22⋊C4×C61—42no—
224C22⋊Dic61—22no—
225C22⋊Dic61—41no—
226C22⋊Dic61—42no—
227C22⋊Dic61—42no—
228C22⋊Dic61—42no—
229C22⋊Dic61—81no—
230#11758199—28no—
231#11758199—44no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235#11758198—42no—
236#11758198—81no—
237#11758198—81no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—81no—
242C4⋊Dic61C2×D412yes—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—42no—
248C4×Dic61—81no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418C22×C412yes—
254C2×#92418C22×C412yes—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61C4×D412yes—
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—48no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—48no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61—84no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—84no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—41no—
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×C61—41no—
311C2×C4×C61C4×D412yes—
312C2×C4×C61C23×C411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—22no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—84no—
336C2×Dic61AGL(1,ℤ/8)12yes—
337D244—22no—
338D244—22no—
339D244—22no—
340D244—22no—
341D244—22no—
342D244—48no—
343D244—41no—
344D244—41no—
345D244C4×D414yes—
346C4×D61—84no—
347C4×D61—84no—
348C8×C61—22no—
349C8×C61—41no—
350#92418—22no—
351#92418—22no—
352#22868—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
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—24no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—816no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C4×C61—22no—
390C4×C61—42no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61C2×C4×D411yescharacteristic
394C4×C61#51811yescharacteristic
395C4×C61#54611yescharacteristic
396C4×C61#55111yescharacteristic
397Dic61—22no—
398Dic61—41no—
399Dic61—42no—
400Dic61—41no—
401Dic61—41no—
402Dic61—81no—
403C2×#447—611no—
404C2×#442—611no—
405C2×#418—611no—
406#2363—611no—
407D4×C22⋊C4—611no—
408#1970—611no—
409#1936—611no—
410#1926—611no—
411#1895D6111yescharacteristic, complemented
412#1879—611no—
413#1879—611no—
414#1862—611no—
415#1854—611no—
416C4×#102—611no—
417#1753—611no—
418C2×C61—42no—
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—44no—
428D61—82no—
429C23×D4—611no—
430C22×D8—611no—
431C22×D8—611no—
432C22×M16C2×D6111yescharacteristic
433C2×#121C2×D6111yescharacteristic
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×#107—611no—
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, complemented
451C2×#102C2×D6111yescharacteristic, complemented
452C2×C22⋊C8—611no—
453C2×#97—611no—
454C2×C4×C8—611no—
455#390—611no—
456#390—611no—
457#390—611no—
458#390—1221no—
459#389—611no—
460#388—1221no—
461#386—1221no—
462#386—1221no—
463#386—1221no—
464#380C2×D6111yescharacteristic
465#379—1221no—
466C4×C4⋊C4—611no—
467C4×C22⋊C4—611no—
468C4×C22⋊C4—1221no—
469#340—611no—
470#340—611no—
471#340C2×D6111yescharacteristic, complemented
472#340C2×D6111yescharacteristic, complemented
473#336—611no—
474#336—611no—
475C61#2286811yescharacteristic, complemented, Sylow
476C25—1221no—
477C22×D4—21no—
478C22×D4—614no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—1222no—
482C22×D4—1222no—
483C22×D4—1221no—
484C22×D4—1222no—
485C22×D4—2441no—
486C22×D4—2441no—
487C22×D4C22×D6111yescharacteristic
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×D8—614no—
493C2×D8—614no—
494C2×D8—1222no—
495C2×D8—1222no—
496C2×D8—2441no—
497C2×D8—2441no—
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505#121—22no—
506#121C4×D6114yescomplemented
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—1221no—
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
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—611no—
538C2×C42—1221no—
539C2×C42—1221no—
540#107—2441no—
541#106—1222no—
542#102—22no—
543#102—41no—
544#102—614no—
545#102—614no—
546#102—614no—
547#102—1222no—
548#102—1222no—
549#102—1222no—
550C22⋊C8—614no—
551#97—1222no—
552C4×C8—2441no—
553#95—21no—
554#95—611no—
555#95—611no—
556#95—1221no—
557#95—1221no—
558C24—21no—
559C24—1221no—
560C24—1224no—
561C24—1221no—
562C24—4881no—
563C24—4881no—
564C24—2442no—
565C24—2442no—
566C24—2442no—
567C24—2442no—
568C24D4×D6111yescharacteristic
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—612no—
578C2×D4—612no—
579C2×D4—612no—
580C2×D4—612no—
581C2×D4—1228no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1224no—
591C2×D4—2444no—
592C2×D4—2444no—
593C2×D4—2444no—
594C2×D4—2442no—
595C2×D4—2442no—
596C2×D4C2×C4×D6112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—4881no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2442no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4C2×C4×D6112yes—
620C22×C4D4×D6111yescharacteristic
621C22×C4#1175822412yes—
622C22×C4C23×D6111yescharacteristic
623D8—1228no—
624D8—2444no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—612no—
632C2×C8—612no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8D4×D6112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—612no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—4881no—
648C4⋊C4C2×C4×D6112yes—
649C22⋊C4—24no—
650C22⋊C4—42no—
651C22⋊C4—1222no—
652C22⋊C4—4881no—
653C22⋊C4—4881no—
654C22⋊C4—4881no—
655C22⋊C4—2442no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2441no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C42—4881no—
668C42—2442no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—4884no—
687C23—4884no—
688C23—4884no—
689C23—4884no—
690C23—4884no—
691C23—2448no—
692C23—2448no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23#1451973712yes—
704C23C2×D4×D6111yescharacteristic
705D4—22no—
706D4—22no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—614no—
711D4—1222no—
712D4—1222no—
713D4—1222no—
714D4—1222no—
715D4—1222no—
716D4—2448no—
717D4—2441no—
718D4—2441no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—612no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—4884no—
748C2×C4—4884no—
749C2×C4—4884no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4#1451973712yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822411yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982311yescharacteristic
762C8—22no—
763C8—41no—
764C8—1222no—
765C8—1222no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—1224no—
781C22—48816no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—4881no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C2×#1451973711yescharacteristic
796C22#1684039611yescharacteristic
797C22#1684040111yescharacteristic
798C22AGL(1,ℤ/8)×D6111yescharacteristic
799C22#1684056111yescharacteristic
800C22#1684056611yescharacteristic
801C22#1684056611yescharacteristic
802C4—22no—
803C4—42no—
804C4—81no—
805C4—81no—
806C4—1222no—
807C4—4881no—
808C4—2441no—
809C4—2442no—
810C4—2441no—
811C4—2441no—
812C4C4×D4×D6111yescharacteristic
813C4#1684023411yescharacteristic
814C4#1684039911yescharacteristic
815C4#1684043511yescharacteristic
816C2—42no—
817C2—82no—
818C2—4882no—
819C2—2444no—
820C2#2144879911yescharacteristic
821C2#2145463211yescharacteristic
822C2#2145466711yescharacteristic
823C2#2145742711yescharacteristic
824C2#2145743611yescharacteristic
825C2#2145795511yescharacteristic
826C2#2145797011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1895C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
cosocleC22×C4×C61C24
hypercenter#1895D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. C2×#16839768C2semidirect
4. #21448861C2semidirect
5. #21448639C2semidirect
6. #21446682C2semidirect
7. #21446517C2semidirect
8. #21446444C2semidirect
9. #21446165C2semidirect
10. #21446164C2semidirect
11. #21446067C2semidirect
12. #21446016C2semidirect
13. #21445633C2semidirect
14. #21445600C2semidirect
15. C61×#1895C2semidirect
19. C2×D4×Dic61C22semidirect
24. #16839895C4semidirect
26. C2×#14519710C22semidirect
27. C2×#14519708C22semidirect
36. C2×#14519687C22semidirect
37. C2×C8×Dic61C22semidirect
39. #16839665C22semidirect
42. #16839661C22semidirect
48. C4⋊C4×Dic61C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839516C22semidirect
54. #16839516C22semidirect
57. C2×#102×C61C22semidirect
58. C2×#102×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
69. C22×D244C2×C4semidirect
80. C2×#11758199C2×C4semidirect
116. #14519699D4semidirect
117. #14519697C2×C4semidirect
118. #14519697C2×C4semidirect
119. C22⋊#92418C2×C4semidirect
135. #121×C61C2×C4semidirect
411. #1895D61semidirect
450. C2×#102C2×D61semidirect
451. C2×#102C2×D61semidirect
471. #340C2×D61semidirect
472. #340C2×D61semidirect
475. C61#22868semidirect
506. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398952
C2×#168398712
C2×#168397682
#214488612
#214486392
#214466822
#214465172
#214464442
#214461652
#214461642
#214460672
#214460162
#214456332
#214456002
C61×#18952
#2286861