Finite Group Databasebeta

← #29700480

Subgroups — #29700480

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×#16839896C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3#21448857C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446682C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446449C211yesmaximal, characteristic, complemented
8#21446257C211yesmaximal, characteristic, complemented
9#21446165C211yesmaximal, characteristic, complemented
10#21446164C211yesmaximal, characteristic, complemented
11#21446064C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C2×C61×#418C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic, complemented
22C22×C22⋊Dic61—21no—
23#16839896C418yescomplemented
24#16839871—24no—
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519699C2211yescharacteristic, complemented
28C2×#14519699C2211yescharacteristic, complemented
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519687C2211yescharacteristic, complemented
33C2×C8×Dic61C2211yescharacteristic, complemented
34#16839665C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839663C2211yescharacteristic, complemented
37#16839662—21no—
38#16839658C2211yescharacteristic, complemented
39#16839653—21no—
40#16839642—21no—
41#16839642—21no—
42#16839638—21no—
43#16839622C2211yescharacteristic
44#16839618—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C4×#11758198—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C23×D4×C61C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C61×#418—24no—
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C23×Dic61—21no—
66C22×C4×D61—21no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—41no—
70C2×#11758199—41no—
71C2×#11758199C2×C414yes—
72C2×#11758199C2×C414yescomplemented
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519751—22no—
76#14519751C2×C414yescomplemented
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—41no—
80D4×Dic61—41no—
81#14519739—22no—
82#14519739—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—44no—
95C2×C22⋊Dic61D411yescharacteristic
96C2×C22⋊Dic61D411yescharacteristic
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104#14519710—41no—
105#14519708—22no—
106#14519699—22no—
107#14519699—41no—
108#14519698C2×C414yescomplemented
109#14519698C2×C414yescomplemented
110C22⋊#92418C2×C414yescomplemented
111#14519687—22no—
112C8×Dic61—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684D411yescharacteristic
117#14519684D411yescharacteristic
118C25×C61—21no—
119C22×D4×C61—22no—
120C22×D4×C61—22no—
121C22×D4×C61—21no—
122C22×D4×C61—22no—
123C22×D4×C61—41no—
124C22×D4×C61—41no—
125C22×D4×C61C2×C414yescomplemented
126C22×D4×C61C2311yescharacteristic
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#117×C61—22no—
135#117×C61—41no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C42×C61—21no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61D414yescomplemented
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—24no—
147C24×C61—42no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—81no—
152C24×C61—81no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C2×D4×C61—28no—
156C2×D4×C61—24no—
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—44no—
166C2×D4×C61—44no—
167C2×D4×C61—44no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61C22×C412yes—
171C2×D4×C61C22×C412yes—
172C2×D4×C61C2×D412yes—
173C2×D4×C61#4112yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61C22×C412yes—
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61#4112yes—
183C22×C4×C61C2411yescharacteristic
184C2×C22⋊D61—24no—
185C2×C22⋊D61—81no—
186C2×C22⋊D61—81no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61—42no—
194C22×Dic61—81no—
195C22×Dic61—81no—
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244C22×C412yes—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
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×C61C2×D412yes—
220C22⋊C4×C61—42no—
221C42×C61—42no—
222C22⋊Dic61—22no—
223C22⋊Dic61—41no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227C22⋊Dic61—42no—
228C22⋊Dic61—42no—
229C22⋊Dic61—81no—
230C22⋊Dic61—81no—
231#11758199—28no—
232#11758199—44no—
233#11758198—24no—
234#11758198—42no—
235#11758198—42no—
236#11758198—81no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61C22×C412yes—
243#11758196—81no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61—81no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418C22×C412yes—
254C2×#92418C22×C412yes—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—21no—
258C23×C61—22no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—22no—
265C23×C61—48no—
266C23×C61—48no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—84no—
278C23×C61—84no—
279C23×C61—84no—
280C23×C61—84no—
281C23×C61—84no—
282C23×C61C4×D412yes—
283C23×C61C22×D411yescharacteristic
284C22×D61—22no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—48no—
297D4×C61—41no—
298D4×C61—41no—
299D4×C61C4×D414yes—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61C4×D412yes—
313C2×C4×C61C23×C411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C22⋊D61—84no—
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—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—41no—
340C2×Dic61—84no—
341C2×Dic61—84no—
342C2×Dic61AGL(1,ℤ/8)12yes—
343D244—22no—
344D244—22no—
345D244—41no—
346D244—41no—
347C4×D61—84no—
348C8×C61—22no—
349C8×C61—41no—
350#92418—22no—
351#92418—22no—
352#22868—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—24no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—42no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—816no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61C2×C4×D411yescharacteristic
376C22×C61D4211yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C61#57511yescharacteristic
380C22×C61#57611yescharacteristic
381C22×C61#57611yescharacteristic
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C4×C61—22no—
390C4×C61—42no—
391C4×C61—81no—
392C4×C61C2×C4×D411yescharacteristic
393C4×C61#51811yescharacteristic
394C4×C61#54611yescharacteristic
395C4×C61#55111yescharacteristic
396Dic61—22no—
397Dic61—42no—
398Dic61—41no—
399Dic61—41no—
400Dic61—41no—
401Dic61—81no—
402Dic61—81no—
403C2×#447—611no—
404C2×#442—611no—
405C2×#418D6111yescharacteristic, complemented
406#2363—611no—
407D4×C22⋊C4—611no—
408#1970—611no—
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—42no—
419C2×C61—44no—
420C2×C61—82no—
421C2×C61#235811yescharacteristic
422C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C61#294811yescharacteristic
424C2×C61#327311yescharacteristic
425C2×C61#327411yescharacteristic
426C2×C61#331811yescharacteristic
427C2×C61#331911yescharacteristic
428D61—82no—
429C23×D4C2×D6111yescharacteristic
430C22×D8—611no—
431C22×D8—611no—
432C22×M16C2×D6111yescharacteristic
433C2×#121—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×#117C2×D6111yescharacteristic
438C22×C22⋊C4—1221no—
439#447—618no—
440#442—1224no—
441C2×#107—611no—
442C2×#106—611no—
443#418—24no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102C2×D6111yescharacteristic
449C2×#102C2×D6111yescharacteristic
450C2×#102C2×D6111yescharacteristic
451C2×#102C2×D6111yescharacteristic
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#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—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—22no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4—611no—
484C22×D4—1221no—
485C22×D4C4×D6114yescomplemented
486C22×D4C22×D6111yescharacteristic
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—614no—
506#121—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—2441no—
511C4×D4—2441no—
512C4×D4—2441no—
513#117—22no—
514#117—41no—
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—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—1221no—
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—21no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—1221no—
540#107—2441no—
541#106—1222no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—614no—
546#102—614no—
547#102—1222no—
548#102—2441no—
549#102C22⋊D6114yescomplemented
550C22⋊C8—614no—
551#97—1222no—
552C4×C8—2441no—
553#95—611no—
554#95—611no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558C24—21no—
559C24—21no—
560C24—24no—
561C24—42no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—81no—
566C24—81no—
567C24—1221no—
568C24D4×D6111yescharacteristic
569C2×D4—28no—
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—24no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—612no—
585C2×D4—1224no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—4881no—
592C2×D4—4881no—
593C2×D4C2×C4×D6112yes—
594C2×D4C2×C4×D6112yes—
595C2×D4#1175822212yes—
596C2×D4C2×C22⋊D6112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—1221no—
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×C8C2×C22⋊D6112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—612no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—4881no—
648C4⋊C4C2×C22⋊D6112yes—
649C22⋊C4—42no—
650C22⋊C4—1222no—
651C22⋊C4—1224no—
652C22⋊C4—4881no—
653C22⋊C4—4881no—
654C22⋊C4—4881no—
655C22⋊C4—2442no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C22⋊C4—2441no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—42no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C42—1221no—
668C42—4881no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—48no—
680C23—48no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—1222no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23#1451973712yes—
704C23C2×D4×D6111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—1222no—
714D4—1222no—
715D4—4884no—
716D4—2441no—
717D4—2441no—
718D4C4×C22⋊D6114yes—
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—612no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1222no—
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—4884no—
745C2×C4—4884no—
746C2×C4—4884no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4#1451973712yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C22×C22⋊D6111yescharacteristic
758C2×C4C2×#1175822411yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982211yescharacteristic
762C8—22no—
763C8—41no—
764C8—1222no—
765C8—1222no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—816no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—4881no—
789C22—4881no—
790C22—4881no—
791C22—4881no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C2×#1451973711yescharacteristic
796C22D4×C22⋊D6111yescharacteristic
797C22#1684040211yescharacteristic
798C22AGL(1,ℤ/8)×D6111yescharacteristic
799C22#1684055811yescharacteristic
800C22#1684056611yescharacteristic
801C22#1684056611yescharacteristic
802C4—22no—
803C4—42no—
804C4—81no—
805C4—1222no—
806C4—4881no—
807C4—4881no—
808C4—2441no—
809C4—2441no—
810C4—2441no—
811C4—2442no—
812C4C2×C4×C22⋊D6111yescharacteristic
813C4#1684023511yescharacteristic
814C4#1684040611yescharacteristic
815C4#1684043811yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—4882no—
820C2#2144879811yescharacteristic
821C2#2145462311yescharacteristic
822C2#2145466711yescharacteristic
823C2#2145742411yescharacteristic
824C2#2145743311yescharacteristic
825C2#2145796111yescharacteristic
826C2#2145797611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#418C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
cosocleC22×C4×C61C24
hypercenterC2×#418D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. #21448857C2semidirect
4. D4×C22⋊Dic61C2semidirect
5. #21446682C2semidirect
6. #21446513C2semidirect
7. #21446449C2semidirect
8. #21446257C2semidirect
9. #21446165C2semidirect
10. #21446164C2semidirect
11. #21446064C2semidirect
12. #21446018C2semidirect
13. #102×Dic61C2semidirect
14. #21445600C2semidirect
15. C2×C61×#418C2semidirect
21. C2×#14519739C22semidirect
23. #16839896C4semidirect
25. C2×#14519710C22semidirect
26. C2×#14519708C22semidirect
27. C2×#14519699C22semidirect
28. C2×#14519699C22semidirect
32. C2×#14519687C22semidirect
33. C2×C8×Dic61C22semidirect
36. #16839663C22semidirect
38. #16839658C22semidirect
45. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
72. C2×#11758199C2×C4semidirect
76. #14519751C2×C4semidirect
108. #14519698C2×C4semidirect
109. #14519698C2×C4semidirect
110. C22⋊#92418C2×C4semidirect
125. C22×D4×C61C2×C4semidirect
143. #102×C61D4semidirect
405. C2×#418D61semidirect
475. C61#22868semidirect
485. C22×D4C4×D61semidirect
549. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
C2×#168398712
#214488572
D4×C22⋊Dic612
#214466822
#214465132
#214464492
#214462572
#214461652
#214461642
#214460642
#214460182
#102×Dic612
#214456002
C2×C61×#4182
#2286861