Finite Group Databasebeta

← #29700484

Subgroups — #29700484

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×#16839874C211yesmaximal, characteristic, complemented
2C2×#16839767C211yesmaximal, characteristic, complemented
3#21448861C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21446686C211yesmaximal, characteristic, complemented
6#21446518C211yesmaximal, characteristic, complemented
7#21446448C211yesmaximal, characteristic, complemented
8#21446258C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446068C211yesmaximal, characteristic, complemented
12#21446020C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C2×C61×#447C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic, complemented
20C2×#14519736C2211yescharacteristic
21C22×C22⋊Dic61—21no—
22#16839874—24no—
23C2×#14519711C2211yescharacteristic, complemented
24C2×#14519709C2211yescharacteristic, complemented
25#16839767—24no—
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic, complemented
32C2×#14519687C2211yescharacteristic, complemented
33C2×C8×Dic61C2211yescharacteristic, complemented
34#16839665—21no—
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839665C2211yescharacteristic, complemented
38#16839661C2211yescharacteristic, complemented
39#16839655—21no—
40#16839642—21no—
41#16839642—21no—
42#16839642—21no—
43#16839622C2211yescharacteristic
44#16839618—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C22⋊C4×Dic61—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×D8×C61C2211yescharacteristic
56C22×D8×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C61×#447C418yescomplemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C23×Dic61—21no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—41no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70D4×Dic61—22no—
71D4×Dic61—22no—
72D4×Dic61—22no—
73D4×Dic61—41no—
74D4×Dic61—41no—
75D4×Dic61—41no—
76#14519736—22no—
77#14519736—41no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—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×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101#14519711—41no—
102#14519709—22no—
103#14519698—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—41no—
108#14519698D414yescomplemented
109#14519687—22no—
110C8×Dic61—41no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684D411yescharacteristic
115#14519684D411yescharacteristic
116C25×C61—21no—
117C22×D4×C61—22no—
118C22×D4×C61—22no—
119C22×D4×C61—21no—
120C22×D4×C61—21no—
121C22×D4×C61—22no—
122C22×D4×C61—41no—
123C22×D4×C61—41no—
124C22×D4×C61C2×C414yescomplemented
125C22×D4×C61C2311yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C2×D8×C61—22no—
130C2×D8×C61—22no—
131C2×D8×C61—41no—
132C2×D8×C61—41no—
133C2×D8×C61C2×C414yes—
134C2×D8×C61C2×C414yescomplemented
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137#121×C61—22no—
138#121×C61C2×C414yescomplemented
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141#102×C61C2×C414yescomplemented
142#102×C61C2×C414yescomplemented
143C22⋊C8×C61C2×C414yescomplemented
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—24no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—42no—
152C24×C61—81no—
153C24×C61—81no—
154C24×C61C2×D411yescharacteristic
155C2×D4×C61—28no—
156C2×D4×C61—24no—
157C2×D4×C61—24no—
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×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—44no—
172C2×D4×C61—44no—
173C2×D4×C61—44no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C2×D4×C61—81no—
177C2×D4×C61—81no—
178C2×D4×C61C22×C412yes—
179C2×D4×C61C22×C412yes—
180C2×D4×C61C22×C412yes—
181C2×D4×C61C2×D412yes—
182C2×D4×C61#4112yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61C22×C412yes—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61#4112yes—
191C22×C4×C61C2411yescharacteristic
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—42no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61—42no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C22×Dic61—81no—
203C22×Dic61—81no—
204C22×Dic61—81no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209D8×C61—28no—
210D8×C61—44no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61C22×C412yes—
216C2×C8×C61C22×C412yes—
217C4⋊C4×C61—21no—
218C4⋊C4×C61C22×C412yes—
219C22⋊C4×C61—24no—
220C22⋊Dic61—22no—
221C22⋊Dic61—41no—
222C22⋊Dic61—42no—
223C22⋊Dic61—42no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227C22⋊Dic61—42no—
228C22⋊Dic61—42no—
229C22⋊Dic61—42no—
230C22⋊Dic61—81no—
231C22⋊Dic61—81no—
232C22⋊Dic61—81no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—81no—
241C4⋊Dic61C2×D412yes—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—42no—
247C4×Dic61—81no—
248#11758194—44no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418C2×D412yes—
255C23×C61—22no—
256C23×C61—21no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—48no—
267C23×C61—48no—
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—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—84no—
285C23×C61—84no—
286C23×C61—84no—
287C23×C61—84no—
288C23×C61—84no—
289C23×C61C4×D412yes—
290C23×C61C22×D411yescharacteristic
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—48no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—84no—
304D4×C61C4×D414yes—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C4×D412yes—
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—84no—
345C2×Dic61—84no—
346C2×Dic61—84no—
347C2×Dic61AGL(1,ℤ/8)12yes—
348C8×C61—22no—
349C8×C61—22no—
350#92418—22no—
351#92418—41no—
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—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—816no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61C2×C4×D411yescharacteristic
383C22×C61D4211yescharacteristic
384C22×C61#54611yescharacteristic
385C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
386C22×C61#57511yescharacteristic
387C22×C61#57611yescharacteristic
388C22×C61#57611yescharacteristic
389C4×C61—22no—
390C4×C61—42no—
391C4×C61C2×C4×D411yescharacteristic
392C4×C61#51811yescharacteristic
393C4×C61#54611yescharacteristic
394C4×C61#55111yescharacteristic
395Dic61—22no—
396Dic61—41no—
397Dic61—42no—
398Dic61—41no—
399Dic61—41no—
400Dic61—81no—
401Dic61—81no—
402Dic61—81no—
403C2×#447D6111yescharacteristic
404C2×#442—611no—
405C2×#418—611no—
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—82no—
422C2×C61#235811yescharacteristic
423C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C61#294811yescharacteristic
425C2×C61#327311yescharacteristic
426C2×C61#327411yescharacteristic
427C2×C61#331811yescharacteristic
428C2×C61#331911yescharacteristic
429C23×D4C2×D6111yescharacteristic
430C22×D8C2×D6111yescharacteristic
431C22×D8C2×D6111yescharacteristic
432C22×M16—611no—
433C2×#121C2×D6111yescharacteristic
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×#117—611no—
438C22×C22⋊C4—1221no—
439#447Dic6118yescomplemented
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
451C2×#102C2×D6111yescharacteristic
452C2×C22⋊C8C2×D6111yescharacteristic
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—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×Dic6114yescomplemented
485C22×D4C22×D6111yescharacteristic
486C22×D4C22×D6111yescharacteristic
487C22×D4C22×D6111yescharacteristic
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×Dic6114yes—
497C2×D8C2×Dic6114yescomplemented
498C2×M16—1222no—
499C2×M16—1222no—
500C2×M16—2441no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505#121—22no—
506#121C2×Dic6114yescomplemented
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—611no—
519C2×C4⋊C4—1221no—
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—611no—
537C2×C42—611no—
538C2×C42—1221no—
539C2×C42—1221no—
540#107—2441no—
541#106—1222no—
542#102—614no—
543#102—1222no—
544#102—1222no—
545#102—1222no—
546#102—1222no—
547#102—2441no—
548#102C2×Dic6114yescomplemented
549#102C2×Dic6114yescomplemented
550C22⋊C8C2×Dic6114yescomplemented
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—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24D4×D6111yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
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—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—24no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4D4×D6112yes—
593C2×D4#1175822412yes—
594C2×D4C22×Dic6112yes—
595C2×D4C22×Dic6112yes—
596C2×D4C22×Dic6112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—1221no—
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×C4D4×D6111yescharacteristic
620C22×C4#1175822412yes—
621C22×C4C22×Dic6112yes—
622C22×C4C23×D6111yescharacteristic
623D8—28no—
624D8—44no—
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×C8C22×Dic6112yes—
637C2×C8C22×Dic6112yes—
638C4⋊C4—21no—
639C4⋊C4—612no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—4881no—
648C4⋊C4C22×Dic6112yes—
649C22⋊C4—24no—
650C22⋊C4—1222no—
651C22⋊C4—4881no—
652C22⋊C4—4881no—
653C22⋊C4—4881no—
654C22⋊C4—2442no—
655C22⋊C4—2442no—
656C22⋊C4—2441no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C42—4881no—
668C42—2442no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23D4×Dic6112yes—
704C23C2×D4×D6111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4D4×Dic6114yes—
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—612no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1222no—
740C2×C4—1221no—
741C2×C4—4884no—
742C2×C4—4884no—
743C2×C4—4884no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
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×C4D4×Dic6112yes—
756C2×C4C23×Dic6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4C2×#1175822411yescharacteristic
759C2×C4C2×#1175822411yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982211yescharacteristic
762C8—22no—
763C8—22no—
764C8—1222no—
765C8—2441no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×D4×Dic6111yescharacteristic
796C22#1684039411yescharacteristic
797C22#1684039911yescharacteristic
798C22AGL(1,ℤ/8)×D6111yescharacteristic
799C22#1684055811yescharacteristic
800C22#1684056311yescharacteristic
801C22#1684056311yescharacteristic
802C4—22no—
803C4—42no—
804C4—1222no—
805C4—4881no—
806C4—4881no—
807C4—4881no—
808C4—2441no—
809C4—2442no—
810C4—2441no—
811C4—2441no—
812C4C2×D4×Dic6111yescharacteristic
813C4#1684023711yescharacteristic
814C4#1684039911yescharacteristic
815C4#1684044311yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2#2144880311yescharacteristic
821C2AGL(1,ℤ/8)×Dic6111yescharacteristic
822C2#2145467111yescharacteristic
823C2#2145743011yescharacteristic
824C2#2145743711yescharacteristic
825C2#2145795311yescharacteristic
826C2#2145796811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#447C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#447D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#16839874C2semidirect
2. C2×#16839767C2semidirect
3. #21448861C2semidirect
4. D4×C22⋊Dic61C2semidirect
5. #21446686C2semidirect
6. #21446518C2semidirect
7. #21446448C2semidirect
8. #21446258C2semidirect
9. #21446169C2semidirect
10. #21446169C2semidirect
11. #21446068C2semidirect
12. #21446020C2semidirect
13. #102×Dic61C2semidirect
14. #21445605C2semidirect
19. C2×D4×Dic61C22semidirect
23. C2×#14519711C22semidirect
24. C2×#14519709C22semidirect
30. C2×#14519698C22semidirect
31. C2×#14519698C22semidirect
32. C2×#14519687C22semidirect
33. C2×C8×Dic61C22semidirect
37. #16839665C22semidirect
38. #16839661C22semidirect
45. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
58. C61×#447C4semidirect
108. #14519698D4semidirect
124. C22×D4×C61C2×C4semidirect
134. C2×D8×C61C2×C4semidirect
138. #121×C61C2×C4semidirect
141. #102×C61C2×C4semidirect
142. #102×C61C2×C4semidirect
143. C22⋊C8×C61C2×C4semidirect
439. #447Dic61semidirect
475. C61#22868semidirect
484. C22×D4C2×Dic61semidirect
497. C2×D8C2×Dic61semidirect
506. #121C2×Dic61semidirect
548. #102C2×Dic61semidirect
549. #102C2×Dic61semidirect
550. C22⋊C8C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398742
C2×#168397672
#214488612
D4×C22⋊Dic612
#214466862
#214465182
#214464482
#214462582
#214461692
#214460682
#214460202
#102×Dic612
#214456052
C2×C61×#4472
#2286861